Constitutive Model for Static Liquefaction

A general, three-dimensional formulation of the elastoplastic refined Superior sand constitutive model is presented. The model is aimed at realistic simulation of liquefaction phenomena occurring in loose saturated granular materials under monotonic static loading. The isotropic hardening/softening is related to plastic deformation and distance to a reference yield surface. The nonassociated flow rule is used with the closed yield surface introduced previously in the Superior sand model. The refined model accounts for the different response of materials with different deposition densities. The model prediction of drained and undrained plane-strain compression is presented and compared with the response in triaxial compression/extension loading. Static and kinematic instability states also are discussed.     

Simple Plasticity Sand Model Accounting for Fabric Change Effects

A simple stress-ratio controlled, critical state compatible, sand plasticity model is presented, first in the triaxial and then in generalized stress space. The model builds upon previous work of the writers, albeit the presentation here is made with extreme simplicity in mind, and three novel aspects are introduced. The first is a fabric-dilatancy related quantity, scalar valued in the triaxial and tensor valued in generalized stress space, which is instrumental in modeling macroscopically the effect of fabric changes during the dilatant phase of deformation on the subsequent contractant response upon load increment reversals, and the ensuing realistic simulation of the sand behavior under undrained cyclic loading. The second aspect is the dependence of the plastic strain rate direction on a modified Lode angle in the multiaxial generalization, a feature necessary to produce realistic stress-strain simulations in nontriaxial conditions. The third aspect is a very systematic connection between the simple triaxial and the general multiaxial formulation, in order to use correctly the model parameters of the former in the implementation of the latter. The simulative ability of the model is illustrated by comparison with data over a very wide range of pressures and densities.     

Micromechanical Analysis for Interparticle and Assembly Instability of Sand

Instability of granular material may lead to catastrophic events such as the gross collapse of earth structures, and thus it is an important topic in geotechnical engineering. In this paper, we adopt the micromechanics approach for constitutive modeling, in which the soil is considered an assembly of particles, and the stress-strain relationship for the assembly is determined by integrating the behavior of the interparticle contacts in all orientations. Although analyses regarding material instability have been extensively studied for a soil element at the constitutive level, it has not been considered at the interparticle contact level. Through an eigenvalue analysis, two modes of instability are identified at the local contact level: the singularity of tangential stiffness matrix and the loss of positiveness of second-order work. The constitutive model is applied to simulate drained and undrained triaxial tests on Toyoura sand of various densities under various confining pressures. The predictions are compared with experimentally measured instability at the assembly level. The modes of stability at the interparticle contact level and their relations to the overall instability of the assembly are also analyzed.     

Liquefaction and Undrained Response Evaluation of Sands from Drained Formulation

A general approach has been established to assess the undrained stress-strain curve and effective stress path under monotonic loading from drained triaxial tests. An appropriate formulation of a drained and drained rebounded (i.e., overconsolidated) triaxial test response is developed that, in turn, allows the assessment of developing liquefaction and the undrained behavior of saturated sands. The formulation presented is based upon reported experimental drained test results that were obtained from different investigators using different testing techniques. This formulation is a function of the confining pressure and basic properties of the sand, such as relative density, uniformity coefficient, and particle shape (roundness), which can be obtained from visual inspection. The approach is verified by comparing predicted and reported (observed) undrained behavior. The developed formulas allow one to predict the potential of sand to liquefy, the type of liquefaction, the peak and residual strength values, as well as the whole undrained stress-strain curve and effective stress path. The simplicity of this approach makes it an attractive general method to characterize the undrained behavior of sands in a preliminary analysis with no need to run sophisticated experimental tests.     

Modeling Liquefaction by a Multimechanism Model

An anisotropic constitutive model was recently presented for describing the stress–strain behavior of granular materials with considerations for the initial and induced anisotropy. The model was developed within the framework of a microstructural theory known as the sliding–rolling theory. The resulting model falls within the definition of multimechanism models. The model was shown to satisfactorily represent the drained and undrained behaviors under monotonic loading. The framework used in the model allows extension to describe the behavior under cyclic loading, which is the subject of the present paper. Specifically, the model is further developed for representing the undrained behavior of granular materials under one- and two-way cyclic loading, some of which cause liquefaction resulting in large strain accumulations and the others lead to limited pore pressure and strain accumulations. The validity of the model is verified using triaxial data on Nevada sand.     

Upper Bound for Cylinder Movement Using “Elastic” Fields and Its Possible Application to Pile Deformation Analysis

A new upper bound failure mechanism for the problem of rigid cylinder motion is presented. The velocity field associated with the mechanism is derived from a known elastic solution by similitude of the deformation field. The obtained upper bound value is 21% higher than the exact solution. However, the failure mechanism is continuous, involving no discontinuity, not even on the cylinder perimeter. The solution has a certain advantage if one, for example, wishes to combine its mechanism with a strain path approach to investigate the T-bar penetration problem. The absence of discontinuities in the mechanism also allows evolution of deformation under serviceability conditions, by associating a mobilized strength as a function of an average strain. Based on this approach, a load transfer function for lateral loading of piles in an undrained clay is suggested. This load transfer function involves nonlinear scaling of a stress-strain curve obtained from a triaxial compression test. An analytical, closed form, solution is given for the case of a hyperbolic stress-strain curve.     

Saturation and Preloading Effects on the Cyclic Behavior of Sand

In order to study pore water pressure response and liquefaction characteristics of sand, which has previously experienced liquefaction, two series of cyclic triaxial tests were run on medium dense sand specimens. In the first test series the influence of the soil saturation under undrained cyclic loading has been studied. It summarizes results of cyclic triaxial tests performed on Hostun-RF sand at various values of the Skempton’s pore-pressure coefficient. Analysis of experimental results gives valuable insights on the effect of soil saturation on sand response to undrained cyclic paths. In the second series of tests, the preloading influence on the resistance to the sands liquefaction has been realized on samples at various histories of loading. It was found that a large preloading induces a reduction of the resistance of sands to liquefaction.     

Pressure-Level Dependency and Densification Behavior of Sand Through Generalized Plasticity Model

Natural soil deposits and man-made earth structures exhibit complicated engineering behavior that is influenced by factors such as the stress level and drainage conditions. The stress conditions within a soil structure vary greatly, ranging from very low to very high values, due to the dead weight, loading and boundary conditions. Saturated sand deposits that exhibit drained conditions under static loading become undrained when subject to earthquake excitations. The Pastor–Zienkiewicz–Chan model has demonstrated considerable success in describing the inelastic behavior of soils under isotropic monotonic and cyclic loadings, including liquefaction and cyclic mobility. This study proposed modifications to the Pastor–Zienkiewicz–Chan model so that effects of stress level and densification behavior are simulated. The proposed model suggested that the angle of internal friction, elastic and plastic moduli are dependent on the pressure levels. Relevant modifications were made to incorporate a power term of mean effective stress on the loading plastic modulus so that a stress-level dependent volume change is obtained in combination with the stress-dilatancy relationship. To better simulate cyclic loading with reference to densification behavior, an exponential term of plastic volumetric strain is included for the unloading and reloading plastic moduli. A total of 11 parameters are needed for monotonic loading, whereas 15 parameters are needed in describing the cyclic behavior. The model simulations were compared with undrained and drained triaxial test results of several kinds of sand under dense and loose states. The predictive capability for monotonic and cyclic loading conditions was also demonstrated.     

Numerical Study of Impact of Soil Anisotropy on Seismic Performance of Retaining Structure

Recent laboratory investigations indicate that the stress–strain–strength responses of granular soils are appreciably affected by the fabric orientation of the soil relative to the frame of principal stresses. Especially, a sand specimen exhibiting a dilative response during triaxial compression may show a contractive response during triaxial extension under otherwise identical conditions. This observation is of practical importance for applications concerning essentially undrained loading conditions, because the effective mean normal stress at failure, and consequently, the shear strength, associated with an undrained contractive path are considerably lower than those following a dilative path. This raises a question about the impact of soil anisotropy on seismic performance of retaining structures subjected to active and passive earth pressures, because the directions of principal stresses in retained soils for the two cases are very different. This note presents a set of fully coupled finite-element analyses incorporating an anisotropic sand model. The analyses reveal that the impact of fabric anisotropy could be significant when the retaining structure is under passive earth pressure conditions.     

Elastoplastic Model for Cemented Soils

This paper presents a model for bonded or cemented soils within the framework of hardening plasticity. The model is based on the concepts that (1) the strength of a cemented soil can be considered to be made up of two components, the usual strength of the soil skeleton and the strength of cementation bonds; and (2) the deformation of the soil is associated with the component of stresses on the soil skeleton (excluding the bonds), as in a reconstituted soil, whereas the cement bonds offer additional resistance at any given strain level. The overall response of the soil under loading can be visualized as two stiffnesses acting in parallel for the given unit strain. Separate stress-strain relations are defined for the two components and they are then combined to give the overall response. The stress-strain relationship for the soil skeleton component is described here using the modified Cam-clay model. A simple model within the elastoplastic framework is proposed for the “cemented” component. The cemented component incorporates strain softening. The input parameters required are minimal, well defined, and easily determined. The model predictions are compared with test data of several soils under drained and undrained triaxial conditions.     

Undrained Anisotropic Monotonic Behavior of Sand from In Situ Tests

A procedure for estimating the undrained stress-strain behavior of sand from drained self-boring pressuremeter and seismic piezocone penetration tests is proposed in this paper. The procedure offers an inexpensive alternative to laboratory testing and avoids the uncertainty of the empirical methods based on index measurements such as the Standard Penetration Test blow count and the tip resistance in a Piezocone Penetration Test (CPTU). To check its validity, the proposed procedure was used to infer the undrained triaxial stress-strain curves and the results were compared with laboratory triaxial tests on undisturbed samples. The undrained limit equilibrium stability of a dike was also assessed using the inferred stress-strain behavior to illustrate the usefulness of the procedure. The result of the stability analysis was found to be in qualitative agreement with the observed performance of the dike during a recent field experiment attempting to trigger static liquefaction.     

Behavior of a Loosely Compacted Unsaturated Volcanic Soil

In this paper, the stress-strain relationship 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.     

Time Effects Relate to Crushing in Sand

Based on previously obtained experimental results, a mechanistic picture of time effects in granular materials is presented. Accordingly, time effects are caused by grain crushing, which in turn is time dependent, as indicated by static fatigue of brittle materials. Triaxial compression tests have been performed on Virginia Beach sand at high pressures, where grain crushing is prevalent, to study effects of initial loading strain rates on subsequent amounts of creep and stress relaxation. Grain size distribution curves were determined after each test and the amount of crushing, as characterized by Hardin’s breakage factor, is related to the energy input to the triaxial specimens. A pattern emerges that indicates the importance of crushing for the axial and volumetric strains, while rearrangement and frictional sliding between intact grains play much smaller roles in the stress-strain and volume change behaviors of granular materials at high stresses and shear strains. Because particle crushing is a time-dependent phenomenon described as static fatigue or delayed fracture, the close relation between time effects and crushing in granular materials is established.     

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.     

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.     

Postcyclic Degradation of Strength and Stiffness for Low Plasticity Silt

Stress-controlled undrained cyclic triaxial tests followed by strain-controlled monotonic compressive shear tests were carried out on normally consolidated and overconsolidated reconstituted Keuper Marl silt to investigate the strength and stiffness degradation characteristics of a low plasticity silt. Special attention was paid to the changes in undrained strength and deformation modulus after undrained cyclic loading. It was observed that cyclic degradation in stiffness for low plasticity silt is more marked than that of strength, and this tendency increases with increasing overconsolidation ratio. It was found that a previously proposed model for predicting postcyclic degradation in strength and stiffness of normally consolidated fine-grained soils could be applied to that of overconsolidated silt but not however to the postcyclic degradation in Young’s modulus. Thus, an attempt was made to correlate postcyclic degradation of overconsolidated silt to the equivalent cyclic shear strain instead of the normalized excess pore pressure. It was concluded that cyclic shear strain was a better parameter than cyclic-induced excess pore pressure for correlating the postcyclic stiffness degradation not only for normally consolidated but also for overconsolidated silt.     

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.     

Effect of Microfabric on Undrained Static and Cyclic Behavior of Kaolin Clay

Microfabric plays an important role in the engineering behavior of soils. Although many studies are available in the literature on the effect of microfabric on the static behavior of soils, the effect on the cyclic behavior is less understood. In the present study, samples with different microfabric were prepared in the laboratory by reconstituting commercially available kaolin clay with different pore fluids under a consolidation pressure of 100?kPa. Consolidated undrained triaxial tests were carried out on these samples under static and cyclic loading conditions. Dispersed samples were found to have monotonic stress-strain behavior with a peak deviatoric stress and higher peak undrained shear strength than the flocculated samples. However, the dispersed samples were found to offer less resistance to cyclic loading. When subjected to cyclic loading, dispersed samples failed within a few cycles under a cyclic stress ratio (defined as the ratio of cyclic deviatoric stress to the undrained shear strength) close to 0.6, whereas in flocculated samples, sudden failure was not observed even at a higher cyclic stress ratio of 0.9, although strains and pore pressures accumulated to higher values. Postcyclic monotonic tests conducted on samples that did not fail under cyclic loading showed an apparent overconsolidation effect caused by cyclic loading in a similar manner, as reported in the literature.     

Use of = 0 as a Failure Criterion for Weakly Cemented Soils

There is considerable uncertainty in the determination of effective stress strength parameters of cemented soils from undrained triaxial tests. Large negative excess pore pressures are generated at relatively large strains (typically 4–5% for cemented silty sand) in isotropically consolidated undrained (CIU) tests, which results in gas coming out of solution during shear and significant variability in the measured peak deviator stress. In this study, different failure criteria for weakly cemented sands were evaluated based on the results of CIU and isotropically consolidated drained triaxial compression tests conducted on samples of artificially cemented sand. The use of = 0 as a failure criterion eliminates the variability between the undrained tests and also ensures that the mobilized failure strength is not based on the highly variable negative excess pore pressures. In addition, the resulting strains to failure are comparable to the strains to failure for the drained tests. Mohr-Coulomb strength parameters thus estimated from the undrained tests are generally lower than strength parameters obtained from drained tests, and the difference between the failure envelopes from undrained tests increases as the level of cementation increases. This divergence is attributed to differences in the stiffness of the cemented soil under the different loading conditions. The stiffness under undrained loading conditions decreases with increasing cementation due to an increase in the generation of positive excess pore pressure at low strains.     

Unified Sand Model Based on the Critical State and Generalized Plasticity

Based on the critical state concept and with the use of a state parameter, a unified generalized plasticity model is proposed for sand. The model uses a nonlinear critical state line. The plastic modulus, loading vectors and plastic flow direction vectors of a generalized plasticity model were modified so that they depend on the state parameter. With a single set of parameters, the model simulates the stress-deformation behavior of sand of different densities and pressure levels, under both drained and undrained conditions. A total of 12 parameters are required for monotonic loading and additional five parameters are included to consider cycling loading. The model is calibrated using the results of a minimum of two triaxial compression tests conducted on specimens of different densities and confining pressures. The model has been validated against the monotonic and cyclic test results of Toyoura sand, Nevada sand, and Fuji River sand. The comparison between simulations and test results showed that the model is capable of simulating sophisticated sand behavior. Its limitation in simulating monotonic loading following series of cyclic loadings of dense sand is discussed.