Reliability analysis of rock slopes involving correlated nonnormals

A two-dimensional rock slope in Hong Kong and a three-dimensional hypothetical tetrahedral wedge are analyzed probabilistically using an intuitive and transparent constrained optimization approach for the first-order reliability method (FORM). The results are compared with Monte Carlo simulations. Simple procedures for incorporating truncated non-normal distributions in reliability analysis are described. The effects of statistical correlations on the computed reliability index are studied. The difference between probabilities of failure inferred from reliability index and from Monte Carlo simulations are investigated via the response surface method. It is shown that the efficiency of reliability-based approach can be combined with the robustness of Monte Carlo simulation. The meanings of reliability index and probability of failure are also discussed.     

Collapse mechanism identification using a system-based objective

A method for identifying stochastically dominant failure modes in rigid-plastic unbraced frames is reviewed. This method is then extended to the system reliability analysis of braced frames and trusses. Significant modes are identified based on their contribution to the system probability of failure. A procedure for the consideration of non-normal random variables in the analysis is presented. The identification procedure is illustrated through examples of the system reliability analyses of braced and unbraced frames and trusses. For the examples presented, good estimates of the system probability of failure were obtained from a small number of identified modes.     

Reliability analysis of ground–support interaction in circular tunnels using the response surface method

The first-order and the second-order reliability method (FORM/SORM) are used to evaluate the failure probability of three performance functions of the ground–support interaction in circular tunnels subjected to hydrostatic stresses. The response surface method (RSM) is used to enable reliability analysis of the implicit convergence-confinement method. The friction angle, cohesion and elastic modulus of the rock mass are considered as basic random variables and are first assumed to obey normal distributions. The quadratic polynomial with cross terms is employed as response surface function to approximate the limit state surface (LSS) at the design point. The strategies for the RSM are presented. The failure probability with respect to different criteria are obtained from FORM/SORM and compared to those generated from Monte Carlo simulations. The results show that the support installation position has great influence on the probability of the three failure modes under consideration. Comparison between analysis using correlated and uncorrelated friction angle and cohesion indicates that the influence of the correlation on the reliability analysis depends on the support installation position and the orientation of the LSS. The reliability analysis involving correlated non-normal distributions and the reliability-based design of the support are also investigated.     

重力式挡土墙稳定性的结构体系可靠度分析

重力式挡土墙结构最主要的失稳模式是倾覆失稳和滑移失稳。为了计算重力式挡土墙稳定性的结构体系失效概率,首先分别建立重力式挡土墙结构抗倾覆稳定性和抗滑移稳定性的功能函数,然后引入结构可靠度分析一次二阶矩法中的验算点法(JC法)分别对两种失效模式进行计算,得出两个相应的可靠度指标。将两种失稳模式视为串联系统,由逐步等效平面法计算结构体系可靠度指标,最后由结构体系可靠度指标计算出该挡土墙稳定性的结构体系失效概率。根据上述方法,利用MATLAB程序计算了某挡土墙,得出了结构体系可靠度指标和结构体系失效概率。     

Probability analysis method using Fast Fourier transform and its application

This paper presents an efficient probability analysis method using Fast Fourier transform taking into account that (1) a probability density function and its characteristic function are a pair of Fourier transforms, and (2) the characteristic function of the sum of statistically independent random variables is given by the product of the characteristic functions of each random variable. The efficient probability analysis method is extended for the sum of correlated non-normal random variables with correlation coefficients expressed by the power of a common value. Expressing the correlated basic variables in terms of two sets of uncorrelated random variables, the characteristic function of their sum can be estimated approximately by the characteristic functions of the correlated basic variables. The probability density function of the sum is obtained using Fast Fourier transform. The accuracy and applicability of the approximation method are investigated based on the estimation error of the cumulant and using numerical examples. Applications of the proposed method to various aspects of structural reliability analysis and design are illustrated.     

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.     

基于顺序组件法的系统可靠度敏感性分析方法

岩土工程一般是由多个失效模式组成的复杂系统,且参数的不确定性对岩土工程的失效模式及可靠指标具有重要影响.为了分析参数不确定性对系统可靠度的影响,提出基于顺序组件法的系统可靠度敏感性分析方法(SCMSA).SCMSA利用SCM组合元件的原理,在计算两元件并联和串联的简单系统可靠度及敏感性的基础上,进一步计算两元件组成的组...     

考虑参数随机性的高层建筑风振舒适度的非线性黏滞阻尼器优化布设

以顶层加速度作为概率特征量,建立目标函数,分别采用基于随机等效线性化系统的频域方法和基于概率密度演化理论的非线性系统时域方法,进行了考虑结构参数随机性的高层建筑风振舒适度控制的黏滞阻尼器优化布设研究。结果表明：在总黏滞阻尼器系数相同的条件下,以顶层加速度标准差和失效概率为目标函数的黏滞阻尼器优化布设方案,在确定性激励作用下均能显著降低结构的风振响应,且相对于未优化的阻尼器均匀满布方案更经济、更有效。以加速度标准差为目标函数的传统阻尼器优化布设本质上是确定性分析方法,对结构可靠度的提高作用有限,而以加速度失效概率为目标函数的阻尼器优化布设,以结构响应的概率密度函数为优化对象,能显著地提高结构的可靠度,有利于改善高层建筑结构的风振舒适度性能。     

露天矿边坡岩体稳定性各向异性分析方法及工程应用

露天矿边坡岩体通常含有大量IV、V级结构面,影响岩体稳定性。针对这种岩体特性,提出了系统的工程分析方法：首先,应用3GSM非接触测量系统对岩体出露结构面现场测试,统计结构面几何参数概率模型;进一步根据Monte Carlo方法生成裂隙网络,分别利用离散介质渗流方法和几何损伤理论,在分析REV尺寸效应基础上,计算岩体渗透张量和弹性张量,实现岩体参数表征;最后,基于等效连续介质模型,建立各向异性岩体渗流应力耦合模型,采用COMSOL有限元软件分析边坡岩体稳定性。应用该方法对抚顺西露天矿南帮进行了实例分析,计算结果与实际吻合较好。提出的露天矿边坡岩体稳定性分析方法能够考虑节理分布导致的岩体各向异性特征,简单合理,具有良好的工程应用前景。     

Benchmark study on methods to determine collapse failure probabilities of redundant structures

Methods to determine system failure probability are compared with respect to their results, capabilities and efficiency. In the case of normally distributed basic variables nearly all methods yield identical results. With non-normal variables, only those methods are reliable which are able to evaluate non-normal safety margins, though with small coefficients of variation the results may differ considerably. Those methods which depend on a plastic limit load analysis to find only one mechanism are unreliable. Since the former methods need the prior evaluation of mode limit state functions and have to consider all modes, their application is restricted to small systems. To evaluate failure probabilities of large systems, an automatic procedure to find the stochastically most relevant modes is necessary.     

Nonlinear analysis and reliability of metallic truss structures

The present study goes into the search for the safety domain of civil engineering structures. The objective is to show how a reliability-evaluation brought by a mechanical sizing can be obtained. For that purpose, it is necessary to have a mechanical model and a reliability model representing correctly the behavior of this type of structure.It is a question on one hand, to propose a formulation for the nonlinear calculation (mechanical nonlinearity) of the spatial structures in trusses, and on the other hand, to propose or to adapt a formulation and a modeling of the reliability. The principle of Hasofer-Lind can be applied, in first approach, for the reliability index estimation, scenarios and the probability of failure.The made check concerned metallic in truss structures. Finally, some structures are calculated using the method adapted by Hasofer-Lind to validate the probability approach of the reliability analysis.     

等效线性化方法在RC框架结构设计中的应用

为研究罕遇地震作用下等效线性化方法在RC框架结构设计中的应用,基于现有的结构非线性响应的等效线性化方法,通过与RC框架结构非线性时程分析结果对比,分析不同的等效线性化方法计算罕遇地震作用下结构地震响应的有效性,并确定等效线性化参数的取值;按基于等效线性化的设计方法及现行规范方法分别设计了分析算例,通过非线性动力时程分析,对比了框架结构实现预期强震破坏模式的效果。结果表明：同时考虑刚度折减和附加阻尼的割线刚度等效线性法可更好模拟结构强震非线性反应;基于等效线性化的设计方法可更好地实现结构在罕遇地震作用下的预期破坏模式。     

Probabilistic Neural Network for Reliability Assessment of Oil and Gas Pipelines

A fuzzy artificial neural network (ANN)–based approach is proposed for reliability assessment of oil and gas pipelines. The proposed ANN model is trained with field observation data collected using magnetic flux leakage (MFL) tools to characterize the actual condition of aging pipelines vulnerable to metal loss corrosion. The objective of this paper is to develop a simulation-based probabilistic neural network model to estimate the probability of failure of aging pipelines vulnerable to corrosion. The approach is to transform a simulation-based probabilistic analysis framework to estimate the pipeline reliability into an adaptable connectionist representation, using supervised training to initialize the weights so that the adaptable neural network predicts the probability of failure for oil and gas pipelines. This ANN model uses eight pipe parameters as input variables. The output variable is the probability of failure. The proposed method is generic, and it can be applied to several decision problems related with the maintenance of aging engineering systems.     

Reliability sensitivity method by line sampling

Reliability sensitivity refers to the derivative of the failure probability with respect to the distribution parameter of basic random variable. Conventionally, this requires repetitive evaluations of the failure probability for different distribution parameters, which is a direct but computationally expensive task. An efficient simulation algorithm is presented to perform reliability sensitivity analysis using the line sampling technique, which gives a good failure probability evaluation for high-dimensional problems and still presents a comparative one for low-dimensional problems. On the basis of the line sampling procedure for failure probability analysis, the concept and implementation are presented for reliability sensitivity. It is shown that the desired information about reliability sensitivity can be obtained by a very limited increase of computation effort based on the failure probability analysis by the line sampling technique. The presented reliability sensitivity algorithm is more efficient than the one based on the direct Monte Carlo technique, especially for cases where the failure probability is low and the number of random variables is large, which is illustrated by several examples. Additionally, limitations of the line sampling based reliability sensitivity method are demonstrated by a numerical example as well.     

Estimating the annual probability of failure using improved progressive incremental dynamic analysis of structural systems

A methodology based on the progressive incremental dynamic analysis has been introduced in this paper to estimate the structural response and the corresponding annual probability of failure. The proposed methodology employs the genetic algorithm optimisation technique and an equivalent single‐degree‐of‐freedom system corresponding to the first‐mode period of a considered structure. The proposed methodology can significantly reduce the number of ground motion records needed for estimating the annual probability of failure. The numerical results indicate that the proposed method can effectively reduce the computational effort needed for computation of probability of failure for the first‐mode dominated structures, which is advantageous as the structure becomes larger. A relatively huge set of single‐degree‐of‐freedom systems as well as three multi‐degree‐of‐freedom systems including 3, 8 and 12 storeyed reinforced concrete structures was taken into account to test the proposed methodology. It has been shown that the probability of failure can be estimated within ±15% error with 95% confidence. The proposed method can speed up the decision‐making process in the probability‐based seismic performance assessment of structures, and it also incorporates the randomness of strong ground motions explicitly. Copyright © 2012 John Wiley & Sons, Ltd.     

基于n维等效方法的岩质边坡楔体稳定体系可靠度分析

 提出岩质边坡楔体稳定体系可靠度分析的n维等效方法,建立考虑多失效模式相关的楔体稳定体系可靠度分析的概率故障树模型。采用四参数b 分布来描述可靠度分析中基本随机变量的分布。最后采用n维等效方法计算楔体稳定体系可靠度,并着重分析随机变量敏感性分析的3个层次及不同层次上的可靠度对基本随机变量的敏感性。结果表明,n维等效方法计算的楔体体系失效概率均在Cornell简单上下限法的范围内,它能够有效地评价楔体体系可靠度。概率故障树模型能够清晰直观地模拟多失效模式相关的楔体体系可靠度问题,忽略失效模式间的相关性将会明显高估楔体体系失效概率。此外,黏聚力和内摩擦角之间的负相关性对边坡的可靠度具有有利的影响。随机变量敏感性分为单一极限状态方程、单一失效模式以及体系可靠度3个不同的层次,在研究随机变量敏感性时必须明确相应的分析层次。水压力和结构面产状的敏感因子较大,因此布置良好的边坡排水系统以及进行详细的地质勘测工作是提高楔体可靠度有效的方法。研究成果为边坡风险分析奠定了一定的基础。     

地震作用下钢筋混凝土框架结构连续倒塌极限状态可靠度分析

将结构连续倒塌的全概率方法应用于地震作用下的结构整体连续倒塌极限状态可靠度分析,采用构件可靠度方法对结构进行地震作用下最可能失效构件的识别,基于改进点估计法的随机Pushdown方法和随机竖向增量动力分析(竖向IDA)方法,进行完好和损伤结构的概率抗竖向连续倒塌能力分析及参数灵敏度分析。采用整体可靠度方法,分析了损伤结构的竖向连续倒塌条件失效概率。基于系统可靠度理论和全概率方法,分析了RC框架结构发生侧向增量倒塌以及构件地震损伤引起的结构竖向连续倒塌的联合失效概率。分析结果表明,按照我国现行规范设计的钢筋混凝土框架结构具有良好的抗连续倒塌能力。     

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。     

Serviceability‐based damping optimization of randomly wind‐excited high‐rise buildings

Fluid viscous dampers are proved to be effective for reducing the response of high‐rise buildings subjected to wind excitations so as to enhance structural habitability, which serves as a critical performance in serviceability design. High‐rise buildings attached with fluid viscous dampers, however, exhibit nonlinearity and even act as stiff systems in most cases of wind‐induced vibration mitigation. The traditional equivalent linearization methods employed in practices often fail to obtain an accurate solution. Equivalent linearization methods, including the energy‐dissipation equivalent linearization method and the statistical linearization technique, are first studied and validated in this paper by the backward difference formula, which was verified to be of high accuracy through the nonlinear dynamic analysis. The damping optimization for habitability control is then proceeded. Two families of serviceability criteria, the minimization of standard deviation of roof acceleration employed in traditional habitability analysis and the minimization of failure probability of roof acceleration proposed in the present study, are addressed. For the logical treatment of randomness inherent in wind excitations and its influence upon structural reliability, the probability density evolution method is employed. Numerical results reveal that the criterion of minimizing failure probability of roof acceleration has better performance in habitability enhancement.     

带有剪力墙(筒体)结构静力弹塑性分析方法与应用

按照弹塑性性能等效、内力等效的原则,介绍了一种采用“等效柱”代替框剪结构中的剪力墙进行静力弹塑性分析的新方法,从而能够按照柱单元的塑性铰来模拟实际结构中剪力墙的塑性性能,并在实际工程中得到了应用,获取了静力弹塑性分析中剪力墙的各种有用的信息,其中包括层间位移、塑性铰出现的先后顺序、位置,以及塑性铰破坏的类型和破坏的程度等。结果表明,该方法是目前对带有剪力墙(筒体)结构进行静力弹塑性分析的有效方法。