A Simple Monte Carlo Method for Locating the Three-dimensional Critical Slip Surface of a Slope

Based on the assumption of the plain-strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope-stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column-based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher.

Numerical analysis of slope collapse using SPH and the SIMSAND critical state model

Geological disasters such as slope failure and landslides can cause loss of life and property.Therefore,reproducing their evolution process is of great importance for risk assessment and mitigation.The recently developed SIMSAND critical state sand model combined with the smoothed particle hydrodynamics(SPH)method is adopted in this work to study slope failure under large deformations.To illustrate the efficiency and accuracy of the SIMSAND-SPH approach,a series of slope collapse studies using the discrete element method(DEM)considering various particle shapes(i.e.spherical,tetrahedral and elongated)is adopted as benchmarks.The parameters of the SIMSAND model are calibrated using DEM triaxial tests.In comparison to the DEM simulations,the runout distance and final slope height are well characterized with the SIMSAND-SPH approach with less computational cost.All comparisons show that the SIMSAND-SPH approach is highly efficient and accurate,which can be an alternative numerical tool to simulate real scale granular flow.

Effects of nonlinear strength parameters on stability of 3D soil slopes

Actual slope stability problems have three-dimensional(3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.

强度空间非均质性与各向异性特征下边坡稳定性极限平衡滑面应力法

实际工程中,土体强度存在空间非均质性与各向异性特征,忽视这些特性将难以可靠地评估边坡稳定性。为此,对强度空间非均质性与各向异性特征下边坡稳定性开展深入研究。首先,改进现有空间非均质性模型和原始Casagrande各向异性模型,拓展其通用性与实用性。其次,对土体强度空间非均质性与各向异性进行耦合,并将其嵌入至拉剪改进模式下Mohr-Coulomb(简称M-C)强度准则当中。然后,在极限平衡理论的框架内,采用滑面应力计算模式代替传统条间力假设模式,并通过构建滑面应力函数以及引入滑面局部安全系数概念和滑面端部应力约束条件,实现边坡拉-剪与压-剪共同作用机制和边坡渐进破坏方式的融入。最后,基于滑体所满足的整体力学平衡条件,建立强度空间非均质性与各向异性特征下边坡稳定性极限平衡严格解答。经后续算例对比分析,提出的方法的可行性与有效性得以验证。此外,研究成果将可用于全面揭示强度空间非均质性与各向异性特征下边坡破坏机制。

Rigorous back analysis of shear strength parameters of landslide slip

A rigorous back analysis of shear strength parameters of landslide slip was presented. Kinematical element method was adopted to determine factor of safety and critical failure surface, which overcomes the disadvantage of limit equilibrium method. The theoretical relationship between the combination of shear strength parameters and stability state was studied. The results show that the location of critical slip surface, F/tan f and F/c depend only on the value of c/tan f. The failure surface moves towards the inside of slope as c/tan f increases. According to the information involving factor of safety and critical failure surface in a specific cross-section, strength parameters can be back calculated based on the above findings. Three examples were given for demonstrating the validity of the present method. The shear strength parameters obtained by back analysis are almost consistent with their correct solutions or test results.

Optics-based metaheuristic approach to assess critical failure surfaces in both circular and non-circular failure modes for slope stability analysis

In many construction projects,a proactive slope stability evaluation is a prerequisite.Although many deterministic or non-deterministic approaches have been commonly used,metaheuristic approaches have resulted in high precision and significant outcomes for slope stability analysis problems.The current work focuses on the reliable assessment of critical failure surfaces associated with the least factor of safety value in both homogeneous and non-homogeneous slopes using a new simplified meta-heuristic approach called optics-inspired optimization(OIO).The algorithm utilizes six different LEM methods as a fitness function for deriving the factor of safety.Experimental analysis over three benchmark studies has been performed to demonstrate the algorithm's robustness and effectiveness.The implementation found more robust results as compared to previous studies.Meanwhile,the algorithm's statistical implication is conducted using the ANOVA test,which inferred better outcomes.With this interpretation,the approach claims to be suitable and efficient for slope stability analysis.

Determination of critical slip surface of fractured rock slopes based on fracture orientation data

The critical slip surface of a fractured rock slope tends to extend along the fractures.Thus,fracture orientation plays a critical role in determining the critical slip surface.Based on fracture orientation data,this paper examines the critical slip surfaces of fractured rock slopes.Given that the surface of a fractured rock slope extends along the fracture surfaces,or the wedges,with each composed of two arbitrary fractures,the critical slip surface is determined via stochastic dynamics.In addition,a fracture frequency method is proposed as a means of analyzing the critical slip surface.According to this method,the critical slip surface slips in whichever direction has the lowest fracture frequency.Based on the stochastic dynamics method and the fracture frequency method,the critical slip surface of the slope is finally determined,that is,the critical slip surface takes the form of a plane passing the slope toe with a dip of 120° and a dip angle of 45°.

THREE-DIMENSIONAL SLOPE STABILITY ANALYSIS BASED ON NONLINEAR FAILURE ENVELOPE

The effects of nonlinearity of strength envelopes on 3D slope stability analysis are investigated.A power relation for the nonlinear envelope is employed to derive the 3D factor of safety equations of an extended Spencer method hich satisfies boty force equilibrium and moment equilibrium.Then,a search procedure is presented based on dynamic programming to determine the 3D critical slip surface for a general slope,Linear and nonlinear strength envelopes used for slope stability computations are obtained by fitting curves to the 103 strength data of consolidated-undrained(CU)triaxial compression tests for compacted Israeli clay.Results of a typical 3D problem show that a linear approximation of the nonlinear strength envelope may lead to a significant overestimation of calculated safety factors.

Slope Stability Analysis of Itakpe Iron Ore Mine, Itakpe, Nigeria

The slope stability of the Itakpe Iron Ore Mine has been carried out using computer software, ROCKPACK III. One hundred and twenty three dip and dip direction values were obtained using compass clinometer. The Itakpe Iron Ore Mine was divided into four benches;241 - 258 m, 263 - 275 m, 276 - 286 m and 308 - 312 m. Joints along the discontinuities were mapped. The data obtained were analyzed using ROCKPACK III. The results indicate that the discontinuities within the critical zone are potentially unstable and can lead to planar failure. The Markland test carried out for wedge failure indicates that the intersection of the discontinuities does not fall within the critical zone hence there cannot be any wedge failure of the slope within the level 241 - 258 m. The presence of discontinuities that plot within the toppling critical zone indicates that there is potential toppling failure on the slope at the 276 - 286 m level. In addition, the toppling failure test shows the absence of discontinuities that plot within the toppling critical zone and this indicates the absence of poten-tial toppling failure of the slope at the 308 - 312 m level. The result of the study will be useful to the man-agement of the Itakpe iron ore mine in having a proper understanding of the failure mechanism of the slopes.

广义对数螺旋型滑面模型的构建与验证

临界滑动面的合理确定是边坡稳定性分析的关键问题之一。传统的边坡滑动面假设方法构造生成的潜在滑动面形式单一,且无法考虑复杂边坡中土层强度参数变化对临界滑动面形状的影响,从而降低了边坡稳定性分析结果的可靠性。基于此,提出一种新的广义对数螺旋型滑面模型,该模型可生成包含传统圆弧滑动面和对数螺旋滑动面在内的多种形式的潜在滑动面;并针对非均质边坡中各土层抗剪强度不同的特点,采用多中心分段构造策略,将该滑面模型应用于非均质边坡稳定性分析中。基于极限平衡理论计算滑动面安全系数并搜索临界滑动面,对边坡进行稳定性评估。选取多个均质边坡及多种型式的非均质边坡(水平分层、倾斜分层和斜折线分层)经典算例与现有研究成果以及数值模拟软件获得的结果进行对比分析,验证该滑面模型的合理性与优势性。研究结果表明:文中方法计算所得安全系数与其他方法相比更小,相对误差在5%以内。能够得到传统滑动面假设方法下难以搜索到的临界滑动面,并与数值模拟结果吻合度较好,稳定性分析结果更接近实际情况。由此说明,此方法用于均质边坡及非均质边坡稳定性分析是合理可行的,有望为工程实践提供更优的临界滑动面解决方案。

考虑超载和纵坡效应的隧道开挖面破坏分析

针对地表超载和纵向坡度影响下的隧道开挖面稳定性问题,提出源于构造破坏机制的初始三角形网格更新策略,应用刚体平动运动单元上限分析(UB-RTME)方法开展非线性规划运算,获得地表临界超载系数σs/c图表与滑移线网破坏模式。结果表明:①以网格更新得到的UB-RTME滑移线网与OptumG2自适应加密网格,均可反映隧道开挖面破坏影响范围及承载关键区域,且UB-RTME以有效间断线及单元速度确定破坏范围,可揭示相对破坏范围S/D2定量数据及滑移线网破坏形态与影响因素的关联规律。②临界超载系数σs/c随纵向坡度角θ增大而显著降低,随埋深比C/D增大而增大,随重度系数γD/c增大而不断减小,随内摩擦角ϕ增大而非线性增大。③对于C/D和ϕ数值较大的情况,网格密度将显著影响UB-RTME运算得到的σs/c数值解精度;网格密度增加后,σs/c计算结果精度显著提高,且体现破坏特征的网状滑移线变得更加光滑。

异形椭球滑面构建及边坡三维稳定性分析

边坡临界滑动面的确定是边坡稳定性分析中的关键问题之一。现实中边坡所处环境往往十分复杂且形状各异,而传统的滑动面模型难以全面适应这些复杂条件。因此,提出了一种基于异形椭球面作为滑动面的三维稳定性分析方法。首先,构建异形椭球方程,并通过空间几何变换生成由半长轴a等六个参数控制的异形椭球。利用异形椭球在短轴上的不对称性,生成Ⅰ型和Ⅱ型两种异形椭球滑面,使用插值方法将两种滑面应用于三维边坡,形成异形椭球滑动面。接着,采用剩余推力法和遗传算法计算边坡稳定性系数,并搜索临界滑动面。通过经典算例进行验证,对比分析了标准椭球滑面与异形椭球滑面的稳定性。结果表明,Ⅰ型和Ⅱ型异形椭球滑面的边坡安全系数分别为2.266和1.994,相较于标准椭球滑面,异形椭球滑面在搜索过程中显示出更快的速度和更稳定的最小安全系数收敛,更适用于复杂边坡。最后,将Ⅱ型异形椭球滑面在工程实例中应用,计算结果与实际情况相符,验证了该方法的可行性。

考虑冻拨影响的寒区渠道衬砌冻胀破坏力学模型分析

地下水浅埋或窄深式衬砌渠道,渠顶竖向冻胀对渠道低温稳定性影响较大,容易产生衬砌断裂、整体上抬冻害,而现有渠道冻胀工程力学模型仅分析渠坡法向冻胀。该研究考虑了渠顶竖向冻胀引起的冻拔与渠坡法向冻胀共同作用,建立了考虑冻拔的渠道冻胀工程力学模型。以冻胀敏感土质为例,应用渠道水–热–力三场耦合数值模拟,研究不同渠坡倾角、不同宽深比、不同地下水位条件下冻胀情况,以探明渠道衬砌冻拔机理,明确冻拔产生时竖向与法向冻胀分布规律。提出了冻拔破坏发生的临界坡长、临界地下水位、冻拔危险位置计算方法,同时给出了冻拔状态下渠道衬砌板内力、渠坡抗冻拔强度等计算方法。结果表明:衬砌冻拔最大拉应力与冻深和渠坡倾角正相关,与地下水位负相关。经数值模型验证,最大拉应力误差为1.5%,冻拔位置误差在16.01%以内。宁夏灌区土质条件下,冻结线半径函数斜率范围为1.047~4.040。模型解释了小型渠道易整体冻拔上抬及宽浅式渠道抗冻拔优越的原因,可以对渠道衬砌抗冻胀结构进行定量分析,为工程设计、规范修订提供参考。

双层土质滑坡临界滑动面判识与失稳机理研究

研究层状土质边坡的临界滑动面和失稳机制是岩土工程中经典的研究课题。聚焦引起边坡失稳破坏的不同诱发机制和触发因素,关注边坡的破坏模式和失稳过程,有利于提供更具针对性的加固措施。针对岩土工程中常见的非均质边坡,研发了适合双层土质边坡的有限元程序。研究了土坡在不同几何形态下,稳定性态、临界滑动面位置、失稳模式及破坏机制的演化规律;推导了非均质土坡的安全系数FS与土体特性和几何形态之间的内在函数关系式;提出了双滑面失稳机理与临界强度比的概念,给出了边坡稳定性态与失稳破坏的临界转折点和双滑面失稳的判别准则;揭示了双层不排水边坡的破坏机制,建立了不排水边坡稳定性态和失稳机理的相关设计图表。工程验证表明,计算所得的边坡稳定数及稳定状态与工程实际非常接近,该运算程序能够精准快速地判定潜在临界滑动面,准确评估边坡破坏机制,为双层土质边坡稳定性分析提供了新的思路和途径。

考虑各向异性空间变异性的边坡可靠度分析

在边坡可靠度分析中,通常采用横观各向异性或各向同性随机场来刻画土体参数的空间变异特性,而忽略了土体参数的各向异性空间变异性,从而可能会得出错误的可靠度评价结果。为此,建立考虑各向异性空间变异性的边坡可靠度随机有限差分方法(RFDM)计算框架,并以一般各向异性空间变异性边坡为参考边坡,从波动范围方向结构、互相关系数、变异系数和波动范围等方面系统地探讨各向异性空间变异性对边坡可靠度的影响。结果表明:基于坐标转换的各向异性随机场模拟方法可以有效地刻画土体参数各向异性空间变异性;应变聚类边坡临界滑面搜索算法适用于复杂临界滑面的精确搜索;相比一般各向异性空间变异性,旋转各向异性空间变异性会高估边坡失效概率,横观各向异性空间变异性会严重低估边坡失效概率,而各向同性空间变异性会在较大和较小的波动范围内分别高估和低估边坡失效概率。

求解边坡临界滑动面的分布估计算法

在求解边坡临界滑动面问题的优化算法中,大多都存在结构复杂、参数取值困难或寻优效果差的缺点。为此,将基于高斯分布模型的分布估计算法与基于简化Bishop法的滑面安全系数计算模型相结合,建立具有简单生物协同和竞争思想的临界滑动面搜索新方法;然后,针对3自由度问题,设计了一种局部搜索方法,以弥补分布估计算法局部搜索性能差的劣势。将标准方法和改进方法分别应用于边坡断面复杂度依次递增的3道算例中,完成对标准方法正交试验结果的极差分析和多因素方差分析,并实现标准算法与改进算法计算结果的对比分析。结果表明:(1)标准分布估计算法可以计算出边坡的临界滑动面;(2)当算例简单时,各控制因素都不会对计算结果产生显著性差异;当算例复杂时,只有种群规模呈现出显著性;(3)改进算法比标准算法的计算结果更佳、搜索速度更快,且有效降低了种群规模大小对计算结果的影响。探索分布估计算法在边坡临界滑动面搜索问题中的应用,为解决该类问题开辟出了一条新的研究途径。初步校验表明,该模型鲁棒性更好,具有广阔的应用前景。

软弱结构面劣化锚固边坡静载演化规律研究

为了探讨含贯通软弱结构面锚固边坡在坡顶局部静载作用下的力学响应特性,在验证模型试验基础上通过数值模拟手段系统研究了锚固边坡的变形模式及应力应变特征。研究结果表明,随着附加荷载的增大,数值模拟与试验的框架梁特征点变形一致,坡面破坏形式呈鼓肚状,实际防护应注重坡体中上部防护,加强坡腰治理。静载作用下软弱结构面改变坡体的位移及应力分布状态,在结构面内部形成剪切-拉伸破坏,并沿其形成一条潜在滑移带,最终形成楔形滑动区。中上排锚索响应明显,软弱结构面异化轴力分布机制,锚固工程施工时应考虑渐进式设计,增强中上排锚索强度和预应力幅值。研究成果可为山区公路防护提供一定的参考价值。

考虑参数空间变异性的无限长边坡可靠度分析

目前有关土体参数空间变异性对边坡稳定性影响的研究没有考虑抗剪强度参数随深度变化的影响。为此,提出了考虑土体抗剪强度参数均值随深度变化的无限长边坡稳定性概率分析方法。采用Karhunen-Loeve展开建立了表征土体空间变异性的随机场模型。探讨了考虑土体抗剪强度参数空间变异性时边坡失效概率和最危险滑动面的变化规律。最后,以无限长边坡稳定性概率分析问题为例验证了所提方法的有效性。结果表明:土体抗剪强度参数的空间变异性对无限长边坡失效概率有明显的影响,边坡失效概率随土体抗剪强度参数相关距离的增加而减小。对于不排水黏性边坡来说,边坡不排水抗剪强度随深度变化越明显,边坡失效概率越小。边坡最危险滑动面大部分都位于边坡底部。对于摩擦/黏性边坡来说,随着边坡抗剪强度随深度变化的增强,边坡失效概率有先减后增的趋势。抗剪强度参数随深度变化不同趋势对最危险滑动面分布规律有明显的影响。不考虑抗剪强度参数均值随深度变化将会导致最危险滑动面最可能出现在边坡底部。

边坡可靠度分析的一种新的优化求解方法

介绍了Low & Tang提出的一种新的可靠度优化求解方法,并将之用于边坡可靠度分析中:该方法适用于任何概率分布的相关变量,不必计算当量正态均值和方差、相关变量独立变换,直接在变量的原始空间内搜索边坡的最小可靠指标和概率临界滑面,可采用任何合适的约束优化方法进行求解,方法清晰简洁。边坡可靠度分析常用的滑面有2个:最小安全系数(变量均值处)对应的确定性临界滑面和最小可靠指标对应的概率临界滑面,但这2个滑面在有些情况下差别较大,Hassan & Wolff提出了一种简化方法可以方便地获得概率临界滑面,但由于方法简单,受到质疑。通过一系列算例分析,优化求解方法得到的概率临界滑面和Hassan & Wolff的简化方法滑面非常接近,显示了简化方法的有效性,值得在工程实践中推广。

岩质边坡楔体稳定分析与临界滑面搜索

在楔体稳定分析中,滑动模式判断正确与否对楔体稳定性评价以及边坡开挖支护方案的选择具有重要意义。探讨Hoek-Bray方法在判断楔体破坏模式时存在的问题和产生错误的原因,并根据楔体破坏的运动学条件对Hoek-Bray方法进行修正,提出理论上较为完备的楔体稳定性计算方法。考虑到现场测量得到的不连续面的产状通常具有一定的离散性和分布范围,导致构成楔体的某一组或两组结构面并非完全确定。鉴于此,提出楔体稳定性的优化分析方法,采用遗传算法搜索具有最小安全系数的楔体及其临界滑面组成,为工程支护设计提供一个具有保守性优点的低限解答,确保边坡的稳定与安全。