Constant Deviatoric Stress Research Articles

Undrained anisotropy and rotational shear in granular soil

The impact of fabric anisotropy on the behaviour of granular soil remains a subject of great interest. In particular, the effects of principal stress rotation on the undrained response of saturated sand are not fully understood. This paper describes an experimental investigation conducted in an automated hollow cylinder apparatus into the undrained anisotropic behaviour of saturated sand in rotational shear, which is defined as a class of non-proportional loading with a continuous rotation of the principal stress directions but a constant deviatoric stress. Special attention in this investigation was placed on the influence of the relative magnitude of the intermediate principal stress, characterised by the parameter b = (σ2 − σ3)/(σ1 − σ3), on the pore pressure response and deformation characteristics. The experimental observations indicate that soil specimens, even in very dense state, were weakened by the build-up of pore water pressure in rotational shear. The intermediate principal stress parameter b was not a negligible factor for the behaviour of saturated sand in the rotation shear, but had significant impact. Under otherwise identical conditions, the soil specimen rotationally sheared under the condition b = 0 exhibited a much stronger resistance to pore pressure build-up and a less dramatic stiffness degradation than that sheared under the condition b = 1·0. This observation is considered to be directly associated with the soil fabric anisotropy.

Flow deformation of liquefied sand under constant shear load and its application to analysis of flow slide of infinite slope

This paper intended to evaluate the behavior of saturated sand and sloped ground subjected to flow failure with seepage of pore water in the ground after earthquake and the resultant liquefaction. Triaxial compression tests of sand with constant deviator stress but changing of pore pressure and volume of the specimens were conducted in this study. It was revealed that the relation between the volume change and the amount of shear strain during deformation depended on the initial density of the sand but it did not much depend on shear stress and initial confining stress levels. Based on this test results and numerical analysis of the seepage of pore water in liquefied ground, a methodology was proposed to predict the deformation of inclined ground due to liquefaction.

Shear strength of overconsolidated clay for repeats of pore water pressure loading

This paper represents the change in shear strength of clay for repetitive pore water pressure loading with the use of both experimental tests and model simulation. Pore water pressure was increased under constant deviator stress to simulate the soil behavior in landslide. Yield stress in pore water pressure was obtained constant for repeats of pore water pressure loading, but failure stress was obtained to decrease. Failure stresses constituted the failure envelopment line in void ratio and effective mean stress space. This exhibits the process of change in both shear strength and state variable of soil caused by repetitive failures during pore water pressure loading cycles. In pore water pressure loading, the strain softening of clay develops due to dilation and the shear strength decreases. On the contrary, the shear strength recovery develops by consolidation effect in unloading. Failure stress varies due to two opposite effects of pore water pressure loading cycle. It was found the failure stress in pore water pressure approached to the balanced one between two opposite effects in repetitive pore water pressure loading cycles.

Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations

The rock mass failure process is characterized by several distinct deformation stages which include crack initiation, crack propagation and coalescence. It is important to know the stress levels associated with these deformation stages for engineering design and practice. Extensive theoretical, experimental and numerical studies on the failure process of intact rocks exist. It is generally understood that crack initiation starts at 0.3 to 0.5 times the peak uniaxial compressive stress. In confined conditions, the constant-deviatoric stress criterion was found to describe the crack initiation stress level. Here, generalized crack initiation and crack damage thresholds of rock masses are proposed. The crack initiation threshold is defined by σ1−σ3=A σcm and the crack damage threshold is defined by σ1−σ3=B σcm for jointed rock masses, where A and B are material constants and σcm is the uniaxial compressive strength of the rock masses. For a massive rock mass without joints, σcm is equal to σcd, the long-term uniaxial strength of intact rock. After examining data from intact rocks and jointed rock masses, it was found that for massive to moderately jointed rock masses, the material constants A and B are in the range of 0.4 to 0.5, 0.8 to 0.9, respectively, and for moderately to highly jointed rock masses, A and B are in the range of 0.5 to 0.6, 0.9 to 1.0, respectively. The generalized crack initiation and crack damage thresholds, when combined with simple linear elastic stress analysis, assist in assessing the rock mass integrity in low confinement conditions, greatly reducing the effort needed to obtain the required material constants for engineering design of underground excavations.

A state-dependent elasto-plastic model for saturated and unsaturated soils

A state-dependent elasto-plastic constitutive model for both saturated and unsaturated soils is presented in this paper. The model, which is developed under an extended critical-state framework, uses two independent stress state variables: net normal stress and matric suction. In addition, the influence of a simplified non-linear soil-water characteristic curve on mechanical behaviour is incorporated in the model by using a bi-linear function. Most importantly, a state-dependent dilatancy formulation is introduced to account for the effects of stress level or stress ratio, internal state (density) and soil suction. In this paper, details of the model formulation and the determination of model parameters are described and reported. By using the new model, numerical simulations of triaxial tests have been carried out on both saturated and unsaturated fine-grained (sandy silt) and coarse-grained (gravelly sand) weathered soils. The simulated triaxial tests include undrained shear tests on saturated specimens, constant water content tests and wetting tests under constant deviator stress on unsaturated specimens. The computed results show that the stress–strain and volumetric-shear–strain relationships at both loose and dense and saturated and unsaturated states can be modelled properly with a single set of parameters. Moreover, the model is capable of capturing some key observed features, such as a sudden increase in shear strain and volumetric strain as suction is reduced under a constant deviator stress.

A state-dependent elasto-plastic model for saturated and unsaturated soils

A state-dependent elasto-plastic constitutive model for both saturated and unsaturated soils is presented in this paper. The model, which is developed under an extended critical-state framework, uses two independent stress state variables: net normal stress and matric suction. In addition, the influence of a simplified non-linear soil-water characteristic curve on mechanical behaviour is incorporated in the model by using a bi-linear function. Most importantly, a state-dependent dilatancy formulation is introduced to account for the effects of stress level or stress ratio, internal state (density) and soil suction. In this paper, details of the model formulation and the determination of model parameters are described and reported. By using the new model, numerical simulations of triaxial tests have been carried out on both saturated and unsaturated fine-grained (sandy silt) and coarse-grained (gravelly sand) weathered soils. The simulated triaxial tests include undrained shear tests on saturated specimens, constant water content tests and wetting tests under constant deviator stress on unsaturated specimens. The computed results show that the stress–strain and volumetric-shear–strain relationships at both loose and dense and saturated and unsaturated states can be modelled properly with a single set of parameters. Moreover, the model is capable of capturing some key observed features, such as a sudden increase in shear strain and volumetric strain as suction is reduced under a constant deviator stress.

Scale Invariance of the Stress Production Mechanism in Polymeric Systems

Stress production in a model monodisperse polymeric material is investigated on multiple scales. The analysis is performed by means of equilibrium and nonequilibrium molecular dynamics. A family of mobile intrinsic coordinate systems is introduced, each system having one axis tied to the end-to-end vector of a generic chain segment of specified length. A similar mobile coordinate system tied to the large semiaxis of the ellipsoidal chains is defined on the chain scale. The atomic level stress is evaluated based on bonded and nonbonded interatomic interactions and averaged in the global coordinate system, to result in the global, system level stress, and in the various intrinsic systems, to result in intrinsic stresses. It is observed that the deviatoric intrinsic stress is scale independent, a bond, a chain segment, and the chain scale intrinsic frame carrying the same stress. The hydrostatic component of the stress tensor scales with the segment length. This concept extends the previously introduced intrinsic stress framework, scale linking the bond and chain scales. During melt deformation, the chain segments stretch and rotate. Chains shorter than the entanglement length mainly rotate during an elongational deformation of limited amplitude, their size remaining essentially constant. Longer chains distort and rotate. Two regimes are evidenced during the return to isotropy of the orientation on multiple scales. The faster mode is associated with the return to equilibrium of the internal structure of the generic chain, while the slower mode is associated with chain rotation in the global coordinate system. The intrinsic deviatoric stress carried by a chain changes during the first mode, and is essentially constant during the second. The physical picture of stress production defined on the scale of a bond (Kuhn segment) in the intrinsic stress framework translates to the chain scale during this late relaxation regime: each rotating chain carries a constant deviatoric intrinsic stress, the preferential chain orientation leading to a nonzero global deviatoric stress.

Laboratory Study of Loose Saturated and Unsaturated Decomposed Granitic Soil

Weathered soils are used extensively as fill materials in slope construction in tropical and subtropical cities such as Hong Kong. The mechanical behavior of loose decomposed fill materials, particularly in the unsaturated state, has not often been investigated and is not yet fully understood. The objective of this study was to understand the mechanical behavior of loose unsaturated decomposed granitic soil and to study the effects of the stress state, the stress path and the soil suction on the stress-strain relationship, shear strength, volume change, and dilatancy via three series of stress path triaxial tests on both saturated and unsaturated specimens. It was found that loose and saturated decomposed granitic soil behaves like clean sands during undrained shearing. Strain-softening behavior is observed in loose saturated specimens. In unsaturated specimens sheared at a constant water content, a hardening stress-strain relationship and volumetric contractions are observed in the considered range of net mean stresses. The suction of the soil contributed little to the apparent cohesion. The angle of friction appeared to be independent of the suction. In unsaturated specimens subjected to continuous wetting (suction reduction) at a constant deviator stress, the volumetric behavior changed from dilative to contractive with increasing net mean stress and the specimen failed at a degree of saturation far below full saturation. It was revealed that the dilatancy of the unsaturated soil depends on the suction, the state, and the stress path.

Influence of generalized initial state and principal stress rotation on the undrained response of sands

The dependence of the undrained behaviour of sand on the initial stress state and the orientation of principal stresses with respect to the bedding planes is assessed under generalized loading paths using hollow cylinder torsional shear tests. The undrained tests were carried out using displacement-controlled loading to confidently capture the post-peak strain-softening response. Undrained behaviour of sands under identical initial states is shown to be dependent on the direction of principal stresses, during and prior to undrained shear, in relation to the direction of bedding planes. The minimum undrained strength of the strain-softening sand is found to be highly influenced by the initial stress state (confining stress, direction of principal stresses, and static shear), even though the friction angle mobilized at the instant of minimum strength is unique. A mere rotation of principal stresses at constant deviator stress alone can lead to a strain-softening response that may culminate in limited or unlimited flow deformation. The susceptibility of sand to liquefaction due to stress rotation increases as the direction of the major principal stress approaches the orientation of the bedding plane. The potential for flow deformation is strongly dependent on the direction of the major principal stress in relation to the bedding planes, and the steady state strength is not uniquely related to the void ratio alone.Key words: liquefaction, hollow cylinder torsion test, principal stress direction, static shear, steady state strength, minimum undrained strength.

Behavior of a Loosely Compacted Unsaturated Volcanic Soil

In this paper, the stress-strain relationsihp and volumetric behavior of a loosely compacted unsaturated decomposed volcanic soil (fill) were studied by conducting three series of triaxial stress path tests: (1) consolidated undrained on the saturated fill; (2) constant water content; and (3) a reducing suction under constant deviator stress on the unsaturated fill. The last two series of tests were designed to simulate the effects of undrained response and rainfall infiltration in initially unsaturated slopes, respectively. It was found that the saturated loose volcanic soil behaves like clay under isotropic compression but it resembles sand behavior when it was subjected to undrained shear. For isotropically consolidated unsaturated specimens sheared under a constant water content, a hardening stress-strain and a nonlinear shear strength–suction relationship are observed. At relatively high suctions, both angle of friction and apparent cohesion appear to be independent of suction. Volumetric contraction during shear is observed in this series of tests. On the other hand, anisotropically consolidated loose unsaturated specimens subjected to a reducing suction change from contractive to dilative behavior as the net mean stress increases. This observed volumetric behavior, unlike the shear strength, is stress path–dependent and cannot be explained by using the existing elastoplastic critical state theoretical framework extended for unsaturated soils.

Stress–strain behaviour of a loosely compacted volcanic-derived soil and its significance to rainfall-induced fill slope failures

The stress–strain behaviour of a soil is crucial to the recognition of the mechanism of slope failure. Triaxial tests, composed of isotropically consolidated drained (ICD) and undrained compression (ICU) tests and anisotropically consolidated constant deviatoric stress path (CQD) tests, were carried out with the aim of investigating the stress–strain behaviour of loosely compacted volcanic-derived soils. The fact that the critical states are the same for ICU, ICD and CQD tests may show that the critical state is independent of the above three stress paths. The critical state line, as defined in critical state soil mechanics, is obtained from the e–log p′ and q– p′ plots based on the results of the above tests. The initial state of the consolidated specimens at initiation of failure may be classified as dilative or contractive in the light of the locations of the soil state relative to the critical state line. For contractional soils, the increased pore water pressure generated by rainfall infiltration leads to a contractive failure in a drained manner, giving rise to high excess pore water pressure. The excess pore water pressure caused by contraction cannot be dissipated instantly, resulting in a decrease in the shear resistance of the soil. The failure process is rapid. The failed soil mass is prone to flow after failure under the action of gravity due to its high moisture content and inflow of surface runoff and rainwater. For dilational soils, the increased pore water pressure resulting from infiltration leads to dilation, which reduces pore water pressure and thus increases the shear resistance of the soil. However, continued rainfall infiltration may be able to equilibrate the reduction in pore water pressure caused by dilation and, therefore, the dilation or displacement can continue. In Hong Kong, volcanic-derived soil is characterized by high permeability. Both the high permeability of volcanic-derived soil and a shallow failure surface make it possible for the reduction in pore pressure to equilibrate relatively quickly. Therefore, the failure is also rapid, at least for poorly compacted fill slopes.

Analysis of rainstorm-induced slide-debris flows on natural terrain of Lantau Island, Hong Kong

Lantau Island, the largest outlying island of the territory of Hong Kong, experienced a severe rainstorm on 4–5 November 1993, which induced >800 slope failures on natural terrain there. Detailed field investigations were carried out to study the failure modes, in relation with various influencing factors. It was found that the occurrence of slide-debris flows has a close relationship with bedrock geology, slope gradient, vegetation cover and micro landform. The failure modes of slide-debris flows may be classified into translational slides and rotational slides, and the former are predominant. Analysis of the hydrological response of colluvial slopes during the rainstorm indicated that the majority of the failures were caused by the development of a perched water table in the thin surface layer of colluvium of volcanic origin due to infiltration during the heavy rain. Undisturbed soil samples from south Lantau have been subjected to anisotropically consolidated undrained compression tests at comparatively low stress levels. Constant deviatoric stress path tests (CQD) simulating the stress path in the field at in situ stress levels have been performed to investigate soil behavior. The CQD test results indicate that the material of slopes at undisturbed state is brought to dilation because of the increase in pore water pressure caused by infiltration of rain water. For a translational slide, the displacement, resulting from dilation, may destroy cohesion along the failure surface and locally within the interior of the slide. The surplus water during the intense rainstorm was able to equilibrate the reduction in pore pressure caused by dilation, and the dilation and displacement may be further increased. The strain-softening after significant strains triggered debris flow mobilization. However, for a rotational slide, the increase in pore water pressure caused by surplus water infiltration during the intense rainstorm could not equilibrate the reduction in pore pressure caused by dilation, much or even all of the sliding block could not mobilize into a debris flow.

Collapse behavior of sand: Discussion

The test data that are presented in paper are of most interest. The two constant deviator stress path tests may be compared with tests done by Lade et al. (1988) and Lade and Pradel (1990) for very loose sand under undrained conditions and by Chu (1991) and Chu et al. (1993) for medium loose to dense sand under non-undrained (or strain path controlled) conditions. It should be noted that testing procedures used in and test results obtained from these tests are verv similar. All above-mentioned tests were conducted uhder a constant deviator load and decreasing effective confining stress conditions. The prefailure instability observed in these tests appears to be same type. Although authors called instability observed in constant deviator stress path tests collapse behaviour, word drained does not carry same meaning as in a drained conventional compression test. This is because pore-water pressure of sample was controlled during tests, and thus volume change of sample is not totally free. As the volume of sample for constant deviator stress (q = 125 kPa) test was essentially unchanged and remained at 0.804 before sample collapse, this test was actually conducted under an undrained condition. Therefore, 'paper by S. Sasitharan, P.K. Robertson, D.C. Sego, and N.R. Morgenstern. 1993. Canadian Geotechnical Journal, 30: 569-577.

Collapse of dry sand

Loose cohesionless saturated materials have proved responsible for a number of serious or catastrophic flow slides. Liquefaction failures with no obvious triggering mechanism have also been recorded. This phenomenon of sudden liquefaction without a presence of cyclic shear stresses is often referred to as spontaneous or static liquefaction. Results from previously published studies suggest that liquefaction is triggered not by the undrained loading and generation of pore pressures but by the collapse of the metastàble sand structure, which in turn generates the driving pore pressures in a saturated material. Hence, the collapse is a characteristic response of a material to certain stress states rather than a result of some enforced undrained loading. This theory is evaluated on very loose dry Ottawa sand. It is shown that the very loose dry sand when subjected to a constant deviatoric stress path significantly changes its behavior at a certain discreet stress state, increases compressibility, and becomes increasingly unstable. This results in collapse – vigorous contraction of the specimen. This structural collapse appears to be equivalent to the pore-pressure generation in collapsing, very loose saturated sand. Key words : dry sand, collapse, liquefaction, stress path, triaxial cell.

Effects of density contrasts on the orientation of stresses in the lithosphere: Relation to principal stress directions in the Transverse Ranges, California

The influence of stresses arising from horizontal density contrasts on the orientation and relative magnitudes of principal stresses in an otherwise uniform lithospheric stress field is investigated. A simple model is constructed, in which a local deviatoric stress due to a density anomaly, embedded within or just below the lithosphere, and a regionally constant deviatoric stress field are each approximated by biaxial tensors. The net stress field is obtained from the sum of the two. Both the relative magnitudes of principal stresses and the magnitude of the angular difference in principal stress direction of the summed tensor compared with that obtained in the absence of buoyancy forces depend on two parameters. The first is the ratio τ/τ′, where τ is a measure of the magnitude of the regional deviatoric stress and τ′ is the magnitude of the stress arising from buoyancy forces associated with the density anomaly. The second parameter is the angle between the trend of the density anomaly and the direction of maximum compressional stress that obtains in the absence of any perturbation by the local buoyancy forces. The directions of the principal axes of the total stress field are found to differ by up to 90° from those of the reference stress field. The model is applied to the Transverse Ranges, California, where the observed 23° difference in orientation of principal horizontal compressive stress compared with the principal compressive stress direction in central California constrains the predicted value of τ/τ′ to be approximately −0.4. This is consistent with an independently calculated range of τ/τ′ in which τ′ is inferred from seismological constraints on the magnitude of density variations underneath the Transverse Ranges and τ is inferred from observations of heat flow along the San Andreas fault in central California. The agreement between the two estimates of τ/τ′ supports the hypothesis that the observed differences in horizontal principal stress orientation in California can be explained by the combined influence of a local negative buoyancy force under the Transverse Ranges and a regional stress field associated with transcurrent deformation within the Pacific‐North American plate boundary zone. The observed counterclockwise angular difference in principal horizontal stress direction in the Transverse Ranges compared with central California implies that the plane of maximum right lateral shear stress is also rotated counterclockwise relative to that in central California. This supports the possibility that the “big bend” in the San Andreas fault may be a consequence of the negative buoyancy forces acting in the Transverse Ranges, and not the cause of Transverse Ranges formation, as has often been assumed.

Flow strengths of quartz aggregates: Grain size and pressure effects due to hydrolytic weakening

Novaculites and quartzite ranging in grain size from 1.2–211 μm have been experimentally deformed at confining pressures of 350–1620 MPa under conditions of constant displacement rate and constant deviatoric stress in order to determine the effects of both grain size and pressure on the rheology of quartzite. The amount of water available to the samples was varied so that flow strengths for the entire suite of samples could be compared at several, nominally equal water concentrations; samples were vacuum dried at 800°C for 12 hours, left as is, or sealed in Pt jackets with 0.03–0.4 wt % water added. Novaculites deformed at 800°C and 10−6 /s−1 in the presence of 0.4 wt % water show a continuous decrease in flow strength with increasing confining pressure over the range 350–1590 MPa. At high confining pressures 950–1600 MPa, constant displacement rate experiments show three distinct grain size effects, corresponding to the three levels of water concentration: (1) “grain boundary hardening” for vacuum‐dried samples, (2) grain size independent strength for as is samples, and (3) “grain boundary weakening” for samples deformed in the presence of water. Although grain boundary‐dislocation interactions may lead to grain boundary hardening and grain boundary sliding to weakening, the details of the mechanical data, in combination with microstructural observations, are inconsistent with existing models of intrinsic grain boundary effects. Instead, the strength‐grain size relations are interpreted as resulting from variations in structurally incorporated water, which, in turn, are controlled by diffusion of water to and from the grain boundaries. Finally, constant stress experiments show that the activation energy Q and stress exponent n for creep do not depend on grain size, so that the different strengths observed must be incorporated in the preexponential terms. However, both Q and n show a continuous decrease with increasing amounts of available water, from Q = 300 kJ/mol and n ≃ 4 for vacuum‐heated samples, to Q = 130 kJ/mol and n = 2.6 for water‐added samples.

Computer Simulation of Creep of Clay

The variable character of the particle contacts in natural illitic clay implies a spectrum of bond strengths. When a sufficiently high external shear stress is applied some weaker interlinking particle groups are transformed to domains which act as slip units. In creep induced by a constant deviatoric stress, the number and heights of thermally activable barriers to slip will vary in space and time. This is encompassed by a stochastic model, a simple version of which was used in a computer simulation. The dependence of the strain on time was found to be logarithmic, in good agreement with experiments. (ASCE)

A stochastic model of the creep of soils

The complex microstructure characteristic of soils points to the need to allow for this heterogeneity in models of plasticity and creep. In particular, the number and heights of thermally activable barriers to slip, in a given volume of soil subjected to a constant deviatoric stress, will vary in space and time. A statistical model embodying such changes in the spectrum of activation energies is outlined. With usual conditions of testing, it yields a linear relation between the creep strain and the logarithm of time. The model is shown to account rather well for typical creep behaviour of undrained clay, and to provide an appropriate framework for the representation and study of the creep of structurally sensitive clay and clayey silt, as well as for less sensitive soils. The determination of the most probable activation energy in the spectrum is discussed. En raison du caractère-complexe de la microstructure des sols, il semble nécessaire de tenir compte de cette hétérogénéité dans des modèles de plasticité et de fluage. En particulier, le nombre et la hauteur des barrières thermoactivables centre le glissement, dans une volume doné de sol soumis à un déviater constant, varieront dans l'espace et dans le temps. L'article présénte dans ses grandes lignes un modèle statistique incorporant de tels changements dans le spectre des énergies d'activation. Dans les conditions habituelles d'essai, on obtient une relation linéaire entre la deformation due au fluage et le logarithme de temps. On peut voir que le modele rend assez bien compte du comportement typique de fluage de l'argile non drainée, et fournit une structure appropriée pour la représentation et l'étude du fluage d'argile à structure sensible et de limon argileux, de même que dans le cas de sols moins sensibles. La determination de l'enérgie d'activation la plus probable dans le spectre y est discuteé.

Nucleation and growth of kink bands

Abstract The geometric and strain properties of an ideal kink band in a perfectly plastic material with one slip surface are determined and two plausible modes by which a kink band can grow while maintaining these properties are presented. The first mode involves change in the orientation of the boundary surface of the kink band as it broadens. In the second mode the initial orientation of this boundary surface is maintained during broadening. A theoretical model is proposed for kink band formation in three stages: first, in an elastically strained material with a suitably oriented planar anisotropy; a small nucleus is either present or develops, and grows in thickness by one or the other or by both of the growth modes; second, as some critical thickness is reached, this nucleus propagates longitudinally until the excessive elastic distortion surrounding its ends is sufficiently relieved, or until the boundary of the body is reached; and third, the band widens by lateral migration of its boundaries, most probably by mode 2 growth. It is proposed that the direction of longitudinal propagation—and hence the orientation of the kink band with respect to principal normal stress—is decided by the value of a, the kink angle, in the nucleus at the time the critical thickness for propagation is reached. A further proposal is that this value of a is in turn decided by a principle of maximum plastic work: the instantaneous increment in strain or in volume within a nucleus is always the one for which the instantaneous increment in plastic work is a maximum at constant deviatoric stress. Calculations based on this theory for the two growth modes working either separately or together as competing processes yield three models of kink band nucleation in reasonable agreement with published experimental data. The most appealing of these models physically is one in which early mode 1 growth is replaced by mode 2 growth as the increments in mechanical work for the two modes become equal.