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.     

复杂加载条件下珊瑚砂抗液化强度试验研究

循环加载方式与应力路径对砂土的抗液化强度有很大的影响。利用GDS空心圆柱扭剪仪对南海珊瑚砂进行了一系列复杂加载条件下均等固结不排水循环试验,探讨了90°突变应力路径下主应力方向角对珊瑚砂抗液化强度的影响。试验结果发现：以循环应力比（CSR）作为应力水平指标,当不控制中主应力系数b的变化时,主应力方向角 对珊瑚砂的抗液化强度并无显著影响;当控制b始终保持0.5时,珊瑚砂的抗液化强度随着 的增加呈现出先减小后增大的趋势,且在 45°时的抗液化强度最低。基于分析循环荷载引起的土单元大、小循环主应力 、 变化,定义了单元体循环应力比（USR）作为一个新的物理指标,发现不同循环加载方式与应力路径条件下施加于珊瑚砂试样的USR与引起液化所需的循环次数NL存在事实上的唯一性关系。通过引自文献的4种无黏性土原始试验数据的再处理,独立地验证了以USR表征砂类土液化强度的适用性。     

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.     

定轴排水剪切试验中各向异性砂土的力学响应

南京云母砂主要由片状颗粒组成,具有较为明显的各向异性特性。采用香港科技大学的自动控制空心圆柱扭剪仪进行了应力主轴方向角分别为10°、30°、60°、80°的密实云母砂定轴剪切试验,研究云母砂的初始各向异性规律。为研究中主应力的影响,又对同一密度的试样在中主应力系数b＝0.1、0.5、1.0三种不同情况下进行定轴剪切试验。试验结果表明,在大主应力方向角从0°～90°的变化过程中,强度先减小后增大,且随着b值的增加强度增大;变形表现出明显的各向异性,随着b值的增加体变增大     

Influences of loading direction and intermediate principal stress ratio on the initiation of strain localization in cross-anisotropic sand

Since cross-anisotropic sand behaves differently when the loading direction or the stress state changes, the influences of the loading direction and the intermediate principal stress ratio (b = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) on the initiation of strain localization need study. According to the loading angle (angle between the major principal stress direction and the normal of bedding plane), a 3D non-coaxial non-associated elasto-plasticity hardening model was proposed by modifying Lode angle formulation of the Mohr–Coulomb yield function and the stress–dilatancy function. By using bifurcation analysis, the model was used to predict the initiation of strain localization under plane strain and true triaxial conditions. The predictions of the plane strain tests show that the major principal strain at the bifurcation points increases with the loading angle, while the stress ratio decreases with the loading angle. According to the loading angle and the intermediate principal stress ratio, the true triaxial tests were analyzed in three sectors. The stress–strain behavior and the volumetric strain in each sector can be well captured by the proposed model. Strain localization occurs in most b value conditions in all three sectors except for those which are close to triaxial compression condition (b = 0). The difference between the peak shear strength corresponding to the strain localization and the ultimate shear strength corresponding to plastic limit becomes obvious when the b value is near 0.4. The influence of bifurcation on the shear strength becomes weak when the loading direction changes from perpendicular to the bedding plane to parallel. The bifurcation analysis based on the proposed model gives out major principal strain and peak shear strength at the initiation of strain localization; the given results are consistent with experiments.     

Experimental investigation of the effect of grading characteristics on the liquefaction resistance of various graded sands

The liquefaction susceptibility of various graded fine to medium saturated sands are evaluated by stress controlled cyclic triaxial laboratory tests. Cyclic triaxial tests are performed on reconstituted specimens having global relative density of 60%. In all cyclic triaxial tests; loading pattern is selected as a sinusoidal wave form with 1.0 Hz frequency, and effective consolidation pressure is chosen to be 100 kPa. Liquefaction resistance is defined as the required cyclic stress ratio which caused initial liquefaction in 10 cycles during the cyclic triaxial test. The results are used to draw relationship between grading characteristics (e.g. coefficient of uniformity and coefficient of curvature) and the liquefaction resistance of various graded sands. It is found that a relationship between cyclic resistance and any of the size (i.e. D₁₀, D₃₀ or D₆₀) would be more realistic than to build a relation between grading characteristics and the cyclic resistance.     

Influence of initial state and intermediate principal stress on undrained behavior of soft clay during pure principal stress rotation

It is important to be fully aware of the dynamic characteristics of saturated soft clays under complex loading conditions in practice. In this paper, a series of undrained tests for soft clay consolidated with different initial major principal stress direction ξ were conducted by a hollow cylinder apparatus (HCA). The clay samples were subjected to pure principal stress rotation as the magnitudes of the mean total stress p, intermediate principal stress coefficient b, and deviator stress q were all maintained constant. The influences of intermediate principal stress coefficient and initial major principal stress direction on the variation of strain components, generation of pore water pressure, cyclic degradation and non-coaxiality were investigated. The experimental observations indicated that the strain components of specimen were affected by both intermediate principal stress coefficient and initial major principal stress direction. The generation of the pore water pressure was significantly influenced by intermediate principal stress coefficient. However, the generation of pore water pressure was merely influenced by initial major principal stress direction when b?=?0.5. It was also noted that the torsional stress–strain relationships were affected by the number of cycles, and the effect of intermediate principal stress coefficient and initial major principal stress direction on the torsional stress–strain loops were also significant. Stiffness degradation occur under pure principal stress rotation. Anisotropic behavior resulting from the process of inclined consolidation have considerable effects on the strain components and non-coaxial behavior of soft clay.

     

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.     

Liquefaction behavior of dredged silty-fine sands under cyclic loading for land reclamation: laboratory experiment and numerical simulation

Medium-coarse sands (CS) were dredged and exhausted in land reclamation. However, the remaining silty-fine sands (FS) were wasted. The liquefaction behavior of dredged silty-FS and the possibility of utilizing the remaining silty-FS as dredger fill source for land reclamation should be investigated. Cyclic consolidation-undrained triaxial tests were performed to investigate the liquefaction resistance of dredged silty-FS under different influencing factors. The cyclic stress ratio (CSR) of dredged silty-FS increased with the increase in initial relative density and consolidation stress ratio and decreased with the increase in silt content and consolidation stress. The CSR first decreased with the increase in clay content up to a threshold value and increased with the increase in clay content. A regression model was created to estimate the relationship between CSR and silt content, clay content, initial relative density, consolidation stress, consolidation stress ratio, and cyclic resistance ratio. Response surface methodology (RSM) was employed to investigate the mutual influence among the five independent variables. On the basis of cyclic triaxial tests, particle flow code models were introduced to investigate the microscopic internal fabric changes of dredged silty-FS and the influence of extended factors on liquefaction. The average microscopic contact force and coordination number between particles controlled the macroscopic mechanical behavior of sands. Sand liquefaction was due to the cumulative loss of coordination number under cyclic loading. The average contact force between particles was linearly decreased to 0 and the coordination number sharply decreased when the sample reached initial liquefaction. On the basis of numerical tests, CSR increased with the increase in D₅₀ and vibration frequency. The influence of vibration frequency was relatively small. In addition, the CS–FS and CS–FS–CS combination layers showed greater liquefaction resistance than the FS layer. In the filling process, the interbed of FS and CS improved the liquefaction resistance of dredged silty-FS to a certain extent.     

主应力方向和偏应力比对TJ-1模拟月壤各向异性的影响

采用空心圆柱扭剪仪对干燥TJ-1模拟月壤试样进行了应力主轴固定的定向剪切试验及不同偏应力比时主应力方向的纯旋转试验。从应力-应变关系角度出发,研究主应力方向、偏应力比对其各向异性的影响,并探讨了上述因素对TJ-1模拟月壤非共轴性的影响。试验结果表明：主应力方向和偏应力比对TJ-1模拟月壤的各向异性均有显著影响;应力主轴旋转引起的非共轴现象比定向剪切时明显,且偏应力比较小时非共轴角随应力主轴旋转呈先减小后增加的趋势,偏应力比较大时非共轴角一直减小直至试样破坏时非共轴现象消失。上述成果可弥补干砂试样非共轴领域的研究空白,并可望为将来月球上基础设施的修建提供技术支持。     

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.     

Unified 3D critical state bounding-surface plasticity model for soils incorporating continuous plastic loading under cyclic paths. Part I: Constitutive relations

The unified three-dimensional (3D) critical state bounding-surface plasticity model gUTS enables clays, silts and sands to be treated within a single framework. Furthermore, loose and dense states of a particular soil subjected to a wide range of confinements are viewed as a single material defined by the same set of constants. The model is able to handle both monotonic and complex cyclic paths including those involving a rotation of the principal stress directions. The model incorporates the following features: combined use of radial and deviatoric mapping rules and the use of an apparent normal consolidation line for sands; use of a non-associated flow rule where the ratio of the rates of volumetric plastic strain to deviatoric plastic strain is a function only of the ratio of deviatoric to mean effective stresses and the Lode angle; adoption of a bi-linear critical state line projected onto the plane of the void ratio versus logarithm of mean effective stress; inclusion of a sub-elliptic, or super-elliptic, segment in the plastic dilatancy surface for stress ratios less than critical; use of elliptic segments in the deviatoric planes; movement of the projection centre in the deviatoric mapping region and incorporation of a plastic stiffening effect for cyclic paths which repeatedly load in the same deviatoric direction.     

真三维状态下土体强度及变形分叉影响

通过引入应力Lode角建立合理的角隅函数描述偏平面形状,对三维Mohr-Coulmb强度准则进行修正,使之能合理反映中主应力比对土体峰值内摩擦角的影响。修正后的准则在偏平面上的强度线与Lade-Duncan准则相似,但更具灵活性,预测结果更符合松砂真三轴试验结果。由于土体在加载过程中常发生应变局部化现象,导致其强度得不到充分发挥。基于非共轴塑性模型的分叉分析研究了应变局部化发生对土体强度发挥的影响,通过与密砂真三轴试验结果对比表明,分叉强度能合理反映在不同中主应力比条件下应变局部化发生对土体强度的降低作用。     

Non‐coaxial elasto‐plasticity model and bifurcation prediction of shear banding in sands

Numerous constitutive models built on coaxial theory and validated under axi‐symmetric condition often describe the stress–stain relationships and predict the inceptions of shear banding in sands inaccurately under true triaxial condition. By adopting an elaborated Mohr–Coulomb yield function and using non‐coaxial non‐associated flow rule, a 3D non‐coaxial elasto‐plasticity model is proposed and validated by a series of true triaxial tests on loose sands. The bifurcation analysis of true triaxial tests on dense sands predicts the influence of the intermediate principal stress ratio on the onset of shear band accurately. The failure of soils is shown to be related to the formation of shear band under most intermediate principal stress ratio conditions except for those which are close to the axi‐symmetric compression condition. Copyright © 2009 John Wiley & Sons, Ltd.     

中主应力与大主应力方向角对软黏土排水变形特性影响

为研究中主应力系数和大主应力方向角对各向异性软黏土变形特性的影响,利用GDS空心圆柱扭剪仪对温州原状软黏土进行了一系列不同中主应力系数和大主应力方向角的排水定向剪切试验。试验过程中在大主应力方向角和中主应力系数不变的条件下,逐渐增加剪应力直至试样破坏。分析了中主应力系数和大主应力方向角对温州原状土偏应力与大主应变关系、体应变、中主应变和小主应变与大主应变关系的影响。试验结果表明：试样的应力-应变关系在中主应力系数和大主应力方向角不同时表现出明显的各向异性。当中主应力系数为0.00和1.00时,大主应力方向角对应力-应变关系的影响较小;而当中主应力系数为0.50时,应力-应变关系中的割线剪切模量随大主应力方向角变化明显。当大主应力方向角为30°时,随着中主应力系数从0.00增加到0.50,中主应变由压缩状态变为拉伸状态;当大主应力方向角为45°时,随着中主应力系数从0.00增加到1.00,中主应变由压缩状态变为拉伸状态。     

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.     

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.

     

利用室内和现场水压致裂试验联合确定地应力与岩石抗拉强度

钻杆式水压致裂原地应力测试系统的柔性会影响最大水平主应力的计算精度。利用空心岩柱液压致裂试验获得的岩石抗拉强度来取代重张压力计算最大水平主应力是降低钻杆式测试系统柔性的负面影响的重要途径。在福建某隧道深度为65 m的钻孔内开展了8段的高质量水压致裂原地应力测试,随后利用钻孔所揭露的完整岩芯开展了17个岩样的空心岩柱液压致裂试验。利用空心岩柱液压致裂所得的抗拉强度平均值为8.40 MPa,与经典水压致裂法确定的岩体抗拉强度8.22 MPa接近。对于20 m的范围内8个测段的原地应力量值,最小水平主应力平均值为8.41 MPa,基于重张压力P_r的最大水平主应力平均值为16.70 MPa;基于空心岩柱抗拉强度的最大水平主应力量值平均值为16.88 MPa,两种方法获得的最大水平主应力平均值基本一致。最大最小水平主应力与垂直主应力之间的关系表现为σ_H > σ_V > σ_h,这种应力状态有利于区域走滑断层活动。通过对比分析可知,对于钻杆式水压致裂原地应力测试系统,当测试深度小且测试系统柔性小时,基于重张压力和基于空心岩柱抗拉强度得到的最大水平主应力量值差别不大,这说明基于空心岩柱的岩石抗拉强度完全可以用于水压致裂最大水平主应力的计算,同时基于微小系统柔性的水压致裂测试系统获得的现场岩体强度也是可靠的。      

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。     

Predicting flow liquefaction,a constitutive model approach

In this paper, flow liquefaction criterion for contractive loose sands is analytically extracted based on the fundamental definition of flow liquefaction. In order to obtain the closed form of this criterion, Dafalias–Manzari constitutive model is employed; so the stress ratio at the onset of flow liquefaction is presented as a function of model parameters, state parameter and void ratio. Flow liquefaction line, as a graphical form of suggested criterion in stress space, shows that the peak points of undrained stress paths with same void ratios are not necessarily in a straight line. In order to validate the reliability of proposed flow liquefaction line to predict the onset of instability, it has been compared with the results of experimental tests performed on Toyoura, Ottawa and Leighton Buzzard sands. The verification results show that the present criterion can satisfactorily predict the onset of flow liquefaction in monotonic and cyclic undrained tests of saturated sands as well as the structural collapse in constant deviatoric stress tests of loose dry sands.