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.     

Stability analysis of slopes in soils with strain-softening behaviour

This paper presents a numerical approach to analyse the stability of slopes in soils with strain-softening behaviour. In these materials, a progressive failure can occur owing to a reduction of strength with increasing strain. Such a phenomenon can be analysed using methods that are able to simulate the formation and development of the shear zones in which strain localises. From a computational point of view, this presents many difficulties because the numerical procedures currently used are often affected by a lack of convergence, and the solution may depend strongly on the mesh adopted. In order to overcome these numerical drawbacks, in the present study use is made of a non-local elasto-viscoplastic constitutive model within the framework of the finite element method. The Mohr–Coulomb yield function is adopted, and the strain-softening behaviour of the soil is simulated by reducing the strength parameters with the increasing deviatoric plastic strain. To assess the reliability of the proposed approach, some comparisons with the results obtained using other constitutive models for soils with strain-softening behaviour are presented. Finally, a slope subjected to a prescribed process of weathering is considered, and the effects of this process on the slope stability are discussed.     

屈服矿柱渐进破坏及应力分布数值模拟

采用拉格朗日元法,在矿柱端面上不存在水平方向摩擦力条件下,模拟了屈服矿柱的剪切带图案、渐进破坏特征、水平应力及垂直应力分布及演变。在弹性阶段,煤的本构关系为线弹性。峰值强度后煤的本构模型取为莫尔库仑剪破坏与拉破坏复合的应变软化模型。数值计算结果表明,矿柱具有渐进破坏特征。破坏首先以剪切带的形式发生在矿柱的4个角上。然后,矿柱两帮的剪切带逐渐向矿柱内部发展,形成两套剪切带网络,直到两套网络重叠,并进一步演化。倾斜的剪切带多次穿透矿柱。当矿柱处于峰值强度后,矿柱水平及垂直应力分布曲面已经变得凹凸不平。凹陷、凸起区分别对应剪切带中心及边缘。矿柱中部的水平应力较边缘大。因此,其边缘的强度较中心低。严格地讲,水平及垂直应力的分布不是单调的,呈现锯齿型。其原因是矿柱发生了条带状局部破坏。矿柱承载能力的不均匀性由矿柱水平应力的不均匀性所决定。     

考虑滑坡渐进破坏的改进简布条分法

为考虑位移因素对于滑坡渐进性发育的影响,基于简布条分法基本原理,提出一个新的能够考虑滑带土抗剪能力与剪切位移关系的滑坡稳定性简化评价方法。该方法从以下两个方面对简布条分法进行了改进：（1）将滑动面剪应力-剪切位移本构模型与沿滑动面的剪切位移模型相结合,以考虑滑坡随着变形发展渐进破坏的过程;（2）提出局部安全系数的概念并对整体安全系数进行重新定义,物理意义更加明确。推导了该方法的计算公式,给出了其迭代计算思路,并编制Matlab计算程序。通过计算实例表明,应变软化边坡的安全系数不仅取决于土的抗剪强度指标,还与其剪应力-剪切位移关系密切相关,基于峰值强度的极限平衡条分法应用于实际工程是偏于危险的。同时该方法还可以有效地模拟边坡从开始破坏到最终滑动面贯通的发育过程,实现了坡体位移与安全系数之间一一对应的定量关系,进而实现边坡的稳定性的预测预报。     

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.     

考虑张拉-剪切渐进破坏的边坡矢量和法研究

针对边坡渐进破坏过程中岩土体强度参数不断劣化现象,采用应变软化模型代替传统的理想塑性模型,提出一种考虑张拉?剪切渐进破坏的边坡矢量和分析方法。从安全系数表达式与最危险滑动面搜索两方面进行研究,首先基于滑动和力的矢量特性,改进矢量和法滑动趋势与安全系数表达式,进而基于改进自适应遗传算法搜索边坡最危险滑动面。算例表明,采用应变软化模型时的矢量和法安全系数与最危险滑动面形态具有动态变化与调整的特性。该基于张拉-剪切应变软化模型的计算方法进一步扩展了边坡矢量和分析法。     

Finite element analysis of progressive failure in long slopes

Progressive failure in long natural clay slopes with an underlying weak shear zone is studied. The clay slope is assumed to be elastic–perfectly plastic, whereas the shear zone may have an elastic–plastic strain softening behaviour. The failure will occur due to the development of large shear deformations in the weak zone. The general behaviour, including the possibility of progressive failure, can be studied by the use of a one-dimensional finite element model. Other interesting matters which can be studied are critical load, critical disturbance and critical length of the slope. Numerical examples show the overall behaviour due to different residual shear strengths of the weak layer, end disturbance or change of pore pressure in the weak layer. Although simple, the proposed finite element model provides a practically applicable tool for the prediction of whether progressive failure will occur and in which manner the local failure will propagate.     

Risk assessment of metals from groundwater in northeast Rajasthan

In Shear strength reduction (SSR) technique, the factor of safety (FOS) is defined as the ratio of the material’s actual shear strength to the minimum shear strength required to prevent failure. Failure surface is found automatically through the zones within the material, where applied shear stresses cross the shear strength of the material. In this paper, a review of the technique is discussed in reference to FLAC. A brief background of the approach together with detailed procedure is presented.An attempt is made to exhibit the shear strength dependency of the strain. As stability of the slope is a function of the shear strength, the development of failure strain reflects the potential failure zone of slope. The shear strain developed in the slope increases with reduction in the shear strength and is reflected in the analysis. The concept of failure ratio (R_f) is incorporated in shear strength reduction technique and is demonstrated. Relationships between the critical shear strength reduction ratio and the safety factor are examined.     

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。     

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.     

A Study of the Failure Mechanism of Planar Non-Persistent Open Joints Using PFC2D

Particle flow code 2D (PFC2D) was adopted to simulate the shear behavior of rocklike material samples containing planar non-persistent joints. Direct shear loading was conducted to investigate the effect of joint separation on the failure behavior of rock bridges. Initially calibration of PFC was undertaken with respect to the data obtained from experimental laboratory tests to ensure the conformity of the simulated numerical models response. Furthermore, validation of the simulated models were cross checked with the results of direct shear tests performed on non-persistent jointed physical models. Through numerical direct shear tests, the failure process was visually observed, and the failure patterns were found reasonably similar to the experimentally observed trends. The discrete element simulations demonstrated that the macro-scale shear zone resulted from the progressive failure of the tension-induced micro-cracks. The failure pattern was mostly influenced by joint separation, while the shear strength was linked to the failure pattern and failure mechanism. Furthermore, it was observed that the failure zone is relatively narrow and has a symmetrical pattern when rock bridges occupy a low percentage of the total shear surface. This may be due to the high stress interactions between the subsequent joints separated by a rock bridge. In contrast, when rock bridges are occupying sufficient area prohibiting the stress interactions to occur then the rupture of surface is more complex and turns into a shear zone. This zone was observed to be relatively thick with an unsymmetrical pattern. The shear strength of rock bridges is reduced by increasing the joint length as a result of increasing both the stress concentration at tip of the joints and the stress interaction between the joints.     

岩土类软化材料的柱形孔扩张统一解问题

用应力一次跌落应变软化模型来模拟岩土软化材料特性，采用双剪统一强度理论的屈眼函数形式，推导了柱形孔扩张问题应力场及位移场的统一计算公式，分析了不同模型、不同软化程度对柱形孔扩张时应力、位移及塑性区开展规律的影响。     

Local soil failure before general slope failure

Slopes are generally characterized by non-uniform stress field. Additional stresses induced by changes in boundary conditions can emphasize local differences in the stress level. As a consequence, every failure process is, at first, local, with formation of plastic zones, then general. This is the subject of this paper, which concerns clay slopes, whose failure generally implies formation of a shear zone. A special consideration is addressed to the simple and special case of infinite slope which is also featured by transition from local to general failure, even if stress conditions are uniform along the potential failure plane.     

煤岩两体模型变形破坏数值模拟

采用拉格朗日元法,在弹性岩石与弹性-应变软化煤体所构成的平面应变两体模型的上、下端面上不存在水平方向摩擦力条件下,模拟了模型的破坏过程、岩石高度对模型及煤体全程应力-应变曲线、煤体变形速率、煤体破坏模式及剪切应变增量分布的影响。结果表明,当模型的全程应力-应变曲线达到峰值时煤体内部的剪切带图案已经十分明显,在模型的应变硬化阶段,煤体中的应变局部化可视为模型失稳破坏的前兆,随岩石高度的增加,模型应力-应变曲线的软化段变得陡峭,这与单轴压缩条件下的解析解在定性上是一致的;煤体应力-应变曲线的软化段变得平缓,煤体消耗能量的能力增强;弹性阶段煤体的变形速率降低;煤体内部的剪切应变增量增加。煤体应力-应变曲线的软化段的斜率、弹性阶段煤体的变形速率、煤体内部的剪切应变增量及塑性耗散能都受岩石高度的影响,说明了岩石几何尺寸对煤体的影响(煤岩相互作用)是不容忽视的。     

大型反倾库岸岩体变形过程及破坏机制数值模拟

随着边坡地质结构、地层岩性和诱发因素的不同,反倾岩体的主控变形破坏模式都会发生改变。金沙江龙蟠边坡岩体主要为反倾向千板岩和砂岩互层状结构,坡脚河床深厚覆盖层构成了边坡的软弱支座。本文运用离散单元法模拟了大型反倾库岸岩体在漫长的地质历史时期中的变形演化过程,并基于反倾岩体变形的时效性观点,引入强度折减法分析边坡在不同阶段的剪切屈服区扩展情况及相应的稳定性状态。结论表明龙蟠边坡变形岩体是重力弯曲蠕变为主导的成因机制,并归纳提出了软基效应和互层效应共同作用下的大规模反倾岩体的累进性剪切破坏模式,俗称龙蟠模式。     

不同类型滑坡渐进破坏过程与稳定性研究

滑坡的类型一般可分为牵引式滑坡、推移式滑坡和复合式滑坡,根据其滑面的发展形态,依次表现为前进式渐进破坏模式、后退式渐进破坏模式和复合式渐进破坏模式。基于岩土体应变软化特性,揭示了滑坡渐进破坏过程的本质是滑带力学参数弱化的过程,初步探讨了3种类型滑坡渐进破坏过程的远动特点和力学特征和滑坡渐进演化过程。以不平衡推力法和3种类型滑坡的演化特征为基础,提出3种类型滑坡渐进破坏过程中临界状态条块确定方法,通过建立滑坡渐进破坏稳定性计算模型和计算公式,提出滑坡随着渐进演化过程的滑带参数取值方法,并阐述了渐进破坏过程的稳定性计算实现过程,实现不同类型滑坡渐进破坏过程的稳定性分析。以3个典型滑坡为例,分析得出滑坡渐进破坏过程中牵引式滑坡和复合式滑坡稳定性降低速率由大到小再到大和推移式滑坡稳定性降低速率由小到大的过程,3种类型滑坡在渐进破坏过程中不同部位对稳定性的贡献不同,验证了不同类型滑坡的变形规律。研究结论可对不同类型滑坡的稳定性发展进行初步预测和为滑坡治理提供指导意义。     

Upper bound finite element analysis of slope stability using a nonlinear failure criterion

In this study, upper bound finite element (FE) limit analysis is applied to stability problems of slopes using a nonlinear criterion. After formulating the upper bound analysis as the dual form of a second-order cone programming (SOCP) problem, the stress field and corresponding shear strength parameters can be determined iteratively. Thus, the nonlinear failure criterion is represented by the shear strength parameters associated with stress so that the analysis of slope stability using a nonlinear failure criterion can be transformed into the traditional upper bound method with a linear Mohr–Coulomb failure criterion. Comparison with published solutions illustrates the accuracy and feasibility of the proposed method for a simple homogeneous slope stability problem. The proposed approach is also applied to a seismic stability problem for a rockfill dam to study the influence of different failure criterions on the upper bound solutions. The results show that the seismic stability coefficients obtained using two different nonlinear failure criteria are similar but that the convergence differs significantly.     

应变软化边坡渐进破坏模式及稳定性可靠度

针对现有考虑应变软化效应的边坡渐进破坏分析模型中计算假定条件不符合实际情况的不足,以三峡库区赵树岭滑坡为研究对象,考虑地下水位波动和地震力的影响,提出用于分析多场耦合条件下应变软化边坡渐进破坏模式及稳定性可靠度的方法.结果表明,地下水位波动和地震力会不同程度地影响滑坡的渐进破坏模式和破坏概率.滑坡在145 m、175 m水位和库水位从175 m陡降为145 m三种工况下整体稳定,但分别有14.119%、20.266%和21.797%的概率发生局部渐进破坏;在烈度为Ⅶ的地震力作用下同时考虑3种蓄水工况,该滑坡分别有34.067%、38.061%和38.405%的概率发生整体渐进破坏;根据滑坡渐进破坏模式指出最佳加固位置应在沿江大道前沿.该分析方法具备可靠性,可为边坡的渐进破坏模式及稳定性评价研究提供参考.      

软黏土中张紧式吸力锚循环承载力简化计算方法

张紧式吸力锚是一种重要的深水浮式平台基础。深水环境中,海底浅层沉积物多为饱和软黏土。软黏土中平均荷载与循环荷载共同作用下吸力锚的循环承载力对其设计至关重要。根据最佳系泊点受倾斜荷载作用下吸力锚的破坏模式,假设不同破坏区土体具有相同的平均剪应力,且平均剪应力与循环剪切强度比等于吸力锚所受静荷载与静荷载和循环荷载之和的比值。结合室内土性试验获得的饱和软黏土样不固结不排水归一化循环剪切强度随归一化平均剪应力的变化关系曲线,建立了破坏区土体不排水循环剪切强度的确定方法。对不同破坏区土体阻力进行分析,按照水平应力具有连续性这一特点,构建了上部滑动楔体破坏区与深部平面流动破坏区交界深度的计算方法,进而提出了计算吸力锚循环承载力的简化极限平衡方法。采用该方法对竖向和水平破坏模式吸力锚循环承载力模型试验结果进行了预测,预测与试验结果基本吻合,最小和最大偏差分别为0.79 %和16.08 %,平均偏差为5.74 %,可较好地反映吸力锚循环承载力随循环破坏次数增加而减小的变化关系,验证了该方法的可行性。     

一种基于强度折减法的次级滑动面分析方法研究

传统强度折减法通常对整个边坡区域进行折减,因而只能得到最小安全系数及对应的最危险临界滑动面。但在工程实践中,边坡的治理范围不能局限于最危险滑动面所包围的区域,不满足规范要求的次级滑动面范围内的坡体亦应得到治理。为了克服传统强度折减法在搜索次级滑动面方面的缺陷,提出了一种新的强度折减法。一般而言,边坡的屈服区域主要集中在滑动面两侧附近,形成一个沿滑动面分布的剪切破坏带,因此,在用强度折减法进行边坡稳定性分析时,只需对剪切破坏带范围内的局部坡体进行折减,则可得到该滑动面的安全系数和滑动面。基于以上认识,假设剪切破坏带沿对数螺旋曲线分布,不断调整对数螺旋曲线的形状以得到不同范围的剪切破坏带,对各种不同的剪切破坏带范围内的坡体进行局部折减计算,即可得到不同的安全系数及对应的滑动面。通过两个边坡算例（单台阶、双台阶）验证了该方法的可行性,并最后讨论了剪切破坏带的宽度对结果的影响。两个算例的计算结果表明,该方法不仅可以得到最危险临界滑动面,亦可得到任意安全系数对应的滑动面。