Progressive failure analysis of shallow foundations on soils with strain-softening behaviour

This paper presents a finite element approach to analyse the response of shallow foundations on soils with strain-softening behaviour. In these soils, a progressive failure can occur owing to a reduction of strength with increasing the plastic strains induced by loading. The present approach allows this failure process to be properly simulated by using a non-local elasto-viscoplastic constitutive model in conjunction with a Mohr–Coulomb yield function in which the shear strength parameters are reduced with the accumulated deviatoric plastic strain. Another significant advantage of the method is that it requires few material parameters as input data, with most of these parameters that can be readily obtained from conventional geotechnical tests. To assess the reliability of the proposed approach, some comparisons with experimental results from physical model tests are shown. A fairly good agreement is found between simulated and observed results. Finally, the progressive failure process that occurs in a dense sand layer owing to loading is analysed in details, and the main aspects concerning the associated failure mechanism are highlighted.     

Progressive failure mechanism in one-dimensional stability analysis of shallow slope failures

In many slopes, overstressed zones can develop where the shear stress is larger than the available shear strength. Along a shear surface within a soil exhibiting a strain-softening behavior, the shear displacement increases while the available shear strength decreases. The excess shear stress is transferred from the overstressed zone to the adjacent zones, providing more shear strength. This stress-transferring mechanism induces stress redistribution within the slope and could enlarge the overstress zone. A one-dimensional model that satisfies the strain compatibility and force equilibrium is proposed for the stability analysis of a slope of strain-softening behavior. This paper’s objective is to facilitate the application of this model to estimate stress distribution along the failure surface of a strain-softening slope and thereafter the stability status. The study presents a set of specific solutions to this model by describing and demonstrating procedures to identify the pattern of a stress state and to calculate stress distribution within a one-dimensional, strain-softening slope. The progressive failure mechanism is also investigated by using the proposed approach. As the magnitude of released stress gets large enough, it induces an overstressed zone adjacent to the initial unstable zone and progressive failure develops. The proposed approach is also applied to study the pattern of stress redistribution. It is found that the pattern of stress redistribution is affected by the magnitude of released stress. It is too complex to be reasonably expressed by simple models. Though some limitations exist, the proposed approach serves as a simple tool for a better understanding of the progressive failure mechanism.     

应变软化岩体分析原理及其应用

应变软化是指应力-应变曲线中轴向应力随应变的增加而减小的现象,许多种类的岩土介质在工程扰动的作用下呈现应变软化的行为。在分析应变软化问题时,其应力-应变关系式中的切线刚度矩阵是非正定的,由此导致计算求解的困难。将岩体应变软化过程简化为一系列脆塑性过程,于是应变软化问题的求解归结为一系列脆塑性过程的分析。基于经典弹塑性力学理论,提出了应变软化过程模拟方法及其相应的有限元求解过程,编制了计算程序,研究了应变软化本构模型中不同强度弱化速率对圆形洞室围岩塑形区分布的影响,进一步分析了应变软化模型对应的隧道径向变形沿洞轴方向的分布特征,并与已有监测数据得到的分布规律进行了对比。初步的研究结果表明,应变软化模型得到的计算结果是比较合理的     

应变软化模拟与圆形隧道衬砌分析

在岩土工程中,有许多类岩体呈现应变软化特性。在应变软化过程中,如果多个材料强度参数分析发生变化,就很难给出软化问题的解析解。已有的文献研究表明,在经典的弹塑性理论框架下,模拟岩土介质的应变软化过程依然值得深入研究。利用应变软化材料强度参数随塑性应变增加而弱化的特点,提出了将应变软化过程简化为一系列的脆性应力跌落与塑性流动过程的思想,应变软化行为的模拟转化为一系列脆塑性过程的分析。将这种模拟应变软化过程的思想方法用于求解均匀初始应力场中应变软化介质内的圆形隧道开挖问题,研究了衬砌对减少岩土开挖扰动的作用以及考虑应变软化对衬砌内力的影响。数值结果表明,对于应变软化岩土材料,忽略其强度软化的行为是偏于危险的。     

基于瑞典条分法的应变软化边坡稳定性评价方法

引入简化的应变协调方程,基于瑞典条分法的基本原理,提出一个新的能够考虑土的剪应力-应变关系的应变软化边坡稳定性简化分析方法。推导了该方法的计算公式,提出了具体算法并编制了计算程序,分析了不同应变软化特性的边坡稳定性。实际应用表明,该方法简单可靠、效率较高,计算所采用的分条数量和初始滑裂面位置对计算结果精度的影响均很小。应变软化边坡的安全系数介于基于峰值强度和残余强度的极限平衡条分法计算结果之间,具体数值不仅取决于土的抗剪强度指标,还与其剪应力-应变关系密切相关。     

Numerical simulation of the undrained stability of slopes in anisotropic fine-grained soils

The undrained stability of slopes in anisotropic fine-grained soils is studied in this paper using the finite element method (FEM). A constitutive model is presented, able to account for the observed variation of undrained strength with loading direction. The model is able to encompass the different strength distributions observed in normally, slightly overconsolidated and heavily overconsolidated soils. A series of stability analyses have been performed to explore the effect of the type of undrained strength anisotropy on the stability and failure mechanisms of slopes of different inclinations. In addition, a real case study of the failure of an underwater slope is analysed with the numerical approach presented. It suggests that, by considering undrained strength anisotropy, the failure can be satisfactorily explained.     

Effect of degree of saturation on mechanical behaviour of unsaturated soils and its elastoplastic simulation

The two stress-state variable approach has been widely used in interpreting unsaturated soil behaviour. However this approach cannot take into account the effect of degree of saturation or water contents on the stress–strain behaviour and strength of unsaturated soils. The triaxial test results presented in this paper show that even if the same path of net stress and suction is followed, the stress–strain relation and strength are different due to different degrees of saturation. When other conditions are the same, the higher the degree of saturation for the soil sample is, the higher the stress ratio corresponding to a given axial strain will be. This effect can be modeled by using an elasto-plastic constitutive model coupling hydraulic and mechanical behaviour of unsaturated soils. Comparisons between the predicted and measured results are presented, which demonstrate that the model can quantitatively simulate the influence of the degree of saturation on stress–strain behaviour and strength of unsaturated soils.     

Arbitrary Lagrangian Eulerian based finite element analysis of cone penetration in soft clay

This paper presents a numerical model for the analysis of cone penetration in soft clay based on the finite element method. The constitutive behaviour of the soil is modelled by modifying an elastic, perfectly-plastic soil model obeying Von-Mises yield criterion to take into account the strain-softening, rate dependent behaviour of soft clay. Since this is a problem involving large soil deformations, the analysis is carried out using an Arbitrary Lagrangian Eulerian method where the quality of the mesh is preserved during penetration. The variation of cone resistance is examined with various parameters such as rigidity index of the soil, in situ stress anisotropy and roughness at the cone–soil interface, which influence the penetration resistance of the cone. A theoretical correlation has been developed incorporating these parameters and the results have been compared with previous correlations based on the cavity expansion theory, finite element method and strain path method. With the increase in strain-softening, relative brittleness of the soil increases and the penetration resistance is significantly reduced. With the rising strain-rate dependency, penetration resistance increases but this increase is independent of the degree of brittleness of the soil.     

ANALYTICAL MODEL OF PROGRESSIVE SLOPE FAILURE IN WASTE CONTAINMENT SYSTEMS

The potential for progressive failure in waste containment systems is an important design consideration. Many common interfaces between components in containment systems exhibit strain-softening behaviour; however, slopes are presently designed using limit equilibrium methods that do not account for these effects. An analytical model is developed to investigate the potential for progressive failure due to strain softening. Results are presented in a non-dimensional form relating the potential for strain softening to the slope geometry, the waste properties and the properties of the containment system interface. The potential for progressive failure increases as (i) the waste stiffness decreases relative to the initial stiffness of the interface resistance, (ii) the length of the slip surface increases and (iii) the rate of strain softening with displacement increases. Analysis of a case study slope failure indicates that the analytical approach produces results that are consistent with field observations and comparable to results from a more sophisticated, numerical analysis. Although simple, this analytical approach serves as a useful design guide to identify cases where it is unsafe to use the peak shear strength in a limit equilibrium analysis.     

基于动力学和材料软化特性的边坡渐进破坏特征研究

边坡的失稳是一个从量变到质变的动态渐进破坏过程,此问题也是边坡领域研究的重点与难点之一。在考虑岩土材料软化特性和动力学求解的基础上,建立了边坡渐进破坏仿真的理论框架;利用ABAQUS软件的动力显式求解模块实现了边坡的渐进破坏仿真;根据塑性应变揭露了剪切带的扩展过程,由软化本构确定了滑面材料的分区演化规律,根据等效塑性应变确定了边坡的滑面,通过滑面位置将边坡分为滑体、滑带、滑床,并分别研究了边坡各分区内部特征点运动学变量的发展过程,从而揭示了边坡的渐进破坏过程;基于材料参数沿滑面的时空分布,利用矢量和法得到了边坡不同演化阶段的安全系数。对比该方法与Bishop法确定的滑面位置与安全系数,发现两种方法峰值和残余强度对应的安全系数比较接近,该方法搜索所得滑面位于Bishop法自动搜索的滑面之间,验证了此方法的合理性及可靠性。最后分析了材料软化特征对边坡稳定性的影响,在保持其他参数不变的条件下,增大残余黏聚力,边坡的滑面位置加深,安全系数的初始值减小,安全系数的快速减小阶段有所推迟,并且快速减小阶段经历的时间有所延长,稳定后的安全系数有所增大。保持其他参数不变,增大残余黏聚力对应的等效塑性应变阈值,边坡的滑面位置加深,安全系数的初始值减小,安全系数的快速减小阶段有所推迟,但快速减小阶段经历的时间基本不变,达到稳定的时间有所推迟,同时稳定后的安全系数略微有所增大。     

中主应力对硬岩破裂机制的影响

采用数值方法模拟硬岩的三轴压缩试验,应用4个本构模型,即Mohr-Coulomb模型、Drucker-Prager模型、应变软化模型及考虑变形模量劣化的应变软化模型,研究中主应力对均质及非均质硬岩破裂机制的影响。结果表明：不论是均质还是非均质岩体,中主应力对采用Drucker-Prager模型的岩体强度影响较大,而对采用其他本构模型的岩体强度影响不大;当非均质岩体采用Mohr-Coulomb模型或Drucker-Prager模型时,中主应力对岩体破坏过程影响不大,但对其破坏模式有较大影响;当非均质岩体采用应变软化模型时,中主应力对岩体破坏过程及其模式均有较大影响。针对工程算例,采用不同的本构模型获得的均质或非均质岩体强度相差很大,除Drucker-Prager模型外,同一本构模型的均质岩体强度远大于非均质岩体。实际工程岩体对中主应力的响应是不同的,故在地下结构设计过程中应根据岩体特性选择合理的本构模型以保证工程安全。     

Developing a 3D elastoplastic constitutive model for soils: A new approach based on characteristic stress

This paper presents a new approach for the development of an elastoplastic constitutive model to predict the strength and deformation behaviour of soils under general stress conditions. The proposed approach was based on characteristic stress, which considers the effect of the intermediate principal stress on the material strength. Referring to the Cam-clay model, the shear dilatancy equation, plastic potential function and hardening parameter for the developed model were all derived using the characteristic stress. The model predictions indicated that the established model could quantitatively reproduce the negative dilatancy behaviour, positive dilatancy behaviour, and three-dimensional strength properties of soils.     

模拟应变软化岩石三轴试验过程曲线

在经典弹塑性理论框架下,认为岩石材料在应变软化过程中遵守摩尔-库仑强度准则,塑性变形服从非关联流动法则。对两组岩石在三轴试验中呈现的应变软化行为进行了分析,获取了峰值前后强度参数的大小。采用应变软化模拟方法,将应力-应变曲线峰后应变软化阶段简化为一系列应力跌落和塑性流动的脆塑性过程,在给定的强度参数演化规律基础上,得到了岩石的应力-应变曲线、侧向应变-轴向应变曲线、体应变-轴向应变曲线和塑性体应变-轴向塑性应变曲线。模拟得到的应力-应变曲线与试验结果吻合较好,其他曲线与相关试验测试规律基本一致。研究成果对确定岩石强度参数与认识岩石峰后强度演化规律有一定的指导意义。     

On the use of effective stress in three-dimensional hydro-mechanical coupled model

In the last decades, a number of hydro-mechanical elastoplastic constitutive models for unsaturated soils have been proposed. Those models couple the hydraulic and mechanical behaviour of unsaturated soils, and take into account the effects of the degree of saturation on the stress–strain behaviour and the effects of deformation on the soil–water characteristic response with a simple reversible part for the hysteresis. In addition, the influence of the suction on the stress–strain behaviour is considered. However, until now, few models predict the stress–strain and soil–water characteristic responses of unsaturated soils in a fully three-dimensional Finite Element code. This paper presents the predictions of an unsaturated soil model in a Three-dimensional Framework, and develops a study on the effect of partial saturation on the stability of shallow foundation resting on unsaturated silty soil. Qualitative predictions of the constitutive model show that incorporating a special formulation for the effective stress into an elastoplastic coupled hydro-mechanical model opens a full range of possibilities in modelling unsaturated soil behaviour.     

Simulation of the progressive failure of an embankment on soft soil

A pragmatic strain-softening constitutive model, which is based on Modified Cam Clay, was applied to the simulation of the progressive failure of an embankment constructed on a deposit of sensitive (strain-softening) clay in Saga, Japan. A comparison of the predictions for this case indicates that if softening is ignored, only relatively small deflections and consolidation settlements are predicted, especially after construction. In contrast, for the case where softening is included in the analysis, progressive failure within the clay induces large shear deformations and finally failure of the embankment is predicted. This comparison suggests that softening-induced progressive failure should be considered in the design of embankments on such soils, and the residual strength of the deposit may have an important influence on the overall factor of safety of the construction. Detailed analyses of predicted excess pore water pressures, shear strains and shear stress levels in the ground indicate that considering the strain-softening process: (a) is associated with the buildup of excess pore water pressure; (b) promotes strain localization; and (c) results generally in a larger zone of soil involved in the failure.     

两种应变软化介质组成的边坡失稳研究

对一个平面滑动型边坡,考虑滑面介质由两种应变软化介质材料组成,对应变软化介质存在损伤软化与水致软化两种软化方式。用指数分布描述滑带介质的剪应力与应变关系,建立了边坡系统的尖点突变模型。通过分析发现,边坡失稳与刚度比和边坡的几何/力学参数有极大关联性,这里考虑刚度比是含水率的函数,随着含水率的增加,刚度比不断发生变化。在一定条件下,由于含水率的增加和刚度比的增大,导致边坡失稳的危险性增大,这是降雨情况下边坡容易失稳的根本原因。     

A large deformation analysis for the assessment of failure induced deformations of slopes in strain softening materials

This paper presents a numerical method that can be used to evaluate the post-failure deformation of slopes and embankments. The method is based on a large deformation finite element analysis employing the updated Lagrangian formulation. It can simulate the changing geometry of slopes during failure. An extended Mohr–Coulomb constitutive model represents the strain softening behaviour of slope material. The results of a series of analyses show that the post-failure deformation of slopes is a function of the rate of strength reduction and also the stiffness of the slope material. These two factors influence the initiation of progressive failure of slopes. The validity of the method is evaluated by simulation of a test embankment failure and comparison of the predicted results with the observed record of the failure.     

降雨对均质各向异性土质边坡稳定性的影响

采用有限元法分析了非饱和均质各向异性土坡中的降雨渗透过程和土水相互作用的变化过程,使用修改的Mohr-Coulomb破坏准则考虑非饱和土的抗剪强度,根据基质吸力变化引起抗破坏强度变化的原理,寻找最危险的滑移面位置,计算最小稳定安全系数,研究了土坡遭受降雨渗透时的安全稳定问题。实例分析结果表明,该法在评判降雨时非饱和土坡的稳定性方面是合理可行的。同时分析数据表明裂隙的存在对土质边坡稳定性的影响是显著的,在对雨水入渗的土边坡稳定性分析时,必须考虑裂隙的影响。     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

Review of fundamental principles in modelling unsaturated soil behaviour

An unsaturated soil is a state of the soil. All soils can be partially saturated with water. Therefore, constitutive models for soils should ideally represent the soil behaviour over entire ranges of possible pore pressure and stress values and allow arbitrary stress and hydraulic paths within these ranges. The last two decades or so have seen significant advances in modelling unsaturated soil behaviour. This paper presents a review of constitutive models for unsaturated soils. In particular, it focuses on the fundamental principles that govern the volume change, shear strength, yield stress, water retention and hydro-mechanical coupling. Alternative forms of these principles are critically examined in terms of their predictive capacity for experimental data, the consistency between these principles and the continuity between saturated and unsaturated states.