SMW工法支护结构失效概率的模糊事故树分析

针对常规事故树不能考虑基本事件发生概率的不确定性这一现状,通过引入模糊集的概念,将常规事故树中基本事件的发生概率模糊化,用三角形模糊数代替确定性发生概率,应用模糊数截集方法,推导了模糊事故树的相关算法。采用模糊事故树方法得到深基坑工程SMW工法支护结构的模糊失效概率,并进行了敏感性分析,找出对顶事件发生概率影响较大的基本事件,确认减小SMW工法支护结构发生事故的相关措施。与常规事故树方法比较表明,模糊事故树方法不仅能达到常规方法的分析目的,而且可以得到深基坑支护工程失效可能性的分布规律。     

考虑地层变异性和土体参数变异性的边坡可靠度分析

现有边坡可靠度分析大多数只考虑土体参数的固有变异性,而忽略了地层变异性的影响。为此,提出了同时考虑地层变异性和土体参数固有变异性的边坡可靠度分析方法,利用耦合马尔可夫链模拟地层分布,采用基于乔列斯基分解的中点法离散土体参数随机场,采用有限元强度折减法计算边坡安全系数,通过蒙特卡洛法模拟进行边坡可靠度分析。利用澳大利亚珀斯市钻孔资料,以边坡可靠度问题为例阐明了同时考虑地层变异性和土体参数固有变异性的重要性,研究了钻孔布置方案对边坡可靠度的影响规律,结果表明:提出的方法能够有效地反映地层变异性和土体参数固有变异性对边坡可靠度的影响。当钻孔数目较少时,模拟的边坡土体类型分布与真实边坡土体类型分布相差较大,此时忽略地层变异性将导致边坡可靠度不精确的估计结果。钻孔布置方案对边坡失效概率和安全系数有明显的影响,钻孔应尽可能多的布置在边坡关键影响区域。边坡失效概率和安全系数统计量与钻孔数目并不呈单调关系,但是随着钻孔数目的增加,边坡失效概率和安全系数统计量逐渐收敛至"精确解"。     

Statistical analyses of inherent variability of soil strength and effects on engineering geology design

Clayey soil strata, as all natural deposits, generally show variability in the values of their geotechnical properties. This is due mainly to geological and environmental processes such as deposition and diagenesis, which introduce heterogeneity, anisotropy and variability to soil properties. Other causes of variability, and thus uncertainty, are the representativeness of samples and errors related to testing procedure, measurement and data processing procedures. To improve our knowledge about the inherent variability in the geomechanical properties of clays, this work presents a case study related to the analysis of the strength variability along a log of marine stiff clay deposits, which are apparently quite homogeneous. The analysis was based on pocket penetrometer strength measurement, performed both punctually and across the whole deposit. The adopted testing procedure, which is fast and reliable, provides a really wide dataset of the investigated soil property, with more than 800 data points. These allow for detailed variability analysis, and a reliable estimation of the coefficient of variation as well as research into the best fitting probability density functions, which are key factors for robust design. The presented case study allows discussion of the inherent variability of soil properties, and its influence on the characteristic values of soil strength in geotechnical design.     

Project cash flow analysis in the presence of uncertainty in activity duration and cost

The inherent uncertainty and imprecision in project scheduling have motivated the proposal of several fuzzy set theory based extensions of activity network scheduling techniques. Building upon these, a cash flow calculation methodology for projects including activities with fuzzy durations and/or costs is proposed in this paper. According to the proposed approach, the project cash flow is represented by an S-surface (as opposed to the traditional S-curve) ensuing by connecting S-curves at different risk possibility levels. The methodology is exemplified by estimating the working capital requirements in a real world road construction project. Furthermore, the benefits of the methodology and its subsequent computerization are discussed. It is believed that the proposed approach may also be useful for both evaluating project proposals during feasibility studies and for performing earned value analysis for project monitoring and control.     

Sensitivity analysis of vertically loaded pile reliability

The purpose of this paper is to examine the influence of geotechnical uncertainties on the reliability of vertically loaded pile foundations and the use of this information in decision-making support, especially when gathering the information necessary for reliability analyses. Two case studies of single pile foundations were selected, and each uncertainty source was investigated to identify which are the most important and influential in the evaluation of vertical pile resistance under axial loading. Reliability sensitivity analyses were conducted using FORM (the first-order reliability method) and MCS (Monte Carlo simulations). The characterisation of uncertainties is not an easy task in geotechnical engineering. The aim of the analyses described in this paper is to optimise resources and investments in the investigation of the variables in pile reliability. The physical uncertainties of actions, the inherent variability of soil and model error were assessed by experimental in situ standard penetration tests (SPT) or from information available in the literature. For the cases studied, the sensitivity analysis results show that, in spite of the high variability of the soils involved, model error also plays a very important role in geotechnical pile reliability and was considerably more important than soil variability in both case studies. From a comparison of the two reliability methods (FORM and MCS), it was concluded that FORM is applicable in simple cases and as a first approach because it is an approximate method and sometimes does not have the capability to incorporate every detail of the problem, namely a specific probability density function or more specific limit conditions.     

Statistical methods in risk evaluation

This paper is concerned with the statistical methods involved in the evaluation of fire risk in an industry.The risk could be expressed in terms of two main components—the probability of fire starting and the probability of damage reaching various levels in a fire. The latter probability involves the concept of probability distribution of fire loss, the nature of which is discussed with reference to statistical and physical considerations. The values of the parameters of this distribution and the probability of fire starting will vary depending on factors such as sources of ignition, size of the property, and the presence or absence of sprinklers.It is shown how results for a group of similar properties could be modified for evaluating the risk in an individual property. For this purpose, detailed particulars of the property and processes will be required. If individual figures for financial losses are available only for large fires the parameters of the probability distribution of fire loss can be estimated by applying the statistical theory of extreme values. Basic principles of this theory and its practical uses are explained. As a project for further research it is proposed that a model based on stochastic processes should be developed for predicting the spread of fire in a building. An outline of such a model is given specifying the data required for estimating and validating the parameters of the model.     

滑坡灾害典型受灾体失效概率计算方法及应用

从系统研究的角度看,滑坡灾害系统包括致灾体子系统和受灾体子系统.滑坡灾害是这2个子系统共同作用的结果.以往的研究主要集中在致灾体稳定性的评价上,没有全面考虑2个子系统对灾害风险的影响,尤其缺少对受灾体子系统的研究.针对这种现状,对一种典型受灾体(框架结构)在滑坡灾害作用下的失效概率计算方法进行探讨:将滑坡灾害致灾模式简...     

Expanded reliability-based design of piles in spatially variable soil using efficient Monte Carlo simulations

Inherent spatial variability is considered as a major source of uncertainties in soil properties, and it affects significantly the performance of geotechnical structures. However, research that considers, directly and explicitly, the inherent spatial variability in reliability-based design (RBD) of geotechnical structures is limited. This paper develops a RBD approach that integrates a Monte Carlo Simulation (MCS)-based RBD approach, namely the expanded RBD approach, with random field theory to model, both directly and explicitly, the inherent spatial variability of soil properties in RBD of drilled shafts. The proposed approach is implemented in a commonly-available spreadsheet environment to effectively remove the hurdle of reliability computational algorithms and to provide a user-friendly graphical user interface to practicing engineers. To improve the efficiency and resolution of MCS at small probability levels, the expanded RBD approach is enhanced with an advanced MCS method called “Subset Simulation”. Equations are derived for the integration of the expanded RBD approach and Subset Simulation. The proposed approach is illustrated through a drilled shaft design example, and is applied to explore the effects of inherent spatial variability (including the scale of fluctuation and correlation structure) and to evaluate systematically the equivalent variance technique that is commonly used to indirectly model inherent spatial variability in current RBD approaches. It is found that inherent spatial variability significantly affects the RBD of drilled shafts, and its effects are considered in RBD using the proposed approach in a direct and explicit manner. In addition, the results show that the indirect modeling of inherent spatial variability using the equivalent variance technique with the simplified form of variance reduction function in RBD might lead to relatively conservative designs in design practice.     

Stochastic key sector analysis: an application to a regional input–output framework

Limits on the precision of technical relationships within input–output frameworks have led to the use of stochastic analytical methods. The notion of stochastic analysis is developed in this paper to discern how the inherent imprecision effect, when aggregated data are utilised, affects the concomitant key sector analysis. Through a Monte Carlo based simulation, the stochastic key sector graph is introduced, with numerical expressions defined which quantify the association of the individual sectors to quadrants of the graph. The technical developments are benchmarked on a small problem, before a stochastic key sector analysis on an aggregated regional input–output table is reported. Comparisons are made between results when the aggregation of sectors is not employed. The paper reveals that aggregation in key sector analysis is inevitably a poor idea. However, it is argued that aggregation is often a practical necessity, so quantifying the uncertainty that is attendant on this aggregation is important, with the “association” expressions introduced potentially central to elucidate this uncertainty. The conclusions of this paper suggest that where analysts and decision makers are obliged to aggregate tables for analytical purposes then problems might be mitigated where marginal sectors are treated with care.     

高等级公路边坡工程风险因子识别及评估

高等级公路的边坡工程由于其存在诸多的不利因素,如地质及环境水文条件、设计施工因素、工程造价与效益控制等,构成了此类工程的一些不确定性.一旦这些风险因素引发边坡灾害事故,后果严重.针对此类工程特点,提出了边坡风险因子识别方法与一般步骤,并讨论了一种利用层次分析法评估边坡工程的风险模型.结合溪洛渡水电站对外专用公路典型边坡工程,识别出该工程运营期内影响边坡稳定性的风险因子,根据技术资料和实际工况,分析了应重点控制的风险因子项,并建立相应风险评估模型.     

基于蒙特卡罗法的崩塌涌浪分析方法

 因目前国内外研究涌浪大多采用确定性的计算方法,忽视参数的随机性。故构建蒙特卡罗法求解崩塌涌浪的基本思想,并引入涌浪计算状态函数。以三峡库区箭穿洞危岩体为例,分析水深、崩塌体入水速度和崩塌体入水体积等随机变量的概率分布,利用蒙特卡罗法分析随机变量的敏感性及涌浪值的概率分布。研究结果显示,箭穿洞危岩体形成涌浪的计算变量敏感性强弱排序为入水速度、入水体积和水深;产生的涌浪值分布符合正态分布,其均值为7.02 m。产生涌浪红色预警区的概率为90.8%,建议对其进行治理,以降低涌浪风险。基于蒙特卡罗法的崩塌涌浪分析方法是今后涌浪研究的重要方向,可以更好地理解涌浪风险,并可用于水库地质灾害风险管理和航道风险管理中。     

基于极限平衡法的边坡稳定性可靠度分析

传统方法对边坡稳定性进行分析时,不能定量考虑土体参数随机性、变异性的影响。为更好地对边坡稳定性进行评价,本文基于传统边坡稳定性计算方法,同时考虑参数的变异性和分布类型的差异,利用蒙特卡洛模拟技术,编制了相应程序。针对某匀质边坡,利用Fellenius法、Bishop法、Janbu法和Morgenstern-Price法进行破坏概率计算。结果表明,安全系数大于1时,边坡仍有破坏的可能,边坡稳定性对参数变异性的敏感度不同,参数变量分布类型也会对边坡稳定性评价结果产生影响。利用可靠度方法得到的可靠度指标、破坏概率等指标,能够定量地描述各参数变异性对边坡稳定性的影响。因此,可以将可靠度的方法和确定性的方法相结合,对边坡的稳定性进行描述,为滑坡风险的评估提供参考依据。     

Multiobjective optimization under uncertainty in tunneling: application to the design of tunnel support/reinforcement with case histories

In this paper, two questions common in tunnel design are addressed: (i) how to choose an optimum solution when more than one conflicting objective must be achieved; (ii) how to deal with data affected both by imprecision and randomness. Fuzzy Set Theory and Random Set Theory are used to develop a general interactive multiobjective procedure, which is then applied to the design of tunnel support/reinforcement. A case history illustrates how the procedure was successfully used in the preliminary design of a total of 40 km of tunnels in Central Italy. It is shown that the procedure allows the designer to become a knowledgeable decision maker because his interaction is required at the key points of the process, and because the trade-offs among the objective functions can be easily assessed. The designer's personal input is valued and clearly defined in its impact on the solution. The case history demonstrates that, without an optimization procedure, it is extremely likely (probability of 99%) that a solution is chosen, which either increases the costs without increasing safety, or decreases the safety without decreasing the costs. Finally, it is shown that both imprecision and randomness can be easily taken into account in tunnel design.     

Reliability analysis of wind response of flexibly supported tall structures

Statistics and probabilistic analyses and risk assessments can be very useful decision‐making tools when dealing with structural–geotechnical problems. Wind loads, dynamic properties of soil underneath the structure and material characteristics of the structure are important factors that affect the wind action on the structure and consequently the structural wind‐induced response. Uncertainties in the estimation of these factors as a result of human error or inherent variability are at the forefront for the use of reliability approaches to evaluate the risk of failure during the service period. In the present study, probabilistic base force analyses for tall structures are performed. The substructure approach in which the soil supporting the foundation is modeled by the foundation compliances as functions of soil shear wave velocity is used to account for the soil–structure interaction efficiently. A three‐variable probabilistic approach is used to account for the uncertainties in shear wave velocity of the soil underneath the foundation, the concrete strength and the design wind speed on the calculated response and the base forces. The second moment approximation using Taylor series expansion is used to perform the probabilistic analyses of the base cross‐section design and resistant forces of a free‐standing tower. The first‐order reliability method is used to examine the failure probability and the contribution to the total uncertainty. The results show that the dynamic response of the tower increases as soil shear wave velocity decreases. For the range of soil shear wave velocity encountered in practice, the base forces of the structure may increase by up to 20% as a result of the foundation flexibility. For the limit state considered in this study, it was found that the reliability index decreases by up to 15% and the probability of failure increases by up to one order of magnitude as a result of the soil–structure interaction effect. Copyright © 2003 John Wiley & Sons, Ltd.     

Maximum entropy probability distributions for flood frequency analysis

It is customary to assume a frequency distribution in flood frequency analysis. The parameters of the distribution are estimated by using observed or transformed data. The fitted distribution is then used to estimate the magnitudes of floods of different frequencies.

The maximum entropy (ME) probability distribution is defined as the 'minimally prejudiced probability distribution which maximizes the entropy subject to constraints supplied by the given information'. In spite of many attractive features of the ME distribution, it has not been used in its general form in practice. The main reason for not using the ME distribution in its general form is that the parameter estimation problem associated with the ME distribution is not easy. Recently this problem has been solved and an algorithm has been developed to estimate the parameters of the ME distribution.

The objective of the research reported in the present paper is to fit ME distributions to flood data. The ME distributions are compared with other well known distributions. The computational aspects and selection of orders of distributions are also discussed. The ME distribution is shown to be versatile and fits a variety of flood data very well.     

强降雨条件下考虑饱和渗透系数变异性的基岩型层状边坡可靠度分析

边坡土体因其自身的不均匀性及试验监测的不准确性,饱和渗透系数表现出一定的变异性。为探索强降雨条件下基岩型层状边坡的稳定性及失稳破坏概率,以笔者前期对基岩型层状边坡降雨入渗及其稳定性模型的研究为基础,结合Monte Carlo法,建立了考虑饱和渗透系数变异性的基岩型层状边坡稳定性可靠度计算模型,并基于MATLAB将这一计算过程程序化。最后,利用建立的基岩型层状边坡可靠度计算模型,得到了张家湾滑坡在不同饱和渗透系数变异系数及降雨强度下的失稳破坏概率,分析了饱和渗透系数变异系数及降雨强度对滑坡失稳破坏概率及安全系数均值的影响。计算结果表明在一定降雨条件下,当失稳破坏概率小于50%时,变异系数越大、滑坡发生失稳破坏的概率越大;当失稳破坏概率大于50%时,变异系数越小、滑坡发生失稳破坏的概率越大。     

极大熵在风险管理中的应用

对工程投资决策中风险管理进行了理论研究，将熵的概念引入到风险管理中，从理论上分析熵是进行风险管理的一种很好的工具，得出极大熵准则适用于在无样本数据的情况下求解随机变量概率分布的结论。     

Structural reliability techniques applied to plume impingement loading of the Space Station Freedom photovoltaic array

A new aerospace application of structural reliability techniques is presented, where the applied forces depend on many probabilistic variables. This application is the plume impingement loading of the Space Station Freedom Photovoltaic Arrays. When the space shuttle berths with Space Station Freedom it must brake and maneuver towards the berthing point using its primary jets. The jet exhaust, or plume, may cause high loads on the photovoltaic arrays. The many parameters governing this problem are highly uncertain and random. An approach, using techniques from structural reliability, as opposed to the accepted deterministic methods, is presented which assesses the probability of failure of the array mast due to plume impingement loading. A Monte Carlo simulation of the berthing approach is used to determine the probability distribution of the loading. A probability distribution is also determined for the strength of the array. Structural reliability techniques are then used to assess the array mast design. These techniques are found to be superior to the standard deterministic dynamic transient analysis, for this class of problem. The results show that the probability of failure of the current array mast design due to the examined failure modes is minute. Significantly, this paper details a structural reliability analysis of a complex aerospace structure for which little statistical information is available.     

Fuzzy AHP approach for selecting the suitable bridge construction method

Selecting an appropriate bridge construction method is essential for the success of bridge construction projects. The Analytical Hierarchy Process (AHP) method has been widely used for solving multi-criteria decision-making problems. However, the conventional AHP method is incapable of handling the uncertainty and vagueness involving the mapping of one's preference to an exact number or ratio. This paper presents a fuzzy AHP model to overcome this problem. The proposed approach employs triangular and trapezoidal fuzzy numbers and the α-cut concept to deal with the imprecision inherent to the process of subjective judgment. A case study that evaluates bridge construction methods is presented to illustrate the use of the model and to demonstrate the capability of the model.