Effects of anisotropy in correlation structure on the stability of an undrained clay slope

Slopes are mainly naturally occurred deposits, so slope stability is highly affected by inherent uncertainty. In this paper, the influence of heterogeneity of undrained shear strength on the performance of a clay slope is investigated. A numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation that considers the spatial variability of the soil properties is presented to assess the influence of randomly distributed undrained shear strength and to compute reliability as a function of safety factor. In the proposed method, commercially available finite difference numerical code FLAC 5.0 is merged with random field theory. The results obtained in this study are useful to understand the effect of undrained shear strength variations in slope stability analysis under different slope conditions and material properties. Coefficient of variation and heterogeneity anisotropy of undrained shear strength were proven to have significant effect on the reliability of safety factor calculations. However, it is shown that anisotropy of the heterogeneity has a dual effect on reliability index depending on the level of safety factor adopted.     

基于塑性极限分析上限法理论的土质边坡可靠度分析

将极限分析的上限定理、有限元离散思想、随机规划理论和蒙特卡洛方法这四者结合起来,提出了一种土质边坡可靠度分析的上限数值方法。首先采用三节点有限单元离散土质边坡,然后将土体的抗剪参数设为随机变量,根据上限定理构建同时满足三角形单元的塑性流动约束条件、单元公共边的塑性流动约束条件和单元速度边界条件的机动许可速度场,并根据内功功率等于外功功率条件建立目标函数,构建土质边坡可靠度分析的上限法随机规划模型。采用蒙特卡洛方法求解上限法随机规划模型,同时提出了一种基于上限法速度场的边坡失效风险系数估算方法,该方法特别适用于具有多种失效模式的边坡风险分析。对2个经典算例进行了深入分析,验证了方法的正确性。     

Influence of heterogeneity on 3D slope reliability and failure consequence

This paper investigates the influence of heterogeneity of undrained shear strength on the reliability of, and risk posed by, a long slope cut in clay, for different depths of foundation layer. The clay has been idealised as a linear elastic, perfectly plastic Von Mises material and its spatial variability has been modelled using random field theory, whereas slope performance has been computed using a parallel 3D finite element program. The results of Monte Carlo simulations confirm previous findings that three categories of failure mode are possible and that these are significantly influenced by the horizontal scale of fluctuation relative to the slope geometry. In particular, discrete 3D failures are likely for intermediate scales of fluctuation and, in this case, reliability is a function of slope length. The risk posed by potential slides has been quantified in terms of slide volumes and slide lengths, which have been estimated by considering the computed out-of-face displacements. The results show that, for a given horizontal scale of fluctuation relative to the slope geometry, there is a wide range of possible slide volumes and slide geometries. Indeed, the results highlight just how difficult it is to compute a 2D slope failure in a heterogeneous soil. However, they also indicate that, for low probabilities of failure, the volumes of potential slides can be small. This suggests that, for some problems, it may not be necessary to design to very small probabilities of failure, due to the reduced consequence of failure in this case. The techniques developed in this paper will be important in benchmarking simpler 2D and 3D solutions used in design, as there is a need to quantify slide geometries when benchmarking simpler methods based on predefined failure mechanisms.     

边坡模糊随机可靠性分析

为合理描述边坡稳定性分析中存在的多种不确定性,应同时考虑随机和模糊两种因素带来的影响.用L-R型模糊数描述随机变量的均值和方差,建立了模糊随机可靠性分析模型.为简化计算,将模糊数通过分解定理,取一系列λ截集,转换为一系列区间数进行计算.在一次二阶矩法基础上,推导了基于瑞典条分法及毕肖普法计算模糊随机可靠度的具体公式.算例表明,该法是合理实用的.     

Influence of length effect on embankment slope reliability in 3D

Embankment slopes composed of spatially variable soils have a variety of different failure modes that are affected by the correlation distances of the material properties and the geometry and total length of the slope. This paper examines the reliability of soil slopes for embankments of different length and uses parallel computing to analyse very long embankments (up to 100 times the embankment height) for a clay soil characterised by a spatially varying undrained shear strength. Based on a series of analyses using the 3D random finite element method (RFEM), it is first shown that the reliability of slopes of various length can be efficiently computed by combining simple probability theory with a detailed 3D RFEM analysis of a representative shorter slope of length 10 times the slope height. RFEM predictions of reliability indices for longer slopes are then compared with results obtained using Vanmarcke's (1977a) simplified 3D method and Calle's (1985) extended 2D approach. It is shown that these methods can give significantly different results, depending on the horizontal scale of fluctuation relative to the slope length, with RFEM predicting a lower slope reliability than the Vanmarcke and Calle solutions in all cases. The differences in the solutions are evaluated and attributed to differences in the assumed and computed failure surface geometries.     

边坡可靠度分析的非侵入式随机有限元法

提出基于非侵入式随机有限元法的边坡可靠度分析方法,并编写计算程序NISFEM。采用有限元滑面应力法计算边坡安全系数,将Hermite随机多项式展开与SIGMA/W和SLOPE/W模块有机结合实现边坡可靠度非侵入式随机分析。根据随机多项式展开系数,给出边坡安全系数前4阶统计矩（均值、标准差、偏度和峰度）和Sobol指标解析表达式,并采用Sobol指标进行边坡可靠度参数敏感性分析。最后,以均质土坡可靠度问题为例,证明该方法在边坡可靠度分析中的有效性。结果表明,边坡可靠度分析的非侵入式随机有限元法能够有效地考虑边坡变形对边坡可靠度的影响,计算效率远远高于蒙特卡罗模拟方法（MCS）,是解决复杂边坡可靠度问题一种有效地分析手段;黏聚力和内摩擦角变异性对边坡安全系数前四阶统计矩具有明显的影响,重度变异性对安全系数前4阶统计矩几乎没有影响;抗剪强度参数间负相关性对边坡安全系数均值几乎没有影响,但对安全系数标准差、偏度和峰度均有明显的影响。此外,随着抗剪强度参数间负相关性的增加,边坡安全系数由近似正态分布逐渐变为明显的非正态分布。     

Reliability back analysis of shear strength parameters of landslide with three-dimensional upper bound limit analysis theory

It is essential to determine the shear strength parameters c and φ on the sliding surface for stability evaluation and engineering design of a landslide. In this study, a new parameter back analysis method is proposed by combining the 2D/3D upper bound method of limit analysis and reliability theory to accurately determine the shear strength parameters for a 3D slope with a single failure surface. The proposed reliability back analysis method overcomes the shortcomings of the traditional deterministic analysis method of slope stability that cannot take into account the randomness and uncertainty of geotechnical parameters. Based on the reliability theory, two methods were studied: first-order reliability method (implemented by spreadsheet and Matlab, called spreadsheet method and constrained optimization method, respectively, in this paper) and Monte Carlo simulation. The optimized values of c and φ were obtained by establishing only one balance equation with the consideration of the pore water pressure or other complex conditions, which can solve the problem of the back analysis of strength parameters for a single 3D sliding surface condition. The correlation research showed that the negative correlation between c and φ greatly affected the back analysis results, and the reliability index values were conservative without considering such a negative correlation. A case study for the back analysis of shear strength parameters is conducted based on a practical landslide model with a broken line slip surface slope in Zhuquedong village, Luxi town, Xiangxi County, Hunan Province, China, and a suggestion for the selection of landslide cross section is presented. The results show that the back analysis results determined by the reliability theory coincide well with the survey and experimental results. The proposed method is found to be more accurate and effective in determining the values of shear parameters than that of the traditional deterministic inversion method.     

三维边坡稳定性分析中的边界约束效应

边界约束条件是影响边坡强度折减有限元分析稳定性计算结果的一个重要因素。结合典型边坡算例计算给出了不同边界约束条件下的三维边坡稳定性安全系数及潜在滑动面,并进行了差异性的对比研究,最后结合存在软弱夹层与地下水的三维边坡开展了应用性研究。结果表明：边界约束条件对边坡稳定安全系数具有显著的影响。在全约束条件下安全系数最大,其次为半约束边界条件,自由边界条件下的稳定安全系数最小,全约束边界比自由边界条件下的安全系数提高大约30%。边界约束条件对边坡潜在滑动面有重要的影响。在土性参数完全相同的条件下,与全约束条件相比,半约束边界条件下的滑体体积更大,滑动面更深,滑出点位置从离坡脚不远处向坡脚变化的过程更加明显。自由边界条件下与二维计算结果较接近。     

Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Safety factor calculation of soil slope reinforced with piles based on Hill’s model theory

How to evaluate reasonably the stability of a soil slope reinforced with piles (SSRP) still is an urgent problem. At present, the three-dimensional (3D) finite element strength reduction method has been used for the soil slope stability analysis. However, to accurately determine the global instability of soil slopes is the key to implementing the strength reduction finite element method. In this paper, the 3D finite element strength reduction algorithm (FESRA), based on Hill’s model theory, is proposed to assess the stability of SSRP and study on the relationship between the safety coefficients of SSRP and the displacements of slope mass. The results show that: (1) the relationship between the safety coefficients of SSRP and the displacements of slope mass agrees with the Hill’s model; (2) the proposed method (3D FESRA based on Hill’s model theory) in this study may take into account simultaneously the pile response and slope stability, and makes the results of SSRP stability analysis reasonable and reliable, which could be used as a reference for the evaluation of stability of the same type of slope; and (3) further study should be done to confirm whether the proposed method in this study is suitable for other types of slopes.     

基于有限元强度折减法的边坡动力稳定性可靠性分析

传统有限元强度折减法在边坡稳定性数值分析中取得了一定的成功,但由于未考虑岩土体材料参数的变异性等不确定性因素,尚不能直接应用于边坡稳定性特别是动力稳定性可靠性分析问题。为此提出了基于有限元强度折减法的地震边坡动力稳定性可靠性分析方法。将有限元极限分析法、动力分析法和可靠性分析法三者耦合,分析求解边坡在地震作用下的动力稳定性可靠性问题,并将这一过程在数值计算程序中得以实现。在计算分析过程中,克服了原方法需不断人工试算才能得到边坡安全系数而无法量化处理问题,并对边坡动力失效准则进行了适用于程序化的改进,使其计算过程完全实现自主运行。结合典型算例分析结果表明,该方法显著的特点是能较全面地反映岩土体的动力特性和边坡岩土体材料强度参数的变异性及相关性,所得结果相对更加合理且更符合工程实际。该方法既是对有限元强度折减法的应用范围的有益推广,也为边坡动力稳定性可靠性问题研究提供了一条新的有效途径。     

二维与三维边坡稳定性分析结果的比较与分析

二维与三维边坡稳定性分析得到的安全系数存在着差异,讨论这种差异与滑体几何尺寸及土体强度参数间的变化规律及其形成机制,可为合理地评价边坡稳定性分析提供理论依据。针对均质三维边坡,利用基于滑面正应力修正模式的极限平衡法分析程序,定性地讨论滑体形态、长高比、坡比、土体强度参数等指标对二维与三维安全系数计算结果差异(以F3/F2表示)的影响,总结F3/F2与影响指标间的变化规律,分析变化规律形成的内在机制。从工程应用的角度,给出需要考虑该差异影响的分界标准。研究表明,F3/F2随着长高比L/H、内摩擦角?及坡比m的增大逐渐减小,随着黏聚力c的增大逐渐增大;对于满足下列条件之一的边坡,宜采用三维安全系数来评价其稳定性,(1) L/H ≤ 5的滑坡体;(2) 5< L/H ≤ 10且 c > 25 kPa(或? < 15°,或m < 1.0) 的滑坡体。研究成果可为合理评价边坡稳定性分析方法提供参考。     

样本数与边坡模糊随机可靠指标关系研究

以模糊随机变量理论为指导,视模糊随机变量的均值为模糊数,基于小样本理论推导了均值模糊数模糊变化范围与样本数的关系式。采用截集敏感性分析法进行了边坡稳定的模糊随机有限元可靠度分析,得到了边坡的模糊随机可靠指标及模糊滑面的位置,研究了样本数与边坡模糊随机可靠指标的关系。分析表明,基于模糊随机变量理论的模糊随机可靠度分析方法是随机可靠度分析方法的自然推广;模糊随机可靠指标与样本数有关,随着样本数的改变,模糊随机可靠指标的中值也会发生微小变化,不是定值;在相同的置信度情况下,模糊随机可靠指标的变化范围随着样本数的增加而减小,可通过增加样本数的方式来减小模糊随机可靠指标的模糊性。     

高边坡结构可靠度的二次处理有限元分析

本文依据强度折减理论,利用MIDAS/GTS有限元软件,分析计算了高边坡结构的安全系数K,找到边坡滑裂带的位置。在此基础上,对有限元输入数据和输出结果进行二次处理,建立基本随机变量c,f与滑裂带中单元的最大(和最小)主应力1(和3)的拟合关系f1(和f3),将其代入高边坡结构的功能函数Z中,使Z由隐式形式变为显式。基于该显式表示的Z,利用Monte Carlo法计算滑裂带中所有失效单元的可靠指标1,并将其单元面积A1作为权重系数,经过加权平均得到边坡结构的整体可靠指标。上述方法使得结合有限元软件计算边坡结构的整体可靠度得以简化。经实例分析可知,本文提出的方法是合理可行的,可使边坡结构整体可靠性分析得以简化,也可为高边坡结构整体可靠性分析提供理论参考。     

Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods

A long slope consisting of spatially random soils is a common geographical feature. This paper examined the necessity of three-dimensional(3 D) analysis when dealing with slope with full randomness in soil properties. Although 3 D random finite element analysis can well reflect the spatial variability of soil properties, it is often time-consuming for probabilistic stability analysis. For this reason, we also examined the least advantageous(or most pessimistic) cross-section of the studied slope. The concept of"most pessimistic" refers to the minimal cross-sectional average of undrained shear strength. The selection of the most pessimistic section is achievable by simulating the undrained shear strength as a 3 D random field. Random finite element analysis results suggest that two-dimensional(2 D) plane strain analysis based the most pessimistic cross-section generally provides a more conservative result than the corresponding full 3 D analysis. The level of conservativeness is around 15% on average. This result may have engineering implications for slope design where computationally tractable 2 D analyses based on the procedure proposed in this study could ensure conservative results.     

Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3-D surface flaw under uniaxial compression

Preexisting flaws and rock heterogeneity have important ramifications on the process of rock fracturing and on rock stability in many applications. Therefore, there is great interest in numerical modelling of rock fracture and the underlying mechanisms. We simulated damage evolution and fracture propagation in sandstone specimens containing a preexisting 3-D surface flaw under uniaxial compression. We applied the linear elastic damage model based on the unified strength theory following the rock failure process analysis code. However, in contrast to the rock failure process analysis code, we used the finite element method with tetrahedron elements on unstructured meshes. It provided higher geometrical flexibility and allowed for a more accurate representation of the disk-shaped flaw with various flaw depths, angles, and lengths through locally adapted meshes. The rock heterogeneity was modelled by sampling the initial local Young's modulus from a Weibull distribution over a cubic grid. The values were then interpolated to the computational finite element method mesh. This method introduced an additional length scale for the rock heterogeneity represented by the cell size in the sampling grid. The generation of three typical surface cracking patterns, called wing cracks, anti-wing cracks, and far-field cracks, were identified in the simulation results. These depend on the geometry of the preexisting surface flaw. The simulated fracture propagation, coalescence types, and failure modes for the specimens with preexisting surface flaw show good agreement with recent experimental studies.     

TGLW220×660型冲洗液离心机转鼓的强度分析

对自行研制应用于地质钻探的TGLW220×660型冲洗液离心机的转鼓建立了三维实体模型,利用有限元分析软件对其在正常工况下的整体结构进行了三维有限元分析与模拟仿真。分析结果表明,离心机转鼓在正常工况下的强度满足要求;传统理论强度校核进一步验证了转鼓设计的合理性和安全可靠性,为TGLW220×660型冲洗液离心机在现场安全使用提供了重要的理论依据。     

考虑参数空间变异性的非饱和土坡可靠度分析

在考虑多个土体参数空间变异性的基础上,提出了基于拉丁超立方抽样的非饱和土坡稳定可靠度分析的非侵入式随机有限元法。利用Hermite随机多项式展开拟合边坡安全系数与输入参数间的隐式函数关系,采用拉丁超立方抽样技术产生输入参数样本点,通过Karhunen-Loève展开方法离散土体渗透系数、有效黏聚力和内摩擦角随机场,并编写了计算程序NISFEM-KL-LHS。研究了该方法在稳定渗流条件下非饱和土坡可靠度分析中的应用。结果表明：非侵入式随机有限元法为考虑多个土体参数空间变异性的非饱和土坡可靠度问题提供了一种有效的分析工具。土体渗透系数空间变异性和坡面降雨强度对边坡地下水位和最危险滑动面位置均有明显的影响。当降雨强度与饱和渗透系数的比值大于0.01时,边坡失效概率急剧增加。当土体参数变异性或者参数间负相关性较大时,忽略土体参数空间变异性会明显高估边坡失效概率。     

基于模糊随机理论的广义可靠度在边坡稳定性分析中的应用

在常规的概率极限状态理论基础上 ,分析了边坡体安全状态的模糊性 ,在此基础上构造了基于MCS以及FORM算法的模糊随机可靠度算法 ,分别就边坡体的滑动失效、渗透破坏两种失效模式作了参数敏感性分析 ,并进一步对边坡体的系统失效模式作了探讨     

强度折减有限元法中的单元阶次影响分析

强度折减有限元法是当前较为有效的边坡稳定性评价方法,且应用越来越广泛。但影响强度折减有限元法的因素有很多,单元阶次是其中比较重要的一个。通过3个经典算例,这些算例分别是二维地基承载力问题、二维边坡和三维边坡问题,分析了单元阶次的选择对强度折减法的影响。计算结果表明：随着单元的增多,线性单元和二次单元都从大于真实解的一侧来逼近真解;相对于二次单元,由于线性单元过“刚”,因此,会过高地估计安全系数,对于实际工程会偏于危险,且误差大,二次单元的误差是线性单元误差的1/8左右。在采用系统最大位移收敛与否的评判标准的基础上,利用二次单元来进行强度折减分析,则可以弥补这种线性单元的不足,得到更加合理的安全系数。二次单元比线性单元更适合于强度折减有限元法。