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。     

基于认知聚类分区方法的边坡可靠度分析

提出了边坡可靠度分析的一种新的全局优化方法--认知聚类分区方法。该方法主要包括5个步骤：分区、随机抽样、计算极径L、回代、计算可靠指标及验算点。给出了相应的计算流程图,并编写了基于C语言的计算程序KCPREL。最后,以岩质边坡稳定可靠度问题为例证明了所提方法的有效性。结果表明,认知聚类分区方法能同时计算出可靠指标和验算点,并能获得全局最优解。该方法的计算精度和蒙特卡洛模拟方法相当,计算效率远远高于传统的蒙特卡洛模拟方法。此外,该方法在分析含有复杂的隐式及非线性功能函数的边坡稳定可靠度问题方面体现出明显的优越性。等步长认知聚类分区方法能全面且均匀地搜索角度,从而得到更准确的验算点。为了保证足够的计算精度及减小计算量,建议步长取10º以内。     

SVM在地下工程可靠性分析中的应用

将支持向量机应用到地下工程可靠性分析中,通过将支持向量机分别与一阶二次矩和蒙特卡洛结合,提出了基于支持向量机的可靠性分析方法,利用数值模拟构造学习样本,通过支持向量机学习,建立变形与随机变量之间映射关系的支持向量机表达,进而实现隧道极限状态函数及其偏导数的显式表达,从而计算隧道的可靠性指标。该方法避免了传统可靠性分析的缺点。算例分析结果表明,该方法计算效率高、结果可靠,对含有大量随机变量的复杂岩土工程可靠性分析具有很大的潜力,具有广泛的应用前景和工程价值。     

基于Spencer法的边坡稳定性可靠度指标分析

在边坡可靠度分析中,考虑Spencer方法计算模型的不确定性,推导出Spencer方法安全系数模型修正系数的概率密度函数,引入了随机场局部平均理论用于分析边坡中土性参数的空间相关性,并在此基础上提出了一种改进的边坡可靠性指标计算方法。     

多失效模式下基于区间非概率的岩质隧道稳定可靠度分析

对于岩质隧道工程的稳定可靠度分析,一方面由于岩体参数的统计数据获取困难使得概率可靠度方法难以适用,另一方面其工程稳定与多种失效模式密切相关,须考虑隧道结构体系的可靠度问题。首先,基于区间理论,通过区间变量形式表征不确定性参数;然后,针对岩质隧道工程中多种失效模式并存的情况,引入结构体系可靠度理念,建立基于区间非概率的岩质隧道结构体系可靠度指标计算及其稳定性评价方法;在此基础上,通过工程实例验证了该方法的合理性;最后,定义不确定性参数的波动幅度,进一步分析各失效模式中不同参数对相应可靠度指标以及结构体系可靠度指标的影响。分析结果表明,各失效模式相应的非概率可靠度指标均随区间变量范围的增大而降低,且同一参数在不同失效模式中表现出不同的影响;另外,不确定性参数的变化还将导致影响岩质隧道结构体系稳定的主要失效模式发生相应的变化。     

Two Methods for Predicting Reliability Index and Critical Probabilistic Slip Surface of Soil Slopes

Two methods of reliability analysis of soil slopes are studied, and the representative flow charts of both methods are illustrated. Method 1 can predict the reliability index and the critical probabilistic slip surface directly and it is computational efficient, but it needs the development of new codes for integrating the reliability analysis code and the slope stability code. Method 2 makes the reliability analysis code call the slope stability analysis code directly, and each code can be considered as an intact part. The main result of Method 2 is the reliability index of soil slope. Combined with the proposed method for locating the critical slip surface, Method 2 can also predict the probabilistic slip surface. Although Method 2 needs much more callings of the subprogram of slope stability analysis code, it needs not the developing of new computer program. Thus, Method 2 is easy to use and can be applied to different reliability analysis methods and slope stability analysis methods.     

土钉支护结构可靠度分析的电子表格法

岩土工程中存在大量的不确定性,因此,进行土钉支护结构的可靠度分析是十分必要的。利用Excel的规划求解及VB编程功能,采用电子表格法,建立了适用于分层土体的电子表格计算模型,进行了土钉支护结构内部稳定的可靠度分析,得出了最小可靠指标及其相应的临界滑面位置。建立的电子表格模型由数据输入模块、土钉计算模块、土层计算模块、可靠指标计算模块及优化求解模块5部分组成。模型建立之后,只需改变电子表格中的输入数据,即可适用于不同土钉支护结构的可靠度分析。算例分析表明：方法正确,计算过程简单直观。它既可用于不同工况下土钉支护结构内部稳定的可靠度分析,也可简化为相应情况下的定值法分析。     

基于改进一次二阶矩法的赵家坡高切坡稳定性分析

为了更客观和科学地评价斜坡的稳定性,采用结构可靠度中的改进一次二阶矩法来分析斜坡的稳定性,同时采用新的、更适于计算机编程的求可靠指标解的迭代方法,对三峡库区赵家坡高切坡第二段稳定性分析标明：（1）潜在滑动面1可靠指标和破坏概率均满足允许风险水平,稳定性程度较高,只需进行表面防护即可;（2）潜在滑动面2可靠指标和破坏概率均不满足允许风险水平,需要进行整体加固并辅以坡面防护;（3）稳定性系数与可靠度分析结果有良好的一致性。     

Confidence level-based robust design of cantilever retaining walls in sand

Reliability-based geotechnical design entails accurate sample statistics (i.e., mean and standard deviation or coefficient of variation, denoted herein as cov) of soil parameters. However, the cov values of soil parameters are difficult to determine with confidence due to the limited availability of high-quality data and inherent spatial variability. As a result, estimated cov values of soil parameters can vary within a wide range, which can result in overdesign or underdesign. In this paper, a confidence level (CL)-based method is proposed to address the problem of geotechnical design in the face of uncertainty. Here, CL is a measure of confidence that the target reliability index will be satisfied in the face of uncertainty in the estimated cov. The proposed method is demonstrated through the design of a cantilever retaining wall in sand. To ensure the practicality of the proposed method, a simplified approach was developed, which requires little extra effort over that required for traditional reliability-based design. To develop the CL-based method further, a metric called the “true reliability index” is proposed, which is the actual reliability index in the face of the uncertainty in the estimated parameter statistics (mainly cov).     

Relevance vector machine‐based response surface for slope reliability analysis

A new computing method is proposed for reliable analysis. The limit state function is implicit and nonlinear in reliability analysis of slopes and is difficult to apply by traditional reliability methods, especially in large‐scale project applications. Relevance vector machines (RVMs) are capable of approximating the limit state function without the need for additional assumptions regarding the function form, as opposed to traditional polynomial response surfaces. RVMs were adapted to obtain the limit state function. We propose an RVM‐based response surface method combined with the first‐order reliability method for slope reliability analysis and describe its step‐by‐step implementation. The reliability index obtained from the proposed method shows excellent agreement with traditional response surface method results. Copyright © 2017 John Wiley & Sons, Ltd.     

An efficient quasi-Newton approximation-based SORM to estimate the reliability of geotechnical problems

The first order reliability method (FORM) is efficient, but it has limited accuracy; the second order reliability method (SORM) provides greater accuracy, but with additional computational effort. In this study, a new method which integrates two quasi-Newton approximation algorithms is proposed to efficiently estimate the second order reliability of geotechnical problems with reasonable accuracy. In particular, the Hasofer–Lind–Rackwitz–Fiessler–Broyden–Fletcher–Goldfarb–Shanno (HLRF–BFGS) algorithm is applied to identify the design point on the limit state function (LSF), and consequently to compute the first order reliability index; whereas the Symmetric Rank-one (SR1) algorithm is nested within the HLRF–BFGS algorithm to compute good approximations, yet with a reduced computational effort, of the Hessian matrix required to compute second order reliabilities. Three typical geotechnical problems are employed to demonstrate the ability of the suggested procedure, and advantages of the proposed approach with respect to conventional alternatives are discussed. Results show that the proposed method is able to achieve the accuracy of conventional SORM, but with a reduced computational cost that is equal to the computational cost of HLRF–BFGS-based FORM.     

考虑能量-时间分布的边坡动力可靠性分析新方法

提出一种考虑能量-时间分布的边坡动力可靠性分析方法。该方法将动态最危险滑动面及其稳定系数以时间序列加以刻画,并根据边坡动力反应的能量分布特征,提取持续时间统计窗,用于对上述时间序列的统计分析,以获取边坡动力模糊失效概率、边坡动力可靠度指标和基于保证率的边坡动力稳定系数。以澳大利亚计算机应用协会边坡稳定考核题为例,应用上述新方法考察其在芦山7.0级主震波形条件下的稳定性,研究了在不同统计窗下的边坡动力可靠性。案例分析表明： （1）新方法能够抓住影响边坡动力稳定的主要时间段,使分析结果更为凝练、可信。（2）通过引入边坡失效状态的模糊判别,使得可靠性评价中能够考虑模糊性,解决了以往常规方法区分度不够的问题。（3）基于保证率的边坡动力稳定系数具有很好的应用前景,它在内涵上体现了可靠性分析,在形式上与静力稳定系数的定义兼容,在数值上反映了边坡瞬时动力稳定系数的保守估计值,在实践上与现行规范的拟静力法具有良好的可比性,因而具有多方面的优势。（4）就本案例而言,动力条件下最危险滑动面的发育位置趋向于静力条件下的最危险滑动面,体现了依据静力和拟静力理论框架所进行的防护工程设计,在动力条件下仍然具有积极的意义。（5）新方法对定量研究现行边坡规范的抗震设计冗余提供了一条途径。提出的新方法为边坡抗震研究提供了新的思路、方法和可供参考的实例。     

基坑土钉支护可靠性分析优化算法

针对基坑工程中岩土参数存在随机性和变异性的特点,基于响应面重构法、遗传算法和禁忌搜索方法研究了土钉墙边坡可靠性分析方法。考虑土钉的加固作用,建立了适用于土钉墙边坡任意形状滑面安全系数计算的改进Morgenstern-Price法。基于响应面原理,将改进Morgenstern-Price法取代传统响应面法中的有限单元法来随机抽样构造响应面函数,建立了一种近似的土钉墙边坡可靠度计算方法。以土体的抗剪强度指标 、 为随机变量,提出了一种能同时确定土钉墙边坡最小可靠度指标 及相应最危险滑面的全局优化计算方法--土钉墙可靠性分析自适应禁忌搜索遗传算法（ATSGA）。结合算例,分别以土钉墙边坡的最小可靠度指标和最小中值安全系数为目标函数,采用ATSGA法搜索其相应的最危险滑动面,结果表明,二者相差较大。     

有限数据条件下边坡可靠度分析的Bootstrap方法

基于Bootstrap抽样技术提出了有限数据条件下边坡可靠度分析方法。简要介绍了传统的边坡可靠度分析方法。采用Bootstrap方法模拟了抗剪强度参数概率分布函数的统计不确定性。以无限边坡为例研究了抗剪强度分布参数和分布类型不确定性对边坡可靠度的影响规律。结果表明：基于有限数据估计的样本均值、样本标准差和AIC值具有较大的变异性,这种变异性进一步导致了抗剪强度参数概率分布函数存在明显的统计不确定性。在考虑抗剪强度参数概率分布函数的统计不确定性时,边坡可靠度指标应为具有一定置信度水平的置信区间,而不是传统可靠度分析中的固定值。边坡可靠度指标的置信区间变化范围随安全系数的增加而增大,同时考虑分布参数和分布类型不确定性计算的可靠度指标具有更大的变异性和更宽的置信区间变化范围。Bootstrap方法为有限数据条件下抗剪强度参数概率分布函数统计不确定性的模拟以及边坡可靠度的评估提供了一条有效的途径。     

边坡可靠度分析的支持向量机法

提出了基于支持向量机（SVM）的边坡可靠度分析新算法。该方法采用均匀设计确定样本点,通过一定数量的确定性计算来训练SVM,拟合边坡的功能函数;采用一阶可靠度方法（FORM）和迭代算法优化SVM模型,获得可靠度指标和验算点信息;在SVM模型基础上进一步通过二阶可靠度方法（SORM）和蒙特卡罗模拟（MCS）计算边坡的失稳概率。以两个典型边坡为例,通过与其他方法比较,证明了该方法的准确性和高效性。结果表明：提出的在标准正态空间（U空间）中取样并构建SVM,在原始空间（X空间）中计算功能函数的算法,有效地解决了具有相关非正态分布变量的可靠度分析问题,并且可很容易扩展到SORM的计算。算例结果证明,该方法的精度高于FORM;而效率优于MCS。分析过程中,边坡安全系数计算和可靠度分析相互独立。因此,该方法既适用于具有显式功能函数的简单问题,也适用于需要软件计算安全系数的实际边坡问题。     

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。     

Genetic algorithms in probabilistic finite element analysis of geotechnical problems

In application to numerical analysis of geotechnical problems, the limit-state surface is usually not known in any closed form. The probability of failure can be assessed via the so-called reliability index. A minimization problem can naturally be formed with an implicit equality constraint defined as the limit-state function and optimization methods can be used for such problems. In this paper, a genetic algorithm is proposed and incorporated into a displacement finite element method to find the Hasofer–Lind reliability index. The probabilistic finite element method is then used to analyse the reliability of classical geotechnical systems. The performance of the genetic algorithm (GA) is compared with simpler probability methods such as the first-order-second-moment Taylor series method. The comparison shows that the GA can produce the results fairly quickly and is applicable to evaluation of the failure performance of geotechnical problems involving a large number of decision variables.     

An adaptive high-dimensional model representation method for reliability analysis of geotechnical engineering problems

In this study, a new reliability analysis method was developed based on the adaptive high-dimensional model representation (HDMR) and applied to geotechnical engineering problems. For practical problems requiring finite element (FE) analysis or other numerical methods to evaluate system responses such as stresses and deformations, an efficient and accurate metamodeling technique is needed because it is not efficient or straightforward to directly adopt the conventional sampling-based or gradient-based reliability analysis approaches. In this work, an adaptive metamodeling approach was created and studied based on the HDMR framework and augmented radial basis functions (ARBFs). In this adaptive ARBF-HDMR technique, a simple and inexpensive first-order ARBF-HDMR metamodel was first constructed to explicitly express a performance function, and an alternate first-order reliability method (FORM) was applied to locate the design point and compute the reliability index. A local window was then defined such that additional sample points were generated and a higher-order HDMR component function was created using ARBF and added to the existing ARBF-HDMR metamodel. The accuracy of the ARBF-HDMR metamodel was improved through this adaptive process, especially in the region surrounding the design point. One mathematical and four geotechnical engineering problems were studied and solved using the proposed adaptive ARBF-HDMR approach. The proposed method was found to be capable of obtaining accurate reliability indices within a few iterations in all test problems.     

边坡稳定可靠度分析的广义可行方向法

在广义随机空间中直接建立验算点的迭代公式,可以方便地解决含相关随机变量的结构可靠度计算问题。在广义随机空间中推导了一种收敛性较好的验算点迭代公式,并应用于边坡稳定的可靠度分析。针对卡基娃混凝土面板堆石坝地震工况坝坡稳定的可靠度分析表明:(1)由于安全系数法采用的输入参数为确定值,故不能考虑参数随机波动的影响。可靠度分析能够反映参数随机性的影响,这对于深入评估工程安全与抗风险能力是有益的。(2)通过引入条件概率方法考虑地震和坝坡失稳同时发生的概率得到的结构可靠指标将提高,而提高的幅度与地震发生概率的大小有关。(3)堆石非线性强度指标具有正相关性,考虑强度指标的相关性将提高边坡稳定的可靠度。     

边坡模糊可靠性分析隶属函数取值界限研究

针对岩土参数取值所具有的随机性、模糊性与区间性特征,建议采用隶属函数表征参数取值,分别构造了岩土参数三角形分布、正态分布与拟正态分布隶属函数,并建立了采用隶属函数取值界限表示的不同截集水平岩土参数区间值确定方法,提出分别采用均值加减2.5倍标准差与3倍标准差确定岩土参数三角形分布与拟正态分布隶属函数取值界限,进而以此为基础采用模糊点估计分析方法对工程算例进行分析,结果表明,在截集水平个数为11时,模糊点估计方法所得边坡稳定模糊可靠性指标与蒙特卡洛法所得随机概率可靠性指标精度相当,截集水平个数为9时,评价结果偏安全,建议在工程分析时,截集水平取0.1⁰.9间的9个,该方法计算过程直接简单,计算代价低,更具工程实用性。