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.     

Skin friction features of drilled CIP piles in sand from pile segment analysis

Numerical pile segment analysis is conducted in this study with an advanced soil model to investigate the skin friction behaviour of a drilled Cast‐In‐Place (CIP) pile installed in sand. Although the interface between the sand and pile is considered rough, thin elements adjacent to the pile are used to include effects of localized shear. Unit weights of fluid concrete and accompanied changes in stress are considered as the effects of pile installation. Changes in effective stresses are the most prominent effect due to pile installation with a change in direction of the major principal stress from the vertical to the radial direction. Shear behaviour of the sand at the interface during the early shear stage is related to the contractive tendency of the sand at small strain levels. Changes in the stress field around the pile with little changes in volumetric strain take place during the early shear stage. Stress redistributions during the early shear stage depend on the direction of the major principal stress before shear. Results of the pile segment analyses for drilled CIP piles show good agreement with design methods. Parametric studies are used to characterize the effects of sand density and pile diameter on the skin friction behaviour of drilled CIP piles. Copyright © 2007 John Wiley & Sons, Ltd.     

复杂应力条件下饱和砂土排水剪切强度的试验研究

针对相对密度为30 %的福建标准砂,利用土工静力－动力液压－三轴扭转多功能剪切仪,在不同初始固结条件下控制试验过程的平均主应力保持不变,改变中主应力系数和主应力方向,进行了应力控制式单调排水剪切试验,着重探讨中主应力系数和主应力方向对砂土剪切强度的耦合影响。试验结果表明：在相同的试验条件下,中主应力系数对饱和标准砂的应力-应变关系具有影响,但对体变特性的影响并不明显。上述现象同初始固结应力比的大小无关。平均主应力一定,广义剪应力随中主应力系数增大而降低的趋势同时依赖于主应力方向的作用。中主应力系数对内摩擦角的放大效应同样受到主应力方向的影响。基于广义双剪应力准则,引入考虑主应力方向影响程度的权重系数,结合试验结果给出了考虑中主应力系数和主应力方向耦合影响的强度指标表达式。     

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.     

Multi-laminate non-coaxial modelling of anisotropic sand behavior through damage formulation

A modified multi-laminate model, to predict non-coaxiality in anisotropic sand, is proposed in this paper. The model can easily be extended to other geo-materials only with implementing some minor provisions. To consider anisotropy of sand, two ellipsoids are utilized to summarize shear and compressive stiffness of material in different directions. Damage concept is used to take into account degradation of material through loading procedure. Ellipsoid of rigidity factors is being changed in both size and dimension, under applied strain path. Variation of ellipsoids results in change of stiffness distribution over different planes. In other words, fabric evolution in material is considered through variation of ellipsoids of rigidity factors. A simple rule is proposed for shear stress-strain relationship in loading-unloading and reloading, which captures most of the natural characteristics of sand behavior. In multi-laminate models, depending on stiffness distribution over sampling planes, stress and strain are not coaxial essentially. To achieve better results, non-coaxiality of shear stress and strain on sampling planes is considered by applying vector field concept. Shear stress in different directions of a sampling plane is considered as a vector field. This field is obtained from strain field, considering shear stiffness in various orientations. The model parameters are calibrated using uniaxial compressive test data in different directions, with respect to bedding plane on an anisotropic sand sample. To investigate capability of the model to predict non-coaxiality, results of the model are compared to experimental results obtained from pure principal stress rotation. Ultimately, good accuracy is observed in results.     

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.     

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.

     

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。     

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。     

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。     

中主应力对饱和松砂不排水单调剪切特性的影响

利用土工静力-动力液压-三轴扭转多功能剪切仪,针对相对密度为30 %的福建标准砂,在不排水条件下控制主应力方向、中主应力系数、平均主应力保持不变,进行了单调剪切试验。以此着重探讨了中主应力系数对相变有效内摩擦角、峰值有效内摩擦角及有效应力路径的影响。研究表明,中主应力系数对在不排水单调剪切条件下饱和松砂的强度参数具有显著的影响,而对有效应力路径及应力-应变关系发展模式影响较小。基于广义双剪强度准则,从理论上探讨了土的强度参数对于中主应力的依赖性,并与试验结果进行了对比。     

Strength criterion for cross-anisotropic sand under general stress conditions

By incorporating the fabric effect and Lode’s angle dependence into the Mohr–Coulomb failure criterion, a strength criterion for cross-anisotropic sand under general stress conditions was proposed. The obtained criterion has only three material parameters which can be specified by conventional triaxial tests. The formula to calculate the friction angle under any loading direction and intermediate principal stress ratio condition was deduced, and the influence of the degree of the cross-anisotropy was quantified. The friction angles of sand in triaxial, true triaxial, and hollow cylinder torsional shear tests were obtained, and a parametric analysis was used to detect the varying characteristics. The friction angle becomes smaller when the major principal stress changes from perpendicular to parallel to the bedding plane. The loading direction and intermediate principal stress ratio are unrelated in true triaxial tests, and their influences on the friction angle can be well captured by the proposed criterion. In hollow cylinder torsional shear tests with the same internal and external pressures, the loading direction and intermediate principal stress ratio are related. This property results in a lower friction angle in the hollow cylinder torsional shear test than that in the true triaxial test under the same intermediate principal stress ratio condition. By comparing the calculated friction angle with the experimental results under various loading conditions (e.g., triaxial, true triaxial, and hollow cylinder torsional shear test), the proposed criterion was verified to be able to characterize the shear strength of cross-anisotropic sand under general stress conditions.     

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。     

复杂应力条件下饱和砂土单调剪切特性的试验研究

利用土工静力-动力液压-三轴扭转多功能剪切仪,针对相对密度为30 %的福建标准砂,进行了复杂初始固结条件下应力路径变化的应力控制式单调排水与不排水剪切试验。控制试验过程的平均主应力保持不变,变化中主应力系数和主应力方向,分别探讨在不同排水条件下中主应力系数和主应力方向对饱和砂土剪切特性的影响。通过对比表明：与排水条件无关,中主应力系数对归一化的应力-应变关系具有影响,但对体变或孔压的影响并不明显。初始条件相同,偏应力比随中主应力系数的增大而降低。主应力方向的影响同样显著,排水试验的主应力方向角不同时应力-应变关系所表现出的变化规律取决于水平面与竖直面上受到的剪应力作用。不排水试验的峰值有效偏应力比随着主应力方向角的增大而减小。     

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.     

On the undrained strain-induced anisotropy of loose sand

An experimental study was carried out to investigate the effects of previous deviatoric strain histories on the undrained behaviour of loose and saturated Toyoura sand and compared with known results of Hostun RF sand. From an initial isotropic stress state, recent deviatoric strain histories in the compression side of the triaxial plane were generated by a standard drained presheared cycle up to a specified mobilized stress ratio. Mainly, the fully liquefied, contractive, unstable and softening behaviour of loose sand was progressively transformed into the non-liquefied, dilative, fully stable and hardening behaviour of dense-like sand, while remaining within a narrow range of loose density. The paper validates and extends the current understanding of strain-induced anisotropy of loose sand. New experimental data support the directional dependency of the instability cone on the stress increment direction, suggest the bifurcation characteristics of loose sand and evidence the important role of past deviatoric strain histories.     

Liquefaction and cyclic mobility model for saturated granular media

A new constitutive law for the behaviour of undrained sand subjected to dynamic loading is presented. The proposed model works for small and large strain ranges and incorporates contractive and dilative properties of the sand into the unified numerical scheme. These features allow to correctly predict liquefaction and cyclic mobility phenomena for different initial relative densities of the soil. The model has been calibrated as an element test, by using cyclic simple shear data reported in the literature. For the contractive sand behaviour a well‐known endochronic densification model has been used, whereas a plastic model with a new non‐associative flow rule is applied when the sand tends to dilate. Both dilatancy and flow rule are based on a new state parameter, associated to the stiffness degradation of the material as the shaking goes on. Also, the function that represents the rearrangement memory of the soil takes a zero value when the material dilates, in order to easily model the change in the internal structure. Proceeding along this kind of approach, liquefaction and cyclic mobility are modelled with the same constitutive law, within the framework of a bi‐dimensional FEM coupled algorithm developed in the paper. For calibration purposes, the behaviour of the soil in a cyclic simple shear test has been simulated, in order to estimate the influence of permeability, frequency of loading, and homogeneity of the shear stress field on the laboratory data. Copyright © 2006 John Wiley & Sons, Ltd.     

Q3砂黄土真三轴强度变形特性研究

为了研究Q3砂黄土强度变形特性,以甘肃永靖黑方台Q3砂黄土为研究对象,利用西安理工大学研制的真三轴仪,进行了3个围压（50、100 kPa 和200 kPa）、3个b值（0、0.25和0.5）和3个含水率（5%、10%和15%）不同工况试样破坏情况的真三轴试验。试验结果发现：（1）真三轴条件下Q3砂黄土剪切破坏方式以侧胀破坏、单缝剪切破坏为主,其次少数土样发生锥形破坏、双缝剪切破坏和T型缝剪切破坏。（2）相同围压和含水率、不同中主应力比（b）的情况下,Q3砂黄土的主应力差随中主应力比增大而增大,应力-应变关系曲线为强硬化型,剪胀现象明显;中主应力比对广义剪应力和广义剪应变之间关系有一定影响,随b值增加,曲线依次增加;随b值的增加,强度降低,广义剪应力与平均球应力比（q/p）与主应变关系曲线逐渐变缓,且曲线依次降低。（3）随含水率增加,Q3砂黄土由固态向半固态转化过程中,不同中主应力比时黏聚力均出现明显降低,但内摩擦角则出现微小增加。     

A non‐coaxial critical state soil model and its application to simple shear simulations

The yield vertex non‐coaxial theory is implemented into a critical state soil model, CASM (Int. J. Numer. Anal. Meth. Geomech. 1998; 22 :621–653) to investigate the non‐coaxial influences on the stress–strain simulations of real soil behaviour in the presence of principal stress rotations. The CASM is a unified clay and sand model, developed based on the soil critical state concept and the state parameter concept. Without loss of simplicity, it is capable of simulating the behaviour of sands and clays within a wide range of densities. The non‐coaxial CASM is employed to simulate the simple shear responses of Erksak sand and Weald clay under different densities and initial stress states. Dependence of the soil behaviour on the Lode angle and different plastic flow rules in the deviatoric plane are also considered in the study of non‐coaxial influences. All the predictions indicate that the use of the non‐coaxial model makes the orientations of the principal stress and the principal strain rate different during the early stage of shearing, and they approach the same ultimate values with an increase in loading. These ultimate orientations are dependent on the density of soils, and independent of their initial stress states. The use of the non‐coaxial model also softens the shear stress evolutions, compared with the coaxial model. It is also found that the ultimate shear strengths by using the coaxial and non‐coaxial models are dependent on the plastic flow rules in the deviatoric plane. Copyright © 2006 John Wiley & Sons, Ltd.     

Anisotropic behavior of the Bushehr carbonate sand in the Persian Gulf

The anisotropy effect is exhibited more prominently in sedimentary depositions, and it relates the soil’s mechanical specifications to the directions of imposed loads. Even though this phenomenon has been comprehensively explored in silica sands, few research has been conducted for studying the anisotropic behavior of marine carbonate sands. To bridge this gap, the present study investigates the anisotropy effect on the mechanical behavior of Bushehr carbonate sand acquired from the north shelf of the Persian Gulf in Iran. Toward this end, some undrained principal stress rotation tests are conducted using a hollow cylinder shear torsional apparatus in such a manner that the direction of the applied principal stresses are fixed along a desired orientation and the total mean stress and intermediate principal stress ratio are kept constant. Furthermore, prior to shearing, the samples are consolidated under three confining pressures and two isotropic and anisotropic states. The results show that dilative behavior is observed in all loading directions after initial contraction; this contradicts the response observed in silica sands. The anisotropy response of soil follows two different trends in the contractive and dilative phases. The relation of soil’s mechanical properties shows a descending trend with the angle of maximum principal stress in the contractive phase; on the other hand, the anisotropy behavior shows a dominant parabola trend in the dilative phase, where the maximum ultimate pore pressure and minimum soil strength occur in the stress direction with an angle of α?=?30°. By increasing the confining pressure in the soil element, the intensity of the anisotropy in some mechanical properties except the soil deformation is reduced. Furthermore, the deviatoric-to-effective mean stress ratio in the phase transformation state from contraction to dilation is independent of the loading direction and consolidation stress state, and it is considered one of the intrinsic properties of sand.