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).     

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.     

Double Strain Softening and Diagonally Crossing Shear Bands of Sand in Drained Triaxial Tests

A comprehensive understanding of the shear behavior of sand in the context of shear band development has not been achieved yet in spite of many detailed research works on each specified subject. In order to observe the entire drained shear behavior of Toyoura sand from the macromechanical point of view, conventional triaxial tests were performed and analyzed up to an axial strain of 30% for various void ratios, initial confining stresses, and stress paths, paying particular attention to volume changes. The strong correlation was found between “double strain softening” and “diagonally crossing shear bands” as a remarkable result. Finally, a qualitative explanation of relations among the stress–strain curve, the failure shape, the dilatancy index–strain curve and the strain localization, could be clearly made. Also, it is concluded that the dilatancy index is an indicator not only of the ratio of the volumetric strain increment to the axial strain increment but also the condition of the strain localization.     

Pore Pressure Generation of Silty Sands due to Induced Cyclic Shear Strains

It is well established that the main mechanism for the occurrence of liquefaction under seismic loading conditions is the generation of excess pore water pressure. Most previous research efforts have focused on clean sands, yet sand deposits with fines are more commonly found in nature. Previous laboratory liquefaction studies on the effect of fines on liquefaction susceptibility have not yet reached a consensus. This research presents an investigation on the effect of fines content on excess pore water pressure generation in sands and silty sands. Multiple series of strain-controlled cyclic direct simple shear tests were performed to directly measure the excess pore water pressure generation of sands and silty sands at different strain levels. The soil specimens were tested under three different categories: (1) at a constant relative density; (2) at a constant sand skeleton void ratio; and (3) at a constant overall void ratio. The findings from this study were used to develop insight into the behavior of silty sands under undrained cyclic loading conditions. In general, beneficial effects of the fines were observed in the form of a decrease in excess pore water pressure and an increase in the threshold strain. However, pore water pressure appears to increase when enough fines are present to create a sand skeleton void ratio greater than the maximum void ratio of the clean sand.     

Effects of Cross Anisotropy on Three-Dimensional Behavior of Sand. II: Volume Change Behavior and Failure

The volume change behavior of cross-anisotropic sand is studied using results of a series of cubical triaxial tests. The relationships between the volumetric response, failure, and shear localization are addressed. Rates of dilation under various three-dimensional stress conditions are evaluated in conjunction with the peak shear resistance and initiation of shear banding in specimens of dense Santa Monica beach sand. The location of the line in principal stress space along which the tendency to deform changes from compressive to dilative (the characteristic line) is determined using two different methods. The uniqueness of this characteristic line for cross-anisotropic materials is analyzed.     

Effects of Silt on Three-Dimensional Stress–Strain Behavior of Loose Sand

An experimental study on the effects of nonplastic silt on the three-dimensional drained behavior of loose sand was performed employing a true triaxial testing apparatus. Laboratory experiments were performed on clean sand and on sand containing 20% nonplastic silt. The results indicate the failure stress levels and the overall trends of the stress–strain behavior were similar for both sands. However, the volume change behavior is significantly influenced by the presence of silt. The silty sand exhibited higher degrees of volumetric contraction during shearing than the clean sand. Relative density was used as the basis of comparison. The development of a shear band appears to have caused failure in all true triaxial testing performed, except in triaxial compression. This form of instability appears to increase its influence on the experimental results as the participation of intermediate principal stress increases. The formation of shear bands also appears to coincide with the cessation of contractive volumetric strain.     

Effect of Microfabric on Mechanical Behavior of Kaolin Clay Using Cubical True Triaxial Testing

Various aspects of the mechanical behavior of kaolin clay are discussed in light of experimental observations from a series of strain controlled true triaxial undrained tests performed on cubical kaolin clay specimens with flocculated and dispersed microfabric, using a fully automated flexible boundary experimental setup with real-time feedback control system. The laboratory procedures used to prepare flocculated and dispersed microfabric specimens are presented. Mercury intrusion porosimetry is used to evaluate the pore structure of these specimens. The influence of microfabric on the consolidation behavior of kaolin clay is evaluated based on the data obtained from K0 consolidation during constant rate of strain tests and the isotropic consolidation during true triaxial tests. Undrained tests on kaolin clay show that the following vary with microfabric of specimen: The shear stiffness, excess pore pressure generated during shear, and strength and strain to failure. For both microfabrics, the observed strength behavior using cubical triaxial testing shows a similar pattern of variation with applied stress anisotropy; hence, only a marginal influence of fabric-induced anisotropy.     

Resonant Column Testing of Sands with Different Viscosity Pore Fluids

The effect of pore fluid viscosity on the stiffness, damping, and liquefaction characteristics of sands was investigated to assess the potential contributions to a centrifuge model seismic response for soils saturated with high-viscosity pore fluid. Resonant column tests with cyclic loading frequencies in the range of 20–45 Hz were performed on a variety of fluids and sand sizes. At a strain level less than 2 × 10?4, the damping increased with pore fluid viscosity and shear strain amplitude, and it decreased with sand particle size. However, at shear strain greater than about 2 × 10?4, the increased skeleton damping tended to mask any effect of additional damping due to fluid viscosity. The liquefaction tests on fine silica sand revealed that the increase in total energy dissipation was not more than 10% for 100 cS oil when compared with water at a driving frequency of 25 Hz. Based on the experimental results, a simple model is proposed to examine the dependency of viscous damping on pore fluid viscosity, loading frequency, particle size, and shear strain amplitude.     

Shear Banding in True Triaxial Tests and Its Effect on Failure in Sand

The occurrence of failure, mechanisms that create failure, and soil behavior in the vicinity of failure have been investigated. One mechanism is smooth peak failure, in which the soil continues to behave as a continuum with uniform strains, and smooth peak failure is followed by strain softening. Another mechanism is shear banding, whose occurrence in the plastic hardening regime limits the strength of the soil. True triaxial tests have been performed on tall prismatic specimens of Santa Monica Beach sand at three relative densities in a modified version of a cubical triaxial apparatus to study the effect of shear banding on failure in the full range of the intermediate principal stress. The experiments show that the strength increases as b [=(σ2 ? σ3)/(σ1 ? σ3)] increases from 0 to about 0.18, remains almost constant until b reaches 0.85, and then decreases slightly at b = 1.0. Shear banding initiates in the hardening regime for b-values of 0.18–0.85. Thus, peak failure is caused by shear banding in this middle range of b-values, and a smooth, continuous 3D failure surface is therefore not generally obtained for soils.     

Induced-Partial Saturation for Liquefaction Mitigation: Experimental Investigation

The technical feasibility of a new liquefaction mitigation technique is investigated by introducing small amounts of gas/air into liquefaction-susceptible soils. To explore this potential beneficial effect, partially saturated sand specimens were prepared and tested under cyclic shear strain controlled tests. A special flexible liquefaction box was designed and manufactured that allowed preparation and testing of large loose sand specimens under applied simple shear. Partial saturation was induced in various specimens by electrolysis and alternatively by drainage-recharge of the pore water. Using a shaking table, cyclic shear strain controlled tests were performed on fully and partially saturated loose sand specimens to determine the effect of partial saturation on the generation of excess pore water pressure. In addition, the use of cross-well radar in detecting partial saturation was explored. Finally, a setup of a deep sand column was prepared and the long-term sustainability of air entrapped in the voids of the sand was investigated. The results show that partial saturation can be achieved by gas generation using electrolysis or by drainage-recharge of the pore water without influencing the void ratio of the specimen. The results from cyclic tests demonstrate that a small reduction in the degree of saturation can prevent the occurrence of initial liquefaction. In all of the partially saturated specimens tested, the maximum excess pore pressure ratios ranged between 0.43 and 0.72. Also, the cross-well radar technique was able to detect changes in the degree of saturation when gases were generated in the specimen. Finally, monitoring the degree of partial saturation in a 151?cm long sand column led to the observation that after 442 days, the original degree of saturation of 82.9% increased only to 83.9%, indicating little tendency of diffusion of the entrapped air out of the specimen. The research reported in this paper demonstrated that induced-partial saturation in sands can prevent liquefaction, and the technique holds promise for use as a liquefaction mitigation measure.     

Analysis of Shear Banding in True Triaxial Tests on Sand

A series of true triaxial tests have been performed on rectangular prismatic specimens of Santa Monica Beach sand at three different relative densities to study the occurrence of failure, mechanisms that create failure, and soil behavior in the vicinity of failure. One mechanism is smooth peak failure, in which the soil continues to behave as a continuum with uniform strains, and smooth peak failure is followed by strain softening. Another mechanism is shear banding, whose occurrence in the plastic hardening regime limits the strength of the soil. Presented here are analyses based on theoretical conditions for localization and subsequent shear banding and on the results of the true triaxial tests. Thus, the strength increases as b [=(σ2 ? σ3)/(σ1 ? σ3)] increases from 0 to about 0.18, remains almost constant until b reaches 0.85, and then decreases slightly at b = 1.0. Shear banding initiates in the hardening regime for b-values of 0.18–0.85. Thus, peak failure is caused by shear banding in this middle range of b-values, and a smooth, continuous 3D failure surface is therefore not generally obtained for soils. The experimental results agree with the theoretical conditions for the occurrence of shear banding and its consequent effect on the 3D failure stress states for soil.     

Computational Model for Cyclic Mobility and Associated Shear Deformation

In saturated clean medium-to-dense cohesionless soils, liquefaction-induced shear deformation is observed to accumulate in a cycle-by-cycle pattern (cyclic mobility). Much of the shear strain accumulation occurs rapidly during the transition from contraction to dilation (near the phase transformation surface) at a nearly constant low shear stress and effective confining pressure. Such a stress state is difficult to employ as a basis for predicting the associated magnitude of accumulated permanent shear strain. In this study, a more convenient approach is adopted in which the domain of large shear strain is directly defined by strain space parameters. The observed cyclic shear deformation is accounted for by enlargement and/or translation of this domain in deviatoric strain space. In this paper, the model formulation details involved are presented and discussed. A calibration phase is also described based on data from laboratory sample tests and dynamic centrifuge experiments (for Nevada sand at a relative density of about 40%).     

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.     

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.     

Effect of Intermediate Principal Stress on Overconsolidated Kaolin Clay

The influence of intermediate principal stress on the mechanical behavior of overconsolidated kaolin clay is investigated using three-dimensional true triaxial testing on cubical specimens. A flexible boundary, true triaxial setup with a real-time feedback control system was used to test soil specimens under stress and strain-control modes. Undrained tests on kaolin clay show that the following vary with intermediate principal stress: the stiffness at small strains, excess pore pressure generated during shear, and strength and strain to failure. Failure occurred at peak deviator stress followed by shear band formations and localized bulging. Prior theoretical formulations of bifurcation and undrained instability support these experimental observations. Analysis of data in the octahedral plane indicates that kaolin clay follows a nonassociative flow rule, which is described by a constant third stress invariant failure criterion with von Mises plastic potential surface.     

State Pressure Index for Modeling Sand Behavior

The effort to model sand behavior within the framework of critical-state soil mechanics would benefit from a state variable that relates the current void ratio and mean pressure of the soil to its void ratio and mean pressure at the critical state. In this paper we propose a state pressure index, Ip, which is defined as the ratio of the current mean pressure to the mean pressure at the critical state that corresponds to the current void ratio. Using this state pressure index, a bounding surface hypoplasticity model for sand is modified so that the phase transformation and failure stress ratios both depend on Ip and merge into the critical-state stress ratio at failure. The Ip dependency introduced enables use of a single set of model constants in modeling sand behavior for various initial confining pressures and densities under both undrained and drained conditions. Dilatancy, strain softening, and strain hardening are simulated for both loose and dense sands. Simulations from the modified model are compared with results of laboratory tests of drained and undrained triaxial compression.     

DSC Model for Soil and Interface Including Liquefaction and Prediction of Centrifuge Test

Realistic predictions of dynamic soil–structure interaction problems require appropriate constitutive models for the characterization of soils and interfaces. This paper presents a unified model based on the disturbed state concept (DSC). The parameters for the models for the Nevada sand, and sand–metal interface are obtained based on available triaxial test data on the sand and interfaces. The predicted stress–strain–pore water pressure behavior for the sand using the DSC model is compared with the test data. In addition, a finite element procedure with the DSC model, based on the generalized Biot’s theory, is used to predict the measured responses for a pile (aluminum) sand foundation problem obtained by using the centrifuge test. The predictions compared very well with measured pore water pressures. The DSC model is used to identify microstructural instability leading to liquefaction. A procedure is proposed to apply the proposed method for analysis and design for dynamic response and liquefaction.     

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.     

Characterization of Failure in Cross-Anisotropic Soils

Drained true triaxial tests on dense Santa Monica Beach sand deposited with a cross-anisotropic fabric have been performed to study the failure condition in the principal stress space. The failure surface was assumed to be symmetric around the vertical axis (on the octahedral plane of the principal stress space), but varying as a function of the Lode angle. Data from previously performed consolidated-undrained true triaxial tests on San Francisco Bay Mud and data from triaxial compression, triaxial extension, and plane strain tests on Toyoura sand showed similar behavior in terms of effective stresses. A three-dimensional failure criterion is proposed for characterization of failure in cross-anisotropic soils, under commonly occurring conditions when loading and depositional directions coincide and no significant rotation of principal stresses occur. This cross-anisotropic criterion is developed using a coordinate rotation of the principal stress space and utilization of an existing isotropic failure formulation. Derivation of the three required parameters is explained and illustrated. The proposed criterion is compared with various experimental results; and it is demonstrated that the failure criterion for cross-anisotropic soils captures the experimental behavior with good accuracy.     

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.