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.     

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.     

结构性黄土的剪切带及强度特性的真三轴试验研究

采用西安理工大学自主研发的真三轴仪,对西安白鹿原黄土进行了不同中主应力比值、不同固结围压的试验研究,探讨了黄土剪切带形成与峰值强度、中主应变与大主应变关系曲线、体应变与大主应变关系曲线特征点之间的联系以及子午平面、 平面上的强度变化规律。分析了真三轴应力条件下黄土强度变形规律和试样剪切带破坏模式和黄土在复杂应力状态下剪切带形成的判断依据和原因,研究表明,真三轴压缩原状黄土具有明显的剪切带,围压和中主应力比值较小时表现为软化,围压和中主应力比值较大时则表现为硬化;中主应变、体应变与大主应变关系曲线较为一致的转折点反映了土变形性状发生变化;与中主应变方向一致的剪切带两侧土结构块体产生相对滑移,剪切带开始形成和发展;土应变曲线的转折点可以作为土固结结构内剪切带形成的判断依据;子午平面上强度线呈线性变化规律, 平面上呈曲边三角形非线性变化规律,并且与 -SMP强度准则较为接近。不同应力条件下剪切带变化复杂的破坏模式与黄土原生的结构特征和加载共同作用的变化有密切联系。     

The role of non‐coaxiality in the simulation of strain localization based on classical and Cosserat continua

It is normally accepted that materials inside the shear band undergo severe rotation of the principal stress direction, which causes non‐coaxiality between the principal stress and principal plastic strain rate. However, classical plasticity flow theory implicitly assumes that the principal stress and the principal plastic strain rate are coaxial; thus, it may not correctly predict the onset of the shear band. In addition, classical continuum does not contain any internal length scales; as a result, it cannot provide a reasonable shear band thickness. In this study, the original vertex non‐coaxial plastic model based on the classical continuum is extended to the Cosserat continuum. The corresponding codes are implemented via the interface of the user defined element subroutine in ABAQUS. Through a simple shear test, the effectiveness of the user's codes is verified. Through a uniaxial compression test, the influence of non‐coaxiality on the onset, the orientation, and the thickness of the shear band is investigated. Results show that the onset of the shear localization is delayed, and the thickness of the shear band is widened when the non‐coaxial degree increases, while the orientation of the shear band is little affected by the non‐coaxial degree. In addition, it is found that the non‐coaxiality can weaken the micro‐polar effect to some extent; nonetheless, the Cosserat non‐coaxial model still has its advantage over the classical non‐coaxial model in capturing the pre‐bifurcation as well as the post‐bifurcation behaviors of strain localization. Copyright © 2016 John Wiley & Sons, Ltd.     

粉细砂的真三轴试验与强度特性

采用柔性真三轴仪对上海粉细砂进行了一系列不同中主应力系数条件下的真三轴试验,针对中主应力对粉细砂强度特性的影响进行了系统分析。基于真三轴试验结果对Mohr-Coulomb强度准则的形状函数进行了改进,并采用试验结果对强度准则进行验证。结果表明,建立在真三轴试验基础上的强度准则能更准确地反映砂土三维应力状态下的强度特性。     

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。     

真三轴条件下Q2黄土的破坏模式与强度特性研究

基于西安理工大学自主研发的新型真三轴试验仪,对不同含水率Q2黄土在不同b值、不同固结围压条件下进行了真三轴试验研究,分析了真三轴试样破坏方式、中主应力对抗剪强度参数的影响以及π平面上的强度破坏面。结果表明,Q2黄土真三轴试样破坏方式主要有侧胀破坏、锥形破坏、梯形破坏、六边形破坏;不同b值应力路经条件下黏聚力与三轴压缩条件下黏聚力的比值在0.9～1.9之间,内摩擦角比值在0.7～1.5之间。土的结构性和土体破坏方式对π平面上的强度破坏面的形状影响较大,固结围压对π平面上的强度破坏面的大小影响较大;原状Q2黄土在π平面上的强度破坏面形状主要呈现梨形和轴对称六边形;随着结构性由强到弱,π平面上的强度破坏面形状由梨形向轴对称六边形变化。     

Predicting the initiation of static liquefaction of cross‐anisotropic sands under multiaxial stress conditions

Experimental evidence has shown that the liquefaction instability of sands can be affected by its material density, stress state, and inherent anisotropy. In order to predict the initiation of the static liquefaction of inherent cross‐anisotropic sands under multidimensional stress conditions, a rational constitutive model is needed. An elastoplasticity model able to capture the influences of intermediate principal stress ratio (b  = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) and loading direction on stress–strain relationships and volumetric properties was proposed. The yield function was formulated to be controlled by Lode angle, loading direction, and material state; the stress–dilatancy was a material state‐dependent function. After using the existing drained hollow cylinder tests to validate the proposed model, this model was used to simulate the existing undrained hollow cylinder tests. During this simulation, the second‐order work criterion was used to determine the initiation of static liquefaction. The results showed that an increase in both the intermediate principal stress ratio and the loading angle induces a decrease in the second‐order work. Static liquefaction is initiated more easily at a stress state with a large intermediate principal stress ratio and a large loading angle, and the mobilized friction angle at the instability points decreases with the intermediate principal stress ratio and the loading angle. Copyright © 2017 John Wiley & Sons, Ltd.     

真三轴条件下原状黄土的非线性本构模型

为了研究复杂应力条件下非饱和原状黄土的非线性本构模型,通过考虑真三轴条件下中主应力和吸力对大主应变的影响,提出了一个考虑中主应力影响的非饱和原状黄土的非线性本构模型。该模型包含12个参数,均可由常含水率非饱和土真三轴试验确定。研究了中主应力对土体变形和强度的影响,探讨了模型参数的变化规律。初始吸力一定时,土体的黏聚力随着中主应力的增大而增大,而内摩擦角随着中主应力的增大呈线性减小趋势。当吸力小于162 kPa时,吸力摩擦角等于21.8°;当吸力大于162 kPa时,吸力摩擦角等于5.5°。初始吸力相同时,不同中主应力条件下土体的体积模量可取为常数。利用该模型预估了常含水率真三轴等向固结试验的吸力变化规律,理论结果与试验结果比较接近。但是对于真三轴剪切试验吸力的预估还需要进行深入探讨。     

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。     

真三轴条件下非饱和黄土的有效应力屈服特性

为了研究非饱和黄土在有效应力空间的屈服特性,利用真三轴仪对非饱和原状黄土进行了不排水等向净应力压缩固结和不同中主应力参数b值的剪切试验,研究了真三轴压缩条件下非饱和黄土的有效应力屈服变化规律。研究结果表明：有效应力比随着中主应力或净围压的增大而减小,中主应力的增大作用对有效球应力的影响大于广义剪应力;由有效应力比?体应变关系曲线确定的剪缩屈服曲线在有效应力空间具有良好的规律性,屈服点的有效屈服应力随着中主应力和初始吸力的增大而增大;π平面上的有效应力屈服强度面和强度破坏面与SMP强度准则稳合较好,有效球应力和初始吸力越大,屈服强度面和强度破坏面越大。提出了真三轴条件下弹性剪应变和塑性剪应变的计算公式,通过分析有效应力与塑性应变关系得出有效应力空间中不同子午平面内的塑性势面呈椭圆形,且随着中主应力的增大,椭圆屈服面增大。     

不同密度粗粒料强度特性的大型真三轴试验

干密度对粗粒料的强度特性有重要影响,特别是三维应力状态下影响更为显著。通过不同密度粗粒料大型真三轴等小主应力等中主应力系数（b=0.25）加载试验和大三轴试验研究了干密度对粗粒料强度特性的影响。结果表明,大型真三轴试验的应力曲线基本呈爬升型,高于和陡于大三轴应力曲线,表现出较强的硬化性;粗粒料强度基本随初始干密度的增大或小主应力的增大呈线性增大;大型真三轴试验强度比大三轴试验强度增大20%～97%,且小主应力越小,强度增大幅度越大;令粗粒料黏聚力为0,则内摩擦角随初始干密度的增大基本呈线性增大,随小主应力的增大而减小;破坏应力比随初始干密度的增大呈线性增大,随小主应力的增大而呈线性减小,大型真三轴试验的破坏应力比小于大三轴试验的破坏应力比。     

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。     

粉质黏土的真三轴试验及强度特性研究

为研究复杂应力路径下粉质黏土强度特性,利用TSW-40型土壤真三轴仪,开展了不同试验条件下粉质黏土的真三轴试验。研究了真三维应力状态下粉质黏土应力-应变曲线变化规律,探讨了含水率、固结围压和中主应力比等试验条件对粉质黏土强度的影响规律,对比分析了真三维应力状态下 平面上粉质黏土试验值与Mohr-Coulomb（简称M-C）强度准则和双剪强度准则的差异。研究结果表明：真三维应力状态下粉质黏土的广义剪应力-剪应变曲线主要表现为应变硬化型。粉质黏土强度随中主应力比和固结围压的增大而增大,随着含水率的增大而减小。 平面上粉质黏土的强度包络线随静水压力 的增大向外逐渐扩展,随含水率 的增大向内逐渐收缩。 平面上M-C强度极限线和双剪强度屈服极限线与试验值对比分析表明,M-C强度准则描述土体强度时结果偏小,采用双剪强度准则时结果偏大。     

Coupled modelling of hydro‐mechanical behaviour of unsaturated compacted expansive soils

The Barcelona basic model cannot predict the mechanical behaviour of unsaturated expansive soils, whereas the Barcelona expansive model (BExM) can only predict the stress–strain behaviour of unsaturated expansive soils without the water‐retention behaviour being incorporated. Moreover, the micro‐parameters and the coupling function between micro‐structural and macro‐structural strains in the BExM are difficult to determine. Experimental data show that the compression curves for non‐expansive soils under constant suctions are shifted towards higher void ratios with increasing suction, whereas the opposite is true for expansive soils. According to the observed water‐retention behaviour of unsaturated expansive soils, the air‐entry value increases with density, and the relationship between the degree of saturation and void ratio is linear at constant suction. According to the above observation, an elastoplastic constitutive model is developed for predicting the hydraulic and mechanical behaviour of unsaturated expansive soils, based on the existing hydro‐mechanical model for non‐expansive unsaturated soil. The model takes into consideration the effect of degree of saturation on the mechanical behaviour and that of void ratio on the water‐retention behaviour. The concept of equivalent void ratio curve is introduced to distinguish the plastic potential curve from the yield curve. The model predictions are compared with the test results of an unsaturated expansive soil, including swelling tests under constant net stress, isotropic compression tests and triaxial shear tests under constant suction. The comparison indicates that the model offers great potential for quantitatively predicting the hydraulic and mechanical behaviour of unsaturated expansive soils. Copyright © 2011 John Wiley & Sons, Ltd.     

中主应力对砂土抗剪强度影响的分析

土的抗剪强度参数一般通过三轴压缩试验确定。而三轴压缩试验中土的应力状态是轴对称的,这往往与实际工程中土体的受力情况不相同。因此,探讨一般应力条件下与三轴应力条件下强度指标之间的相互关系是至关重要的。基于砂土的空间滑动面强度准则即SMP准则,针对不同中主应力系数,通过数值分析探讨了中主应力系数对砂土抗剪强度指标的影响。分析结果表明,中主应力对土的抗剪强度指标具有显著的影响,一般地在平面应变条件下这种影响最大。     

基于颗粒流程序的真三轴应力状态下堆石体的变形和强度特性研究

采用三维颗粒流程序,模拟了堆石体的真三轴试验,不仅研究了堆石体在三维应力条件下的宏观应力变形特点,而且将细观与宏观参数联系起来,进一步完善了对堆石体的研究。试验过程采用等中主应力比路径加载。通过比较堆石体真三轴颗粒流模型试验和室内真三轴试验结果,表明颗粒流程序能较好地模拟堆石体的力学特性。颗粒流数值试验结果表明,中主应力对堆石体在三向应力状态下的强度和变形特性均有显著的影响。应力比参数b从0～1变化过程中,中主应力面先压缩后膨胀,小主应力面一直处于压缩状态;中主应力对内摩擦角、弹性模量和泊松比也均有影响。从细观上看,围压越高,b值越大,颗粒配位数越大,孔隙率越小,故从细观角度解释了堆石体的宏观应力变形现象。     

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。     

Numerical simulations of simple shear with non‐coaxial soil models

This paper investigates the effects of a non‐coaxial model on simulated stress–strain behaviour of granular materials subject to simple shearing under various initial conditions. In most cases, a significant difference of predictions between coaxial and non‐coaxial modelling is found during the early stage in shearing. With the increase in shearing, non‐coaxial simulations approach and tend to coincide with coaxial simulations. It is also found that the roles of non‐coaxial modelling in simulating simple shear behaviour are considerably influenced by hardening rules, flow rules, initial static lateral pressure coefficients. In some cases, the non‐coaxial modelling gives a similar simulation as the coaxial modelling. In other cases, the non‐coaxial modelling decreases the hardening response or softening response of materials, compared with the coaxial modelling. Under certain conditions, the predicted peak strength of materials with non‐coaxial modelling is larger than that for coaxial modelling. Some of these observations can be attributed to the amount of principal stress rotation in various cases analysed. Others can be attributed to the difference between the directions of the non‐coaxial plastic flow and those for coaxial plastic flow. Copyright © 2005 John Wiley & Sons, Ltd.     

水泥土各向异性变形特性研究

采用研制的真三轴仪进行水泥土单向加荷试验,研究水泥土的各向异性变化规律,探讨应力对侧向膨胀的影响。结果表明,单向加荷条件下,加荷方向均产生压缩,而侧向膨胀主要与剪应力增量 有关;大主应力 单向加荷, ,中主应力 、小主应力 方向产生侧向膨胀;中主应力单向加荷, 时, 方向产生侧向膨胀, 时,无侧向膨胀;小主应力单向加荷, ,试样不产生侧向膨胀;对于相同应力增量,试样侧向膨胀和压缩应变均随初始固结应力的增大而减小。能量分析表明,试样的侧向膨胀与某一方向的约束程度相关,约束越强,侧向膨胀量越小;约束越弱,侧向膨胀量越大。