A rigorous solution for the stability of polyhedral rock blocks

Block theory has been widely applied to stability analysis of rock engineering due to its clear concept and elegant geometrical theory. For a general block with multiple discontinuity planes, it is assumed that contact is only maintained on a single plane (single-plane sliding) or two intersecting planes (double-plane sliding) in block theory analysis. Since the normal forces and shear resistances acting on the other discontinuity planes are omitted, it can cause unreasonable estimations of block failure modes and incorrect calculation of factors of safety. In this study, a new method is presented that permits to consider the contribution of the normal forces and shear resistances acting on each discontinuity plane to the block stability. The proposed method meets all of the force-equilibrium and moment-equilibrium conditions and provides a rigorous solution for stability of general blocks with any number of faces and any shape. Some typical polyhedral blocks in rock slopes are analyzed using block theory and the proposed method. The results indicate that the traditional block theory may give a misleading conclusion for the predictions of stability and sliding direction of rock blocks when contact occurs on more than two discontinuity planes.     

基于结构面抗剪强度演化的块体动力稳定性分析

传统块体理论仅针对块体的静力稳定性分析,而未涉及到动力稳定分析。因此,借用Newmark法累积滑移量的概念,基于块体理论对定位块体在地震历时作用下的动力稳定性进行了研究,提出了以块体累积滑动位移和动安全系数两个指标共同评价块体动力稳定性。提出一种接触面识别及面积计算算法,它考虑了接触面积变化对块体稳定的不利影响,也可用于块体滑动的大变形分析,考虑了块体滑动过程中结构面抗剪强度的演化,可对复杂的凸形块体及凹形块体进行静、动力稳定性分析。将其应用于三峡升船机乘船箱左侧边坡的块体稳定分析中,结果显示块体在强震作用下发生了一段距离的滑动,但震后仍可保持稳定     

基于离散元的边坡矢量和稳定分析方法研究

基于离散元方法对获取的块体单元、节理的应力场处理后得到坡体整体应力场,结合矢量和法安全系数的定义提出了一种边坡稳定性分析方法即VSM-UDEC法。首先通过滑块试验验证了多种情况下UDEC接触应力计算和单元应力的精确性,结果表明,UDEC接触应力和块体单元应力的精确程度很高（接触应力相对误差基本低于0.2%）,能够满足矢量和安全系数计算要求。采用VSM-UDEC法分别对直线型滑面和圆弧型滑面算例进行了分析,并与相应的理论解和严格极限平衡法（Morgenstern-Price法）进行了对比。结果表明,对于直线型滑面VSM-UDEC法安全系数与理论解几乎相同,而对于圆弧型滑面该方法与极限平衡法结果基本一致。最后将VSM-UDEC法运用到锦屏I级水电站左岸边坡工程实例中,结果表明,假设块体为刚体时VSM-UDEC法安全系数与极限平衡法（Sarma法、Morgenstern-Price法）结果吻合较好,此外,VSM-UDEC法能够考虑坡体内结构面对稳定性的影响,较极限平衡法更能反映边坡的变形分布情况。鉴于UDEC在模拟边坡破坏方面优点较多且矢量和法安全系数物理意义明确,VSM-UDEC法有望在边坡稳定性分析中有较好的应用前景。     

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。     

楔形双滑面稳定性动态分析及其在削坡治理中的应用──以神府-东胜和准格尔煤田露天采场斜坡为例

本文提出了可以连续地计算任何坡高不同坡角的双滑面楔形四面滑体的稳定系数, 以便求得某一稳定性系数的最优化坡角。本方法经神府-东胜及准格尔煤田采场斜坡验算, 得知两煤田采场斜坡还有较大的安全储备。     

楔形双滑面稳定性动态分析及其在削坡治理中的应用──以神府-东胜和准格尔煤田露天采场斜坡为例

本文提出了可以连续地计算任何坡高不同坡角的双滑面楔形四面滑体的稳定系数，以便求得某一稳定性系数的最优化坡角。本方法经神府－东胜及准格尔煤田采场斜坡验算，得知两煤田采场斜坡还有较大的安全储备。     

节理岩体关键块体稳定的概率分析

基于地下岩体受节理面的控制,节理面的几何和力学参数随机分布,从而导致岩体系统具有高度不确定性,提出以关键块体理论为基础,考虑节理几何和力学参数随机性的岩体开挖可靠度分析方法,并给出了块体稳定的总失效概率评价模型。以澳大利亚阿德莱德地区一铜矿地质条件为例,以节理面倾角、倾向、摩擦系数和黏聚力为随机变量,通过Monte Carlo模拟和概率图方法,进行了岩体可靠度和失效概率的计算。最后,采用条件概率的分析方法,计算了单面滑动块体的总失效概率。计算结果表明,块体沿单面滑动并且出现的概率为11.0%,总的失效概率为3.85%,超过一般岩体工程可允许的风险水平,认为该方法可以作为评价块体可靠性的依据。     

Generalization of two-dimensional discontinuous deformation analysis for forward modelling

This paper provides the theoretical basis for a forward numerical model of rock block systems. This method was developed to compute stress, strain, sliding and opening of rock blocks; rigid body movement and deformation occur simultaneously. Input data consist of block geometry, loading forces, the deformability constants E and v, and the restraint or boundary conditions of the block system. Output data give the movements, deformations, stresses and strains of each block, and the sliding and detachment or rejoining of blocks. The forces acting on each block, from external loading or contact with other blocks, satisfy the equilibrium equations. Equilibrium is also achieved between external forces and the block stresses. Furthermore, this analysis fulfills constraints of no tension between blocks and no penetration of one block into another. To acheive equilibrium and satisfy these constraints, simultaneous equations are solved repeatdly with partial changes of the coefficients each time the contact constraints are chosen.     

Effects of the foot evolution on the behaviour of slow-moving landslides

The paper presents a time-dependent 2D numerical model which has been developed with the purpose of highlighting the effects of the slope foot evolution on the behaviour of slow-moving landslides. The model allows to quantitatively analyse how foot mass variations can influence the stability and the movement rates of the landslide.The landslide body is modelled as composed of two rigid blocks sliding on two different planes and interacting through a common boundary, which position is assumed fixed during the analysis. A finite difference approach is used to discretize the time. For each time increment, changes in model parameters are allowed, including variations in shearing resistances, groundwater level and block masses (in order to simulate foot erosion). During each iteration, the overall stability of the system is checked computing the safety factor, assuming that the percentage of mobilized shear strength is the same for the three surfaces. If the system is not stable or if it is not at rest, the velocity of the system is computed solving the momentum equations for the two blocks taking into account destabilising and resisting forces, the mechanical interaction between the blocks and viscous components. Computed velocities are iteratively used to compute mass accumulation at the foot, which in turn results in a change of the stability condition of the system.Examples are provided in order to highlight the roles of the model parameters. Finally, the application to a real landslide (Vallcebre, Spain) is presented which shows the advantage of considering the foot mass in the analysis of the displacement trends and the possibility to take into account the foot erosion in the long-term behaviour of the slope.     

土石混合体边坡细观特征对滑面形成影响研究

土石混合体是由软弱的土颗粒与刚度较大、强度较高的块石混合而成,因此土石混合体边坡失稳时,其滑动面受块石-土形成的细观结构特征影响,导致边坡稳定性分析存在诸多困难。本文基于一典型的土石混合体边坡,建立颗粒离散元数值模型,通过室内试验标定土体细观参数,结合强度折减法分析土石混合体边坡与纯土体边坡破坏模式及滑面形态的差别。结果表明:块石的存在使得土石混合体边坡的接触力链分布极不均匀,块石的存在使接触力链形成闭环,增大了滑动面积,对边坡有加固作用;土石混合体边坡的滑面发展趋势总倾向于穿过块石间的缝隙,滑面的发展与块石分布状况相关联;当块石含量达到20%以上时,边坡稳定性显著提高;块石含量达到30%~50%时,滑坡以局部块体运动为主,无法形成连续的滑动面。研究成果可为土石混合体边坡的变形破坏机理分析提供依据与参考。     

考虑岩桥破坏的块体稳定性分析方法

经典块体理论在进行块体可移动性分析和稳定性计算时是分步独立进行的,默认不可移动块体是稳定的,对不可移动块体不再进行稳定性分析。实际工程中,某些阻碍岩石块体运动的“岩桥”可能发生破坏,使得不可移动块体发生滑动。当块体的规模比较大时,在重力作用下破坏局部岩桥的可能性会增高。文中提出一种考虑岩桥破坏的块体稳定性分析方法,不再默认不可移动块体绝对稳定,计算块体稳定系数时,将阻碍块体移动的岩桥的抗剪切力纳入到块体的抗滑力中。该方法首先找出块体所有可能的滑动面和裂隙交线,识别块体沿每一个方向运动时需要破坏的岩桥,基于摩尔-库仑强度准则计算出块体沿每个方向运动时的稳定系数,然后,选取最小的稳定系数作为块体的实际稳定系数,最小稳定系数对应的方向即为块体最有可能的运动方向。     

边坡稳定性分析的条块稳定系数法

鉴于传统条分法对边坡安全系数定义和使用的局限性,引入了条块稳定系数的概念。分析了条间力推力线高度的影响因素,假定条间力传递时都具有相同的条间力稳定系数 ,并考虑了条块重力偏心矩的影响。根据条块的力和力矩平衡关系以及条间力假定,建立了求解条块稳定系数的四元方程组。在此基础上,求得条块稳定系数随滑动面的分布状况。根据条块稳定系数随滑动面的分布规律划分了滑体的主滑段、抗滑段和牵引段,大致判断滑坡的滑动模式。根据滑面上抗滑力和下滑力之比的定义,求解边坡整体稳定系数。采用传统条分法和所建立的条块分析法分别以圆弧滑动和折线形滑动的两个实例进行了验算,说明了条块分析法的优越性和可靠性。     

动荷载作用下隧道围岩块体稳定性分析及其应用

隧道围岩中的结构面将岩体切割成块体,块体在自然状态下的静力平衡因为隧道开挖而被打破,临空面的产生和动荷载的施加都可能导致块体的滑移,进而引起围岩失稳。以往应用块体理论寻找关键块体时,多只考虑纯重力的作用,而忽视了爆破振动、地震等动荷载对诱发失稳灾害的重要作用。将爆破振动荷载和地震荷载转化为等效静力,并通过数学计算求出使块体安全系数最低的动荷载方向,再利用关键块体理论矢量分析方法分析隧道围岩的稳定性。在长岗隧道中的应用表明,考虑动荷载作用下的块体安全系数明显小于只考虑重力作用时的安全系数,原本稳定的块体也可能在动荷载作用下变成关键块体导致围岩失稳,这与长岗隧道现场记录的破坏现象相符。     

多剖面合力法分析滑坡稳定性

滑坡稳定性分析最重要的是精度。滑面和坡面是空间三维变化曲面,造成滑体厚度各处变化很大。滑坡稳定性分析通常选择中轴线或其附近的一个所谓“代表性纵断面”进行安全系数计算。由于采用单位宽度纵剖面计算,在多数情况下只能代表该纵剖面两侧不大范围宽度滑体的局部稳定性,而不能代表滑坡整体稳定性,因此提出多纵剖面合力法进行滑坡稳定性分析。为减少多剖面勘探成本的人财物力投入,把滑动面分成了简单滑面和复杂滑面两类。对简单滑面滑坡最少只打两个纵断面共2~4个钻孔,应用几种滑面曲线函数,绘制辅助横剖面,将所需要的多个计算纵剖面剖出。多剖面合力法是基于空间平行力系可移动原理,对各剖面划分条块,把每个剖面条块的剪应力与抗滑力分解成水平与垂直分力,然后计算每个剖面剪应力与抗滑力的垂直与水平分力各自的合力,再对各剖面的剪应力与抗滑力的水平与垂直分力求合力,计算出滑坡的抗滑力与下滑力,得到剪应比——滑坡的稳定系数。用简单滑面和复杂滑面两个滑坡实例进行了分析,验证方法的有效性。     

Lower bound limit analysis of wedge stability using block element method

A lower bound limit analysis approach based on the block element method is proposed to analyze wedge stability problem. The search for the maximum value of the factor of safety is set up as a nonlinear programming problem. Sequential quadratic programming (SQP) algorithm from a reasonable initial value is applied to obtain the optimal solution. This approach provides a strict lower bound solution considering the sliding mode and rotation effect simultaneously. The deviations of the factor of safety between the present and traditional limit equilibrium methods are positively correlated with both the friction angle and the dip of the discontinuity surface.     

Comparative study of Sarma's method and the discontinuous deformation analysis for rock slope stability analysis

This paper presents a comparative study of two methods, Sarma's method and the discontinuous deformation analysis (DDA), for rock slope stability analysis. The comparison concerns the stability analysis of two classic rock slopes. The study shows that the DDA, which accounts for the block kinematics, provides a very different factor of safety as compared with Sarma's method. More realistic reaction forces around each rock block can be obtained by the DDA, including the thrust forces between rock blocks and the forces between the base and the blocks. The DDA's result shows two possible directions for the relative movement between two contiguous blocks at the initiation of slope failure. It also indicates that the limit equilibrium condition may not occur along the interfaces of rock blocks at the initiation of slope failure. The determination of realistic interaction forces around each block will be very important in rock slope stability analysis if nonlinear failure criteria are considered.     

Boundary Element based Discontinuous Deformation Analysis

A Boundary Element based Discontinuous Deformation Analysis (BE‐DDA) method is developed by implementing the improved dual reciprocity boundary element method into the open close iterations based DDA. This newly developed BE‐DDA is capable of simulating both the deformation and movement of blocks in a blocky system. Based on geometry updating, it adopts an incremental dynamic formulation taking into consideration initial stresses and dealing with external concentrated and contact forces conveniently. The boundaries of each block in the discrete blocky system are discretized with boundary elements while the domain of each block is divided into internal cells only for the integration of the domain integral of the initial stress term. The contact forces among blocks are treated as concentrated forces and the open–close iterations are applied to ensure the computational accuracy of block interactions. In the current method, an implicit time integration scheme is adopted for numerical stability. Three examples are used to show the effectiveness of the algorithm in simulating block movement, sliding, deformation and interaction of blocks. At last, block toppling and tunnel stability examples are conducted to demonstrate that the BE‐DDA is applicable for simulation of blocky systems. Copyright © 2016 John Wiley & Sons, Ltd.     

三维边坡稳定分析的有限元弹塑性迭代解法

针对已知滑动面的三维边坡稳定分析问题,在塑性力学上限定理的基础上,提出了求解安全系数的三维有限元弹塑性迭代解法。对于滑动面的非线性特性,采用常规的矩形（平面）或立方体（空间）单元来描述,应力则符合相关联流动法则的Mohr-Coulomb强度准则。通过对弹塑性增量理论中流动法则的分析,证明了当结构达到极限状态时,滑动面内切向应力的方向与滑体的主滑方向一致,说明最终以滑动面内的切向应力作为滑体滑动力的有效性。通过迭代的方式,逐步降低滑动面材料的抗剪参数,使边坡达到极限状态,不仅快速求得了滑动面的安全系数,且能够得到边坡在接近临界失稳状态时滑动面内切向应力的分布情况和边坡的变形规律,为边坡采取加固措施提供了参考依据。最后,以椭球面滑动和楔形滑动2个经典算例和工程实例,验证了该方法的有效性和正确性。     

爆破影响下岩质高边坡浅表层块体稳定性研究

摘要:岩质高边坡整体稳定性主要受软弱结构面及其组合控制,在组合有利的情况下,边坡主要发生浅表层块体失稳,开挖时的爆破振动作用是影响浅表层块体稳定的重要因素。本文以大渡河中游某岩质块状结构高边坡为例研究浅表层块体的稳定性,在总结浅表层块体失稳特征的基础上,实测爆破振动曲线,进行块体稳定性评价。研究结果表明,开挖后已失稳浅表层块体大多小于10m3,80%受软弱结构面控制,70%集中在马道下缘;实测的浅表层块体爆破振动加速度曲线显示,与邻近围岩相比,浅表层块体振动持续时间长,频率低,峰值小;等效静力法评价结果较爆破参数推算法更适用于临界失稳浅表层块体的稳定性评价。     

弯曲结构面几何条件的图解方法及其应用

分析岩体和山体稳定性的主要问题也就是确定结构面及临空面之间的相对位置关系及组合方式。坐标投影作图法是一种以正投影为基础,以分析岩石工程中结构面的几何关系及由其切割出来的块体的稳定性为目的的图解方法。对于弯曲结构面,采用“以直代曲”的原理,将其简化为有限个小平面的集合体进行分析。以蛇蟠岛国际旅游度假村清风洞室群1号洞为例,采用坐标投影作图法对弯曲结构面进行分析,来解决弯曲结构面几何条件的描述和确定问题。