考虑参数空间变异性多层土坡系统可靠度分析

多层土坡在岩土工程实际中十分常见,不仅土体参数存在一定的空间变异性,而且土体框架呈现明显的层状分布特征,然而目前对考虑土体参数空间变异性的多层土坡稳定可靠度研究的远远不够。提出了基于多重响应面边坡系统可靠度分析的蒙特卡洛模拟（MCS）方法,给出了计算流程图,系统地研究了考虑土体参数空间变异性的多层土坡系统可靠度问题。结果表明,提出方法能够有效地分析考虑参数空间变异性低失效概率水平的多层土坡系统可靠度问题,并且具有较高的参数敏感性分析计算效率。     

基于广义子集模拟的土坡系统可靠度分析

如何有效地评价边坡的系统可靠度并识别出对边坡稳定性具有重要影响的关键滑面一直是边坡稳定性分析的关键问题。提出了基于广义子集模拟的边坡系统可靠度分析方法及代表性滑面识别方法,并推导了基于广义子集模拟的边坡系统可靠度计算公式及边坡中滑面对边坡系统失效的相对贡献量化公式。基于广义子集模拟计算结果,采用概率网络评价方法识别边坡代表性滑面。以一个双层黏性土坡和芝加哥国会切坡算例验证了所提方法的有效性。结果表明：提出的基于广义子集模拟的边坡系统可靠度分析方法可有效地估计边坡系统及其单一滑面的失效概率,对于具有低失效概率水平边坡可靠度的求解,其计算效率明显优于传统蒙特卡洛模拟方法。此外,对于单个失效模式而言,广义子集模拟与子集模拟计算效率相当。对于多个失效模式的失效概率计算问题,广义子集模拟不需要重复对每个失效模式失效概率进行计算,计算效率明显优于子集模拟。提出的代表性滑面选择方法是在系统失效概率及单滑面失效概率的高效计算基础上实现的,代表性滑动面能够较好地代表边坡系统失效,从而有效地降低了边坡系统失效概率对代表性滑面数目及代表性滑面失效概率估计准确性的依赖性。     

基于响应面法的边坡稳定二阶可靠度分析

提出了基于响应面法的边坡稳定二阶可靠度分析的实用算法。选择U空间中的随机变量,通过空间变换和相关矩阵分解,计算试验点的功能函数;通过迭代算法构造响应面、以确保通过最小的计算量获得最优精度,并在此基础上进行FORM/SORM计算。以一岩石边坡的平面滑动问题为例,通过与蒙特卡洛模拟、FORM及随机响应面法的比较,证明了该方法的准确性和高效性。分析了参数的相关性及试验点取值范围对计算结果的影响,讨论了可靠度分析结果中参数敏感性和物理属性问题。该方法可为实际边坡问题的可靠度分析提供参考,并可以用来进行基于可靠度分析的加固设计。     

基于随机响应面法的边坡系统可靠度分析

提出了一套基于随机响应面法的边坡系统可靠度分析方法。该方法首先从大量潜在滑动面中筛选出代表性滑动面。针对每条代表性滑动面,采用Hermite多项式展开建立其安全系数与土体参数间的非线性显式函数关系（即随机响应面）。然后,采用直接蒙特卡洛模拟计算边坡系统失效概率。在蒙特卡罗模拟中,采用所有代表性滑动面的随机响应面计算每一组样本所对应的边坡最小安全系数。最后,以两个典型多层边坡系统可靠度问题为例验证了该方法的有效性。结果表明：文中提出的边坡系统可靠度分析方法能够有效地识别边坡代表性滑动面,具有较高的计算精度和效率,并且确定代表性滑动面时无需计算滑动面间的相关系数。同时该方法可以有效地计算低失效概率水平的边坡系统可靠度,为含相关非正态参数的边坡系统可靠度问题提供了一条有效的分析途径。此外,多层边坡可能同时存在多条潜在滑动面,基于单一滑动面（如临界确定性滑动面）或者部分代表性滑动面进行边坡系统可靠度分析均会低估边坡失效概率。     

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。     

基于响应面函数的可靠度分析及其应用

针对地下工程稳定性分析与评价准则存在众多的不确定性因素，将响应面函数与有限单元分析相结合，借助于JC法，用确定性的数值分析方法来解决功能函数不能明确表达的结构可靠度分析问题，在此基础上，采用能量释放率作为评价地下工程图岩系数的稳定性准则，将提出的方法应用于金川公司龙首矿1280米盲竖井卷扬机硐室稳定性可靠度分析，获得较为满意的结果。     

基于多重响应面法的基坑位移反分析

基坑变形的反分析涉及数值模型与优化方法的耦合,常具有计算量大、使用不方便的特点。为此,提出1种可用于基坑变形反分析的多重响应面法,该方法在基坑地下连续墙不同深度处分别采用二次多项式表示地下连续墙水平位移与土层弹性模量之间的隐式关系,在此基础上利用位移观测对基坑土层弹性模量进行反分析。该方法可以解开数值模型和优化算法的耦合,从而具有较高的计算效率。工程应用实例表明,多重响应面法对基坑土层弹性模量进行反分析具有使用方便、计算效率高、计算结果准确的优点,非常适合求解基坑工程的位移反演问题。     

基于响应面法的软岩隧道湿喷纤维混凝土支护结构可靠度分析

由于湿喷纤维混凝土支护结构物理、力学参数和喷层厚度的离散性及混凝土强度破坏准则难以用支护材料参数显式表达,对该类隧道支护结构进行可靠度分析十分困难,提出采用响应面方法计算湿喷纤维混凝土支护结构的可靠度方法,并给出了计算流程,其中围岩-支护结构的确定性分析采用非线性有限元方法,可靠度分析采用2次响应面法.以赣州-龙岩铁路金华山软岩隧道湿喷纤维混凝土支护结构为研究对象,对该支护结构的可靠度进行分析与计算.分析结果表明,金华山隧道湿喷纤维混凝土支护结构可靠度指标高,处于安全状态.     

岩土工程可靠度分析的改进响应面法研究

为了提高响应面法的计算效率和精度,对现有的全局响应面法进行了改进。采用径向基函数（RBF）神经网络,代替目前常用的BP网络,迭代过程中在超锥体的范围内构造响应面,逼近隐式的非线性功能函数。数值算例分析表明,与通常的响应面法相比,改进全局响应面法的迭代次数和有限元分析次数均大幅减少,节省机时,有利于提高计算精度。同时,以浅基础和挡土墙为工程背景进行可靠度分析,表明该方法能以较快的收敛速度和较少的有限元分析次数,获得较高精度的可靠度指标,适用于岩土工程的可靠度分析。     

基于多源试验数据空间变异土体参数概率反演及边坡可靠度更新

岩土工程现场勘察试验通常只能获得有限的试验数据,据此难以真实地量化土体参数的空间变异性。提出了考虑土体参数空间变异性的概率反演和边坡可靠度更新方法,基于室内和现场两种不同来源的试验数据概率反演空间变异参数统计特征和更新边坡可靠度水平,并给出了计算流程。此外为合理地描述土体参数先验信息,发展了不排水抗剪强度非平稳随机场模型。最后通过不排水饱和黏土边坡算例验证了提出方法的有效性,并探讨了试验数据和钻孔位置对边坡后验失效概率的影响。结果表明：提出方法实现了空间变异土体参数概率反演与边坡可靠度更新的一体化,基于有限的多源试验数据概率反演得到的土体参数均值与试验数据非常吻合,明显降低了对参数不确定性的估计,更新的边坡可靠度水平显著增加。受土体参数空间自相关性的影响,试验数据对钻孔取样点附近区域土体参数统计特征更新的影响明显大于距离取样点较远区域。     

Full probabilistic design of slopes in spatially variable soils using simplified reliability analysis method

ABSTRACT

A simplified reliability analysis method is proposed for efficient full probabilistic design of soil slopes in spatially variable soils. The soil slope is viewed as a series system comprised of numerous potential slip surfaces and the spatial variability of soil properties is modelled by the spatial averaging technique along potential slip surfaces. The proposed approach not only provides sufficiently accurate reliability estimates of slope stability, but also significantly improves the computational efficiency of soil slope design in comparison with simulation-based full probabilistic design. It is found that the spatial variability has considerable effects on the optimal slope design.     

Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines

This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.     

System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines

A data driven multivariate adaptive regression splines (MARS) based algorithm for system reliability analysis of earth slopes having random soil properties under the framework of limit equilibrium method of slices is considered. The theoretical formulation is developed based on Spencer method (valid for general slip surfaces) satisfying all conditions of static equilibrium coupled with a nonlinear programming technique of optimization. Simulated noise is used to take account of inevitable modeling inaccuracies and epistemic uncertainties. The proposed MARS based algorithm is capable of achieving high level of computational efficiency in the system reliability analysis without significantly compromising the accuracy of results.     

Probabilistic failure analysis of infinite slopes under random rainfall processes and spatially variable soil

Rainfall-induced landslides occur during or immediately after rainfall events in which the pore water pressure builds up, leading to shallow slope failure. Thereby, low permeability layers result in high gradients in pore water pressure. The spatial variability of the soil permeability influences the probability such low permeability layers, and hence the probability of slope failure. In this paper, we investigate the influence of the vertical variability of soil permeability on the slope reliability, accounting for the randomness of rainfall processes. We model the saturated hydraulic conductivity of the soil with a one-dimensional random field. The random rainfall events are characterised by their duration and intensity and are modelled through self-similar random processes. The transient infiltration process is represented by Richards equation, which is evaluated numerically. The reliability analysis of the infinite slope is based on the factor of safety concept for evaluating slope stability. To cope with the large number of random variables arising from the discretization of the random field and the rainfall process, we evaluate the slope reliability through Subset Simulation, which is an adaptive Monte Carlo method known to be especially efficient for reliability analysis of such high-dimensional problems. Numerical investigations show higher probability of slope failure with increased spatial variability of the saturated hydraulic conductivity and with more uniform rainfall patterns.     

Identification of representative slip surfaces for reliability analysis of soil slopes based on shear strength reduction

Although a slope may have numerous potential slip surfaces, its failure probability is often governed by several representative slip surfaces (RSSs). Previous efforts mainly focus on the identification of circular RSSs based on limit equilibrium methods. In this paper, a method is suggested to identify RSSs of arbitrary shape based on the shear strength reduction method. Monte Carlo simulation is used to generate a large number potential slip surfaces. The RSSs are identified through analyzing the failure domains represented by these samples. A kriging-based response surface model is employed to enhance the computational efficiency. These examples shows that the RSSs may not always be circular, and that the suggested method can effectively locate the RSSs without making prior assumptions about the shape of the slip surfaces. For the examples investigated, the system failure probabilities computed based on the shear strength reduction method are comparable to, but not the same as those computed based on the limit equilibrium methods. The suggested method significantly extends our capability for identifying non-circular RSSs and hence probabilistic slope stability analysis involving non-circular slip surfaces.     

Probabilistic reliability analysis of multiple slopes with genetic algorithms

Uncertainty estimation and consideration in engineering is an important practice to design reliable structures especially in geotechnics since the level of control with regards to the material parameters is relatively low. The definition of reliability indices to approximate the probability of failure allows for a better assessment of stability with fewer computations than using alternative methods. Nonetheless, yet an optimisation problem needs to be solved. In this work, a genetic algorithm is developed to solve this optimisation problem considering the limit equilibrium method to search for multiple critical failures. Study cases are presented to illustrate the capabilities of the method.     

Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P _f ?<?0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P _f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P _f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P _f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.     

地震效应下三维非均质土坡稳定性极限分析

基于极限分析上限定理,采用拟动力法研究了地震效应下非均质土坡的三维稳定性,并通过重度加大法（GIM）推导出边坡安全系数的显式表达式。此外,采用遗传算法进行优化,将所得结果进行对比验证,详细分析了地震条件下相关参数对边坡稳定性的影响。分析结果表明：边坡高度一定时,宽高比、边坡倾角的增大以及土体内摩擦角、非均质系数的减小均会造成安全系数的降低;拟静力法获得的结果相比于拟动力法较大,两种方法结果的差值会随着水平地震系数、有效内摩擦角的增大而增大,随着边坡倾角的增大而减小;土体放大系数的增大会导致安全系数减小,而地震波周期及波速的变化几乎对安全系数没有影响;滑动面轨迹受水平地震系数的影响较大,而受非均质系数的影响相对较小。     

Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables

This paper proposes a stochastic response surface method for reliability analysis involving correlated non-normal random variables, in which the Nataf transformation is adopted to effectively transform the correlated non-normal variables into independent standard normal variables. Transformations of random variables that are often used in reliability analyses in terms of standard normal variables are summarized. The closed-form expressions for fourth to sixth order Hermite polynomial chaos expansions involving any number of random variables are formulated. The proposed method will substantially extend the application of stochastic response surface method for reliability problems. An example of reliability analysis of rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed stochastic response surface method. The results indicate that the proposed stochastic response surface method can evaluate the reliability of rock slope stability involving correlated non-normal variables accurately and efficiently. Its accuracy is shown to be higher than that for the first-order reliability method, and it is much more efficient than direct Monte-Carlo simulation. The results also show that the number of collocation points selected should ensure that the Hermite polynomial matrix has a full rank so that different order SRSMs can produce a robust estimation of probability of failure for a specified performance function. Generally, the accuracy of SRSM increases as the order of SRSM increases.