从各向异性的角度解释和模拟土的非共轴特性

从发挥面的角度出发,分析论证各向异性是引起岩土材料出现非共轴现象的根本原因,得到与材料力学一致的结论。当共轭的两发挥面与沉积面的夹角不相等时,主应力面上将出现塑性应变增量的切向分量,所以塑性应变增量的主方向与应力的主方向非共轴。按照这一结论,对非共轴的数值模拟,也应当根据各向异性本构模型进行。为考虑各向异性影响新近提出的各向异性变换应力法,改变了各应力分量的相对大小,得到的各向异性变换应力张量与真实应力张量的主方向不一致,因此也能反映非共轴。利用各向异性变换应力法,能够在现有的弹塑性本构模型的框架下,描述土的非共轴现象。以各向异性UH模型为例,预测各种加载条件下的非共轴变形,验证了该方法的有效性。     

A laboratory study of anisotropic geomaterials incorporating recent micromechanical understanding

This paper presents an experimental investigation revisiting the anisotropic stress–strain–strength behaviour of geomaterials in drained monotonic shear using hollow cylinder apparatus. The test programme has been designed to cover the effect of material anisotropy, preshearing, material density and intermediate principal stress on the behaviour of Leighton Buzzard sand. Experiments have also been performed on glass beads to understand the effect of particle shape. This paper explains phenomenological observations based on recently acquired understanding in micromechanics, with attention focused on strength anisotropy and deformation non-coaxiality, i.e. non-coincidence between the principal stress direction and the principal strain rate direction. The test results demonstrate that the effects of initial anisotropy produced during sample preparation are significant. The stress–strain–strength behaviour of the specimen shows strong dependence on the principal stress direction. Preloading history, material density and particle shape are also found to be influential. In particular, it was found that non-coaxiality is more significant in presheared specimens. The observations on the strength anisotropy and deformation non-coaxiality were explained based on the stress–force–fabric relationship. It was observed that intermediate principal stress parameter b(b = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) has a significant effect on the non-coaxiality of sand. The lower the b-value, the higher the degree of non-coaxiality is induced. Visual inspection of shear band formed at the end of HCA testing has also been presented. The inclinations of the shear bands at different loading directions can be predicted well by taking account of the relative direction of the mobilized planes to the bedding plane.     

Experimental investigation on the deformation characteristics of granular materials under drained rotational shear

Rotational shear is the type of loading path where samples are subjected to cyclic rotation of principal stress directions while the magnitudes of principal stresses are maintained constant. This paper presents results from an experimental investigation on the drained deformation behaviour of saturated sand in rotational shear conducted in a hollow cylinder apparatus. Two types of granular materials, Leighton Buzzard sand and glass beads are tested. A range of influential factors are investigated including the material density, the deviatoric stress level, and the intermediate principal stress. It is observed that the volumetric strain during rotational shear is mainly contractive and most of strains are generated during the first 20 cycles. The mechanical behaviour of sand under rotational shear is generally non-coaxial, i.e., there is no coincidence between the principal axes of stress and incremental strain, and the variation of the non-coaxiality shows a periodic trend during the tests. The stress ratio has a significant effect on soil response in rotational shear. The larger the stress ratio, the more contractive behaviour and the lower degree of non-coaxiality are induced. The test also demonstrates that the effect of the intermediate principal stress, material density and particle shape on the results is pronounced.     

Formation of shear bands in sand bodies as a bifurcation problem

The paper reports on the results of theoretical and experimental investigations on the spontaneous formation of shear bands in sand bodies. The phenomenon is considered as a bifurcation problem. Consequently, material response and configuration-dependent loading determine the bifurcation mode. Both Coulomb's and Roscoe's solutions of inclination of the shear band can be correct theoretically and experimentally. The first one holds for non-rotating stress axes, the second one for co-rotating stress and strain increment axes during failure. Values in between can occur if the rotation of principal stress axes is not equal to one of these limits. If Coulomb's inclination of shear band occurs, there is a thin deforming material layer separating rigid bodies. Inside the shear band non-coaxiality of strain increment and stress holds from the beginning. If Roscoe's inclination of shear band occurs, it is separating two deforming bodies. Inside the shear band strain increment and stress are coaxial at peak.     

Modeling of the simple shear deformation of sand: effects of principal stress rotation

The paper presents a simple constitutive model for the behavior of sands during monotonic simple shear loading. The model is developed specifically to account for the effects of principal stress rotation on the simple shear response of sands. The main feature of the model is the incorporation of two important effects of principal stress on stress–strain response: anisotropy and non-coaxiality. In particular, an anisotropic failure criterion, cross-anisotropic elasticity, and a plastic flow rule and a stress–dilatancy relationship that incorporate the effects of non-coaxiality are adopted in the model. Simulations of published experimental results from direct simple shear and hollow cylindrical torsional simple shear tests on sands show the satisfactory performance of the model. It is envisioned that the model can be valuable in modeling in situ simple shear response of sands and in interpreting simple shear test results.     

Analysis of double shearing in frictional materials

The concept that the flow of granular materials is governed by shear on certain critical planes is used to formulate an elastic–plastic model. When the elastic strains are neglected, the Double Shearing model becomes identical to the rigid-plastic model of de Josselin de Jong which he named the Double Sliding model. After a discussion of the model, the small strain formulation is used to describe general boundary-value problems. A comparison is then made between the coaxial Mohr–Coulomb yielding and the Double Shearing model on the basis of several numerical simulations. The non-coaxiality of the axes of principal plastic strain rate and principal stress in the Double Shearing model leads to essentially different behaviour for stress rotations in comparison to the coaxial model. The Double Shearing model predicts in general lower limit loads because, for a given state of stress, it allows for several possible directions of plastic flow rather than a unique direction which derives from a plastic potential.     

基于广义位势理论的土的非共轴特性研究

传统的塑性位势理论隐含了应力主方向和塑性应变增量主方向共轴的假定,无法客观地描述主应力轴旋转过程中的非共轴现象。基于广义位势理论提出的拟弹性弹塑性本构模型,把总的塑性应变分解为满足弹性分解准则的拟弹性部分和符合传统塑性理论假设的纯塑性部分,分解后建立的模型更为合理和简便,同时又可以解决土的非共轴问题。通过单剪试验结果的验证表明,基于广义位势理论的拟弹性弹塑性模型的模拟效果较好,传统的弹塑性模型（共轴模型）模拟得到的主应力方向和塑性主应变增量方向保持共轴,而拟弹性弹塑性模型（非共轴模型）的模拟结果则能够合理地描述主应力轴旋转过程中的非共轴特性,结果更符合实际,从而为解决土的非共轴特性问题提供了一种有效的方法。     

考虑主应力方向变化的原状软黏土应力应变性状试验研究

为反映真实工程条件下主应力轴旋转应力路径引起土体性状的变化,对杭州地区正常固结原状软黏土在固结不排水的主应力轴定向剪切和主应力轴单调旋转条件下的应力-应变关系进行试验研究。研究发现,不同主应力方向的定向剪切路径下,随主应力方向变化,试样中各应变发挥程度显著不同,但破坏时的临界八面体应变变化较为稳定,且当八面体应变达到5%时,强度发挥程度已接近甚至超过90%。若剪切过程中增加了主应力幅值不变的不排水主应力轴单调旋转应力路径,只要破坏时主应力方向一致,经历与未经历主应力轴旋转试样的临界应变分量接近,但主应力轴旋转会影响加载阶段试样主应力、主应变增量方向所表现出的不共轴性,并且此影响随旋转时剪应力水平的提高而趋于显著,即使在临界破坏状态下依然明显。试验结果表明,由于土体原生各向异性、黏塑性等性质的存在,并不适宜用相关联流动法则来分析主应力轴旋转条件下土体的应力-应变关系特征。     

Strain refraction in layered systems

Strain refraction across competence contrasts is presented as a simple model consisting of two components, a homogeneous strain and a heterogeneous simple shear. For Newtonian materials, the ratio of the layer-parallel simple shear component in adjacent layers is the inverse of their viscosity ratio. Strong changes in ellipsoid size, shape and orientation are predicted across viscosity contrasts.The geological implications of strain refraction theory are considered within the context of the ‘cleavage/strain debate’. The particular relationships of relative competence and strain revealed by the refraction model may contribute to the problem of why cleavages of different morphologies in rocks of different lithologies (and kinematic histories) should appear to be subparallel to the XY planes of measured strain ellipsoids. Competent rocks should develop dominantly layer-orthogonal strain, and incompetent layers shear-dominated deformation. A variety of structural features ranging from cleavage refraction, changing lineation orientations, folds transected by cleavage, changes from coaxial to non-coaxial deformation, and ramp-flat fault geometry may be the result of stress and strain refraction in rocks.     

杭州软黏土非共轴特性的试验研究

利用空心圆柱扭剪仪对杭州软黏土进行了一系列不排水试验,包括对原状软黏土在不同主应力方向上的定向剪切试验和主应力轴旋转试验以及对重塑软黏土的主应力轴旋转试验,主要研究不同应力路径下软黏土非共轴角的发展特性以及中主应力系数b、初始剪应力水平和次生各向异性对其非共轴特性的影响。试验结果表明,软黏土的非共轴特性虽与砂土存在相似之处,但又不尽相同。原状软黏土在定向剪切条件下的非共轴角均较小,并且与加载方向有关,然而受剪应变发展的影响,试样接近破坏时的非共轴角并不为0°;主应力轴旋转条件下,无论原状还是重塑黏土其非共轴角均随主应力方向角? 增加而循环波动变化,且周期约为90°;非共轴角基本随中主应力系数b的增加而减小,但这种影响并不十分显著;剪应力水平对非共轴角的大小和发展趋势均存在一定的影响。对于重塑土的试验表明,软黏土的非共轴特性并不完全由土体的初始各向异性所决定,次生各向异性的影响也很大。     

Numerical Analysis of Blast-Induced Stress Waves in a Rock Mass with Anisotropic Continuum Damage Models Part 1: Equivalent Material Property Approach

Summary This paper uses the concept of anisotropic damage mechanics to analyze dynamic responses of a granite site under blasting loads. An anisotropic continuum damage model is suggested to model rock mass behavior under blasting loads. The effects of existing cracks and joints in the rock mass are considered by using equivalent rock material properties obtained from both field and laboratory test data. The anisotropic damage accumulations are simulated by continuous degradation of equivalent material stiffness and strength during loading process and are calculated using the exponential function with respect to the principal tensile strain in three directions. The suggested models are programmed and linked to an available computer program Autodyn3D through its user's subroutine capability. Stress wave propagation and damage zone in the rock mass induced by underground explosions are simulated. Numerical results of damaged area, peak particle velocity and acceleration attenuation as well as acceleration time histories and Fourier spectra are compared with those from independent field tests.     

Drained deformation characteristics of granular soil under pure principal stress axis rotation: impact of sample preparation

The distinct initial fabrics of sand may give rise to dramatically different responses to the applied loading, as evidenced by numerous laboratory tests reported in the literature. In this study, both dry deposition (DD) and moist tamping (MT) methods were employed to prepare sand specimens to generate different initial fabrics. Drained tests were conducted on these specimens under pure principal stress axis rotation while keeping the principal stress components constant. The factors that may influence the deformation characteristics of sand, such as deviatoric stress q, coefficient of intermediate principal stress b, and mean principal stress p, were also taken into consideration in the tests. Test results show that the developments of three normal strain components with number of cycles are very different between DD and MT specimens, which is also closely related to the factors of q, b, and p. It is seen that DD specimen tends to generate larger contractive volumetric strains than MT specimen, which is more significant when q and b increase or p decreases. The shear stiffness of DD specimen is greater than that of MT specimen. The shear modulus ratio, G_j/G₁, increases with the increase of q and b or the decrease of p, which is more prominent in DD specimen than in MT specimen. It is also shown that DD specimen appears to exhibit stronger non-coaxiality than MT specimen, in which such difference of non-coaxiality tends to decrease with the increase in number of cycles.

     

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.

     

偏应力比和应力主轴偏转角同时变化下饱和砂土变形特性研究

利用空心圆柱扭剪仪对饱和砂土进行了应力主轴固定和偏应力比增大（即定向剪切）、偏应力比不变和应力主轴单调旋转（即纯应力主轴单调旋转）、偏应力比和应力主轴偏转角同时增加、偏应力比和应力主轴偏转角分段增加4个系列的排水剪切试验,着重分析不同应力路径下饱和砂土的变形特性及主应力和主应变增量方向变化规律。试验结果表明,纯应力主轴单调旋转下,主应力增量方向在45°～135°范围内变化,主应变增量方向逐渐偏向主应力方向;偏应力比和应力主轴偏转角同时增加下,砂土变形不断增大,当主应力增量方向 45°时,主应变增量方向与主应力增量方向基本一致,但当 45°时,主应变增量方向逐渐偏离主应力增量方向。当应力状态在偏应力比 0.75、应力主轴偏转角 45°范围内时,体应变、最大剪应变与应力路径无关,且后期纯应力主轴旋转下砂土变形不受前期加载历史的影响。     

砂质混合粘土的孔隙水压力和残余变形特性研究

以砂质混合粘土为例,通过实施不同初始固结比水平的动力循环荷载试验,考察了土的孔隙水压力和残余变形的发生过程。探讨了当将土的不等向固结分为初始剪应力和等向固结两种应力状态时,孔隙水压力和残余变形的预测方法。提出了归一化的孔隙水压力和累积损失能量及残余变形和有效应力比间的关系模型。     

An Anisotropic Model for Granular Material Based on Experiments

Soil is a heterogeneous material and most natural soil deposits show a definite stratification. The mechanical behaviour of such material is generally different in different directions, especially in the direction parallel and perpendicular to the stratification. A series of isotropic compression tests were carried out to study the behavior of granular material produced under controlled stratification in the laboratory. These tests were conducted both on cylindrical and square prismatic tri-axial specimens. It was observed that for hydrostatic loading, the strain response was different in different directions, especially in directions parallel and perpendicular to the direction of soil deposition. A definite trend of anisotropy was observed in the deformation pattern. The observed anisotropy is modeled in this paper by treating soil-dilatancy as a variable quantity. The equation of the plastic potential surface of the model which obeys a non-associated flow rule, is assumed to be dependent on three main variables confining pressure (\(\sigma_{3}\)), void ratio (e) and the angle of bedding plane orientation (δ) during deposition. The angle of bedding plane orientation (δ) was measured with respect to the direction of the major principal stress. The model has a cap yield surface in the isotropic stress direction, which is supplemented by a shear hardening Mohr–Coulomb surface in the deviator direction. This paper focuses on predicting the anisotropic strain response of stratified soil deposits subjected to isotropic compression. The proposed anisotropic model incorporates within an existing strain-hardening sand model, a modified cap yield surface and a modified plastic potential function related to the cap surface, to account for the anistropic response observed in isotropic compression tests. The two dimensional stress–strain model was extended to three dimensional Cartesian space. The strain anisotropy observed in the isotropic compression tests was predicted by the three dimensional anisotropic model proposed for granular materials.     

各向异性砂土K0试验研究

静止土压力系数K0是岩土工程分析计算中的重要力学参数之一。实际工程中墙后填土由于碾压都具有不同程度的各向异性。制备了不同沉积方向的砂土试样,通过三轴排水剪切试验研究了砂土的各向异性。在研制应变路径试验设备的基础上给出了静止土压力系数的测量方法,研究了不同沉积方向对于K0的影响,并将试验测得的静止土压力系数与Jaky公式以及土压力离心模型试验结果进行了对比,离心模型试验结果与材料单元试验结果一致,证明了测量方法的有效性及结果的正确性。研究结果表明,各向异性条件下的K0值比各向同性时明显偏大。     

Cyclic degradation and non-coaxiality of soft clay subjected to pure rotation of principal stress directions

Foundation soils are often under non-proportional cyclic loadings. The deformation behaviour and the mechanism of non-coaxiality under continuous pure principal stress rotation for clays are not clearly investigated up to now. In order to study the effect of pure principal stress rotation, a series of cyclic undrained tests on Shanghai soft clay subjected to cyclic rotation of principal stress directions keeping the deviatoric stress constant under the pure rotation condition were conducted using hollow cylinder apparatus. Based on this, the evolutions of excess pore pressure and strains during cyclic loading were investigated, together with the effects of the intermediate principal stress parameter and the deviatoric stress level on stress–strain stiffness and non-coaxiality. The result can provide an experimental basis for constitutive modelling of clays describing the behaviour under non-proportional loadings.     

A multilaminate constitutive model accounting for anisotropic small strain stiffness

In this paper an extension of existing multilaminate soil models is presented, which can account for inherent and stress‐induced cross‐anisotropic elasticity in the small strain range and its dependency on the load history. In the multilaminate framework, material behaviour is formulated on a number of local planes in each stress point, and the macroscopic response of the material is obtained by integration of the local contributions. Strain‐induced anisotropy, which adds to the stiffness anisotropy inherently present in the material, is therefore intrinsically taken into account. Micro–macro relations between local parameters on plane level and global parameters on macroscopic level are obtained by the spectral decomposition of the global elastic compliance matrix. The model is implemented into a finite‐element code, and model predictions are compared with experimental data of triaxial tests on different soils involving small and large load cycles. The importance of cross‐anisotropic elasticity within the small strain range for predicting ground deformations in geotechnical boundary value problems is discussed at the example of an excavation problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Determination of silica sand stiffness

Site investigation and evaluation of properties of soil or rock are important aspects of geotechnical design. Determination of the ground stiffness is one of the important parameters in geotechnical engineering. Since the measurement of shear modulus is very sensitive to soil disturbance, especially for sand, determination of the stiffness of soil in the field is more reliable than in laboratory tests on sampled specimens. Measurement of shear modulus is one of the most common applications of self-boring pressuremeter testing. As an in situ device, the pressuremeter provides a unique method for assessing directly the in situ shear modulus of a soil. This paper describes a laboratory study of silica sand stiffness, which varies with stress level and strain amplitude. The results show that the elastic shear modulus value is mainly dependent on the value of the mean effective stress and relative density.