Stress-dilatancy Relation Research Articles

Behavior of Steel Furnace Slag, Coal Wash, and Rubber Crumb Mixtures with Special Relevance to Stress–Dilatancy Relation

AbstractThe influence of rubber crumbs on the dilatancy behavior and critical state of steel furnace slag (SFS), coal wash (CW), and rubber crumbs (RC) mixtures was investigated via a series of mon...

Stress–Dilatancy For Crushed Latite Basalt

Abstract In this article, the stress–dilatancy relationship for crushed latite basalt is analysed by using Frictional State Theory. The relationship is bilinear, and the parameters α and β determine these two straight lines. At the initial stage of shearing, the mean normal stress increment mainly influences breakage, but at the advanced stage, it is shear deformation that influences breakage. At the advanced stage of shearing, the parameter αpt represents energy consumption because of breakage and βpt mainly represents changes in volume caused by breakage during shear. It is also shown that breakage effect is significant at small stress levels and the η-Dp plane is important to fully understand the stress–strain behaviour of crushed latite basalt in triaxial compression tests.

A Simple Method for Assessing the Peak Friction Angle of Sand at Very Low Confining Pressures

Abstract This article presents a simple experimental method that may be used to assess the peak friction angle of sand at very low effective confining pressures (i.e., <10 kPa). Soil strength at very low confining pressures is important to a variety of geotechnical problems, including small-scale 1-g physical modeling and micro-gravity environments. It is often very difficult to assess friction angles at very low confining pressures in conventional element tests because some factors, such as specimen self-weight and machine friction, become significant. Currently, there are no published methods available to measure the peak friction angle of sands below a mean effective stress at failure of about 6 kPa. To address this need, a simple tilt test method is proposed that involves preparing a soil to a specified relative density within a steel mold and then tilting the mold to induce a shallow slope failure. Based on infinite slope analysis, the tilt angle at which the slope fails is equal to the peak friction angle. A modified stress-dilatancy relationship is also proposed that can be calibrated for a specific soil using a combination of tilt test and triaxial test data. This relationship can be used to predict peak friction and dilation angles over the low stress range.

Stress-Dilatancy of Cambria Sand for Triaxial Tests at High Pressures

In this paper, the stress-dilatancy relationship of Cambria sand for drained triaxial compression and extension tests at high stress level is investigated. The stress dilatancy relationship is obtained by use of frictional state theory and experimental tests data published in literature. It is shown that stress-dilatancy relationship is bilinear, described by three parameters of frictional state theory: critical frictional angle and two other parameters. It is accepted that critical friction angle is independent of confining pressure. The two additional parameters are strongly dependent on confining pressure and different for initial and advanced stages. The point at which the values of these parameters change is termed as Transformation Shear Point. This point is not simply visible either in stress ratio-strain or the volume strain-shear strain relationship which are traditionally shown in soil mechanics papers. Transformation Shear Point is very characteristic in stress ratio-plastic dilatancy plane. Thus, stress ratio- plastic dilatancy is very important for describing stress-strain behaviour of soils. The relationship shown in the paper can be used in soil modelling in the future.

Influence of Dilation on the Strength of Sand – Steel Interfaces

In this paper the sand-steel interface behaviour is analysed on the basis of frictional state theory. It is shown that for a small stress level the influence of dilatancy is fundamentally similar for sand-steel and sand-sand behaviour for a direct shear test. The use of the new parameter describes the influence of surface roughness on stress-dilatancy relationship. The peak strength of sand-steel is analysed. Values of the new parameter grow with normalised roughness for smooth surface and are constant for intermediate and rough surfaces. It is also shown that values of normalised friction coefficient obtained theoretically are similar with those shown in literature.

Particle breakage energy and stress dilatancy in drained shear of rockfills

Particle breakage can be quite considerable even at low-stress levels, and it has a significant influence on the stress dilatancy of rockfill materials. In order to reasonably quantify the energy consumed by particle breakage, which has yet to be satisfactorily addressed, a function of friction ratio relating to the distortional strain and critical state stress ratio is proposed in this paper. The friction ratio references the widely accepted evolution rule of particle breakage and the new calculated energy consumption by particle breakage is proved to result in a reasonable distribution against increasing strain. Then, the rate of energy consumption per unit volume of aggregates is certified and suggested to be a linear relationship with the proposed friction ratio. Additionally, a stress dilatancy relationship for rockfill materials, based on modified Rowe's dilatancy law, is derived and verified by successfully predicting the stress dilatancy of drained rockfill triaxial specimens. It is believed to be an effective stress dilatancy for the study of elastoplastic constitutive model of rockfill materials.

3-D DEM simulations of drained triaxial tests on inherently anisotropic granulates

A series of triaxial tests were simulated by the discrete element method (DEM) to study the effect of inherent anisotropy on the mechanical behaviours of granulates. In this study, clumps consisting of a collection of rigid spherical balls were used to simulate irregular-shaped particles, and the multi-layer under-compaction method was employed to prepare the anisotropic specimens with different initial density and fabric. The macroscopic responses including the strength characteristic, the volumetric response, the critical state and the stress–dilatancy relationship were carefully examined. In addition, two microscopic descriptors, the particle orientation (PO) fabric and contact normal (CN) fabric, were mainly monitored and investigated to shed light on the underlying micro-mechanics. The results show that comparing to the experimental results on natural sands, the typical macro-mechanical behaviours of anisotropic granulates can be successfully captured in the DEM simulations. Specimens with smaller inclination angle are more dilative. Nevertheless, the influence of the inherent anisotropy on the shear–dilatancy relation seems to be limited. The joint invariants NP representing the relative orientation between the particle fabric direction and stress direction can be taken as an indicator of critical state. The rearrangement of the CN is more sensitive to the applied force than that of PO.

Study of the effects of anisotropic consolidation on granular materials under complex stress paths using the DEM

We adopt the discrete element method with a periodic boundary to investigate the comprehensive effects of initial anisotropic consolidation derived from an initial stress ratio ( $$K_{\mathrm{c}})$$ under complex stress paths (b). Both the initial stiffness and deformation mechanisms are systematically analyzed. The dilatancy rate and the stress–dilatancy relationship depend on stress paths and $$K_{\mathrm{c}}$$ . Meanwhile, the distinction between the critical-state mechanical responses under different stress paths also depends on the initial stress ratio. The equation of the relationship between the excess friction angle and peak state parameter is conceptually given, where the coefficients are related to both the initial stress ratio and stress path. At the microscopic level, the properties of contact forces, coordination number, and anisotropies of the assemblies are discussed. The samples with different initial stress ratios exhibit different extents of distinction in terms of various coordinate numbers. The probability density functions of both contact normal and tangential forces are evidently affected by the initial stress ratio, and the effects of the initial stress ratio gradually vanish as shearing proceeds. The strong force chain networks under different conditions of $$K_{\mathrm{c}} $$ and b are explored, showing the comprehensive mechanism of force transmission. At the same strain level, the proportion and the magnitude of strong contact forces strengthen with the improvement of initial anisotropic consolidation, and the initial anisotropic consolidation can evidently improve the ability of the assemblies to cluster along the intermediate principal direction with the increase of b. Different anisotropy parameters show different sensitivities to the initial stress ratio. The fabric-based strength descriptor is linearly correlated to the stress ratio under different $$K_{\mathrm{c}} $$ conditions. The fabric and small-strain stiffness are combined to investigate the macro- and microscopic connections that are subject to inherent anisotropic consolidation as well as the intermediate stress ratio.

Instability of sands under axisymmetric proportional strain and stress loadings

This paper compares the pre-failure instability of sands under axisymmetric proportional strain and axisymmetric proportional stress conditions. Based on a deviatoric hardening plasticity model, the critical hardening moduli under both conditions were obtained by the second-order work criterion. In the proportional strain condition, the instability of sands depends on the stress–dilatancy relationship and the imposed strain proportion ratio. Loose sand is prone to instability; dense sand maintains stable behaviour under the undrained condition, butit may become unstable in expansive loading. In the proportional stress condition, dense sand shows stable behaviour; loose sand can be stable as long as the stress proportion is at a sufficient distance from zero. A material state-dependent elasto-plasticity model was used to predict the instability of sands in triaxial tests under the proportional strain condition, constant mean stress condition, and constant shear stress condition; the predicted instability behaviour agrees well with the experimental data.

An analytical solution for geotextile-wrapped soil based on insights from DEM analysis

This paper presents a novel analytical solution for geotextile-wrapped soil based on a comprehensive numerical analysis conducted using the discrete element method (DEM). By examining the soil–geotextile interface friction, principal stress distribution, and stress–strain relations of the constituent soil and geotextile in the DEM analysis, a complete picture of the mechanical characterization of geotextile-wrapped soil under uniaxial compression is first provided. With these new insights, key assumptions are verified and developed for the proposed analytical solution. In the DEM analysis, a near-failure state line that predicts stress ratios relative to the maximums at failure with respect to deviatoric strain is uniquely identified; dilation rates are found to be related to stress ratios via a single linear correlation regardless of the tensile stiffness of the geotextile. From these new findings, the assumptions on the stress-state evolution and the stress–dilatancy relation are developed accordingly, and the wrapped granular soil can therefore be modeled as a Mohr–Coulomb elastoplastic solid with evolving stress ratio and dilation rate. The development of the proposed analytical model also demonstrates an innovative approach to take advantage of multiscale insights for the analytical modeling of complex geomaterials. The analytical model is validated with the DEM simulation results of geotextile-wrapped soil under uniaxial compression, considering a wide range of geotextile tensile stiffnesses. To further examine the predictive capacity of the analytical model, the stress–strain response under triaxial compression conditions is solved analytically, taking both different confining pressures and geotextile tensile stiffnesses into account. Good agreement is obtained between the analytical and DEM solutions, which suggests that the key assumptions developed in the uniaxial compression conditions also remain valid for triaxial compression conditions.

Stress-Dilatancy for Soils. Part III: Experimental Validation for the Biaxial Condition

Abstract The validation of the general stress-dilatancy relationship is shown based on biaxial compression test data presented in the literature under drained and undrained conditions. Rowe’s and Bolton’s relationships can be treated as simplified forms of the general stress-dilatancy relationship. The stress ratio values are a function of not only the dilatancy but also the intermediate principal stress, the non-coaxiality angle defined by Gutierrez and Ishihara and the stress-strain path. For many granular soils, the critical frictional state angle of the shearing resistance Φo = Φ′cv and parameters α and β are functions of the drainage condition, the stress level and the stress and strain paths.

Stress-Dilatancy for Soils. Part IV: Experimental Validation for Simple Shear Conditions

Abstract This paper validates the frictional state theory using published experimental data from simple, direct and ring shear tests. Simple shear is treated as a special case of plane strain conditions. In order to define complete stress and strain, additional assumptions are made: in the direct shear and ring shear tests, simple shear is assumed to occur in the shear band. For Φo = Φ′cv = Φ′r, the stress-dilatancy relationship obtained from the frictional state theory is similar to the relationships proposed by Taylor and Bolton. Further experiments, especially those that use a hollow cylindrical shear apparatus, are necessary to fully validate the frictional state theory in simple shear conditions.

Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials

The critical state is significant to the mechanical behaviors of granular materials and the foundation of the constitutive relations. Using the discrete element method (DEM), the mechanical behaviors of granular materials can be investigated on both the macroscopic and microscopic levels. A series of DEM simulations under true triaxial conditions have been performed to explore the critical state and dilatancy behavior of granular materials, which show the qualitatively similar macroscopic responses as the experimental results. The critical void ratio and stress ratio under different stress paths are presented. A unique critical state line (CSL) is shown to indicate that the intermediate principal stress ratio does not influence the CSL. Within the framework of the unique critical state, the stress–dilatancy relation of DEM simulations is found to fulfill the state-dependent dilatancy equations. As a microscopic parameter to evaluate the static determinacy of the granular system, the redundancy ratio is defined and investigated. The results show that the critical state is very close to the statically determinate state. Other particle-level indexes, including the distribution of the contact forces and the anisotropies, are carefully investigated to analyze the microstructural evolution and the underlying mechanism. The microscopic analysis shows that both the contact orientations and contact forces influence the mechanical behaviors of granular materials.

Micromechanics-based multimechanism bounding surface model for sands

Within the multimechanism framework, a micromechanics-based sand model is presented based upon the bounding surface and critical state theories. This model follows the assumption that the macroscopic responses of sands can be determined by summing the contributions from a macroscopic volumetric mechanism and an infinite number of virtual microscopic shear mechanisms in various orientations. Each virtual shear mechanism characterizes the microscopic shear deformations and the dilatancy-induced volumetric deformations in three mutually perpendicular directions. The deformations in each direction are described by using a microscopic shear stress–strain relationship founded upon the bounding surface theory and a microscopic stress–dilatancy relationship, respectively. The shear strength with the SMP yield criterion and the stress–dilatancy relationship introduce a state variable for compatibility with the critical state theory. The correlations between the microscopic and macroscopic model parameters are established, and most of them are defined by soil parameters with a clear physical meaning. With a spatial distribution of microscopic shear mechanisms, the model can intrinsically consider the stress-induced anisotropy, the non-coaxial behaviour of stress and strain increment in their principal directions, and the effect induced by principal stress rotations without requiring additional model parameters. The comparison of the simulated and experimental results indicates its excellent capability in predicting sand responses in stress–strain curve as well as stress path under different drainage and loading conditions.

Effect of aspect ratio on triaxial compression of multi-sphere ellipsoid assemblies simulated using a discrete element method

Here, we present a numerical investigation of the mechanical behavior of ellipsoids under triaxial compression for a range of aspect ratios. Our simulations use a multi-sphere approach in a three-dimensional discrete element method. All assemblies were prepared at their densest condition, and triaxial compression tests were performed up to extremely large strains, until a critical state was reached. The stress–strain relationship and the void ratio–strain behavior were evaluated. We found that the stress–dilatancy relationship of ellipsoids with different aspect ratios could be expressed as a linear equation. In particular, the aspect ratio influenced the position of the critical state lines for these assemblies. Particle-scale characteristics at the critical state indicate that particles tend to be flat lying, and the obstruction of particle rotation that occurs with longer particles affects their contact mechanics. Lastly, anisotropic coefficients related to aspect ratio were investigated to probe the microscopic origins of the macroscopic behavior. A detailed analysis of geometrical and mechanical anisotropies revealed the microscopic mechanisms underlying the dependency of peak and residual strengths on aspect ratio.

Stress-Dilatancy for Soils. Part II: Experimental Validation for Triaxial Tests

Abstract Different forms of the stress-dilatancy relations obtained based on the frictional theory for the triaxial condition are presented. The analysed test data show that the shear resistance of many soils is purely frictional. The angle Φ0 represents the resistance of the soil as a combined effect of sliding and particle rolling on the macro-scale during shear at the critical frictional state. The stress-plastic dilatancy relations differ not only for triaxial compression and extension but also for drained and undrained conditions. The experiment investigated shows the correctness of the frictional state theory in the triaxial condition.

Constitutive Modeling for Transparent Granular Soils

AbstractTransparent granular soil was recently found to be greatly useful for observations of the internal deformation in geotechnical model tests. Therefore, it is necessary to investigate the stress–strain and stress–dilatancy behaviors of transparent granular soil and also to propose a constitutive model for this material. In this study, drained triaxial shearing tests were conducted to investigate the stress–strain and stress–dilatancy relations of transparent granular soil. It was found that this material showed a state-dependent stress–strain behavior similar to that of sands. A state-dependent constitutive model within the framework of the critical-state theory was proposed to describe the stress–strain and stress–dilatancy behaviors of this material. This model was found to well describe the stress–strain behaviors (e.g., strain softening and volumetric expansion) and the hook-shaped stress–dilatancy behaviors from the test data in both the Group A (for the calibration of material constants) and G...

Fibres and soils: A route towards modelling of root-soil systems

The addition of flexible fibres to granular, cohesionless soils, has a marked influence on the stress:strain and volumetric response. Experimental observations provide inspiration for the development of continuum models for the mechanical, pre-failure behaviour of these fibre/soil mixtures. Such generic models and the deduced mechanisms of response should be applicable to other combinations of soils and flexible fibres such as plant roots. Two features are particularly important: the distribution of the orientations of fibres (no method of preparation produces an isotropic distribution) and the allowance for the volume of void space not only occupied, but also influenced, by the presence of the fibres.A simple shear element is used as a quasi-one-dimensional demonstrator platform for the presentation of the continuum constitutive model. Such an element represents a familiar configuration in which phenomena, such as dilation and friction, can be directly observed. A basic constitutive model for sand is adapted to this simple shear element; the fibres are added as a separate component able to withstand tension but without flexural stiffness. As the soil-fibre mixture deforms, the straining of the soil generates stresses in favourably oriented fibres. The model is used to clarify some aspects of the response of the fibre-soil mixtures: the influence of fibres on the volumetric behaviour; the existence and nature of asymptotic states; and the stress–dilatancy relationship.

Modeling the Stress-Dilatancy Relationship of Unsaturated Silica Sand in Triaxial Compression Tests

AbstractIt is well known that partial saturation increases the shear strength and dilatancy of unsaturated sand. However, little research has been carried out on the actual stress-dilatancy relationship. This paper shows that the increase in peak shear strength caused by partial saturation is consistent with an increase in dilatancy, and that conventional stress-dilatancy theories are still valid for unsaturated sand. The use of state indexes as a proxy for dilatancy were investigated and extended to unsaturated sands. Additionally, these indexes can be used to establish a critical state line that is based on material properties only. The validity of the stress-dilatancy theories and the use of state indexes offer simplicity in modeling the shear behavior of unsaturated sand. This will be demonstrated in this paper with the Nor-Sand model, with which the wetting collapse can be explained as a consequence of a loss of dilatancy characteristics.

Elastoplastic Constitutive Model for Rockfill Materials Considering Particle Breakage

AbstractParticle breakage has a great influence on stress-strain behaviors of rockfill materials. A new relative breakage was proposed for rockfill materials. A critical state line incorporating particle breakage was termed as a breakage critical state line (BCSL). It was found that the BCSL position of rockfill materials pertained to the relative breakage. An elastoplastic model considering state dependence and particle breakage was proposed for rockfill materials. The effect of particle breakage was incorporated into the proposed state parameter, dilatancy stress ratio, stress dilatancy relation, bounding stress ratio, and plastic modulus in the proposed model. The model considering particle breakage can well predict the stress-strain and particle-breakage behaviors of rockfill materials at various confining pressures.