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Fragmentary clay — a difficult waste material
Engineering Geology 51 (1998) 77–88
Fragmentary clay — a difficult waste material Jaroslav Feda * Institute of Theoretical and Applied Mechanics, Prosecka´ 76, 190 00 Prague, Czech Republic Received 11 February 1998; accepted 27 June 1998
Abstract The clayey cover of the coal seam in Northwestern Bohemia is excavated in the form of a fragmentary and blocky clay, and then deposited into large landfills >100 m high. Due to overburden pressure and increased moisture content, the clay changes from a granular to a saturated cohesive material. This transition is modelled by laboratory experiments considering the effects of stress, water and time. They provide characteristic values of the compression index, shear parameters and the coefficient of secondary compression and their variation. Due to high porosity, the source of a metastable structure, the material is collapsible. Bifurcation collapse and breakdown are differentiated. The latter acquired the form of a diffusion process. The prospects of the mathematical modelling of the collapsible behaviour are outlined. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Collapse; Diffusion; Fragmentary clay; Metastable structure; State transition
1. Introduction Thirty meter thick seams of brown coal are mined at depths of 150 m by open-cast mining methods in Northwestern Bohemia. The layer above the coal consisting of Neogene clays and claystones is excavated, removed by rail and belt transport and placed into landfills >100 m high (Fig. 1). The total annual production of this waste amounts to 150–200 mil. m3. Tips are either internal (within the already exploited mines) or external (outside them on a virgin ground ). They occupy an area of ca 100 km2. Landslides are frequent at their periphery. In addition to the stability phenomena, one has to study the (considerable) landfills’ settlement in order to exploit * Corresponding author. Tel: +42 2 882334; Fax: +42 2 884634; e-mail: [email protected]
their crowns for building activity and/or for municipal solid waste disposal. Poorly compacted fills of other fragmentary cohesive geomaterials may pose similar problems. The originally fragmentary material (Fig. 2) consisting of blocks of up to 0.5 m in size is gradually decomposed, when exposed to rainwater, overburden pressure and time, into a cohesive water saturated material. Intact clay possesses a porosity of ca 40%, a liquid limit of 73–92%, a plasticity index of 50–60% and natural water content ranging from 25 to 33%. The clays are water saturated, of illitic–kaolinitic nature (sometimes with a montmorillonitic admixture), with 50% of particles <0.002 mm and 95%<0.063 mm. The admixture of carbonates may amount to 13%. In addition, gypsum and iron sulphates were found, the ignition loss may increase to 16.6%. Scanning electron
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Fig. 1. Radovesice landfill—southern boundary (capacity of 109 m3, max height of 200 m)—Dykast (1993).
ˇ SA–fragmentary clay in situ (Dykast, 1993). Fig. 2. Internal landfill of VC
microscopy (SEM ) was carried out parallel and perpendicular to layering. One observed a laminated and open fabric with a parallel arrangement of particles and small traces of cementation. The result of the hydrometer analysis is sensitive to the initial water content of the specimen (wet specimens are more dispersed ). Two porosities of the clayey mass may be
defined: intragranular (n , e ), that is, that of the i i intact clayey fragments, and intergranular (n , e ) e e between the clayey fragments. Both are interrelated by Eqs. (1) and (2): n =n (1−n )+n t i e e
(1)
e =e (1+e )+e t i e e
(2)
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when n , e are the total porosity and void ratio, t t respectively. Since n amounts to ca 40% (e =2/3) i i and if n (e ) is ca 66±5% (2±0.5), then the mean t t n (e ) is ca 43% (0.8). The material is thus a e e typical double-porosity geomaterial (measured by mercury porosimetry, the internal pore size is ca 0.01 mm, the external pore size of fragmentary clay may be of the order of 0.5 mm). High total porosity results from the double-porosity nature of the fragmentary clay and is the source of some spectacular features of its behaviour.
2. Possible structural mechanisms Structural mechanisms causing the transition from the ‘granular’ to ‘cohesive’ behaviour may be represented by: $ Crushing of fragments. Crushing is a familiar process with brittle grains (Feda, 1982). The compression curve of a material undergoing grain crushing has a characteristic garlandlike form1. Since the wet clayey fragments are relatively weak, this cataclastic deformation takes place more often with wet than with dry clay. $ Ductile fragments are not crushed but squashed. This means that such fragments are not disintegrated but compressed and deformed in a ductile manner. Wet fragmentary clay is predisposed to this type of deformation. Reduction of pore sizes accompanying squashing results in strain hardening. $ Fragment rearrangement. Mutual sliding and rotation of fragments leads to densification and strain hardening. $ Contact bonding. Fragments of wet clay stick one to another and to the metal (e.g. to the oedometer’s wall ). Sticking develops at about an oedometer load of s≥50 kPa. Bonds between fragments reduce the compression until they are broken. They thus hinder the rearrangement. 1By a ‘garland’ a series of half-wreaths is understood, mutually joined and hanging often on walls as a decoration. With garlandlike compression, the compression curve consists of a series of segments (see curves Nos 3 and 4 in Fig. 7). It is well observed, for example, with compression of sand grains undergoing crushing [see e.g. Feda (1982), p. 244].
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As a product of elementary mechanisms, the following complex structural processes take place: $ Diffusion. Originally the term has been used for the description of the heat conduction phenomena. The process of heat conduction may be generalized to cover all processes spreading from one source and governed by the same partial differential equation of the parabolic type. Its graphical image if plotted to the semilogarithmic scale is an S-curve. In soil mechanics, primary consolidation is a well known diffusion process. $ Percolation. If a system consists of two components (say clay and sand ) participating on the system’s response then their proportion governs the form of the response. This may range from that typical of one component (e.g. from ‘sandy’ behaviour) to that of the other one (e.g. to ‘clayey’ behaviour). Double-porosity geomaterials due to the high porosity, triggering different structural mechanisms, are prone to develop the percolation phenomena. $ Normalized behaviour. This occurs if a set of constitutive functions (describing seemingly various processes) may be reduced to a single one in a dimensionless form. The processes characterized by those functions are governed by the same set and interrelations of dimensionless arguments and, consequently, the processes they describe are therefore similar. Thus, for example, linear Mohr–Coulomb envelope confirms identical, stress-independent micromechanisms of strength mobilization, contrary to nonlinear envelope indicating the occurrence of stressdependent (e.g. cataclastic) phenomena. $ Collapse. Collapse is a sudden change of the mechanical behaviour caused by transforming the soil from one structural configuration to another one. It is visualized by a stepwise deformation (e.g. in the case of a load-controlled compression) or by a stress step (when strain-rate controlled compression is applied ). Collapse is to be expected with soils of high porosity because of the metastable structure. Fragmentary clay belongs to this class of geomaterials. Collapse may take on two forms: breakdown (the total change of the structure; such is the collapse due to inundation, hydrocol-
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lapse) or bifurcation (‘branching-off ’) collapse [a jumplike change of a constitutive parameter, for example, of the deformation modulus or angle of internal friction owing to the kink of a constitutive function like with a bilinear shear envelope or compressive curve; it indicates a change of the deformation mechanism, well observed, for example, with triaxial specimens reinforced with plastic strips — see, for example, Atmatzidis and Athanasopoulos (1994)].
3. Shear resistance In order to study the behaviour of a fragmentary clay, a series of laboratory experiments was undertaken modelling the fragmentary nature of the original clayey waste by a fragmentary clay with fragment sizes 1–2, 2–4 and 4–8 mm. The material was tested (oven) dry, wet (at the natural water content) and inundated (saturated) in the triaxial (undrained tests), oedometer and shear box (drained tests) apparatuses. Loose and dense specimens were prepared (mean total porosities of ca 71 and 62%). The total porosity seemed to play a secondary role in the mechanical behaviour with respect to other factors, similarly like the fragment size (with a few exceptions). Fig. 3 depicts the Mohr–Coulomb envelopes of
the shear box test results2 (dry, wet and inundated specimens; normal stress stepwise increased until the final value when the constant rate of shearing was applied) with fragment sizes 1–2, 2–4 and 4–8 mm in the common normal stress range (s= 0–300 kPa). All of them are bilinear with a characteristic kink at s =100–200 kPa. The principal crit factor governing the shear behaviour is the water content. The fragment size seems to be, especially with inundated specimens, of no importance. Experiments with different deformation rates and applying the common or multi-stage method yielded the same results. Triaxial CSL (critical state line) drawn by a broken line coincides with the shear box results but its kink is shifted to ca 250 kPa (Fig. 4). The occurrence of bilinearity is ascribed to the transformation of the structure with the elevating load. For s
Fig. 4. CSL of saturated fragmentary clay of different fragments’ sizes (Boha´cˇ, 1996).
Fig. 3. Mohr–Coulomb envelopes of fragmented clay—low stress level, shear box tests+CSL (triaxial tests).
2Though aware of the Hill alternative of the failure locus [see e.g. Feda (1982)], the author adheres to the Mohr–Coulomb failure envelope conventionally used in soil mechanics and defined, for example, by Lambe and Whitman (1969) or Parry (1995).
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recoverable after the test from the oedometer ring in a fragmentary form. This indicates the origin of ‘squashing’, contrary to the dry clay recoverable after being loaded at least up to s=1 MPa. Cohesive behaviour of wet clay is mainly the result of squashing while that of dry specimens is to be ascribed to grain interlocking and crushing. Fig. 5 presents the extent of crushing (as determined by sieving) for a single-step oedometer loading of dry specimens. The extent of crushing increases as s increases (and is much higher in a shear box than in an oedometer). Bi- (or multi-) linear strength envelope is not specific for a fragmentary clay. It is typical for fiber reinforced sand, for some soils like calcarenites, cloddy compacted clay etc. It results from a sudden change of the structural mechanism at some critical stress level (e.g. in the fiber reinforced sand the transition from slip to yield or stretch of reinforcing fibers). Within both intervals of behaviour, ss , the structural microcrit crit mechanism is not affected by the stress level, the behaviour is physically isomorphous (effective w∞= const.). In the opposite case, when the transition from one structural mechanism to another one is gradual, nonlinearity would result.
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While Fig. 3 deals with the low stress level (s≤300 kPa), Fig. 6 extends the stress range to s=2 MPa. Trilinear strength envelopes may be recorded (dry and wet specimens), in addition to a bilinear one (inundated specimens). While the simplicity of the latter one (with the single s #150 kPa) reflects the simplest structure availcrit able, that is, that of a saturated clay, the most complex one (series of s #100–200, 500 and crit 1000 kPa) corresponds to the most complex structure of wet clay where bonding due to the contact sticking plays an important role. Kinking indicates the bifurcation collapses resulting perhaps from the percolation effects. At high stress level, wet and inundated clay show roughly parallel shear strength envelopes. This phenomenon can be interpreted as the effect of the high degree of saturation of wet specimens due to the compression by high s-values. The results of the isotropically consolidated triaxial drained and undrained tests of the same water saturated material (2–4 mm) are also depicted in Fig. 6. The triaxial envelope either agrees with the shear box tests (inundated specimens) or, at least, triaxial and shear box w∞ are similar (dry specimens). Fragment crushing with
Fig. 5. The amount of a fragment’s crushing (oedometer, shear box) of originally 2–4 mm dry fragmentary clay; residuum (% of the original weight) on the sieves with labelled openings after the load application or shear strength mobilization.
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Fig. 6. Mohr–Coulomb envelopes of fragmentary clay—high stress level [shear box and triaxial data by Pachta and Krˇ´ızˇova´ (1996)]; CID, CIUP, drained and undrained triaxial tests.
triaxial specimens may be expected to be smaller than in the shear box (and similar to oedometer tests in Fig. 5). This may be the explanation of the somewhat lower strength of dry specimens. One may conclude that fragmentary clay generally possesses a multilinear strength envelope. This has serious consequences for the stability analysis. One must either differentiate the values of the strength parameters according to the stress level in question or match the original multilinear envelope by a nonlinear function. Multilinearity (the effect of a series of bifurcation collapses) manifests sudden stress-bound structural changes (debonding, crushing, slip etc.). Parametric study of the (usually ‘boot shaped’) slope failures indicated the relevant shear stress parameter to be w∞=16° and c∞=40 kPa (Stanek, 1992). This corresponds with the strength parameters of inundated specimens in Fig. 3.
4. Compression Different structural mechanisms, differentiated by the stress level and the water content in question, may be expected when compressing the fragmentary clay. Fig. 7 shows some recorded compression curves plotted to the arithmetic and
logarithmic stress scales. No. 5 belongs to the natural intact clay with reversible and linear compression up to 1 MPa. No. 2 represents the bilinear compression curve typical for dry specimens ( less frequent and often multilinear with wet specimens). The compression is elastoplastic (ca 60% of the deformation represented by No. 2 compression curve is irreversible). If fragment crushing prevails, a garlandlike compression curve results (No. 3, dry specimens; No. 4, wet specimen desiccating during compression). Inundated specimens (No. 1) are compressed linearly in a semilogarithmic plot, like reconstituted clays. A generally applicable model of the compression curve has an S-shaped form in a semilogarithmic plot. This may be expressed by a trilinear function and each branch characterized by its midpoint — Fig. 8 (dotted line indicates one linear interval and its midpoint). The most frequent value of the (oedometric) compression index C =0.35 c (C =De/D log s). This roughly corresponds to the c value of the compression index l=0.1 (for triaxial K tests of water saturated specimens; in those 0 tests, the value of K was found to be ca 0.55 to 0 0.75). There is a group of specimens with the second maximum C =1. Those are very loose wet c specimens. The great dispersion of C reveals that c the specimens’ structure is rather sensitive to their
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Fig. 7. Series of oedometric curves of fragmentary clay of various granulometry and water content (arithmetic and logarithmic plots).
preparation which need not be perfectly under control (due to the many influencing factors). The S-shaped compression curve suggests that the process of compression is actually a diffusion process (i.e. spreading of the plastic, collapse, compression from the loaded boundary). There is some evidence that diffusion processes really take place in the field. Vaughan (1995) observed: ‘…collapse… started in the top of the fill, and took about one week to affect the bottom of the fill, a rate of penetration of the collapse front of about
2×10−5 m s−1. Collapse compression was up to 6%, and settlement of the 1.5 m thick fill was about 0.4 m’. In the discussion by Skempton and Vaughan (1994) one may read: ‘An interesting feature of the collapse recorded at gauge CS3 was that it occurred as a wave starting from the top of the fill, taking about two weeks to reach the bottom … it seems that the collapse was caused either by a very small inflow of water, or by some other mechanism …’. Water inundation of dry or wet specimens
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Fig. 8. Oedometric compression index C versus axial stress c relationship.
resulted in a hydrocollapse (step-like change in the void ratio De or compression strain De). Fig. 9 shows some of the results. One may see that: $ There is no effect of the fragment size, specimens of 1–2 mm size showing the same hydrocollapse like those of 4–8 mm size. $ Dry specimens are more prone to collapse. The respective curve in Fig. 9 is shifted upwards and to the right. This may be explained by the effect of the stormy decay of dry fragments when inundated and by the effect of small densification of dry material for the given s-value. The magnitude of hydrocollapse depends, among
Fig. 9. Hydrocollapse (collapse after the specimen’s inundation) of initially dry and wet specimens of two fragment’s sizes [data from Pachta and Krˇ´ızˇova´ (1996)]; De, De, void ratio and strain decrements or increments.
others, on the porosity of soil. This is reduced by a stepwise raising load. After some critical pressure no collapse takes place ( Fig. 9 — for wet specimens this pressure is ca 1.5–2 MPa). Since the compressibility of dry specimens is about one-third of that of wet specimens, their critical pressure is much higher. Since hydrocollapse represents a specific form of soil compression — the effect of one state parameter, load, is replaced with hydrocollapse by another state parameter, water content — one expects that the process of diffusion (spreading of the collapse of structure) will take place even in this case. Fig. 10 confirms this expectation (S-shaped curve; similar results were found by the author with collapsible loess). Hydrocollapse is the most conspicuous form of collapse. The so-called immediate collapse is another form recorded with fragmentary clay. It is the compression of the specimen (mostly wet; with dry specimens less compression was recorded) within the first 5 min after the load application. A bell-shaped curve may describe this type of collapse (for stepwise loading) similarly like in Fig. 9 in the case of a hydrocollapse. However, it is of bifurcation (strain hardening by multilinear logarithmic creep) and not diffusive in nature. Another type of collapse is represented by timedependent instabilities. These may be classified as diffusion processes ( Fig. 11) and bifurcation col-
Fig. 10. Time-dependent oedometric compression of an inundated specimen of fragmentary clay [originally wet specimen s=60 kPa, 4–8 mm — Za´lesky´ et al. (1996)].
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Fig. 11. Time-dependent oedometric compression of the diffusive character of two wet specimens (1–2 mm, 4–8 mm) at s=952 kPa.
lapses ( Fig. 12). A typical garlandlike form appears (Fig. 13) if fragment crushing intervenes. Due to the bifurcation collapse, the value of the coefficient of secondary compression C (= a
Fig. 12. Secondary compression of a dry specimen of 2–4 mm fragmentary clay loaded in an oedometer at 952 kPa. (a) Secondary compression, experimental data; (b) hyperbolic transformation.
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De/D log t) may be considerably changed, similarly like the deformation modulus in Fig. 7 (No. 2). Fig. 11 presents two examples of the time-dependent collapses taking the form of diffusion processes. With such diffusion collapses, one may calculate the coefficient of diffusion c as for the k coefficient of primary consolidation. c is typically k one to two orders of magnitude smaller. Time-dependent bifurcation collapses may be treated like the multilinear strength envelope: either ‘per partes’ (each linear part separately) or transforming the linear constitutive function into a smooth one. Fig. 12b shows, as an example, the latter procedure — a successful replacement of the bifurcated logarithmic creep curve by a smooth curve of a hyperbolic creep.
5. Laboratory versus field behaviour To be sure that phenomena observed in the laboratory are also reproduced in nature, laboratory studies should be combined with field studies. The important property of wet fragmentary clay, its contact sticking, can adversely affect open coal mining technology. Sticking increases in the field as per the proportion of montmorillonite (and, consequently, with an increase of the index of plasticity) and considerably aggravates both rail and belt transport of the clayey waste. Contact bonding of the fragmentary clay as found in the laboratory thus corresponds to the experience in the field. In the laboratory, a small size oedometer (10 cm diameter, 19 mm height) and shear boxes (6×6×2.5 cm) were used. If the size of the specimen is increased for about one order of magnitude (oedometer 78.5 cm in diameter and specimen’s height of 26.2 cm), and the tested fragmentary clay almost retains its in situ granulometry, the same phenomena as in the laboratory are observed (Dykast, 1993): $ E of ca 7 MPa in the range of s=0.3–1 MPa oed (Fig. 7, No. 2); $ time-dependent diffusion is recorded as in Fig. 11 ( Fig. 14); and $ the diffusion nature of the hydrocollapse is confirmed to be as in Fig. 10 (see Fig. 15).
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Fig. 13. Secondary compression of a wet specimen 2–4 mm of a fragmentary clay loaded in an oedometer at 339.3 kPa.
The same S-shaped compression curve as in the laboratory has been constructed from the record of the time-dependent settlement of the Erveˇnice corridor [80–130 m high landfill, see Vlk in Dykast (1993)]. Time-dependent records of the vertical movements by individual settlement gauges of this corridor displayed similar bifurcation points as for the laboratory records (Dykast, 1993) — Fig. 16. The annual settlement variation in the longitudinal cross-section of the Velebudice landfill
Fig. 14. Recorded S-shaped mean time-dependent settlement curve of the Erveˇnice corridor (80–130 m high landfill ) after Vlk (Dykast, 1993).
Fig. 15. Time-dependent compression recorded with the natural wet fragmentary clay inundated at 1 MPa in a large oedometer.
Fig. 16. Time-dependent vertical displacements of measuring points of the Erveˇnice corridor [in Dykast (1993)].
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(35–60 m high) falls within 150–380 mm (after 12 years have elapsed), that is, the settlement dispersion is considerable ( Fig. 17). The Erveˇnice corridor depicts a similar excessive variation of settlement (15–150 cm, Fig. 18), partly generated by the gradual placement of the clayey waste into the embankment. Such a large dispersion agrees with the strong variation in the laboratory C c values (Fig. 8). Thus the principal phenomena observed with tests in the laboratory investigation are confirmed
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either on a considerably larger scale or directly in the field (time-dependent bifurcation, diffusion, extreme variation of compression, sticking).
6. Conclusions Fragmentary clay (i.e. a geomaterial consisting of clayey fragments of up to 50 cm in size) is a typical double-porosity geomaterial. Though its total porosity amounts to ca 70%, the porosity of
Fig. 17. Maximum and minimum settlement of the Velebudice landfill [after Dykast (1993)].
Fig. 18. Variation of the settlement of the Erveˇnice corridor along its axis over different years (Dykast, 1993).
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individual (water saturated) fragments is equal to ca 40%. The material represents the waste (an overburden of the open-cast brown coal seam) which is tipped, as a rule, to a height of >100 m. The behaviour of the clay fragment depends mainly on the state parameters: stress ( load ); water content; and time. The material changes, in the course of time and due to the exposure to the climatic conditions, from a ‘granular’ to ‘cohesive’ clayey mass. The latter, which is water saturated and if combined with the high pore water pressures, affects adversely the slope stability (creating a kind of a non-bearing core within the landfill ). In addition, a large settlement is produced by the gradual structural changes of the material. For reclamation purposes, one has to be able to predict the stability and deformation of landfills. Generally, multi-linear strength envelopes and compression curves have been found. Points of singularity (marking the so-called bifurcation collapses) designate the transition from one structural system to another. Diffusion processes may be found with load-dependent compression, compression due to inundation and time-dependent compression. They may be also observed in the field. While the angle of internal fiction (depending on the water content, which is the principal state parameter) varies within 15–53°, the mean C (in c the oedometer) is equal to 0.35, the mean l (in the triaxial K -test) is 0.1. C varies in the range of 0 a 0.1–45%. The extreme variability in the mechanical parameters can be explained by the sensitivity of the fragmentary clay to numerous structural factors, namely the extremely high porosity of the material in question. Attention is drawn to the collapsible behaviour. In addition to the well understood hydrocollapse (drop of the suction to zero), there are many collapses of the breakdown nature taking on the form of diffusion processes (hydrocollapse due to particle disintegration, time-dependent collapse). Further on, bifurcation collapses occur (immediate collapse, multilinearity of some compression curves, of strength envelopes, of secondary compression curves).
Although all this behaviour is emphasized owing to the double-porosity nature of the investigated geomaterial it is believed that the same phenomena occur with many (problematic) soils. With the shift of the attention of soil mechanics from the artificially prepared to the natural soils, those phenomena should be constitutively modelled. This presently occurs on a rather insufficient scale.
Acknowledgment This research was supported by the Grant Agency of the Academy of Sciences of the Czech Republic (Grant No. A2071803) which is gratefully acknowledged.
References Atmatzidis, D.K., Athanasopoulos, G.A., 1994. Sand–geotextile friction angle by conventional shear testing. In: Proc. XIII. ICSMFE, New Delhi, vol. 3, pp. 1273–1278. Boha´cˇ, J., 1996. Compressibility and Strength of Granulated Clay. Research Report of the Faculty of Science of the Charles University, Prague (in Czech). Dykast, I., 1993. Properties of landfills in SHR as foundation media. PhD. Thesis, Civil Engineering Faculty of the Czech Technical University, Prague (in Czech). Feda, J., 1982. Mechanics of Particulate Materials — The Principles. Elsevier–Academia, Amsterdam–Prague. Lambe, W.T., Whitman, R.V., 1969. Soil Mechanics. Wiley, Chichester. Pachta, V., Krˇ´ızˇova´, H., 1996. Geotechnical Laboratory Tests. Research Report of SG-Geotechnika, Prague (in Czech). Parry, R.H.G., 1995. Mohr Circles, Stress Paths and Geotechnics. E. and F.N. Spon. Skempton, A.W., Vaughan, P.R., 1994. The failure of Carsington dam — discussion. Ge´otechnique 45 (4), 734 Stanek, J., 1992. Stability of High Landfills of Clayey Soils. Research Report of the Research Institute of Brown Coal Most (in Czech). Vaughan, P.R., 1995. Criteria for the use of weak and weathered rocks for embankment fill and its compaction control. In: Proc. XIII. ICSMFE, vol. VI, pp. 195–206. Za´lesky´, J., Kos, J., Sala´k, J., 1996. Deformation and strength of unsaturated soils. Research Report of the Civil Engineering Faculty of the Czech Technical University, Prague (in Czech).
Fragmentary clay — a difficult waste material Jaroslav Feda * Institute of Theoretical and Applied Mechanics, Prosecka´ 76, 190 00 Prague, Czech Republic Received 11 February 1998; accepted 27 June 1998
Abstract The clayey cover of the coal seam in Northwestern Bohemia is excavated in the form of a fragmentary and blocky clay, and then deposited into large landfills >100 m high. Due to overburden pressure and increased moisture content, the clay changes from a granular to a saturated cohesive material. This transition is modelled by laboratory experiments considering the effects of stress, water and time. They provide characteristic values of the compression index, shear parameters and the coefficient of secondary compression and their variation. Due to high porosity, the source of a metastable structure, the material is collapsible. Bifurcation collapse and breakdown are differentiated. The latter acquired the form of a diffusion process. The prospects of the mathematical modelling of the collapsible behaviour are outlined. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Collapse; Diffusion; Fragmentary clay; Metastable structure; State transition
1. Introduction Thirty meter thick seams of brown coal are mined at depths of 150 m by open-cast mining methods in Northwestern Bohemia. The layer above the coal consisting of Neogene clays and claystones is excavated, removed by rail and belt transport and placed into landfills >100 m high (Fig. 1). The total annual production of this waste amounts to 150–200 mil. m3. Tips are either internal (within the already exploited mines) or external (outside them on a virgin ground ). They occupy an area of ca 100 km2. Landslides are frequent at their periphery. In addition to the stability phenomena, one has to study the (considerable) landfills’ settlement in order to exploit * Corresponding author. Tel: +42 2 882334; Fax: +42 2 884634; e-mail: [email protected]
their crowns for building activity and/or for municipal solid waste disposal. Poorly compacted fills of other fragmentary cohesive geomaterials may pose similar problems. The originally fragmentary material (Fig. 2) consisting of blocks of up to 0.5 m in size is gradually decomposed, when exposed to rainwater, overburden pressure and time, into a cohesive water saturated material. Intact clay possesses a porosity of ca 40%, a liquid limit of 73–92%, a plasticity index of 50–60% and natural water content ranging from 25 to 33%. The clays are water saturated, of illitic–kaolinitic nature (sometimes with a montmorillonitic admixture), with 50% of particles <0.002 mm and 95%<0.063 mm. The admixture of carbonates may amount to 13%. In addition, gypsum and iron sulphates were found, the ignition loss may increase to 16.6%. Scanning electron
0013-7952/98/$ – see front matter © 1998 Elsevier Science B.V. All rights reserved. PII: S0 0 1 3 -7 9 5 2 ( 9 8 ) 0 0 03 7 - 4
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Fig. 1. Radovesice landfill—southern boundary (capacity of 109 m3, max height of 200 m)—Dykast (1993).
ˇ SA–fragmentary clay in situ (Dykast, 1993). Fig. 2. Internal landfill of VC
microscopy (SEM ) was carried out parallel and perpendicular to layering. One observed a laminated and open fabric with a parallel arrangement of particles and small traces of cementation. The result of the hydrometer analysis is sensitive to the initial water content of the specimen (wet specimens are more dispersed ). Two porosities of the clayey mass may be
defined: intragranular (n , e ), that is, that of the i i intact clayey fragments, and intergranular (n , e ) e e between the clayey fragments. Both are interrelated by Eqs. (1) and (2): n =n (1−n )+n t i e e
(1)
e =e (1+e )+e t i e e
(2)
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when n , e are the total porosity and void ratio, t t respectively. Since n amounts to ca 40% (e =2/3) i i and if n (e ) is ca 66±5% (2±0.5), then the mean t t n (e ) is ca 43% (0.8). The material is thus a e e typical double-porosity geomaterial (measured by mercury porosimetry, the internal pore size is ca 0.01 mm, the external pore size of fragmentary clay may be of the order of 0.5 mm). High total porosity results from the double-porosity nature of the fragmentary clay and is the source of some spectacular features of its behaviour.
2. Possible structural mechanisms Structural mechanisms causing the transition from the ‘granular’ to ‘cohesive’ behaviour may be represented by: $ Crushing of fragments. Crushing is a familiar process with brittle grains (Feda, 1982). The compression curve of a material undergoing grain crushing has a characteristic garlandlike form1. Since the wet clayey fragments are relatively weak, this cataclastic deformation takes place more often with wet than with dry clay. $ Ductile fragments are not crushed but squashed. This means that such fragments are not disintegrated but compressed and deformed in a ductile manner. Wet fragmentary clay is predisposed to this type of deformation. Reduction of pore sizes accompanying squashing results in strain hardening. $ Fragment rearrangement. Mutual sliding and rotation of fragments leads to densification and strain hardening. $ Contact bonding. Fragments of wet clay stick one to another and to the metal (e.g. to the oedometer’s wall ). Sticking develops at about an oedometer load of s≥50 kPa. Bonds between fragments reduce the compression until they are broken. They thus hinder the rearrangement. 1By a ‘garland’ a series of half-wreaths is understood, mutually joined and hanging often on walls as a decoration. With garlandlike compression, the compression curve consists of a series of segments (see curves Nos 3 and 4 in Fig. 7). It is well observed, for example, with compression of sand grains undergoing crushing [see e.g. Feda (1982), p. 244].
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As a product of elementary mechanisms, the following complex structural processes take place: $ Diffusion. Originally the term has been used for the description of the heat conduction phenomena. The process of heat conduction may be generalized to cover all processes spreading from one source and governed by the same partial differential equation of the parabolic type. Its graphical image if plotted to the semilogarithmic scale is an S-curve. In soil mechanics, primary consolidation is a well known diffusion process. $ Percolation. If a system consists of two components (say clay and sand ) participating on the system’s response then their proportion governs the form of the response. This may range from that typical of one component (e.g. from ‘sandy’ behaviour) to that of the other one (e.g. to ‘clayey’ behaviour). Double-porosity geomaterials due to the high porosity, triggering different structural mechanisms, are prone to develop the percolation phenomena. $ Normalized behaviour. This occurs if a set of constitutive functions (describing seemingly various processes) may be reduced to a single one in a dimensionless form. The processes characterized by those functions are governed by the same set and interrelations of dimensionless arguments and, consequently, the processes they describe are therefore similar. Thus, for example, linear Mohr–Coulomb envelope confirms identical, stress-independent micromechanisms of strength mobilization, contrary to nonlinear envelope indicating the occurrence of stressdependent (e.g. cataclastic) phenomena. $ Collapse. Collapse is a sudden change of the mechanical behaviour caused by transforming the soil from one structural configuration to another one. It is visualized by a stepwise deformation (e.g. in the case of a load-controlled compression) or by a stress step (when strain-rate controlled compression is applied ). Collapse is to be expected with soils of high porosity because of the metastable structure. Fragmentary clay belongs to this class of geomaterials. Collapse may take on two forms: breakdown (the total change of the structure; such is the collapse due to inundation, hydrocol-
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lapse) or bifurcation (‘branching-off ’) collapse [a jumplike change of a constitutive parameter, for example, of the deformation modulus or angle of internal friction owing to the kink of a constitutive function like with a bilinear shear envelope or compressive curve; it indicates a change of the deformation mechanism, well observed, for example, with triaxial specimens reinforced with plastic strips — see, for example, Atmatzidis and Athanasopoulos (1994)].
3. Shear resistance In order to study the behaviour of a fragmentary clay, a series of laboratory experiments was undertaken modelling the fragmentary nature of the original clayey waste by a fragmentary clay with fragment sizes 1–2, 2–4 and 4–8 mm. The material was tested (oven) dry, wet (at the natural water content) and inundated (saturated) in the triaxial (undrained tests), oedometer and shear box (drained tests) apparatuses. Loose and dense specimens were prepared (mean total porosities of ca 71 and 62%). The total porosity seemed to play a secondary role in the mechanical behaviour with respect to other factors, similarly like the fragment size (with a few exceptions). Fig. 3 depicts the Mohr–Coulomb envelopes of
the shear box test results2 (dry, wet and inundated specimens; normal stress stepwise increased until the final value when the constant rate of shearing was applied) with fragment sizes 1–2, 2–4 and 4–8 mm in the common normal stress range (s= 0–300 kPa). All of them are bilinear with a characteristic kink at s =100–200 kPa. The principal crit factor governing the shear behaviour is the water content. The fragment size seems to be, especially with inundated specimens, of no importance. Experiments with different deformation rates and applying the common or multi-stage method yielded the same results. Triaxial CSL (critical state line) drawn by a broken line coincides with the shear box results but its kink is shifted to ca 250 kPa (Fig. 4). The occurrence of bilinearity is ascribed to the transformation of the structure with the elevating load. For s
Fig. 4. CSL of saturated fragmentary clay of different fragments’ sizes (Boha´cˇ, 1996).
Fig. 3. Mohr–Coulomb envelopes of fragmented clay—low stress level, shear box tests+CSL (triaxial tests).
2Though aware of the Hill alternative of the failure locus [see e.g. Feda (1982)], the author adheres to the Mohr–Coulomb failure envelope conventionally used in soil mechanics and defined, for example, by Lambe and Whitman (1969) or Parry (1995).
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recoverable after the test from the oedometer ring in a fragmentary form. This indicates the origin of ‘squashing’, contrary to the dry clay recoverable after being loaded at least up to s=1 MPa. Cohesive behaviour of wet clay is mainly the result of squashing while that of dry specimens is to be ascribed to grain interlocking and crushing. Fig. 5 presents the extent of crushing (as determined by sieving) for a single-step oedometer loading of dry specimens. The extent of crushing increases as s increases (and is much higher in a shear box than in an oedometer). Bi- (or multi-) linear strength envelope is not specific for a fragmentary clay. It is typical for fiber reinforced sand, for some soils like calcarenites, cloddy compacted clay etc. It results from a sudden change of the structural mechanism at some critical stress level (e.g. in the fiber reinforced sand the transition from slip to yield or stretch of reinforcing fibers). Within both intervals of behaviour, s
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While Fig. 3 deals with the low stress level (s≤300 kPa), Fig. 6 extends the stress range to s=2 MPa. Trilinear strength envelopes may be recorded (dry and wet specimens), in addition to a bilinear one (inundated specimens). While the simplicity of the latter one (with the single s #150 kPa) reflects the simplest structure availcrit able, that is, that of a saturated clay, the most complex one (series of s #100–200, 500 and crit 1000 kPa) corresponds to the most complex structure of wet clay where bonding due to the contact sticking plays an important role. Kinking indicates the bifurcation collapses resulting perhaps from the percolation effects. At high stress level, wet and inundated clay show roughly parallel shear strength envelopes. This phenomenon can be interpreted as the effect of the high degree of saturation of wet specimens due to the compression by high s-values. The results of the isotropically consolidated triaxial drained and undrained tests of the same water saturated material (2–4 mm) are also depicted in Fig. 6. The triaxial envelope either agrees with the shear box tests (inundated specimens) or, at least, triaxial and shear box w∞ are similar (dry specimens). Fragment crushing with
Fig. 5. The amount of a fragment’s crushing (oedometer, shear box) of originally 2–4 mm dry fragmentary clay; residuum (% of the original weight) on the sieves with labelled openings after the load application or shear strength mobilization.
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Fig. 6. Mohr–Coulomb envelopes of fragmentary clay—high stress level [shear box and triaxial data by Pachta and Krˇ´ızˇova´ (1996)]; CID, CIUP, drained and undrained triaxial tests.
triaxial specimens may be expected to be smaller than in the shear box (and similar to oedometer tests in Fig. 5). This may be the explanation of the somewhat lower strength of dry specimens. One may conclude that fragmentary clay generally possesses a multilinear strength envelope. This has serious consequences for the stability analysis. One must either differentiate the values of the strength parameters according to the stress level in question or match the original multilinear envelope by a nonlinear function. Multilinearity (the effect of a series of bifurcation collapses) manifests sudden stress-bound structural changes (debonding, crushing, slip etc.). Parametric study of the (usually ‘boot shaped’) slope failures indicated the relevant shear stress parameter to be w∞=16° and c∞=40 kPa (Stanek, 1992). This corresponds with the strength parameters of inundated specimens in Fig. 3.
4. Compression Different structural mechanisms, differentiated by the stress level and the water content in question, may be expected when compressing the fragmentary clay. Fig. 7 shows some recorded compression curves plotted to the arithmetic and
logarithmic stress scales. No. 5 belongs to the natural intact clay with reversible and linear compression up to 1 MPa. No. 2 represents the bilinear compression curve typical for dry specimens ( less frequent and often multilinear with wet specimens). The compression is elastoplastic (ca 60% of the deformation represented by No. 2 compression curve is irreversible). If fragment crushing prevails, a garlandlike compression curve results (No. 3, dry specimens; No. 4, wet specimen desiccating during compression). Inundated specimens (No. 1) are compressed linearly in a semilogarithmic plot, like reconstituted clays. A generally applicable model of the compression curve has an S-shaped form in a semilogarithmic plot. This may be expressed by a trilinear function and each branch characterized by its midpoint — Fig. 8 (dotted line indicates one linear interval and its midpoint). The most frequent value of the (oedometric) compression index C =0.35 c (C =De/D log s). This roughly corresponds to the c value of the compression index l=0.1 (for triaxial K tests of water saturated specimens; in those 0 tests, the value of K was found to be ca 0.55 to 0 0.75). There is a group of specimens with the second maximum C =1. Those are very loose wet c specimens. The great dispersion of C reveals that c the specimens’ structure is rather sensitive to their
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Fig. 7. Series of oedometric curves of fragmentary clay of various granulometry and water content (arithmetic and logarithmic plots).
preparation which need not be perfectly under control (due to the many influencing factors). The S-shaped compression curve suggests that the process of compression is actually a diffusion process (i.e. spreading of the plastic, collapse, compression from the loaded boundary). There is some evidence that diffusion processes really take place in the field. Vaughan (1995) observed: ‘…collapse… started in the top of the fill, and took about one week to affect the bottom of the fill, a rate of penetration of the collapse front of about
2×10−5 m s−1. Collapse compression was up to 6%, and settlement of the 1.5 m thick fill was about 0.4 m’. In the discussion by Skempton and Vaughan (1994) one may read: ‘An interesting feature of the collapse recorded at gauge CS3 was that it occurred as a wave starting from the top of the fill, taking about two weeks to reach the bottom … it seems that the collapse was caused either by a very small inflow of water, or by some other mechanism …’. Water inundation of dry or wet specimens
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Fig. 8. Oedometric compression index C versus axial stress c relationship.
resulted in a hydrocollapse (step-like change in the void ratio De or compression strain De). Fig. 9 shows some of the results. One may see that: $ There is no effect of the fragment size, specimens of 1–2 mm size showing the same hydrocollapse like those of 4–8 mm size. $ Dry specimens are more prone to collapse. The respective curve in Fig. 9 is shifted upwards and to the right. This may be explained by the effect of the stormy decay of dry fragments when inundated and by the effect of small densification of dry material for the given s-value. The magnitude of hydrocollapse depends, among
Fig. 9. Hydrocollapse (collapse after the specimen’s inundation) of initially dry and wet specimens of two fragment’s sizes [data from Pachta and Krˇ´ızˇova´ (1996)]; De, De, void ratio and strain decrements or increments.
others, on the porosity of soil. This is reduced by a stepwise raising load. After some critical pressure no collapse takes place ( Fig. 9 — for wet specimens this pressure is ca 1.5–2 MPa). Since the compressibility of dry specimens is about one-third of that of wet specimens, their critical pressure is much higher. Since hydrocollapse represents a specific form of soil compression — the effect of one state parameter, load, is replaced with hydrocollapse by another state parameter, water content — one expects that the process of diffusion (spreading of the collapse of structure) will take place even in this case. Fig. 10 confirms this expectation (S-shaped curve; similar results were found by the author with collapsible loess). Hydrocollapse is the most conspicuous form of collapse. The so-called immediate collapse is another form recorded with fragmentary clay. It is the compression of the specimen (mostly wet; with dry specimens less compression was recorded) within the first 5 min after the load application. A bell-shaped curve may describe this type of collapse (for stepwise loading) similarly like in Fig. 9 in the case of a hydrocollapse. However, it is of bifurcation (strain hardening by multilinear logarithmic creep) and not diffusive in nature. Another type of collapse is represented by timedependent instabilities. These may be classified as diffusion processes ( Fig. 11) and bifurcation col-
Fig. 10. Time-dependent oedometric compression of an inundated specimen of fragmentary clay [originally wet specimen s=60 kPa, 4–8 mm — Za´lesky´ et al. (1996)].
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Fig. 11. Time-dependent oedometric compression of the diffusive character of two wet specimens (1–2 mm, 4–8 mm) at s=952 kPa.
lapses ( Fig. 12). A typical garlandlike form appears (Fig. 13) if fragment crushing intervenes. Due to the bifurcation collapse, the value of the coefficient of secondary compression C (= a
Fig. 12. Secondary compression of a dry specimen of 2–4 mm fragmentary clay loaded in an oedometer at 952 kPa. (a) Secondary compression, experimental data; (b) hyperbolic transformation.
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De/D log t) may be considerably changed, similarly like the deformation modulus in Fig. 7 (No. 2). Fig. 11 presents two examples of the time-dependent collapses taking the form of diffusion processes. With such diffusion collapses, one may calculate the coefficient of diffusion c as for the k coefficient of primary consolidation. c is typically k one to two orders of magnitude smaller. Time-dependent bifurcation collapses may be treated like the multilinear strength envelope: either ‘per partes’ (each linear part separately) or transforming the linear constitutive function into a smooth one. Fig. 12b shows, as an example, the latter procedure — a successful replacement of the bifurcated logarithmic creep curve by a smooth curve of a hyperbolic creep.
5. Laboratory versus field behaviour To be sure that phenomena observed in the laboratory are also reproduced in nature, laboratory studies should be combined with field studies. The important property of wet fragmentary clay, its contact sticking, can adversely affect open coal mining technology. Sticking increases in the field as per the proportion of montmorillonite (and, consequently, with an increase of the index of plasticity) and considerably aggravates both rail and belt transport of the clayey waste. Contact bonding of the fragmentary clay as found in the laboratory thus corresponds to the experience in the field. In the laboratory, a small size oedometer (10 cm diameter, 19 mm height) and shear boxes (6×6×2.5 cm) were used. If the size of the specimen is increased for about one order of magnitude (oedometer 78.5 cm in diameter and specimen’s height of 26.2 cm), and the tested fragmentary clay almost retains its in situ granulometry, the same phenomena as in the laboratory are observed (Dykast, 1993): $ E of ca 7 MPa in the range of s=0.3–1 MPa oed (Fig. 7, No. 2); $ time-dependent diffusion is recorded as in Fig. 11 ( Fig. 14); and $ the diffusion nature of the hydrocollapse is confirmed to be as in Fig. 10 (see Fig. 15).
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Fig. 13. Secondary compression of a wet specimen 2–4 mm of a fragmentary clay loaded in an oedometer at 339.3 kPa.
The same S-shaped compression curve as in the laboratory has been constructed from the record of the time-dependent settlement of the Erveˇnice corridor [80–130 m high landfill, see Vlk in Dykast (1993)]. Time-dependent records of the vertical movements by individual settlement gauges of this corridor displayed similar bifurcation points as for the laboratory records (Dykast, 1993) — Fig. 16. The annual settlement variation in the longitudinal cross-section of the Velebudice landfill
Fig. 14. Recorded S-shaped mean time-dependent settlement curve of the Erveˇnice corridor (80–130 m high landfill ) after Vlk (Dykast, 1993).
Fig. 15. Time-dependent compression recorded with the natural wet fragmentary clay inundated at 1 MPa in a large oedometer.
Fig. 16. Time-dependent vertical displacements of measuring points of the Erveˇnice corridor [in Dykast (1993)].
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(35–60 m high) falls within 150–380 mm (after 12 years have elapsed), that is, the settlement dispersion is considerable ( Fig. 17). The Erveˇnice corridor depicts a similar excessive variation of settlement (15–150 cm, Fig. 18), partly generated by the gradual placement of the clayey waste into the embankment. Such a large dispersion agrees with the strong variation in the laboratory C c values (Fig. 8). Thus the principal phenomena observed with tests in the laboratory investigation are confirmed
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either on a considerably larger scale or directly in the field (time-dependent bifurcation, diffusion, extreme variation of compression, sticking).
6. Conclusions Fragmentary clay (i.e. a geomaterial consisting of clayey fragments of up to 50 cm in size) is a typical double-porosity geomaterial. Though its total porosity amounts to ca 70%, the porosity of
Fig. 17. Maximum and minimum settlement of the Velebudice landfill [after Dykast (1993)].
Fig. 18. Variation of the settlement of the Erveˇnice corridor along its axis over different years (Dykast, 1993).
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individual (water saturated) fragments is equal to ca 40%. The material represents the waste (an overburden of the open-cast brown coal seam) which is tipped, as a rule, to a height of >100 m. The behaviour of the clay fragment depends mainly on the state parameters: stress ( load ); water content; and time. The material changes, in the course of time and due to the exposure to the climatic conditions, from a ‘granular’ to ‘cohesive’ clayey mass. The latter, which is water saturated and if combined with the high pore water pressures, affects adversely the slope stability (creating a kind of a non-bearing core within the landfill ). In addition, a large settlement is produced by the gradual structural changes of the material. For reclamation purposes, one has to be able to predict the stability and deformation of landfills. Generally, multi-linear strength envelopes and compression curves have been found. Points of singularity (marking the so-called bifurcation collapses) designate the transition from one structural system to another. Diffusion processes may be found with load-dependent compression, compression due to inundation and time-dependent compression. They may be also observed in the field. While the angle of internal fiction (depending on the water content, which is the principal state parameter) varies within 15–53°, the mean C (in c the oedometer) is equal to 0.35, the mean l (in the triaxial K -test) is 0.1. C varies in the range of 0 a 0.1–45%. The extreme variability in the mechanical parameters can be explained by the sensitivity of the fragmentary clay to numerous structural factors, namely the extremely high porosity of the material in question. Attention is drawn to the collapsible behaviour. In addition to the well understood hydrocollapse (drop of the suction to zero), there are many collapses of the breakdown nature taking on the form of diffusion processes (hydrocollapse due to particle disintegration, time-dependent collapse). Further on, bifurcation collapses occur (immediate collapse, multilinearity of some compression curves, of strength envelopes, of secondary compression curves).
Although all this behaviour is emphasized owing to the double-porosity nature of the investigated geomaterial it is believed that the same phenomena occur with many (problematic) soils. With the shift of the attention of soil mechanics from the artificially prepared to the natural soils, those phenomena should be constitutively modelled. This presently occurs on a rather insufficient scale.
Acknowledgment This research was supported by the Grant Agency of the Academy of Sciences of the Czech Republic (Grant No. A2071803) which is gratefully acknowledged.
References Atmatzidis, D.K., Athanasopoulos, G.A., 1994. Sand–geotextile friction angle by conventional shear testing. In: Proc. XIII. ICSMFE, New Delhi, vol. 3, pp. 1273–1278. Boha´cˇ, J., 1996. Compressibility and Strength of Granulated Clay. Research Report of the Faculty of Science of the Charles University, Prague (in Czech). Dykast, I., 1993. Properties of landfills in SHR as foundation media. PhD. Thesis, Civil Engineering Faculty of the Czech Technical University, Prague (in Czech). Feda, J., 1982. Mechanics of Particulate Materials — The Principles. Elsevier–Academia, Amsterdam–Prague. Lambe, W.T., Whitman, R.V., 1969. Soil Mechanics. Wiley, Chichester. Pachta, V., Krˇ´ızˇova´, H., 1996. Geotechnical Laboratory Tests. Research Report of SG-Geotechnika, Prague (in Czech). Parry, R.H.G., 1995. Mohr Circles, Stress Paths and Geotechnics. E. and F.N. Spon. Skempton, A.W., Vaughan, P.R., 1994. The failure of Carsington dam — discussion. Ge´otechnique 45 (4), 734 Stanek, J., 1992. Stability of High Landfills of Clayey Soils. Research Report of the Research Institute of Brown Coal Most (in Czech). Vaughan, P.R., 1995. Criteria for the use of weak and weathered rocks for embankment fill and its compaction control. In: Proc. XIII. ICSMFE, vol. VI, pp. 195–206. Za´lesky´, J., Kos, J., Sala´k, J., 1996. Deformation and strength of unsaturated soils. Research Report of the Civil Engineering Faculty of the Czech Technical University, Prague (in Czech).