基于克里金代理模型与子集模拟的边坡高效可靠度分析

作为一种高效且准确的代理模型,克里金方法近年来被广泛用于边坡高效可靠度分析。然而,传统方法一般直接将克里金模型与蒙特卡洛模拟耦合进行可靠度分析,导致其在高维小失效概率的边坡可靠度计算中容易出现内存占用过大甚至溢出而无法求解的问题。为此,提出一种基于克里金代理模型的子集模拟方法,以高效解决小概率水平的边坡可靠度分析问题。该方法首先采用一定数量的样本校准克里金模型并进行精度验证,然后基于构建的模型开展子集模拟边坡可靠度计算。最后,采用一个单层粘性土坡与一个工程实例土坡验证所提方法的有效性,并研究回归模型、相关函数模型以及训练样本对该方法精度的影响。结果表明：（1）该方法可以有效计算边坡的失效概率,并且比传统方法更高效;（2）构建克里金模型时,采用10倍随机变量数的训练样本即可得到满足计算精度需求的模型,而额外增加训练样本对计算结果影响较小。     

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。     

Slope reliability analysis using a support vector machine

The first-order second-moment method (FOSM) reliability analysis is commonly used for slope stability analysis. It requires the values and partial derivatives of the performance function with respect to the random variables for the design. Such calculations can be cumbersome when the performance functions are implicit. Implicit performance functions are normally encountered when the slope is geologically complicated and the limit equilibrium method (LEM) is used for the stability analysis.

To address this issue, this paper presents a support vector machine (SVM)-based reliability analysis method which combines the SVM with the FOSM. This method employs the SVM method to approximate the implicit performance functions, thus arriving at SVM-based explicit performance functions. The SVM method uses a small set of the actual values of the performance functions obtained via the LEM for complicated slope engineering. Using the SVM model, a large number of values and partial derivatives of the performance functions can be obtained for conventional reliability analysis using the FOSM. Examples are given to illustrate the proposed SVM-based slope reliability analysis. The results show that the proposed approach is applicable to slope reliability analysis which involves implicit performance functions.     

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。     

考虑前期降雨过程的边坡稳定性分析

基于三峡库区实测降雨资料,研究了不同初始条件对不同土体边坡稳定性影响,建议了能够反映边坡含水状态的初始条件选取方法。在此基础上,采用非饱和渗流分析方法研究了前期降雨对不同土体边坡稳定性影响,以典型的砂土和黏土边坡为例初步探索了前期降雨对边坡稳定性影响规律。结果表明：初始条件对不同土体边坡稳定性影响不同;建议将多年平均降雨量对应的稳态渗流场作为初始条件进行非饱和渗流分析。边坡土体渗透系数越低,边坡稳定性受前期降雨的影响越大、影响时间也越长。砂土和黏土边坡稳定性分析时建议至少考虑15 d以上的前期降雨,对于砂土边坡还应根据这15 d前面5 d的降雨情况确定是否需要增加计算天数。短历时高强度前期降雨对砂土边坡稳定性影响更大,而长历时低强度前期降雨对黏土边坡稳定性影响更大。累积前期降雨量可以作为判断边坡最小安全系数出现时刻的依据。砂土边坡出现最小安全系数时刻与10 d累积前期降雨量最大的时刻较为吻合,而黏土边坡则与15 d累积前期降雨量最大的时刻较为吻合。     

考虑地层变异的边坡稳定不确定性分析

目前涉及岩土体不均匀性的岩土问题可靠度分析大多只考虑岩土体的固有变异,即岩土体特性参数的不均匀性,未考虑涉及不同岩土体材料的地层变异。地层变异在实际滑坡中广泛存在,其表现为不同类型岩土材料(如黏土、粉土、砂土)的互相嵌套,或一种类型岩土体在另一种较均质岩土体中的随机分布。为此,提出了利用钻孔资料评估考虑地层变异时边坡稳定不确定性的分析方法。根据已有钻孔资料设计了不同的钻孔布置方案,建立了表征地层变异的马尔可夫链模型,采用有限元强度折减法进行边坡稳定性分析,探讨了钻孔布置方案对评估边坡稳定安全系数和失效概率不确定性的影响。以澳大利亚珀斯市钻孔资料为例,分析了所提方法的有效性。结果表明,钻孔布置方案对边坡稳定安全系数和失效概率的不确定性评估有重要影响。考虑地层变异时,边坡稳定安全系数可以用Johnson分布来描述;边坡稳定安全系数统计量和失效概率不一定随钻孔数量增加而单调变化,边坡影响区域以内钻孔对评估边坡稳定安全系数的不确定性最为有效;当钻孔数目逐渐增加时,边坡安全系数均值逐渐收敛至精确值。     

Slope reliability analysis accounting for spatial variation

A practical and transparent procedure is described for implementing a generalized limit equilibrium method via cell-object-oriented constrained optimization in the spreadsheet platform. The formulation allows switching among the Spencer, Bishop simplified and wedge methods on the same template by specifying different side-force inclination and different constraints of optimization. Search for the critical circular or non-circular slip surface is possible. The deterministic procedure is extended probabilistically by implementing the first-order reliability method via constrained optimization of the equivalent dispersion ellipsoid in the original space of the random variables. This procedure is illustrated for an embankment on soft ground, and for a clay slope in southern Norway, both involving spatially correlated soil properties. The effects of autocorrelation distance on the results of reliability analysis are studied. Shear strength anisotropy is modelled via user-created simple function codes in the programming environment of the spreadsheet. The meaning of probability of failure is discussed.     

基于改进遗传算法的边坡可靠度分析

采用基于概率的可靠性分析方法来分析边坡的稳定性,以克服目前大多数分析方法以确定性安全系数为评判标准的弊端。对于每次搜索中给定的滑移面,结合拉格朗日乘子法提出边坡可靠度的计算模型;采用遗传算法搜索关键滑移面,提出边坡的适应度函数。为克服标准遗传算法在进化过程中无法调节全局搜索和局部搜索速度、且可能陷入次优解的缺陷,改进了子代中最佳个体的确定方法,来并以相邻两代的群体多样性特征值增量为导向,动态调节交叉概率和变异概率,以保持群体的多样性和搜索的有效性。实例分析结果表明,本文方法可以提高遗传算法的搜索能力和收敛速度,保证解全局最优;该法适用于边坡稳定可靠度分析,且前处理简单;在遗传操作前预优化可靠指标计算模型能大大减少遗传算法中的计算量,节约机时。     

基于Weibull分布的红砂岩颗粒崩解破碎演化规律

红砂岩在我国分布广泛,由于含水率的变化使其崩解破碎十分显著。采用湖南株洲地区的红砂岩样,进行室内静态与扰动崩解试验。基于Weibull分布建立了红砂岩颗粒崩解破碎级配曲线演化模型,分析了模型参数λ与k的意义。分析表明,Weibull分布参数λ与k的大小及变化速率体现了红砂岩颗粒崩解破碎的演化过程。在建立模型的基础上,求得了相对崩解比的计算公式,并验证了计算公式的正确性。依据试验结果与模型计算值,讨论了耐崩解性指数与崩解比的异同及所采用试验方法的不同对试验结果造成的影响。在已有成果的基础上,验证了Weibull分布模型应用于岩石颗粒崩解破碎演化过程的可行性。     

考虑强度各向异性的边坡稳定有限元分析

天然沉积的土层总是表现出一定程度的强度各向异性,但现有的边坡稳定有限元分析极少考虑各向异性的影响。对大型有限元软件ABAQUS进行二次开发,使其能够考虑土体黏聚力随大主应力方向的变化,动态更新增量迭代求解过程中边坡不同位置处的抗剪强度,进而提出具备安全系数自动搜索功能的各向异性边坡稳定分析方法。计算结果表明,均匀边坡的有限元解与极限分析上限解相差很小。如果采用土体固结方向的黏聚力并按各向同性评价缓坡的稳定性,可能严重高估安全系数,尤其是在黏聚力较高的情况下。与极限分析不同,建立的强度更新有限元模型能够分析成层边坡的稳定性。     

Slope failure analysis considering anisotropic characteristics of foliated rock masses

Weak planes affect the strength and deformational behaviors of rock slopes, and the anisotropic characteristics of rock mass should be considered in slope stability analysis. Effects of joint plane orientations on failure mechanism and strength response of inherently anisotropic rock samples were firstly investigated. The specimens with various orientations of joints were evaluated under uniaxial compression, Brazilian tensile, and direct shear tests. By treating the foliated rock as transversely isotropic materials, the relevant elastic constants and strength parameters were obtained from experimental results. The slope damage zone was then investigated using Comsol Multiphysics code based on Hoffman criterion. It is indicated that the failure mechanism and strength response depend highly on the inclination of specimens with respect to the loading direction. For disks with the same inclination angle, the value of tensile strength has an increasing trend with the total fracture length. Numerical results show that partial slope mass failed in single slope and no large-scale landslide occurred. The failure pattern in numerical results agrees well with the field observations. The cooperation between the experimental results and the numerical results allows an in-depth analysis of the experimental results and thus better understanding the dominant effect of joints on the deformation and failure of rock mass.     

Computer reliability analysis of coal-cleaning distribution curves

Three types of distribution curve error are defined, i.e., the fitting deviation, the real deviation and the test error. Since the absolute distribution curve is never known, both the real deviation and the test error are unknown. Only the fitting deviation can be calculated and is a measure of the difference between a calculated distribution curve and the experimental data. However, the real deviation is of primary importance in evaluating the reliability of calculated distribution curves. This paper uses a microcomputer to simulate absolute distribution curves and obtains numerical relationships between the real deviation, the fitting deviation and the test error.More than 500 tests using a microcomputer show that a relationship exists between the fitting deviation, test error and real deviation. In most cases, the fitting deviation and the real deviation are close to each other. Both the fitting and the real deviation are smaller than the test error if the selected model is suitable.     

抗剪强度参数概率分布的最大熵估计及边坡可靠度分析

提出了基于最大熵原理的抗剪强度参数概率分布估计方法。首先简要介绍了最大熵原理估计抗剪强度参数概率分布的基本步骤。其次,基于模拟数据分别验证了最大熵原理估计抗剪强度参数概率分布和边坡失效概率的有效性,并比较了最大熵原理、选优识别和核密度估计方法的不确定性建模精度和稳健性。最后,以一组残积土抗剪强度参数试验数据并结合无限边坡稳定分析为例研究了最大熵原理在抗剪强度参数概率分布和边坡失效概率估计中的应用。结果表明：最大熵原理能够有效地估计抗剪强度参数的概率分布和边坡失效概率。与传统的选优识别和核密度估计相比,最大熵原理估计抗剪强度参数概率分布和边坡失效概率的精度和稳健性都更高。最大熵原理避免了核密度估计过分依赖有限样本数据的缺点,又克服了选优识别可能未将真实分布包括在备选概率分布集合中的缺陷。此外,基于有限数据估计的抗剪强度参数概率分布和边坡失效概率具有较大的离散性。     

约束随机场下的边坡可靠度随机有限元分析方法

目前边坡可靠度中常用的简化分析方法,不考虑边坡土体的空间变异性,每次计算整个边坡都取用相同的强度参数,由离散点试样试验得到的土体参数统计特性只能反映点特性,而边坡的稳定性受滑面上平均抗剪强度特性控制,因此,需要考虑空间范围内的平均特性。描述空间变异性的随机场理论对变异性较高的土体,实际上高估了其空间变异性。把随机场理论和地质统计中的区域化变量理论结合起来,建立约束随机场,并在此基础上进行Monte-Carlo随机有限元分析。计算实例表明,在高变异性条件下约束随机场能有效降低完全随机场的模拟方差,得到更低的破坏概率。对比了随机有限元和简化法的计算结果表明,简化法在土体强度变异性很高时其结果并非偏于保守。另外也指出了可靠度分析中存在的边坡尺度效应和简化法的适用条件。     

Slope stability analysis in the Three Gorges Reservoir Area considering effect of antecedent rainfall

Effects of different initial conditions of pore water pressure distribution on slope stability are investigated based on rainfall data in the Three Gorges Reservoir Area. A method to incorporate the initial condition of pore water pressure distribution into the slope stability analysis is suggested. Then, sandy and clayey slopes are taken as examples to investigate the effect of antecedent rainfall on slope stability. Results indicate that the influence of antecedent rainfall on the slope stability increases as the saturated permeability coefficient of the soil decreases.     

边坡稳定性分析中的剩余推力法

基于传统的剩余推力法思路,推导了包括地表水、地下水、地震力、锚固力等外荷载综合作用下的边坡稳定性和剩余推力计算公式,以实例给出了剩余推力法在MicrosoftExcel中的实现方法,从中可以清晰看出剩余推力法的实质.比较了用同一安全系数但采用不同的折减方法所获得的剩余推力变化趋势.通过上述4类荷载的敏感性分析,指出了剩余推力法应用中应注意的基本问题.运用Excel中加载宏"规划求解”工具,可以方便实现确定性框架下临界滑动面的随机搜索.     

Slope stability analysis using evolutionary optimization techniques

Slope stability optimization, in the presence of a band of a weak layer between two strong layers, is accounted for in complicated geotechnical problems. Classical optimization algorithms are not suitable for solving such problems as they need a proper preliminary solution to converge to a valid result. Therefore, it is necessary to find a proper algorithm which is capable of finding the best global solution. Recently a lot of metaheuristic algorithms have been proposed which are able to evade local minima effectively. In this study four evolutionary algorithms, including well‐known and recent ones, such as genetic algorithm, differential evolution, evolutionary strategy and biogeography‐based optimization (BBO), are applied in slope stability analysis and their efficiencies are explored by three benchmark case studies. Result show BBO is the most efficient among these evolutionary algorithms and other proposed algorithms applied to this problem. Copyright © 2016 John Wiley & Sons, Ltd.     

考虑计算参数不确定性的边坡稳定分析

岩土体当中存在大量的不确定因素,给边坡的稳定性分析判断带来了困难。在分析了计算参数的不确定性是影响分析可靠性的主要原因的基础上,运用模糊集理论考虑计算参数的不确定性,提出了模糊参数的具体构造方法和边坡稳定的不确定性分析思路。该方法可以根据不同隶属度下的参数截集区间,计算出相应隶属度下的安全系数区间,并可由此得到边坡的可靠性指标和安全系数建议值。通过不同算例研究表明,使用此方法能充分考虑计算参数的不确定性,得到的安全系数更加科学可靠。