Instability Conditions of Loose Sand in Plane Strain

When a loose sand specimen is loaded under an undrained condition, it may become unstable. The instability conditions may be specified by an instability line determined using undrained tests. However, the instability behavior of sand has seldom been studied under plane-strain conditions. Experimental data obtained under both triaxial and plane-strain conditions are presented in this paper to define the instability conditions of loose sand under plane-strain conditions. Using the state parameter, a unified relationship can be established between the normalized slope of instability line and the state parameters for both axisymmetric and plane-strain conditions. Using this relationship, the instability conditions established under axisymmetric conditions can also be used for plane-strain conditions.     

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.     

Influence of Stress Ratio and Stress Path on Behavior of Loose Decomposed Granite

This paper presents results from four series of triaxial compression tests of loosely compacted decomposed granite (DG) or silty sand on both isotropically and anisotropically consolidated specimens. These tests included undrained tests, drained tests with constant deviator stress, and a decreasing mean effective stress path. The silty sand possessed high compressibility during isotropic compression. The observed high compressibility is probably attributed to the loose soil structure created by using the moist tamping method and the presence of crushable feldspar in the soil. Static liquefaction behavior and the so-called “reversed” sand behavior were observed in all undrained tests. This “reversed” sand behavior can be readily explained by the high compressibility of DG leading to the nonparallel and converging nature of the initial state line and the critical state line. Preshearing resulted in a more brittle response in the postpeak behavior. The higher the initial stress ratio (ηc), the smaller the ductility. Structural collapse of DG was observed. This collapse is characterized by a sudden large increase in both the axial and contractive volumetric strains. The mobilized angles of friction at collapse range from 31.8° to 38.7°, which are smaller than the critical state angle (?col′), but higher than the mobilized friction angle of the instability line (28.1°) determined by the isotropically consolidated undrained tests. A trilinear approximate relationship can be found between ?col′ and ηc and a liquefaction potential index is introduced to provide a simple preliminary design parameter for static liquefaction and instability prone slopes.     

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.     

Monotonic and Cyclic Liquefaction of Very Loose Sands with High Silt Content

The results from an experimental study on sands with high nonplastic silt content are presented. Drained and undrained triaxial compression tests, undrained cyclic triaxial tests, and drained∕undrained instability tests were performed on specimens of loose Nevada sand with 40% silt content. The behavior was observed to be somewhat different from previously published tests with sands at lower silt content. The greater silt content appears to provide a more volumetrically contractive response throughout the entire stress-strain curve. However, some aspects of the response were similar to sands with lower silt content. Monotonic undrained tests indicated “reverse” behavior, i.e., static liquefaction occurred at low confining pressures and increasing dilatant volume-change tendency was observed with increasing confining pressure. Analyzing the results using the concepts of steady state resulted in a unique steady-state line only when undrained tests were sheared from the same isotropic compression line. When specimens of different initial densities were tested at the same initial confining pressures, the resulting steady-state points did not fall on the same steady-state line.     

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.     

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.     

Instability in Granular Materials: Experimental Evidence of Diffuse Mode of Failure for Loose Sands

The influence of three loading paths on the collapse of loose sand is analyzed with a particular attention paid to the onset of collapse and the mode of failure exhibited. Experimental results on conventional undrained triaxial compression tests, constant shear drained tests, as well as quasi-constant shear undrained path are presented, compared, and analyzed. It is now recognized that some collapses can occur before the Mohr-Coulomb plastic limit criterion is reached, and our recent results obtained with the new arrangement built up highlight that these collapses occur under a diffuse mode of failure. An extensive experimental series of tests shows that the first negative value of the second-order work computed using experimental data corresponds to the loss of controllability. Moreover, it is shown that the stress ratios at collapse and the corresponding mobilized angles of friction are very close for all types of tests. For similar void ratios, the onset of collapse is thus largely independent of the loading path under drained and undrained conditions but depends on a stress state to bring the material inside the unstable domain and also on the current direction of the stress increment. Indeed, it appears that the orientations of the stress increments at collapse for all tests are the same, what explains, according to the second-order work criterion, that collapse occurs at the same stress ratio. A potentially unstable domain, depending on the stress increment direction, can thus be defined.     

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).     

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.     

Assessment of the Undrained Response of Sands under Limited and Complete Liquefaction

The technique presented deals with the assessment, based on drained test behavior and formulation, of the undrained postcyclic stress-strain behavior of sands under limited or complete (full) liquefaction and its associated strength. At present, there is no particular procedure that allows assessment of such undrained postcyclic behavior that could develop full (pore-water pressure ratio, ru = 1) or limited (ru<1) liquefaction. The prediction of the undrained postliquefaction (full or limited liquefaction) response presented here is based on basic properties of sand such as its relative density (Drc) [or (N1)60 blowcount], the effective angle of internal friction (φ), the roundness of the sand grains (ρ), and the drained axial strain at 50% stress level (ε50). The technique presented accounts for the excess pore-water pressure induced by cyclic loading (Δuc) and the postcyclic excess pore-water pressure generated under undrained monotonic loading (Δud).     

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.     

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.     

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.     

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.     

Liquefaction Resistance of Sandy Soils under Partially Drained Condition

In order to simulate the effect of drainage on soils adjacent to gravel drains that are installed as countermeasure against liquefaction, several series of cyclic triaxial tests were performed on saturated sands under partially drained conditions. The condition of partial drainage under cyclic loading was simulated in the laboratory using triaxial testing equipment installed with a drainage control valve to precisely regulate the volume of water being drained from test specimens. Effects of both drainage conditions and loading frequencies on cyclic response were incorporated through the coefficient of drainage effect, α*. Experimental results showed that for sand exhibiting strain softening, the partially drained response was controlled by the critical effective stress ratio while for sand showing strain hardening behavior, the controlling factor was the phase transformation stress ratio. Moreover, test results indicated that the minimum liquefaction resistance under partially drained conditions can be used as a parameter to describe the liquefaction resistance of sands improved by the gravel drain method. From these results, a simplified procedure for designing gravel drains based on the factor of safety (FL) concept was proposed.     

Stress Deformation and Fluid Pressure of Bone Specimens under Cyclic Loading

Cyclic loading has been known to induce fluid flow and thus mechanotransduction in bones. In the past, four-point bending tests have been used exclusively in studying fluid flow in bones. In order to better understand the mechanism of deformation and fluid flow under loading, compression tests were done on trabecular bone specimens under drained and undrained conditions. In the drained tests, the volume change was observed, whereas in the undrained tests, excess pore fluid pressure was measured. Cyclic loading tests were conducted in addition to monotonic loading tests to observe the permanent volume change or excess pore fluid pressure with loading cycles. A fast loading rate gave a sharp rise in the excess fluid pressure compared to a slow loading rate. The strength and stiffness of the specimens appeared to deteriorate with an increased speed of loadings, but there was no appreciable difference between the results obtained from drained and undrained tests. The drained and undrained tests as described allowed a better understanding of bone behavior under loadings for a coupled stress-flow analysis.     

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.     

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.     

Microbially Induced Cementation to Control Sand Response to Undrained Shear

Current methods to improve the engineering properties of sands are diverse with respect to methodology, treatment uniformity, cost, environmental impact, site accessibility requirements, etc. All of these methods have benefits and drawbacks, and there continues to be a need to explore new possibilities of soil improvement, particularly as suitable land for development becomes more scarce. This paper presents the results of a study in which natural microbial biological processes were used to engineer a cemented soil matrix within initially loose, collapsible sand. Microbially induced calcite precipitation (MICP) was achieved using the microorganism Bacillus pasteurii, an aerobic bacterium pervasive in natural soil deposits. The microbes were introduced to the sand specimens in a liquid growth medium amended with urea and a dissolved calcium source. Subsequent cementation treatments were passed through the specimen to increase the cementation level of the sand particle matrix. The results of both MICP- and gypsum-cemented specimens were assessed nondestructively by measuring the shear wave velocity with bender elements. A series of isotropically consolidated undrained compression (CIUC) triaxial tests indicate that the MICP-treated specimens exhibit a noncollapse strain softening shear behavior, with a higher initial shear stiffness and ultimate shear capacity than untreated loose specimens. This behavior is similar to that of the gypsum-cemented specimens, which represent typical cemented sand behavior. SEM microscopy verified formation of a cemented sand matrix with a concentration of precipitated calcite forming bonds at particle-particle contacts. X-ray compositional mapping confirmed that the observed cement bonds were comprised of calcite.