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.     

SANISAND-FN: An evolving fabric-based sand model accounting for stress principal axes rotation

SANISAND is the name of a family of bounding surface plasticity constitutive models for sand within the framework of critical state theory, which have been able to realistically simulate the sand behavior under conventional monotonic and cyclic loading paths. In order to incorporate the important role of evolving fabric anisotropy, one such model was modified within the framework of the new anisotropic critical state theory and named SANISAND-F model. Yet the response under continuous stress principal axes rotation requires further modification to account for the effect of ensuing noncoaxiality on the dilatancy and plastic modulus. This modification is simpler than what is often proposed in the literature, since it does not incorporate an additional plastic loading mechanism and/or multiple dilatancy and plastic modulus expressions. The new model named SANISAND-FN is presented herein and is validated against published data for loading that includes drained stress principal axes rotation on Toyoura sand.     

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.     

The influence of the intermediate principal stress on rock failure behaviour: A numerical study

The influence of the intermediate principal stress on rock strength has been studied comprehensively by previous researchers. However, the reason why rock strength firstly increases and subsequently decreases with the increase of intermediate principal stress is still unclear. In this paper, the mechanism of the intermediate principal stress effect on rock failure behaviour is revealed through a numerical method using the EPCA3D system (Elasto-Plastic Cellular Automaton). In this study, both homogeneous and heterogeneous rocks are considered. The heterogeneity of a rock specimen is modelled by introducing Weibull's statistical distribution. Two criteria, i.e. the Drucker–Prager and Mohr–Coulomb models, are used to determine whether a meso-scopic element in the rock specimen is in a failure state or not during the polyaxial stress loading process. The EPCA3D simulation reproduces the typical phenomenon of the intermediate principal stress effect that occurs in some rock experiments. By studying the EPCA3D simulated acoustic emission and complete stress–strain curves illustrating failure initiation, propagation and coalescence in the failure process of rocks, the essence of the intermediate principal stress effect is tracked. It is concluded that the heterogeneous stress distribution induced by the natural heterogeneity of rocks and the effect of the loading platen are two of the reasons producing the intermediate stress effect. Studies indicate that a moderate intermediate principal stress delays the onset of local failure, which in turn leads to an increase in the rock strength. However, once the intermediate principal stress reaches a certain value, local failure will be formed through the application of the intermediate principal stress. It is the number of failed elements in the pre-peak region that determines whether the rock strength decreases or not. The extent of rock strength reduction when the intermediate principal stress reaches a certain value is lessened with the increase in the minimum principal stress.     

中主应力系数影响下的冻结砂土损伤本构模型

人工冻结法是饱水砂层开挖过程中常用的止水和临时支护方法,通过冻土损伤特性研究为冻土力学特性和冻结体稳定性分析奠定基础。为研究冻结砂土的损伤力学特性,在-5℃下进行了不同中主应力系数的冻结砂土三维室内试验。从冻土微元破坏服从Weibull随机分布的特点出发,将Drucker-Prager强度准则作为冻土微元统计分布变量,利用应变等价性假说,建立了三维应力状态下冻结砂土损伤本构模型;在此基础上,讨论模型参数F₀与m和中主应力系数的关系,对模型参数进行合理修正,建立中主应力系数影响下的冻结砂土损伤本构模型,并与试验结果进行对比。分析结果表明：参数F₀和m随着中主应力系数的增大呈现先减小后增大的趋势;参数F₀反映了冻结砂土的强度特性,参数m代表了冻结砂土的延性及脆性特征,考虑中主应力系数影响的冻结砂土损伤本构模型能很好地模拟冻结砂土应力-应变全过程曲线。研究成果为人工冻结法工程设计提供一定的理论依据。移动阅读     

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     

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.

     

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。     

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。     

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.

     

主应力轴旋转条件下冻结黏土的动强度特性北大核心CSCD

研究冻土动强度对寒区工程和人工冻结工程施工及安全性评价具有重要意义。为了揭示主应力轴旋转对冻结黏土动强度特性的影响,利用空心扭剪仪开展不同围压下冻结黏土动三轴和空心扭剪试验,探讨了主应力轴旋转对冻结黏土动强度、动黏聚力和动内摩擦角变化规律的影响。结果表明:主应力轴旋转导致冻结黏土试样的动强度降低,围压越低主应力轴旋转对动强度影响效果就越明显;随着震动次数的增多,主应力轴旋转条件下冻结黏土动黏聚力衰减速度相对于主应力方向固定时加快;不同于主应力轴方向固定条件下动内摩擦角随震动次数增多而衰减的特点,在主应力轴旋转条件下动内摩擦角随震动次数增多而增大。另外,研究显示主应力轴旋转条件下动强度、动黏聚力和动内摩擦角均与震动次数的对数呈良好的线性关系,用线性方程对其进行了拟合,并给出拟合系数和确定系数。     

主应力轴循环旋转下高密实粉土稳定性影响研究

为研究主应力轴循环旋转对粉土性状影响,对长江入海口高密实饱和粉土进行了主应力轴180°转幅的循环旋转试验。试验发现,等向固结的高密实粉土在恒定动剪应力比的主应力轴循环旋转下能发生孔压达到初始围压水平的液化破坏,但液化前孔压开展会因动应力水平的不同而呈现以渐变相态点和激变相态点区分的3阶段变化形式,或仅以激变相态点区分的两阶段变化形式。试样应变开展则始终呈现由崩塌点区分的两阶段变化形式,且孔压激变相态点与应变崩塌点同步反映了土体结构崩塌状态,崩塌状态时主应变差双向幅值限制在0.2%～0.4%这一较小范围内。试样进行主应力轴旋转达到崩塌时的应力状态与频率无显著关系,可由 - 空间中一条准不稳定状态线归一化。而以崩塌状态为终点进行归一化的主应力轴循环旋转下孔压振次曲线,可用修正的Seed公式进行较好拟合     

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。