Strength and Weathering of Rock As Boundary Layer Problems

5±1 3±2

Grain size d/mm 0.40 + 0.09 0.65 ±0.17 0.24 + 0.07 0.16 ±0.03

ArengfA, ;nPar?;cM/ar/?oc%.S'freMgfA. Co^cep^ 7t

16 14 12 10 o o.

't 6 4 2 0 0

20

40

60

80

Fig. 1.45 Point toad test: stress at failure piotted versus the respective sampie diameter after Wijk e? a/. (1977) for Bohus Granite.

where F is the averaged force at the m o m e n t the core is split" (Wijk e? a/., 1977) and d is equal to the original core diameter. These measurements can be used to compare the values of strength obtained by adopting the approach introduced in Sec. 1.3 for calculating AFf/AAo. For each diameter, a set of 15 to 20 samples were tested. Figure 1.45 (redrawn from Wijk e/ a/., 1977) shows the Cp^T values and the ranges (or standard deviations), for the stress at failure calculated using Eq. (1.16) versus the sample diameters. From this figure, the m e a n values were extracted, and with the help of Eq. (1.16), the force at failure, Fptjr, w a s back calculated as a function of the area A o s d^ (Table 1.11). These values for the force at failure were plotted against their corresponding original areas in Fig. 1.46. Looking at the coefficient of correlation, the experimental results m a y best be described by a straight line. The slope of the best straight line is regarded as a measure of strength and, as defined above, by the following differential quotient ,

I dFf PLT )

72 Are/:g^ an6? ^a^AerMg q/^^oc^ ay RoMM Jayy Z,ayer Pro^/em^ Table 1.11 Point toad test values: diameter and stress as after Wijk ef a/. (1977), from which force and area have been back calculated. Diameter, d mm

Point load test strength, opLT MPa

Area, A(, = d d

Ff.PLT - CpLT A o

Hi'

MN

8 10 22 32 42 52 62

13.25 14.58 10.26 9.25 8.72 9.01 7.88

6.40E-05 1.00E-04 4.84E-04 1.02E-03 1.76E-03 2.70E-03 3.84E-03

3E-02-

8.48E-04 1.46E-03 4.97E-03 9.47E-03 1.54E-02 2.44E-02 3.03E-02

/ * #^^^

2E-02-

1E-02-J F,,pLT = 3.009 A.+ 1E-03 R = 0.9962 OE+00- f 0E+O0

i 1E-03

^

i

2E-03

3E^)3

4E^)3

Fig. 1.46 Back calculated force at failure plotted versus the corresponding initial area for the point load experiments of the Bohus granite.

Note that the straight line has been constructed from modal values for each sample diameter where a number of tests were m a d e and a frequency distribution obtained for each diameter. Thus, a great number of measurements is indirectly involved in this figure. Wijk e? a/. (1977) suggest a value of 8 M P a for the strength. A look at the second column of Table 1.11 shows

&reMg^/!, ;'?! Par^cM/ar /!ocA Are^g^.' Concept 73

that the quotient of force at failure and d^ calculated using Eq. (1.16) is not a constant but depends on d^. The limiting value for OpLT for d^ —> °° is 8.0 M P a . This means that here too, a general straight line was found which does not go through the origin of the co-ordinates. The value proposed by Wijk ef a/. (1977) is almost exactly the same as the one that was found using Eq. (1.17), which is 8.01 M P a . Samples of the same granite were loaded to failure in the direct tension test. Again, these are experiments that were executed by Wijk e? a/. (1977). Here, "the uniaxial tensile strength, o*Di, is defined as _ 4Ff DT CDT= ^— nd^

,- .g. (LIB)

where again FfDT is the average force at the m o m e n t that the rock core is broken" (Wijk e? a/., 1977), and d denotes the original diameter of the samples where d = do. Again, a large number of samples was investigated. The range of diameters tested was from 6 m m to 62 m m ; the lengths of the core samples (1) were chosen as d, 2d and 4d. Figure 1.47 shows the plot of o*DT versus the sample diameter published by Wijk. B y using the m e a n values for each diameter, the force at failure was back calculated with Eq. (118) (Table 1.12) and the strength determined from the slope of the straight line AFf/AA(, (Fig. 1.48). The value found was 8.09 M P a and this is in agreement with the result of Wijk e? a/. (1977). From Fig. 1.47, it can be deduced that the strength values calculated with Eq. (1.18) belong to a linear relationship between force at failure Ff and geometrical cross sectional area A(,. Again a general straight line is found. The single strength values in Fig. 1.45 approach a limiting value from above, whereas in Fig. 1.47, they approach the value from below. In summary, the evaluation method of Wijk e? a/. (1977) requires a large number of measured values to obtain with sufficient certainty an approximate value for strength for an infinite diameter. The proposed usage of regression calculus to determine the slope of the straight line between force at failure and the cross sectional area is a safer w a y to cope with such experimental scatter. Nonetheless, all evaluation methods and both measuring techniques produce the same values in this case.

74 &rewgf% an6? ^a^Aer/Hg q/*^ocA <M RoM^&i/y Layer Pro5/emj

^.

2 ^

20

+

-+-

30

40

50

60

70

d/mm Fig. 1.47 Direct tension test. Stress at failure plotted versus the respective sample diameter after Wijk e? a/. (1977) for Bohus granite.

Tabte 1.12 Direct tension test values. Diameter and stress as after Wijk ef a/. (1977), from which force and area have been calculated. Length, 1

Diameter, d

Direst tension test strength, Coi

Area, Ao = jcd^/4

Ff,DT - CttT

mm

MPa

m'

MN

mm

7 11 23 33 44 54 62 6 10 22 32 42 8 21 31 41

6.74 7.23 7.74 8.71 7.71 8.71 7.63 4.57 8.14 7.06 11.43 8.86

3.85E-04 9.50E-04 4.15E-03 8.55E-03 1.52E-02 2.29E-02 3.02E-02 2.83E-04 7.85E-04 3.80E-03 8.04E-03 1.39E-02 5.03E-04 3.46E-03 7.55E-03 1.32E-02

2.59E-03 6.87E-03 3.22E-02 7.45E-02 1.17E-01 1.99E-01 2.30E-01 1.29E-03 6.39E-03 2.68E-02 9.19E-02 1.23E-01 4.22E-03 2.83B-02 5.54E-02 1.19E-01

4d 4d 4d 4d 4d 4d 4d 2d 2d 2d 2d 2d d d d d

8.4 8.17 7.34 9.03

&rengf/[, in Par^ct//ar /!oc^ &reMg(A. Concepfs 75

JE-U
/^< 2E02-


* F, Di = 8.0897 A. + 2.2253E-04 R = 0.9908

OE+OQ. ^ 0E+00

^'

)

1E-03

2E-03

) 3E-03

4E-C3

Ao/m^ Fig. 1.48 Back catcuiated force at faiiure ptotted versus the origina) area for direct tension tests for Bonus granite.

The last investigation of this series looks at the strength obtained from very thin samples, e.g. glass threads. Whereas the sample areas of the granite specimens investigated by Wijk e? a/, were some 10 ^ m^, Brook (1977) executed point load tests on Darley Dale Sandstone and Dolerite (no details are given in their paper) within limits of 0.1 x 10"^ to 4 x 10"^ m^. T h e samples tested were in the form of discs, cores and blocks. The results of these tests are summarised in Tables 1.13-1.15 and Figs. 1.49 and 1.50. The figure describing the values of the back calculated force at failure versus the cross sectional area resembles that of glass threads (Fig. 1.34), in which the results found by Griffith and Gooding can be seen respectively. It is interesting to note from these results that proportionals, if they exist at all, seem to be the exception for rocks. The reasons w h y force at failure does not have a proportional relationship with cross sectional area are not yet known. Based on the evidence so far, the main obstacle to further understanding of the absolute value of strength for rocks seems to be the fact that completely different structured materials, like sandstone, granite and marble, can have either similar magnitudes or the same value of strength.

76 Are/!g?A an
In other words, rocks with different textures and/or structures and mineralogy, can have either the same or a similar spectrum of cohesive forces. Thus the aim of future investigations must be to study the forces in and between the components of a rock rather than concentrating on their spatial distribution. At present, two strategies are possible, both of which are in their initial stages: * T h e first method could attempt to expand Hirschwald's observations, in particular, by investigating the microscopic form of the fractured surfaces, a method k n o w n as fractography. Experiments have shown that the fracture in Penrith sandstone failed in tension can occasionally

Table 1.13 Petrographic analysis: unweathered Darley Dale Sandstone. Volume

%

Mineral Quartz Plagioclase Chlorite Iron oxides Accessories

50 ±10 40 ±7 5±2 4+ 1 1±0.5

Grain Diameter d/mm 0.5 to 0.1 0.2 to 0.1 0.2 to grain boundaries 0.1 to grain boundaries 0.1

Dolerite (Whin Sill): fine grained variety

Crystal Plagioclase Augite ophitic Chlorite Iron oxides Accessories

Volume %

Crystal shape and size d/mm

60 ±10 25 ±8 8±2 5±2 2±1

laths, 0.1 xO.01 either, 0.1 x0.08 or 2 x 1 adjacent to feldspars, 0.1 xO.01 irregular, 0.2 to 0.01 0.01

NOTE: Neither Brook (1977) nor Broch and Franklin (1972), whose results are reworked here, describe the rocks they have tested. The above descriptions are for typical examples of the Darley Dale Sandstone and the dolerite (unnamed) used by Broch and Franklin: the dolerite is thought to have come from the Whin Sill in Northern England.

&re/:gy/[, in Par^ct
Table 1.14 Results of point toad tests of Darley Date Sandstone samples.

Force, Ff/kN

Area, A„/m2 Cores 1.96E-03 4.63E-03 l.t8E-02 2.25E-02 4.58E-02 5.53E-03 7.14E-03 9.02E-03 9.73E-03 1.51E-02 1.94E-02 2.00E-02 3.00E-02 3.95E-02 1.80E-03 3.22E-03 3.92E-03 4.35E-03 6.59E-03 7.84E-03 8.20E-03 8.24E-03 9.4tE-03 1.06E-02 1.51E-02 1.65E-02 1.86E-02 2.t2E-02 2.t6E-02 2.95E-02 3.70E-02

Blocks

Discs

0.90 2.5i 5.00 8.31 14.24 2.53 3.73 4.31 4.31 6.76 6.37 7.71 10.39 1.47 1.76 2.73 2.02 3.59 3.57 3.57 3.92 3.92 5.41 5.80 6.16 5.76 5.59 8.55 10.00 9.31

77

78 -Areng?/: ant? P%gfAer;ng q/^^oc^ aj FoM/?oar)' Layer P w ^ / e w j

Table 1.15 Results of point load tests of Dolerite samples.

Area, A./m^

Force, Ff/kN Cores

1.6iE-03 4.71E-03 1.06E-02 2.24E-02 4.60E-02 5.49E-03 6.82E-03 8.59E-03 1.04E-02 1.53E-02 1.97E-02 2.87E-02 3.98E-02 2.08E-03 3.69E-03 3.69E-03 4.82E-03 6.35E-03 7.37E-03 7.84E-03 7.84E-03 7.37E-03 9.25E-03 1.12E-02 1.45E-02 1.55E-02 1.91E-02 2.13E-02 2.24E-02 2.95E-02 3.65E-02

Blocks

Discs

4.31 11.18 19.49 26.75 51.57 10.86 15.88 18.47 20.35 25.18 29.14 34.16 41.41 3.76 5.22 6.27 12.67 12.71 14.31 11.61 14.71 1545 14.31 24.31 24.31 23.92 25.14 30.39 24.63 34.67 34.27

AreMg^A, ;n Par;[CM/ar /!ocA &?*e^/!. Concept

OE-^OO

1E-03

2E^)3

3E-03

4E^)3

79

5E^)3

Fig. 1.49 Force at failure versus the initial geometrical sample area for Darley Dale Sandstone for three different types of sample shapes after Brook (1977).

60 50 -.

40 z ^

30

20 10

0E+00

1E-03

2E-03

3E-03

4E-03

5E-03

A^m' Fig. 1.50 Force at failure versus the initial geometrical sample area for Dolerite for three different types of sample shapes after Brook (1977).

80 &rengf/[ an
intersect quartz grains but usually remains either in the cement or between the cement and the grains. In contrast, electron micrographs of a tensile fracture in marble have revealed that the fracture more often than not goes through grains. T h e well k n o w n mechanism of slip twinning in calcite m a y play an important role here (Butenuth and de Freitas, 1995) In this context, a well-known experience of petrologists is worth mentioning: " W h e n technically deforming calcite its planes of slip twinning are oriented into the shear planes." (Troger, 1969). * T h e second method consists principally of using physico-chemical reactions which selectively destroy the bonding of the rock so as to observe and quantitatively measure this destruction. This is in effect a form of weathering the w a y in which nature destroys rocks, and is the approach that will be pursued here. S o m e introductory remarks about possible reactions shall be m a d e first, and followed by some newer experimental observations involving the systems water with sandstone and sandstone with an aqueous solution respectively. With both, an attempt is m a d e to evaluate the effective cohesive forces and their spatial distribution in virgin rock from a study of its disintegrated condition.

1.4 Physico-Chemical Reactions, Suitable for a Selective Destruction of Rock Structure A few examples belonging to this heading were shown in Fig. 1, such as congelifraction, salt wedging, swelling of gels etc. Conventionally, the first two types of processes were subsumed under physical weathering, and the others under chemical weathering. O n e c o m m o n thing about them is that under suitable conditions within the system, they are able to do mechanical work. The pressures developed need to be high enough to locally overcome cohesive forces within the rock structure. The m a x i m u m inner pressure developed with congelifraction at - 2 2 ° C is 211.5 MNirT^. In the context of this book it is supposed that an external phase, e.g. water, "recognises" the

S?reng?/i, /n ParM'cu/ar PocA: A/-g/ig//<. Conce/?;.s- 81

Fig. 1.51 Upper: Btock with a stratification structure, exfohated by congetifraction, stream in the Atps near Mauvoisin, 2500 m above sea teve], Massif Great St. Bernard, Switzertand (Butenuth, !97t) Energy conversion, A E , as a function of distance, r, w h e n a particte approaches a so! id surface.

same zones of weakness as those "seen" by a mechanical strength test and can thus selectively destroy rock fabric. Herein lies the problem of the technique. Nevertheless, one does observe isotrope congelifraction in nature (Fig. 1.51, upper part). Another example of the selective destruction of structures was described by Smith (1964). H e impressively described the

82 Are^^A o/:^ ^a?Aer;/:g q/^Roc^ 6M ^OMM^o/y Zoyer Pw^/ew^

disintegration of the structure in brass into polyhedral grains using mercury. A s in rocks, the fluid phase needs a certain route to reach its reaction area. The zones of weakness acted on by such a phase are often identical with those that are able to conduct water. Nevertheless, this idea needs to be considered with caution as the following exemplifies: w h e n there is a distribution of pore sizes each having a different m e a n value in a rock, then the rate at which water is able to invade is a time function, and with this, the zones of its effectiveness also become functions of time (Fitzner, 1970). Furthermore, this group of processes should also include chemical reactions where the reaction between the solid and the liquid phase coming into contact with each other causes an increase in solid volume. Here, the mole volume of the solid product is greater than that of the solid educt. The wellk n o w n process of anhydrite reacting with water to form gypsum might be considered a model of this process. Under suitable external environmental conditions, the volume enlargement of the solid educt with respect to the solid product leads to work being done on the environment. A s result of the named processes, vermicular gypsum is formed. Another example is the reaction between solid calcium oxide and water, to form calcium hydroxide. In this case, investigations using an electron microscope showed (Frey, 1995) h o w the increase in volume initiated cracks on the surface into the original oxide grains impressively. These and similar experiences have been accumulated and published by Butenuth e? %/. (1992). This type of heterogeneous reactions plays an important role in the chemical weathering of rock. A s such reactions mainly take place in the surface layers of educts, they are systematically considered surface reactions. Therefore, it makes no difference if these reactions take place on the outer or inner surfaces of a sample, or within its pore volume. Other heterogeneous reactions, such as in the corrosion of steel, are of such great economic significance that the nucleation of cracks of this kind w a s investigated quantitatively (Schutz, 1991). In addition, heterogeneous reactions play a role in the protection of mineral substances (Gard, 1964). The initial step for surface reactions is usually an adsorption of the liquid reaction partner onto the surface of the solid reactant. A s some of these processes lead to considerations of molecular interactions, which are also used to calculate strength values, some basic ideas on adsorption will n o w be outlined.

ArewgfA, !/:Par^'cM/ar7?oc^&re/!g^. Concept 83

1.4.1 A<%sorprioH Adsorption is defined to be the increase in concentration of substances at an interface compared to the concentration of the same substances in the adjacent phase. The processes which cause adsorption are generated by the so-called uncompensated force fields at the interface. If for example a solid body is either cleaved or torn, n e w surfaces with uncompensated force fields are created and this is an unstable state. The immediate result is the adsorption of atoms, ions or molecules from the surrounding. A n important reactant in nature is water, which is practically always present either in liquid or gaseous form. Even in extremely arid areas, desert lacquer or vamish can develop on rock surfaces. In general, adsorption preceding chemical processes m a y be described by two sequential steps; usually the first step is attributed to a physical process (physisorption) the second one to a chemical process (chemisorption). The sequence of these two steps can occasionally be reversed. A s pointed out by Hauffe (1974), this happens if liquid water is adsorbed at a virgin silica surface. The siloxane bonds are split off first in a chemical reaction (chemisorption); in the next step, physical adsorption of more water molecules at the newly formed-OH groups generally occurs. T h e lower part of Fig. 1.51, shows the general situations due to physisorption and chemisorption in a schematic manner. It demonstrates the principal course of energy conversion, which happens w h e n a particle approaches a solid surface. The change of energy (AE) on the ordinate is plotted versus the distance (r) on the abcissa. The particle is attracted at great distances (long range forces). At first w h e n it is approaching the surface, energy is released. O n approaching nearer, repulsive forces become increasingly efficient; these are short range forces, and at a certain distance (r„ ^ compensate the long range forces. Equilibrium I shows physisorption. This state corresponds to the relative m i n i m u m in Fig. 1.51. To distinguish the two types of adsorption Wedler (1970) stated that: "According to the type of bonding of the adsorbents one talks of physisorption w h e n only van der Waals forces act, of chemisorption, w h e n the bond is more similar to chemical bonding forces". "...Physisorption and chemisoption are distinguished by the strength of their bonding, which is reflected in the magnitude of the adsorption heat

84 ArengfA ana* f^ea^enyig q/^^ocA: ay RoHMaary Zayer Pro^/emy

concerned. The adsorption heat is, in the case of physisorption, similar to condensation enthalpies, and in the case of chemisorption, similar to reaction enthalpies". If the activation energy (AEA) (Fig. 1.51) is sufficiently low to allow the particle to achieve the absolute m i n i m u m II, then chemisorption occurs. The n e w equilibrium distance will be r^ ^. With any form of adsorption, the energy state of the newly produced naked surface is lowered, which leads to m a n y consequences. Energy-distance curves are needed to describe the interactions between ions and molecules, particularly for the simple relationships used to calculate the strength of crystalline bodies (a subject considered later). The surface concentration of physisorbed particles, expressed for example in mole nrr^, depends, at constant outer conditions, on the concentration of the same particles in the solution, e.g. in mole 1"', the size of the surface in m^, and the quality of the surface. The surface quality of minerals, silicates in particular, is almost always greatly changed with time. In the next section, such phenomena are demonstrated by experimental observations. 2.4.2

TTieybwMfz'on q^ change;? SMr/ace s f m e t r e s ^Mn'ng

In opposition to c o m m o n opinion that rocks only undergo extremely slow reactions, a number of experimental observations show that comparatively fast boundary layer reactions take place at mineral surfaces. Feldspar is an important mineral within silicatic rocks, especially igneous rocks. Within the carbonate rock group, calcite is the most important mineral. Reactions of the alkali feldspar sanidine, (K, N a ) [Al Si^Og], shall be examined at first, and then investigations of the carbonate calcite, Ca[C03]. W h e n pulverised feldspar is sprinkled into water or a dilute acid (Fig. 1.52, upper part), the p H value increases steeply in the aqueous solution with time (Fig. 1.52, lower part). Alkali ions m o v e from the solid surfaces into the solution, whereas hydrogen ions migrate onto the surface. The reason for this occurrence lies in the fact that rock-forming minerals are, practically without exception, salts of strong bases and effective weak acids. T h e process mentioned has been often described as ion exchange. A s has been shown by extensive analytical work, this view cannot be maintained. During a true ion

AreMgyA, ;n Parf;cM/ar 7!oc^ & r e M g ^ . Concept

#

85

n

Silicon

3 a

+ =

Water

20 CjXlfjS

mol x (300 cm.3)-i 10

Fig. 1.52 T w o dimensional picture of the alkah feldspar structure which m a y serve for discussion of the analytically determined concentrations of the different molecular species occurring in the adjacent solution during dissolution experiments, see lower part of figure (Butenuth ef a/., 1992).

exchange reaction, the exchanger remains chemically intact, but in the rock reactions discussed here, alumina and silica occur in the solution right from the beginning. The exchanger is thus changing its chemical composition and its original, mostly polymer, anionic structure with time. The polymer anion structure disintegrates and transforms into the so-called H-fbrm. A structural sketch is shown in Fig. 1.52 (upper part). At first, the feldspar at the interface with water transforms into an unordered layer of silicatic acids and aluminium hydroxide of changing composition; this produces leached layers. With a change of the outer variables, i.e. p H value and temperature (Fig. 1.53), the composition of the solute continues to change after longer periods of time (72 hours) then it slows down, and with it the changes of the gel layer. This layer is probably similar to the group of allophanes, which occur particularly in aluminium-rich soils (andosoles).

86 &re/!g^ an
Fig. 1.53 Stoichiometric ratio of aluminium and silicon during dissolution of sanidine (Butenuth e; a/., 1992).

The thickness of such leached layers lies at several hundred Angstrom units and remains constant on minerals which have been exposed for a long period of time (Correns, 1967). In view of their thickness, such gel layers are thus of colloidal dimensions. This finding is important subsequently. In summary, the dissolution of silicatic minerals has to be seen as an incongruent process. This is even true for the dissolution of olivine, a nesosilicate (Butenuth gf a/., 1992). It is probable that further development of the unordered gel layers over longer periods of time leads to the normal, ordered phases of solid scilicic acid: "As the statistical evaluation of silicic acid analyses of natural hydrological systems: such as rivers, springs, ground waters shows again and again modal cluster values around the solubility values of pure silicic acid and its modifications: it therefore seems very probable that the colloidal dissolution load and the condensation products of

AreMg;A, !H PorHcu/Hr ^?ocA: Areng^. ConcepM

87

Fig. 1.54 Saproiite: weathered granite.

low molecular silicic acids are identical, and that the surfaces of all silicate rocks which are in contact with aqueous solutions, are covered in the same or similar way, by gel layers of a microcrystalline character" (Butenuth, 1990). Under the influence of such reactions and others at mineral surfaces, m a n y rocks are destroyed. Amongst other intermediate products are the socalled saprolites. Figure 1.54 shows such a body of rock, which is m a d e up

88 &reMg?A an;/ ^ a ^ e r w g q^/?oc^ <M FoMM^ary Zayer ProA/ew^

of granite, on the beach of the Bretonic coast, France (photograph from Butenuth, 1971). Saprolites have nearly completely lost the strength of the original rock from which they come, and one is usually able to rub them away just between the fingers alone. The selective destruction of m a n y rocks to small grain aggregates, the so-called granular disintegration, is an important process in areas of w a r m humid climate and is a regional, landscapedetermining characteristic of these regions. The cements of silicatic sandstones seem to be of a similar nature to those suspected in saprolites, i.e. microporous, colloidal layers between the sediment grains. The model (Fig. 1.28, upper part), has to be then adjusted accordingly. Further observations will be reported later. In older publications, analytical chemical investigation methods were used exclusively to follow surface reactions occuring on and in silicate rocks. In addition to observing surface reactions on calcite, physical experiments on these surfaces were also m a d e (Butenuth, 1991). These were done on polished cleavage surfaces and the measurements were both quickly and continuously made. In the same measuring cell, time-dependent measurements of p H and acoustis reflectance were m a d e to investigate the directional dependency of ultrasound reflection and ultrasound velocity with time at the cleavage surface. The latter experiments were done with an acoustic microscope on which a line focus lens was mounted. The p H measurements indicate the transport of protons and correspondingly, the operation of certain chemical processes. The ultrasound measurements are able to show physical surface changes which accompany these chemical processes. Despite the completely different lattice structure of calcite from sanidine, the experiment confirmed that the starting rate of proton conversion is similarly as high as that of sanidine. Although the ultrasound reflection depends on the angle at all times, the definite impression obtained from these results is that the anisodesmic character of the original lattice is intensified by surface reactions (Fig. 1.55). O n e of the basic difficulties lies in the fact that hardly any method to investigate boundary layer reactions have been adopted from other research areas or developed to help study the problem of strength. A n overall important aim of this work is to quantitatively investigate surface changes that occur during chemical reactions and the concommittant change of strength.

&re/:^/:, i'n Par^cM/ar jRocA^ &rey]gfA. Concept 89

Fig. 1.55 Angular and time dependence of the reflectance function, R, of a catcite cleavage face in contact with water; polar co-ordinate diagram. The approximate time duration of the different runs on the same face of the crystal were (I) 0-576 s, (II) 696-1207 s, (V) 2050-3426 s (Butenuth ef a/., 1992).

Fig. 1.56 Calcite crystals treated with sodium fluorite solution which produced surface layers of fluorite (Gard, 1964): no scale given by author.

A n example of the implication the change of mole volume from the solid educt phase to a solid product phase can have is illustrated in Fig. 1.56. This shows what happened to calcite that was treated with a sodium fluoride solution and subsequently changed into calcium fluoride. The previously

90 Arewg?A awa* P%a?Aerwg o/^^oc^ as ^OMMcfary Z,ayer Pro^/ews

smooth surface of the crystal is roughened and ripped open after the conversion because with the conversion from calcite to calcium fluoride, the mole volume is diminished, leading to a reduction of the surface layer. This is a further example of chemically induced crack formation (Butenuth and de Freitas, 1995). Three basic conclusions emerge from this chapter: * A critical investigation of the influence of textural parameters on the strength of rock has shown, that regardless of texture, rock possesses a statistical distribution of strength values which lies in the range of some M N m " 2 . * A critical investigation of the measuring techniques used to obtain these values for strength shows that the term "tensile strength" has only a simple meaning in accordance with its normally used definition, w h e n rocks are either quasi-isotropic, or isotropic, and w h e n the force at failure versus the geometrical cross-sectional area does not need to be described by a proportional but shows a linear dependency. * T h e strength values of sandstones depends upon the kind of cements, which in turn depend on their chemical nature, the nature of the mineral surface and the water content. Porosity, pore size diameters and the size of the particles of the cement play an important role. The forces within the cement and between the cement and sand grains (in the case of sandstone usually quartz grains) are obviously m u c h smaller than those within the grains. T h e spatial distribution of these forces can apparently be "sensed" by chemical reactions that selectively take place, particularly in the regions of mineral surfaces. Reactions with fluid phases obtain their selectivity either by their access to reaction spaces, e.g. within the pore volume of the rock, by uptake of water in existing cements, or by producing solid products with greater mole volumes than those of the solid educts. These ideas are supported by what has been described for reactions in metal textures, as well as reactions in silicate and calcific rocks. These sorts of reactions are well k n o w n as weathering reactions and are of regional importance, but they are m u c h less considered with respect to aspects of rock strength; a detailed discussion of these processes is presented later. Before going further, s o m e strength values are estimated

Areng/A, !H Parf;'cM/ar.RocA;,S'frengfA. C o n c e p t 9t

using the so-called simple lattice theory. This is desirable in order to have a basis for comparison with the order of magnitude experimentally observed for rock strength. Additionally, one hopes that with the help of a theoretical approach, such calculations m a y indicate h o w a molecular approach to strength produces predictions which are up to a thousand times greater than those determined experimentally.

Chapter 2

Physico-Chemical Elements of the Strength of Pure Phases with Ionic Linkage

It is not the intention of this chapter to find exact strength values of pure phases using the lattice theory. Rather, the aim is to study the extent to which such calculations can be linked with structural characterisations of rock models described in Chapter 1 and the values of tensile strengths that might arise. Porosity shall be used as an example. Sandstones are porous, and their porosity varies between 7 and 1 5 % by volume. Three layers of a cubic body with a porosity of 1 6 . 7 % by volume is shown in Fig. 2.1. T h e pores are m a d e up of cubic-like volume elements and the layers lie in direct contact above one another in a body representing rock. T h e positions of pores were determined statistically with a dice and they rarely penetrate more than two or three layers of such a "rock". If such a body is loaded from outside, the flux of forces is normally channelled through material chains. W h e r e there are pores, the flux of forces deviates, but as the porosity is relatively low, this does not happen very often. At present, no lateral forces be considered. Thus at this place, it is enough to look at the simple lattice theory where only the elements of chains are ordered in series. This model will help to understand the principal steps needed for the calculation of tensile strength. Another complication is that the simple grains of a sandstone are linked to one another by cement. It is thus to be expected that the members of the chains have different spring constants. A similar conclusion is drawn from the fact that the sediment grains within a chain will have 92

P/rHMCo-CAeTmca/ F/ewe/:H q/^/[e &re/:g^ q/^PM/*e PAa^gy 93

Fig. 2.1 Three random layers of a sandstone mode). The position of pores was determined by a die statistic.

different crystallographic orientations in comparison with the line of force applied by an external source. Thus, the mechanical properties of the chain elements have to be viewed as different. These and other difficulties of the sandstones described later have to be examined, at least in principle. To understand the nature and properties of single bonds in the atomic region, pure phases are considered. Phases are defined as materials in which

94 Are/igfA antf ^a^Aen'Mg q/*7!oc^ as Rouna'ary Layer Pw^/ewy

the same physical and chemical properties exist at every place. Thus, pure phases, in contrast to mixed phases (solutions), are m a d e up out of one component only. In this definition it is not given "expressis verbis", that a quantity of any material is necessarily limited. The existence of limitations to the concept of phases are indirectly acknowledged by the words "at every place". A number of properties can no longer be defined w h e n the portions of the phase regions examined are too small, as w h e n the degree of dispersion reaches the magnitude of colloidal dimensions. The main characteristic of highly dispersed phases is that the surface properties, in comparison to the volume properties of the materials considered, are quantitatively no longer negligible. Thus, w h e n this occurs, the internal energy not only depends on temperature and volume but also on the magnitude of surface development. The upper limit of colloidal dimensions is often fixed at 1 urn. A vivid example of change in property with decreasing particle size is shown in Fig. 2.2. O n the left side, a golden South African Rand is depicted. This solid piece of gold shows all the properties of a piece of metal, such as metallic sheen, an electric conductivity typical of metals etc. O n the right side, a vase of ruby glass can be seen. Borries and Kausche (1940) were the first to visualise and depict the domains of the "neglected dimensions" by means of an electron microscope. The colloidal gold particles, the dispersion of which in the glass melt causes the ruby colour, have a diameter of 30 urn, which is smaller than the size limit for the arbitrarily-defined colloidal region given above (1 p.m). The great difference in properties between the state of solid gold and that of colloidal gold is evident. Another example, this time taken from petrography, is given in Fig. 2.3. The figure shows needle like exsolution lamellae of feldspar in granite (microperthite) of Tiruttani, near Madras, South India. The thickness of the single needles is in the order of micrometers. Colloidal phases need to be looked at separately because of their enormous surface development. In this book, two forms of dispersion of solid silicic acid are considered: sols and gels. These two forms differ in their mobility. Whereas sols are usually spheres of some hundred A units which are described as having a glass-like consistency (known as the Carman model), gels are space filling structures which are m a d e up of chains where the units making up the chains are the previously mentioned sol particles. This model needs the

PAy.Hco-C/!e?n;ca/ E/emenM q/*;Ae Areng!A q/*PMre PAo^as 95

—

-^

Fig. 2.2 G o M in two different forms. Macroscopic phase (ieft): South African coin with its usuat appearance. CoHoida) fine suspended materia) (right) in ruby giass with strongty aitered properties. Highiy dispersed metats seem biack.

Fig. 2.3 Microperthite: thin section of granite from Tiruttani, near Madras, South India. Materia): Butenuth ()969), Thin section: Dr. Kranz Kemforschungsanatge Jutich.

96 ArengfA ancf ^ a ; A e r M g q//!oc^ a.! RoMw^a^y Z,oyer ProA/e?m

following modifications to be considered as far as natural systems are concerned: * W h e n sol particles aggregate in natural water bodies, an intermediate form with a restricted mobility seems to exist. In this context, they are called flocks. In other literature, they otherwise seem to be k n o w n as flocculates. Such flocks can be transported in moving waters, settle extremely easily and can be easily transported into grain packings where they m a y constitute cements. * In opposition to the Carman model, ordered structures are found in m a n y colloidal fine dispersions, including the well-known modifications of SiC*2. However, which modification develops under which environmental conditions seems to be unknown. * A particular problem seems to be the uptake of water by silica gels. The problem lies in the uncertainty in viewing the silicic acid/water system as either a homogeneous or a heterogeneous system. Considering these uncertainties, experimental results must always be carefully viewed.

2.1 Force- and Energy-Distance Functions Consider the formation of an ionic crystal, here sodium fluoride, from the respective hypothetical ionic gas containing N a + and F" ions. The formation of a crystal might occur in two principal steps: * the formation of ion pairs and afterwards, * the assembly of these ion pairs to form the three dimensional crystal. The formation of ion chains can be considered as an intermediate step which will n o w be discussed.

2.2.2 FomzafM?! q/l'oM pairs Consider a hypothetical gas of sodium and fluorine ions, N a + and F", which combine under the influence of attracting forces. The force-distance

P/rUHCo-CAeMHCa/ F/emeMf.s q/^Ae A r e / : ^ q/*Pure P/iasa? 97

function of mutual attraction can be described by Coulomb's law written as follows: 2

Fc=

r^

.

(2-1)

Zna+ and Zp- are the numbers of unit charges per ion e(,: unit charge in electrostatic units (e.s.u.); eo = 4.8029 x 10"'^ e.s.u. r: distance of ions, nucleus to nucleus, in c m Fe: Coulomb force in dyn; 10^ dyn = 1 N ; as distinct from Coulomb energy in erg; l(f erg = 1 N m . Following their mutual attraction, Na+ and F " ions combine to form ion pairs (Na+ F"). Because r —> 0 cannot be imagined, r approaches a certain minimal distance, r<,. For these reasons it follows that a second force field has to exist, that becomes increasingly important at small distances, and that corresponds to a repulsive force, FRp, often described as follows (Greenwood, 1973): Fnp=--be-('/p)r P

p.2)

where b and p are constants considered later. The total force influencing the particles (F^ss) during ion association results in

FAss -

/ r^

be-("p)r.

(2.3)

p

Force equilibrium occurs at the distance r = To, hence FAss = 0

at

r = r<,.

(2.4)

This condition [Eq. (2.4)] is suitable for the constant b in Eq. (2.3) to be eliminated; thus ZNa+ZF-eope+C^-

b=

p

(2.5)

98 Arengf/: an
Introducing Eq. (2.5) into Eq. (2.3)

rkss - ZNa+Zp-eo

J r2

Le-d/pXr-r.) r2

(2.6)

All equations used so far work under the condition that the ions are in a vacuum. Figure 2.4 is the graphical representation of Eq. (2.6). The product outside the square brackets, m a d e up of three factors, is arbitrarily considered equal to one in this diagram. The equilibrium distance of a sodium fluoride ion pair is To = 2.31 A (Greenwood, 1973) and the constant p for noble gas ions is 0.35 A (Bom, 1919), and it is with these data that the curves of Fig. 2.4 have been calculated. T o achieve smaller distances than To, a compressive force (negative sign) has to be applied to the ion pair, if looking at the process from an outside co-ordinate system and along a line that links the two ions from centre to centre. A s given in Eq. (2.6), this relationship is unequivocal. This is not the case w h e n the distance of the two nuclei is

+ 0,1 — Extension

- 0,1 Shortening

Fig. 2.4 The total force (F^ss) versus the distance of particies (r) for two ion pairs W. E.: Arbitrary Units.

PAUHCO-CAemica/ Foments q/*^e ^re^g^A q^Pure PAa^g^ 99

increased (Fig. 2.4). A b o v e the equilibrium distance, a tensile force acts o n the ionic pair, and it is possible to read from the graph two distance values for one given force. The only exception is the m a x i m u m point of the graph (FAss, max)- This difficulty can be excluded if FAgg, max is interpreted as the force at failure, thus the curve is only allowed to go up to this point. The force-distance function [Eq. (2.6)] is not linear. It shows a m a x i m u m and is asymmetrical with respect to Tg (if the force-distance function would be strictly symmetrical, no thermal expansion of condensed phases would exist). To shorten the distance, a bigger force than that needed to enlarge it by the same amount is needed, i.e. the "bond spring" exhibits a non-linear but reversible behaviour. Thus the non-linear behaviour of a force-extension curve is in itself no proof for irreversible processes occurring in a sample during its deformation. In the case of Eq. (2.6), linear behaviour is only an approximation for small changes of the distance in the neighbourhood of r^ which at m a x i m u m might be 2 % of the equilibrium distance. For sodium fluoride this corresponds to approximately Ar = + 0.05 A . W h e n the two ions N a + and F" approach small distances from very large distances, energy is released under the condition that the temperature of the system is kept constant. W h e n r < To, work has to be invested. The energy distance graph follows from Eq. (2.6) by integration between the limits r^, (the distance separating two ions at the beginning of their approach), and r

AUAss = ZNa+Zp-eo

- 1 + — - -R-e^P(e-(^> - e-(^p))

(2.7)

using the approximation r^ » r, results in

AU Ass = ZNa+Zp-eo

.I + -P-e-(l/p)(r-r,) 2

(2.8)

and w h e n only the total energy conversion up to r„ is needed, r = r^ and the energy conversion is given by the following expression

AU Ass

ZNa+ZF-eo ^

1-

(2.9)

100 &/*en^/: a/!
To calculate the energy conversion for a mole of ion pairs instead of the conversion for a single ion pair equation, Eqs. (2.7) and (2.9) have to be multiplied by Avogadro's number (N^). Figure 2.5 shows the graphs which were drawn according to Eq. (2.8) for the ion pairs (Na+ F"), (Na+ CI*), (Na+ Br") and (Na+1"). With increasing

Fig. 2.5 Converted energy, AUAss, versus the distance, r, of the ions for different ion pairs W . E. = A.U.: Arbitrary Units.

P/iysico-CAefMica/ E/eweMM o/*?Ae &/*e/)g^ o/*PM/*e PAajas 101

equilibrium distance of the sodium halogenide ion pairs, the amount of converted energy decreases [see position of the minima in Eq. (2.9)]. Polarisation phenomena have not been taken into account in this approach. Having considered the formation of ion pairs, the formation of ion chains will be looked at next. 2.1.2

F o m M f i o M q/lon d M m s

The formulation of ion pairs from single ions based on central forces has been considered until now. Dipoles result if two ions of opposite signs combine, and little "rods" with a positive and a negative charged end are formed. At the ends of such dipoles, other ions can be added under further energy release. The Coulomb forces between spherical ions are good examples of the forces between poles (point charges). The corresponding force fields have spherical symmetry, i.e. are not dependent on any direction, and cannot be satisfied. Figure 2.6 shows such a force field in a model experiment using spherical magnets and iron powder. The attraction force decreases here with distance proportional to r*"^ unlike that for charged ions [Fig. 2.7 (top)].

Fig. 2.6 Visualisation of a "force field" around a magnetic sphere in a mode! experiment: "sphere magnet" and iron filings.

102 Areng^A a/!^ ^a^er/ng q^7!oe^ en RoHnaary Layer PwA/e7m

6. Buternjth, W. Ziesmann (1994)

F = 26.391 * U.446

t—1—1—!

Fig. 2.7 Upper diagram: Force of separation of two magnetic spheres, F, versus their distance, r (experimental data set: Butenuth and Ziesman, 1994). Lower diagram: Visualisation of the force field between two magnetic spheres with increasing distance.

PAy.H'co-C/:eMHca/ E/ewew^ q/Me Arey:g^ q/^PMre PAaray 103

. -

(

DsO^eO

. ..

^ — ^

\.

2 x r„ (a)

!

3 x r. 1o.t.
! [ ]

i..: 11.55

1o.!l 6,46.

1o.!l! 13.86

1o,IV 12,92

1o.V 9,24

1o,V! 1o.V!t 12.92 4,62

Nm

N,v

Nv

Nvi

6

4

4

4

lo.VII! 16,15

1o,IX 7,85

1o.X 22,61

^-<

^W^-*

^a 5

2

Nvm 5

2

Nix

Nx U3.

3

7

N,.,a: = IN; = XN,Na+r) + XN,^+j-, = 19 + 23 = 42

O Na*

OF OJ

(b)

- . ..

eeG^HsD ! r.,i !

(c)

!

2 x r. 1

3 x r.,i

.

To.2 t 2 x r., ! x r„,2

! 1

(Na"F*)

! 2

(Na+J*)

Fig. 2.8 Visualisation of the formation of: (a) uniform and (b), (c) composed ion chains for the discussion of their energy conversions.

104 .Sfreng;/: ana* ^af/ier/ng q//!oc/; ay
To m a k e the total energy conversion in forming a three dimensional ion crystal from an ionic gas, e.g.

NAxNa+ + N A x F 1 mole 1 mole

->[Na+F-] 1 formula unit ionic crystal

ionic gas NAi Avogadro's constant

plausible, an intermediate step, the formation of a hypothetical ionic chain, has to be considered first (Zemann, 1966). This is the subject of the following discussion. The formation of a chain built up from N a + and F" ions m a y be described like this: to the first ion, e.g. Na+, two other oppositely-charged ions coming from an initial distance r^ are added at equilibrium distances To. This process continues as shown in Fig. 2.8(a). The first three steps of energy conversion are shown in Table 2.1. Here only those conversions of the far reaching Coulomb potentials of attraction and repulsion are taken into account but not those of the quickly decreasing short range potentials of repulsion. In the central column of Table 2.1, the equilibrium distance of each newly added ion from the central N a + ion in

Tabte 2.1 Energy conversion when forming a uniform ion chain.

F-Na+F-

! x To attraction

-, ZNa+ Zp e^

ixr. Na+F-Na+F-Na+

2 x ro repulsion

^ Z^a+Zn-eo 2xr.

F-Na+F-Na+F-Na+F-

3 x ro attraction

T Z]^a+ Zp- %

3xr. etc.

etc.

etc.

PAy^/co-CAewMa/ E/eTHenM o/*^Ae Are^gzA q/*PMre PAasa? 105 Fig. 2.8 (hatched) is indicated. The respective energy conversions are listed in the right hand column of the table (after Zemann, 1966). The summation over the partial amounts listed in Table 2.1 gives the total energy conversion of a single ion pair within a chain, A U ^

A U K = ^ * ^ ' ° 2(1-1/2 + 1/3-1/4 + .-.). To

(2.10)

The infinite series in the bracket has a definite limit value, In 2 = 0.693. This means that the energy release producing an ion pair within a chain is 1.386 times the energy released at the formation of an isolated ion pair. In Fig. 2.8(a), two fluorine ions were added from the sides to the sodium ion, which is located in the middle. N o w consider the case of composed chains which are m a d e up of elements of different chains with varying spring constants. Unlike the situation illustrated in Fig. 2.8(a), a fluorine ion is added on the left side whereas an iodine ion is added on the right side in Fig. 2.8(c). Such considerations are useful from a systematic point of view, but have only a very limited application because the salts of sodium fluorine and sodium iodine constitute a system of unlimited miscibility in the melt but of complete immiscibility in the solid state. Figure 2.8(c) thus describes a purely hypothetical case only. Nevertheless, the calculations show the characteristics of such chains. Table 2.2, like Table 2.1 shows the single steps of addition of ions and the partial amounts of energy conversions. The total sum of the partial sums is equal to A U x, averaged

_ AU(Na+F-) + AU(Na+t-) "

(^-11)

which is the arithmetic average of the energy conversion of an ion pair in the two homogeneous chains. The result pre-supposes that the limiting value of In 2 in both columns is sufficiently reached and Fig. 2.9 gives an indication of h o w quickly the progression converges. After 15 iterative steps, the discrepancy is about 4 % . If the partial chains are of different lengths, the total average value of energy conversion m a y be smaller or bigger than the classical value of convergence. Thus it is possible that the energy convergencies of chain elements can fluctuate [Fig. 2.8(b)].

106 &reng?/[ an;? ^a^Aerwg q/^7?oc^ a.! ^OM/!^ary Layer Pro/j/ew^

Table 2.2 Energy conversions and summations when forming a composed ion chain.

1 X r,,,(Na+[')

1 * *o,(Na+F")

^.(Na+J")

^Na^ Zp e<, 2 X To (Na+p-<

+

2 X To ( M a + D 2ro,(Na+F")

3r, o,(Na"^F

3 X To (^a+,-)

3r, o,(Na***J

)

Partial sum, left: 2 ZNa*^ Zp e^

2r,o,(Na*^J

)

2 Z N a + Z j * e^

ZNa^Zy-ep 3 X To (Ma+F )

^Na+ Zj e„

)

Partial sum, right: 2

ZNa^Z, e„

1(1-1/2 + 1/3- -)

*o,(Na+F")

1(1-1/2 + 1/3- .)

*o,(Na+r)

Total sum:

A U K = - Z c a t , . n Z A n , . n e . ( I - ^ + I/3-<<<) fo,(Na F )

**o,(Na ] )

V

7

This figure provides the opportunity to study practical limitations and difficulties of such calculations in a little more detail. Let a non-uniform chain be m a d e up of the elements sodium fluorine and sodium iodine. Let these chain elements be of different lengths and follow each other in no orderly fashion. Let it be assumed further that the total chain can be understood as the s u m of the equilibrium distances. Polarisation phenomena of single ions, for example at the junction between two different chain pieces, are thus excluded. A t such junctions, the ionic distance jumps from f(Na+ F-)= 2.31 A to r(Na+ [-)= 3 2 3 A. Under these circumstances the s u m of the partial lengths of the uniform chains is lo,l -N;r(Na+F-)o

and

lo,j =Njr(Na+I-)o

(2-12)

P/iy^/co-CAew/ca/ E/e/neHfy q / ^ e Are/!g^/[ q^Pure P A a ^ M 107

Composed chain

^*^<*

0,6931

Fig. 2.9 Energy conversions for a composed chain with an increasing number of iteration steps.

and the total length *o, tota] ** ^ o , i + ^ o , j -

(2.13)

T h e total energy conversion of such a chain has three parts: the conversions of ion pairs in each section of the partial chains and those at places where different ionic chains meet. T h e final amount A U ^ , averaged* depends on the length of the adjacent chains, as shown above AUx,totai = X ( N ; - 2) X AU(Na+F-) + X ^ m =1 nij = 1 + (m; + mj) X AUK, averaged -

" 2) * AU(Na+I-) (2.14)

The number N ; and Nj are always multiples of 0.5 but they are not always multiples of the n u m b e r of ion pairs in the chains [note the

108 -Arengf/: ant? W^a?/!er;'Mg q/"7?oc% ay RoM/:^ayy Z,oyer P w A / e m j

arrow in Fig. 2.8(b)]. The reason for this is that there are two bonds per ion chain. 2.1.3

Force-e?ongafM)H curves ybr Mn{/bwz a n ^ compose;? chains

The force at which tensile failure occurs has been viewed as the m a x i m u m of the force-distance function, which results from attractive and repulsive forces in the atomic region. In line with this point of view, the m a x i m u m value of force is considered to be the result of a continuous deformation starting from the equilibrium distance and continuing up to its ultimate value, which is the m a x i m u m for the force-distance function. Similar ideas of structural elements at an atomistic scale to these, have been proposed for macroscopic conditions. Helical springs can be considered an example of structural elements whose stress-strain behaviour provides a basis for such concepts (see also the basic diagram outlined by Ondracek (1986), Fig. 1.11). This behaviour m a y n o w be considered. The force, F, applied to a single, i.e. isolated, spring leads to an elongation, Al = (1 - 1„). A s long as the deformation does not lead to permanent changes of the spring quality, the process is reversible. In the simplest case, the elongation is proportional to the applied force and can be described by Hooke's law F = ks(l-1.)

(2.15)

where kg! spring constant. The quotient of force and elongation of the sample can be used to determine the spring constant as long as Eq. (2.15) can be regarded as being valid. In cases where the force is a non-linear function of the elongation, the spring constant has to be found by mathematical derivation of this function: then this constant is itself a function of length or elongation respectively. S o m e measurements of coil springs, either in isolation or in series, are n o w considered. Figures 2.10(a) and 2.10(b) show measurements conducted with three commercial, outwardly identical coil springs (1), (2) and (3). Spring (3) has been measured as a single, isolated spring only; spring (2) has

PAy.HCO-C/;efM;ca/ F/e?HeHf.s q / ^ e A r e ^ A q/^PMre PAa.res 109

f,,, . 40.S1 . tTS.M (1,., . 1 -,) F,„.M.:7.iM.zm,„-l.,„)

7 / "i* K^)-

a)

K f ! i ![!!]]][ ) b)

Fig. 2.10 Force, F, versus elongation, (1 - 1„) diagrams for isoiated springs and springs linked together in chains.

been measured as a single, isolated spring and in series with spring (1). Spring (1) has only been measured in series with spring (2). All experiments have been done with increasing and decreasing load and thus their reversibilities have been checked.

1 10 Are^g^A a/!^/ P%<2;/]eriMg o/*J?ocA: ay RoMM^ary fayer ProMem.?

Empirically, all springs need a certain initial force (Fo) which need not be strictly reproducible, before the actual Hooke range of elastic responses begins. Therefore Eq. (2.15) can be written as follows ( F - F o ) = ks(l-lo)-

(2.16)

This kind of representation is shown in Fig. 2.10 by the lower dashed and dotted straight lines. Spring (2) has the same spring constant as spring (1), apart from a small measuring error, both w h e n measured as a single isolated spring and w h e n measured in combination with spring (1). Spring (1) has practically the same spring constant as spring (2). Both springs then have a c o m m o n averaged spring constant of ks,, =ks,2 = 104.84 pond cm"' - 1 0 6 9 N n r ' . N o w the properties of single springs and of springs combined in series will be considered, in particular, their elongations, their spring constants and their strains, w h e n the outer load (F - F^) is kept constant. The properties for the single spring are defined as follows elongation: 1; = (1; -lo,i), spring constant: ks,; =

(F-Fo) -—-, Vi

(2.17) (2.18)

lo, i)

(li-loi) strain: E; = — - — ^ - .

(2.19)

For the spring elements operating in series the following basic equation holds lt.tat=ll+l2+" = Xli

(2-20)

and lo.tota] -lo,l +^0,2 *!

= E*o,i -

(221)

P/:y.H'co-C/ie?n;ca/ E/eme/]^ q/*;Ae A ^ e ^ A q/^PM/-e P A a s M

!! 1

Thus it follows for the difference in length Otctat -Ic,total) = X 1 , - X l c , , - X ( l i - 1 . , , ) .

(2.22)

B y combining Eqs. (2.20)-(2.22) with Eqs. (2.16)-(2.19), the following properties of two spring combinations result: (F-Fp)_(F-Fo) (Itotat - lo, totat ) ^ - T ks, total

(F-Fp)

— T *^s,l

+ "*T *^s,2

' 1

1 '

(2.23)

or (I totat " lo, totat) - (F " Fo ) +. kg,] kg,2 y

(2.24)

Beyond that, from Eq. (2.23) it results ks,iks,2

'-'°^"i, .' + k . ' ^s,t + k s , 2

(2<25)

The total elongation of the combination is proportional to the s u m of the reciprocal spring constants of the single springs, under the pre-condition that (F - Fo) is kept constant. The spring constant of the combination is equal to the quotient of the product and the s u m of the single spring constants. The strain of the combination is derived from Eq. (2.22) by simplifying with l^totat- The total strain Etotai, is Etotat =

(1 totat " l o , totat) : Io,totat

(2.19b)

The total elongation is equal to the s u m of elongations of the single springs, Eq. (2.22) introduced into Eq. (2.19b) Etota!

(!j-!o,l) + (l2-io,2)

y

—

*o, totat

— -

(2.26)

! 12 A r e n g ^ a^cf ff&a;/]er;ng
Rewriting according to Eq. (2.19) (ti-lo,i) = e,lo,i

(2.27)

results in

Etotat=

Ellp,l +E2lp,2 1 ^ ^ lo, tota]

(2.28)

or Etotal - Ei

— —

+ E2

— -

.

(2.29)

Shortening the length fractions by the symbol A. in Eq. (2.29) Etotal=ElXt+E2X2.

(2-30)

The elongation of the total spring combination is the s u m of the elongations in the single springs. The s u m of length fractions, X, equals to one. The following results are found w h e n the initial lengths of the two springs and their spring constants are of the same magnitude ks,tota)=-r^--

(2.31)

The link between the total strain of the spring combination and that of the single springs is Etotal=Ei-

(2.32)

The properties which can be seen and formulated for macroscopic coil spring combinations are n o w transferred to ionic chains. First, consider the homogeneous chains m a d e up from the ionic pairs (Na+ - F"), (Na*** - CI") or (Na+ - 1 " ) . The dash (-) m a y be understood to be the bond spring. The ion distance r is then equivalent to the length 1 of the macroscopic springs.

P/YyMco-C/SefHi'ca/ F/ewewM q f ^ e Are/:g;A ofPure Phases

1! 3

* l.o. AU-10IB

t (Na" F-) ^(Na^CI-: r-1010

(Na^l-) 0.0-

'Isolated Ion pair

1.0Ion pair in the chain

-)

(Na^ CI-)

(Na^ F

''

F .„9 V 10^

2.31

(Na^ I-

Z.82JI 3.Z3

") l.S-r

1.0
f^(Na^l rlO .10

1

?^'

^!^.'^1

Fig. 2.11 Energy conversion (AU), force (F), and spring constant (k) versus ionic distance (r).

H 4 Are/:g^ a;:J ^a^AeW/?g o/^/?oc^ on FoM/i^ary Zayer Pro^/ew^

In Fig. 2.11(a)-(c), the energy conversions have been plotted for the three compounds: A U in N m [2.11(a)] the force, F in N [2.11(b)] and the spring constant, kg in Nm"', as a function of the ionic distance, r in m [2.11(c)]. They have been indicated in the diagrams with the following symbols: (Na+ - F-) (Na+ - CI") (Na+-I) For each ion pair, the functions for the isolated pair as well as for the pair in the uniform chain have been calculated and plotted in Fig. 2.11. The energy distance function for the isolated pair was AUAss = ZNa+Zci- Co

1+ JLe-(i/p)(r-

r.)

(2.8)

According to Eq. (2.10), the energy conversion for an ion pair in the homogeneous chain was A U K = ^ ^ - E ° 2(1-1/2 + 1/3-1/4 + ---)

(2.10)

which is equivalent to A U K - ZNa+Zci* eo

1 +Ag-('/p)(r-r.) 2m2.

(2.10a)

The first and the second derivatives of Eqs. (2.8) and (2.10a) give the distance function for the force and the equivalent of a spring constant regarding r as follows FAss - ZNa+Zci" eo

+J Le-(t/p)(r-r.) r' r'

(2.33)

PAy^;co-C/[ew/ca/ F/eMienM q/*?Ae Arewg^A o/*PM/*e PAa^e^ t! 5

and FK - Z N a + Z c r eo + J

Le-(l/p)(r-ro) 2 1 n 2

r^

r.

(2.34)

as well as

ks.Ass - Z N a + Z c r Co - —

+ —e-('/p)('*-''-.) l

2

(2.35)

and

ks.Ass.K - Z N a + Z c r 6o

2 —+

1 -(l/p)(r-r.) 2 In 2. —^

(2.36)

All absolute values for the ion pair in the uniform chain are enlarged by the factor 2 In 2 = 1.363 as compared with the isolated ion pair. B y introducing eo in electrostatic units and r in cm, the energy results in erg, the force in dyn and the spring constant in dyn cm"'. For conversion into c o m m o n units, the following equations shall be used 10? erg = 1 Joule = 1 N m = 2.389 x 10" kcal = 0.102 k p m and respectively 103 d y n = l N = 1.019716 x lO^kp. The diagrams of Fig. 2.11 make it evident once again that energy, force and the spring constant are non-linear functions of the ion distance. H o w can the spring constant of a chain consisting of two different springs, but at equal force, be determined? To answer this question, it is necessary to first determine the spring constant for each spring separately and then to put these values into the equations given above for the macroscopic springs. This question is considered for two cases:

!) 6 &re/?g;A a/:^ W^afAenng o/"7?oc^ a^ RouM^ary Layer PwA/emy

(1) W h e n the outer force is very small or zero. In this case r = r^ and the spring constants can be directly calculated from, Eq. (2.35). ks, (Na+ F-) (0) = 119.34 N m ' i , k, (Na+ ct-) (0) = 86.37 N n r ' and ks, (Na+ i-) (0) = 68.60 Nnr*. (2) For a general force, for example F = 1 x 10*^ N ; see Fig. 2.11. B y intercepting the curves in Fig. 2.11(b) with a horizontal line at the required force, chosen here as 1 x 10"^ N , and dropping from these intercepts the verticals to the curves of the respective spring constants, the points of intercept so identified [Fig. 2.11(c)] represent the values of the spring constants required for the previously chosen force. In this w a y the following spring constants on the ordinate from Fig. 2.11(c) have been found ks, (Na+ F-) (1) = 85.0 Nm-', lq, ^ + cr) (1) - 52.5 Nm*', ks,(Na+i-) (1) = 34.3 Nnr'. At the m a x i m u m of the force distance curve, the functions of the spring constants go through zero. W h e n the spring constants listed above and a force of 1 x 10'^ N are used, the respective lengths are as follows l(Na+ F-) (1) = 2.40 x 10-1° ^ i ^ + ^ I(Na+.-)(!) = 3.43 x 10-1° m .

(1) = 2.97 x 10-'° m ,

The respective elongations are (l(Na+F-) (l)-lo(Na+F-) (0)) = 2.40 X 10*1° m - 2 . 3 l x 10*1° m =

0.09 x 10-i° m (l(Na+ ci-) (1) - l(Na+ c<-) (0)) = 2.97 x 10*1° m - 2.82 x 10*1° m = 0.15 x 10-i° m (l(Na+1-) (1) - l(Na+ f ) (0)) = 3.43 x 10*'° m - 3.23 x 10*1° m = 0.20 x 10-i° m Finally the extensile strains are E(Na+ F-) (1)X 100 = 3.90% E(Na+ C1-) (1) X 100 = 5.32% C(Na+ f-) (1)X 100 = 6.19%.

.PAygico-CAewnca/ E/e7Menf.s q/^e Areng^A o/Pure PAases

117

With the help of these data, the interesting properties of chains m a d e up of the three components m a y be calculated. But n o w the question arises h o w to calculate the ultimate strength of a chain knowing the properties described above. This is considered in the next section. 2.1.4

E s i w M f e q^f^e f/teoreficR/ sfrewgf^!

Figure 2.12 shows an elementary cell of the cubic face centred rock salt lattice, in which all three of the ion compounds considered so far crystallise. Such a cell is similar to that of other interesting substances, such as M g O , C a O and as a derivative (crystallo-chemical) of the rock salt lattice, the similarly-structured calcite.

+ c

<°*o Fig. 2.12

Elementary ceH of rock salt iattice.

1! 8 Areng?/: an
In the rock salt lattice, ion chains m a y be considered which traverse the cell from top to bottom and are parallel to the crystallographic c-axis. They correspond to the chains considered w h e n any (lateral) energetic interactions between them are excluded. The figure shows that the basal plane of the cell is crossed by 4/4 + 4/2 + 1 - 4 chains. This means that the effective sectional area of the single chain equals to a^/4 or the number of chains per m ^ is 1/0.25 a^, if the unit of ao is m . A s the force at failure (F^) for a single chain is the m a x i m u m value of force in the force-distance function, which can be taken from Fig. 2.11(b), it then holds that,

°'=^i^r

(2.37)

In numbers and for the ion chains of the above named materials, with the exception of calcite, it follows that CK, (Na+ F-) = 51.54 G N m - 2 , o*K, (Na+ a-) = 25.15 G N m - 2 ,
P/:y.H'cc-C7:ewiiC6t/ E/e/nen^ q/*^Ae A r e ^ A ofPt/re Phages ) )9

d - a .1/2 o -1/2 d* --Q.(2)

1/2

d-(2)

d = a^.(2)-1/2 d* = a^.(2)

d

-1/2

= d

d = a -1/2-(3)1/2 * d = a_

d - d2(3)

1/2

Fig. 2.13 First, second and third co-ordination sphere around the central sodium ion.

120 .5?reMgf/: an;/ W^a^Aerwg q/'^oc^r 6M FoM/:^yy Zoyer Pro^/ew^

respectively) corresponds to a strain at failure of about 2 4 % (!). In comparison to measurements on brittle materials, this strain seems to be m u c h too high. Most rocks fail in tension with strains of just a few percent or even less. (2) A s mentioned in the estimation used above, energetic interactions between the chains were neglected. Their effect will n o w be considered. The principal effect of the first co-ordination sphere, as well as the structure of the second and the third sphere, m a y be seen in Fig. 2.13. Around the central sodium (black) ion, six chlorine ions are arranged in the form of a regular octahedron in the first sphere, twelve further sodium ions are arranged in the form of a cubo-octahedron in the second sphere, and finally the central ion is surrounded by eight ions in the form of a cube in the third sphere. It is sufficient to consider the influence of the octahedrons on the central chain. The four chlorine ions arranged in a square exert a repulsion not only between themselves, but also on the two chlorine ions at the upper and the lower tip of the octahedron. Thus the sodium-chlorine bond in the chain is weakened on the whole. This idea of chains going through areas is expanded in the next section, where it becomes clear that chains as such can become very complicated three dimensional structures. This leads to difficulties w h e n applying the concepts used so far. 2.L5

SzVi'dc acz^ & a m s

The considerations introduced up to n o w were particularly important for solids crystallising in the rock salt lattice. For silicatic rocks, the Si-O-Si chains have to be discussed. They differ from the sodium halogenide chains in several respects: * Silicon is four times positively charged and oxygen two times negatively charged, if the comparison is started with concepts of heterogeneous bonds only. * In nearly all modifications of silica, except high-crystobalite, all Si-O-Si bonding directions are not stretched, and bond angles are smaller than 180°.

PA_HS!co-CAe7M;ca/ F/e?nenf.! q/*^e Areng;A o/*PMre PAcyes ! 2i

r-.4+ = 0.39 8

'Si

r^ 2- - 1,32 8

Fig. 2.14 Screwed chain of regular tetrahedra and its projection onto the base.

! 22 Arengf/; a/!^ ^a?Ae/*M^ q/'.RocA: aj RoMMcfayy Z,aye/* ProA/ew^

* The first co-ordination sphere consists of oxygen ions arranged as a tetrahedron and not an octahedron. * In m a n y silicates, as also in quartz, the tetrahedron chains are screwshaped. * The Si-O bond is not purely heteropolar (i.e. not purely ionic). According to Pauling (1964) an ionic bond fraction of about 5 0 % has to be assumed. The bond is about halfway between the heteropolar and the homeopolar bond (i.e. electron pair bonding). Figure 2.14 shows a screw-shaped chain m a d e up from regular tetrahedra with stretched Si-O-Si bonds, and the projection of the central Si-O-Si chain on its base. The angle between the Si-O bonds within a tetrahedron, the so-called tetrahedron angle is 109.47°. The Si-O distance and the length of the sides of each tetrahedron determined experimentally are 1.6 A and 2.62 A respectively and therefore about 6 % smaller than the sum of the ion radii. F r o m this fact, it is concluded that the bonding forces should be higher than in the case of pure ion bonding. Although energy-distance functions have been formulated for mixed types of bonds, the other problems outlined above will not be fully solved on applying them. The fraction of the force and the respective energy requirement needed to extend the screw-shaped chain cannot be easily estimated in particular. Despite these difficulties, it is possible to m a k e some progress on understanding the properties of these chains if the following approach is adopted: the equations given above for the isolated ion pair and ion bonds are used to obtain a first approximation. Next, a better value is derived, taking into account the energetic surrounding of a single bond for the ion pair within the crystal lattice with the help of the lattice energy per formula unit (see below). Finally, theoretical strengths are considered which have been derived in other ways by Griffith and later by Orowan; here the approach followed by Salmang and Scholze (1982) will be used. The result of the first of these steps is demonstrated in Figs. 2.15(a) and 2.15(b) where the energy distance function of Si^-O^" is given in comparison to the one of Na+-Cl". In forming an isolated ion pair (Si^-O^") from the ion gas concerned to the equilibrium distance, which has been accepted here

P/]y.n'co-C/]efM;ca/ E/e7Menf.s q f ^ e ArgMg^A of P^re PAasas 123 t 10

(a)

(b) Fig. 2.15 (a) Energy conversion, A U , versus ionic distance, r; (b) Force, F, versus ionic distance, r.

124 Are/:g;A <2H
to be 1.71 A (sum of radii), the energy conversion is about eleven times bigger than that produced in forming an isolated Na+-Cl" ion pair. The m a x i m u m value of the force-distance graph is bigger than the comparative value for Na+-Cl" by a factor of 15 [Fig. 2.15(b)]. The main reason for this has to be in the fact that the product of the charge values is eight times bigger than that in rock salt. The smaller equilibrium distance between S i ^ and O^* in comparison to rock salt naturally also has an influence. Note the strain at failure at the m a x i m u m of the force-distance function is 4 0 % in this case, as compared with 2 4 % for Na+-Cl*! According to these figures, it has to be expected that the strength of silicatic chains is essentially bigger than that of the sodium halogenide chains. The following section is concerned with the second step mentioned above, i.e. h o w to calculate a value for lattice energy of a compound. So it is no longer concerned with the chains but with the bulk of the material.

2.2 The Lattice Energy The total amount of energy liberated from an ion gas to a crystal m a y be denoted as A U ^ . This numerical value is negative. The related positive energy that is necessary to transform a formula unit of the crystal into one mole of ion gas is called the lattice energy, AU^. Thus, AUc^-AUnr-

(2-38)

The lattice energy can be determined in two ways. In the first the concept is continued which has been started above in forming a one dimensional chain of infinite length, i.e. summing up the potentials of attraction and repulsion affecting an ion. This thought is extended to the sum of influences in three dimensions. The s u m of the energy required to form a chain was shown to be bigger than that for an ion pair by a fixed factor of 2 In 2. It is also possible to produce a sum of energy amounts when considering a three dimensional structure. Even here, this leads to a fixed, concrete, structure characteristic number: the Madelung constant. Madelung

P/pwco-CAefH/ca/ E/eme/!^ q/*^Ae &/-e^/! q/Pure PAasay 125 Table 2.3 Madelung constants for welt-known lattice structures. Lattice type

Madelung constant

N a CI Cs CI Zn S (Zincb)ende = Sphalerite) Zn S (Wurtzite) CU2O (Cuprite) CaF2 (Fluorite) Ti O2 (Rutile) Ti O2 (Anatase) Si02 (P-Quartz) AI2O3 (a-Corundum) Cd J2

1.7476 1.7627 1.6381 1.641 4.1155 5.0388 4.816 4.800 4.4394 25.0312 4.71

constants are different for different structures of co-ordination spheres, see Table 2.3. Once the Madelung constant is known, it is possible to formulate the energy- and force-distance functions in principally the same w a y as was done above for chains. However, as soon as difficulties arise in more exact description of the bonds, or if values are required just for comparison, the second w a y to determine the lattice energy is chosen. This second w a y uses energy conversions which are exclusively experimentally determinable and is based on the first law of thermodynamics in the form of Hess's law (H. Hess, 1802-1850: Professor of Chemistry in St. Petersburg). The law states that the amount of energy converted in the formation of a chemical compound is independent of the experimental w a y in which the compound has been formed. This fact has been used by B o m and Haber for solving the problems of determining lattice energies. A s an example, the formation of a formula unit of sodium fluoride crystal from the ion gas with both methods, indicated by I and II, m a y be considered. Method I corresponds to the above described method, in which the energy conversion was calculated from the force-distance functions. Method II includes macroscopically measurable magnitudes only. The following sketch illustrates the principles.

!26 "frengfA a/!^ "^ea^en^g o^7?oc^ as BoMngary Layer ProA/e?m

( N a r )pajrs of ions

4- 1 —

(Na+

+

II-AU^ron^,y

H-AUion^on

1

(F-^o,^

(Na°)g„ !

(F°)gas

H-AU^o,

1 1 11 - 1 /2 * A Udissociation

!

< [Na+F"]crysta!

!

.. <-

H

—

[Na°]crysta!

+

1/2 . (Fz)gas

A U 298 K

For Method II, the following energy conversions are used Ionisation energy: Sublimation energy: Electron affinity: 1/2 Dissociation energy: Reaction energy:

AU;onisation = + 4 9 5 6 9 x 1 0 ^ N m (mol)"' AUsubiimation = +l-0039x 10^ N m (mol)"' AUdectron afHnity= "3.3255 x 10^ N m (mol)"' 1/2 AUdissocJation =+0-7655 x 10^ N m (mol)"' A U % g ^ = -5.7014 x 10^ N m (formula unit)*'.

The energy s u m according to Method I, taking the Madelung constant ibr rock salt lattice into account is -8.815 x 10^ N m (formula unit)*'. The energy s u m according to Method II, taking into account the correct signs, results in-9.101x10^ N m (formula unit)"'. The two values differ by about 3 % and thus are equal in the frame of errors. After this verification, the concept of the B o m - H a b e r Cyclic Process becomes clearer and shows that the total energy conversion is k n o w n in either Method I or II. Thus it is possible to determine the energy conversion of one of the other processes by calculating the difference between the value of the total energy conversion k n o w n in one w a y and that of all other energy conversions except the one under consideration. It was with such an intention as this that the first investigations of this kind by B o m and Haber were undertaken to determine values for the electron affinity of halogens. For the silicatic phases, the values for the steps of Method II are known. Here it w a s found that the lattice energy A U ^ equals AUxr = -135.27 x 10^ N m (formula conversion)"'. The energy conversion from the

P/iy.Hco-C/:e?H;'ca/ F/efnenf.? of ^ e A r e ^ A o/Pure 7%a.?e.y 127

ion gas to the ion pairs in a crystal is found by dividing with the Madelung constant and again with Avogadro's number AUxr, Ass = "5-06 x 10"'^ N m (ion pair in the crystal)"'. This energy value has been indicated in Fig. 2.15(a). Despite the fact that this value is m u c h closer to the respective value for rock salt, the statement made above that the energy value and thus the strength of the material should be m u c h bigger than the respective value for the halide remains true. This is valuable additional information. Nonetheless, it is not easy to deduce the force versus distance curves for ions from a comparison of single energy amounts. Furthermore, such an approach does not seem to give m u c h insight to the most important question, i.e. the reasons for the reduction of the experimental strength by a factor of a hundredth to a thousandth of its theoretical values.

2.3 Strength According to Orowan's and Griffith's Considerations The equations given by Orowan, and earlier by Griffith, evade the subject of the strain which occurs at failure: "The Orowan statement assumes, that in a tensile experiment the invested energy for destroying a solid needs only that strain which causes neighbouring ions of an initial distance To to be permanently separated; the minimal energy is that used to form the n e w surface" (Salmang and Scholze, 1982). This statement is obviously of limited use w h e n applying it to rock as these are composed bodies, at least w h e n the presence of different phases leads to the presence of different forces. The determining equation for the theoretical strength given by Orowan is

fW °f=J— E: a modulus of elasticity NrrT^ y: a surface energy N m per m ^ or a surface tension in N m " ' Toi the equilibrium distance of the ions to be separated.

(2.39)

t28 &re/;gy/: a^c/ ^ a ^ e r M g q/^J?oc^ as ^OMMa'a/y Aoyer Pro^/e/M^

If Of the tensile strength of a crystal, is required in a given direction, e.g. parallel to its c axis, then E and y have to be chosen accordingly. E, as well as y and r„ are macroscopically measurable magnitudes. But even this fact does not remove the difficulties of obtaining o*f by this fascinating approach. Variations of the numerical values of Gf in particular the explanation of surface work and its eventual changes, cannot be immediately interpreted in terms of their molecular causes as will be shown below. It might be for such reasons that Salmang and Scholze (1982) considered it necessary to give only the estimated strength values of ceramic materials with the help of Eq. (2.39). With the averaged values of E = 1 0 " N m " ^ , y = l N n r * and ro = 3 x l 0 " ' ° m one finds 1 8 G N m - 2 . For A ^ C ^ , o*f = 43 G N m " ^ ; this is the same order of magnitude as was found for sodium halogenide chains. The fact repeatedly stressed in this text is that there is a big discrepancy between the calculated and experimentally determined stress values required to cause tensile failure, as illustrated in the upper part of Fig. 2.16. Possible reasons for such material behaviour can n o w be considered beginning with the homogeneous material — glass (lower part of Fig. 2.16). Causes for the decrease in strength values as given in literature are discussed first. In parallel to the equation by Orowan [Eq. (2.39)], a similar relationship by Griffith can be considered

Of

(2.40)

1: is half the length of the long axis of a rotation ellipsoid which is taken to represent a model crack within the structure of the solid. This equation says that a crack formed like an ellipsoid of the length of 21 causes, w h e n loaded vertically to the long axis, a stress concentration which can lead to crack initiation. Considering the same averaged values as before, see the O r o w a n equation [Eq. (2.39)], a comparison of Eqs. (2.39) and (2.40) shows a critical crack length, 21, of about 4 x 10"'" m or 4 A for the special strength value of 18 G N n r ^ (after Salmang and Scholze, 1982).

P/!yy;'co-CAe?w'ca/ E/efMenfy q/^Ae A r e M g ^ q/"PMre PAayay 129

ThecfBCtcal

Ftaodcal

EtperimBntal eatpaTjEBOBS

1-10

e*„ MM

2tns200)

1-10"

&iffdth-Crada

<3 }

C<

2ooXttM 2 m

1-10"

1' 2 m tns 0,2 <

Fig. 2.16 Strength of glass and possible reasons for its reduction (lower part of figure after Hinz, 1969).

130 &re/:g^ ancf ^a/AerMg q/^ocA: ay RoH^^aTy Zayer Pw^/e?m

F r o m the Griffith equation it follows that an increase of the crack length of a factor 100 results in a reduction of the strength value by a factor of 10. Thus the length in question has to increase from a few Angstrom units to a few p m to reduce the strength to 1 % of its former value, and it needs to increase to a few tenths of a millimetre to reduce the strength to 1 % of its former value. Such a treatment of the Griffith equation m a y seem crude; however it demonstrates that the model of an isolated Griffith crack in a homogeneous surrounding can hardly be applicable for crack lengths that are a few Angstrom units long in a surrounding of lattice dimensions. Even though these calculations lead to the correct orders of magnitude for strength, other mechanisms seem to exist which could also be responsible for the dramatic reduction in strength. Before such mechanisms (shown in Fig. 2.16 in the form of experimental influences on the strength of glasses) are further discussed, the basic situation shall be described once again in the words of Schwarzl and Staverman (1956): " A real understanding of breakage phenomena cannot be gained by macroscopic observations alone. T h e statistical scatter of the measured results and the dependence of the breakage phenomena on the dimensions of the sample, as well as the morphology of the breakage plane, inevitably lead to the conclusion that, for breakage, certain inhomogeneities or notch systems (the microstructure) play a decisive role. The most suitable material constant that best describes breakage is thus the distribution of notches within the material with respect to their strength: i.e. the number of notches per unit volume which, for the macroscopic stress state with the components T, a and i + di, o* + do*, leads to failure. If the distribution of the microstructure in relation to their strength is known, then it is possible to deduce, with the help of the statistical breakage theory, the macroscopic breakage properties. F r o m direct investigations of the microstructure it cannot be hoped to find the distribution of the notch strengths but at best the distribution of their geometrical nature: i.e. the number of notch locations per volume unit, having a certain length, a certain width and a certain orientation in the material". Even though these remarks originate from a monograph by the authors on artificial polymers, it can be assumed that these conclusions are of a

P/]y.HC0-C/:e7?Hca/ F/eTHenfy o/*y/!e &rg/:g^ q/*PM/*e PAases

! 31

basic character which also hold true for other materials. Nevertheless other influencing factors have to be expected in anisotropic bodies like rocks. Figure 2.16 shall n o w be considered in more detail. In the figure, there are suggestions for inhomogeneities and notches which can occur in glasses listed. A logarithmic strength scale is given on the left hand side. The horizontal lines indicate decades of strength, and the respective hypothetical numerical values of Griffith flaw lengths have been noted. Reasons are given on the right side for a departure from the theoretical strength, either in the form of words or drawings. The causes for these departures are grouped as follows: * * * *

structural heterogeneities juvenile glass threads chemically strengthened glasses physically strengthened glasses.

The basic idea of the molecular glass structure has been developed by Zachariasen (1933). The idea consists in visualising glass as a statistically uniform formation of locally irregular network elements which are m a d e up of Si02 tetrahedra. In the presence of further oxides, particularly alkali- and earthalkalioxides, this picture is to be modified as follows. Whereas in pure silica glass, each "bridge oxygen", (O^") is bound to two Si^+ ions, this is no longer true in the presence of N a 2 0 for example. At places where N a + ions occur, the rings have been broken open and s Si-O-Na bonds have been formed. Deviations of the statistical uniformity happen for example, w h e n first swarms and then nuclei of n e w phases are formed. The size of such pre-ordered or ordered areas is between 10 to 20 A. Extensive electronmicroscopical investigations showed that w h e n the nuclei grow further, the crystalline domains can become several thousand A or a few tenths of a u m respectively (see for example Oberlies and Dietzel, 1957; Kuhne and Skatulla, 1959). Recently Vbgel (1993) published an extensive compilation of "Glasfehler" (glass faults) with m a n y microscopic investigations.

132 AreHg?/: an J ff&afAerMg q/^/?oc^ aj RoMM^ayy Zayer Pro^/ewy

O n e of the m u c h discussed partial problems in this area is the state of the crystallites and their structural linkage with the amorphous surrounding. Similar thoughts have been discussed in case of so called partially crystalline organic chemical polymers. Unlike crystals, crystallites are not idiomorphous, although their internal structure is identical. Stress zones between the domains have been frequently postulated. Walenkov and Porai-Kuschiz (1936) assumed that one has to distinguish between an inner, more ordered and an outer less ordered part of the crystallites and "that all crystallites are linked by their outer highest strained parts to a continuous net". It is not possible to exhaustively cover this big and especially important area for natural as well as synthetic materials. Nonetheless, there is no doubt that such supermolecular structures have a determining influence on the mechanical properties of materials: for example a crystal content of about 2 4 % by volume enhances the elasticity modulus of natural rubber by a factor of 100 (Leitner, 1955). VMve7M7e g/ays f^rea^ "For juvenile, i.e. in surfaces which have not been touched, a certain freedom from cracks is to be assumed; in this case by completely healing or diminishing Griffith cracks (e.g. by fire polishing or hydrofluoric acid etching) it is possible, at least for short periods of time — as long as nothing comes in touch with the surface — to achieve higher strengths" (Hinz, 1969). Threads of such kind have been investigated by Griffith and later by Gooding (see above). Regarding an interpretation of these phenomena as indicating the absence of Griffith cracks, surface strengthened glasses have to be considered. 5Mr%ice ^^e^g^eMg^ g/anay With this term, the two categories used in Fig. 2.16 — chemically strengthened glass and physically strengthened glass — are combined. A s far as the phenomena described are concerned, compressive stresses are

P/rnH'co-C%e7Hic%/ .EVeynenfj q/*;Ag AygngzA q/*PM/-e P/iayay ] 33

created in a surface layer and tensile stresses in the interior of the bodies; these are the cause for an increased strength. The stress distribution has been proven via stress optics using polarised light in the visible range of wave lengths. This means that the mechanically changed domains are at least in the order of a few tenths of a micrometer (the wavelength of visible light is about 0.4 to 0.8 a m ) . These pre-stressed layers were created either physically by quenching the surface of the still hot glass (as in the safety glass for windscreens) with the result that non-uniform thermal strains are preserved between the outside and inside of the body, or by chemically replacing smaller cations in the surface layer of the glass by bigger ones (Li+ —> N a + or N a + —> K+). The second method seems to lead to thinner but higher pre-stressed outer layers as compared with the first method. In a subsequent chapter, the chemical change of surface layers, again with the aim of changing strength, will be examined. Such processes are not limited to glass and to the replacement of special ions by others. To finish this brief compilation, it shall be noted that in all the methods mentioned, only a change in strength is discussed but not an absolute level of strength (see Fig. 2.16). The next section considers the order of thermal stresses required for a special arrangement of pre-stressed layers to be obtained.

2.4 The Order of Magnitude of Thermal Surface Stresses for a Central Symmetric Phase Arrangement In the previous section it w a s mentioned that compressive stresses can be initiated in the surface layers of the bodies under consideration through different thermal extension coefficients. T h e compressive stresses for a special geometry of the system are n o w assessed. T h e system is illustrated in Fig. 2.17. A crystal sphere k, is surrounded by glass g. T h e necessary equations for this geometry are derived by Lundin (1959).

134 Are^g^A aM6? ^a/Aerwg o/^7?oc^ as RoHnaary Layer PwA/ems

Fig. 2.17 A sphere consisting of a crystai and glass.

Stresses in the crystal

R3 C*K,rad -On,tan

^

- - A

(2.41)

Stresses in glass 3 ^ Cg, rad **

A

x^

(2.42)

r^

^R3 Cg,tan= + (l/2)A

x^

R 3^ r^

(2.43)

Positive values denote compressive stresses, negative values denote tensile stresses. The factor A in Eqs. (2.41) and (2.42) is explained as follows: (<*K -ctg)AT

A =

l-2nx

1V

R

3\

R^ 1 l + ]^g+2^(l-2ng) 2E, r^

+-

(2.44)

PAy.s;co-C/:e/mca/ F/e7neMf.s o/'^e AreM^;/] q/^Pt/re PAajay 135

For the definition of R, r, and x, see Fig. 2.17. The symbols of Eq. (2.44) are defined as follows: a;: AT: Uj: E;:

thermal extension coefficient temperature difference Poisson constants elasticity coefficients.

Equations (2.41)-(2.43) are discussed with the following questions in mind: * W h a t are the stresses at the interface between the crystal and the glass (x = R)? * W h a t are the stresses occurring in the glass? A n d finally * what is the m a x i m u m stress in the glass for R3

r^

= 1?

Under the circumstances of the situation being considered, only tangential stresses exist at the interface between crystal and glass. The following equation gives their values

°S''^+

Eg(ctx - a g ) A T (i-,g) '

(2-45)

With the values Ug = 0.17; Eg = 7 0 G N m ^ and A T = 5 0 0 K , it follows that Og, tan = +42169(otn - ctg) G N r n ^ . T h e extension coefficients are about 0.5 x 10"^ for glass and 12 x 10"6 Kr* for quartz parallel to ao. With these, w e get an approximate compressive stress value o*g, tan = +0-42 G N m - 2 .

136 &reMgf/: anc/ ^ a ^ e n T t g q/^oc% a^ Rt?M/!(/a^y Zoyer Pro^/ew^

Whereas under the circumstances described (x = R and R^/r^- i) rio radial stresses should exist in the glass, compressive stresses whose absolute value is about 2 % of the theoretical strength of silica glass, exist. This magnitude of order is consistent with surface strengthened glass (see Fig. 2.16).

2.5 Surface- and Interfacial-Energy Apart from the elasticity modulus, Eq. (2.39) also includes the surface energy which is needed for the determination of strength according to Orowan. Thus, either a knowledge of or an ability to experimentally determine surface energy is pre-supposed. This does not seem to pose a problem for fluids but is m u c h more complicated for solids. Either one uses the simple lattice theory of crystalline bodies with their assumptions and problems again, or one makes use of one of the m a n y proposed experimental methods.

Fig. 2.18 Chain of ions: (1) in its equilibrium state, (2) stretched and (3) broken.

P/!y.Hco-CAe7H!'ca/ J?/e7Menf.! q/^^Ae Are/;^A q^PM/*e PAayes !37

To begin with, the term "surface work" is looked at in more detail (Fig. 2.18). A chain of ions is depicted once again. In State 1, its length is lo- In Step I, the chain is strained elastically and reversibly to State 2 where its length is If. At this length the chain breaks (Step II). The two newly formed pieces of chain bounce back to their neutral position (State 3) and the potential energy invested elastically becomes free again. This is not true for the broken bond, but the amount of elastic work is negligible. In opposition to this, work has to be invested for breaking the bond itself. The following equations show these facts again in short form: Step I: elongation from 1„ to If I 1 ->2 T = constant V = constant A U i = AWelastic extension = + f ' F dl.

(2.46)

Step II: breakage of chain at If

n 2->3 T = constant V = constant A U H =-AWg]astjc ^tension + A U A A U n = - j ' F d l + yAA.

(2.47)

The s u m of changes of the internal energy A U ^ i is therefore AUtotai=yAA.

(2.48)

Equation (2.48) provides a definition of a specific surface energy, for example, in case of the crystallographic plane (hkl)

138 Arengf/: ana? f%af/[er;'ng q/*^oc^ as F o u n d r y Layer P w ^ / e w s

8(/ Y=

(2.49) ^ ^

/T,V,(hk])

Its determination, experimentally, and the reliability of the different experimental methods by which this can be done are topics considered in the paragraphs that follow as they decide the practical applicability of the Orowan equation. The approach of Meyer (1968) will be followed for describing these methods. However, important attributes of the definition of surface energy need be explained before this. The work required to create a unit of n e w crystal surface with indices (hkl) in vacuo can be called specific surface work y, [Eq. (2.49)]. This is retained in the n e w surfaces as specific surface energy, which thus depends on the orientation of the surface to which it refers. Thus it can be appreciated that if breakage occurs in a non-vacuum, a stable interface can only be produced w h e n the uncompensated force fields generated during breakage are satisfied by subsequent reactions. This shall be illustrated once again by a sketch in which processes are described that have been already mentioned. It is the interaction of water with virgin surfaces of solid silicic acids according to the text of Hauffe e? a/. (1974).

Siloxane group

Silanol groups

O OH OH / \ chemisorption 1 1 ^ -Si-O-Si-Si-0-Si-+H20 irreversible 1 1

!

H

OH

1

H H / \ 0 0

OH

1

physisorptiort

-Si-0-Si-+H20 !

!

1

H \ / O

1

1

-Si-O-Sireversible

!

1

PAnMco-CAewHca/ E/eweM^ o/^Ae i^^eKg^A q/*PMre PAa.se.! 139

The so-called (OH)-group density is about four (OH)-groups per (10 A ) ^ at the newly formed silica surfaces. The highest acceptible adsorption heat might be about 10 kcal per mole H 2 O adsorbed (Lange, 1965). This leads to a specific adsorption heat, measured in Nm"*, of 0.28 Nirr*. Assuming an approximate surface energy of about 1 NirT* (see above), one realises that the interface energy is some 1 0 % smaller than the surface energy. With regard to the uncertainties, not only in the number but also in the quality of surface reactions involved in such calculations, a remark by Eucken (1944) m a y be cited: "With the adsorption of, especially, steam onto glass one achieves large thicknesses up to several hundred molecular layers; such processes cannot be called adsorption, but a sort of swelling (creating a sort of gel), which penetrates relatively deep into the surface structure of the glass". Similar model ideas are the basis for calculation of electrochemical potential differences of "long aged" ("formierte") glass membranes, which are used for p H measuring electrodes, for example. Another technical area, the polishing processes, particularly of optical glasses, provides the following experiences about the character of surface layers: described by Dunken (1990): "The remaining polished layer is for silicate glasses up to 1 urn thick and impoverished directly after polishing in alkaline ions that can be leached out easily by water. Furthermore, in the end phase of the polishing processes, in which with water it is dry polished, dissolved glass components are again deposited on the surface. Density and refractive index differences between the polished layer and glass volume can be determined". The manifestation of such polished layers is apparently similar to that of the weathered layers at silicate surfaces, i.e. leached layers. In this context, Fig. 2.19 shows an electronmicroscopical photo of w i n d o w pane glass after treatment with 70°C w a r m water after two weeks (Cotterill, 1985): a gel-like layer with cracks has formed. In such cases, the interfacial energy is very different due to exothermic reactions with neighbouring phases. Before the experimental procedures for the determination of surface energies are described, the order of magnitude of the specific surface energies will be compared with other frequently used energy terms of thermodynamics (after Huttig, 1941). O n e mole gold ( M A u = 196.967 gmol"*; p = 19.3gcm"^) be formed in a cube of side length ao,Au = 2.165 x l O ^ m ; its surface area

140 ArengfA aM
!

)

10 pm Fig. 2.19 Eiectronmicroseopical micrograph of window pane glass after a treatment with 70°C warm water after two weeks (Cotterill, 1985).

So Au = 28.12 x 10*4 m^. The specific surface energy of gold is y = 2.539 Nm"'. O n the basis of this valid values of surface energy can be estimated. It is easy to see that the total energy to to be invested in cutting a cube to face lengths of 100 A is in the order of the melting energy, A U m - 12 770 N m mol*', at ^

= 1064.76°C.

Edge length of particles Number of particles m mol*' 2.165x10-2 1.000x10-^ 1.000x10-" 1.000x10-6 1.000 xlO-s

1 10.15 10.00x106 10.00 x 10'2 10.00 xlO's

Total surface area, A m^mol*'

AUA N m mol"'

28.12x10-" 60.89 x 10-" 6.10x10-' 6.10x 10' 6.10x103

0 0.008 1.547 154.900 15 487.900

P/rnMco-C/tem/ca/ F/e?Henfs q/^;Ae &re/?g;A q/TMre PAa.yas' 141

^

1

-

I

<<

''

<

^ '' '<

<) <<

L y '

< !^ J

<<

^ ^3 z Z ^ ^ - ^ ^ e ^ u N s S ^ ^

I

! '<

<<

, l

^f -?*B ^S. t^ C% ^ c3 *S F'^ ^

' B

Fig. 2.20 Co-ordination numbers of the crystaHine phases and numbers of closest neighbours in the melted phase (Steeb e/ a/., 1969). *: crystalline phase; -: molten phase.

At the normal melting point in this case, 1064.76°C, the lattice structure is destroyed, and a liquid, the melt is formed. Figure 2.20 shows the coordination numbers of the crystalline phases and numbers of their closest neighbours in the melted phase (Steeb e? a/., 1969). The co-ordination number for the close-packed structures is twelve. It reduces to a little over ten w h e n it melts (see arrow for gold in Fig. 2.20). Whereas the number twelve in the lattice of the solid material is exactly correct for any metal atom looked at, the number 10 is the most frequent value which is derived from X-ray scattering experiments. There are thus variations in the co-ordination number around this value from place to place. "This can be explained in such a w a y that during melting voids are created in the crystal..." (Glocker, 1971). If the surface energy is in the magnitude of the melting heat, one m a y deduce that w h e n a n e w surface is mechanically created not only are atoms separated, but a highly disordered surface structure is also created. This effect is not included in the so-called elementary lattice theory. After these introductory remarks, it is clear that certainty about surface energy values of solids can only be gained from experiments. But even such determinations have difficulties: "In opposition to the surface energy of

142 ArengfA an6? ^HayAenMg q/^7?ocA <M FoMMt/ary Zoyer ProA/ew^

liquids the determination of surface energy of crystals is m u c h more difficult and the values gained accordingly to different methods vary within broad limits, often by orders of magnitude," after Meyer (1968). This problem is substantiated by overviewing the different experimental techniques used. Cleavage method The upper part of Fig. 2.21 shows the measuring principle. A crystal has been already notched and the thin upper plate, is pulled upwards by the force F. With this, the leaf spring is elastically loaded until the crack has enlarged by a distance dx and the n e w surface area d A - 2d(dx) is created. The related differential surface has been taken from the potential energy of the elastically deformed springs. So the surface energy equals

Y=7yE—y2. 16 x^

2.50)

The symbols used in Eq. (2.50) are explained in Fig. 2.21. The practical importance of the method is limited by the following factors: * it is necessary to k n o w the elastic modulus of elasticity of the investigated material a /?r;or; for the evaluation of Eq. (2.50); and * the values depend here too on the nature of the neighbouring phase. A n d most particularly, * pure (elastic) deformations of the crystals can only be achieved rarely. Also pre-existing deformations of the crystals under investigation play an important role: "For perfectly re-crystallised synthetic crystals of (LiCl) the magnitude of y^oo) = 340 erg cnrf^, whereas for weakly deformed (hardened) crystals Ynoo) w a s determined as 1015 erg cm-2" (Meyer, 1968). Links between the states of elastically and plastically deformed crystals have been schematically illustrated the lower part of in Fig. 2.21 (after

PAysico-CAefHica/ E/emeHfJ q/*^Ae Are/!g?/[ o^Ptvyg PAaye.! 143

— & ) dx j^-1

Fig. 2.21 Upper part: cleaving a crystat. L o w e r part: states after elastic and plastic crystal deformation (Cotterill, 1985).

144 ArengfA an
Cotterill, 1985). T h e author mentions that "Five idealised states of a crystal are identified here. The perfect crystal (top) can be deformed elastically (upper middle) up to a few percent strain, and still recover its original condition w h e n the stress is removed. If the elastic limit is exceeded, the resulting plastic deformation introduces dislocations which permanently change the shape of the crystal (middle). T h e strain energy can be reduced by polygonisation (lower middle), during which a polycrystalline structure can be established; the dislocations re-arrange themselves, primarily by glide, into groups which constitute the grain boundaries. If the temperature is sufficiently high (bottom), the boundaries are removed by the climb process. The crystal has returned to its perfect state, but it has adopted a n e w shape." For non- or partial-crystalline materials, other mechanisms of plastic deformation have to be discussed. Particularly difficult circumstances are found, w h e n under the influence of outer mechanical loading, twins are created or other n e w modifications are formed. Such processes can be observed for carbonate rocks, especially calcitic limestones. Reliable values of surface energy generated using the cleavage method require that particular conditions are maintained for experimental investigation. Dissolution heat All energies stored during comminuting processes enhance the internal energy of the ground phases. Thus in these cases, the internal energy is a function of temperature, volume and the surface area of the samples. Therefore, the dissolution heat of initially ground material is higher than that for the uncomminuted solid. The difference is mainly due to the energy stored in the newly formed surface. T h e difficulties, which are also linked to this method of determining the surface energy, have the same origins as those associated with the cleavage method. Plastic deformations and phase changes which occur during grinding naturally influence the internal energy of the phases as well. Apart from these difficulties there are two other additional problems: * the small caloric effects demand extremely accurate measurements; and

P/pwco-CAefmca/ E/emenf.! q/^^e AreMg^A q/*PMre PAases 145

* the amount of heat additionally developed in dissolving the samples represents an integral value. This value cannot be afterwards attributed to the differently indexed phases, which are formed during comminution. All these difficulties, w h e n put together, lead to the conclusion that no more than the right order of magnitude for the surface energy can be expected from this technique. W h e n the bodies to be investigated are glasses, then additional effects occur, which are linked to the expression of "Einfrierwarme". The G e r m a n verb "einfrieren" is equivalent to "freeze in" ("Warme" = "heat") which shall here only be mentioned (Haase, 1956). The determination of the surface energy according to the Gibbs-Thompson equation over the slightly enhanced solubility of small crystallites, m a y also have to be considered. In particular, the technique makes it impossibile to relate the measured effects to a particular crystallographic plane, this puts the method side by side the already mentioned ones. Sometimes the question has also been discussed, which particle radius should be put into the Gibbs-Thompson equation, as usually particle radii distributions occur in solid precipitates. Abrasive strength (Schteiffestigkeit) V o n Engelhardt and Haussiihl (1965) determined surface and interfacial energies as part of the investigation on strength and hardness of crystals in abrasive experiments. In these experiments, a specimen (e.g. crystal) orientated in a given direction is abraded against a rotating plate. The work involved and the change in volume are measured, and the n e w areas created (as indicated by the grain size of the debris) are calculated. F r o m these data, interfacial and surface energies m a y be calculated. The authors give the following reasons for their choice of the measuring method: "The measurement of ultimate strength in tension would be physically clear. In practice such a measurement of strength is badly suited for this task, because as already mentioned, the tensile strength of a single experiment is determined by the singular, most effective point of weakness in the whole sample, and thus can vary widely. The number and kind of failure initiating inhomogeneities which can exist, and thus the tensile strength which is

146 -SfrengfA ana* ^ a ^ A e r M g q^7!oc^ ay RoMMaary Zayer Pro^/e/M^

measured, largely depend on the prehistory of the sample, particularly its surface condition, and for statistical reasons on the sample dimensions. To have a reliable averaged value for a particular kind of a crystal very m a n y single measurements would have to be made, and even then one would never be sure if a sort of material specific strength is measured or a value which is due more to the sample production and history". "To be independent of the inner and outer inhomogeneities characterised as Griffith cracks, strength should be measured over relatively small crystal domains and the measurements should be as such that it is possible to average them over a great number of single processes". It is thus expected that this test constitutes a w a y to avoid certain problems already described and that on small crystal domains, numerous places could be potentially used to test strength. Figure 2.22 shows surface photographs of abraded quartz samples parallel to their base after an experimental duration of half an hour. The required "great number of single processes" is evident. Further, it becomes obvious, that the average crack length and its area frequency depends on the kind of neighbouring phase (benzene or octanol in this case). Naturally the plastic deformation of the strained crystals plays a role in these experiments too. T h e authors tried to achieve relative values of the "specific free interface energy of one and the same crystal kind in different liquids." A n important result of this work is shown in Fig. 2.23. The relative volume of abrasion

Fig. 2.22 Photographs of abrased quartz sample surfaces (von Engelhardt and Hausstihl, 1965). Unfortunately no scale is given by the authors. Left: distribution of cracks after abrading under benzene. Right: under octano).

/%Hs;'co-CAe7?H'ca/ E/e?neMf.s q/^^Ae Arey]g^ q/^Pure P/]aje.s 147

^-°°-j—!—!—!—)—J—)—)—!—!—k °

5

*=i -3 = r .10**

Fig. 2.23 Relative volume of abrasion, Vc/V„, of lithium fluoride versus concentrations of active substances in solution (after von Engelhardt and Haussuhl, 1965).

Vc/Vo of lithiumfluoride is plotted versus the concentration of surface active substances in solution with xylene. The surface active substances chosen were stearic acid: C H s - f C F ^ - C O O H dodecyclamine: C H 3 - ( C H 2 ) n - N H 2 n-octanol: C H 3 - ( C H 2 ) ^ O H . T h e figure proves that the abrasive strength of a solid, here lithiumfluoride, decreases with increasing concentration of surface active substances dissolved in a non-polar solvent. To explain this phenomenon, von Engelhardt and Haussuhl (1965) wrote: "Since the plastic properties of a specific crystal chiefly depend on the forces and the structure of the lattice, they are therefore, in general less influenced by an external medium, so w h e n strength is essentially determined by the specific free surface energy has to depend on the kind of the external medium." D u e to this explanation, the single curves of Fig. 2.23 express a diminution of the interfacial energy and this was thought to be associated with a Langmuir adsorption process of the surface active molecules at the solid surface. The particular conditions for this method of testing are very complex. For example the authors showed that functions of the kind depicted in Fig. 2.23, in the case of equal functional groups, depend quantitatively on

148 .S^rengf/i ant? H^a^Aer/Mg q^Roc^r <M FoMMRfary Zaye^ P/*o^/emy

the length of the radical chains expressed by their carbon atom number. The complications originated by the solid surfaces, the adsorbents, m a y be recognised w h e n considering the iso-potential lines which exist on it, Fig. 2.24. The conditions for the (lOO)-surface of potassium chloride are shown, according to Orr (1939). In the upper part of this figure, the ion

1,235 Kcalmo!-i 1,320 Kcalmoi-' 1,410 Kcalmol-' 1,495 Kca! mol"'

V: 1,410 KcalmolVI: 1,320 KcalmolVII: 1,325 Kcalmol-

Fig. 2.24 Upper part: ion arrangement of a K C 1 crystal in a (100) surface. Lower part: iso-potential lines (after Orr, 1939).

P/rnHco-CAefmca/ F/efMenM o/*^e Are^g;/; q/^PMre PA<MM 149

arrangement in this (100) surface and the places for four energetically different adsorption positions are given. In the lower part all points of energetically equal positions are linked by contour lines. The values and their respective spatial and energetic distances for the adsorption of argon are also listed. The number and situation of long molecules per unit area at such surfaces obviously depend strongly on their surface demand, the degree of molecular coiling of their chains and the atomic distances in the functional group relative to the distance between the contour lines. The disordered structures of solids in their surface layers, and thus their surface- or their interfacial tensions, have hardly been included in such thoughts. For all these reasons the abrasive strength method does not seem to be very appropriate for studying rock, particularly in view to properties of crystallographic planes. Considering Fig. 2.22 further increases such doubts for another reason: it shows that the separation of particles from a certain surface is combined with the formation of cracks, which do not lie in the plane considered but penetrate some w a y into the crystal; this means that the n e w areas created by the process of abrasion are not fully accounted for. The adsorption processes discussed therefore do not occur solely at the depicted base plane of the crystal. T h e preceding extensive discussion shows that even with the inclusion of surface energies, no essential advantage in the understanding of the basic problem is reached.

2.6 Overview of the Problems of Strength in Relation to Different Bondings in Materials The basic problem w h e n mechanically separating a macroscopic sample of solid or liquid material into two or more portions is that the attractive forces between atoms, ions and molecules, have to be overcome. This is why, in the previous sections, models of lattice forces based on the simple lattice theory, particularly for ionic solids, have been reviewed. Then experimental results were discussed, that have a relationship to the generation of n e w surfaces and the energy needed to do so. It has also been mentioned that according to findings by Euken and later by Correns, that the calculated strength values of solids are very m u c h bigger than those experimentally

150 &rengf/i an;/ ^a?/[en/!g q/^/?ocA as RoM/iJa^y Zayer P^o^/e/m

found. Results of rock salt are n o w considered taking the experimental details into account and comparing them with the experimental results on rock samples. Subsequently other bonding types, particularly according to experiences m a d e in polymer materials, will be introduced into the discussion. In Sec. 2.1.4, the concept of a theoretical strength of a material built up of ions was introduced. Rock salt was used as an example in this context. To experimentally verify such calculated values, rock salt samples were tested in direct tension. The results in literature are reported in the form of stresses which were derived by dividing the force at failure by the initial cross sectional areas. A s has been discussed in detail in Sec. 1.4, this procedure includes the presumption that the force at failure Ff, and the initial surface area Ao, are proportional to one another. To verify this presumption for rock salt samples, the strength values taken from literature were back calculated into the respective forces at failure knowing their initial cross sectional areas. Here the types of functions were found w h e n plotting force at failure versus the initial cross sectional areas, just like those already cited for rocks. T w o types of curve are revealed * general straight lines, thus not proportionals, and * curves which are bent towards the Ag axis. These functions are depicted again in Fig. 2.25. The situations, as they were found in rock salt, are n o w presented. Figure 2.26 shows results which were published by Stranski. Here examples of samples measured in different environments are considered; for example dry, in standing water after exposing the samples to flowing water, and in flowing NaCl solutions upto 2 5 % . All data are collected in Table 2.4. In all these cases the cross sectional areas vary from 10"'° m ^ to a m a x i m u m of 1.51 x l O ^ m ^ . These measurements can be described as straight lines as follows: (l)dry: Ff= 2 . 3 5 x 1 0 ^ + ( 1 . 3 6 5 4 x 1 0 ^ , lr 1 = 0.9599 (2) wet: Ff= 0.3428 +(6.1565 xl07)A„, lr 1 = 0.9951 (3) N a C l solution: Ff = 1.34+ (6.41 x 10^)A., I r I = 0.9943. Thus the strength values determined with the straight line approach vary from 61.6 to 137 M P a .

PAy.nco-C%e7Mi'ca/ E/gTMenfy q/f/:e ^ r e w g ^ q/*PMre PAasas

15)

Fig. 2.25 The two types of curves respectively found from experimental data sets w h e n ptotting Ff versus Ao.

The earlier investigations by Sohncke in 1869 also showed a linear relationship between Ff and A o (see Fig. 2.27): Ff = 7.9065 + (4.9906 x l O ^ A ^ ! r ] = 0.8988. Here the cross sectional area ranged from 0.76 to 1.46 x 10"^ m^, and the respective strength is 0.499 M P a . Such results imply that the strength of a material depends more on the area of the sample than on the environments. This suspicion is strengthened by the results which were obtained from glass threads with similar and smaller cross sectional areas than those used to test salt. Nonetheless, the following difficulties encountered w h e n comparing data from literature should be kept in mind: (1) The descriptions of the environmental conditions encountered in the literature are often insufficient, e.g. Stranski (1942) talks about wet samples but does not mention for h o w long the samples were in water, similarly it is not stated h o w and at which temperature samples

152 Areng/A ana* fHafAenng q/^RocA: as #
(a)

Stranski (1942): dry 6.00 F,-:.3M6E-02* 1 36KE*
4.00

2.00 -L

0.00 0.00E+00

2.00E-08

4.00E-08

Stranski (1942): wet

(b)

1.20 <

.

0.80 -

/

F, = 0.3423+ 6.1565E-07-A. R = 0.9951

0.40 <

.

onn -

1.00E-08

O.OOE*-00

(c)

2.00E-08

Stranski (1942): NaCl solution up to 2 5 %

/

S.00

4.00 .

^ % 0.00 -

000E+0O

^

^ F, = l .3369 * 6 406SE*07 - A. R = 0.9943 1

1.00E-07

2.00E-07

Fig. 2.26 Ff versus A ^ for rock salt for three different environments (after Stranski, 1942), (a) dry; (b) wet; (c) N a C l solution u p to 2 5 % .

PAy^fco-C^ewfca/ F/ewe7!^ qf^Ae ArengZ/i q/*PMre PAajas

Tab!e 2.4 Ff as function of A;,; experimental data after Stranski (1942).

Stranski (1942)

Stranski (1942)

dry

wet

A./m2

Ff/N

A<,/m2

Ff/N

4.07E-10 (8.32E-9 8.71E-09 3.02E-09 (9.33E-9 1.00E-08 8.13E-09 1.74E-08 3.89E-08 1.95E-08 (3.31E-08

0.45 2.89) 1.82 0.47 0.13) 1.03 0.65 2.70 5.64 1.91 1.75)

(7.08E-10 (8.13E-10 (8.13E-9 7.24E-09 8.91E-09 1.00E-08 1.00E-08 1.95E-08

0.85) 0.71) 1.48) 0.82 0.87 0.98 0.92 1.55

Ff= 2.3506* 10-2+1.3654* 10S* A . r = 0.9599 without () values

Ff= 0.3428+ 6.1565* 10^* A^ r = 0.9951 without () values

Stranski (1942) in flowing NaCl solution up to 2 5 % A./m2

5.50E-10 (8.13E-9 4.36E-09 7.24E-09 8.32E-09 8.32E-09 2.00E-08 3.89E-08 8.13E-08 (8.91E-8 1.23E-07 1.51E-07 (1.51E-7

Ff/N 0.80 5.40) 1.91 2.00 1.75 1.67 3.34 3.41 6.65 2.90) 9.40 10.82 8.19)

Ff= 1.3369 + 6.4068* 10?* A„ r = 0.9943 without () values

153

154 &reMg;% a^
Sohncke (1869): NaC). Rod axis paraiie! to [100]

MU.UU '

80.00 -

F,== 7.9065+ 4.9906 *10^A. R == 0.8988

4

60.00 -

40.00 -

20.00 -

-i

0.00-

i

5.0

0.0

10.0

A^m^10^

Sohncke (!869) Rod axis parallel to []00] A./m^ *10 ^ 13.7 [3.0 14.6 9.6 10.2 [0.7 7.6 )0.6 8.8 ]].7

13.5 8.9 12.2

Ff/N

80.20 69.96 75.86 52.76 61.62 66.95 48.54 54.02 52.61 73.85 81.26 45.73 66.56

Fig. 2.27 Values after Sohncke (1869).

15.0

PAy.si'co-C7!e7M:ca/ E/e/ney!M q/^^Ae Are/ig^A o/Pt/re PAasey 155

were dried or if another method for drying them was applied. Similar considerations hold true for work which has been done on glass threads, e.g. Schurkow (1932) and Gooding (1932). (2) Stranski's (1942) work showed that it cannot be concluded without doubt in which direction samples were tested. Further he seems to have used natural crystals and crystals originating from salt melts. (3) Most authors worked on cylindrical samples but some worked on right angular prisms. (4) Hardly any author mentions anything about mechanical influences like loading rates used etc. The possible importance of point (2) above shall be demonstrated with a set of data taken from Schmid and Vaupel (1929) where N a C l has been tested in three crystallographic directions, viz. [100], [101] and [111]. In Fig. 2.28, Ff versus A o was plotted for each of the three directions and in Table 2.5, the appropriate data are listed. It can be seen that for similar areas, the force for failure depends on the lattice direction that is subjected to pull. The most important results of this literature survey and of experiments executed within the framework of the investigations presented here are: uniform bodies, like wolfram, rock salt, and glass and composite materials, particularly rocks, have two characteristics in their strength in c o m m o n with regard to: - all measured values are m u c h lower than would have to be expected on the basis of principal valency bondings between the structural elements within a material, and - there are two types of dependencies between force at failure and cross sectional area of the samples investigated. Furthermore (and this observation seems important) all rock types which are of main interest here like sandstones, limestones, and granites are isotropic in view of their strength behaviour, with the exception of those samples which experienced directed superimposed pressures. The investigation described has strengthened the impression that for rocks at least (which are the subject of discussion here) an explanation of

156 ArengfA ana* !%af/:er;Hg q/*7?oc^ as RoMMaary Layer P w 5 / e w s

Schmid and Vaupel (1929): NaCI, rod axis parallel to [100] S0.00 . 60.00 . ^.

40.00 4- 20.00 . — 0.00 -& 0.0OE+0O

-41.0CE-05

2.00E-0S

Schmid and Vaupel (1929): NaCI, rod axis parallel to [101] 120.00

eo.oo 40.00 0.00 0.00E+00

1.60E-06

A^m

Schmid and Vaupel (1929): NaCI, rod axis parallel to [111] 200.00

100.00

0.00 O.OOE+00

4.00E-06

Fig. 2.28 Fr versus A „ for N a C I after Schmid and Vaupel (1929) in three different crystallographic directions.

P/rnHCO-CAeMHca/ E/ewew^ q/*;Ae Arewg?A o/'Ptvre P/M.KM ! 57

Table 2.5 Ff and A . values for NaCl after Schmid and Vaupel (1929) in three crystaHographic directions. Schmid and Vaupel (1929)

Schmid and Vaupel (1929)

Rod axis parallel to [100]

Rod axis parallel to [11 ]

Ao/mm^ a, g/mrn^

Ao/rr.2

Ff/N

A„/mm^ o, g/mm -

A„/m2

Ff/N

18.30

383

1.83E-05

68.76

0.77

11680

7.70E-07

88.23

2.52

1980

2.52E-06

48.95

0.66

12150

6.60E-07

78.67

1.16

3435

1.16E-06

39.09

2.65

6800

2.65E-06

176.78

1.51

2650

1.51E-06

39.25

0.51

13120

5.10E-07

65.64

1.22

2450

1.22E-06

29.32

3.38

4440

3.38E-06

147.22

0.92

2180

9.20E-07 19.67

1.05

11400

1.05E-06

117.43

0.58

3430

5.80E-07

19.52

0.57

15800

5.70E-07

88.35

0.75

2670

7.50E-07

19.64

0.44

13500

4.40E-07

58.27

0.72

2770

7.20E-07

19.57

0.48

12360

4.80E-07

58.20

0.31

3180

3.10E-07

9.67

0.26

11500

2.60E-07

29.33

0.30

3390

3.00E-07

9.98

0.27

10950

2.70E-07

29.00

0.14

4350

1.40E-07

5.97

0.20

14900

2.00E-07

29.23

0.21

2420

2.10E-07

4.99

0.24

12650

2.40E-07

29.78

0.17

3010

1.70E-07

5.02

0.26

11600

2.60E-07

29.59

0.10

2610

9.70E-08

2.48

0.11

13500

1.13E-07

14.97

0.05

4020

4.50E-08

1.77

0.01

16100

1.20E-08

1.90

0.46

3250

4.60E-07

14.67

0.01

15000

1.20E-08

1.77

0.51

2970

5.10E-07

14.86

0.01

24700

7.40E-09

1.79

0.25

4050

2.50E-07

9.93

0.17

2920

1.70E-07

4.87

0.19

2660

1.90E-07

4.96

0.05

4160

4.90E-08

2.00

Schmid and Vaupel (1929)

Rod axis parallel to [101] A„/mm^ c!, g/mm ^

A./m2

Ff/N

1.44

8350

1.44E-06

1)7.96

0.93

9630

9.30E-07

87.86

1.41

4250

1.41E-06

58.79

0.65

9180

6.50E-07

58.54

0.32

9450

3.20E-07

29.67

0.40

5000

4.00E-07

19.62

0.02

8950

2.00E-08

1.76

!58 AreMg;/: an
the low strength values by processes which mainly reduce cohesion of solids possessing principal bondings mechanically is practically out of the question. It is m u c h more likely that the values found reflect processes which overcome secondary valency forces. The influence of Griffith cracks or notch systems either at the boundaries of or in samples cannot be excluded, but it seems that their effectiveness for rocks, and possibly all samples can only be discussed against a background of already very low strength. Notch systems change strength values only in the range of the general scatter of these low values. Furthermore other molecular species are immediately adsorbed on freshly created surfaces so that these forces which reduce strength, must be of another kind than those in the interior of the solid. At this point, the concept of a spectrum of bonding forces in the sample, as w a s assumed and accepted by Huttig (1941), Schwarzl and Staverman (1956), and by von Engelhardt and Haussuhl (1965) can be introduced as it seems to provide an explanation for the radical reduction of values found experimentally in comparison to those ones found by calculation, whereby the secondary valency forces seem to be of the greatest importance for the cohesion of rock samples. To support such ideas, some examples are referred to where the dominant role of secondary valency forces can be deduced by the chemical nature of the solids. After this there will be a reminder of the basic differences in these forces. Finally the discussion returns to sandstones on the basis of experimental findings. A n overview, in the form of a table of strength values, is given for different types of attraction potentials by Elias (1972). These values were originally put together on the basis of adhesion by gluing. "In the case where the adherent is fully covered by adhering groups and each group demands an area of 25 A^, there are about 5 x 10'^ groups per c m ^ present. With this number and the k n o w n bond strengths one finds:

chemica] bonds

490-2450 M N m - 2

hydrogen bonds

200-780 M N m - 2

van der Waa)s bonds

80-200 M N m - 2

(dispersion forces, dipoie forces) experimenta) values

20 MNm-2".

P/ryM'co-CAeffHca/ E/emeuM q/'^Ae Arey:g;/! q/*PMre PAcyay

! 59

This compilation shows with clarity that the introduction of other kinds of bond strengths between molecular units could by itself explain the range of variation of the experimentally found strengths values. The range is extended once more by a factor of 10 in the direction of reduced values if liquids and, for example, substances with a high water content are included. Pohl (1947) deduced that the tensile strength of water is about 3.3 M N n r ^ . This value plays an important role in plant physiology since the sucking height of trees is limited by it. M o h r (1971) cites figures between 3 and 5 M N m " ^ . For ether, Pohl refers to 6.9 M N m " ^ . This indication of fluid containing, particularly water containing, cements is of great interest in view of the strength of rocks. B y considering the strength of materials according to either their chemical or crystal structure, or other reasons, it is possible to understand w h y they have different strength values in different directions. Let the first example of this kind be wood, which has m a x i m u m and m i n i m u m tensile strength values in two perpendicular directions according to data taken from a bigger table in 7ajcAe?!^McA^r cAewnArer MH<^ PAyjfArer D'ans-Lax (1967). According to this the strength of w o o d parallel to the fibre is between 63 and 162 M N n r T ^ and orthogonal to the fibre, between 2 and 10 M N m ^ . it is obvious that within the fibre other chemical bond forces exist than between them. In respect of pure cellulose fibres, Holleman-Richter (1961) mentions that "It must be assumed that the special mechanical properties of cellulose, which has a mechanical strength near that of metals, are based on the parallel assemblage of the long molecule chains. Without any doubt the hydrogen bonds between the (OH)-groups of neighbouring chains play an important role. Thus their split off, for example by methylation is combined with an essential change of the physical properties." (Fig. 2.30). Another example is described by Elias (1972): "To estimate the tensile strength of polyethylene first it m a y be assumed that in a rod of polyethylene all molecular chains are orientated parallel to the long axis of the rod. In a tensile experiment all chains shall be broken once at a covalent bond". For this failure, 16.7 G N m " ^ are required. "Experimentally, tensile strengths of 0.017 G N m " 2 m a x i m u m were observed; that means about one order of magnitude lower values of force were required than those corresponding to the theoretical strengths derived from dispersion forces."

160 &refig;A and ^H/Aen/!^ o/Roc% a^ RoMM^ar)' Z,a^er Pro5/ew.s-

n

/

: . , -

OH

O'.-' :-: ^

O

r,, ;, '-!

OH

:;-; a;-! c

C:-i

,. ^

rr

"

,,

.o^

.:'; /

o

,

:-!

Oi!

Fig. 2.30 Top: Formuta of cettutose (Lehnartz, )952); Bottom: Rotten wood.

For this decrease of strength by one order of magnitude to occur, texture influences are obviously responsible. According to Elias: "From this it can be concluded that not all bonds are equally loaded but only that of a fraction of chains, whose orientation corresponds to the external stress direction. Furthermore the tensile strength is decreased by inhomogeneities." A detailed picture of such processes has been already proposed by B u n n and Alcock (1945), Fig. 2.31 upper Part (a) and (b). The sketch shows a section from a partly crystalline high polymer with random orientation of the crystallites compared with the external stress direction. The authors wrote: "For pulling

PAys/co-C/ieywca/ E/gmenf.? o/*^Ae Are/?g;/[ q/*PMre PAa.say 161


,

(b)

Fig. 2.31 Polymer crystallites and orientation of force lines in them w h e n applying external stress (Bunn and Alcock, 1945).

a single chain molecule out of the lattice structure in the directions of the chains [Fig. 2.31(a)] the van der Waals forces along the whole of the lattice portion must be overcome at the same time. In the case where only thirty links of the chains are built in the lattice the force to overcome the atomic attractions is already of the order of magnitude of principal valences. In the case where a tensile force effects a link of the chain, in an unordered region oblique to the chain direction [Fig. 2.31(b)], then one link after the other can be pulled off against the relatively w e a k van der Waals forces. This is a similar case to that of a pasted strip being drawn off." These are examples out of nearly an infinite number. They show at least two different facts undoubtedly: * wherever there are w e a k bonds within a material, the strength is also small in those respective directions and vice versa; and * the term "inhomogeneities", which is often used in literature, has m a n y meanings and most do not refer to cracks in the sense of Griffith. In general, this term is used for interfaces where only small

162 .Sfreng;/: an^ P ^ a ^ e n ^ q^7?oc^ a^ BoM/!^ary Layer Pw^/e?m

bonding forces act. These weak bonding forces can either be due to the structure or texture within the samples themselves or due to certain environmental influences, which can represent effective w e a k bonds. Thus the discussion of interfaces, or better boundary layers within the investigated materials is of great importance. In the following, some principal possibilities for distinguishing between forces of different nature shall be indicated: further details can be obtained from textbooks on physical chemistry. F r o m n o w on, the term "intermolecular forces" instead of "secondary valency forces" shall be used. T h e difference in character between intemolecular bonding and intramolecular bonding is that the former is not based on an electron transfer, neither a total one, as in polar bonding, nor a partial one as in the non-polar bonding. The intermolecular forces are, on the contrary, interactions between permanent or electrical dipoles, both of which are put together under the n a m e of "van der Waals forces", (Ulrich and Jost, 1966). The force-distance law is important for the model of the strength of bonding. W h e n two ions interact in vacuum the force decreases with r"^, see above; if an ion with a permanent dipole interacts in the direction of the dipole axis, the force decreases with r"^, if two dipoles interact on a line on which both dipole axes lie, the force decreases with r"**. Finally the forces between permanent and induced dipoles and dispersion forces decrease with r"6. Taking temperature movements for di- and multipole molecules into account, their respective direction distribution has to be introduced. It also follows that the forces belonging to this group of phenomena are temperature dependent. They decrease inversely in proportion to the absolute temperature. Apart from these bonds which are weak by nature, it is possible to weaken strong bonds, like those of ions by environmental influences. These circumstances be explained by Eq. (2.34), which was used above to describe the interactions of ions in vacuo. This equation is n o w rewritten as Eq. (2.52) for the case where ionic interactions do not occur in vacuum but in the presence of a dielectric with a permittivity of iy, see below: FK = ^ ^ ° 2 1 n 2 J ^

Le-(t/p)(r-r.) r'

(2.52)

PAy.MCO-CAewH'ca/ E / e w e M ^ o/^^Ag &re/]g^ o/*PMre PAajas

163

Tr" dyn Force at failure, Tensile strength experiment

2?

(NaCI)K r.= 2,82A

1?'

^

^

^-^S^^^^^

^f- 7f- 7f-

^

^

0,3

^^

V

^

^

^

-?)^ ^

^

^

8

^

strain at failure, tensile strength experiment

^

^

^

^

/f ^

^

^F

yr Fig. 2.32 Force at failure, Fx, f, upper, and strain at failure, e^, f, lower, as a function of dielectric constant, iy, and coefficient of repulsion, p.

164 & r e ^ A ant? (%a?Aer;Mg q/*7?oc^ as ^
The calculated force at failure of rock salt versus the permittivity is plotted in Fig. 2.32. O n the inclined axis pointing to the back of the figure p is indicated, which in Eq. (2.51) was set at 0.35 A . In the three dimensional figure, this is the equivalent of the front side of the figure. It can be seen that the force plotted decreases hyperbolically with the permittivity. In the dielectric water (\)/ = 81), the acting force is reduced to 1 % at the same distance. In opposition to this, the strain at failure is not influenced (lower part of Fig. 2.32). Thus in this case the bond strength of a strong bond is substantially lowered. O n the other hand no bigger change has to be expected in p as the cause for observed changes in the force at failure. B o m and Mayer (1932) derived values for seventeen alkali halides which are compiled in the following table.

0.357 A 0.382 A 0.382 A (0.460 A )

Rb

NaF CI Br J

- A 0.326 A 0.334 A 0.384 A

CsF CI Br J

KF

0.319 A

average value over seventeen values: +11.4% 0.345 -10.1%

LiF CI Br J

CI Br J

0.316 A 0.326 A 0.351 A

CI Br J

0.356 0.340 0.351

A A A A

- A 0.310 A 0.327 A 0.355 A

Born and M a y e r (1932) wrote about the constant p: "The proper theoretical expression for the repulsion potential contains most probably an exponential factor e " ^ with an exactly constant p, but this is certainly multiplied by other functions (polynoms) of r (see Pauling 1. c ) . Therefore to the constant, p, no simple physical meaning can be attributed."

Chapter 3 Strengthening of Grain Packings by Intermolecular Forces

In a previous chapter, a fundamentally n e w question w a s asked viz. could the low isotropic strength of sandstones be considered as the result of a strengthening of loose grain packings by cements which were infferred into them but not by a reduction in strength of crystalline phases present, see Sec. 1.2.3. This question arises anew if the cohesion in rock samples is represented by intermolecular forces as n o w seems probable. Figure 3.1, in which 129 tensile strength values are compiled, collected over more than eighty years, mainly of Bunter Sandstone samples collected from between the Black Forest in the West and the Heuscheuergebirge in the East of Germany, but also far beyond, in Northern England close to the Scottish border, Penrith Sandstone, suggest that this is so. The variation of the tensile strength of fluid water has been indicated at the abscissa for comparison. About one sixth of all results of the tensile strength show values in the region of the strength of water, whereas the majority of values are smaller. The validity of the presumption that the strength of samples is given by cements be thus accepted, however it is assumed that this cement could either be water or at least a water rich phase. Further, the more specialised question can be asked, i.e. under which circumstances is water able to cause cohesion in the range shown in Fig. 3.1. U p to now, water was viewed under two aspects, both of which influence bond strength: * the chemical change of surface or boundary layers respectively; and

165

166 A r e ^ A an6? ^ a ^ e r / M g q/*,Roc% ^ FoM/i^ayy Zayer Pw^/e/m

Hirschwald (1912)

Alfes (1993)

[p]

Heuscheuer

^

pi

Pirna

HP] Burg-Preppach

^H

MCrtingen

P3

Worzeldorf

Sander Tensile Strength-

[+] Stadtoldendorf

Butenuth

f#l Ostervald

^)

Penrith, trocken

rl

[^

Penrith, gesattigt

Hiltenberg

en 14 pm

0,27 pm

MN.m Tensile Strength of water '0,06 pm Pore Diameter 0,15 MN-m

5 MNm

Fig. 3.1 Tensile strength values from different locations for sandstones.

Arewg^e/!iA[g q^Gra/n Pac^Mgy Ay 7n;erwo/ecM/ar Forces 167

change of environment with a change in the dielectric constant particularly when Coulomb attraction takes place. A third aspect shall now be emphasised, that of capillary attraction. The technical importance of capillary effects for the strengthening of ground ores with water has been studied in metallurgy some years ago. The practical aim of these experiments was the formation of so-called "Green Pellets". Before models for this kind of strengthening of loose grain packings are introduced a reminder of some relevant basics shall be given.

3.1 Surface Tension of Liquid Water in Selected, Simple Systems If no outer forces are acting, a small amount of a liquid takes the form of a sphere of minimal surface area at a given volume. After a forced change of form by an outer force acting on it for a short time, it returns spontaneously to its original shape (the sphere) after the force has been released. It is for this reason that the minimum surface area, under otherwise constant conditions, corresponds to a minimum of free enthalpy, an equilibrium state. The change of free enthalpy is in general dG = d H - T d S

(3.1)

with G: free enthalpy H: enthalpy S: entropy T: absolute or thermodynamic temperature. A change in entropy during development of an interfacial surface consists, for example, of a change in orientation of small, particularly polar, molecules when an interface surface is built up [Fig. 3.2(a)]. Water molecules in a liquid surface are oriented in such a way that the oxygen atoms face the outside, whereas the hydrogen atoms face the interior of the liquid (Frumkin,

168 &reng?/] a n ^ !^ea;/!en/:g q/*7?oc^ a.s 3oM/:^ayy Z,ayer Pro^/em^

surtace O"

^/^ (a)

01

V^H*

0^

*n/^H*

inside the liquid phase

(b) solid

liquid

(c)

(d)

(e)

Fig. 3.2 (a) Orientation of water molecules in a liquid surface; (b) Forces influencing a molecule (black) within a liquid and its surface. In the first case, the s u m over all forces results to zero, in the second case, a force directed inwards results; (c) Boundary angle between solid and liquid; (d) Pressure exerted by a sphere on a solid surface by surface tension of a liquid; (e) T w o glass plates glued together under the influence of a water droplet.

SfrengfAen/ng q^Cra;/] PacAr/wg^ Ay 7n(erwo/ecM/ar Forces 169

1924). Even if thermal agitation of the particles do not allow such a strict order as shown in the sketch, the existence of a preferential orientation cannot be doubted nonetheless. A change in enthalpy occurs because the water molecules of the interior, where they are surrounded by other water molecules and thus free of forces, are brought to a position in the n e w formed surface in which the components of force are directed exclusively to the interior. These conditions are sketched in [Fig. 3.2(b)] (after Wolf, 1957). If the change of free enthalpy is related to a square centimetre of the newly formed surface, then one talks about surface energy of the liquid with the unit erg cm"^ (= 10"^ N m / m ^ ) or of a surface tension with the unit dyn cnT* (= 10*^ N m ) . The numerical value for both the magnitudes is the same, which can be easily seen. The latter results by dividing the former by the meter. This magnitude is often denoted as Yhauid/easeous ^ h ^ appropriate numerical value for water at 20°C is Ytinuid/saseous" 72.75 erg/cm^ = 0.07275 N m / m 2 (D'ans-Lax, 1967). The index indicates that the adjacent gaseous phase is the vapour of the liquid. To compare the surface energies of different liquids the concept of a molar surface energy is introduced: as the demand for space of the molecules in different liquids is different, one compares always, in relation to one square centimetre, amounts of energy, which are necessary for the transition of different numbers of molecules from the interior to the surface. This effect can be excluded if one starts with a molar volume of the liquid (V°t d) imagining it to be a cube and then calculates the area of one side of the cube. Its value is (V",; ^ ) ^ . Water has a molar volume of V°w,ter = M ^ / p ^ r = 18 g mol-'/l g c m ^ = 18 cm^mol-', ( V ° ^ , f 3 resulting in this case in 6.868 c m ^ m o l ^. The multiplication of this value with the surface energy that relates to a square centimetre leads to the molar surface energy y^ ^ ^ = 499.67 erg m o l " ^ . This kind of molar surface tension or molar surface energy respectively will be drawn into the discussion later on. In this case, energy amounts are considered, which are necessary to lift always the same number of particles ( N J ^ 3 from the interior onto the newly formed surface ( V ° ^ ^ ) ^ . The number of particles considered is 7.13 x 10'3 molecules.

170 AreMgfA ana* ^ a ^ A e n n g q/^7?oc^ as RoMM^a/y Zayer Pro^/ewj

3.2.1

T7ie sfrcsses resMZfzn^yrom w e f r m ^ a s o M &y a h'^MZ^

"Characteristic for the behaviour of a liquid in contact with a surface of a solid is the phenomenon of wetting. This is due to the rivalry between * attraction forces between the particles of the fluid and those of the solid interface, and * the particles of the liquid amongst themselves. The work, which can be w o n reversibly, w h e n producing a square centimetre of fluid/solid interface is usually termed "Haftspannung" (adhesion tension), Y ^ ; ^ ^ (Eucken, 1944). If 'liquid/solid

^liquid/gaseous

then the liquid spreads on the solid surface. This also occurs under the simultaneous development of a n e w liquid/gaseous surface, i.e. the liquid can wet the solid completely.

If 'iiquid/soiid

Miquid/gaseous

then a boundary angle, 3, is produced at the flat surface of the solid [Fig. 3.2(c)] and incomplete wetting occurs. This situation can also be considered from a slightly different point of view. Considering the forces acting at point P, one gets 'tiquid/solid

'iiquid/gaseous ^

^*

If 3 = 0°, cos 3 = 1 ; then Y,

.i; ,,, = Y<

'Itqutd/soitd

^/

: a condition of complete wetting.

'hquid/gaseous

r

o

If 3 = 90°, cos 3 = 0 then Y

d/ id = 0: a condition of no wetting

and if 3 > 90° then < 0: a condition for repulsion between solid and liquid.

ArengfAew/ng of Gra/w Pac^Mgj Ay TnfefTMo/ecH/ar Forces ! 7!

3.L2

E^ecf q/'a^esMfi renszon m seZgcfe^, s z ^ J e sysfeyns

Microscopically small particles are pressed onto a base w h e n wetted and in contact with a liquid/gas boundary [Fig. 3.2(d)]. W h a t is the magnitude of the compressive pressure so created? The water droplet on the surface is pulled up to the equator of the sphere, if a sphere like particle is used. The force acting at the equator is 2nryn .^^. If this force is moved parallel to itself into the centre of gravity, in this case equal to the middle of the cross sectional circular area, the tension P equals to p _ 2nry[iquid/soiid _ 2y]iquid/soiid nr^

r

In the case of a nearly or a complete wetting event, Y]jt,uid/soiid "^s got the same value as YijQ..id/easeo s- ^ tMs case Eq. (3.2) represents the final result. For water at 20°C, the numerical equation is P = JX3j)-HiMN/m2. D i n urn The problem presented here has been discussed in similar terms to those used w h e n considering sensitive microscopical objects which have been brought onto glass slides from suspensions (Anderson, 1952), see below. The relationship for P and D has been noted d o w n for some diameter ranges in Table 3.1 and Fig. 3.3. In comparison with Fig. 3.1, it can be seen that an approximate diameter range d o w n to about a few hundredths of a u m would create pressures or stresses respectively which are in the order of magnitude found for experimentally derived values of tensile strength for sandstones. These numbers will be m a d e more precise later. Thus, water or water rich substances could possibly be substances that exist between grains and act as cements, if pores of the named order of magnitude exist between sand grains. The pores between the original sand grains are of the same order of magnitude as the grains themselves; they would thus be m u c h too big for capillarity alone to generate the strengths measured. If capillarity is considered a major source of strength, it would be necessary for the substances between the grains to be meso- to microporous.

172 <%reMgf/! ana' ^afAering o^7!ocA as RoMMaary Layer ProA/em^

Tab!e 3.1 Calcu!ated values for tension, P, at given diameters, D.

urn

P MNm 2

250

0.0012

Mesoscopic pores; particularly determined by mercury porosimetry

2.0 to 0.06

0.15 to 5.0

Pores that exist in silica gels that were hydrothermally treated, Table 3.2

1.5 to 0.005

0.2 to 60

D

Sand grains

3,4 * 0,2

0,088

Fig. 3.3 Tension, P, versus sphere diameter, D.

Tabte 3.2 Influence of the conditions of hydrothermat treatment on the pore structure of silica (Unger, 1979). [NFLUENCE O F T H E CONDITIONS OF H Y D R O T H E R M A L T R E A T M E N T O N T H E P O R E S T R U C T U R E O F SILICA [81, 85] Sample No.

Pore structure parameters

Treatment conditions

Specific pore volume, Vp (ml/g)

Mean pore diameter, D (nm)

too

210* 121* 39* 20* 1.4*

0.73 0.70 0.72 0.78 0.70

10.0"* 22.0"* 74.0*" 290.0"* 1420.0"*

5 10 15 20

50 50 50 50

330* 63* 51* 48* 38*

1.07 t.09 1.06 1.15 1.06

10.5"* 68.0*" 88.5*" 88.0*" 88.5*"

0.5 1.0 1.5

1 1 1

498" 432** 395" 356"

0.63 0.93 0.94 0.94

5.1$ 7.25 8.0^ 8.65

Temperature (K)

Duration (h)

Pressure (bar)

la lb lc Id le

383 453 523 573

4 4 4 4

2 10 50

2a 2b 2c 2d 2e

523 523 523 523

3a 3b 3c 3d

373 373 373

Specific surface area, R (rn^/g)

'Determined by adsorption of krypton (samples )a-]e, 2a-2e); Am(Kr) = 0.215 nm^/atom. '"Determined by adsorption of benzene vapour and by mercury porosimetry (samp)es la-)e, 2a-2e). ^Determined by adsorption of nitrogen (samptes 3a-3d); using the desorption isotherm and the method of Pierce.

174 Arengf/: anaf H^a^er;7]g q/*Roc^ 6W RoH^^ary Layer Pw^/eym

Figure 3.3 shows in the form of a diagram the relationship between P and D, and shows the accuracy with which D should be known, if the error in P should be of equal amounts. For example, the pressures 3.4 and 0.4 M N n r ^ each have the same absolute error of ±0.2 M N m " ^ . In both cases the error for the diameter is unsymmetrically mirrored at the function but in the first case, it ranges from -0.25 urn to +0.75 urn, in the second from -0.005 to +0.06 urn only. The demands on the accuracy of measurement thus increase considerably with decreasing diameter. In the last illustration in Fig. 3.2(e) is depicted the case of two glass plates pressed together by a water droplet, Pohl (1947). Here again Eq. (3.2) holds, but with the important difference that the radius is that which occurs at the hollow border of the droplet as the visible limiting circle. In the case of water rising in pores, the effective pore radius has to be used.

3.2 Water Strengthened Grain Packings Water strengthened packings have been discussed in different areas of natural science and engineering for a long time. In this case, it is found that the tensile strength of an aggregate strengthened in this w a y is inversely equal to the internal traction stresses generated by the capillary forces. In the following two models are discussed. For this discussion, the dissertation of Izgiz (1969) is followed. In this work, the author described the properties of pellets of iron ore in its "green condition"; for more details and discussions, the reader is referred to the work. T w o main models are presented: * "In the case of small liquid amounts being present, liquid bridges between the grains of the packing develop". T h e degree of void filling by liquid is smaller than 0.2 or 2 0 % by volume. * "For the case that all voids are filled with liquid and that at the surface between the grains concave menisci are developed, the strengthening is exclusively reached by capillary depression" (Fig. 3.4). For the first model (liquid bridges), the following expression w a s found for the tensile strength, o*p, FB^

AreMg?/!en;'ng q/*Cra/M P a c ^ w g ^ ^y /M^erwo/ecM/ar Forcas

175

(a)

(b) Fig. 3.4 T w o models for agglomerates filled with a liquid: (a) liquid bridges are formed between the particles of the agglomerate; (b) the pores within the agglomerate are totally liquid filled.

_9 (?F, F B *" ^Yliquid/gaseous H

(1-P)

1

r

2ri

W)

(33)

surface tension of the liquid P volume of gas filled voids divided by total volume: porosity representative average radius of sphere like particles TT contact angle of liquid at solid half centri angle of liquid bridges, if i^ = 0 and P 10° < p < 40° then 2.2 < f(f3, p) < 2.7. Figure 3.5 illustrates i^ and p.

Yliquid/gaseous

176 Arewg^A ana* !^a;Ae/-!7!g q/^oc% an 5oMwa!H?y Zayer Pw^/ew^

Fig. 3.5 Definition of symbols used in Eq. (3.3) (after Rumpf, i96i).

Mode!: iiquid bridges

o.i

Fig. 3.6 Strength as a function of porosity and averaged pore suction, f(#, P) = 2.2.

-Arengf/:e?!;ng q^Cra;n Pac^/wg^ Ay /n^ermo/ecM/ar / w e a r

177

Figure 3.6 shows the function [Eq. (3.3)] in an overview. The above mentioned value for the surface tension of water has been used here. The values for porosity have been varied between those for the densest sphere packing, with a porosity of 0.26, and a very high value of 0.5, which corresponds to a loose packing of mono-dispersed sands. For f(^, P), the lower value of 2.2 has been used. If all units used at first are in the cm-g-s system then the result is in dyn cnr^. The conversion of units is as follows: 1 dyn cm-2 = 1.02 x 1 0 ^ kp m"^ and l k p m - 2 = 9.81Nm-2. In opposition to the second model, this liquid bridge model contains a dependence on the porosity of grain packing. Thus even though the model is concerned with the strengthening of grain packings, a dependency on porosity is evident. The pre-condition for the second model is the total saturation of the pore volume with a liquid (water in general). A n interface with air (against its o w n vapour) only occurs at the outer surface (at the openings of the capillaries). There, concave menisci develope. "In this case the grain bonding of the green pellet is sustained by the capillary depression of the liquid surface" (Izgiz, 1969). It then holds true again that r<

^Ytiquid/gaseous

P=

:

(34)

IK

with r^: effective capillary radius. According to Eq. (3.4), the pressures to be expected attain M N m ^ if the pore radii are in the order of a few tenth of micrometers. For sand grain packings with pore diameters of the same order as that of the grains, i.e. at a few tenths of a millimetre, the calculated values are at a few thousandths of a M N n r ^ which are too small to explain the properties of a rock.

178 Arengf/; an6? ^a^er//;g q/^^oc^ ay Z?CM7?&:ry Layer P/*oA/ew^

To demonstrate that the model just outlined is realistic, an example for granulates of fine sand (42 u m < diameter < 87 u m ) is given (Newitt and Conway-Jones, 1958). To produce the granules "a charge of material with a k n o w n moisture content was placed in the granulator and the drum was rotated at a pre-selected speed" (Newitt and Conway-Jones, 1958). Granules of a range of sizes were made at a moisture content of 67.5%v [i.e. % v = volume of liquid/volume of solids x 100 (Newitt and ConwayJones, 1958)]. "To obtain a direct measurement of strength, granules were crushed between two parallel fiat plates, one of which constituted the pan of a spring balance. A steadily increasing load was applied to the granule and the m a x i m u m value registered by the balance before collapse was taken as the breaking load" (Newitt and Conway-Jones, 1958). Figure 3.7 shows the result of these tests. The breaking load, L, is plotted versus the diameters, D, of the granules and the relationship could be described by a parabola L=17.5D2.

(3.5)

Moisture: 67.5 % Amount of granulation Minutes revolutions 4 90 180 12 270 16 360 24 540 32 720

25

-20 o *o m o -" 15 O)

!$2 a) si 10 -j

5

0

J

0

I

t-

0.2 0.4 0.6 0.8 1.0 D - Granule Diameter (in.)

1.2

Fig. 3.7 Variation of breaking load with granute diameters for fine sand (Newitt and ConwayJones, 1958).

Arengf AeniMg q^Cra:^ PocAMg! ^y /M^erwo/ecM/ar Forcay 1 79

Table 3.3 Calculated force at failure, Ff = L, and geometrical area, A^.

Newitt and Conway-Jones

D

A . = n*r2 r = D/2

m

m2

L Ff N

2.00E-04 4.00E-04 6.00E-04 8.00E-04 1.00E-03 1.20E-03 1.40E-03 1.60E-03 1.80E-03 2.00E-03 2.20E-03 2.40E-03 2.60E-03 2.80E-03 3.00E-03

3.14E-08 1.26E-07 2.83E-07 5.03E-07 7.85E-07 1.13E-06 1.54E-06 2.01E-06 2.54E-06 3.14E-06 3.08E-06 4.52E-06 5.31E-06 6.16E-06 7.07E-06

2.95E-04 1.18E-03 2.66E-03 4.72E-03 7.38E-03 1.06E-02 1.45E-02 1.89E-02 2.39E-02 2.95E-02 3.57E-02 4.25E-02 4.99E-02 5.78E-02 6.64E-02

It w a s checked that the granules can be regarded as spheres and that their cross sectional area can be described by n r ^ which could be considered as the effective failure surface. Plotting the force at failure versus the cross sectional area of granules, an excellently defined straight line with a slope that represents strength is found at 9375 N m ' ^ (Fig. 3.8). Taking this value and introducing it into Eq. (3.4) and using the value 0.3 N n r ^ is used, water at 20°C for 2y.. .^, [see Eq. (3.2)], one finds the effective diameter to be 32 urn which is 10 a m smaller than the lower limit of the particle distribution reportedly used (see above). T h e latter w a s achieved by sieve analysis. Without wishing to exaggerate the accuracy of this analysis, the opposite effect had to be expected as it has been demonstrated that pores close to big particles and close to container walls pores are bigger than those in the interior of the packing (Fig. 3.9). Similar circumstances could be realised in

180 .&reM,gf/:
Newitt a n d C o n w a y - J o n e s (1958)

8.00EO2 F, - 1.1787E-0419375.33 Ao R-0.9999

^

4.00E-02--

0.00E+00 0.00E+00

4.00E^)6

8.00E-06

Fig. 3.8 Ff versus A „ of granules of fine sand.

Fig. 3.9 M o d e ] of large spheres embedded in small spheres (Cumberland and Crawford, 1987).

.Rreng^emng o/Cra<w PacA
!ntet of red ink

150

mm

Soaking by filter paper Migration of red ink through a sphere fiHed sand iayer

note: bigger pores ctose to bigger grains and surfaces Fig. 3.10 Mode) experiment to study iiquid transport through an inhomogeneous sphere packing.

182 Are/:g;A a^tf ^ a ^ e r / n g o/^oc% a^ ^
an experiment that was conducted a bit differently (see Fig. 3.10). A Petri dish was filled with sand in which some steel spheres were half immersed into the sand. Water was subsequently introduced in such a w a y that the pores were emptied of air. Finally red ink was introduced on one side of the petri dish and was sucked with the help of a strip of filter paper through the packing. At the end of the experiment the steel spheres were removed. The following results were observed: * as expected, the ink concentration w a s greatest close to the m u c h bigger spheres, and * the concentration of colour decreased from the place where the ink was added to the opposite side of the strip furthest from this place. This means that some adsorption of colour occurs along the path of the solution. According to both the models (liquid bridges and complete pore filling), the strength of the aggregate is indirectly proportional to the surface tension of the binding fluid. This relationship has also been experimentally verified by Newitt and Conway-Jones (1958) (Table 3.4). Here different surface tensions were used by producing different alcohol/water mixtures. Particle sizes and other environmental parameters were kept constant. T h e measurements confirm impressively this part of the previously mentioned equations. Unfortunately these experiments were only done with granules of a single size.

Tab!e 3.4 Strength of granules in dependency of surface tension of liquid (Newitt and Conway-Jones, 1958). Newitt and Conway-Jones (1958) Alcohol % vol.

Water % vol.

Specific gravity g/cm^

Surface tension at 20°C dynes/cm

Granule strength oz/sq.in

0 10 30 100

100 90 70 0

1.000 0.985 0.964 0.792

72.8 50.2 35.0 22.3

18.9 13.7 10.3

5.5

<S7re/ig;/ieH;ng q^ Grain Pac^/ng^ Ay /n^ernio/ecM/ar Porcey ] 83

Fig. 3.11 M o d e ! of balls of cottonwool to demonstrate surface tension, (a) Water saturated cotton wool balls under water, no capillary forces; (b) Water saturated cotton wool ball, partially lifted above water; at the water-air interface of the ball, the ball is pressed together from the sides; (c) Cotton wool ball submerged again; capillary forces have disappeared.

Izgiz (1969) did not only test granules m a d e up of spheres but also of plate and needle like particles. H e found higher strength values for the latter two sorts of particles with higher specific surface areas than those for granules m a d e from spheres only. The strength of water lies between 3 and 5 M N m " ^ , a range where the respective pore diameters need to be between 0.1 and 0.06 u m for measured rock strengths to be explained by capillarity. Here it must be mentioned that such strength values should disappear if the development of interfaces towards their o w n vapour is m a d e impossible. This is obviously then the case w h e n the samples are completely submerged (Fig. 3.11). Without such interfaces, all effects caused by capillary forces disappear.

Chapter 4

The Behaviour of Sandstone Samples under Water; Weathering Processes

If specimens of rock such as Bunter Sandstone, are submerged under water, all capillary forces (which need interfaces against air or their o w n vapour respectively) should vanish. T h e forces remaining are those built up by physical or chemical reactions between water and one or several phases of the rock. Processes that belong here are: * Processes which are able to bring the rock cement into real or colloidal solutions. T h e transformation of space filling, stationary gels into mobile, transportable sols is called peptisation. * The volume increase of phases of rocks with the taking up of water, in some cases k n o w n as swelling. * The volume change of rock phases with water by chemical reactions forming n e w solid product phases, like the production of gypsum from anhydrite. During all these processes, which belong to weathering in its widest sense, forces can occur if the conditions of the processes are suitable. N o outer forces, like in the tensile strength test, are transferred on the sample here. If such outer forces are permitted, they are superimposed on any existing inner ones.

184

7%e ReAawoMr q^^aw^^one &:^!j?/e^ Mwcfer Wa^er, Wea^er/ng P r o c e ^ M 185

Volume changes occur in practically all of the above mentioned cases so that a measurement of these changes in comparison to their initial state is a means to demonstrate the existence of these processes and to quantify them. Volume changes are very accurately determinable, as shown below. O n the bottom of streams, which flow in the Bunter Sandstone in the High Black Forest, Germany, lies loose cream coloured sand surrounding bigger, outwardly little changed blocks of sandstone. In the Eifel, in the Bunter Sandstone outcrops, landslides were observed, in which complete destruction of the solid rock had occurred. In both these cases, forces of the type named above have a major influence.

4.1 Definitions and Conventions First s o m e definitions and conventions are introduced. Subsequently laboratory experiments of the Bunter Sandstone/Water system are discussed. 4.U

SzgM coMueMfMMsybr forces

In Fig. 4.1, a sign convention for forces is sketched, which m a y be radially applied to a sphere-like particle of a granular aggregate. The convention for direction has been chosen such that a tensile force applying stress from outside a sample has a positive sign. This is the same direction in which a volume increase could take place if, in the interior of the aggregate, phases are present that either swell in the presence of liquids, or convert from a solid phase of a smaller mole volume into a solid product with a bigger mole volume. \

+ F

Fig. 4.1 Sign convention for forces.

! 86 .Sfrengf/: awcf ^ea^er;/?g q / ^ o c % a^ RoM/!^a/y Z,oye/* Pro^/ew^

4.1.2

SwgHm,6?q/'7'od(s

The term "swelling" is not used uniformly in literature. It can be found used to describe a change of length, as w h e n one material is stored in a layered host material. So the deposition of water between the (0001) — layers of clay which results in the dimensions of the latter being enlarged, has been measured quantitatively by X-ray techniques. The disadvantage of this definition lies in the fact that it is not possible to calculate portion changes from length changes without additional assumptions. For this reason the degree of swelling (q) has been defined as the quotient of the swollen to the unswollen volume q =^ ^ -

(4.1)

In the case of isotropic swelling, the two definitions can be converted into the following

q =

iswollen

(4.2)

D'ans-Lax (1967) shows values for the shrinkage and swelling of rocks as a length quotient in the unit of m m / m , which is 0.45 m m / m for sandstone. Here a further definition was used, the quotient of length change to the initial length. But its transformation into the first poses no difficulties. The numerical value of 0.45 m m / m quoted by D'ans-Lax for sandstone seems extraordinarily small. But if one thinks about the fact that the largest part of the length is taken up by quartz grains which lie one after the next in a row and do not swell, the change in length must be due to the substances between grains with a m u c h smaller initial length. A rough estimate shows that in this case, higher local degrees of swelling are to be expected.

4.1.3

Sysfem a n d sysf^m changes

It has already been stated several times that systems are able to work or to build up forces only under special circumstances. The special circumstances are linked to the m a k e up of the system and with it the ability to measure processes. To elucidate these circumstances, refer to Fig. 4.2. In this figure

77;e Z?eAaviOHr q/*^aM^^one ^awp/ey MM^er ^a^er, ^fea^er;?:g P r o c e ^ M 187

^

^

Surrounding

H—-^—H

H-^ .]

THAnhydriteH

Ctosed system

Open system

Fig. 4.2 For the definition of a system.

two different systems are illustrated. A system is defined as a space which is separated from its environment by either real or imaginary walls and in which, in the context of this investigation, material is always included. In general, this material consists of several phases which, for this work, are physically and/or chemically able to react. Systems are classified as follows: * closed systems, and * open systems. In the first type, an exchange of energy, but not of material with the surrounding is allowed. In the second, energy and matter can be exchanged. Isolated systems, where the exchange of neither is allowed, are hardly relevant in this context. Systems are often depicted as cylinders with mobile, weightless and frictionless working pistons, which allow the exchange of volume work between the system and that environment. The open system can be symbolised by a cylinder with, for example, porous walls which allow the exchange of gas and water, but not that of solid phases. To explain what is meant by particular measuring circumstances, the following irreversible chemical reaction is presented C a [SO4] + 2 H 2 O -> C a [SO4] 2 - H 2 O anhydrite fluid water gypsum 1x45.99 2x18 1x74.21 The numerical values, which are written under the chemical symbols, characterise the mole volumes which are multiplied with the stoichiometric

188 Jfrewg?/: an
conversion numbers 1, 2 and 1 of the three compounds. First the number of moles of anhydrite and fluid water which are demanded by the chemical equation are introduced into a closed system. Then the reaction to gypsum takes place. The total volume change occurring under these circumstances is: 74.21 - (45.99 + 2 x 1 8 ) = -7.78 cm^ per formula unit. Note the negative result, indicating a volume decrease. Under these circumstances, the normal air pressure acting on the system will m o v e the piston of the closed system downwards. A reaction force in the opposite direction does not occur. The reason for this is that the water molecules are packed more densely in the dihydrate gypsum than they are w h e n in water. Completely different results are observed if the experiment is executed in an open system. In this open system only one mole of anhydrite will be considered present initially. To react, water enters through the porous walls. In this case the volume change is positive as the anhydrite converts to gypsum 74.21 - 45.99 = +28.22 cm^ per formula unit. The volume increases by 6 1 . 4 % in the conversion to anhydrite. In this case, the piston rises up in the open system and can release forces onto the environment. In this way, vermicular gypsum might develop. Thus the appearance of forces in a system, and their magnitude, depends on the system itself. Another problem that m a y greatly influence a change in reaction volumes and thus the thermodynamic situation of such processes appears w h e n mixtures are formed within a system (Table 4.1). In this table, solid/liquid biphasic systems with different degrees of dispersion, are symbolised. In principle, these can be read from a scale which indicates the particle diameters of the solid particles. The diameter range from a few micrometers d o w n to a few angstroms. If the particle diameters are of the order of a few micrometers or more, then the biphasic system behaves as a mechanical mixture. In this case, the surface terms are negligible in comparison to the volume property terms. Their total volume is thus additive in the volumes of the two single phases. These mechanical mixtures are m a d e up of two phases. If the particle size diameters are in the order of a few angstroms, the system contents are called true solutions or mixtures. True solutions m a d e up out of initially solid and fluid phases, are principally not additive in their volumes. True solutions or mixtures behave as single phases and are m a d e up of two

7%e #eAav;'oMr q/*^a/!Jyfoy!e &wp/ey Mw^er Wafer, tfeafAenng ProceMe^ 189 Table 4.1 Systems and their properties with increasing linear dimensions.

1

d/nm

1

)

1

10" !

10-3 1

1 True solution

10 ^ 1

10' 1 Colloidal solution

10" _[

10 +' 1

1

1

10^ 10+3 1 Mechanical mixture

Dissolved silicic acids in water

Gel and gel flocks

Quartz grain packing and pore water

O n e phase

?

T w o phases

Volumes not additive

?

Volumes always additive

components. Between mechanical mixtures and true solutions lie colloidal solutions, where the thermodynamic circumstances are complicated and cannot be looked at as being given a /?rfor;'. If colloidal fine dispersed solid phases are present in a system, the situation needs to be investigated by experiments. The same applies w h e n real mixtures are formed — investigations to quantify the magnitudes of the mixture (e.g. their partial mole volumes) are also necessary. In the following section, s o m e preliminary experiments of the Bunter Sandstone/Water system are discussed.

4.2 Direct Observations and Photographic Registration of the Bunter Sandstone/Water System Irregular, sharp-edged rock pieces 1 to 2 c m diameter were put into a glass flask (Fig. 4.3). R e d sandstone pieces seen in the photo originate either from

190 Ar
Nr. 6; 4.8.1995; magnification: 0.57 : 1

Fig. 4.3 Upper: Sandstones that can macroscopicaHy be differentiated. Lower: Bunter Sandstone/water system after three weeks.

the Bunter Sandstone of the Eifei, in the area of Gerolstein or from the Perm of Northern England, from Penrith close to the Scottish border. The two Bunter sandstone pieces which are in the centre of the photograph are either very rich in iron and thus similar to ortstein, or laminated, where the laminae contain different amounts of iron. These local differences in the iron content need to be investigated further. First, four samples of macroscopicaHy

77)e ReAavwHr q^^aM^j^Me ^awp/e^ t//:^er Wa?er, Wea^AeW^g Proce^M

191

homogeneous colour (and thus equally distributed iron content) were chosen (left side of Fig. 4.3). They were placed in a glass flask which w a s then filled with water to its upper limit. The ground glass stopper with a capillary tube of 0.5 m m diameter was subsequently introduced quickly so that the displaced water was pushed up to the upper end of the capillary tube. The flask so prepared w a s observed in transmitted light and during several weeks photographs were taken. The lower part of Fig. 4.3 shows the flask after three weeks of reaction time; changes are visible. The system was under normal pressure and close to normal temperature. A s the temperature changed throughout the day and fluctuated over a number of weeks, it w a s recorded every hour and an average obtained. In the next section, this averaging procedure and its necessity will be explained. 4.2.2

Aueraged reacfzoM femperafMre a n d w e a r n e n n g regi'me

The room temperature fluctuations mentioned above can be seen in Fig. 4.4. Their averaging was done with the help of the mean value formation of the integral calculus, which gave a result of 21°C (+1, -2°C). The necessity for the diligent determination of the reaction temperature can be seen from the lower part of Fig. 4.4. The figure shows the changes of the m e a n temperature of a year and its yearly variations as they have been determined with respect to their geographical latitude. If one chooses a temperature of 9°C as characteristic for the middle European region, then this value has to considered as the average reaction temperature for all chemical reactions, which determine the weathering processes of rocks. The highest averaged temperature of the year on the surface of the Earth is 29°C at the so-called thermal equator (14°N latitude). Finally, our heated buildings are at about 21°C, approximately at the tropic of Cancer. A s the sketch in the lower part of the figure shows, this value roughly indicates the limit of lateritic weathering. The great difference seen in the weathering processes between the temperate and subtropical to tropical zones, where the amplitude of the annual temperature is approximately equal to that of the daily temperature, is due to a temperature difference of 12°C. Local deviations like the extrapolated temperature of the surface of rock blocks (Fig. 4.5) for example,

192 -Rreng;/! a/it? ^a^AerMg q/J?oc% CK RoHMaary Layer FroA/ew^

2.5.1995

,

22 21.17 'C

20

IB

16 10

20 time h

geographische Breite

20 ^ b ^ ^ < )) )

-90 . „ c nacn Hann-Surmg

naeh Ganssen-Hadrich Fig. 4.4 Upper: Temperature recorded during experiment illustrated in Fig. 4.3 and its variation with time. Lower: Temperature, geographical latitude and distribution of lateritic weathering.

Rock: Chamokite, Locatity: Menambakkam. ctoseto Madras. !ndta; Measurement: 27.8.1969

Fig. 4.5 The surface temperature of a M o c k of rock, determined by extrapolation of the course of temperature at different times of the day to the depth of zero in the rock interior.

are exempt from this. Temperature has been measured both as a function of depth in the rock and of time of the day. M a x i m u m values of 40°C were reached. Examples of temperatures on the Earth surface are provided by Hann-Suring (1940), temperatures associated with the distribution of lateritic soils by Ganssen-Haderich (1945), and measurements of surface temperatures by Butenuth (1969). For comparisons with natural conditions, it is thus necessary to fix temperature values for laboratory experiments precisely. The other environmental conditions of the experiments executed here were: air pressure practically constant, 1 A t m ; p H of the tap water used about 5.5. 4.2.2

R e s i t s q/* dz'recf o&serpafM)M &y p^orograp^z'c re^/sfrahon

The results of the direct observations are contained in a series of photographs, which were taken over a time period of 22 weeks (March-August 1995).

194 Areng?/: an J ffeafAerwg o^/?ocA: a^ FoM^a'ary Z,a^er Pro^/ew^

The time dependent development of the identical system, m a d e up of Bunter Sandstone and water, was followed. All photographs were taken in transmitted light as it w a s possible to register the colours of the system more realistically in this way. The disadvantage of this kind of presentation is a slight haziness of the pictures as they were taken in the scatter light of colloidal solutions. T h e series of photographs has been reproduced as Fig. 4.6. Subsequently an observation method is introduced where the lighting is introduced by a set of mirrors (Fig. 4.7). T h e first of these photographs (upper left) gives an impression of the system after three weeks of reaction time and occasional shaking of the glass flask. Here, some noticeable changes are already very pronounced: * T h e originally sharp edged rock pieces are partially disintegrated. T w o of them can be seen indistinctly as rounded residual bodies on the left and right side of the flask. The disintegrated material is deposited on the base of the glass flask; it is mainly separated in two layers that lie on top of each other: a finer cream like coloured top and a coarser, darker lower layer (see photographs). * T h e solution has developed a distinct colloidal character, as the strong Tyndall scattering of light shows. In colloidal solutions, a ray of light can be followed along its complete path through the solution. In the case of true solutions, it is only possible to see the refraction or reflection of light at the wall of the container. Note that the light paths of the reflected light rays at the glass wall in the upper part of the flask. * The solution in the standing flask has two colours, yellow and red, and is layered with the red colour concentrated in the lower part. This colour layering shows a separation by sedimentation of colloidal material that is present in the solution. It has to be expected that these layers also contain compounds of trivalent iron which obviously originate from the Bunter Sandstone samples. It can be said in summary that reactions with water take place which * lead to either a smoothening of the edges of samples or to their partial disintegration at their exterior;

77te BeAaf MM/* q^^ani&/o?;e ^a?M/?/e^ MM
16.3.1995 three weeks 6.4.1995 six weeks

1.6.1995 fourteen weeks Fig. 4.6 Devetopment of a system Bunter sandstone/water with reaction time.

i 95

) 96 Areng/A and %%af/ief7ng q/*J!oeA a^ Rount/ary Layer Pro^/ew^

4.8.1995 twenty two weeks

4.8.1995 twenty two weeks

twenty two weeks

Fig. 4.6 (cont'd)

* resulting in forces which are positive in the sense of Fig. 4.1, and that * colloidal phases participate in these processes. The next few photographs of the system, corresponding to 6-22 weeks, show two additional features. The first is that w h e n sedimentation of the red substance is mainly finished, the yellow colour dominates in the solution. Thus both colloids involved can migrate separately from one another and are not coupled to one another. The second feature is a development of white efflorescences on the surface of the residua! bodies, as well as on the surface of the sediment layers. At first they can be seen as sheaves or flame-like bundles of threads after nine weeks. Later they laterally grow together to form solid white small blocks (see after 14 and 22 weeks). O n e observes a strongly damped oscillation of the structures to their neutral position, w h e n exerting a sudden rotational m o v e m e n t of the container, a process similar to that occurring in gels. A further disintegration of the rounded residual bodies within this time period was not observed.

7%e ReAawour q/*&[wt^^o/[e &[wp/e^ M/
! 97

20.9.1995 Nach e i n e r W o c h e , ohne Schut teln Beleuchtung Ober Spiegel Kolloidale Losung, Effloreszenzen

Fig. 4.7 Behaviour of a Bunter sandstone sampte in an unmoved system: iHumination over mirrors.

Another point is illustrated by the photographs in Fig. 4.7. The y e H o w and red coHoids, which were mentioned above, were observed after occasionally shaking the glass flask at the beginning of the reactions. But do other colourless colloids exist? T o answer this question, see the arrangement of photographs in Fig. 4.7. O n e of the irregularly formed samples shown in Fig. 4.3, was put in a test tube and immersed in tap water and observed;

!98 .SfreHgf/: a n ^ ^ a ^ A e r M g q/^7?oc^ as #OHM&try Z,ayer ProA/em^

but the sample w a s not shaken this time. Light was introduced by a tilted mirror which was put under the glass and allows a change of ray breadth and incident angle of light. The results are documented in Fig. 4.7. The photographs show that after only a week in the unstirred system, a colloidal but uncoloured solution was produced. The path of the light ray is visible for its entire length. The fomerly edged sample has changed its shape to the round bottom of the test tube, which would have not been possible without overcoming the cohesion forces in the interior of the material. Finally, white efflorescences are also visible at the surface of the sample surface, which in this sort of illumination are even more visible than in Fig. 4.6. With these observations, it is quite certain that at least three different colloidal fine intergranular substances of different chemical composition exist. This is considered further in the following section. 4.2.3

Jnorganzc-c^emzcaJ 2vMffo analysis ( E D X ) q^ fTie wiec/MHzcaHy a^sfrngMis^aMe phases

After the direct observation of the weathering processes described above, a microscopic investigation of the single phases separated mechanically by sedimentation was m a d e according to the scheme shown in Fig. 4.8. Samples were taken using a graduated pipette, from three heights of the flask, after a reaction time of six weeks (Fig. 4.6): from the colloidal solution (I) the cream coloured finely grained layer (II) and the layer of coarse sediment (III). The samples of material in suspension so obtained were dried on microscopic slides and then with the E D X (energy dispersive X-ray microanalysis system) method in the scanning electron microscope, investigated to obtain their chemical brutto analysis. The results of this technique are not regarded as being very accurate. Nevertheless, an impression of the relative elementary composition can be achieved. These results are given in the right side of Fig. 4.8. The drying residues seemed to show a radial distribution of material. Therefore the E D X analysis was m a d e from the middle and the rim of each sample. All samples investigated contained compounds of silicon, aluminium and iron, but in different relative and absolute amounts. The signal for silicon compounds is of the same height for practically all samples and in all samples investigated, higher than those of aluminium and those of the colouring iron compounds. In the residue the proportions between silicon

71he ReAaviOMr q^5'a/*a'jfoy!e &vw/?/e^ M/)
Fig. 4.8 Scheme of sampling to investigate the chemical brutto analysis and microscopical observation of phases for different materials.

and the other c o m p o u n d s are very high. This m e a n s , that the c o m p o u n d s o f

silicon, in comparison to those of aluminium and iron, are enriched in the solution. The rock samples are desiheated as would occur if silica gels that were binding particles together were to change into mobile silica sols or gel flocks (see below). In contrast to this, most of the colloids of aluminium and iron return by sedimentation back into precipitates after having been shaken. It has already been mentioned that a time dependent separation of the two iron colloids takes place because of their different sedimentation velocities. It is less clear if such sedimentary differentiation with time also produces a shift in location for the aluminium and iron compounds, but this is to be

200 ArengfA ana* W^a^er/Mg q/*^ocA <M 3oMMt/ary Layer Pw^/eMy

expected. The hint for this can be seen in Fig. 4.8. In all drying residues a strongly coloured red rim was developed. The first droplet extracted from the suspension and then dried w a s placed over a mirror so that the top as well as the bottom of the droplet and its drying residue could be seen simultaneously in the photograph taken. These show that the red rims of the residues mentioned above have about the same thickness above and below, and are thus not at the interface of the glass with the solution, but are concentrated at the surface of the droplet. It is possible that different compounds have different surface charges on the respective colloids. Other lines of evidence suggest that the separation of iron and aluminium colloids can occur during weathering processes. O n e line is shown by the photograph in Fig. 4.9. It w a s taken from a street which runs at the steep east slope of the C a r d a m o m Hills, Southern India. T h e view looks across the Indian plain which stretches nearly parallel to the East coast of India. The fn .M?M soils are in this central area of lateritic weathering, with yellow and red brown mottled colours. A local separation of coloured and non-coloured soil colloids is also probable.

Fig. 4.9 View from the Eastern siope of the Cardamom Hii!s into the South Indian Coastai ptane (G. Butenuth, )969).

77:e FeAawoMr of &/:^fo/:e & w p / M M/!^er Wafer, W e a ^ e r M g P w c e ^ e ^ 201

Table 4.2 Chemical composition of fourteen different ores of different locations.

Ore

nEkmentX lO^mol

Principal components

Anamur Hekimhan Nigde Kangal Hasancelebit Edremit Sakarya Adana Divric C-P Balikesir Kesikkoprii Divrik A. Venezuela Kiruna

Fe

Al

Si

758,6 979,4 1011,8 989,4 1025,9 1021,6 436,0 798,5 894,1 1146,0 1083,0 1056,8 1068,1 1018,3

148,1 9,8 15,9 84,3 43,5 17,9 95,1 2,0 94,5 12,4 8,4 33,9 30,4 16,9

334,5 54,6 151,8 100,7 98,7 162,3 146,8 24,0 196,6 75,6 152,1 70,9 17,1 44,9

1 AI2O3 : n SiOz 4,52 11,14 19,09 2,35 4,54 18,13 3,09 24,00 4,16 12,19 36,21 4,18 1,13 5,31

G. G. G. H. H. H. D. H. H. H. Mag. Mag.

H. G. G. G. P. C. 1. M. H.

Legend: G.: goethite; H.: hematite; D.: dolomite; P.: pyrophyllite; C : calcite; 1.: illite; M.: magnesite; Mag.: magnetite After Izgiz (1969)

Another line is that the enrichment of iron compounds to the development of ores might be possible by this way. In connection with this the brutto analysis of 14, ores (mostly from Turkey) is presented. The compilation in Table 4.2 is taken from the dissertation by Izgiz (1969). Apart from the brutto analysis the table includes the results of phase analyses. Summarising the results so far: 7%e jM&y?aMcay oefwee?! graffM of ?Ae FMH?er &!M6&?OMe q/^Ae Ef/e/ are /na%e Hp of co//o:aa/y;He c o w ^ O M M ^ q/*j///con, a/MwfM;'MW an;/ ;*ron, wA/cA joroAa^/y /7!;gra?e fn gY^o/M^'oH joroce^ey /HoepeHaenffy yrow one anofAer, #H
202 Areng?/! aM6? ^ a ^ e ? * M g q/^7!ocA a.y ^oMM^a/y Zayey Pw^/gym

Electron micrographs will be able to give indications about the size and morphology of the colloidal particles. 4.2.4 P r g h ' m m a n / remarks on f7!e morp/voZogi/ o/ f^!g

The following remarks are m a d e with respect to photographs of the air dried residues of the different suspensions, I and II, as illustrated in Fig. 4.9. These photographs were m a d e by a scanning electron microscope ( S E M ) . The samples were investigated at two stages in their preparation for investigation by S E M , for either changes or artefacts respectively which might have developed because: * capillary forces which could have influenced the samples became active w h e n drying the samples on the glass slides, and * the air-dried samples, which might still contain water, are introduced into a vacuum in the electron microscope. T h e first of these t w o difficulties, the drying of sols with the formation of gel-fragments has been described by Her (1979) in a drawing (Fig. 4.10). A consequence of vacuum in the microscope is the formation of border cracks, which can be seen on the left side of Fig. 4.11 (see arrows). Thus the following remarks about morphology of the suspended phases are only preliminary. Sizes have to be considered in particular with regard to this reservation. First, Fig. 4.11 is considered in more detail. The figure looks similar to an aerial photograph of a island, which is bounded towards the open sea (on the left) by a chain of dunes. The dunes resemble the gelfragments which are schematically shown in Fig. 4.10, strongly suggesting they are agglomerates containing water and which are m a d e up of m u c h smaller sol particles. There are desiccation cracks crossing the dunes (similar to rills) between these which lead into the interior of the island. They show that the junction between the droplet and the glass upon which it sits, i.e. the bottom of the island obviously consists of a coherent film. This photograph shows a detail of the rim area of the dried residue of the colloidal solution (I), which in Fig. 4.8, has a blood red colour.

7%e ReAawoM/* q/^&?!^?o/!e & w p / M MM^er ^a^er; ^eafAer;/!^ Proce^e^ 203

(a) #^#?* *^ US* *A

(c) ^otnanRyowBHrw (d) (e

) M^#!HM^

Evaporating film of silica sol to gel and drying: Schematic cross-section. (a) sol; (b) concentrated sol, beginning of aggregation; (c) gel compressed by surface tension; (d) fracturing of gel by shrinkage: (e) dried loose gel fragments. W : Water surface; S: Solid substrate. Fig. 4.10 Fragmentation of gels (Her, 1979).

The surface of the island is covered with a mass of rounded bodies far into its interior and the proximity of the rim has accumulated rectangular platelets, some of which show oriented needle like growths radiating from them. The white line at the bottom of the figure marks a length of 100 um. The order of magnitude of the picture elements described can then be estimated, with the previously given reservation in mind. The diameter of a single dune is a few tens of micrometers, the length of idiomorphous platelets is about 10 u m , and the diameter of the particles distributed over the island is 1 u m .

204 Strength and Weathering of Rock as Boundary Layer Problems

Fig, 4.11 Drying residue, I, red residue. Magnification 500 : 1.

A photograph of the latter is given in Fig. 4.12 at a higher magnification. Here it can be seen that apart from the discreet particles of about 1 |im9 an additional great number of smaller particles which resemble the smaller irregular formed platelets is to be found. All these particles (the bigger round ones and the smaller platelets) seem to be made up of even smaller primary particles. Thus there seems to be a more or less steady development of the size of agglomerates from sol sized particles to gel flocks. More will be said later about the idiomorphous particles. These morphological findings are strongly reminiscent of the diagenesis of colloidal intergranular substances, which are probably made up of primary particles, whose size can go down to a few tenths of a micrometer and whose pore diameters are thus expected to be in the same order of magnitude.

The Behaviour of Sandstone Samples under Water; Weathering Processes 205

Fig. 412 Microphotograph of the widely scattered round particles of Fig. 4.11 at higher magnification.

As no diffraction patterns of the single phases have been made up to now, a comparison between the effects of weathering residues seen on a macroscopic scale might assist in phase analysis. The coarse sediment (III) naturally contains quartz grains, which were accumulated when the sandstone disintegrated. Figure 4.13 shows a series of photographs in which the magnification of such a quartz grain increases. Its surface is not smooth but covered with a morphologically amorphous rough layer, which has been

206 Strength and Weathering of Rock as Boundary Layer Problems

•ll^li|illli«llill

, | i i i l i i i f c | i l i i i i •••

lllllilllllilllli;)

••iiii^iiii

mmmmmmimmMmi

iismttBimmmmim

i|^™i i i^-m^ '

*&*' i«!:Illllll Fig. 4.13 Rounded quartz grains in the coarse sediment, III, from top to bottom increasing magnification: 200 : 1; 500 : 1 and 1000 : 1.

77:e ReAav/oMr of &/!^;o^e & w p / e ^ M^^er Wafer; Weaf/:er:ng Precede.? 207

described in literature more than once as an overgrowth. Such surfaces were described by Pittman (1972) as follows: "Presolved surfaces between quartz grains vary from selectively smooth to rough with ridges, knolls, furrows and pits." A n d at another place: " M u c h of the area between overgrowth and nucleus is void space which forms the "dust line" visible in thin section". 4.2.5

Sn&sfHMces a n ^ pro&^cfs q/ Jarerific w g a f ^ e r m g sef Jree w n e n immersing BMMfer San^sfone samples in wafer

The E D X analysis has shown that silicon, aluminium and iron compounds were present in all phases developed (in solution, suspension and sediment) w h e n immersing Bunter Sandstone samples in water. This sequence also reflects their relative amounts. Furthermore, it became evident that the relative amounts of silicon compounds in the solution are m u c h higher in comparison to that of the sediments at the bottom of the flask. This means that the Bunter Sandstone samples were desilicified during the immersion. The temperature at which the experiments were conducted was about 21°C as it exists at the northern limit of the weathering processes on the Earth. Finally, the initial samples were partially destroyed untill they reached the roundness of the residual lumps. For these reasons, it is interesting in particular to try and predict the types of compounds of the chemical elements mentioned, based on experiences of lateritic weathering. "Bauxite and the strongly contaminated laterite are mechanical mixtures of boehmite, gibbsite, diaspore, alumogel, iron hydroxide and others, and belong to the sedimentary rocks" (Strunz, 1982). In this list only aluminium and iron compounds are found; it does not contain those of silicon, either in the form of silicates or amorphous/crystalline silicic acid. The latter have obviously been removed by lateritic weathering w h e n laterites where produced. However, they are still present in the cements of Bunter Sandstone and in ores (Table 4.2). Taking both these observations into account, one could classify these silicon compounds as components of materials which are not yet laterites, but on their w a y to becoming laterites, because they are partially desilicified but otherwise still show the same elementary combination w h e n immersed in water. Valeton (1988) explained the material separation as follows: "Because of the small solubility of Fe^*, a separation between Fe^+ and Si generally

208 Aren^f/: aH^ ^a^AerMg q/*/?ocA #s RoMM^ary Layer Pw6/ewj

happens and oxides and hydroxides of iron in an amorphous and crystalline form are formed". S o m e remarks are necessary concerning to the expressions emphasized in bold. "There is no proof of the existence of a defined hydroxide Fe(OFf)3". (Cotton-Wilkinson, 1967). The hydroxide of divalent iron, Fe(OH)2, is k n o w n to exist, but is extremely sensitive to oxidation. "That is w h y iron(II)-hydroxide turns dark practically instantly, if it is precipitated in the presence of oxygen". (Cotton-Wilkinson, 1967). N o r m a l hydroxide of iron in the presence of the ubiquitous oxygen therefore does not exist. O n the other hand, compounds of the type M e O ( O H ) ( M e = metal), particularly of the trivalent iron and aluminium are widely found. They were systematically classified as oxide hydroxides (e.g. by Glemser and Riek, 1958). The solubility of single ions (Fe3+) does not exist. This term is always linked to a solid phase of idiomorphous crystals of a given stoichiometry at all times. Under the given circumstances, w h e n colloidal fine particles are involved, the existence of thermodynamic equilibria of the commonly k n o w n kind has to be doubted. O n the basis of extensive investigations, Wefer (1966) concluded that w h e n iron (III) solutions are precipitated, hematite (a-Fe203) and goethite (a-FeO(OH)) always form in parallel. These seem to be in equilibrium between themselves and with the solution, even though the rate with which equilibrium is reached m a y be small. O n e argument that led the author to this conclusion were the star-like intergrowths regularly found between goethite and hematite in samples (upper part of Fig. 4.14). Isgiz (1969) w a s able to show that such star-like intergrowths also occur in natural iron ores even though they are somewhat changed in form (middle part of Fig. 4.14). In both cases, these aggregates of intergrown crystals are only of the order of magnitude of a few micrometers in size, but their idiomorphous character is beyond doubt; even their crystallographic phase relationship could be derived (Fig. 4.14). The rectangular platelets with needle-like growths in Fig. 4.11 point in an imperfect w a y in a similar direction as the star-like intergrowths just described. The blood red rim of the dried residue (I) could also contain hematite and goethite. A similar result w a s obtained in the Bodenkunde (Soil Science) (Scheffer-Schachtschabel, 1976): "It is he (hematite) that

77:e Z?e%av
^

209

<

orientated intergrowth hematite-goethite

star like twins of goethite crystals

-, -#

^

"["<)]

"=tt

Fig. 4.14 Oriented intergrowth of hematite and goethite. Upper: Precipitations of preparations; Middle: Turkish Nidge-or; Lower: V o l u m e increase at the formation of a water containing phase.

210 AreMg?A an<^ t%af/:e?*;7]g q/^oc% aj RoMM^ary Zayer P/*oA/ewj

colours m a n y soils of the tropics and subtropics blood red (Munsell-colours 5YR-5R). Often he is associated with goethite". With regard to aluminium compounds, gibbsite (y-Al(OH)3) seems to be the substance most frequently found in lateritic soils (SchefferSchachtschabel, 1976). In this reference, there is an impressive microphotograph to be found of gibbsite crystals of about 4 p m from a laterite of Cameroun. The existence of such crystals seems to necessitate an extensive erosion of silicon compounds (Scheffer-Schachtschabel, 1976). The compounds of silicon which remain are probably silicon gels and sols. In total, a certain relationship of the products (which were either set free of water or were developed in the presence of water) with products of lateritic weathering is unmistakable. A more detailed description of the state of these products with the help of diffraction results needs still to be done. In view to the partial destruction of the Bunter Sandstone samples, a very important question is h o w their volume changes. S o m e observations to this question are addressed in the following section. 4.2.6

O^seruahons q / p o Z M m e changes q/^ Buffer Saw
It has been described above that such samples w h e n immersed in water partially disintegrate. This finding can be explained by either negative forces, which are directed into the interior of the samples, disappearing during immersion (capillary forces in particular) or by positive forces which develop in the opposite, outward direction. Naturally processes in both directions could also be involved. The values, which are tabulated in the Taschenbuch fur Physiker und Chemiker and describe the swelling of sandstone samples, produce forces which are directed to the outside during the uptake of water with an increase in volume probable. A s quartz grains are unable to swell, these processes must be found in the domains between the grains. Although the types and the details of these processes are unknown, there are a number of clues which point to directions deserving further study. At first, one has to think of water uptake by previously water-free phases, similar to what has been described for the conversion of anhydrite into gypsum. This idea can be checked for those phases which are only possible according to the

7%e FeAawoMr q/*^aM^?o;:e & w p / e ^ Mw^er f%t?er, l^eaZAerMg Proce^M 21 1

Table 4.3 Mote volumes of lateritic products.

Substance

Modification

V ° cm^moi '

Brutto formular Oxide AI2O3 Fe203

corundum hematite

25.55 30.42

diaspore boehmite goethite

17.72 19.38 21.32

gibbsite (bayerite)

31.95 (31.16)

Oxidehvdroxide AIO(OH) FeO(OH)

Hvdoxide A!(OH)3

explanations given above (see also Table 4.3 and the lower part of Fig. 4.14). The oxides of the elements of interest here, aluminium and iron, usually originate from their solutions by first developing water containing complex ions by hydrolysis, and then follow a series of subsequent condensation steps. Here the p H value of the solution plays an important role. There are natural gels amongst the precipitated products which contain water and are X-ray amorphous substances. Clirachit, an alumogel, is one example of such a gel. Less seems to be k n o w n about the reversal of the reactions under the same conditions, particularly at the same values of pH. The reaction equation written in the bottom left of Fig. 4.14 has thus only a hypothetical character. But this and analogous formulations are able to identify which principal volume changes are possible under such circumstances, if they exist. The answer can be deduced from the values given for the mole volumes V ° in Table 4.3. According to the equation in Fig. 4.14, the volume decreases by -9.065 cm^ per formula conversion but the solid volume increases to 38.35 cm^ per formula conversion, if the reaction takes place in a closed system. The circumstances are thus similar to those of the conversion of anhydrite to gypsum.

2)2 A r e M g ^ an;? W ^ a ^ e n n g q/*/?oc^ as FoMMaary Layer Pw^/e/n^

Fig. 4.15 Expenmenta] set-up to determine votume changes in the Bunter Sandstone/deaired water system. Volumes of single spaces, see Figs. 1: 1.483 ctrP ± 0.43%; II: 99.28 cnrp ±0.33%; III: 14.10cm3±10.6%.

A s often in situations like this, one has to test the situation experimentally. S o m e aspects of experimental verification become clear from Table 4.4 and subsequent figures. Figure 4.15 shows a quasi-closed system to measure the change of the total volume AV. The rock samples were introduced into the bottom of the central glass tube. It is closed at its top by a ground joint. The socket of the ground joint forms an extension of the tube from which a tap allows the glass tube to be closed. At the side of this measuring system, there is a vertical capillary tube which makes it possible to measure any changes of the total volume which occur within the glass tube once it is closed. The diameter of the vertical tube is 4 m m and a millimetre scale w a s

7%e ReAawoMr q^^aM^^o/:e ^am/7/ey M/!^eA- !Fa^er; WeafAenng Proce^e^ 2t3

attached to it which allows changes in height of Ah = ±0.5 m m to be measured and so a volume change of A V = ±0.0063 cm^ is the limit of what can still be detected. Small volume changes are expected due to evaporation losses in the vertical tube and temperature changes of the system. Furthermore, immanent volume changes take place in the system which are based on the interactions between fluid water and the substances in the pores of the sample. These are compounds which are listed above and possibly also pore air, as explained later. To execute an experiment, the measuring system, including the top, is filled up to the opened tap with deaired water from the side with a niveau vessel and the tap subsequently closed. The top is constructed in such a w a y that air bubbles which rise at the beginning of the experiment can be collected in it. The capillary tube at the side is attached to the vessel in such a w a y that any rising air bubbles are unable to enter it. To further hinder such a possibility, its diameter is reduced in size next to the wall of the vessel. For experiment I, three sandstone samples were introduced one above the other: m „ ic^er = 2.930 g, m ^ middle = 4.900 g and m ^ upper = 4.880 g, thus in total m o totat = 12.710 g. The temperature of the system varied between 18 and 23°C. The results are shown in Table 4.4 and Fig. 4.16, which show the changes of the total volume A V (in cm^) with time and temperature. The three dimensional diagram allows the temperature variation in the top plane to be seen. The points and squares emphasised in black are places where the temperature at which they were measured were very nearly the same, i.e. 20.5 ± 0.5°C. Figure 4.17 shows these points again. They describe a graph which can be approximated by the following empirical function: A V = -0.823e-(4?.°3i/t).

(4.3)

Here, t is measured in hours and A V in cubic centimetres. The curve has a point of inflexion (index w ) whose co-ordinates, t^ and A V ^ are given in Fig. 4.17. The curve that was constructed through the points measured was calculated according to Eq. (4.3). For long times t -> °°, the process approaches the extrapolated value given by the dashed line in Fig. 4.17 of A V ^ = -0.823 cm^. In the upper part of the diagram, measurements indicate the evaporation of water from an otherwise empty capillary tube of 4 m m diameter. A s expected the effect is relatively small (5%) compared to the

214 AreMg;/: an;7 t%a?/ieriHg q/"/?oc/: ^ RoM/!&!7y Zayer ProMe/m

2 t 50

^

6 t/d g I [ t f t 100 150 t/h - i — i — i — ! J^ i — i — t — : J/ : — i — t !

0,0--

AV/cm-"

-

0.5-^ Fig. 4.16 Volume changes as a function of time, t, and temperature, i^.

-1.0

! i t! 2 0 < <9-°C < 2 1 Fig. 4.17 Changes of the tota] volume, at constant temperature, in dependency of the time.

77[e Re%av;onr q^&K^jfowe &w/?/e^ Mno'er Wafer; WeafAeWng ProceMe^ 215

t

]

0 010—

! ^ ^

!

I t 1 t

t

= 23,52 h

!

t - ' *-

/ 3- h-' w/cm

^-2

/

*

)

-

_i 1?

)

!

__^^.

r<

^^V,l =

/i 0,000-^

^i

!

\

t

r<^

^ "

!

t

i i i 50

150

100 t/h d(AV)

W:

dt

Fig. 4.18 Rate of volume change, w, with time, t.

limiting value of the total system. The points measured in Fig. 4.17 m a k e it undoubtedly clear that an isothermal volume change (a decrease) of the system takes place with time. The empirical equation [Eq. (4.3)] which describes this change does not naturally explain the change with time but it allows two important conclusions to be drawn: * an extrapolation for long times and thus a limiting value for the total volume change; and * the formation of the velocity-time function of the process to be described. The latter one is graphically illustrated in Fig. 4.18. The function goes through a first point of inflexion, t^, an absolute m a x i m u m at t^ax, and a second point of inflexion at t^. With this, the definition with which a volume change in a given time takes place is also fixed.

216 &reng;/: a^!^ %?a?/]er;'Hg q/^J?oc^ a^ FoMMJa/y Zayey Pm^/ew^

18

20

< ^\

!

22

i

!

*^*/°C

)

—^. m = ' 1.4314 + 0,0308 ^ !r! = 0,986

^4^

,^^

-.^^ = -*gj4i---l31111111 mi5*!si ^-r3--

---,2

Z

^-

— .? ,

3

t

Fig. 4.19 Changes of volume, AV, with temperature, i^.

Finally, these measurements allow one to at least estimate another property of the system — its thermal expansion behaviour. This is illustrated in Fig. 4.19 and Table 4.4. The figure shows volume change as a function of temperature at a time w h e n the rate of change with time can be regarded as small in comparison to that with temperature. T h e values are first measured in the direction of increasing temperature values. Subsequently a cooling and a heating period was inserted and finally the heating which started from the beginning is continued. The results demonstrate reversible conditions. T h e temperature coefficient of the system was found to be 3.08 x 10"2 cm3(°C)"'. O n the basis of this, together with the starting volume, a thermal volume expansion coefficient of 2.7 x l O ^ K r ' w a s estimated. The one for pure water is 2.07 x 10"^ K r ' at 20°C, and 3.03 x 1 0 ^ K*' at 30°C. A method therefore which allows to determine the main properties of the system and its changes with time and temperature has therefore been described. To explain these properties, some preliminary observations are m a d e in the following section; these need to be verified by more detailed measurements later.

7%e Be^av/oxr q/^^aM^^one ^awp/e^ M/!^er P%tfer,' H^ea^Aerwg ProceMe^ 217 Tab!e 4.4 Volume measurement, Experiment I, for the system Bunter Sandstone/Water: time and temperature dependency. Date and Time

Time

#

Ah

h

°C

^

0,00 2,75 4,00 5,75 8,00

21,0 21,5 22,0 22,0 23,0

-0,00 -0,50 -0,50 -0,60 -0,65

-0,0000 -0,0628 -0,0628 -0,0754 -0,0817

15,75 20,00 21,00 22,00 23,25 31,50 32,50

20,0 21,2 22,2 21,0 21,0 23,0 23,0

-0,80 -0,80 -0,65 -0,72 -0,80 -0,45 -0,45

-0,1005 -0,1005 -0,0817 -0,0905 -0,1005 -0,0565 -0,0565

AY

^

22.11.95

12" 15""

16" 18""

20"

8" 9" 10" IP" 19" 2Q4S 24.11.95

2" 4" 5" 6" g45

945

12" 13" 14" 16" 25.11.95 1"

3" 4" 6" 6" 745 10" 12" 13°"

a

Ah

h

°C

^

115,00 116,00 116,75 117,25 118,25 121,40 122,90 127,65

19,8 19,6 19,0 20,0 20,0 21,0 21,0 22,5

-4,70 -4,50 -4,50 -4,45 -4,45 -4,45 -4,40 -4,05

-0,5906 -0,5655 -0,5655 -0,5592 -0,5592 -0,5592 -0,5529 -0,5089

136,40 140,15 153,15

19,0 21,0 22,0

-5,00 -4,75 -4,45

-0,6283 -0,5969 -0,5592

10""

159,15 166,15

19,0 21,0

-5,05 -4,90

-0,6346 -0,6158

30.11.95 8" 20"

188,40 200,40

20,8 22,5

-5,30 -4,60

-0,6660 -0,5781

207,65

20,5

-5,55

-0,6974

Time

7" 8" 9"" pM 103" 13"!

15" 20"" 28.11.95

4"' 8"" 21"" 29.11.95

3"" 38,00 40,00 41,00 42,00 42,50 45,50 48,00 49,00 50,00 52,00

20,0 20,0 20,0 18,5 19,5 20,8 21,0 21,8 21,8 22,0

-2,30 -2,30 -2,50 -2,60 -2,55 -2,37 -2,40 -2,30 -2,30 -2,15

-0,2890 -0,2890 -0,3142 -0,3267 -0,3204 -0,2978 -0,3016 -0,2890 -0,2890 -0,2702

61,00 63,00 64,00 66,00 66,50 67,50 70,25 72,00 72,75

20,0 19,5 19,0 18,0 19,0 20,0 20,0 20,0 21,0

-2,80 -2,85 -3,00 -3,30 -3,25 -3,20 -3,20 -3,30 -3,25

-0,3519 -0,3581 -0,3770 -0,4147 -0,4084 -0,4021 -0,4021 -0,4147 -0,4084

1.12.95

7"

7"" (399,4 h)

1 ! 1 1 i ! !

19"

-4,20 -4,10 -4,00 -3,90 -3,80 -3,90 -3,85 -4,00 -3,85 -4,00

1

11" 13"" 15"" 15"

19,0 18,0 20,0 20,0 21,0 21,0 21,5 21,0 21,6 21,0

-0,5027

Ah

°C

^

cm3

20,0 21,0 21,3 21,5 21,8 22,0

-6,50 -6,25 -6,20 -6,15 -6,00 -5,95

-0,8168* -0,7853* -0,7790* -0,7728* -0,7540* -0,7477*

sudden fall irroom temperature

!

g45

88,75 90,25 91,00 91,50 92,50 94,00 95,75 97,75 99,00 103,00

#

AV„„a!

9.12.95

26.11.95 6" 7" 7"

Av

^n7

27.11.95

23.11.95

400

Time

Date and

End of

20,3 20,3 20,3 20,0 20,5 21,0 21,2 21,7 21,9 23,0

-6,05 -6,10 -6,15 -6,20 -6,15 -6,15 -6,10 -6,05 -6,02 -5,80

e - W = 0,8889

2! 8 &re/:gy/: a/:^/ %%af/:er;Mg q/^7?oc^ ay RoM^^a^y Layer P w ^ / e M M

4.2.7

lA^crea^oMfs q/'^ore az'r

In the drawing of the measuring device (Fig. 4.15), some measures are described to quantitatively monitor volume changes of the system and to hinder the uncontrolled movement of ascending pore air from samples w h e n immersing them in water: * the cone of the ground joint at the measuring vessel and its socket with the extension at the top enables air bubbles present to be trapped easily; * the shape of the capillary tube next to the measuring vessel first descends to prevent air bubbles from entering it; and * the small capillary radius relative to the sample space. Contrary to expectation, these measures proved to be unnecessary for Experiment I. Pore air did not ascend in the deaired water or if so, only in negligible amounts. Nonetheless, the total volume was reduced, so it cannot be excluded that the pore air dissolved in the previously deaired water. This idea will n o w be pursued a little further. According to the thermodynamics of mixed phases, the isothermal dissolution of solid and gaseous phases in a fluid can only happen in the following way: the phase which needs to be dissolved has first to be transformed into a fluid at the same temperature and only then the mixing of the two components takes place. A s with a phase transformation, latent heat is always exchanged; the solutions so originated have to always be considered real solutions. Thus if pore air is dissolved in deaired water, it is first transformed into its condensed phase. The transformation of a gas into its fluid is linked to a large reduction of its volume (to about a thousandth of its initial volume). In the case described here, a volume change of 0.0823 cm^, this indicates a residual amount of gas still in solution, which lies below the measuring limit chosen here, and thus cannot be measured. In this case, the volume change indicated practically the total volume of pore air in the sample. Under these circumstances, a rough estimate of about 1 4 % by volume would be found, which seems plausible. Despite this seemingly sensible agreement in the porosity value of 1 4 % by volume between the different measuring techniques

7%e .Be/iaw'our q/^&M^yo^e ^awp/e^ Mmier ffafer, ^ea^er/^g Proce^e^ 219

it m a y not be forgotten that a swelling of the solids seems to be certain according to the literature values already previously cited and could also result in a net reduction in the volume of the system, particulary if swelling is accompanied by an increase in the density of water molecules (as w a s illustrated in Fig. 4.2). Such changes have neither been added to by the measurements of the author, nor has their influence on the total volume change of the system been investigated. Here too, further investigations are needed in future. Nonetheless, it can already be concluded n o w that the reduction of the total volume accompanying the submergence of porous sandstone can be caused by at least two principally different processes: * by dissolution of pore gases in the undersaturated or deaired water; and * through denser packing of water in the water containing reaction products of the cements in the intergranular spaces. It is thus necessary to find out something about the relative proportions of the partial processes.

Chapter 5

Conclusions from the Ageing Experiments of Bunter Sandstone in Water and the Distribution of Substances and Forces in Samples

The main intention of this work is to obtain a better understanding of the w a y cohesive forces in the interior of samples which were mostly sandstone produce the range of tensile strength values that are macroscopically found, with the most frequent value obtained being about 2 M P a (Fig. 3.1). A means to investigate these inner forces m a y be provided by the disintegration of samples, by letting them react with fluid phases into which they are brought into contact (Fig. 1). To estimate the relative magnitude of these forces, the three dimensional distribution of all the phases in the rock must be known. Models of this kind are n o w developed based on the experience gained with these samples and described in previous chapters. In doing this, a contribution to the larger subject of weathering shall also be made.

5.1 Models for the Material and Pore Distribution in Bunter Sandstone S o m e preliminary steps in the use of such models to further understand certain aspects of bounded aggregates, such as rocks, have been introduced 220

Co/!c/M.M'on.TyrofH fAe y4geMg Rcper/wey:^ q/^RMW^er .San^fone 221

Filler Cement

Open Pores Contact Cement Fig. 5.1 M o d e ! of the materia! distribution in sandstone (Houseknecht, !967).

in previous chapters: e.g. the spatial distribution of the crystallographic axes system (Fig. 1.28) or the distribution of water in grain packings (Fig. 3.4). A s starting point for sandstones the model proposed by Houseknecht (1967) (Fig. 5.1) can be considered. This model shows a packing of grains, each of which is surrounded by a layer of so called "Contact cement". The pores in this grain packing are filled with a second type of cement, the socalled "filler cement", as well as with pore gases. To compare this model with the results described in this work, e.g. Fig. 4.13, it can be assumed that the "contact cement" between these rough surface layers is identical with what is otherwise termed "overgrowth" in other literature. It seems to be several p m thick and its morphological appearance has been described in more detail by Pittman (1972). This "contact cement" does not show any idiomorphous forms and looks like a shapeless dry gel body. Note that the model pre-supposes that a spatial distribution of the axial systems, with no preferential orientation, exists with the grains of diameters of 0.2 to 0.3 m m ; for an explanation of this, see Fig. 1.28 and the relevant text. The particular part of this body that is able to react with water seems to be the filler cement. In the Houseknecht model, no further descriptions of its properties are given. N o w the presence of cements in sandstones is undoubted for the following reasons:

222 Are^gyA an;? ^ a ^ A e n n g o/^J?oc^ ay RoHnagry ZLaye/* ProA/en]^

* it makes a solid sandstone from previously loose sand, and * the porosity of sandstones is around 5 to 1 5 % by volume, m u c h smaller than that of sand which is normally around 38 to 5 0 % by volume. The absolute strength of sandstone and its change w h e n weathering takes place depends on the structural details of the cements. That is w h y the results described in this text are added to the Houseknecht model (Fig. 5.2). Here it is extremely important to appreciate the relative size relationships of the single structural and textural elements, as has been done above with the aid of electron microscopy:

Structural element (particles) sand grains contact cement filler cement primary particles

Diameter in )im 200-300 some a few some tenths or less

This summary of diameters of the single structural elements shows once again, that their values go over at least three orders of magnitudes. Thus in an approximate w a y it can be seen that this then also holds true for the pore diameters between the particles. The relative dimensions of three of the four structural elements can be seen in Fig. 5.2. The primary particles are not indicated; they could have at most have been shown as dots. The figure has been constructed as follows: the view illustrates a material bridge between two sand grains. In direct contact with the actual quartz grains is the dry gel body which has usually been described as an overgrowth and was called contact cement in the Houseknecht model. In this layer lies the dust-line often observed, and of which no account is taken here. It is obviously made up of air inclusions. The filler-cement is adjacent to the contact cement. According to all experimental evidence accumulated and described here, it is m a d e up of water containing gel flocks. These consist of primary particles with a diameter which is at least ten times smaller than those of the flocks they form. Physical and/or chemical reactions with a fluid phase that has

CoHc/Hs/oH.yyro?H ;/?e ^4ge;'Mg EAper;'7ne/:?y q/"RMM^er &M
Fig. 5.2 Fi]]er cement between sand grains in three different states: structural elements according to scale.

been brought into contact with such a sample take place most likely with the filler cement. This is m a d e up of water containing colloidal compounds of iron, aluminium and silicium, colloids which are obviously able, independently of each other, to m o v e w h e n they are sedimented or transported in moving water. Air is most probably also included between particles of all sizes. In

224 &y*e^g;/i an;? W^a?/[e/*:'^ q/^7?ocA #,y ^OM/!Hfayy Layer ProA/em^

the figure, the filler cement bridge between two quartz grains has been divided into four sectors with R o m a n numbers I to IV. Sectors I and II are considered as normal cements. The idea being reflected here is that this material neither shows any further drying features nor does it swell in the presence of water, but it can be the means of applying capillary forces on the neighbouring grains. In the remaining two sectors III and IV, this is different: III represents a drying gel (gel fragmentation after Her, see above) and IV represents the swelling of gels. These sectors need to be further investigated. But first the question of pore diameters that span three or more orders of magnitude shall be further verified by another direct and two indirect methods. 5.1.1

E x p e n m g n f a / pore ^ M m e f e r ^I'sfn&MfzoH^MMcfz'on

The values referred to here were measured with the help of mercury porosimetry and have been taken from Fitzner (1988). F r o m m a n y rock types measured, an untreated Bunter Sandstone, "Weser rot", was chosen for comparison with the results of this work. It is practical to plot the diameter

0.50

Fig. 5.3 Pore diameter distribution of an untreated Bunter Sandstone, "Weser rot", measured with the mercury porosimetry (after Fitzner, 1988).

Co/:c/M^;o/!^yro/K ?Ae ^4gewg Exper;weM?y q/^^M/:^e/* .San^sfoMe 225

distribution function as a semi-log plot. To achieve the comparison, the division of the abscissa has been changed into a linear one. A s expected, large diameters between the sand grains in the 100 urn range, as well as the diameters in the 10 urn range are not shown, however following diameter ranges of a few micrometers as well as those of a few tenths of a micrometer, are clearly indicated. The most frequent value lies in this material at about 0.5 urn which, according to electron microscopy, is a dimension that lies between the diameters of gel flocks and the primary particles which constitute them. Although this is facinating, it must be remembered that porosity does have its limitations; the lowest values measured by the mercury porosimetry method and depicted in this diagram are about 0.1 urn. Finally, it has to be remembered that the measurements reported by were not conducted on exactly the same material. Despite these shortcomings, the two measuring methods (porosimetry and electronmicroscopy) give results that agree very well. This means that measuring errors probably exist but can only slightly shift the results. This agreement is of great importance for the following discussion.

5.1.2

Dzamefers q/coHozWa/ sc&'wenfsyrom SMspeyisz'ons q/^ J a n ^ s M e masses q/*M!Men&ad!, Ez/eZ (2989)

It is possible that the landslide mass of Murlenbach (Chapter 4), the sediments on the bottom of streams in the Bunter Sandstone in the High Black Forest, Germany, and the reaction products between Bunter Sandstone and water in the laboratory experiment, could all be the result of the same or similar interaction processes between rock and water. It is thus of interest to examine the size of the colloidal particles present in the landslide mass and the pores that develop between them after sedimentation. This has been done by Frey and Butenuth (unpublished and reported here) with the help of Stoke's law (Fig. 5.4). In these experiments, an interesting observation that the suspended material in the sedimentation column separated itself into two clearly divided horizons: an upper, yellow layer, and a lower, orange layer, was made. To obtain definite dimensions for the particle radii, knowledge of the particle density is needed. In this case the density of quartz was assumed, which definitively gives grounds for a certain error; nonetheless, the results are of great interest. The following values were found:

226 Arengt/; an
B 0

10

30

^ 30

orange red Ah = -0.382 + 0.5846 t; vs= 0.6766 x 10*s cms*' I r 1 = 0.995 =0.06766 urns"' = 67.66 nms*' = 676.6 As*' yellow Ah = -2.449 + 0.36461; vg= 0.4220 x 10"S cms"' ]rl = 0.993 =0.0422 urns"' = 42.20 nms*' = 422.0 As"' Fig. 5.4 Sedimentation of colloidal material in the suspension of sliding masses of Miirtenbach, Eifel (after Frey and Butenuth, unpublished).

Derange = 0 3 5 urn

and

DyeHow = 0.28 urn.

These values are in reasonable agreement with the results of the two methods previously discussed, viz. porosimetry and electron microscopy. F r o m this agreement it might also follow that the diameter of the sedimented gel flocks and those in the contact bridges illustrated in Fig. 5.2 hardly differ.

Co/!c/M^;o^yyro/n fA
5.2.3

D M w e i e r s q/*f/!e coHoi'&? sMspewsMn /oad q/'nuers

The observations referred to in this short section are not connected with Bunter Sandstone, but are presented as further examples of colloids in suspension in natural geological systems. They refer to the suspension loads of the upper part of the Rhone and Steinwasser, both glacier run-offs of the Alps. The amazing agreement in the order of magnitude of gel flocks, which is observed in both cases, m a y shed some light on diagenetic processes of rock formation (Butenuth, 1990). To determine the particle diameter distribution of the suspended load, the single particles were measured with the method of equal area circles. In total 7000 particles in electron micrographs (Transmission Electron Microscopy, T E M ) of the same magnification at 6800 : 1 were measured. At this magnification, 1 urn in nature equals to 6.8 m m in the image and the absolute measuring error on the image equals ±0.5 m m , whereas the relative measuring error of the diameter of these particles is about 7 % : 1 u r n ± 0 7 um. In Fig. 5.5, the results are shown graphically. The particle distributions of these two Swiss streams show little difference and look like logarithmic normal distributions, where the most frequent value lies at 0.25 um. In most cases, the form of the particles are platelets which are m a d e up of m u c h smaller particles.

100

Fig. 5.5 Particte diameter distribution of the filtered suspension )oad of the surface waters of Rhone and Steinwasser, Switzerland.

228 AreMg^A ant/ P%a?/:er;Mg q/^/?oc^ as RoMHdary Z,ayer ProA/ewy

The order of magnitude of the particle suspension load found here, a few tenths of a micrometer, is thus in good agreement with the one determined by the sedimentation method from the disintegration of Bunter Sandstone in water and the one determined by porosimetry on intact samples. The origin of the particles of the suspension load of rivers shows, that gel flocks of this order of magnitude can be transported in flowing water, a fact whose significance does not seem to have been noted sufficiently in explanations of diagenetic processes. 5.2.4

Confacf &n'^ges an J f/!^'r Zoa^ & e a r m g cross secfzon

With pore sizes of a few hundreds of a micrometer between the contact bridges and a few tenths of a micrometer within the bridges, different failure mechanisms, at least for grain size packings strengthened by capillary forces, might be operating. If the bridges are separated by large distances their load bearing cross section will be important to the mechanical strength of the whole. A material, m a d e up of two phases under uniaxial loading, can n o w be considered. Principally, strength is defined as follows Ff O f = —

(5.1)

with the already introduced abbreviations; and by the proportional Ff=OfAo.

(5.1a)

Generally it is supposed that Eq. (5.1a) is fulfilled w h e n the material tested is made up of one generally solid phase. Sometimes, the equation was confirmed w h e n the body tested was m a d e up of two or more phases. Such bodies shall be called mechanically homogeneous even though they are heterogeneous in a thermodynamic sense and are composites in the technical sense. M a n y rocks belong into this category. There is thus the important question if oligo- or poly-phase systems can be regarded as mechanically homogeneous. The following model tries to give a preliminary answer. First it should be sufficient to look at a body which is m a d e up of two phases only: cement, index C, and quartz glass, index Q. All samples are considered to be cylindrical, of radius R, diameter D, and length Lo and L respectively.

CoMc/M.HOH.yyro?7i ;Ae ^ge;'Mg E^er;/ne/:^ q/^^MM^e/* &:Haf,sfaHe 229

Undeformable plates for the transmission of forces are attached at the sample ends. All samples are loaded in parallel to their cylinder axis. The following models are differentiated in their spatial phase distribution and the kind of cement they contain. T h e first of these models is m a d e from the densest packing of quartz glass rods of radius r and diameter d. First consider air to be between the rods; the upper part of Fig. 5.6, shows the model from the top and the side. Under the influence of an outer loading the sample of the length Lf will be destroyed over the total cross section by Ff, the force at failure. Here the quotient of air, t^, with cross sectional area of aq for the single rods equals to the porosity of samples Pc- This is 9.3% of the area or volume (lower part of Fig. 5.6). This finding is correct as long as the condition ac « A ^ is fulfilled as the density of packing is smaller at the outer boundary of the total than in its interior. The force to fail N Q rods can then be expected to be " f *" O Q , theoretical N Q a Q - 0*Q theoretics) A.Q.

(5.2)

A s long as air is assumed as the cement, no additional forces occur. Subsequently the measured force at failure is equal to the force at failure that belongs to the load carrying quartz cross sectional area AQ. A s the latter is proportional to the cross sectional area of the samples Ao, Eq. (5.2) can be rewritten as follows Ff = G*Q, theoretical ^ Q A g .

(5.3)

Equation (5.3) describes a proportional between Ff and Ag, but the gradient, the so-called technical strength of the packing of the rods, is smaller than o*Q, theoretica) by the factor ^Q. For Ff, this means Ff - °*Q rod packing A.Q.

(5.4)

The strength of this packing is thus about 1 0 % smaller than the so-called theoretical strength of quartz. But according to experience, the measured strength is m u c h smaller. Thus to adjust this first model to realistic strength values, the carrying cross section must be strongly diminished (Fig. 5.7). The diameter of the quartz glass rods and their density of packing shall remain unchanged at the sample ends, so that the total cross sectional area

230 AreMgfA an;/ H^ea^er/ng q/*^oc^ as BoMn^ary Layer ProA/e?m

Staben

Planar view

Side view

^Dreieck A

Dreieck

^Dreieck

^Dreieck

'

2. r h 2

= \/(2r)^ - r^ = r V 3

° ^^'^

^dreizipflige Flache^ r

^

= "

V? - 3/6.TTr

TT 2V3

Fig. 5.6 Mode!: Densest packing of quartz rods; Cement: air. "Fiachenbruche im Inneren der dichtesten Packung von Staben": area ratios in the interior of the densest packing of rods; "Aufsicht": ptanar view; "Seitenansicht": side view; "Dreizipfetige Fiache": three peaked area.

Co/:c/M.y;'oH.yyro7H ?Ae ^ g e M g Exper/we/?M q/^MM^er .San^fcne 23)

A^o - TT- R

°Q

=*n-^

Q,tragend

Fig. 5.7 Adjusting the mode) of a densest packing of quartz rods, reducing carrying cross sections (aq tragend) by groves cut tike rings round the gtass rods.

232 Areng?/! an;? ^a^Ae/*//?g o^/!oc^ a^ Ron/:^a/y Zayer Pro^/ewj

Ag of the cylindrical sample is not changed. But n o w ring-like groves are introduced into each rod (one in the upper part of Fig. 5.7, several in the lower part of Fig. 5.7). In all these cases the carrying cross sectional are N o quartz rods, and thus the strength of the bundle of rods is the same. Introducing the term "reduction of the cross sectional area" Nnnp^

where p: is the radius of the grooved rods the force at failure Ff can be written as follows O Q , rod packing with reduced cross section ** C Q , theoretical^QVQ-

(5-7)

Equation (5.7) shows the principal importance of the model on which it is based: 7n ?/n.y e^M^^'on, ?Ae 7Macro.s'cop!C6[//y wea-yMre^ -y?re?!g?n q/^ ?ne ?o?a/ .yawp/e, JeferwnHeG? accorcffng fo F;?. (5.7^, M aMr;'oM?e6? /o ^o/ney^c/or^ cnarac^e/*M/ng ^/zg geo/ne^ry a n ^ on ^ne ^^rgng^n q/ ^ne or^Wge^. fne na^Mre q/f/ze.s'e or^Wge^ can n o w oe ^MCM^e^f oa^e<7 on ^Ae /n/cro^co/7/ca//?n^*ng^

The grooves shown in Fig. 5.7 could also be formed in another way, examples are shown on the left in Fig. 5.8. The last of these examples forms a transition to a sphere packing of primitive hexagonal structure with porosity (Pc = 0.395 (see middle and right of Fig. 5.8) which lies in the range of values between 38 and 5 0 % by volume: the range often measured in loose sand grain packings. T h e load carrying cross sectional area and thus the strength of such a quartz rod packing, is equal to zero as long as the cement is pre-supposed to be air. But w h e n the model is changed in such a w a y that air is replaced by either a liquid or a solid cement, which is able to wet the quartz glass spheres first only in the direction of pull, then a strength is again measured. Both models have in c o m m o n the fact that if the load carrying cross sectional area disappears, the strength value of the whole also

CcHC&yt'ofMyrofH fAg y4ge/Mg &per/?Me?!M q/^^M/]fer &:M6&f0Me 233

Primitive hexagonal Elementary cell Plate/Plate

Sphere/Plate

!

Sphere/Sphere

:

i + + + + + +

+ + + +

y

V,.,al = r3 X 4 X T?3

Vo

^ °

= 1 x r^ x 4/3 x TT

' 3-V3

? c = 0.395

Fig. 5.8 M o d e l for the transition: densest rod packing —> sphere packing.

tends towards zero. The following cases will be discussed in which this phenomenon occurs. To do this, use is m a d e of Eq. (5.5). Furthermore the demonstrated findings of dry and swelling gels, as shown in domains III and IV of Fig. 5.2 will be of importance to the discussion. 5.2.5

Loca/ a n ^ h'wc & p g M & ? ? f !fi/?Mc?ices, wMc/i can a^eci f^c carn/wg cross secfzofi o/ san^sfonc sampfes

The load carrying cross section in the models described above, including those also w h e n describing the transition from rods to a primitive, hexagonal packing of spheres, has always been quartz glass, which is largely inert to physical and chemical attack from water and aqueous solutions. This situation completely changes w h e n the carrying cross sectional bridges between the sand grains (as in Fig. 5.2) are made up of different chemical compounds. Such differences are in the foreground within the framework of this piece of work on Bunter Sandstone. These could be

234 Are^g/A an
* capillary interactions between water and colloids in the contact bridges in either the presence or absence of air inclusions; * dissolution or particularly peptisation of gels; * drying of gels; and * swelling, i.e. the volume increase of solid educts w h e n taking up water and producing solid products. Before these effects are discussed in more detail, it is appropriate to note the arguments which support the inclusion of time and locality dependency on these interactions. O n e of the most important arguments for considering local and time dependent material changes in such discussions is the big area of weathering phenomena as observed in buildings and art objects; this is the area where the sanding, sheeting and granular disintegration of rocks belong. The m o d e m technique, developed by Fitzner and his school (1988), of damage mapping, makes these phenomena qualitatively and quantitatively accessible in a visual way. In addition to this there are the long k n o w n forms of natural, predominantly chemical weathering, like desquamation, shell-like weathering, and granular disintegration, which show such processes starting at the outside of the rock and progressing to its inside. These local changes are the result of so-called time reactions. In the first few minutes, they are relatively quick, but get slower with increasing time. Further arguments follow from the results of the ageing experiments described earlier; it has been described that Bunter Sandstone samples partially disintegrate w h e n aged in water. Figure 5.9 shows that the disintegration of the originally irregular samples took place on the outside and that the residual bodies retained a constant form over a long period of time (twenty two weeks). A s in the case of natural weathering, the reactions taking place were dependent on the place within or at the surface of the samples. In opposition to these processes, it should also be remembered that the Trifels castle in the Southern Pfalzer-Wald has survived for nearly 1000 years on its Bunter Sandstone cliff without severe weathering. In the following, only such processes are discussed where changes of rock samples were observed which occurred in time periods that are usual for laboratory experiments. The discussion follows the order in which these processes were listed.

Conc/M.si'oH.Tyro7H fAe ^ge/^g E x p e n w e M ^ q/*3Mn?er A w ^ f o n e 23 5

Fig. 5.9 Formation and appearance of Bunter Sandstone bodies after the ageing of irreguiar initial bodies in water.

co^^ac^ or/Jge^ m e^Aer fAe prejgMce or a^ence o/ a;r wc/M^foM^ The general laws of interaction between fluids and grain packings have been introduced in Chapter 3. In contrast to the situations discussed there, the materials in the contact bridges between sand grains are obviously structurally m u c h more complicated; namely gel flocks with or without air inclusions, in which water or aqueous solutions are included. In Fig. 5.10, some details about the concept of the formation of gel flocks, and gels, from their corresponding sols, as they have been partially derived from literature and particularly from newer observations at springs, rivers and subsurface waters have been collated (Frey e? a/., 1994). All natural waters, including rain water, contain small amounts of dissolved monomeric orthosilicic acid, F^SiC^. Additionally, and in still smaller amounts, the first condensation step, the disilicic acid, H6Si20?, also seems to be always present. Solid sol particles of diameters between 0.001 and 0.01 urn dependent on the p H value and their salt content (Her, 1979) are formed in these low molecular silicic acid solutions by polycondensation. In general, they are considered to be m a d e up of siliceous glass as described by Carman. Under special circumstances, particularly in an alkaline milieu, such glasses are able to further crystallise to cristobaiite or quartz. Sol particles are freely movable. F r o m such sols, spatial networks with big pores are formed by

236 -Areng?/: an(/ ^a;/;er;/!g o/*/?ocA; <M FoM^a'a/y Layer Pro^/ew^

^/^////^z///^' <

sol particles with dispersed

Fig. 5.10 Formation of gel flocks and gels from silicic solutions.

Conc/M.HOfMyw?M 7Ae ^4ge
agglomeration of the previously described spheres (Fig. 5.10) to form gel flocks and/or gels. Gel flocks are wide spread in flowing waters. They are particularly distinguished by their ability to m o v e with the suspended load (Frey ef a/., 1994). Gels are mainly space-filling stationary materials and water is dispersed in silicic acid gels. The state of bonding for this water is complex and lies between the main valence bonded ( O H ) groups at one side and free water at the other side. Putting all the structural problems aside, it remains highly likely that the higher organised forms of gel flocks or silicic acid gels consist of sol particles. The electron microscopic investigations have shown, that the gel particles present were m a d e up of primary particles of 0.1 ]j.m or less. With these observations, a connection to the experiments just described for the formation of gel flocks or gels in natural systems can be m a d e because in the contact bridges of Bunter Sandstone samples, one has to take account of pore diameters d o w n to 0.01 u m . According to the equations given in Sec. 3.1, the m a x i m u m strength values based on capillary forces alone, are then to be expected to reach a few tens of megapascals. This simple estimate is n o w complicated by the following problems: * because pores exist with diameters which range over four orders of magnitude, the effective strength of such bridges will lie in the distribution function of the pores in such bridges; and * the described models will depend on defined geometrical factors even though these are influenced by the above mentioned processes. DM.yo/M?;'oH or/7gp?Ma?;'oH q/*ge/^ Figure 5.10 illustrates processes in the formation of agglomerates from sols, their coagulation and their gel formation. The reverse of these processes, the transition of gel flocks or gels into sols is called peptisation. The direct observations described in Sec. 4.2 which looked at the partial destruction of the sandstone samples have s h o w n that even after the sedimentation of the coarser colloidal particles, the colourless solutions above the sedimented material still exhibits strong Tyndall scattering. These solutions thus include very fine colloidal particles which still have not sedimented. It is suspected that these particles originate from the peptisation of the gels in

238 Arengf/: OH;? ^a^en'/:^ q/*^ocA: ay FoMM^a?y Zayer Pro^/eym

the samples. R e m e m b e r that in Sec. 4.2.2, gel like efflorescences were observed at the surfaces of sediments and residual bodies. Finally, it has to be concluded all experiences with natural waters that true solutions of low molecular silicic acids are present in addition to the colloids in these solutions. It is therefore reasonable to assume that some sort of equilibrium m a y exist between the different forms of silicic acid in the described system: an equilibrium between true solution and silicic acid sol, and between the sol and a form of a gel. This idea is schematically presented in Fig. 5.11. Nonetheless, it has not yet been possible to prove this suspicion, even though it has already been expressed in older literature. Stauff (1960) mentions in a similar context, that the formation of sols to gels can only be thought of if so-called stabilisers are present and continues: "Even though the stabilising factors can be generated by different causes, there can be no doubt about their nature. There are two main factors which have to be m a d e responsible: (1) electrical charge and (2) mechanical hindrance in the boundary layer of the colloidal particles". Whether there is a difference in charge between the inside and outside of the sols on one side, and on the gels on the other side, cannot be decided at present. For this reason, question marks have been added to the arrows of the equilibrium in Fig. 5.11. Should the arrows be correct does not imply that the original sample would be formed again. "Le sourire de Reims" The original would be thus lost, even after such weathering in equilibrium. Whereas the reasons for such processes are not quite clear at present, their existence is out of any question: summarising silicic acid is carried out of the samples and transported from their interior to the surface of sediments and residual bodies. It is probably coming out of the filler cement, which is usually present either in pores or bridges between the grains. This transport of silicic acid from the interior of samples can thus bring about a reduction of the load carrying cross sectional area and thus add to a reduction of effective cohesive forces within the whole. T h e transport out of the bigger pores of the sand grain packing, additionally leads to an increase of the effective porosity and to an increase of pore diameters in the outer parts of the sample, as Fitzner (1988) has demonstrated in m a n y partially weathered building rocks.

CoMc/MMOfMyrom (Ae ^ge/ng Expert/ne/!^ q^FM/:^er .Sant/sfone 239

< True solution of H„SiO,,

Colloidal solution S1O2 - sol

Fig. 5.11 T o the question about equilibria between dissolved materials and colloids.

Fitzner (1988) writes, with regard to sheeting in "Rotem Mainsandstein": "The profile shows a very noticeable increase of the total porosity in the region of the shell and in particular in the zone of disintegration. Within the distribution of pore radii a clear shift to an increase of pores can be noticed in these sandstones". Dry/ng q/'ge/.y The drying of gels is given in the form of a model sketch by Her (1979) in Fig. 4.10. Here a solid plate onto which a gel layer was deposited was assumed, and its surface w a s at the same time its interface towards either air or the o w n fluid vapour respectively; on this matter note the arrows in Fig. 4.11 as well. The free surface in this case does not agree with that

240 Areytg^/t aw
in the Houseknecht model where the upper surface as well as the lower surface is fixed to a grain, so that the exit of water is only possible laterally. This is a difference, in so far as, adsorption forces act from both sides of the drying material in the latter case. Because water normally can only exit laterally, shrinkage which results diminishes the load carrying cross section of the bridges and their strength would decrease. In opposition to this, the water content of the cement decreases continuously with time, causing the strength of the bridges to increase. With further drying, cracks begin to form within the bridges (fragmentation after Her) but the strength of the material in the bridge increases further. It thus follows that the strength of such samples with drying gels should pass through a m a x i m u m . Preliminary experiments to observe this were performed by Butenuth and Kiisters (1997). Brass plates were glued together with silica gel (Fig. 5.12). With an initial area of 4 x 10"^ m^, strength values were measured between 0 to 20 hours, black dots in the plane of the three dimensional diagram, and suggest that so far the ideas described seem to be correct. Once the cracks have expanded through the total cross section of the bridges, the strength reduces to zero (Fig. 5.2, sector III). Nevertheless, it remains uncertain whether the water content of silicic acid is really able to reach zero by simple drying in limited periods of time. 5we//;*Mg, ;'.e. a vo/Mwe ;'Hcre<3.ye q/'-yo/ZJ e^MC^ w%eH /a^t'Mg Mp

The classical cases of this type, e.g. the formation of salthydrates, oxidehydrates, hydroxides etc. have been dealt with in earlier chapters. A basically different form of swelling is found in the system of colloidal fine silicic acid and water. This can be deduced from Fig. 5.13, which was already k n o w n in 1897: had the system in question be heterogeneous and had both substances been in the form of independent pure phases, the vapour pressure of the water taken up would have had to be independent of composition and would have to be practically equal to that of pure water at a given temperature. But it can be seen in Fig. 5.13 that the composition is only fixed w h e n not only the temperature, but also the vapour pressure is independently fixed. This sort of behaviour can happen in several cases; for example

CoHc/H.H(MMyro?H fAe ^ g e w g Rcperzwe/tM q/^FMM^er &tn<%sfoHe 241

Fig. 5.12 Strength of gtued brass plates in dependency of drying duration (Butenuth and Kusters, 1997).

* with true mixtures (solutions); and * w h e n water is adsorbed at a large surface of a highly dispersed phase. In case of true solutions, the value for the pressure should approach p/po= 1 and the water content, ^waten should approach 1. The graph in Fig. 5.13 comes from very high water contents, as might exist in the area between I and II, w h e n first dewatering the material and the

242 Areng?/; an
0.2308

0.0000

0.0

1.0

0.5 ("/"o^O

3 Fig. 5.13 Mass fraction of water in silicic acid gel plotted versus the respective relative water pressure; the measurements were done in the order that is indicated by the arrows (after van Bemmelen, 1897).

pressure condition is about 1. But when reversing the direction of experiment it does not go back to where it came from. Thus in this area the process is irreversible. This m a y be due to a structural change of the high water containing gel, including a volume change. The further course of the graph presented by Van Bemmelen (Fig. 5.13) is reversible but again shows a peculiarity. Between Points II, HI and V, the graph shows a hysteresis; an area in which the points of water uptake, (Points III, V and VI) and those of giving off water are different. This phenomenon is k n o w n with adsorption-, desorption-experiments and always

CoMc/M.HOH.yyro??: fAe ^4gewg Expen/Mew^ q/*RM^^er .Sandyfone 243

occurs in porous materials w h e n pores with extremely small diameters are present in samples. O n the basis of work by Sing and Her (1979) states that: "Starting at zero pressure (A) a typical adsorption isotherm exhibits several stages: first an increasing fraction of surface is covered by adsorbed molecules (B). At a certain point (C) the surface becomes covered with a single layer of molecules. At this stage those pores with diameters only two or three times the diameter of the adsorbate molecules will also be filled. At higher vapour pressures (D) larger pores begin to be filled. W h e n p nears po (E) liquid fills all pores and gives a measure of the pore volume" (Fig. 5.14). It is adsorption with capillary condensation. For the quantitative interpretation of the hysteresis, at least five different models have been developed (see Gregg and Sing, 1967). Few, if any hints can be received from the adsorption properties of silicic acid gels, which allow conclusions on a change of the specific volumes, or the mole volumes, or the partial mole volumes of the partners in the colloidal mixtures to be made. In contrast to this are the phenomena about the adsorption of fluid water and the values given by D'ans-Lax for the swelling of different rocks described in Sec. 2.5. In other

0.0 A

0.5 B

C

1.0 (P/P.) D

E

Fig. 5.14 Adsorption of vapour at fine particeled silicic acid in the presence of capillary condensation (after Her, 1979).

244 .SfreMg;/: aM6? ^ a ^ A e r w ^ o/"^oc^ #s Fot/^^ayy Zayer Pro^/e/m

words the question is: are these special kinds of dispersions which create hydrogels n o w mechanical mixtures or true mixtures in a classical thermodynamic sense? A decision over this question is a precondition for all further discussions over phenomena of dissolution and swelling, as well as a countless number of other problems. For example, preliminary experiments, which originally were started with another aim in mind came to surprising results in the light of this discussion (Butenuth e? a/., 1996). The example from comparing density measurements m a d e on minerals and rocks, with an organic solvent, n-heptane, and aqueous solutions, is given in Sec. 1.2.2. In both cases, that of a dry and that of a swelling cement, the sectors HI and I V of Fig. 5.2, cracks in and through the contact bridges have to be expected and thus a reduction of the load carrying cross sectional area in the sample should result.

5.2 Summarising Remarks in View to the Results of the Ageing Experiments Schwarzl and Staverman (1956) had stated that "If the distribution of microstructure is k n o w n with respect to their strength then, on the basis of this and with the help of the statistical failure theory, macroscopical fracture properties can be deduced also". This sentence provided the principal idea for the investigation of rock samples with regard to the distribution of phases and forces operating between them. A s an experimental method for such investigations, the destruction of rock samples by the action of water and/or aqueous solutions, which acts o n their structures under different external conditions, have been considered. The process of congelifraction, frost/thaw changes and saltwedging etc. have also been used like this for a long time already. This means that the proposal to investigate processes using systems which are initiated by water is a logical expansion of methods of investigation already used. In fact, some experience with such a programme was described in the previous sections. The most important result supported by such models is going to be the ability to disentangle the problem of strength into its geometrical factors and

Conc/M,HOH.?yro?H fAe ^4geMg ExperiMe/!^ o/'RMw^er
properties that might characterise the quality of its load carrying bridges. The task to quantitatively formulate the effects of the single factors is solvable if their qualitative nature, as well as their time dependent changes, is secured. With regard to the strength of Bunter Sandstone, there is little doubt, that it is determined by the capillary forces of aqueous phases in pores of small to very small diameter residing within colloidal boundary layers, which glue the sediment particles together. Thus fluid water has an ambivalent role: it enables processes which lead to the destruction as well as the strengthening of rocks. If these processes lead to rock destruction or to the formation of n e w phases respectively, the weakening and strengthening of rock is only a question of the chemical and physical circumstances which operate. Their experimental and theoretical systemisation is the task of further investigation. Concepts concerning the destruction of rocks which have developed furthest are linked to a volume increase w h e n water passes into a solid product phase under suitable conditions as described in Chapter 4: congelifraction, the formation of salthydrates, and so-called saltwedging etc. result. For information concerning these experimental investigations, their systematic application and their results the reader is referred to Fitzner ef a/. (1991), as well as Fitzner and Basten (1992).

References

Al-Derbi M , 1997. Evidence for the constant nature of tensile strength in Sadus limestone, Saudi Arabia. Ph.D. Thesis, Geology Department, Imperial College, London University. Al-Samahiji D K , 1992. Experimental investigation of the tensile failure of rock in extension. Ph.D. Thesis, Geology Department, Imperial College, London University. Anderegg F O , 1939. Strength of glass fibres. /nJ. Fng. CAew. 31 (3), 2 9 0 298. Anderson TF, 1952. Stereoscopic studies of cells and viruses. FJgc^ Af/cK ^ w e ^ M2?Mra/Mf 86, 91. Anderson JC, Leaver K D , Rawlings R D and Alexander JM, 1990. M3?er;<2/ &?;ence. Chapman and Hall, London. Anonymous, 1967. Bibliographie der Glasoberflache und ihre Behandlung Zusammenstellung fur Symposium der Union Scientifique Continental du Verre U S C V , 6-9 June 1967, Luxembourg. Anonymous, 1993. What is the mechanism of formation of these particles? J. /nf. 3bc. RocAr AfecA. 1 (2), 66. Apelt G, 1934. EinfluB von Belastungsgeschwindigkeit und Verdrehungsverformung auf die ZerreiBfestigkeit von Glasstaben. Zef^cA?: PAy& 91, 336-343. Apuani T, King M S , Butenuth C and de Freitas M H , 1995. Measurements of the relationship between sonic wave velocities and tensile strength in anisotropic rock. Geological Society of London-Borehole Research Group, 19-20 September 1995. Bahat D, 1991. ?ec^oMq/rac^ograp/:y. Springer Verlag, Berlin. Ball A, Bullen FP, Henderson F and Wain H L , 1970. Tensile fracture characteristics of heavily drawn chromium. P M . Mag. 21, 701-712.

246

Re/erencas 247

Bankwitz P and Bankwitz E, 1995. Fractographic features on joints of K T B drill cores Bavaria, Germany. In A m e e n M S (ed), Frac^ograpAy.' Frac^Mre TbpogropAy a^ a 7bo/ f^ Pr^c^Mre Afec/zaMfc^ a/!J 57ras,y y4n^/y^M. Geological Society, Special Publication No. 92. Pages 39-58. Bard JP, 1986. Af;'cro.y?rMC?Mf*ay q/^7gMeoM^ <27!6?A/g?<27Morp/H'c T^ocAy. D. Reidel Publishing Company, Dordrecht. Bares R A , 1985. A conception of a structural theory of composite materials. In Brandt A M and Marshall IH (eds), #r;'??/e Afa^rzx Cowpo^^e^ 7. Elsevier Applied Science, London. Pages 25-48. Barth, Correns and Eskola, 1970. D;e E n M e A M n g ^er Ge^^e/ne. E;/! ZeAr^McA 6?er Pe^roggMe^e. Springer Verlag, Berlin. Blyth F G H and de Freitas M H , 1984. ^ Geo/ogyyor Fngf^ggr^. Edward Arnold. B o m M , 1919. Die Elektronenaffinitat der Halogenatome. ^rA. JeM^cA. PAyj. Cg^. 21/22, 679-685. B o m M and Mayer JE, 1932. Zur Gittertheorie der Ionenkristalle. Z. PAyy. 75, 1-18. Brady B H G and Brown ET, 1993. 7?ocA; AfgcAaw/c^ybr iVHJgT^roMMJAfz'TMHg. Chapman and Hall, London. Braitsch O, 1957. Uber die naturlichen Faser- und Aggregationstypen beim SiC*2, ihre Verwachsungsformen, Richtungsstatistik und Doppelbrechung. Rg^r M;'n. 5, 331-372. Broch E and Franklin JA, 1972. The point load strength test. /nf. J. Z^oc^ AfgcA. M;'7H'Hg ^cf. 9, 669-697. Brook N , 1977. A method of overcoming both shape and size effects in point load testing. Proc. Co^/J Poc^r Ting, University of Newcastle, England. Pages 53-70. Broutman LJ and Krock R H , 1967. Modern Cow^o^;7e Afafg^M^. AddisonWesley Publishing Company, Reading. Bunn C W and Alcock T C , 1945. The texture of polythene. 7r<27M. Faraway 5bc. 41, 317-325. Burland JB, 1989. Preface. Proc. 7^f. C A a & ^ w ^ . , Brighton Polytechnic, 4-7 September 1989, Thomas Telford, London. Pages 1-4. Butenuth C, 1991. Kinetic responses of cleavage faces of calcite to aqueous solutions. Ph.D. Thesis, Imperial College.

248 AreMg?/: anc/ ^o^e/*;'/:g q/*J?oc^ as FoMna'ary Zayer P w A / e m s

Butenuth C, 1997. Comparison of tensile strength values of rocks determined by point load and direct tension tests. 7?ocA: A/ec/z. J?ocAr Fwg. 30 (1), 65-72. Butenuth C and de Freitas M H , 1991. Reindichte von Gesteinen Zeitaufwand und Genauigkeit ihrer pyknometrischen Bestimmung mit n-Heptan als MeBflussigkeit. CeopAy^. P^rq^ L^fv. Ze%?z;'g 4 (3), 121-126. Butenuth C and de Freitas M H , 1995. The character of rock surfaces formed in mode I. In A m e e n M S (ed), FTYZc/cgrap/zy.* 7vYZC?M7*e 7qpogrop/:^ a.y a 7bo/ ;*M .Frac^Mre an^ A r e ^ ^/!<^/y^M. Geological Society, Special Publication, No. 92. Pages 83-96. Butenuth C and Frey M - L , 1995. Geschwindigkeit diagenetischer Wiederverfestigung von Rutschmassen des Buntsandsteins von Miirlenbach, Sudeifel. W?yy. (7ww. 1, 53-54. Butenuth C, de Freitas M H , Kasig W , Butenuth G and Frey M - L , 1992. Chemically induced crack formation, an intermediate stage of weathering, Part I, Survey on principal surface reactions. W ^ . L^ww. Z H 7 4, 261-266. Butenuth C, de Freitas M H , Al-Samahiji D K , Park H-D, Cosgrove J W and Schetelig K, 1993. Observations on the measurement of tensile strength using the hoop test. A??. J. 7?oc^r AfecA. Afz'nfMg & i CeowecA. ^ ^ ^ 30 (2), 157-162. Butenuth C, de Freitas M H , Park H-D, Schetelig K, van Lent P and Grill P, 1994. Observations on the use of the hoop test for measuring the tensile strength of anistropic rock. /H?. J. .RocA; MecA. Af/nz'Hg 5cf. GeomecA. ^ ^ ^ 31 (6), 733-741. Butenuth G, 1990. Physikalisch-chemische Reaktionsbedingungen in hydrogeochemischen Raumen. Beobachtungen an Fliissen, Teil II. ^\yy. (/ww. 3, 141-156. Butenuth G, Butenuth E, Riitten B and Golembowski N , 1977. Zur Charakterisierung warmebehandelter Eisen-III-Oxide Probeneigenschaften und Auflosekinetik bei Raumtemperatur. Fer Z)?. ^feraw. Ce^. 54, 73-78. Butenuth G, Frey M-L, Gotthardt R and Kasig W , 1993a. Entsaurungsvorgange von Carbonatgesteinen. Frzwe^// 46 (2), 272-279. Butenuth G, Frey M-L, Gotthardt R and Kasig W , 1993b. Quicklime properties and limestone genesis. Zement-Kalk-Gips, Nr. 9, E: 268-272.

/?e/erencM 249

Cemic L, 1988. rAerwo^ynaw/Ar /n <7er Af;wgra/ogfg. Springer Verlag, Berlin. Chalk 1989. F w c . 7n;. CAa/Ar^/^., Brighton Polytechnic, 4-7 September 1989, Thomas Telford, London. Clyne T W and Withers PJ, 1993. ^4n 7Hfro<s?Mc?;'oH ?o Me^a/Afa^fx Cbwtpo.nYg.y. Cambridge University Press, Cambridge. Comelissen H A W , Hordijk D A and Reinhardt H W , 1986. Post peak behaviour of light weight versus normal-weight concrete. In Brandt A M and Marshall IH (eds), 57rMc?Mre an<7 CracA: Prop<3g<3;foH fn ^rf?f/e Afa??ix Cowj7oy^e Afa^ena^. Elsevier Applied Science, London. Pages 509525. Cotton F A and Wilkinson G, 1967. y4Morg<3HMc/;g CAgfn/g. Verlag Chemie, Weinheim Bergstrasse. Correns C W , 1968. E;n/M%rMMg fn J;'g Af;7!gra/ogfg. Springer Verlag, Berlin. Cotterill R, 1985. 7%g Caw^rzWgg CM/<7g ^o ^ g A7<2?gr;'<3/ ^ r M . Cambridge University Press, Cambridge. Cumberland DJ and Crawford RJ, 1987. 77;g P a c i n g q/Parfzc/g^. Elsevier, Amsterdam. D'ans-Lax, 1967. 7aycAen&McAyMrCAew;'^erMnJPA^/^er. Springer Verlag, Berlin, de Boer, 1958. The shapes of capillaries. In Everett D H and Stone FS (eds), 7%g ArMc?Mre <2H<7 Pro^gr^e^ q/*PoroM^ A7<3?gr/<2/.y. P w c . 70^A 5yw^<. Co//o^^on 7?g.y. <Soc., University of Bristol, 2 4 - 2 7 March 1958, Butterworths Scientific Publications, London. Pages 68-94. Der GroBe Duden 1963. Etymologie, Bibliographische Institut, Band 7, Mannheim, de Sautels PE, 1974. A7;'ngra/g, Aviy^a/Jg, &g;'Mg. Ott Verlag Thun, Franck'sche Verlagsbuchhandlung, Stuttgart. Dieter G E , 1988. Afgc/tafn'ca/ Afg;a//Mrgy. M c G r a w Hill Book Company. Dunken H, 1990. Glasbearbeitung aus physikalisch-chemischer Sicht. Afz'M. F/. CAgw. G g & DDJ? 37, 998-1000. Elias H-G, 1972. AfaAvofMo/g^M/g. Huthig und W e p f Verlag, Basel. Eucken A, 1944. 7,g%r&Mc/z ^gr CAg/MMcAgn 7%y.y& Fa^^f 77; AfaAirozM^^H^g ^fgr A/a^gWg, Tg^anaf 2.* TfonJgM^/gr^g 7-*Aa^gn MnJTVg/eroggng -$y.y?ew!g. Akademische Verlagsgesellschaft, Becker und Erler, KOM-Ges., Leipzig.

250 AreMg?/; aM^ ^ a ^ A e r M g
Fairhurst C, 1964. O n the validity of the Brazilian test for brittle materials. 7n7. J 7?oc4r AfecA. M ' w m g ^cf. 1, 535-546. Farmer IW, 1983. Fng/Hegrfng FeAaMOMr q/"J?ocAy. Chapman and Hall, London. Fast JD, 1960. Fn^op/e. Philips Technische Bibliothek, D. B. Centen's Uitgesversmaatschappij, Hilversum. Fitzner B, 1970. Die Prufung der Frostbestandigkeit von Naturbausteinen. Dissertation R W T H Aachen. Fitzner, B. 1987. Erfassung und Beurteilung von Verwitterungsschaden an Sandsteinen. "Sonderausgabe Bautenschutz Bausanierung". Fitzner, B. 1988. Untersuchung der Z u s a m m e n h a n g e zwischen d e m Hohlraumgefuge von Natursteinen und physikalischen Verwitterungsvorgangen. Af:^. /nge/!feMrgeo/. 7Vy<3froggo/. 29. Fitzner B and Basten D, 1992. Gesteinsporositat Klassifizierung, meBtechnische Erfassung und Bewertung ihrer Verwitterungssubstanz. Jahresberichte aus d e m Forschungsprogramm Steinzerfall-Steinkonservierung, Band 4; Ein Forderprojekt des Bundesministers fur Forschung und Technologie, Emst und Sohn. Fitzner B and Kownatzki R, 1988. Kartierung und empirische Klassifizierung der Verwitterungsformen und Verwitterungsmerkmale von Natursteinen an geschadigten Bauwerkspartien. Zeitschrift fur Bauinstandhaltung und Denkmalspflege; Sonderheft Bausubstanzerhaltung in der Denkmalpflege, 2. Statusseminar des Bundesministeriums fur Forschung und Technologie, 14-15 Dezember 1988. Fitzner B, Heinrichs K and Kownatzki R, 1991. Verwitterungsverhalten a m Bauwerk und petrographische EigenschaAen verschiedener TriasSandsteine. Jahresberichte aus d e m Forschungsprogramm SteinzerfallSteinkonservierung, Band 3; Ein Forderprojekt des Bundesministers fur Forschung und Technologie, Emst und Sohn. Flexner A , Honigstein A and Pollishook B, 1989. Geology, geotechnical properties and exploitation of chalk in Israel — A n overview. CAa/Ar, P w c . /H;. CA%Mr5y77%7., Brighton, 4-7 September 1989, Thomas Telford, London. Forstner U, 1989. C o H ^ m / H a ^ ^ J f m e H ^ . Lecture Notes in Earth Sciences Vol. 21, Springer Verlag, Berlin.

7?e/ere/!ce^ 2 5 1

Frey M - L , 1995. Z u s a m m e n h a n g e zwischen Branntkalk- und Kalksteineigenschaften. Dissertation R W T H Aachen, Publikation demnachst. Frey M - L , Butenuth C, Kasig W and Butenuth G, 1994. Kolloidale Kieselsauren und die Rolle von Gelflocken als Vehikel fur Umweltgifte. Sediment ologisches Colloquium der R W T H Aachen, Professor A. Muller, 15 July 1994. Frumkin A , 1924. Phasenkrafte an der Trennflache gasformig/flussig Adsorption und Lagerung der Molekiile aliphatischer Verbindungen. Zef^cAr PAyy. CAew. Ill, 190-210. Fuchtbauer, 1988. 5e<%??!e7!?e MM^^e^fweM^ge^^efne. Emst Schweitzerbartsche Verlagsbuchhandlung Nagele und Obermiller, Stuttgart. Ganssen R and Hadrich F, 1965. ^4?/a.y z^r ^oofgM^Mn^e. BI Hochschulatlas, Bibliographisches Institut, Nr. 301a-301e. Gard JA, 1964. A study of the reaction between calcite and sodium fluoride. Proc. j?r6? EM?: 7?eg;oHa/ Co^/J E/ec/roM Mfcrojcopy. Prague, 26 August-3 September 1964, Vol. A. Pages 333-334. Gentier S, Poinclou C and Bertraud L, 1991. Essai de traction sur anneux hoop tensile test application aux schistes ardoisiers. R31682 B R G M , Orleans, France. Glemser O and Riek G, 1958. Zur Bindung des Wassers in den Systemen AI2O3/H2O, S i O z ^ O und Fe203/H20. Zgf^cAr ,4norg. ^//gew. CAew. 297, 175-188. Glocker R, 1971. Afa^erfa/prM/MMg w:Y ^on^ge^j^raA/en 5. y4M/7age. Springer Verlag, Berlin. Gooding EJ, 1932. Investigation on the tensile strength of glass. J. 5bc. C / a ^ 7ecA. 16, 145-170. Greenwood N N , 1973. /o?:e7!%7*M?<2//e, Gf^er<3fe/g^e MnJM'cA^yo'cA/owg^McAe Pe^z'MJMMgen. Verlag Chemie. Griffith A A , 1920. The phenomena of rupture and flow in solids. PA;7. 7/YWM. L o w & w A221, 163-198. Griffith A A , 1924. The theory of rupture. In Biezens C and Burgers J (eds), Pwc. V^/n;. Congr. /3tpp/. AfecA., Delft, 1924. Pages 55-63. Grill PR, 1993. Ermittlung der Zugfestigkeit an Gesteinen der kontintentalen Tiefbohrung Metabasiten mit Hilfe des hoop tests. Unveroffentlichte

252 -Sfrengf/:
Diplomarbeit, Lehrstuhl fur Ingenieur- und Hydrogeologie der Rheinisch Westfalischen Technischen Hochschule Aachen. HaaseR, 1956. rAerwoay^aw/^ JgrAfMcApAayen. Springer Verlag, Berlin. Haber F, 1919. Betrachtungen zur Theorie der Warmetonung. %r%. D?. /%yj& Cej. 21/22, 750-768. Halpin JC, 1984. P n w e r OM Co7M/?o.y;7e Afa^erM/y.* ^^a/y^M. Technomic Publishing Company, Inc. Lancaster, Pennsylvania. Hann J and Siiring R, 1940. In Bluthgen J (ed), ZeAr^Mc/z Jer ^//ggme;7:eM Geogro^Afe. Fancf 2. yU/gewefHe A^/;wageograpA/e. Walter de Gruyter Verlag, Berlin. Pages 1966. Hatch F H , Wells A K and Wells M K , 1961. P^w/ogy q/*^e TgweoM^ ^ocA^. Thomas Murley and Co. Hauffe K. and Morrison SR, 1974. ^ayo/p^'on. Ff^e Ffn^ArMwg //: ^;'e P w N e w e Jer ^ayo^p^oM. Walter de Gruyter Verlag, Berlin. Hawkes I, Mellor M and Gariepy S, 1973. Deformation of rocks under direct tension. 7n?. J. J?ccA AfgcA. A/;'7HHg 5c;*. 10, 493-507. Heitfeld K H , 1970. Aufgaben und Zukunftsaussichten der Ingenieurgeologie. Ceo/. A/;'H. 10, 103-112. Hinz W , 1970. 57/;Aa;e ^ . 1. V E B Verlag fur Bauwesen Berlin. Hirschwald J, 1912. /fan^McA <^er ^M^gcA^McAgM Gay?e;'7MprM/MMg. Verlag von Gebriider Bomtraeger. Hobbs B E , Means W D and Williams PF, 1976. ^4n 6*W/;*7!e o/*&rMC/Mra/ Geo/ogy. John Wiley and Sons, N e w York. Holleman AF, 1961. In Richter F (ed), Ze/;r&Mc/; a^r Orga^Mc/ze/! CAew/e. Walter de Gruyter Verlag, Berlin. H o m b o g e n E, 1979. tf&rAyzv/Te. Springer Verlag, Berlin. Houseknecht O W (see Winkler E M , 1994). Howell FC, 1969. Far/y A/an. Time-Life International, Nederland N.V. Hudson JA, 1989. J?ocA AfecAafncy PrfMc^/ay ;'n Fng//!eer;7?g Prac/;ce. CIRIA, Butterworths, London. Hull D, 1992. ^M /M^o^MC^'on ^o Cowpoy;Ye A/a?er/a/.y. Cambridge University Press, Cambridge. Huntington H B , 1958. The elastic constants of crystals. In Seitz F and Turnbull D (eds), .So/fJ 5Ya?g P/zyyfcy. ^Jva^cej ;M 7?gyearc/z a^a* y4/y/fca^'oM& Vol. 7. Academic Press, London. Pages 213-351.

J?e/erencas 253

Hurtig E, 1963. Untersuchungen iiber die Fortpflanzungsgeschwindigkeit von p-Wellen in Sedimentgesteinen. Geophysik und Geologie, Folge 5. Hiittig G, 1941. Die Frittungsvorgange innerhalb von Pulvem, welche aus einer einzigen Komponente bestehen.- Ein Beitrag zur Aufklarung der MetaH-Keramik und Oxyd-Keramik. A^o//of
254 &reMg?/: an6? ^ a ^ e r / ^ q/^J?oc^ <M 5oM^<^a/y Zayer Pw^/em^

Lange K R , 1965. The characterisation of molecular water on silica surfaces. J. Co//o;a*. &?;'. 20, 231-240. Leggewie R, Ftichtbauer H and El-Najjar R, 1977. Zur Bilanz des Buntsandsteinbeckens KomgroBenverteilung und Gesteinsbruchstiicke. C^o/. 7?MH&c/;aM 66, 551-577. Lehnartz E, 1952. CAewMcAe PAyyfo/ogfe. Springer Verlag, Berlin. Leitner M , 1955. Youngs modulus of crystalline unstretched rubber. 7ra?M. Fara&xy ^oc. 51, 1015. Leopold L B , W o l m a n M G and Miller JP, 1964. F/Mvfa/ Procay.s'g.y z*M Ggo/MOTpAo/ogy. W . H. Freeman, San Francisco. Lind I, 1993. Porosity heterogeneity in chalk. Eighth Annual Meeting Aachen Sedimentology Group, 7-9 October 1993. Lundin ST, 1959. Studies of three axial white ware bodies. Diss. Royal Inst. Techn. Stockholm. Pages 197. Madelung E, 1918. Das elektrische Feld in Systemen von regelmaBig angeordneten Punktladungen. ZefAycA?: PAy.M'Ar. 19, 524-533. M a n n U, 1993. Characterisation of pore space in sedimentary rocks; recent considerations. Eighth Annual Meeting Aachen Sedimentology Group, 7-9 October 1993. Marc R and Jung H, 1930. D;e PAyyfAra/McAe CAeone m z'Arer ^nwena'MMg a ^ ProMe/M^ aer Af;'7!^ra/og;'e, Pe^rograpAfg MH^ Cec/ogfe. Verlag Gustav Fischer, Jena. Mathews F L and Rawlings R D , 1994. Co7Mpo.y;7e A/a^er/a/^.' Fng/ngeTiHg a^a* ^cz'g^ce. Chapman and Hall, London. M c M a h o n CJ Jr, Vitek V and Kameda J, 1976. Mechanics and mechanisms of intergranular fracture. In Chell G G (ed), Deve/opwew^ ;'M FracfMre AfecAaTHcy 2. Applied Science Publishers, London. Pages 193-246. Meyer K, 1968. PAy^/^a/McA-cAe/MMcAe &M^a//ograp/zfe. V E B Verlag fur Grundstoffindustrie. M o h r H, 1971. LeAr^McA a*er P/7a^zenpAyyfo/ogfe. Springer Verlag, Berlin. Muller H, 1924. Die ZerreiBfestigkeit des Steinsalzes. PAyy. ZefAycA?: 25, 223-224. Muller K H H , 1931. Temperaturabhangigkeit von Glasstaben. Ze/^cA^ PAyy. 69, 431-457. Nadai A, 1950. 7%eory q/*P/ow an^ Prac^Mre o/'&
^e/ereMcar 255

Neville A M , 1993. Properf/as q/*CoHcre;g. Longman. Newitt M C and Conway-Jones JM, 1958. A contribution to the theory and practice of granulation. 7^^^^. ZtyfM. CAem. P?!g. 36, 422-440. N y e JF, 1985. PA^fca/Proper^gy q/Cry^^^. Oxford Science Publications. Oberlies F and Dietzel A, 1957. Uber die Struktur des Quarzglases. C/ay^gcAn. Rgr. 30 (2), 37-42. Ondracek G, 1986. Microstructure-thermomechanical-property correlations of two-phase and porous materials. Maf. CAgw. PAy^. 15, 281-313. Orowan E, 1945. Notch brittleness and the strength of metals. In Stanworth JE (ed), PAy.MC<2/ Propgr^g^ q/ C/a^. Clarendon Press, Oxford. 89, 165-215. Orr W J C , 1939. Calculations of the adsorption behaviour of argon on alkali halide crystals. 7?an^. Para^ay ^oc. 35, 1247. Otto W H , 1955. Relationship of tensile strength of glass fibres to diameter. J. ^ w . Cera/mc ^oc. 38 (3), 122-124. Park H-D, 1995. Tensile rock strength and related behaviour revealed by hoop tests. Ph.D. Thesis, University of London, Imperial College. Passas N , 1997. Petrophysical studies of Penrith sandstone pertinent to its behaviour in extension. Ph.D. Thesis, London University. Passas N , Butenuth C and de Freitas M H , 1996. Technical Note: Rock porosity determinations using particle densities measured in different fluids. Cgo/ggA. 7 e ^ n g J . 19 (3), 310-315. Pauling L, 1964. D;g A7a?Mr Jgr CAewMcAen Rfn^MHg. Verlag Chemie, Weinheim BergstraSe. Pittman E D , 1972. Diagenesis of quartz and sandstones as revealed by scanning electron microscopy. J. ^gJ/wen^. Pg?ro/. 42, 507-519. Pohl R W , 1947. Fz'n/MArMMg ;'n Jz'g AfgcA<2M;'%, ^^MJ^'Ar MH6f PHarmg/gArg. 10. Aufl, Springer Verlag, Berlin. Powell PC, 1994. FngrnggfiHg w;7A FYArg-Po/y/wgr Law/Ha^gy. Chapman and Hall, London. Preston R D , 1958. The ascent of sap and the movement of soluble carbohydrates in stems of higher plants. In Everett D H and Stone F S (eds), 7%g ArMCfMre aM6? Propgrf;'g.r q/PoroMj Ma/grM^. Proc. 70?A 6yw!p. Co//o^^on P.e& 5bc, University of Bristol, 24-27 March 1958, Butterworths Scientific Publications, London. Pages 366-382.

256 &rengf/: an
Price JN, 1960. The compressive strength of coal measure rocks. Co//z'ery Fng. Pages 283-292. Price JN, 1966. PaM/? a/2 J ^b;'y!^ Deve/qpwe^^ ;*M RW^/e a n ^ ^ewz-^W^/g 7?ocAr. Pergamon Press, Oxford. Price J N and Cosgrove J W , 1991. ^Ha/y^M q/* Ceo/ogfca/ ArMC^Mre^. Cambridge University Press, Cambridge. Reifenberg A and Buckwold SJ, 1954. The release of silica from soils by the orthoposphate anion. J. .SozV. 5W. 5, 106-115. Reuss A , 1929. Berechnung der FlieBgrenze von Mischkristallen auf Grund der Plastizitatsbedingungen fur Einkristalle. Zg;'^cA^ ^ngewanJ/e ATa/A. AfecA. 9, 49-58. Roulin-Moloney A C , 1988. Frac?og7*apAy anaf Faf/Mre AfecAa^MW^ q/ Po/ywer^ aw^/ Cowpo^f/e^. Elsevier Applied Science, London. R u m p f H, 1961. Strength of granules and agglomerates. In Knepper W A (ed), ^gg/owera^'oM. Interscience, N e w York. Rutter E H , 1972. The influence of interstitial water on the behaviour of calcite rocks. 7ec/oHqpAy.y;*c.y 14, 13-33. Salmang H and Scholze H, 1982. T&rawMTc. 7e;7 7. ^//gewetne GrMHaVagen MM6? wfc/:^ge E;'ge^^cAa/?e/!. Springer Verlag, Berlin. Schon J, 1983. Pe;rqpAy.n7<. Ferdinand Enke Verlag, Stuttgart. Schmid E and Boas W , 1935. Avi^a/^/a^zf/a'?, Afi;Y ^o^a*erer ^erMcAyfcA^gMng Jer Me^a//e. Verlag von Julius Springer, Berlin. Schmid E and Boas W , 1968. PAM?;'c;Yy q/*Crny?a/.y. Chapman and Hall Ltd. Schmid E and Vaupel O, 1929. Festigkeit und Plastizitat von Steinsalzkristallen. Z e ^ c A ^ PAy& 56, 308-329. Shurkov S, 1932. Uber den EinfluB von adsorbierten Oberflachenschichten auf die Festigkeit feiner Quarzfaden. PAy^. Zef/^cAr. ^owfe^M^fo^ 1 (1), 123-131. Schiitze M , 1991. Die Korrosionsschutzwirkung oxidischer Deckschichten unter thermisch-chemisch-mechanischer Werkstoffbeanspruchung. In Petzow F and Jeglitsch F (eds), A7a^er/a/^MMa'/fc/!-7gc/:MMcAg 7?e;7:e, Ran J 10. Gebruder Bomtrager, Berlin. Schwarzl F and Staverman AJ, 1956. Bruchspannung und Festigkeit von Hochpolymeren. Drittes Kapitel in "Die Physik der Hochpolymeren", Vierter Band: Theorie und molekulare Deutung technologischer

7?e/erencas 257

Eigenschaften von Hochpolymeren Werkstoffen, Stuart H A (ed). Springer Verlag, Berlin. Sella A and Voigt W , 1893. Beobachtungen uber die Zerreissungsfestigkeit von Steinsalz. ^4w!. PAy.y. Pages 636-656. Smekal A, 1936. The nature of the mechanical strength of glass. J. 5bc. G/a.M 7ec/:. 20, 432-448. Sohncke L, 1869. Uber die Cohasion des Steinsalzes in krystallographisch verschiedenen Richtungen. ^M?!. PAy^. C/zew. 17, 177-200. Steeb S, 1968. ^c/:we/zyf?-M^MreM. Springer Tracts in M o d e m Physics, Vol. 47. Springer Verlag, Berlin. Stranski IN, 1942. Uber die ReiRfestigkeit abgeloster Steinsalzkristalle. #eK D?. CAew. Ge^. 75, 1667-1672. Strunz H, 1982. AffMera/ogMcAe 7b&e//gn. Akademische Verlagsgesellschaft, Guest und Portig, Leipzig. The Reader's Digest Oxford Wordfinder, 1993. Clarendon Press, Oxford. Tullis J and Yund R, 1992. The brittle-ductile transition in feldspar aggregates: A n experimental study. In Evans B and W o n g T-F (eds), FatJ? an;/ 7r6!H.sjPorf Properffas q/' 7?oc%5. Academic Press, London. Pages 89-117. Ulich H and Jost W , 1966. ^*M/*zay LeAr&McA Jer PAyn^a/McAeH CAewfe. Dr. Dietrich Steinkopf Verlag, Darmstadt. Underwood E E , 1970. gM<2M?;'?af;'ve Aereo/ogy. Addison Wesley, Reading. Unger K K , 1979. PoroM^ 57/;ca. Journal of Chromatography Library, Vol. 16. Elsevier, Amsterdam, van Bemmelen JM, 1897. Die Absorption, das Wasser in den Kolloiden, besonders in d e m Gel der Kieselsaure. Ze/^cAr ylMorg y4//gew. CAew. 13, 233-384. van Bemmelen JM, 1899. Die Absorption. IV Abhandlung. Die Isotherme des kolloidalen Eisenoxyds bei 15°. Ze;'?.$cAf: y4?!org. ^4//gem. CAew. 20, 185-211. von Borries B and Kausche G A , 1940. Ubermikroskopische Bestimmung der Form und GroBenverteilung von Goldkolloiden. A^o//. Zef^cA^ 90, 132-141. Vangerow EF, 1973. GrMnafn/? 6?er P^Mo^^o/ogze. Teubners Studienbiicher der Biologie.

258 Areng?/? < w ^ f%a?/;er;'ng q/*7?ocA a.y ^oM^^a/y Zqye/- ProA/ew^

van Lent P, 1993. Bestimmung von Zugfestigkeiten an Paragneisen der Kontinentalen Tiefbohrung mit Hilfe des Hoop Tests. Unveroffentlichte Diplomarbeit, Lehrstuhl ftir Ingenieur- und Hydrogeologie der Rheinisch Westfalischen Technischen Hochschule Aachen, van Vlack L H , 1989. F/gwen^ q/"Ma^grM/ .Science a^of F ^ g m e e ^ g . Sixth Edition, Addison Wesley, Reading. Vogel W , 1993. G/a-y/eA/e/: Springer Verlag, Berlin. Voight W , 1928. Ze/zr&McA a*gr AJ/*M^a//pAy^/Ar. Teubner Verlag, Leipzig. Vollertsen F and Vogler S, 1989. f%rA3?q/?Sw.s.yefMc/!6[/?eM MMJAf/Aro^rM^Mr Carl Hanser Verlag, Miinchen. von Engelhardt W and Haussiihl S, 1965. Festigkeit und Harte von Kristallen. For^cA^ Mfne/i 42, 5-49. von Engelhardt W and Stoffler D, 1970. A/oH6?gayfefHe fw Af/Aw-s^op, D/a ^er/e 1.' C / ^ e ^ Herausgegeben von den Optischen Werken Carl Zeiss, Oberkochem/Wurthemberg, VergroBerung: - 50 : 1. Walenkow N and Porai-Koschiz E, 1936. X-ray investigation of the glassy state. Ze^cA?: ATr^a//. 95, 195-229. Wedler G, 1970. ,4%*.wfp?;*oH. Chemische Taschenbiicher, Bd. 9, Verlag Chemie, Weinheim. Wefers K, 1966a. Z u m System FezOs-HzO. 1. Teil. R
7?e/erencay 259

X u S, de Freitas M H and Clarke B, 1988. The measurement of tensile strength of rock. Proc. in?. 5bc. ^?oc% AfecA. 5ywp., Rock Mechanics and Power Plants, Madrid. Pages 125-132. Zachariasen W H , 1933. Die Struktur der Glaser. G7a.y?ec/;. .Ber 11, 120123. Zemann J, 1966. &M?a//cAe/M;e. Sammlung Goschen, Bd. Nr. 1220/1220a.

Index

A

axes systems

abrasive strength 145 acoustic microscope 88 adhesion tension 171 adsorption 82, 83, 139, 147, 242 heat 139 adsorption-desorption behaviour 43 ageing 210, 220, 234, 244 agglomeration 237 aggregate(s) 208 granular 185 mono-mineralic 22 tensile strength 174 aggregation 1 states of aggregation 1 air inclusions 235 aluminium colloids 201, 207, 223 alumogel 211 amorphous 15 amphibolite 64 anhydrite 187, 188 anion structure 85 anisotropy xxiv, 15, 18 macroscopic one-dimensional 18 applied geology 39 aqueous solutions 235 area cross sectional 179, 229, 232, 238, 244 geometrical cross sectional 68 reaction 42, 82 internal surface 42, 43

B

261

2

bauxite 207 body initial 235 residual 238 bond(s) spring 112 strength 164 weak 161 bonding 26 forces 158 types 26 boundary layers xxiv, 2, 162, 165, 238 boundary reactions 84, 88 breakage phenomena 130 bridge strength 232, 240 brutto analysis inorganic chemical 195 Bunter sandstone 49, 50, 64, 165, 184, 185, 189, 190, 194, 201, 210, 220, 224, 225, 228, 233, 237, 245

c calcite 80, 88 capillary 183 attraction 167 condensation 243 depression 174, 177 effects 167

262 &re/:g^ anaf ^a;Aer//?g q/'J?oc^ 6M BoM7!^ary Layer Pro^/ew^

forces 174, 184, 224, 228, 237, 2 interactions 235 cement(s) 184, 222, 223, 229, 240 chemical mixture of 48 contact 221, 222 dry 244 filler 221, 222, 224 liquid 45, 48 normal 224 oxidic 51 silicatic 51 solid 45 swelling 244 water containing 159, 171 chain sodium halogenide 128 chalk 2 change in volume 145 changed surface structures 84 chemical bonds strength 159 chemical compounds 233 chemical reactions 82, 90, 184, 191 chemical weathering 80, 82, 234 of rock 82 chemically strengthened glass 131, 132 chemisorption 83 cleavage method 142 closed system 187, 188 coagulation 237 cohesion xxi, 158 reduction of 155, 158 cohesive forces xxiv, 76, 80, 220 effective 238 reduction of cohesive forces 238 colloidal boundary layers 245 colloidal compounds 199, 201, 213 aluminium 223 iron 223 silicium 223 colloidal dimensions xxiv, 34, 86, 94 colloidal dissolution load 86

colloidal fine compounds 201 colloidal fine particles 208 colloidal mixtures 243 colloidal particles 237, 238 colloidal phases 196 colloidal sediments 225 colloidal solutions 184, 189, 194, 198, 202 colloids xxi, 199, 200, 223, 235 aluminium 201 colourless 197 iron 201 red 194, 197 yellow 194, 197 comminuting processes 144 composite materials 15, 18, 27 definition 10 strengthening 17 composite(s) xxiv, 1-3, 8, 10, 15, 26 man-made 8, 18, 27 metal-matrix 17 natural composites 2, 27 properties of composites 3 composite systems 25 composition 2, 3 compounds aluminium 201, 207 aluminium colloids 201, 207 chemical 201, 207 iron 223 silicium 223 silicium colloids 223 compressive pressure 171 compressive strength 18, 39, 56 concepts xxiv, 1 condensation 211, 235 congelifraction 80, 244 isotrope 81 construction 3 contact bridges 226, 228, 235, 237, 244 models 229

/H6?ex 263

Coulomb law 97 Chemically induced crack formation 9( crack initiation 128 cross section(s) 233 cross sectional area 57, 150, 179, 229 232, 238, 244 crystal(s) 2, 18, 20, 22, 144, 149 aggregate 20 structure 159 crystallites 160 crystallographic directions 155

D damage mapping 234 definition(s) rock strength xxiv strength xxiv, 57 deformation(s) 142 plastic 144 density bulk 37 measurements 38, 39, 244 O - H groups 139 particles 37, 38 water molecules 219 description sample environment 30 technical use of rock 33 desorption 242 destruction of rock xx, xxi, 87, 245 dielectric 164, 167 direct tension 150 test 70, 73 directional dependence 2 disintegration 228, 239 granular 88, 234 rocks 194, 234 dislocation(s) 144 dispersion 15, 94, 188

dissolution 237 heat 144 processes 201 distribution(s) forces 244 particles 31 phases 244 pore diameters 224 drying of gels 224, 239 dust line 222

E E D X analysis 198, 207 effective porosity 238 effluorences 196, 198, 238 elastic modules 22, 24, 132, 136, 142 elasticity 20, 22 elongation 108, 110, 111, 116 energy interfacial 139 internal 144 surface 136, 139, 141, 169 energy conversion(s) 104, 125 chain of ions 105 single ion pair 105 three dimensional ion crystal 104 energy-distance curve 84, 99 energy-distance functions 96, 99, 122, 125 environment 188 equilibrium 238 equilibrium distance 98, 101, 124 experimental procedures 60 acoustic microscopy 88 cleavage method 142 direct tension test 70 electron microscopy 237 hoop test 60 surface energy 139

264 ArengfA aw^ ^ayAerwg q/*7?ocA ;n 3oM/:^ar^ Aoygr ProA/ewy

F fabric models of fabric 3 failure 48 mechanisms 59 surface 48, 179 feldspar 84 fibre 8 filler cement 221, 222, 234 flocculates 96 flocks 96 gel 199, 204, 222, 225-228, 235, 237 fluids(s) surface tension 182 force at failure 63, 150, 164, 179 force(s) intermolecular 165 force-distance-function(s) 96, 99, 125 force-elongation curve composed chain(s) 108 uniform chain(s) 108 formation ion chains 101 ion pairs 96 three dimensional crystal(s) 96 formula conversion 211 fractography 76 fracture fracture processes xxiv fracture surface 49 frost/thaw 244

G gel(s) 51, 64, 94, 139, 184, 201, 222, 235, 237, 238, 242 drying of gel(s) 224, 239 flocks 199,204,222,225-228,235, 237 natural 211

silica 96, 199, 210, 228, 235, 237 swelling of 80, 224 gel-like layer 86, 139 geological material(s) 5, 18 geology 3 applied 39 geometrical cross sectional area 68 glass 128, 131 glass thread(s) 59, 75, 151 chemically strengthened 131, 132 juvenile 131, 132 physically strengthened 131,132 strength 59 surface strengthened 132 gneiss 64 goethite 208 grain packings 165, 228, 238 water strengthened 174, 177 grain(s) quartz 49, 80, 186, 205, 207, 210, 222, 224 sand 222, 232, 235 granite(s) 56, 64, 76, 155 granular aggregate(s) 185 granular disintegration 88, 234 granule(s) 178 green pellet(s) 177 Griffith 127, 128 cracks 146 gypsum 187, 188

H hematite 208 heterogeneities 131 structural 131 heterogeneous reactions xxi, 82 homogeneous material 128 mechanically 228 homogeneously composed body 57 Hooke's law 108

M a r 265 hoop test 60, 68 experimental set-up hydrogel 48 hydrogen bond(s) strength 159 hydrolyosis 211

60

I inclusion(s) air 235 increase strength 133 inhomogeneities 130, 145, 160, 161 initial body 235 initial cross sectional area 150 inorganic chemical brutto analysis interaction(s) capillary 235 interface 2, 83 interfacial energy 136, 139 interfacial tension 149 intergranular materials 45 properties 51 intergrowth 208 intermolecular forces 165 internal energy 144 internal surface area 42, 43 ion chain 101, 112 colloids 200, 222 exchanger 84 pair 96, 101, 114, 115 isolated system 187 isothermal volume change 215 isotrope congelifraction 81 isotropic 2, 15 isotropic strength 165

J juvenile glass threads

131, 132

L landslide 50, 185, 225 lateritic soils 193, 210 lateritic weathering 191, 200, 207, 210 lattice theory 92, 141 energy 124 salt 118 layer(s) gel-like 139 leached 85 pre-stressed 133 leached layer(s) 85 limestone 39, 56, 64, 155 liquid bridges 174, 177 load suspended 227, 237

M macroscopic properties 17 Madelung constant 124, 126 magnitudes of specific surface energies 139 man-made composite(s) 8, 18 mapping damage 234 marble 64, 75 material bridge 222 material change(s) local 234 time dependent 234 material science 2, 3, 18 purposes 18 material strengthening 15 material(s) dispersion 15 fibre 15 geological 5-8 intergranular 45, 51 man-made 5-8, 18 non-crystalline 144 partially-crystalline 144

266 ArengfA a n ^ ^o/Aer;/!g q/^/?oeA ay RoMnaary Zayer Pro6/emy

particle 15 properties 3, 30 measuring techniques xxiv destructive xxiv non-destructive xxiv volume(s) 210, 218 mechanical mixtures xxi, 1, 2, 32, 188, 189, 207, 244 mechanically homogeneous 228 melting heat 141 mercury porosimetry 224, 225 methods to determine rock strength 60 microstructure 17, 130, 244 migration of colloids 196,201 mineral 22 surface quality 84 mixed phase 1, 94 mixture(s) 48, 88 mechanical 188, 189, 207, 243 real 189 true 243 model(s) 233 Bunter sandstone 220 contact bridges 229 modulus elasticity 132, 136 shear 22 molar volume 185, 187, 189, 243 partial 189, 243 mono-mineralic aggregate(s) 22 mono-mineralic rock 22

N natural gel(s) 211 natural system(s) 237 natural water(s) 235, 238 non-polar fluids/solvents 147 normal cement 224 notch system(s) 52, 53, 130, 158 nucleation of cracks 82

o O - H group density 139 open system 187, 188 overgrowth 207, 221, 222

P packings grains 238 partial mole volume 189, 243 particle(s) 15, 37, 204, 222 colloidal 237, 238 density 36 diameter 17, 188 sand sized 36 peak stress 44 pellets 174 green 177 Penrith sandstone 48, 64, 76 peptisation 184, 237 phase(s) 1, 2, 31, 187, 188 composition 2, 3 distribution 3 mixed phase 1, 94 pure 1, 92, 93 water rich 165 phase change(s) 144 physical weathering 80 physically strengthened glass 131, 132 physico-chemical elements of strength xxiv reactions 80 physisorption 83 plastic deformation 144 point load test 70 Poisson constant 22 Poisson ratio 25 polycondensation 235 polyethylene strength 159 polymer 85 pore air 218

/wfex 267 pore diameter 222 distribution 224 pore form(s) 43, 44 pore shape(s) 36, 42 porosimetry 226, 228 mercury 224, 225 porosity 32, 33, 36, 37, 39, 44, 48, 92, 177, 218, 222, 229 effective 238 reduced porosity 48 total 239 pre-stressed layer(s) 133 predictive geotechnics xx pure phase 1, 92, 93

Q quartz 33, 146, 235 crystals 33, 49 grain(s) 49, 80, 186, 205, 207, 210, 222, 224 theoretical strength 229 quasi-closed system 212

R reaction(s) area 42, 82 chemical 184, 191 physical 184 space(s) 90 real mixture(s) 189 reduction cohesion 158 strength 130, 158 region(s) 1, 2 in space 33 residual body 235, 238 resolidification 50, 51 river(s) 227, 228, 235

rock(s) 1, 2, 8, 15, 82, 84, 87, 186, 194, 243-245 disintegration 194, 228, 234, 239 properties 3 salt 118, 150, 164 salt lattice 126 silicate 87 strength xxiv, 1 strengthening 245 weathering processes 191

s salt (rock salt) lattice 118, 126 salt wedging 80, 244 sample surface 52, 53 sand grain(s) 222, 233, 235 sand size particle(s) 36 sandstone 1, 34, 39, 45, 48, 53, 56, 76, 92, 155, 156, 165, 171, 184, 186, 210 13, 219, 221, 222, 233, 239 Bunter sandstone 49, 50, 64, 165, 184, 189, 190, 194, 201, 220, 224, 225, 228, 233, 237, 245 disintegration 205, 228 Eifel 48 Penrith 48 saprolite 88 sediment(s) 207 colloidal 225 sedimentary rocks 207 selection of stones 3 selective destruction of bonds in rock 80 rock structure 80 rocks 88 structures 81 shear modulus 22 shrinkage 186

268 Areng?/) aH6? ^ a ^ e n / ! g q/^7!oc^ ay FoM/:^a/y Z,ayer P w ^ / e w y

silica gel(s) 96, 199, 210 sol(s) 96, 199, 210 silicate rock(s) 87 silicic acid 86, 201, 238, 240 chain(s) 120 silicium colloids 223 soil(s) 200 lateritic 193, 210 sol(s) 51, 94, 184, 204, 210, 235, 238 sol particle(s) 202, 204, 235 aggregate 96 solution(s) 94, 188, 198, 207, 241 aqueous 235 colloidal 189, 194, 202 real 218 true 188, 189, 194, 241 spatial distribution of 2, 90, 221 components 27 crystallographic axis system(s) 33, 221 forces 90 interaction of forces 27, 90 phase(s) 220, 229 regions 33 water in grain packings 221 specific free surface energy 146, 147 specific surface energy 138, 139 specific volume 243 spectrum of bonding forces 158 spring(s) 235 spring constant 108, 110, 115, 116 stiffness 22 strain 8, 110, 111, 116, 120, 144 strain at failure 164 strength xxiii, xxiv, 1-3, 32, 36, 40, 44, 52, 53, 59, 67, 88, 127, 130, 150, 155, 159, 222, 244 abrasive 145 aggregate 182 bond(s) 26, 164

bridge(s) 232, 240 chemical bond(s) 159 crystallographic direction(s) 155, 159 definition 57 experimental values 158 glass threads 59 Griffith 127, 128 hydrogen bond(s) 158 increase 133 influence of water 67 isotropic 165 liquid(s) 169 Orowan 127, 128 packing 228 pure phases 92 reduction 130 rock 44, 53, 88 silicatic chain(s) 124 tensile 33 test xx theoretical 117, 127, 131 van der Waals bond(s) 159 water 159 strength measuring techniques xxii, xxiv, 1 change(s) 88, 150 compressive 18, 39, 56 destructive xxii, xxiv non-destructive xxii, xxiv tensile 33 unconfined compressive 18 strengthening of fluid(s) 182 grain packings xxiv, 165, 174, 177, 229 water 174, 183 stress 150 concentration 128 zones 132 distribution 26

M e * 269 pattern 45 peak(s) 44 structural heterogeneities 131 subsurface water(s) 235 supermolecular structure(s) 132 surface energy 136, 139, 141, 169 layer 133, 139, 146 quality of minerals 84 reaction(s) 82, 88 strengthened glass 132 tension 167, 177, 182 of fluids 182 term(s) 188 suspended load 227, 228, 235 suspension(s) 207, 225 swelling 184, 186, 210, 219, 240, 243 isotropic 186 of gel(s) 80, 224 of rock 186 system 186-188, 213, 216, 218, 219 change 186 closed 187 definition 187 isolated 187 natural 237 open 187, 188 quasi-closed 212

quartz 229 salt 116 technical strength 57, 229 theoretical strength 117,127,131 values 165, 220 water 159, 165 wood 159 texture 2 thermal volume expansion coefficient 216 three dimensional distribution of crystallographic axes system 220 phases 220 total porosity 239 true solution(s) (mixture(s)) 188, 189, 194, 241 Tyndall scattering 194, 237 types of bonding 26 testing 60

T

van der Waals bonds 159 strength 158, 162 volume change 145, 184, 210, 211, 213, 215, 216, 218, 242 change isothermal 215 decrease 188, 211 increase 184, 185, 188, 211, 240, 245 molar 185, 187, 243 partial mole 243 property 20, 188

take up of water 184,240 technical properties 17 technical rock science xix, xx technical tensile strength xxiii, 59, 229 temperature coefficient 216 tensile strength 33, 52, 57, 92, 159, 174 aggregate 174 comparison of 70 failure 60 measurement 53 polyethylene 159

u uncompensated force fields 83, 138 unconiined compressive strength 18, 60 uniaxial tension 22 uptake of water 90,96,210

V

270 ArengfA an
specific 243 total 212, 218, 219 volume expansion coefficient thermal 216

w water natural 235, 238 subsurface 235 surface tension 167, 177 take-up 184, 210, 240 tensile strength 159, 165

weakbond(s) 161 weathered layer(s) 139 weathering 222, 234, 238 chemical 80,184,234 lateritic 191, 200, 207, 210 physical 80, 184 processes xxiv, 184, 191, 207 reaction(s) 43, 84, 90 wetting 170 wood strength 159

STRENGTH AND WEATHERtNG OF ROCK AS BOUNDARY LAYER PROBLEMS by Christine Butenuth (7mper/a/ Co//ege, L7K) This book is addressed mainly to younger geoscientists and students of geologically related subjects, It discusses: (1) the concepts, definitions and experience of strength, particularly rock strength, with application of experimental techniques; (2) the physical-chemical aspects of the strength of pure phases; (3) strengthening of grain packings by "intermolecular forces"; (4) the behaviour of Buntersandstone samples underwater and lessons for understanding weathering processes; (5) deductions concerning the distribution of substances and forces in Buntersandstone samples from observing the response of samples underwater.

The urgency of environmental studies has been the main driving force for this book. The discussion of single problems is wide-ranging, particularly for chemical and physical topics, so as to enhance the reader's understanding. The book is m o r e a research account than a textbook. Thus, n o "completed", well-defined subject area is presented; on the contrary, m a n y questions are raised which should form the basis for future research. T h e book has been written to stimulate lively debate.

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ISBN 1-86094-24/ '

Imperial College Pr M/MW./'cp/'ess.ca^

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