Probabilistic stability analysis of earth dam slope under transient seepage using multivariate adaptive regression splines

Earth dams are widespread throughout the world and their safety has gained increasing concern from geotechnical engineering societies. Although probabilistic stability analysis approach has been widely applied to the safety assessment of geotechnical structures, few studies have been performed to investigate the effects of water level fluctuations on earth dam slope stability considering uncertainties of soil parameters. This study proposes an efficient probabilistic stability analysis approach by integrating a soft computing algorithm of multivariate adaptive regression splines (MARS). The calibration of a MARS model generally requires a large number of training samples, which are obtained from repeated runs of deterministic seepage and slope stability analyses using the GeoStudio software. Based on the established MARS model, the earth dam slope failure probability can be conveniently evaluated. As an illustration, the proposed approach is applied to the probabilistic stability analysis of Ashigong earth dam under transient seepage. The effects of the uncertainties of soil parameters and water level fluctuation velocity on the earth dam slope failure probability are explored systematically. Results show that the MARS-based probabilistic stability analysis approach evaluates the earth slope failure probability with satisfactory accuracy and efficiency. The earth dam slope failure probability is significantly affected by the water level fluctuation velocity and the coefficient of variation of the effective friction angle.

     

基于截尾概率分布的基坑突涌模糊可靠度分析

岩土工程可靠度分析中,计算参数具有随机性,稳定性评价具有模糊性。传统的Monte Carlo模拟方法计算可靠度时,往往假定参数概率分布在正负无穷之间分布,与真实情况不符,而且其计算效率也往往较低。规范推荐的基坑突涌验算公式,计算结果往往偏于保守。引入截尾概率分布的确定方法,对参数概率分布进行截尾处理;提出拉丁超立方抽样与最大熵原理结合来确定结构响应概率分布的方法,并将其与模糊可靠度原理结合,构建了基于抽样模拟的模糊可靠度计算模型;推荐了考虑土体抗剪强度的突涌验算公式。将所提方法应用于某深基坑工程突涌分析中,其结果表明,基于截尾分布的抽样可以有效避免参数抽样值为负数的情况,所提计算模型效率明显优于传统的Monte Carlo模拟方法,模糊可靠度的计算结果比经典可靠度更符合工程实际情况。     

考虑参数空间变异性的无限长边坡可靠度分析

目前有关土体参数空间变异性对边坡稳定性影响的研究没有考虑抗剪强度参数随深度变化的影响。为此,提出了考虑土体抗剪强度参数均值随深度变化的无限长边坡稳定性概率分析方法。采用Karhunen-Loeve展开建立了表征土体空间变异性的随机场模型。探讨了考虑土体抗剪强度参数空间变异性时边坡失效概率和最危险滑动面的变化规律。最后,以无限长边坡稳定性概率分析问题为例验证了所提方法的有效性。结果表明：土体抗剪强度参数的空间变异性对无限长边坡失效概率有明显的影响,边坡失效概率随土体抗剪强度参数相关距离的增加而减小。对于不排水黏性边坡来说,边坡不排水抗剪强度随深度变化越明显,边坡失效概率越小。边坡最危险滑动面大部分都位于边坡底部。对于摩擦/黏性边坡来说,随着边坡抗剪强度随深度变化的增强,边坡失效概率有先减后增的趋势。抗剪强度参数随深度变化不同趋势对最危险滑动面分布规律有明显的影响。不考虑抗剪强度参数均值随深度变化将会导致最危险滑动面最可能出现在边坡底部。     

考虑参数空间变异性的失稳边坡参数概率反分析

概率反分析能够有效地考虑岩土体参数不确定性并融合现场监测数据和观测信息等更新岩土体参数统计特征,进而使得边坡稳定性评价更为符合客观工程实际,然而目前参数概率反分析几乎没有考虑参数固有空间变异性的影响。结合多重响应面和子集模拟提出了考虑岩土体参数空间变异性的边坡参数概率反分析方法,并以芝加哥国会街切坡为例,融合边坡失稳和滑动面入滑点与出滑点的大致位置这两个现场观测信息,概率反分析得到边坡不排水抗剪强度参数的后验统计特征。结果表明:本文提出方法可以有效地解决考虑参数空间变异性的低概率水平边坡参数概率反分析问题,具有较高的计算效率。子集模拟中每层随机样本数目对计算结果具有重要的影响,常用的500组样本点难以获得满意的计算结果。此外,土体参数空间变异性对概率反分析计算结果具有重要的影响,考虑参数空间变异性边坡参数由平稳随机场更新为非平稳随机场,与工程实际相符,然而忽略参数空间变异性更新后的参数仍服从平稳分布。     

Probabilistic modeling of graded timber material properties

The probabilistic modeling of timber material characteristics is considered with special emphasis to the modeling of the effect of different quality control and selection procedures used as means for quality grading in the production line. It is shown how statistical models may be established on the basis of the same type of information which is normally collected as a part of the quality control procedures and furthermore, how the efficiency of different control procedures may be quantified and compared. The tail behavior of the probability distributions of timber material characteristics plays an important role in the overall probabilistic modeling. Therefore a scheme for estimating the parameters of probability distribution parameters focusing on the tail behavior has been established using a censored Maximum Likelihood estimation technique. The proposed probabilistic models have been formulated such that they may readily be applied in structural reliability analysis and their format appears to be appropriate for codification purposes of quality control and selection for grading procedures.     

Probabilistic Baseline of Finite Element Model of Bridges under Environmental Temperature Changes

The material properties and structural stiffness of actual bridges fluctuate with variations in environmental temperature; therefore, it is not appropriate to use a determined finite element model (FEM) as the baseline model for localizing the structural damage of bridges. To address this issue, we proposed the concept of the probabilistic baseline of FEM of bridges under variable environmental temperature, that is, we established reasonable probability distributions of the physical parameters of bridges that are suitable for damage localization with varying environmental temperature. First, a method is presented to obtain the probabilistic baseline of FEM of bridges, which imports cluster analysis into stochastic FEM updating. Unlike the conventional methods, the measured natural frequencies first are classified into different clusters using the Gaussian mixture method (GMM), with each cluster consisting of measured data that satisfy the same Gaussian distribution. Then, the conventional methods of stochastic FEM updating can be conveniently implemented to obtain the probabilistic baseline of FEM for each cluster. Second, for each cluster, the mean values and covariance of the updating parameters are updated in two sequential steps, and a new approach is proposed for determining the initial covariance of the updating parameters. The results of an actual example show that predetermining a reasonable initial covariance for the updating parameters can accurately and efficiently obtain the updated results. Finally, the effectiveness of the presented method is verified through the monitoring data of an actual bridge.     

A two-dimensional limit equilibrium computer code for analysis of complex toppling slope failures

Evaluation of blocky or layered rock slopes against toppling failures has remained of great concern for engineers in various rock mechanics projects.Several step-by-step analytical solutions have been developed for analyzing these types of slope failures.However,manual application of these analytical solutions for real case studies can be time-consuming,complicated,and in certain cases even impossible.This study will first examine existing methods for toppling failure analyses that are reviewed,modified and generalized to consider the effects of a wide range of external and dead loads on slope stability.Next,based on the generalized presented formulae,a Windows form computer code is programmed using Visual C#for analysis of common types of toppling failures.Input parameters,including slope geometry,joint sets parameters,rock and soil properties,ground water level,dynamic loads,support anchor loads as well as magnitudes and forms of external forces,are first loaded into the code.The input data are then saved and used to graphically draw the slope model.This is followed by automatic identification of the toppling failure mode and a deterministic analysis of the slope stability against this failure mode.The results are presented using a graphical approach.The developed code allows probabilistic introduction of the input parameters via probability distribution functions(PDFs)and thus a probabilistic analysis of the toppling failure modes using Monte-Carlo simulation technique.This allows calculation of the probability of slope failure.Finally,several published case studies and typical examples are analyzed with the developed code.The outcomes are compared with those of the main references to assess the performance and robustness of the developed computer code.The comparisons demonstrate good agreement between the results.     

建筑结构荷载随机参数的概率加权矩法计算

用概率加权矩理论来计算建筑结构荷载随机模型的参数，推导了极值Ⅰ型分布与样本概率加权矩的关系，用概率加权矩法计算其分布参数，并与其他方法的结果进行了比较，说明了概率加权矩法的正确性和实用性。     

基于概率屈服准则的弹塑性随机有限元分析

基于偏微分技术，采用增量理论建立了弹塑性随机有限元增量初应力法的计算格工，考虑屈服准则的不确定性，对岩体Drucker-Prager屈服准则进行随机分析，以代替随机有限计算中屈服准则的定值分析，最后，编制了基于概率屈他准则的弹塑性随机有限元分析程序，并对两个算例进行了分析和讨论，得出了结论。     

EVALUATION OF THE PROBABILITY OF FAILURE WITH UNCERTAIN DISTRIBUTION PARAMETERS

Formulations are presented for estimating probability of failure considering uncertainty of distribution parameters in time invariant and time variant reliability analyses. Based on the formulations the probability of failure can be calculated by recursively using the first order reliability method. Also, a more efficient approximate analysis procedure by using the point estimate method to estimate the probability of failure is given. In this analysis procedure, the point estimate method is used to discretize the uncertain distribution parameters in the time invariant reliability analysis, and to discretize the time-independent random variables and uncertain distribution parameters in the time variant reliability analysis. The probability of failure is then obtained by weighting the probability of failure conditioned at each of discrete points. The conditional probability of failure can be calculated by using first order reliability method, second order reliability method or any other convenient methods. The use of point estimate method to treat uncertain distribution parameters in calculating probability of failure is less computer time consuming than the one of recursively using FORM. Illustrative numerical examples of calculating probability of failure are presented.     

Multiobjective Optimization of Uncertain Structures Through Fuzzy Set and Random Set Theory

An interactive procedure to solve multicriteria optimization problems is proposed and discussed. A fuzzy set is used to model the engineer's judgment on each objective function. The properties of the compromise solution obtained are investigated along with the links between the present method and those based on fuzzy logic. Uncertainty affecting the parameters is modeled by means of fuzzy relations or fuzzy numbers, whose probabilistic meaning is clarified by random set and possibility theory. Bounds to the probability that a solution satisfies a constraint can be calculated and procedures that consider the lower bound as a constraint or as an objective to be maximized are presented. Some theorems make the computational effort particularly limited in a vast class of practical problems. The relations with a recent formulation in the context of convex modeling are also stressed. Two examples show the effectiveness of the proposed approach.     

System reliability analysis for mixed uncertain variables

Uncertainties in a physical system should be modeled accurately to obtain an accurate estimate of its safety. Based on the amount and type of information available, either probability theory or possibility theory can be used. In probability theory variation in the parameters is modeled using probability density functions and in possibility theory it is modeled using fuzzy membership functions. But when dealing with a combination of both probability distributions and fuzzy membership functions, the computational cost involved in estimating the bounds of reliability increases exponentially because one reliability analysis, which is a computationally expensive procedure, is performed at each possibility level. Moreover, the failure of structural systems is governed by multiple limit-state functions, all of which are to be taken into consideration for determining its safety. These limit-state functions are often correlated and the accuracy of the estimated system reliability is dependent on the ability to model the joint failure surface. To reduce the computational cost involved without loss of accuracy, high quality function approximations for each of the limit-states and the joint failure surface are developed in this paper. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed methodology.     

Predicting probabilistic distribution functions of response parameters using the endurance time method

The main objective of this study is the development of endurance time (ET) excitations in order to take structural response uncertainty into account for use in performance‐based earthquake engineering. There are several uncertainties in earthquake engineering, including earthquake occurrence, structural response, damage, and loss. In the current research, structural response uncertainty is directly included in the ET method, which is an analysis method used for performing structural behavior assessment under seismic actions. Conventional practice of the ET method does not provide any information about seismic response distribution. Despite the simplicity of the ET method, it is an accurate dynamic analysis approach in which structures are subjected to predesigned intensifying acceleration functions, also known as ET excitation functions (ETEFs). In this study, the ETEF generating procedure is modified in order to include the exceedance probability of structural responses observed at an intensity measure. This proposed method is applied to generate new ETEFs; then they are utilized in assessing distribution responses in three structure case studies. Finally, response distributions obtained by the ET method are compared with incremental dynamic analysis so as to investigate the proposed method efficiency. Results show that response probabilistic distributions that are predicted using the ET method match those obtained by incremental dynamic analysis.     

Optimum selection of photovoltaic modules using probabilistic approach based on capacity factor estimation

In this paper, the optimum selection of photovoltaic module using probabilistic techniques based on capacity factor estimation is proposed. The approach entails modelling the solar irradiance characteristics of the site by fitting probability distributions to the irradiance data for different hours of a typical day in each month of the year. The parameters of the probability distribution that best fits the solar irradiance data for a particular hour are thereafter used to estimate the capacity factor of different designs of PV modules. The module with the highest average capacity factor across all the months is identified as the best suited module for the given site. The proposed technique is investigated using 5 years data (2008–2012) of solar irradiance and temperature. The choice of the year of observation of the data was due to accuracy and completeness of the data for the period. The data sheets of 10 commercially available PV modules were also obtained from different manufacturers. The proposed method is simple, easy to use, and can be applied to any solar regimes around the world.     

基于遗传算法的土坡三维可靠度分析

 边坡稳定分析的三维安全系数方法和三维可靠度分析方法一般均需人为给定一个与滑坡体宽度相关的参数或仅针对固定三维滑面进行分析计算。由于这样计算得到三维安全指标并不是最小值，因此难以反映边坡真正的安全度水平。引入随机场局部平均计算模型，考虑土性参数的空间相关性，边坡存在一个最小可靠指标对应的三维滑坡形态，这为采用优化方法进行土坡稳定三维可靠度分析奠定基础。对最小三维可靠度指标与三维临界滑面存在的缘由进行分析。遗传算法是一种优秀的全局寻优算法，可以有效解决边坡稳定分析临界滑面搜索问题。引入土性参数的空间相关模型，结合边坡稳定的三维简化毕肖普方法，直接以边坡稳定的三维可靠度指标为优化目标，建立基于遗传算法的边坡稳定三维可靠度分析方法。该方法无需滑坡宽度的假定，可以得到真正的边坡稳定三维可靠指标及对应的三维临界滑面。算例说明该方法的有效性。     

Application of probabilistic analysis to assess the relative severity of crack-like weld defects

This paper describes how probabilistic fracture mechanics calculations have been used to assess the notional probability of fracture of a number of crack-like weld defects in an offshore structure. The results were used in a decision making context to establish a rational repair sequence, so that the defects could be repaired on an order-of-merit basis. This was necessary in order to minimize risks because of the possibility of the repair programme being curtailed, for instance, by bad weather. The analysis procedure, which is based on the probabilistic treatment of a standard deterministic fracture model, could be applied in any similar situation where appropriate information is available. An important new aspect is the way in which fracture probabilities are assessed for defects which are large compared with the size of fracture toughness test specimens.     

岩土参数概率分布类型及其选择标准

 岩土参数的概率分布类型对风险评价和可靠度分析具有相当大的影响,对其研究是一项基础性的重要工作。从分析总结各种概率分布类型的产生背景、所描述对象的物理意义着手,将其分门别类,发现大致有5大系列,即Bernoulli分布系列、Poisson分布系列、极值分布系列、中心极限分布系列和用于统计分析的分布系列。然后研究岩土参数被建模为随机变量时影响其不确定性的因素,得出用中心极限分布系列对其描述较为合理,在此基础上,详尽地对比隶属于中心极限分布系列的正态、对数正态分布的各种特性,提出在二者之间如何选择的标准,即当变异系数小于30%且偏度系数小于0.025时选择正态分布,反之,选择对数正态分布。另外,论证泊松比更适合建模为b 分布的事实。最后,用一统计实例诠释本文所提观点的正确性。研究成果对岩土工程的风险评价和可靠度分析具有重要的参考价值。     

Probabilistic assessment of road vehicle safety in windy environments

Several wind- and weather-related accidents of road vehicles occur every year, especially at exposed locations where topographical features magnify the wind effects. The most notable ones involve high-sided vehicles. The objective of this paper is to investigate parameters influencing wind-related accidents of road vehicles. A general probabilistic model, based on reliability approach, is outlined and applied for assessment of road vehicle stability in windy environments. The numerical model is defined on a finite set of basic variables with prescribed probabilistic characteristics. The basic variables are wind velocity and direction; frictional coefficient; camber of the road and vehicle speed. The accident point is defined in the space of basic variables and the probability of accident is assessed. The theory presented is applied to a multitude of scenarios to explore the interrelation between the various basic variables and how they affect the probability of accident given in terms of the so-called accident index. The analysis demonstrates that wind-related accidents are the consequence of a combination of several basic variables as represented by the accident index. The study suggests that available methods of probabilistic mechanics and theory of reliability can be of value for analysis of wind-related traffic accidents and potential applications of the presented methodology are outlined.     

关于改进中国规范中土液化判别准则的建议

基于BP网络的人工神经元模型和可靠度理论,建立极限状态的抗液化阻力比函数和液化概率函数。沿用原抗震规范中液化标准贯入锤击数基准值概念,建立了简化的液化判别概率方法。该法以液化标准贯入锤击数作为估计液化势的基本依据。基准值是给定地面加速度、土层埋深、地下水位的液化临界锤数,也与震级大小和液化概率有关。为了对不同震级和土层中任一点进行液化判别,引入土层埋深水位以及震级大小对基准值的修正系数。为了方便工程应用,也给出了按地震分组的液化判别方法。     

考虑参数空间变异性的边坡可靠度分析非侵入式 随机有限元法

提出了考虑土体参数空间变异性的边坡可靠度分析的非侵入式随机有限元法。采用Karhunen-Loeve级数展开方法表征土体抗剪强度参数空间变异性,其中通过wavelet-Galerkin技术求解Fredholm积分方程得到相关函数的特征解。基于有限元滑面应力法计算边坡安全系数,采用随机多项式展开将隐式函数表达的安全系数替换为显式函数表达的安全系数,并编写了计算程序NISFEM。研究了所提方法在考虑土体参数空间变异性的边坡稳定可靠度分析中的应用。结果表明：提出的非侵入式随机有限元法极大地提高了考虑土体参数空间变异性的边坡可靠度分析的计算效率,为解决复杂边坡稳定可靠度问题提供了一条有效的途径。考虑抗剪强度参数空间变异性的边坡可靠度分析存在临界变异系数,其随边坡安全系数的增加而增大。当抗剪强度参数的变异系数小于临界变异系数时,忽略土体参数空间变异性将会高估边坡失效概率。当边坡安全系数小于1时,边坡失效概率并不总是随着抗剪强度变异系数的增加而增大。此外,土体黏聚力和内摩擦角随机场间相关性对边坡失效概率具有十分明显的影响。