Dilatancy and Shear Strength of Sand at Low Confining Pressures

Sand dilates with shearing at a rate that increases with increasing relative density (DR) and decreases with increasing effective confining stress (σc′). The peak friction angle of a sand depends on its critical-state friction angle and on dilatancy. In this paper, we develop a simple correlation between peak friction angle, critical-state friction angle, and dilatancy based on triaxial compression and plane-strain compression test data for sand for a range of confining pressures from very low levels to approximately 196 kPa.     

Numerical Simulation of the Influence of Initial State of Sand on Element Tests and Micropile Performance

This paper presents a state-dependent constitutive model for sand formulated within the critical-state framework and its implementation into a numerical analysis (FLAC3D) program. The implemented model was verified by using drained triaxial results on sands. The proposed model is shown to capture the stress path dependent behavior of sand over a wide range of densities and confining pressures well based on a unique set of parameters. Numerical simulations of the behavior of a micropile under vertical loading shows that the side and tip resistance, and thus the total resistance of the pile, are functions of the “in situ state” of soil as defined by the state parameter ψ = e-ec in which e is the void ratio and ec the void ratio at the critical state.     

Shear Strength and Stiffness of Silty Sand

The properties of clean sands pertaining to shear strength and stiffness have been studied extensively. However, natural sands generally contain significant amounts of silt and∕or clay. The mechanical response of such soils is different from that of clean sands. This paper addresses the effects of nonplastic fines on the small-strain stiffness and shear strength of sands. A series of laboratory tests was performed on samples of Ottawa sand with fines content in the range of 5–20% by weight. The samples were prepared at different relative densities and were subjected to various levels of mean effective consolidation stress. Most of the triaxial tests were conducted to axial strains in excess of 30%. The stress-strain responses were recorded, and the shear strength and dilatancy parameters were obtained for each fines percentage. Bender element tests performed in triaxial test samples allowed assessment of the effect of fines content on small-strain mechanical stiffness.     

Direct Shear Tests on JSC-1A Lunar Regolith Simulant

A series of direct shear tests were conducted on the JSC-1A lunar regolith simulant in a 101.6-mm- (4-in.-) diameter container. The direct shear test provides a unique mode of failure that aids the development of excavation tools for the Moon. Relative density and normal load were varied to study the strength behavior of such granular material at peak and critical state conditions. The values of the internal friction angle ranged from 30 to 70°. A relationship between the internal friction angle of the direct shear and the published triaxial compression test results is presented. Additionally, the measured dilatancy angle is related to the difference in peak and critical state stress friction angles.     

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.     

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.     

Sydney Soil Model. II: Experimental Validation

This paper presents simulations of the mechanical behavior of reconstituted and natural soils using a new model presented in a companion paper and referred to as the “Sydney soil model.” It is demonstrated that the performance of the proposed model is essentially the same as that of modified Cam clay model when describing the behavior of clays in laboratory reconstituted states. The model has also been employed to simulate the drained and undrained behavior of structured clays and sands, including calcareous clay and sand. Five sets of conventional triaxial tests and one set of true triaxial tests have been considered. It is demonstrated that the new model provides satisfactory qualitative and quantitative modeling of many important features of the behavior of structured soils, particularly in capturing various patterns of the stress and strain behavior associated with soil type and structure. A general discussion of the model parameters is also included. It is concluded that the Sydney soil model is suitable for representing the behavior of many soils if their ultimate state during shearing can be defined by an intrinsic and constant stress ratio M* and a unique relationship between mean effective stress and voids ratio, i.e., a unique p′-e curve.     

Reappraisal of Size Effect of Bearing Capacity from Plastic Solution

A simplified method for estimating the ultimate bearing capacity of surface footings on sand is described with special attention to the dependency of the angle of internal friction of sand on confining stress. An extended slip line method is developed, in which the dependency of the angle of internal friction on the confining stress is formulated from results of conventional triaxial compression tests for various sands. Based on results from a comprehensive series of calculations employing the extended slip line method, the writers reappraise size effects on bearing capacity and investigate the relationship between strength parameters of sand and size effects on bearing capacity. A modified formula and several diagrams that provide a simple estimation method are proposed to consider size effects on bearing capacity. A comparison between estimations using the formula and ultimate bearing capacities measured from several series of centrifuge tests demonstrates the practicability of the proposed method for both strip and circular footings.     

Effects of Cross Anisotropy on Three-Dimensional Behavior of Sand. I: Stress–Strain Behavior and Shear Banding

The significance of material cross anisotropy in sands is underscored and experimentally evaluated in a series of true triaxial tests on Santa Monica beach sand in a cubical device. Failure patterns, initiation and development of shear banding, and complete stress–strain behavior are described for the entire range of the Lode angle under general three-dimensional loading conditions. Localized failure was found to govern the ultimate resistance of the sand for intermediate values of parameter b = (σ2?σ3)/(σ1?σ3) in each of the three sectors of the octahedral plane. Variations of the friction angle are fully described and show its significant dependence on the inherent cross-anisotropic material structure.     

Failure and Dilatancy Properties of Sand at Relatively Low Stresses

Analysis of geotechnical problems concerned by low confinement such as design of shallow foundations and analysis of slope stability and soil liquefaction requires modeling of the soil behavior at low stresses. This note includes a laboratory study of the behavior of Hostun RF sand at low cell pressure (20–50?kPa). Isotropic and triaxial compression drained tests were performed. Drained tests show that both failure and dilatancy angles at low stresses are stress dependent. The contractive/dilative phase transition is observed for loose sand, which may result from the overconsolidated nature of this sand for low values of cell pressure.     

Postpeak Strength of Interfaces in a Stress-Dilatancy Framework

Laboratory sand-steel interface tests, using a range of sand sizes on a wide range of surface roughnesses, have been conducted using a direct shear apparatus modified to enable reliable measurements of both friction and dilation. The paper looks at the minimum interface strength after peak, termed here the postpeak strength, and assesses its dependence on roughness, density, and stress level. Its upper limit is the large displacement direct shear friction angle, related to but not equal to the critical state friction angle. When data are normalized by this value, they show linear dependence on the logarithm of relative roughness in the intermediate zone between smooth and rough. Once the roughness dependence of the postpeak strength has been allowed for, dilatant interfaces are found to follow classical stress–dilatancy relationships. It appears that there is no fundamental difference in the responses of sand-on-steel or sand-on-sand interfaces.     

Critical State of Granular Materials Based on the Sliding-Rolling Theory

By representing the assembly by a simplified column model, a constitutive theory was recently developed for a two-dimensional assembly of rods. This theory, referred to as the sliding-rolling theory, is extended in this paper to represent the triaxial stress-strain behavior of granular materials. The sliding-rolling theory provides a dilatancy rule and an expression for the slope of the line of zero dilatancy in the stress space. These rules are then combined with triaxial observations to provide a microstructural interpretation of the critical state of granular materials. According to the theory, the slope of the critical state line in the stress space depends on the interparticle friction angle and the degree of contact normal anisotropy. To verify the basic ideas of the sliding-rolling theory, numerical experiments are conducted using the discrete-element method on three-dimensional assemblies of spheres.     

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.     

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.     

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.     

Shear Strength and Stiffness of Sands Containing Plastic or Nonplastic Fines

This paper presents the results of a systematic laboratory investigation on the static behavior of silica sand containing various amounts of either plastic or nonplastic fines. Specimens were reconstituted using a new technique suitable for element testing of homogeneous specimens of sands containing fines deposited in water (e.g., alluvial deposits, hydraulic fills, tailings dams, and offshore deposits). The fabric of sands containing fines was examined using the environmental scanning electron microscope (ESEM). Static, monotonic, isotropically consolidated, drained triaxial compression tests were performed to evaluate the stress-strain-volumetric response of these soils. Piezoceramic bender element instrumentation was developed and integrated into a conventional triaxial apparatus; shear-wave velocity measurements were made to evaluate the small-strain stiffness of the sands tested at various states. The intrinsic parameters that characterize critical state, dilatancy, and small-strain stiffness of clean, silty, and clayey sands were determined. All aspects of the mechanical behavior investigated in this study (e.g., stress-strain-volumetric response, shear strength, and small-strain stiffness) are affected by both the amount and plasticity of the fines present in the sand. Microstructural evaluation using the ESEM highlighted the importance of soil fabric on the overall soil response.     

Elastoplastic Model for Clay with Microstructural Consideration

Clay material can be considered as a collection of clusters, which interact with each other mainly through mechanical forces. From this point of view, clay is modeled by analogy to granular material in this paper. An elastoplastic stress-strain relationship for clay is derived by using the granular mechanics approach developed in previous studies for sand. However, unlike sand, clay deformation is generated not only by the mobilizing but also by compressing clusters. Thus, in addition to the Mohr-Coulomb’s plastic shear sliding and a dilatancy type flow rule, a plastic normal deformation has been modeled for two clusters in compression. The overall stress-strain relationship can then be obtained from the mobilization and compressing of clusters through a static hypothesis of the macro-micro relations. The predictions are compared with the experimental results for clay under both drained and undrained triaxial loading conditions. Three different types of clay, including remolded and natural clay, have been selected to evaluate the model’s performance. The comparisons verify that this model is capable of accurately reproducing the overall behavior of clay, which accounts for the influence of key parameters such as void ratio and mean stress. A section of this paper is devoted to show the model’s capability of considering the influence of inherent anisotropy on the stress-strain response under undrained triaxial loading conditions.     

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.     

Shear Strength Behavior of Fiber-Reinforced Sand Considering Triaxial Tests under Distinct Stress Paths

The results of drained triaxial tests on fiber reinforced and nonreinforced sand (Osorio sand) specimens are presented in this work, considering effective stresses varying from 20 to 680?kPa and a variety of stress paths. The tests on nonreinforced samples yielded effective strength envelopes that were approximately linear and defined by a friction angle of 32.5° for the Osorio sand, with a cohesion intercept of zero. The failure envelope for sand when reinforced with fibers was distinctly nonlinear, with a well-defined kink point, so that it could be approximated by a bilinear envelope. The failure envelope of the fiber-reinforced sand was found to be independent of the stress path followed by the triaxial tests. The strength parameters for the lower-pressure part of the failure envelope, where failure is governed by both fiber stretching and slippage, were, respectively, a cohesion intercept of about 15?kPa and friction angle of 48.6?deg. The higher-pressure part of the failure envelope, governed by tensile yielding or stretching of the fibers, had a cohesion intercept of 124?kPa, and friction angle of 34.6?deg. No fiber breakage was measured and only fiber extension was observed. It is, therefore, believed that the fibers did not break because they are highly extensible, with a fiber strain at failure of 80%, and the necessary strain to cause fiber breakage was not reached under triaxial conditions at these stress and strain levels.