A non‐coaxial constitutive model for sand deformation under rotation of principal stress axes

A constitutive model for the simulation of non‐coaxiality, an aspect of anisotropic behavior of sand subjected to the rotation of the principal stress axes, is presented in this paper. Experimental studies have shown that non‐coaxiality or non‐coincidence of principal plastic strain increments with principal stress axes under loadings involving the rotation of principal stress axes may be considerable. Besides, the rotation of the principal stress axes results in dramatic effects on stiffness and dilatant behavior of sand. Therefore, the consequences of principal stress axes rotation on deformational behavior, dilatancy and soil stiffness must be taken into account in theoretical and practical problems. To this aim, the following steps are taken: (1) A general relationship for flow direction with respect to possibility of non‐coaxial flow is developed. Moreover, special circumstances linking non‐coaxiality to instantaneous interaction between loading and soil fabric are proposed. (2) Proposing novel expressions for plastic modulus and dilatancy function, the model is enforced to provide realistic simulations when sand is subjected to the rotation of the principal stress axes. Finally, with numerous examples and comparisons, the model capabilities are shown under various stress paths and drainage conditions. Copyright © 2007 John Wiley & Sons, Ltd.     

主应力轴变化下非共轴对砂土剪胀特性影响

传统塑性剪胀模型在描述应力比和塑性应变增量关系时都是基于共轴塑性流动法则,从而认为土体的剪胀性仅与应力比有关。大量试验结果表明,在涉及主应力轴变化的复杂应力条件下塑性流动过程中应力-应变是非共轴的,因而在分析砂土剪胀特性时非共轴是不可忽视的因素。为了研究主应力轴变化的复杂应力条件下非共轴对砂土剪胀特性的影响,利用空心圆柱仪对饱和砂土进行了一系列定轴剪切试验、纯主应力轴旋转试验以及组合加载试验。试验结果表明,不同应力路径下应力-应变非共轴都会引起剪胀曲线偏离Rowe直线,通过Gutiereez提出的考虑非共轴因子的修正剪胀方程可以修正非共轴引起的偏差,从而使得Rowe剪胀方程适用于涉及主应力轴旋转等更加复杂的加载条件。     

交通荷载引起的主应力轴旋转室内试验模拟探讨

为了通过室内试验研究交通荷载引起的主应力轴旋转对土体循环特性的影响,以单个移动荷载和列车荷载为例,分析了主应力轴旋转特点。以此为基础,结合空心圆柱仪的加载特点,给出了室内模拟主应力轴旋转的加载方法。竖向动应力可以用具有静偏应力的正弦荷载模拟,动剪应力可以用正弦荷载模拟,两者的相位差为 。为了模拟交通荷载引起的主应力差变化的特点,两种动应力的幅值应该是不同的。当试验中施加无应力反向的竖向动应力时,大主应力夹角在 ～ 和 ～ 之间变化。     

A kinematic hardening soil model considering the principal stress rotation

In this article, a typical and representative kinematic hardening soil model is first studied to investigate its capabilities to reproduce soil responses under principal stress rotations (PSR). It is found that the model is capable of reproducing the non‐coaxiality very well. It can qualitatively capture the trends of responses of different stress and strain components, without the capability to quantitatively reproduce these responses. Its prediction of volumetric responses is the poorest and can give wrong results in many cases. The underlying reasons for these capabilities and defects are analyzed in detail. The model is subsequently modified to better take into account the PSR influences. An additional new flow rule and plastic modulus for the PSR are developed. One important feature of the model is that it is developed in the general stress space with six stress variables. Therefore, it can take into account multiple PSRs at different directions. Another feature is that it retains the linear stress rate–strain rate relationship, which facilitates its numerical implementations. In addition, the universal characteristic of the theory makes it equally applicable to other kinematic hardening models. Copyright © 2012 John Wiley & Sons, Ltd.     

Multi-laminate framework of soil models—plasticity formulation

This paper presents plasticity formulation of the multi-laminate framework of soil models. Soil element is assumed to be an assemblage of perfectly fitting polyhedral blocks and irreversible deformations are assumed to occur due to sliding, separation/closing of the boundaries. Using an appropriate summation of mechanisms, the total plastic strains are obtained by evaluating contributions from an infinite number of randomly oriented planes in space. The paper provides a general plasticity formulation and examines various constitutive theories which can be incorporated into the framework.     

考虑主应力轴旋转的基坑开挖应力路径研究

首先对应力路径的概念进行丰富和扩展,提出考虑主应力轴旋转的三维应力路径,然后采用数值方法,对基坑开挖过程中的应力路径进行了深入分析,研究了基坑内外各种应力路径及其规律,结果表明：开挖过程中无论横向还是竖向,应力路径都表现出卸荷特性,且坑内卸荷量大于坑外卸荷量,使得坑内应力变化及主应力轴旋转较坑外大;随着离基坑中心距离的增大,坑内应力变化减小,主应力轴旋转趋缓;开挖过程对坑外应力变化及主应力轴旋转的影响随离围护墙距离的增大而减小。坑内应力路径总体表现为平均压应力p减小,广义剪应力q减小,主应力轴偏转角? 增大;坑外应力路径总体表现为p减小,q增大,? 增大。最后归纳出基坑开挖过程中坑内与坑外的典型应力路径,以指导基坑工程实践设计分析和室内试验模拟。     

Non-coaxial behavior modeling of sands subjected to principal stress rotation

Acta Geotechnica - This paper attempts to clarify the necessary elements for describing the non-coaxial behavior of sand in the plasticity framework based on the critical-state soil mechanics. Such...     

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     

单轴压缩湿砂土试样主应变轴偏转规律试验研究

利用自主开发的基于粒子群优化的数字图像相关方法,获得了单轴压缩湿砂土试样观测平面内主应变轴偏转角的时空分布规律。采用双三次样条插值方法,获取了任意位置的主应变轴偏转角,分析了土样将来出现剪切带位置、剪切带的中心及其尖端附近和剪切带外的主应变轴偏转角随纵向应变的演变规律。研究发现,随着纵向应变的增加,在土样观测平面内,主应变轴偏转角的范围由分散逐渐变得稳定,大部分区域最终分布在-10°~10°之间。当出现较清晰的剪切带以后(硬化阶段后期),剪切带内不同位置处主应变轴偏转角基本趋于恒定或稍有下降,大致稳定在-5°~5°之间,这与剪切带外的点的主应变轴偏转角均处于发展之中不同;而在剪切带尖端附近的点,主应变轴偏转角随纵向应变的演变规律比较复杂。     

Effects of principal stress rotation on wave-induced soil response in a poro-elastoplastic sandy seabed

In this study, a constitutive model is developed in order to investigate wave–seabed interactions. This model takes into account the impact of principal stress rotation (PSR) and is based on the generalized plasticity theory, in which plastic strain generated by PSR is considered an additional item in the constitutive relationship of soil. The normalized loading direction and plastic flow direction were determined based on the stress tensor invariant. Comparisons between the present model and previous Hollow Cylinder Apparatus tests and geotechnical centrifugal wave tests show good agreement. Numerical results show the effects of PSR on predictions of liquefaction potential due to: (a) the cumulative impact of plastic strain in the seafloor and (b) the buildup of pore pressure. Parametric study shows that the model parameters, including the wave and seabed parameters, have significant effects on the wave-induced soil liquefaction.

     

基于主应力轴旋转理论的修正Terzaghi松动土压力

基于土体主应力轴旋转理论,提出了Trapdoor上方土体侧向土压力系数的一般表达式,从而修正了传统的Terzaghi松动土压力计算公式。对于无黏性土,该系数是一个只与土体有效内摩擦角相关的参数,其值介于1.0和被动土压力系数Kp之间,且随着有效内摩擦角的增大而增大。黏性土的侧向土压力系数则与Trapdoor上覆土体厚度、重度、有效黏聚力和有效内摩擦角及Trapdoor宽度等参数有关。与传统计算方法相比,修正后的Terzaghi松动土压力计算结果与国内外Trapdoor模型试验结果及FLAC数值分析结果更为吻合,可广泛应用于地下管道、地基局部沉陷及隧道工程的土拱应力分析。     

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.     

主应力轴旋转下小偏压固结密实粉土崩塌特性及孔压模型研究

为研究主应力轴旋转复杂动应力对偏压固结粉土的性状演变影响,以空心圆柱试样为对象,开展具有不同初始固结比的密实粉土（Dr＝70%）在不排水主应力轴循环旋转下的系列试验。结果表明：①初始固结比不大于1.5时,主应力轴旋转导致试样发生中低应变崩塌,进而液化的脆性破坏模式;而固结比大于1.5时,试样变为应变持续稳定开展至高应变,孔压最终进入动态平衡的延性破坏模式,且不同固结比下试样发生崩塌液化和稳态延性破坏的孔压峰值间不存在交叉。②小偏压固结试样的液化峰值孔压和崩塌孔压均随固结比增加而有规律地下降,但受动剪应力水平影响很小,这与等压固结试样的崩塌孔压值受控于剪应力水平有很大差异。③相同初始球应力水平下,崩塌振次反映的小偏压固结试样强度高于等压固结试样,但在偏压条件下强度与固结比不存在单调变化关系,表明小偏压固结试样崩塌除受制初始围压水平外,很大程度上还取决于偏压程度。④基于上述试验结果,提出了主应力轴循环旋转下小偏压固结粉土的孔压预测模型,该模型不仅突显了崩塌状态对相变及液化破坏的重要预测作用,还反映了固结比和动剪应力对孔压开展的综合影响。     

基于固定主应力轴假设的砂堆基底应力凹陷的研究

对砂堆三棱柱的基底应力分布及应力凹陷现象进行了研究,基于固定主应力轴假设（FPA假设）将砂堆分为应力状态已知的I区和应力状态未知的II区,并假设了II区内的多种剪应力分布来求解II区内的应力状态,最后,将不同剪应力分布假设下砂堆中线上的静止土压力系数值与Kulhawy公式计算值对比,可得出如下结论：基底法向应力存在应力凹陷现象,自然休止角越大（砂堆越紧密）,应力凹陷程度、应力凹陷范围越大;不同剪应力分布假设下,II区应力分布形态不同,法向应力极小值所在处也不同。剪应力二次方分布假设和三次方假设下砂堆基底应力分布最为合理、最为符合真实情形。     

Non-coaxiality of soft clay generated by principal stress rotation under high-speed train loading

Plenty of geomechanics tests and theories have confirmed the existence of non-coaxiality while soil is subjected to principal stress rotation. This paper investigated the influence of one particular principal stress path, which is a ‘heart-shape’ stress path that is normally induced by high-speed train loading, on the non-coaxiality of reconstituted soft clay. Hollow cylinder apparatus was employed to carry out series of undrained dynamic tests. The goals of this study were to (1) reveal the essential factors of complex cyclic loading paths that influence non-coaxiality in clayey soil and (2) quantify the influence of the factors on variation in non-coaxiality under the high-speed training loading. To analyze the non-coaxiality under high-speed train loading, (a) the pure rotation stress path was utilized as comparison for underling the different influence that ‘heart-shape’ stress path has from other conventional cyclic stress paths. (b) Two variables, dynamic stress ratio and tension–compression amplitude ratio, were introduced in analyzing the evolution of the non-coaxial angle. (c) Based on the test results, equations for describing the revolution of non-coaxiality were proposed which can help to describe the variation in non-coaxial angle under complex loadings quantitatively and understand the influence of the major factors of the stress path intensively.

     

动态围压下空心圆柱扭剪仪模拟主应力轴旋转应力路径能力分析

针对英国GDS公司动态空心圆柱扭剪仪（HCA）在主应力轴旋转试验中能够实现三向动态加载（轴力、扭矩、内围压或外围压）的功能,通过严格的数学推导,提出了3种易于实现又与实际工程背景相符合的应力路径加载方式。当三向动载满足相应的条件时,可以实现（1）平均主应力p和剪应力幅值q保持恒定的应力路径（应力路径1）;（2）中主应力参数b = 0.5、剪应力幅值q为常数的应力路径（应力路径2）;（3）平均应力p保持不变、主应力旋转角90º突变的应力路径（应力路径3）,其中应力路径1、2为模拟海洋波浪荷载作用下的应力路径试验提供了理论依据,应力路径3可用于模拟地震荷载作用下的土体动力特性。以上3种应力路径均不能在两向动态HCA仪中实现     

Time-dependent multilaminate model of rocks—a numerical study of deformation and failure of rock masses

A new model for rocks and rock-like material with multiple planes of weakness is proposed. The behaviour of the assembly applies tensile and Mohr-Coulomb shear limits on each such plane with possible strain dependence of frictional properties. The visco-plastic algorithm which allows the incorporation of time effects is used to obtain static solutions. The model is illustrated in actual context by applications to stability of rock slopes and behaviour of tunnels. A generalization of the model to include arbitrary three-dimensional distribution of laminae in ‘quasi-plane strain’ is included. The effect of various flow rules adopted for plastic straining is indicated.     

考虑主应力方向的土体非线性弹性模型

剪正应力比综合反映了摩擦材料的变形与破坏特性。通过分析主应力的大小与方向变化所引起的剪正应力比,结合剪正应力比-剪应变分量的双曲线关系,提出了一种能考虑主应力方向的土体非线性弹性本构模型。考虑到土体初始剪切模量、各向异性峰值强度与应力历史、加载方向密切相关,给出了模型参数的取值方法,进而得到了分量形式的应力-剪应变关系。分别采用应力路径三轴试验、纯主应力轴旋转试验以及主应力方向固定的剪切试验验证了模型的合理性。预测结果与试验结果对比表明,提出的非线性弹性模型能较好地描述复杂应力路径下土体变形特性。     

Constitutive modeling of principal stress rotation by considering inherent and induced anisotropy of soils

In order to simulate the soil response during principal stress rotation, anisotropic unified hardening (UH) model is developed within the framework of elastoplastic theory. Without introducing any additional mechanism to display the role of stress rotation specifically, this model achieves the simulation by considering the material anisotropy. The effect of inherent anisotropy is reflected using the anisotropic transformed stress method, but a new formula for the stress mapping is adopted to keep the mean stress unchanged. Analysis indicates that from the view of the transformed stress tensor, the anisotropic soil is subjected to loading during pure rotation of principal stress axes, so that plastic strains can be calculated. To represent the induced anisotropy, a fabric evolution law is proposed based on laboratory and numerical test results. At the critical state, the fabric tensor reaches a stable value determined by the stress state, while the critical state line is unique in the plane of void ratio versus mean stress. The anisotropic UH model has concise formulation and explicit elastoplastic flexibility matrix and can provide reasonable predictions for the deformation of anisotropic soils when principal stresses rotate.     

循环荷载下考虑主应力旋转的软土力学响应研究

目前用于轨道路堤分析计算的参数多是通过三轴试验获得,而列车荷载经过时土单元应力路径与循环三轴试验加载路径的显著差异可能导致预测失真而引发工程问题。针对某城市轨道进行了三维计算,并分析了移动列车荷载下土单元应力幅值、循环周数、主应力轴旋转的分布规律。在该基础上,采用空心圆柱循环扭剪试验对该复杂应力路径进行了模拟,研究了饱和软黏土的孔压及变形累积特性。结果表明,列车荷载经过时地基土单元大主应力将在(－90°, 90°)内发生旋转;该主应力轴旋转将显著促进软黏土孔压和应变的累积,竖向应力幅值为15 kPa时,循环扭剪试验产生的孔压值比循环三轴试验高77%,累积应变增大了近50%;随着循环应力水平提高,二者累积孔压及累积应变的差值还会进一步增大,甚至出现循环三轴下仅产生较小应变而循环扭剪下已破坏的本质性差异。