基坑体系可靠度的条件概率计算方法

基坑存在多种失效模式,考虑失效模式之间的相关性,双界限法计算体系失效概率存在计算结果区间范围较大的弊端。利用均匀试验和非参数回归方法建立响应面,在响应面的基础上,对Monte Carlo模拟生成的随机参数进行插值,得到各个失效模式指标,结合Pearson相关系数检验两两失效模式之间的相关性,用条件概率方法计算基坑体系失效概率,提出了基于条件概率考虑多失效模式相关的基坑体系可靠度分析方法。在此基础上,通过1个典型算例进行对比分析,计算结果表明,该方法不仅计算简便,而且结果可靠,其结果可为基坑体系可靠度分析理论提供一条新的途径。     

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.     

System probabilistic model of rock slope stability considering correlated failure modes

In this paper, a system reliability analysis of rock slope stability with considering all input parameters as stochastic parameter is presented. To perform reliability analysis a cut-set system has been used. For this purpose, Sequential Compounding Method (SCM) as a powerful method for reducing the computational time and accurate evaluation is employed to determine the reliability indices with considering correlations between failure modes which are calculated by defining equivalent linear safety margin for each failure mode. Furthermore, the 3-D system probability of failure surface is presented and the probabilistic model is developed to evaluate the rock slope probability of failure.     

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。     

Efficient system reliability analysis of rock slopes based on Subset simulation

How to efficiently assess the system reliability of rock slopes is still challenging. This is because when the probability of failure is low, a large number of deterministic slope stability analyses are required. Based on Subset simulation, this paper proposes an efficient approach for the system reliability analysis of rock slopes. The correlations among multiple potential failure modes are properly accounted for with the aid of the “max” and “min” functions. A benchmark rock slope and a real engineered rock slope with multiple correlated failure modes are used to demonstrate the effectiveness of the proposed approach.     

Extension of subset simulation approach for uncertainty propagation and global sensitivity analysis

The subset simulation (SS) method is a probabilistic approach which is devoted to efficiently calculating a small failure probability. Contrary to Monte Carlo Simulation (MCS) methodology which is very time-expensive when evaluating a small failure probability, the SS method has the advantage of assessing the small failure probability in a much shorter time. However, this approach does not provide any information about the probability density function (PDF) of the system response. In addition, it does not provide any information about the contribution of each input uncertain parameter in the variability of this response. Finally, the SS approach cannot be used to calculate the partial safety factors which are generally obtained from a reliability analysis. To overcome these shortcomings, the SS approach is combined herein with the Collocation-based Stochastic Response Surface Method (CSRSM) to compute these outputs. This combination is carried out by using the different values of the system response obtained by the SS approach for the determination of the unknown coefficients of the polynomial chaos expansion in CSRSM. An example problem that involves the computation of the ultimate bearing capacity of a strip footing is presented to demonstrate the efficiency of the proposed procedure. The validation of the present method is performed by comparison with MCS methodology applied on the original deterministic model. Finally, a probabilistic parametric study is presented and discussed.     

Efficient system reliability analysis illustrated for a retaining wall and a soil slope

Although first-order reliability method is a common procedure for estimating failure probability, the formulas derived for bimodal bounds of system failure probability have not been widely used as expected in present reliability analyses. The reluctance for applying these formulas in practice may be partly due to the impression that the procedures to implement the system reliability theory are tedious. Among the methods for system reliability analysis, the approach suggested in Ditlevsen 1979 is considered here because it is a natural extension of the first-order reliability method commonly used for failure probability estimation corresponding to a single failure mode, and it can often provide reasonably narrow failure probability bounds. To facilitate wider practical application, this paper provides a short program code in the ubiquitous Excel spreadsheet platform for efficiently calculating the bounds for system failure probability. The procedure is illustrated for a semi-gravity retaining wall with two failure modes, a soil slope with two and eight failure modes, and a loaded beam with three failure modes. In addition, simple equations are provided to relate the correlated but unrotated equivalent standard normals of the Low and Tang 2007 FORM procedure with the uncorrelated but rotated equivalent standard normals of the classical FORM procedure. Also demonstrated are the need for investigating different permutations of failure modes in order to get the narrowest bounds for system failure probability, and the use of SORM reliability index for system reliability bounds in a case where the curvature of the limit state surface cannot be neglected.     

System Reliability Assessment for a Rock Tunnel with Multiple Failure Modes

This paper presents a practical procedure for assessing the system reliability of a rock tunnel. Three failure modes, namely, inadequate support capacity, excessive tunnel convergence, and insufficient rockbolt length, are considered and investigated using a deterministic model of ground-support interaction analysis based on the convergence–confinement method (CCM). The failure probability of each failure mode is evaluated from the first-order reliability method (FORM) and the response surface method (RSM) via an iterative procedure. The system failure probability bounds are estimated using the bimodal bounds approach suggested by Ditlevsen (1979), based on the reliability index and design point inferred from the FORM. The proposed approach is illustrated with an example of a circular rock tunnel. The computed system failure probability bounds compare favorably with those generated from Monte Carlo simulations. The results show that the relative importance of different failure modes to the system reliability of the tunnel mainly depends on the timing of support installation relative to the advancing tunnel face. It is also shown that reliability indices based on the second-order reliability method (SORM) can be used to achieve more accurate bounds on the system failure probability for nonlinear limit state surfaces. The system reliability-based design for shotcrete thickness is also demonstrated.     

Efficient system reliability analysis of soil slopes using multivariate adaptive regression splines-based Monte Carlo simulation

System effects should be considered in the probabilistic analysis of a layered soil slope due to the potential existence of multiple failure modes. This paper presents a system reliability analysis approach for layered soil slopes based on multivariate adaptive regression splines (MARS) and Monte Carlo simulation (MCS). The proposed approach is achieved in a two-phase process. First, MARS is constructed based on a group of training samples that are generated by Latin hypercube sampling (LHS). MARS is validated by a specific number of testing samples which are randomly generated per the underlying distributions. Second, the established MARS is integrated with MCS to estimate the system failure probability of slopes. Two types of multi-layered soil slopes (cohesive slope and c–φ slope) are examined to assess the capability and validity of the proposed approach. Each type of slope includes two examples with different statistics and system failure probability levels. The proposed approach can provide an accurate estimation of the system failure probability of a soil slope. In addition, the proposed approach is more accurate than the quadratic response surface method (QRSM) and the second-order stochastic response surface method (SRSM) for slopes with highly nonlinear limit state functions (LSFs). The results show that the proposed MARS-based MCS is a favorable and useful tool for the system reliability analysis of soil slopes.     

基于高效随机有限元法的边坡风险评估

提出了基于子集模拟的边坡风险评估的高效随机有限元法（RFEM）,推导了基于子集模拟的边坡失效概率和失效风险的计算公式,并给出了基于高效RFEM的边坡可靠度分析和风险评估流程图。采用一个边坡算例验证了所提方法的有效性。结果表明,基于子集模拟的高效RFEM可以视为是对基于蒙特卡洛模拟的传统RFEM的改进,显著地提高了失效概率和失效风险的计算效率以及失效样本的产生能力,非常适用于分析小失效概率的可靠度问题,极大地增强了RFEM在边坡可靠度分析和风险评估中的实用性。高效RFEM将边坡的整体失效风险分解为对应不同概率水平的边坡失效风险,并量化了它们对整体风险的相对贡献度。在该方法中,边坡可靠度分析和风险评估与确定性边坡有限元分析互不耦合,极大地简化了它们的计算过程。此外,土体不排水抗剪强度的竖向空间变异性对边坡失效风险具有显著的影响。     

心墙堆石坝渗透稳定可靠性分析的随机响应面法

将大规模渗流有限元计算与随机响应面法相结合,对双江口心墙堆石坝进行渗透稳定可靠性分析。在基于随机响应面法的可靠度分析框架内,堆石坝稳定渗流有限元计算过程和可靠度分析过程分开独立进行,通过对心墙渗透坡降较大区域的节点建立统一的渗透稳定功能函数,采用渗流有限元分析方法和随机响应面法,计算出该区域每个节点处的渗透破坏失效概率,并将最大失效概率作为心墙的失效概率。最后,分析了心墙渗透系数、覆盖层渗透系数、上游水位与心墙具有最大失效概率节点处渗透坡降的相关关系,以及心墙渗透系数和上游水位的变异性对心墙渗透破坏失效概率的影响。计算结果表明,随机响应面法3阶Hermite展开就能够保证良好的计算精度,且计算耗时较小;双江口堆石坝心墙具有最大失效概率节点处的渗透坡降与上游水位密切相关,而与心墙本身的渗透系数呈弱负相关关系,与覆盖层渗透系数的相关性不显著;随着上游水位变异性的增大,心墙失效概率急剧增大,而这种效应对于心墙渗透系数并不明显。研究成果为随机响应面法在实际工程中的应用奠定了一定的基础。     

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。     

考虑空间变异性条件下的边坡稳定可靠度高效敏感性分析

在有限数据条件下,可靠度敏感性分析是研究各种不确定性因素对边坡失稳概率影响规律的重要途径。基于直接蒙特卡洛模拟和概率密度加权分析方法提出了一种高效边坡稳定可靠度敏感性分析方法。所提出的方法通过随机场表征岩土体参数的空间变异性,并采用局部平均理论建立岩土体参数的缩维概率密度函数,用于概率密度加权分析中高效、准确地计算不同敏感性分析方案对应的边坡失稳概率。最后,通过一个工程案例--詹姆斯湾堤坝说明了所提出方法的有效性和准确性。结果表明：在敏感性分析过程中,所提出的方法只需要执行一次直接蒙特卡洛模拟,避免了针对不同敏感性分析方案重新产生随机样本和执行边坡稳定分析,节约了大量的计算时间和计算资源,显著提高了基于蒙特卡洛模拟的敏感性分析计算效率;在概率密度加权分析中采用岩土体参数的缩维概率密度函数能够准确地计算边坡失稳概率,避免了有偏估计,使概率密度加权分析方法适用于考虑空间变异性条件下的边坡稳定可靠度敏感性分析问题。     

System reliability analysis for near-surface radioactive waste disposal facilities

The low- and intermediate-level radioactive wastes are generally disposed in near-surface disposal facility (NSDF). The NSDF is composed of engineered barriers. The probabilistic safety assessment model has been developed to analyse the performance of NSDF. The endpoints of the assessment are the concentration of the radionuclide in the groundwater and the corresponding dose rate of the radionuclide. The barrier system can have multiple failure modes but practically the possible failure modes are failure of top cover, failure of waste container, degradation of waste form and failure of bottom cover, which are usually considered as independent failure events. Through a sensitivity analysis, the most critical parameters affecting the design reliability for failure criteria are identified as the groundwater velocity and distribution coefficient. The study shows that for the NSDF considered, there is a high degree of dependence between the failure modes, and demonstrates the probability of the simultaneous occurrence of failures. Thus, the need to consider the system reliability in the NSDF is highlighted. The study also advocates the use of optimisation techniques to evaluate the probability of failure, which provides a better estimate of the probability of failure, as validated from the results obtained from Monte Carlo simulations.     

考虑优势流作用的降雨入渗边坡可靠度分析

降雨诱发滑坡是世界上最普遍的地质灾害,而关于降雨入渗对边坡的可靠度分析,优势入渗的影响被长期忽视。使用Comsol Multiphysics对降雨条件下优势入渗做数值求解,利用无限边坡模型计算边坡安全系数;并应用改进Cholesky分解法生成空间相关随机场,使用蒙特卡洛方法分析降雨过程中边坡的可靠度。结合确定性与可靠度计算对比均质入渗与优势入渗在降雨过程中边坡安全性变化：（1）降雨强度较低时,优势入渗安全性较好,而降雨强度较高时,均质入渗更稳定;（2）均质入渗中参数空间变异性是边坡失稳破坏的关键因素,而优势入渗的边坡失稳则由湿润峰快速推进所导致;（3）针对优势入渗模型研究,发现基质域与优势域水力交换强度较大时边坡有更大概率失稳,而较小的水力交换强度可能影响边坡底部的失稳破坏。     

岩体结构面强度的可靠度分析

基于岩体结构面破坏的Mohr-Coulomb准则和可靠度理论,视结构面和岩块强度参数以及结构面倾角为随机变量,分析了结构面强度参数的变异性对结构面破坏概率的影响,探讨了结构面破坏概率随结构面倾角的变化规律,提出了结构面和岩块破坏概率的计算公式,找出了影响结构面破坏概率的主要因素。结果表明,岩体结构面强度的可靠度分析比传统的定值分析方法更为客观合理。     

A system reliability approach for evaluating stability of rock wedges with correlated failure modes

This paper proposes a system reliability approach for evaluating the stabilities of rock wedges considering multiple correlated failure modes. A probabilistic fault tree is employed to model the system aspects of the problem. The system reliability analysis is performed using an N-dimensional equivalent method taking into account correlations between different failure modes. Reliability sensitivity analyses at three different levels, namely, single limit state function level, single failure mode level, and system reliability level, were carried out to study the effect of changes in variables on the stability of the wedge. An example case was analysed to illustrate the proposed approach. The stability of the wedge can be evaluated efficiently using the proposed system reliability approach in a more systematic and quantitative way. The probabilities of failure of the wedge from the N-dimensional equivalent method are fairly consistent with those from the Monte Carlo simulation method. The results demonstrate that the probability of failure will be overestimated if the correlations between different failure modes of the wedge are not taken into account. They also demonstrate that the relative importance of different failure modes to the system reliability of the wedge can differ considerably and be treated systematically and quantitatively by the proposed approach. The sensitivity results are highly dependent on the selected sensitivity analysis level.     

基于ABAQUS-ANFIS-MCS的岩质边坡可靠性分析

针对岩质边坡工程稳定性分析中参数的不确定性,基于ABAQUA建立了平面破坏型边坡有限元分析模型。并用该模型进行了边坡稳定状态的数值模拟,以获得进行ANFIS分析的数据。同时基于自适应神经模糊推理系统建立了岩体力学参数与边坡抗滑力和下滑力的映射模型,分析得到抗滑力和下滑力的统计特征。根据蒙特卡罗模拟方法用MATLAB语言编写了求解边坡的破坏概率和可靠度的计算程序,对湖南雪峰水泥原料矿山的露天矿边坡进行可靠度分析。研究结果表明,该方法具有避免编写冗长的有限元计算程序、节省机时、计算精度高的优点。     

双滑块边坡锚固系统时变可靠性分析

考虑锚杆锚固段从岩体中拔出、拉杆拉断、拉杆从注浆体中拔出等失效模式,利用系统可靠性原理和极限平衡分析方法,并基于Monte-Carlo抽样原理提出双滑块岩质边坡锚固系统破坏概率的直接求解方法。同时考虑锚杆钢筋的腐蚀与软弱滑动面抗剪强度c、? 的时变性,建立了考虑锚杆多失效模式双滑块岩质边坡锚固系统的时变可靠性模型。算例计算结果表明：软弱滑动面上的强度参数c、? 的时变性和注浆体与围岩之间的抗力时变性对锚固系统的破坏概率的影响较大,而锚杆的腐蚀对锚固系统破坏概率的影响不明显。     

锚杆挡土墙可靠度分析与计算方法

提出了锚杆挡墙中肋柱锚杆体系的串-并联模型。将肋柱视为连续梁,锚杆视为弹性支座,引入锚杆与锚固段周围岩土体的复合刚度系数,用位移法导出了各根锚杆所受荷载的统一计算公式。考虑各功能函数之间的相关性,运用系统可靠性理论,提出了单根锚杆3种破坏模式的串联系统与多根锚杆并联系统的体系可靠度计算方法,并编制了计算程序。对一工程实例进行计算,并对计算结果进行了分析,发现单根锚杆的3种失效模式并非相互独立,每种失效模式对锚杆可靠度的影响也不一样,而3根锚杆并联系统的失效概率近似等于在其他锚杆均未破坏的条件下每根锚杆单独失效概率之和。