Three‐dimensional elasto‐plastic model for unsaturated compacted soils with different initial densities

This paper presents an elasto‐plastic model for unsaturated compacted soils and experimental results obtained from a series of suction‐controlled triaxial tests on unsaturated compacted clay with different initial densities. The initial density dependency of the compacted soil behaviour is modelled by establishing experimental relationships between the initial density and the corresponding yield stress and thereby between the initial density and the location and slope of normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure surface and the yield surface in the deviatoric plane are given by the extended SMP criterion. A considerable number of the isotropic compression, triaxial compression and extension tests on unsaturated compacted clay with different initial densities were performed using a suction‐controllable triaxial apparatus, to measure the stress–strain–volume change in different stress paths and wetting paths. The model has well‐predicting capabilities to reproduce the mechanical behaviour of specimens compacted under different conditions not only in isotropic compression but also in triaxial compression and triaxial extension. Copyright © 2003 John Wiley & Sons, Ltd.     

复杂应力路径下堆石料本构关系研究

已有研究表明,土石坝内堆石料在坝体填筑过程的应力路径可近似为等应力比的路径（q/p=常数）,水库蓄水时应力路径将发生转折,呈复杂的应力路径形态（dq/dp=常数）。在大型三轴仪上进行了两种应力路径的排水试验,即等应力比路径下的偏压试验和复杂应力路径下的剪切试验。根据试验结果提出了一个堆石料应力路径增量非线性弹性模型,模型采用三模量形式除可以描述堆石料等应力比路径的应力-应变特征外,通过转折后的路径特征构造合适的柔度矩阵,能够表达转折应力路径下的本构关系。对试验曲线进行拟合表明,应力路径模型能够较好地反映堆石料在复杂应力路径下的应力与变形特性。     

A generalised D matrix for anisotropic elastic granular media

A matrix relating stress and elastic strain tensors for anisotropic particulate materials has been derived. The magnitude of the matrix depends on the state of the material anisotropy. Anisotropy in granular materials depends on strain because normal and tangential particle contact forces, as well as the spatial distribution of the contacts, vary with stress and strain. However, the rotation tensor and the strain tensor cannot be independent; they must satisfy certain constraints to meet the requirement for macroscopic stress tensor symmetry. These conditions and constraints lead to the derivation of the matrix presented in this article. The principal directions of the stress tensor and strain tensor are generally not coincident, and the values of deformation parameters, Young's modulus and Poisson's ratio, are direction dependent; these two aspects are also discussed in this paper. Whereas this matrix can be used in static numerical analyses for elastic problems, we note that this relationship can also be used as a basis upon which to derive a fully incremental stress–strain relationship for anisotropic granular materials in the plastic state, where the anisotropy is evolving with strain.     

Creep behavior of unsaturated cohesive soils subjected to various stress levels

This paper presents the results of an experimental investigation carried out on disturbed clay samples to analyze their creep behavior. The experimental program included compression triaxial tests with varied degree of saturation of the samples and stress level. Triaxial tests were performed at imposed strain rate varied from 0.005 to 0.10%/min. Various stress paths have also been tested including isotropic consolidation and deviatoric stress. The obtained results showed that shear deformation increases with the initial degree of saturation and stress level of clay samples. At fixed stress level and for both isotropic and deviatoric stress paths, the initial degree of saturation and the second invariant of the strain tensor varied with a similar trend. The variation of axial creep strain is correlated with time in a semi-logarithmic function.     

On the effects of deformation induced anisotropy in isotropic materials

Effects of recoverable deformation induced anisotropy in the elastic stiffness of isotropic materials are described. In isotropic materials, thermodynamics predicts coupling of hydrostatic and deviatoric responses. It is shown that the coupling of the two responses is more significant than previously recognized in the literature. Properly accounting for the coupling of hydrostatic and deviatoric responses requires re‐evaluating elastic materials characterization data, allowing for the coupled response. The result is an apparent decrease in the pressure sensitivity of the elastic shear modulus. The decrease in the pressure sensitivity of the shear modulus leads to stress paths that are more tangential to the yield surface in stress space, resulting in an increase in predicted elastic strain at each step of an elastic–plastic stress update. Consequently, predicted plastic strains and, in particular, volumetric plastic strains, are smaller than if recoverable deformation induced anisotropy had been neglected. The result is an associated plasticity model, which appears to be non‐associated. Copyright © 2012 John Wiley & Sons, Ltd.     

一种适用于各向异性土体的破坏准则

自然界的土体通常具有各向异性的特点,而传统的破坏准则大多只适用于各向同性的土体。结合应力张量和反映材料各向异性状态的组构张量,定义了修正偏应力及其不变量,提出了适用于各向异性土体材料的破坏准则。给出了共轴条件下正交各向异性和横向各向异性材料在一般应力空间的破坏曲线以及不同应力区中主应力系数b与摩擦角的关系曲线,并分析了它们的特性以及与各向同性材料相应曲线的区别。通过与真三轴试验数据的比较,表明该准则能很好地描述各向异性土体材料的强度特点。     

A simple model for isotropic non-linear elasticity of frictional materials

A simple isotropic nonlinear elastic model has been developed to describe the behaviour of granular materials immediately after stress reversal. Its three parameters can be measured in the same drained triaxial test.     

Effects of Previous Deviatoric Strain Histories on the Undrained Behaviour of Hostun RF Loose Sand

The effects of previous deviatoric strain histories on the undrained behaviour of very loose and saturated Hostun RF clean sand are investigated in this paper. From an initial isotropic stress state in the triaxial plane, strain histories are generated by isotropic consolidation followed by standard drained triaxial preshear or presheared cycle, either in compression or in extension, up to a desired value of axial strain or mobilized stress ratio. Deviatoric strain histories are achieved by having nearly the same void ratio at the beginning of the undrained shearing for all tested samples. Subsequent undrained behaviour in triaxial compression and extension is analyzed in detail. Previous deviatoric strain histories can progressively transform the compressive and unstable behaviour of loose sand into a dilative and stable behaviour of dense-like sand, while being loose. Experiments show a common response induced by recent strain histories in terms of effective stress paths, independently of the axial strain attained during the drained presheared cycle, a unique initial gradient of the effective stress paths, a progressive appearance of dilatancy, an evolution the undrained behaviour and a systematic partial static liquefaction associated with softer behaviour when sheared in the opposite direction of the initial presheared direction. This paper offers a comprehensive understanding of the mechanisms of a specialized induced anisotropy created by simple linear stress paths in the classical triaxial plane.     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

A density‐dependent elastoplastic hydro‐mechanical model for unsaturated compacted soils

This paper presents a three‐dimensional elastoplastic constitutive model for predicting the hydraulic and mechanical behaviour of unsaturated soils. It is based on experimental results obtained from a series of controlled‐suction triaxial tests on unsaturated compacted clay with different initial densities. Hydraulic hysteresis in the water‐retention behaviour is modelled as an elastoplastic process, with the elastic part modelled by a series of scanning curves and the elastoplastic part modelled by the main drying and wetting curves. The effect of void ratio on the water‐retention behaviour is studied using data obtained from controlled‐suction wetting–drying cyclic tests on unsaturated compacted clay with different initial densities. The effect of the degree of saturation on the stress–strain‐strength behaviour and the effect of void ratio on the water‐retention behaviour are considered in the model, as is the effect of suction on the hydraulic and mechanical behaviour. The initial density dependency of the compacted soil behaviour is modelled by experimental relationships between the initial density and the corresponding yield stress and, thereby, between the initial density and the normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure and yield surfaces in the deviatoric stress plane are given by the Matsuoka–Nakai criterion. Model predictions of the stress–strain and water‐retention behaviour are compared with those obtained from triaxial tests with different initial densities under isotropic compression, triaxial compression and triaxial extension, with or without variation in suction. The comparisons indicate that the model accurately predicts the hydraulic and mechanical behaviour of unsaturated compacted soils with different initial densities using the same material constant. Copyright © 2006 John Wiley & Sons, Ltd.     

Exploring the undrained induced anisotropy of Hostun RF loose sand

The effects of recent history on the undrained behaviour of very loose and saturated Hostun RF clean sand are investigated in this paper. From an initial isotropic stress state in the triaxial plane, recent histories are generated by isotropic consolidation followed by standard drained triaxial preshear in compression, up to a desired value of axial strain or mobilized stress ratio, and unloading to an initial stress ratio. Subsequent undrained behaviour in triaxial compression is analysed in detail. This paper contributes to the traits explaining the progressive transformation of a compressive and unstable behaviour of loose sand into a dilative and stable behaviour of dense-like sand by previous history, while remaining in the same state of loose density. Experiments show a large pseudo-elastic domain induced by recent history in terms of effective stress paths, function of the initially mobilized stress ratio level, a unique initial gradient of the effective stress paths depending on the stress ratio at the beginning of the undrained shearing, a progressive appearance of dilatancy and a surprising evolution the undrained behaviour of loose sand. Experimental results evidence the important role of the recent deviatoric strain history, from any initial isotropic or anisotropic stress state. This paper also offers a comprehensive understanding of the history mechanisms created by simple linear stress paths with fixed direction in the classical triaxial plane.     

K0固结条件下粗粒土变形及强度特性研究

采用大三轴剪切仪对不同相对密度的双江口心墙坝覆盖层料,进行了K0固结及各向等压固结条件下的排水剪切试验,探讨了K0固结过程中粗粒土的变形特性。将K0固结与等压固结条件下的排水剪切试验的结果进行了对比分析。结果表明,K0固结加载阶段,平均主应力p与体应变? v之间、剪应力q剪应变? s之间的关系都可用幂函数形式表示。K0固结稳压阶段,? a-t关系呈指数关系。与等压固结试验相比,K0固结试样的排水剪强度略大。K0固结排水剪试验所得到的初始弹性模量Ei、初始泊松比vi均大于等压固结排水剪试验相同应力条件下的弹性模量、泊松比;且K0固结条件下试样的剪胀性也较为明显。     

Constitutive modelling of granular materials using a contact normal-based fabric tensor

This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

     

控制应力路径散体材料真三轴试验强度特征的离散元模拟与细观机制分析

通过一系列真三轴离散元数值试验,模拟了不同应力路径下的等b试验中散体材料的强度特征。根据模拟结果详细地分析了三维应力条件下中主应力和应力路径对散体材料峰值强度的影响,研究了峰值摩擦角、峰值应力比的变化规律,并根据真应力的概念和组构张量的演化结果分析了散体材料的强度成因。研究表明,在不同类型的数值试验中峰值偏应力随b参数的变化规律不同,但采用初始围压归一化后的应力-应变曲线规律一致。峰值强度线的斜率只与b值有关而与应力路径无关,且随着b值的增加,峰值应力比qf /pf逐渐减小,数值模拟结果与室内试验结果吻合较好;随着应变的发展,数值试样的组构也随之发生变化,产生了明显的应力诱发各向异性;散体的强度为颗粒摩擦及材料各向异性共同作用的结果;理论上,组构比-应力比坐标系中破坏点位置仅取决于颗粒摩擦角 ,而数值模拟结果与理论值的差异源于颗粒间咬合和滚动摩擦的影响,其影响与颗粒表面摩擦系数有关,也受空间应力状态的影响。     

应力状态对粗粒料力学特性影响的大型真三轴试验

土石坝所处的应力状态较接近平面应变应力状态或三维应力状态,而常规三轴试验低估了粗粒料的力学性能。应用大型真三轴仪对常规三轴应力状态、平面应变应力状态和真三轴应力状态（ 0.25, 为中主应力系数, 、 、 分别为大、中、小主应力）下粗粒料的力学特性进行了压缩试验研究。试验结果表明：相同小主应力下,常规三轴试验、平面应变试验、真三轴试验的大、小主应力之差与大主应力方向应变的关系曲线依次变高变陡。某一试验加载条件下,体应变随球应力的增大而增大,初始剪切阶段增加较慢,随后呈线性增大,不同小主应力的体应变曲线较为接近。平面应变试验强度和真三轴试验强度比常规三轴试验强度有较大增长,真三轴试验强度增加百分比大于平面应变试验强度增加百分比。初始弹性模量随小主应力的增大呈线性增大。平面应变状态下中主应力系数随大主应力方向应变的增大而增大,初始剪切阶段增长较缓,之后近似呈线性增大。相同小主应力下,从常规三轴应力状态至平面应变应力状态再到真三轴应力状态,小主应力方向应变均为膨胀变形,且膨胀变形依次增大。同一试验加载条件下,小主应力较小时,应力比（偏应力与球应力之比）与偏应变的关系曲线位于上方。     

Microplane damage model for jointed rock masses

The paper presents a new microplane constitutive model for the inelastic behavior of jointed rock masses that takes into account the mechanical behavior and geometric characteristics of cracks and joints. The basic idea is that the microplane modeling of rock masses under general triaxial loading, including compression, requires the isotropic rock matrix and the joints to be considered as two distinct phases coupled in parallel. A joint continuity factor is defined as a microplane damage variable to represent the stress‐carrying area fraction of the joint phase. Based on the assumption of parallel coupling between the rock joint and the rock matrix, the overall mechanical behavior of the rock is characterized by microplane constitutive laws for the rock matrix and for the rock joints, along with an evolution law for the microplane joint continuity factor. The inelastic response of the rock matrix and the rock joints is controlled on the microplane level by the stress–strain boundaries. Based on the arguments enunciated in developing the new microplane model M7 for concrete, the previously used volumetric–deviatoric splits of the elastic strains and of the tensile boundary are avoided. The boundaries are tensile normal, compressive normal, and shear. The numerical simulations demonstrate satisfactory fits of published triaxial test data on sandstone and on jointed plaster mortar, including quintessential features such as the strain softening and dilatancy under low confining pressure, as well as the brittle–ductile transition under higher confining pressure, and the decrease of jointed rock strength and Young's modulus with an increasing dip angle of the joint. Copyright © 2014 John Wiley & Sons, Ltd.     

不同应力路径下粗粒料力学特性试验研究

采用大型三轴试验机,对粗粒料进行了常规三轴、等p和等应力比等不同应力路径的试验。通过对试验结果进行对比分析,研究了粗粒料在不同应力路径下的应力-应变、变形和强度特性,并对粗粒料的卸载体缩现象进行了分析和探讨。结果表明,应力路径对粗粒料的应力-应变和变形特性影响较大,而对强度特性影响较小;卸载体缩主要是由偏应力比η的变化所引起的,与应力路径关系很大。     

Coupling pore-water pressure with distinct element method and steady state strengths in numerical triaxial compression tests under undrained conditions

The undrained shear behaviour of sands has been a key topic after the devastating geo-disasters during the 1964 Niigata Earthquake in Japan. Extensive geo-technical soil tests, especially undrained triaxial compression tests, have revealed that the liquefaction phenomenon was the major cause for the disaster expansions. To numerically reproduce the liquefaction phenomenon, the pore-water pressure was coupled with a distinct element method. In this model, the dynamic changes in pore-water pressure were taken into consideration by the changes in volumetric strain and modulus of compressibility of water in the respective measurement spheres. Fluid-flows among the measurement spheres were controlled by Darcy’s law. The effective stress paths and steady state strengths in undrained triaxial compression tests associated with the wide ranges of initial void ratio were investigated. The effective mean stresses of medium-dense to dense numerical specimens at the steady state were negatively proportional to the initial void ratio. Loose numerical specimens reproduced quasi-liquefaction with the effective mean stresses that were less than 25% of the initial value. The medium-dense numerical specimens reproduced the phase transformation that was a typical characteristic of granular materials. The rolling restraints did not much influence of the effective angle of internal friction but strongly affected pore-water pressure behaviour within a certain range of initial void ratio.     

堆石料等应力比路径四模量增量非线性模型

已有研究表明,土石坝内堆石料在施工填筑期的应力路径可近似为主应力比为常数的路径。根据大型三轴仪上进行的两种应力路径排水试验,即等向压缩的固结试验和等应力比值的剪切试验,提出了一个四模量增量非线性模型。模型除给出了堆石料体积模量K和剪切模量G的表达式外,对剪应力产生的体积应变和平均主应力产生的剪切应变也分别采用了交叉模量J1、J2表达。通过与试验数据的对比表明,四模量增量非线性模型能够较好地预测堆石料在等应力比路径下的应力-应变关系。     

A Laboratory Experimental Study of the Hydromechanical Behavior of Boom Clay

This paper reports some results of a large experimental program on Boom Clay conducted in Grenoble in the framework of the European project SELFRAC. The program included isotropic compression up to relatively high stress, drained triaxial compression tests at different cell pressures, as well as permeability measurements under isotropic and deviatoric stress. Local measurement of axial and radial displacements allowed the detection of strain localization during deviatoric loading. The permeability of Boom Clay is found to depend on the mean effective stress. The response of Boom Clay during deviatoric loading appears to be strongly affected by the swelling experienced during the isotropic stage preceding triaxial compression. The rate of swelling decreases with isotropic stress. The longer the swelling before shear, more the response under shear becomes ductile and the lower the initial stiffness. Permeability depends on the mean effective stress and it is found to decrease of about two orders of magnitude when the mean stress increases from 1 to 32 MPa. Permeability during shear loading is essentially constant and does not seem to be affected by strain localization. These results are complemented by a few observations obtained using X-ray microtomography in the framework of the more recent European project TIMODAZ. These findings illustrate the impact of pre-existing inclusions and fissures on specimen deformation upon deviatoric loading in the laboratory.