Principal Deviatoric Strain Increment Ratios for Sand Having Inherent Transverse Isotropy

The behavior of sand on the π plane, including the relation between the principal deviatoric strain increment ratios, is not fully understood. The objectives are: To clarify experimentally the relation between the principal deviatoric strain increment ratios for sand in a wide range of b values and to discuss the basic shear behavior, taking particular notice of inherent transverse isotropy and noncoaxiality. From the experimental results on sand with inherent transverse isotropy, it was observed that the relation between the principal deviatoric strain increment ratios is fundamental and is related to the shape of the failure surface and the extent of strain localization. A new equation for the principal deviatoric strain increment ratios is proposed to model the influence of the incremental stress.     

Contraction, Dilation, and Failure of Sand in Triaxial, Torsional, and Rotational Shear Tests

The response of a saturated fine sand (Nevada sand No. 120) with relative density Dr ≈ 70% in drained and undrained conventional triaxial compression and extension tests and undrained cyclic shear tests in a hollow cylinder apparatus with rotation of the stress directions was studied. It was observed that the peak mobilized friction angle for this dilatant material was different in undrained and drained tests; the difference is attributed to the fact that the rate of dilation is smaller in an undrained test than it is in a drained test. Consistent with the findings of others, the material is more resistant to undrained cyclic loading for triaxial compression than for triaxial extension. In rotational shear tests in which the second invariant of the deviatoric stress tensor is held constant, the shear stress path (after being normalized by the mean normal effective stress) approached an envelope that is comparable but not identical in shape to a Mohr-Coulomb failure surface. As the stress path approached the envelope, the shear end deviatoric strains continued to increase in an unsymmetrical smooth spiral path. During the rotational shear tests, the direction of the deviatoric strain-rate vector (deviatoric strain increment divided by the magnitude of change in Lode angle) was observed to be about midway between the deviatoric stress increment vector and the normal to a Mohr-Coulomb failure surface in the deviatoric plane. The stress ratio at the transition from contractive to dilative behavior (i.e., “phase transformation”) was also observed to depend on the direction of the stress path; therefore this stress ratio is not a fundamental property. Results from torsional hollow cylinder tests with rotation of stress directions are presented in new graphical formats to help understand and interpret the fundamental soil behavior.     

Instability and Static Liquefaction on Proportional Strain Paths for Sand at Low Stresses

The behavior of Hostun RF sand on proportional strain paths at low confining pressures (20 to 100 kPa) is considered in this paper. In such paths, a constant dilation rate is imposed during shear. The usual features of pore pressure increase (contracting material) or decrease (dilating material) are here observed depending upon whether the imposed dilation rate is respectively greater or smaller than the “natural” dilation rate at failure (as measured in a drained test). Particular attention is given to the static liquefaction phenomenon, which is seen to occur for loose as well as dense sand provided the imposed dilation rate is large enough to lead to a continuous pore pressure increase during shear. Instability tests performed at low confining pressures on proportional strain paths show that the instability line is strain path dependent. It does not coincide with the peak deviator stress line in proportional strain paths tests, in general, but does coincide with the line d2W = 0 (nil second increment of total work).     

Modeling the Stress-Strain Relations of Sand in Cyclic Plane Strain Loading

A modeling procedure to simulate stress-strain relations of sand subjected to cyclic loading is proposed. Results from drained plane strain compression, extension, and cyclic loading tests on Toyoura sand are analyzed. The monotonic loading behavior is simulated by the generalized hyperbolic equation to use as the skeleton curves in the simulation of cyclic behavior. To construct hysteretic stress-strain curves based on the skeleton curves, the Masing’s rule is generalized to the proportional rule consisting of the internal and external rules. The drag rule is then introduced to simulate cyclic stress-strain behavior in which the stress amplitude increases at a decreasing rate during cyclic loading with a constant strain amplitude. It is assumed that any plastic shear strain increment taking place in a certain direction drags the whole skeleton curve for loading in the opposite direction towards the direction of the concerned shear strain increment. The measured cyclic stress-strain behavior is well simulated by the proposed method.     

Effects of Particle Crushing in Stress Drop-Relaxation Experiments on Crushed Coral Sand

Stress relaxation and stress drop-relaxation tests have been performed to complement a test series performed to study strain rate, creep, and stress drop-creep effects on crushed coral sand. Drained experiments with constant effective confining pressure of 200 kPa were performed in which triaxial specimens of crushed coral sand were loaded to initial stress differences of 500, 700, and 900 kPa, followed by stress drops of 0, 100, 200, 300, and 400 kPa at which points the axial strains were kept constant while the axial stress relaxation and the volumetric strains were observed. The stress drops produced delays in initiation of stress relaxation that were proportional with the magnitudes of the stress drops. The experiments show that sands do not exhibit classic viscous effects, and their behavior is indicated as “nonisotach,” while the typical viscous behavior of clay is termed “isotach.” Thus, there are significant differences in the time-dependent behavior patterns of sands and clay. A mechanistic picture of time effects in sands is proposed.     

Characterization of Cemented Sand by Experimental and Numerical Investigations

In this study, the effects of cementation on the stress–dilatancy and strength of cemented sand are investigated through experimental characterizations using triaxial tests and numerical simulations using the discrete element method. At small strains, dilatancy is hindered by the intact bonding network that produces a web-patterned force chain. After yielding, the increase in the dilatancy accelerates. Two competing but intimately related processes determine the peak strength: Bond breakages cause a strength reduction but the associated dilatancy leads to a strength increase. This finding and the experimental observation that the dilatancy at the peak state increases with increasing cement content explain why the measured peak-state strength parameters, c′ and ?p′, are relevant to the cement content. With increasing strain, the force-chain distribution gradually changes to a thick columnar shape, which mostly appears inside the shear band. At the ultimate state, the cementing bonds remain to form clusters, even within the shear band. The existence of clusters not only helps maintain the overall volumetric dilation but also prevents force-chain buckling, which in turn increases the associated strength.     

Stress Dilatancy and Fabric Dependencies on Sand Behavior

A stress dilatancy model with embedded microstructural information, originally developed by the writers, is used to illustrate the pivotal importance of dilatancy and fabric on the behavior of sand. Fabric, as a second-order tensor, enters into the stress dilatancy equation obtained from a microscopic analysis of an ensemble of rigid particles. Model simulations of sand behavior are carried out in triaxial stress conditions along strain paths with varying degrees of controlled dilation (or compaction) including isochoric deformations as a particular case. Under particular strain paths and fabric conditions, it is shown that a relatively dense sand can succumb to instability or liquefaction under other than isochoric (undrained) conditions. This phenomenon is in accord with laboratory experiments in which dilation or compaction is controlled by modulating the amount of water flowing in or out of a sand specimen during shearing. Mixed drained–undrained loading paths are also simulated with particular reference to fabric dependence at a fixed void ratio. Model simulations capture most of the observed characteristics of sand response, such as instability and asymptotic behavior under various conditions.     

Cyclic Critical Stress States of Sand with Nonfrictional Effects

New observations of experimental facts are made in this study to understand the physical essentials regarding the changes in mobilized maximum stress and phase-transformation stress states of saturated sands subjected to cyclic undrained shear applications. Saturated sands are not purely frictional materials that are governed only by frictional law (i.e., the shear-normal stress ratio). They are also characterized by the following effects of nonfrictional behavior: (1) Irreversible dilatancy effect; (2) viscous effect at large strain rate; and (3) coupling effect of viscous to frictional resistance. It was found that the first effect reduces the limiting shear resistance, whereas the second and third effects increase it. Based on this finding, 2D and 3D criteria that consider both the frictional and nonfrictional effects are developed by introducing several new concepts such as the “true effective stress,” “moving stress space,” and “moving spatially mobilized plane.” Their effectiveness is confirmed experimentally.     

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.     

Possibility of Postliquefaction Flow Failure due to Seepage

This study examines the postliquefaction flow failure mechanism, in which shear strain develops due to seepage upward during the redistribution of excess pore water pressure after an earthquake. The mechanism is addressed as both a soil element and a boundary value problem. Triaxial tests that reproduce the stress state of a gentle slope subjected to upward pore water inflow were performed, with the results showing that shear strain can increase significantly after the stress state reaches the failure line. In addition, when subject to equivalent volumetric strain, shear strain is considerably larger in loose sand conditions than in dense sand. Compared with consolidated and drained test results, the dilatancy coefficient β, which indicates the rate of dilation, is the same as that obtained from pore water inflow tests. Torsional hollow cylinder tests were also performed to ascertain the limit of dilation of sand specimens. It was found that the β values are nonlinear in behavior. In addition, a postliquefaction flow failure mechanism based on one-dimensional consolidation theory and shear deformation behavior as a result of pore water inflow is proposed.     

State-Dependent Strength of Sands from the Perspective of Unified Modeling

This paper discusses the state-dependent strength of sands from the perspective of unified modeling in triaxial stress space. The modeling accounts for the dependence of dilatancy on the material internal state during the deformation history and thus has the capability of describing the behavior of a sand with different densities and stress levels in a unified way. Analyses are made for the Toyoura sand whose behavior has been well documented by laboratory tests and meanwhile comparisons with experimental observations on other sands are presented. It is shown that the influence of density and stress level on the strength of sands can be combined through the state-dependent dilatancy such that both the peak friction angle and maximum dilation angle are well correlated with a so-called state parameter. A unique, linear relationship is suggested between the peak friction angle and the maximum dilation angle for a wide range of densities and stress levels. The relationship, which is found to be in good agreement with recent experimental findings on a different sand, implies that the excess angle of shearing due to dilatancy in triaxial conditions is less than 40% of that in plane strain conditions. A careful identification of the deficiency of the classical Rowe’s and Cam-clay’s stress–dilatancy relations reveals that the unique relationship between the stress ratio and dilatancy assumed in both relations does not exist and thereby obstructs unified modeling of the sand behavior over a full range of densities and stress levels.     

Relating Kα to Relative State Parameter Index

The effect of an initial static shear stress on the undrained cyclic loading resistance of saturated sand, as observed in laboratory testing, is often expressed in terms of a correction factor, Kα. Prior research has demonstrated that Kα depends on the state of the sand, as commonly represented by its relative density and confining stress conditions. This dependence of Kα on state is intuitively consistent with critical state concepts, but the implementation of this dependence in practice has been hindered by the absence of simple methods for estimating state and its effects without having to perform an extensive program of laboratory testing. In this paper, a simple index for representing state is derived from Bolton’s (1986) relative dilatancy index and shown to provide a reasonable and practical index for describing the variation of Kα with both relative density and confining stress.     

Sampling Disturbance Effects in Normally Consolidated Clays

The effects of sampling disturbance are investigated by performing single element triaxial tests in which specimens of normally consolidated resedimented Boston blue clay are disturbed according to the “perfect sampling approach” (PSA) and the “ideal sampling approach” (ISA). The effects of PSA and ISA disturbance on the compression and undrained shear behavior of the soil are quantified by comparison with the intact behavior. The results indicate that the release of shear stress associated with PSA disturbance causes a modest change in the engineering properties of the soil. The effects of ISA disturbance are, on the other hand, very significant and increase systematically with the amplitude of the strain imposed. An increase in disturbance causes a decrease in the compression ratio, a decrease in the undrained strength, and an increase in the strain at failure and the recompression ratio, but has a minor effect on the preconsolidation pressure. These effects derive from the decrease in effective stress and from the damage to the soil fabric that occur as a result of sampling. The loss in undrained strength is primarily controlled by the decrease in effective stress and the post-disturbance strength ratio (cu/σs′) may be related to the “induced” overconsolidation ratio (IOCR = σvc′/σs′) through a SHANSEP equation.     

Probabilistic Models for Cyclic Straining of Saturated Clean Sands

A maximum likelihood framework for the probabilistic assessment of postcyclic straining of saturated clean sands is described. Databases consisting of cyclic laboratory test results including maximum shear and postcyclic volumetric strains in conjunction with relative density, number of stress (strain) cycles, and “index” test results were used for the development of probabilistically based postcyclic strain correlations. For this purpose, in addition to the compilation of existing data from literature, a series of stress-controlled cyclic triaxial and simple shear tests were performed on laboratory-constituted saturated clean sand specimens. The variabilities in testing conditions (i.e., type of test, consolidation procedure, confining pressure, rate of loading, etc.) were corrected through a series of correction schemes, the effectiveness of which were later confirmed by the discriminant analyses results. Volumetric and shear strain boundary curves were developed in the cyclic stress ratio versus N1,60,CS or qc,1 domain. In addition to being based on significantly extended and higher quality databases, contrary to the existing judgmentally derived deterministic ones, proposed correlations have formal probabilistic bases, and so provide insight regarding uncertainty of strain predictions or probability of exceeding a target strain value. Probabilistic uses of the proposed correlations were illustrated by three sets of examples. A companion paper applied and calibrated the proposed volumetric strain correlation to semiempirically evaluate postearthquake settlement of level, free-field sites. For the calibration, case history soil profiles, composed of a broad range of sand types and depositional characteristics, shaken by a number of earthquakes, were used. Superior predictions of field settlements by this laboratory data-based cyclic strain assessment approach were concluded to be strongly mutually supportive.     

Implicit Algorithm for Modeling Unsaturated Soil Response in Three-Invariant Stress Space

An implicit integration algorithm has been refined to predict the stress–strain–strength response of unsaturated soil under suction-controlled, multiaxial stress paths that are not achievable in a conventional cylindrical cell. The algorithm supports numerical analyses in a deviatoric plane by using a mixed control constitutive driver, in conjunction with a generalized Cam-Clay model that also incorporates the influence of a third stress invariant, or Lode-angle θ, within a constant-suction scheme. True triaxial data from a previously accomplished series of suction-controlled triaxial compression, triaxial extension, and simple shear tests on 10-cm cubical specimens of silty sand, were used for the tuning and validation of the refined algorithm. The elliptical Willam–Warnke surface was adopted for simulation of unsaturated soil response in three-invariant stress space. Reasonably satisfactory agreement was observed between experimental and predicted deviatoric stress versus principal strain response for different suction states, as well as between experimental and predicted strength loci in a deviatoric plane.     

Degradation of Stiffness of Cemented Calcareous Soil in Cyclic Triaxial Tests

The deformation characteristics of artificially cemented calcareous soil subjected to undrained cyclic triaxial loading are investigated at different confining pressure and cyclic stress levels. The influence of cementation on the shear stiffness is investigated by comparing the behavior of cemented and uncemented soils with similar initial conditions. It is observed that the deviator stress and the deviatoric strain at yield reduced with increasing number of cycles for cemented sand due to progressive degradation of bond, which results in significant decrease in stiffness. On the other hand, a strain-hardening effect is observed in uncemented sand and this results in increasing yield stress and strain with progressive number of cycles. A linear relationship between degradation index and number of cycles is observed for cemented sand. This relationship has been synthesized in the form of an empirical equation by modifying a previously proposed equation for cohesive soils. This empirical equation was further used to evaluate the fatigue life of soils by adopting a failure criterion.     

Performance of a Three-Dimensional Hvorslev–Modified Cam Clay Model for Overconsolidated Clay

It is well established that critical state soil mechanics provides a useful theoretical framework for constitutive modeling of soil. Most of the critical state models, including the popular modified Cam clay (MCC) model, predict soil behavior in the subcritical region fairly well. However, the predictions for heavily overconsolidated soils, in the supercritical region, are not so satisfactory. Furthermore, the critical state models were developed from triaxial test data and extension of these models into three-dimensional (3D) stress space has not been investigated thoroughly. In the present work, experiments were carried out to obtain stress–strain behavior of overconsolidated soil in triaxial compression, extension, and plane strain conditions. A novel biaxial device has been developed to conduct the plane strain tests. The experimental results were used to formulate Hvorslev–MCC model which has MCC features in the subcritical region and Hvorslev surface in the supercritical region. The model was generalized to 3D stress space using the Mohr–Coulomb failure criterion. A comparison of the model predictions with test results has indicated that the Hvorslev–MCC model performs fairly well up to the peak supercritical point, during which deformations are fairly uniform and the specimens remain reasonably intact. Limitations of this simple model in predicting postpeak localization are also discussed. The model’s predictions for volumetric response in different shear modes seem to agree reasonably well with test results.     

Effect of Loading Mode on Strain Softening and Instability Behavior of Sand in Plane-Strain Tests

Experimental data to study the effect of loading mode on the strain softening and instability behavior of sand under plane-strain conditions are presented in this paper. A new plane-strain apparatus was adopted to conduct K0 consolidated drained and undrained tests under both deformation-controlled and load-controlled loading modes. The drained behavior of very loose and medium dense sand and the undrained behavior of very loose sand under plane-strain conditions were characterized. The test results show that the loading mode affects the postpeak behavior and controls whether strain softening or instability will occur in the postpeak region. Shear bands occurred in tests conducted on medium dense sand, but not in tests for very loose sand. The failure line and critical state line are not affected by the loading mode. The study also shows that the concept of a unique “ultimate state” for both dense and loose sand as previously established based on conventional drained triaxial tests is not supported by the plane-strain data.     

Drained Cyclic Behavior of Sand with Fabric Dependence

The behavior of sand is characterized by dilatancy, an increase in overall volume as particles move over each other when the sand assembly is subjected to shear stresses. A stress-dilatancy model for sand in the cyclic loading regime, taking into account microstructural changes, is presented. The model is subsequently integrated into a constitutive model based on hypoplasticity so as to accurately calculate volume changes induced by fabric and dilatancy changes during cyclic loading. Furthermore, it is assumed that fabric evolution is a function of the ratio of deviatoric to mean principal stress. Some numerical examples that capture the effect of fabric changes on the drained cyclic behavior of sand are presented. Among others, it is found that initial fabric can drastically alter both the dilatancy response and net volume change at shakedown conditions even though the initial void ratio and confining pressure are kept unchanged. The void ratio here is defined as the volume of voids to that of solids.     

Shear Band Formation in Plane Strain Experiments of Sand

A series of biaxial (plane strain) experiments were conducted on three sands under low (15 kPa) and high (100 kPa) confining pressure conditions to investigate the effects of specimen density, confining pressure, and sand grain size and shape on the constitutive and stability behavior of granular materials. The three sands used in the experiments were fine-, medium-, and coarse-grained uniform silica sands with rounded, subangular, and angular grains, respectively. Specimen deformation was readily monitored and analyzed with the help of a grid pattern imprinted on the latex membrane. The overall stress-strain behavior is strongly dependent on the specimen density, confining pressure, sand grain texture, and the resulting failure mode(s). That became evident in different degrees of softening responses at various axial strains. The relationship between the constitutive behavior and the specimens' modes of instability is presented. The failure in all specimens was characterized by two distinct and opposite shear bands. It was found that the measured dilatancy angles increase as the sand grains' angularities and sizes increase. The measured shear band inclination angles are also presented and compared with classical Coulomb and Roscoe solutions.