Principal Strain Increment Research Articles

An anisotropic hypoplastic model for clays considering the non-coaxial behavior

Previous experimental tests on clays have confirmed the non-coincidence of principal strain increments with principal stress axes even though the stress rate is colinear with the current stress. To simulate the non-coaxial behavior of saturated clay subjected to monotonic proportional or non-proportional loading with constant principal stress rate directions, an anisotropic hypoplastic model is presented in this paper. The model is proposed by incorporating an improved anisotropic asymptotic state boundary surface (ASBS) and a non-coaxial asymptotic strain rate direction into the original explicit-ASBS hypoplastic model. The non-coaxial flow results from a non-coaxial stress rate defined by a Gram-Schmidt orthogonalization process based on a reference stress tensor. The capability of the proposed model is demonstrated by simulating the test data performed in hollow cylindrical apparatus (HCA) on Wenzhou clay and Shanghai clay with different drainage conditions and initial consolidation states. In addition, a series of numerical stress probing tests have been conducted to gain further insights into the properties of the proposed model.

Anisotropic and Noncoaxial Behavior of Soft Marine Clay under Stress Path Considering the Variation of Principal Stress Direction

The influence of the variation in the principal stress direction on the anisotropic and noncoaxial behavior was investigated through several hollow cylinder apparatus (HCA) tests that were performed on reconstituted soft clay specimens under a stress path with a fixed or continuous rotation of the major principal stress axis. In particular, the varying amplitude of the deviator stress (q) and intermediate principal stress coefficients (b) were focused upon. The results indicated that the shear stiffness and strength were strongly dependent on the fixed major principal stress angle. Furthermore, apparent noncoaxiality was observed between the orientations of the major principal strain increment and the major principal stress. Consequently, the noncoaxial behavior of the reconstituted soft clay was sufficiently and effectively described using rose and polar diagrams. Furthermore, the data fluctuation indicated that the noncoaxiality of soft clay was strongly dependent on both q and b during the pure principal stress rotation (PSR). The results obtained for undisturbed clay and sand are not expected to be applicable to reconstituted clay, because its behavior is in contrast to the former two. Regarding reconstituted soft clay, the degree of noncoaxiality was observed to increase during the second rotation (N = 2) compared with that during the first rotation (N = 1). However, this trend gradually weakened with an increase in q or b values. Moreover, regardless of whether N = 1 or 2, the degrees of noncoaxiality decreased with the increase in q for b = 0.5 whereas it increased with the increase in b values for N = 1. However, those for b = 1 were the smallest for N = 2. The results are expected to provide an experimental basis for the constitutive modeling of soft clay with fixed and continuous rotations of the major principal stress axes in ocean engineering.

Experimental Study on the Anisotropy and Non-coaxiality of Frozen Standard Sand under Different Principal Stress Directions

Owing to the limitations of the apparatus, the influence of its principal stress direction on the anisotropic behavior and non-coaxiality of frozen soil has not been fully considered in previous studies. At a temperature of -10°C, a series of hollow cylinder tests for frozen standard sand (FSS) was conducted under different directional angles of major principal stress and mean principal stresses in this study. The experimental results indicate that the stress-strain-strength anisotropy and non-coaxiality of the FSS are highly dependent on the principal stress direction. The stress components of the FSS vary linearly with increasing shear stress at different directional angles of the major principal stress and mean principal stresses. With a linear increase in shear stress, the strain components of the FSS exhibited a nonlinear increasing trend. The FSS strength gradually decreased as the directional angle of the major principal stress and the mean principal stresses in the test range increased. Under the different principal stress directions, the non-coaxiality of the FSS, non-coincidence of the direction of the principal strain increment and the principal stress direction, were observed. The directions of the principal strain increment and principal stress gradually tended to be coaxial as shear stress increased. Although the non-coaxial angle of the FSS increased gradually with an increase in the directional angles of the major principal stress, it did not change with the change in the mean principal stress. The non-coaxial angle of the FSS was observed to be as large as 35° in the early stage of shearing under different mean principal stresses.

Experimental Investigation on the Deformation and Noncoaxial Characteristics of Fiber-Reinforced Aeolian Soil under Traffic Load

The cumulative plastic deformation of a foundation associated with traffic loading causes subgrade instability, and eventually, failure of retaining structures. In the present study, hollow torsional shear tests were conducted on fiber-reinforced aeolian soil involving varying fiber contents, cyclic deviator stresses, cyclic shear stresses, and consolidation confining pressures using the Small-Strain Hollow Cylinder Apparatus, developed by GDS Instruments Ltd. (GDS SS-HCA). This enabled an investigation of the deformation characteristics and noncoaxial angle changes of fiber-reinforced aeolian soil under a heart-shaped stress path. The results indicate that fiber-reinforced soil deformation under cyclic loading involves axial (ɛz), radial (ɛr), circumferential (ɛθ), and shear (γzθ) strains, and deformation increases with increasing the cyclic number. The strain increases rapidly during the first 200 cycles and then gradually. The axial deformation decreases with increasing fiber content when the fiber content is less than 2‰ and increases when the content is more than 2‰. The plastic strain and total deformation decrease with increasing confining pressure but increase as the cyclic dynamic stress and cyclic shear stress amplitudes increase. Functional equations of the cumulative axial plastic strain and vibration numbers are proposed. The relationships between the model parameters, including the fiber content and cyclic torsional shear stress, are analyzed. The principal stress axis rotation causes variations between the major principal strain increment and the principal stress directions, representing the noncoaxial angle (β). The noncoaxial angle fluctuates during each loading cycle, exhibiting a V shape, for principal stress axis angles (ασ) from −90° to −45° and −45° to 30°, and decreasing at angles varying from 30° to 90°, with a maximum noncoaxial angle of approximately 30° per cycle.

Non‐coaxial hypoplastic model for sand with evolving fabric anisotropy including non‐proportional loading

AbstractNon‐coaxial response refers to the deviation between the directions of the principal stress and plastic strain increment. In this paper, an extended hypoplastic model is proposed based on the anisotropic critical state theory, to describe the non‐coaxial and anisotropic response of sand subjected to both monotonic loading and rotation of principal stress axis. A fabric tensor that characterizes the internal structure of sand is introduced into a hypoplastic model, to reflect the effect of fabric anisotropy on the dilatancy and strength of sand. A Lode‐angle‐dependent hypoplastic potential surface is employed, rendering the flow direction no longer co‐directional with the stress tensor in the deviatoric plane. The fabric tensor is further incorporated into the flow direction, enabling the model to generate a non‐coaxial response. Upon shearing, the fabric evolves toward the loading direction following a properly defined evolution law, and the model response becomes purely coaxial at the critical state when the fabric becomes co‐directional with the loading direction. The tangential loading effect is further introduced to simulate the stiffness degradation of sand during undrained rotational shearing. The model is demonstrated to be capable of simulating the prismatic yet complex anisotropic behavior of sand under both proportional and non‐proportional loading conditions.

Effect of initial deviatoric stress on anisotropy of marine clay during principal stress rotation

The effect of the initial deviatoric stress direction and magnitude of deviatoric stress q on the strain components and non-coaxial behavior of soft marine clay during principal stress rotation was experimentally examined. The strain components and pore water pressure depended considerably on the deviatoric stress direction and q. Through polar diagrams, a notable non-coaxiality was observed between the orientations of the major principal strain increment and major principal stress, and the non-coaxial angle fluctuated with variations in the initial deviatoric stress direction and q. The results can provide an experimental basis for constitutive modeling of continuous major principal stress axes for ocean engineering.

Micromechanical analysis of non-coaxiality between stress and strain increment in granular materials

It is known that non-coaxiality between the directions of the principal stresses and the principal plastic strain increments in granular material is physically resulted from the material and mechanical anisotropy as well as their evolutions. A novel study was conducted to verify the contributions of the material and mechanical anisotropies to the magnitude of non-coaxiality during the rotation of the principal stress orientation. Micromechanical analysis indicates that the non-coaxial behavior can occur in a granular assembly with mostly non-sliding contacts acting. Moreover, the magnitude of non-coaxiality is a function of the stress level, the ratio of contact stiffness, the material and mechanical anisotropy as well as their evolutions. This has been confirmed by numerical simulation. The numerical results indicate that the non-sliding interparticle connectivity is one of the dominant sources of non-coaxiality. The interparticle sliding has been found to reduce the magnitude of the non-coaxiality.

Experimental study of stress anisotropy and noncoaxiality of dense sand subjected to monotonic and cyclic loading

Abstract The noncoaxiality of the principal stress direction and plastic principal strain increment has been broadly recognized as an influencing parameter for design of soil structures. Here we performed a series of systematic hollow cylinder experiments to study the effects of stress anisotropy on the noncoaxiality of dense Babolsar and Toyoura sands. A total of 25 undrained torsional shear tests were carried out under constant mean confining pressure, and fixed principal stress directions, α. We investigated the stress-strain behavior of dense sands for different α-directions, and cyclic stress ratio, CSR, under monotonic and cyclic loading conditions. The results show that the noncoaxiality value depends on the CSR, the level of plastic strain, and α-direction. Independent of the principal stress direction, maximum noncoaxiality value was observed at peak shear strength when there is most interlock between sand particles. Minimum noncoaxiality was recorded in α = 45° tests, in which the direction of maximum shear stress coincided with the horizontal bedding plane direction (weakest plane).

Improved Boundary Conditions for a 3D DEM Simple Shear Model

In this study, a 3D simple shear model using DEM is built based on the boundary condition of an NGI‐type bidirectional simple shear apparatus. Stack of rings used as lateral constraints in a bidirectional simple shear test is modelled by layers of clumps which is possible to be moved by particles; different contact types and parameters are used to model the sand‐loading caps, sand‐latex membrane, and sand‐sand contacts. A simple shear test using the bidirectional simple shear apparatus is performed for the calibration of the 3D DEM simple shear model. By analyzing the simulation results, the following can be concluded. (1) Rings generated by clumps can provide an accurate boundary condition, effective in computation since no contact force is needed for a clump. (2) In the simulation, the orientation of average contact force changed dramatically during shear. It is in the vertical direction (90°) before shear and changes to 45° at 40% shear strain. No shear band is observed which is consistent with the test, and particles move uniformly. (3) In the simulation, the degree of noncoaxiality is the greatest at the beginning of shear, and it is decreased during shear. However, the degree of noncoaxiality is still large at 20% shear strain where there is a 10° difference between the rotation angle of principal stress and principal strain increment.

Effect of Stress Direction on the Undrained Monotonic and Cyclic Behaviour of Dense Sands

Geotechnical design may be unsafe if the anisotropic behaviour of soil is not considered. The behaviour of anisotropic materials depends on the principal stresses and their directions. A detailed experimental programme was conducted to study the effect of stress direction on the monotonic and cyclic behaviour of dense sand. A total of 20 undrained tests were performed at a constant mean confining stress (σ'0m) constant intermediate principal stress ratio (b= (σ2-σ3)/(σ1-σ3)), and principal stress directions (α). Two fine sands, Babolsar and Toyoura, were selected as the test materials. The isotropic consolidated specimens were prepared using the wet tamping technique. The results showed that the major principal stress direction had little considerable effect on the mobilized friction angle at steady state or phase transformation. The results showed that stress direction had a significant effect on the non-coaxiality between the principal strain increment direction and the principal stress direction. The soil fabric was led to significant non-coaxiality value before the peak shear strength. Increasing the octahedral shear strains decreased the non-coaxiality value due to destruction of the soil particle interlock (soil fabric). The effect of stress direction on non-coaxiality and excess pore water pressure generation was also investigated.

Effect of bedding direction of oval particles on the behavior of dense granular assemblies under simple shear

Initial fabric anisotropy can greatly affect the shear behavior of particulate materials during shear. The bedding plane effect induced by particle orientation is one of the main fabric anisotropic factors that may affect other factors. It is hard to experimentally examine the effect of bedding direction of particles on the shear behavior of particulate materials, such as sand. A 2D discrete element method (DEM) is employed in this paper to study the influence of different orientations of oval particles on the behavior of dense assemblies under simple shear. As well as the macroscopic shear behavior, the evolution of particle orientation, contact normal, and inter-particle contact forces within the samples with different initial bedding angles during shear have been extensively examined. It was found that the initial bedding direction of the particles has great influence on the non-coaxiality between the directions of principal stress and principal strain increment. The bedding direction also affects the strength and dilatancy responses of DEM samples subjected to simple shear, and the samples with larger bedding angles exhibit higher shear strength and larger volume dilation. A modified stress-force-fabric relationship is proposed to describe the effect of particle bedding direction on the shear strength of samples, and the new equation can better describe the stress-force-fabric relationship of assemblies with initial anisotropic fabrics compared with the existing model.

Influence of the intermediate principal stress and principal stress direction on the mechanical behavior of cohesionless soils using the discrete element method

In this paper, the Discrete Element Method (DEM) is employed to numerically explore the response of hollow cylinder specimens of granular soils under complex stress paths. Two series of numerical tests are conducted to clarify the effects of the principal stress direction α and the intermediate principal stress through the b-value on the mechanical response of granular materials. The effects of α and b-value on the non-coaxiality of the principal stress and the principal plastic strain increment directions are investigated. It is observed that b-value and α significantly affect the non-coaxial behavior of granular materials. Finally, the results are discussed and compared with those obtained from physical laboratory tests.

Bearing capacity of non-associative coaxial granular materials by upper bound limit analysis and finite elements

ABSTRACTIn this paper, an upper bound estimate of the limit load on non-associative coaxial granular materials is presented. The kinematic approach of the upper bound limit analysis has been utilised. The failure mechanism is assumed to coincide with the direction of the shear bands at every point throughout the body. The shear band orientation in non-associative coaxial materials, i.e. those with the same major principal stress and major principal strain increment directions, can be found based on the angle of dilation and the major principal stress direction. Therefore, having known the stress field at limiting equilibrium, the orientation of the shear bands and hence, the failure mechanism can be obtained. In this study, the stress field is first determined by the method of stress characteristics. Then, the finite element interpolation technique is used to interpolate the stress field and to find the orientation of the shear bands at every point within the field. Once the failure mechanism and the stress state at every point along velocity discontinuities have been found, the upper bound limit analysis has been performed to estimate the limit load.

A DEM investigation on simple shear behavior of dense granular assemblies

A micromechanical investigation on simple shear behavior of dense granular assemblies was carried out by discrete element method. Three series of numerical tests were performed to examine the effects of initial porosity, vertical stress and particle shape on simple shear behavior of the samples, respectively. It was found that during simple shear the directions of principal stress and principal strain increment rotate differently with shear strain level. The non-coaxiality between the two directions decreases with strain level and may greatly affect the shear behavior of the assemblies, especially their peak friction angles. The numerical modelling also reveals that the rotation of the principal direction of fabric anisotropy lags behind that of the major principal stress direction during simple shear, which is described as fabric hyteresis effect. The degrees of fabric and interparticle contact force anisotropies increase as particle angularity increases, whereas the orientations of these anisotropies have not been significantly influenced by particle shape. An extended stress-dilatancy relationship based on ROWE-DAVIS framework was proposed to consider the non-coaxiality effect under principal stress rotation. The model was validated by present numerical results as well as some published physical test and numerical modelled data.

Cyclic Behaviors of Granular Materials under Generalized Stress Condition Using DEM

AbstractMost behaviors of granular materials have been studied under the limit conditions of stress paths such as cyclic triaxial compression and extension tests. Furthermore, the macrobehavior and micromechanical response of granular materials under more comprehensive cyclic loading tests in the generalized stress condition are not well understood. The objectives of this paper are to ensure the ability of the Discrete Element Method (DEM), to simulate the macrobehavior of granular materials under various cyclic stress paths of the generalized stress condition, and to explore the micromechanical response. To this end, four different cyclic stress paths under generalized stress simulations, following the stress-controlled method on a sample of spheres, were conducted. To check the validity of DEM results, the experimental results of the real sand under cyclic stress programs were used. The macrobehaviors, indicated by the stress–strain–dilation relationship and the directions of principal strain increment ...

Undrained response of reconstituted clay to cyclic pure principal stress rotation

A series of monotonic and rotational shearing tests are carried out on reconstituted clay using a hollow cylinder apparatus under undrained condition. In the rotational shearing tests, the principal stress axes rotate cyclically with the magnitudes of the principal stresses keeping constant. The anisotropy of the reconstituted clay is analyzed from the monotonic shearing tests. Obvious pore pressure is induced by the principal stress rotation alone even with shear stress q0=5 kPa. Strain components also accumulate with increasing the number of cycles and increases suddenly at the onset of failure. The deviatoric shear strain of 7.5% can be taken as the failure criterion for clay subjected to the pure cyclic principal stress rotation. The intermediate principal stress parameter b plays a significant role in the development of pore pressure and strain. Specimens are weakened by cyclic rotational shearing as the shear modulus decreases with increasing the number of cycles, and the shear modulus reduces more quickly with larger b. Clear deviation between the directions of the principal plastic strain increment and the principal stress is observed during pure principal stress rotation. Both the coaxial and non-coaxial plastic mechanisms should be taken into consideration to simulate the deformation behavior of clay under pure principal stress rotation. The mechanism of the soil response to the pure principal stress rotation is discussed based on the experimental observations.

Undrained anisotropy and non-coaxial behavior of clayey soil under principal stress rotation

In this study, a series of undrained tests were conducted on both intact and reconstituted clay using an automatic hollow cylinder apparatus. Monotonic shearing tests with fixed principal stress directions were carried out, pure and cyclic principal stress rotation tests were also performed. The non-coaxiality, defined as the non-coincidence of the principal plastic strain increment direction and the corresponding principal stress direction, of clayey soil was studied experimentally. The effects of the intermediate principal stress, shear stress level, and inherent anisotropy were highlighted. Clear non-coaxiality was observed during pure principal stress rotation, in both intact and reconstituted clay. The influence of the intermediate principal stress parameter, shear stress level, and inherent anisotropy on the non-coaxial behavior of the clayey soil was found to be insignificant when compared with the sand. The non-coaxial behavior of the clayey soil depended more on the stress paths. Under undrained conditions, the contribution of elastic strain to the direction of the total principal strain increment cannot be ignored.

Asymptotic axes of stress tensors and strain increment tensors in mechanics of compressible continua

New tensor representations of the stress state and the kinematics of compressible flows are obtained in the paper with the use of the notion of asymptotic directions of the symmetric stress tensor and the strain increment tensor. The exposition is based on terminology and notation typical of the mathematical theory of plasticity, but all main results remain valid for stresses and strains in compressible continua. The simplest and most efficient forms of the stress tensor for “completely plastic,” “semiplastic,” and “nonplastic” spatial stress states are found, where the asymptotic stress axes serve as the most natural reference frame ensuring new symmetric tensor representations of stresses different from the spectral ones. Similar representations can be extended to the stress increment tensor. Two-dimensional curvilinear grids such that the strain rates of their elements are always zero are chosen on the surfaces orthogonal to the directions of the “intermediate” principal strain increment. Incremental relations for the sliding rates along the grid lines are obtained, and these relations generalize the Geiringer equations along the characteristic lines, which are well known in the theory of plane deformation of perfectly plastic bodies. The generalization readily applies to spatial flows, and the possible flow compressibility is taken into account as well.

Particle-Scale Insight into Deformation Noncoaxiality of Granular Materials

AbstractThis paper explores the mechanism of deformation noncoaxiality from the particle scale. A multiscale investigation has been carried out with the particle-scale information obtained from discrete element simulation on granular materials. The specimens were prepared anisotropically and sheared in various loading directions. The deformation noncoaxiality, i.e., noncoincidence between the principal stress direction and the principal strain increment direction, was observed. The directional statistical theory has been used to study the anisotropies in material fabric and particle interactions, and to characterize them in terms of direction tensors. Based on the stress-force-fabric relationship, the stress direction was determined from these direction tensors. In monotonic loading, it was observed that the force anisotropy is always coaxial with the loading direction, i.e., the strain increment direction, while the fabric anisotropy only gradually approaches the loading direction. This noncoincidence be...

Non-Coaxial Plasticity Constitutive Modeling of Sands

Classical coaxial plasticity constitutive models implicate an inevitable limitation that directions for principal stress and that for principal plastic strain increment are always coaxial. They are not capable of simulating non-coaxial phenomena during the rotation of principal stress axis. In this paper, a three-dimensional, non-coaxial plasticity constitutive model for sands with a modification of Lade angle dependent shape function is introduced to describe the non-coaxial behavior under principal axes rotation. A series of numerical simulations of hollow cylindrical torsional shear tests are performed. The results show that the proposed constitutive model can predict the variations of principal plastic strain increment directions with principal stress directions reasonably.