Risk-based probabilistic thermal-stress analysis of concrete arch dams

The probabilistic risk of arch dam failure under thermal loading is studied. The incorporated uncertainties, which are defined as random variables, are associated with the most affecting structural (material) properties of concrete and thermal loading conditions. Karaj arch dam is selected as case study. The dam is numerically modeled along with its foundation in three-dimensional space; the temperature and thermal stress distribution is investigated during the operating phase. The deterministic thermal finite element analysis of the dam is combined with the structural reliability methods in order to obtain thermal response predictions, and estimate the probability of failure in the risk analysis context. The tensile overstressing failure mode is considered for the reliability analysis. The thermal loading includes ambient air and reservoir temperature variations. The effect of solar radiation is considered by an increase in the ambient temperatures. Three reliability methods are employed: the first-order second-moment method, the first-order reliability method, and the Monte-Carlo simulation with Latin Hypercube sampling. The estimated failure probabilities are discussed and the sensitivity of random variables is investigated. Although most of the studies in this line of research are used only for academic purposes, the results of this investigation can be used for both academic and engineering purposes.     

一种与结构可靠度分析几何法相结合的响应面方法

提出一种迭代格式的响应面方法,以模拟实际工程中常见的功能函数不能明确表达的极限状态曲面.结合结构可靠度分析中的几何法,可直接应用现有的确定性的结构分析程序,对大型结构进行可靠度分析.数值结果表明本文方法具有较好的效率和精度.     

Seismic system reliability analysis of bridges using the multiplicative dimensional reduction method

Abstract

A combined method of finite element reliability analysis and multiplicative dimensional reduction method (M-DRM) is proposed for systems reliability analysis of practical bridge structures. The probability distribution function of a structural response is derived based on the maximum entropy principle. To illustrate the accuracy and efficiency of the proposed approach, a simply supported bridge structure is adopted and the failure probability obtained are compared with the Monte Carlo simulation method. The validated method is then applied for the system reliability analysis for a practical high-pier rigid frame railway bridge located at the seismic-prone region. The finite element model of the bridge is developed using OpenSees and the M-DRM method is used to analyse the structural system reliability under earthquake loading.     

Stochastic representation of blast load damage in a reinforced concrete building

In building engineering, deterministic analyses of system level disaster scenarios, including buildings subject to explosive loading, have been widely researched and as a result there are many sophisticated methods and algorithms for simulation of such events. Similarly structural reliability or “risk-based” analyses are also well developed and the computation of the probability of failure of a structural system is readily achievable. This paper combines the Monte Carloethod, used in many structural reliability algorithms, with a simplified but conservative progressive collapse structural model. This resulting algorithm is then used to generate a dataset representing the percentage damage a ten storey reinforced concrete building sustains when subject to an explosive load of a given magnitude located randomly in the ground floor car park. The progressive collapse structural model has a non-linear transient finite element method at its core. The explosive location, magnitude and duration, as well as the building imposed loading are all modelled as random variables. Using this preliminary model, a statistical analysis of the generated data provides evidence that the percentage damage in a concrete framed building due to an explosion is Weibull distributed.     

Reliability-based design optimization of adhesive bonded steel-concrete composite beams with probabilistic and non-probabilistic uncertainties

It is meaningful to account for various uncertainties in the optimization design of the adhesive bonded steel-concrete composite beam. Based on the definition of the mixed reliability index for structural safety evaluation with probabilistic and non-probabilistic uncertainties, the reliability-based optimization incorporating such mixed reliability constraints are mathematically formulated as a nested problem. The performance measure approach is employed to improve the convergence and the stability in solving the inner-loop. Moreover, the double-loop optimization problem is transformed into a series of approximate deterministic problems by incorporating the sequential approximate programming and the iteration scheme, which greatly reduces the burdensome computation workloads in seeking the optimal design. The validity of the proposed formulation as well as the efficiency of the presented numerical techniques is demonstrated by a mathematical example. Finally, reliability-based optimization designs of a single span adhesive bonded steel-concrete composite beam with different loading cases are achieved through integrating the present systematic method, the finite element analysis and the optimization package.     

Comparison of response surface and neural network with other methods for structural reliability analysis

The evaluation of the failure probability and safety levels of structural systems is of extreme importance in structural design, mainly when the variables are eminently random. Some examples of random variables on real structures are material properties, loads and member dimensions. It is necessary to quantify and compare the importance of each one of these variables in the structural safety. Many researchers studied structural reliability problems and nowadays there are several approaches for these problems. Two recent approaches, the Response Surface (RS) and the Artificial Neural Network (ANN) techniques, have emerged attempting to solve complex and more elaborated problems. In this work, these two techniques are presented, and comparison are carried out using the well known First Order Reliability Method (FORM), Direct Monte Carlo Simulation and Monte Carlo Simulation with Adaptive Importance Sampling technique with approximated and exact limit state functions. Problems with simple limit state functions (LSF) and closed form solutions of the failure probability are solved in order to highlight the advantages and shortcomings using these techniques. Some remarks are outlined regarding the fact that RS and ANN techniques have presented equivalent precision levels. It is observed that in problems where the computational cost of structural evaluations (looking for the failure probability and safety levels) is high, these two techniques may turn feasible the evaluation of the structural reliability through simulation techniques.     

Novel decoupled framework for reliability-based design optimization of structures using a robust shifting technique

In a reliability-based design optimization (RBDO), computation of the failure probability (P_f) at all design points through the process may suitably be avoided at the early stages. Thus, to reduce extensive computations of RBDO, one could decouple the optimization and reliability analysis. The present work proposes a new methodology for such a decoupled approach that separates optimization and reliability analysis into two procedures which significantly improve the computational efficiency of the RBDO. This technique is based on the probabilistic sensitivity approach (PSA) on the shifted probability density function. Stochastic variables are separated into two groups of desired and non-desired variables. The three-phase procedure may be summarized as: Phase 1, apply deterministic design optimization based on mean values of random variables; Phase 2, move designs toward a reliable space using PSA and finding a primary reliable optimum point; Phase 3, applying an intelligent self-adaptive procedure based on cubic B-spline interpolation functions until the targeted failure probability is reached. An improved response surface method is used for computation of failure probability. The proposed RBDO approach could significantly reduce the number of analyses required to less than 10% of conventional methods. The computational efficacy of this approach is demonstrated by solving four benchmark truss design problems published in the structural optimization literature.     

Adaptive sampling — an iterative fast Monte Carlo procedure

An iterative Monte-Carlo simulation procedure for structural analysis is suggested. This proposed new approach utilizes results from simulation to adapt the importance sampling density to the specific problem. Considerable reduction of the statistical error of the estimated failure probability is achieved. Most important, problems connected with optimization procedures commonly used in structural reliability are avoided. This makes the suggested procedure especially attractive for systems reliability analyses.     

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。     

A PDEM-based perspective to engineering reliability: From structures to lifeline networks

Research of reliability of engineering structures has experienced a developing history for more than 90 years. However, the problem of how to resolve the global reliability of structural systems still remains open, especially the problem of the combinatorial explosion and the challenge of correlation between failure modes. Benefiting from the research of probability density evolution theory in recent years, the physics-based system reliability researches open a new way for bypassing this dilemma. The present paper introduces the theoretical foundation of probability density evolution method in view of a broad background, whereby a probability density evolution equation for probability dissipative system is deduced. In conjunction of physical equations and structural failure criteria, a general engineering reliability analysis frame is then presented. For illustrative purposes, several cases are studied which prove the value of the proposed engineering reliability analysis method.     

On the probabilistic analysis of reinforced concrete beams in shear and bending

In this paper, probabilistic models are developed for evaluation of structural reliability of reinforced concrete beams. The proposed approach is based on known deterministic models of failure and the Level 2 method. For the purpose of analysis, the failure functions are defined for the combined effect of shear and bending. A stochastic dependence in properties and in loads at different points along the beam is considered and the failure of elements is defined as a series system of failure modes. It is shown that the stochastic dependence along structural members is an important factor and should be taken into account in design practice.     

Asymptotic analysis of asymmetric reliability margin

By a first-order-reliability-method (FORM)-based asymptotic analysis the influence of the coefficient of skewness of resistance upon the probability of failure of a reliability problem is studied. The fundamental case of the reliability margin with three-parameter log-normal resistance and normal action effects is considered. First-order-term formulas for the reliability index and weight factors corresponding to the design point and some other points of failure surface are obtained. The study of the points of failure surface is aimed at finding a convenient separated form of a deterministic condition for a reliability verification at the target level with an explicit occurrence of the coefficient of skewness. Following a suggested procedure, some error estimates of several simplified reliability verifications are presented.     

Spatial time-dependent reliability analysis of reinforced concrete slab bridges subject to realistic traffic loading

Resistance and loads are often correlated in time and space. The paper assesses the influence of these correlations on structural reliability/probability of failure for a typical two-lane reinforced concrete (RC) slab bridge under realistic traffic loading. Spatial variables for structural resistance are cover and concrete compressive strength, which in turn affect the strength and chloride-induced corrosion of RC elements. Random variables include pit depth and model error. Correlation of weights between trucks in adjacent lanes and inter-vehicle gaps are also included and are calibrated against weigh-in-motion data. Reliability analysis of deteriorating bridges needs to incorporate uncertainties associated with parameters governing the deterioration process and loading. One of the major unanswered questions in the work carried out to date is the influence of spatial variability of load and resistance on failure probability. Spatial variability research carried out to date has been mainly focused on predicting the remaining lifetime of a corroding structure and spatial variability of material, dimensional and environmental properties. A major shortcoming in the work carried out to date is the lack of an allowance for the spatial variability of applied traffic loads. In this article, a two-dimensional (2D) random field is developed where load effects and time-dependent structural resistance are calculated for each segment in the field. The 2D spatial time-dependent reliability analysis of an RC slab bridge found that a spatially correlated resistance results in only a small increase in probability of failure. Despite the fact that load effect at points along the length of a bridge is strongly correlated, the combined influence of correlation in load and resistance on probability of failure is small.     

钢筋混凝土框架结构体系可靠度分析

结构体系可靠度是一个40年来尚没有得到很好解决的问题,即使对于理想弹塑性体系,经典的结构体系可靠度分析也往往会遭遇两个难以克服的困难:相关失效与组合爆炸。近年来,基于概率守恒原理的随机事件描述,提出了广义密度演化方程,从而将确定性系统和随机系统分析纳入到统一的理论框架之中。基于这一进展,结合结构非线性全过程分析的位移控制算法,本文推导了结构静力非线性发展过程的概率密度演化方程。采用纤维梁柱单元进行结构非线性分析,研究钢筋混凝土框架结构的体系可靠度,并与Monte Carlo法进行对比分析。研究结果证明了概率密度演化理论对结构体系可靠度分析的适用性。     

Closed form solution for reliability design of beams

Most of the research papers in the area of Reliability are concerned with the evaluation of probability of failures for various limit states or calculation of safety index (β). There are few papers in the area of inverse formulation of reliability. This paper specifically deals with the design of various reinforced concrete members for given probability of failure levels. The probability-of-failure levels for various members are taken from literature and the reliability design problem is formulated as a polynomial equation in terms of the design parameters. The solution of the polynomial is obtained using some standard techniques which, in turn, gives the design values of the members for that specified probability of failure. This approach is applicable to any reinforced concrete member and the results have direct application for practicing engineers.     

Uncertain linear systems in dynamics: Retrospective and recent developments by stochastic approaches

This paper provides an overview along with a critical appraisal of available methods for uncertainty propagation of linear systems subjected to dynamic loading. All uncertain structural properties are treated as random quantities by employing a stochastic approach. The loading can be either of deterministic or stochastic nature, described by white noise, filtered white noise, and more generally, by a Gaussian stochastic process.The assessment of the variability of the uncertain response in terms of the mean and variance is described by reviewing the random eigenvalue problem and procedures to evaluate the first two moments of the stochastic (uncertain) response. Computational procedures which are efficiently applicable for general FE-models are the focus of this work.Most recent developments for the reliability assessment–besides a retrospective review–are summarized, with particular emphasis on numerical Monte Carlo Simulation approaches. This review comprises methods to assess the first excursion probability directly by efficient numerical methods. General “black box” procedures and approaches applicable only for linear systems are critically discussed. Specific procedures applicable to linear systems subjected to general Gaussian excitation are subsequently addressed. Methods applicable for deterministic structural systems are introduced first. Finally, a procedure to exploit the solutions for deterministic linear systems for stochastic uncertain systems in an efficient manner is described.     

Reliability-based optimization of steel truss arch bridges

A reliability-based optimization approach is developed and applied to minimize the weight of steel truss arch bridges subject to probabilistic (the overall probability failure of the structure) and deterministic (stress and deflection) constraints. The method intelligently integrates the genetic algorithm (GA), the finite element method and the first order reliability method. A real-coded/integer-coded method is used to realistically represent the values of the design variables. Three GA operators consisting of constraint aggregate selection procedure, arithmetic crossover, and non-uniform mutation are proposed. The finite element method (FEM) and the first order reliability method are used to compute the value of the probabilistic and deterministic constraint functions. A numerical example involving a detailed computational model of a long span steel arch bridge with a main span of 550 m is presented to demonstrate the applicability and merits of the present method. Finally, several important parameters in the present method are discussed.     

Reliability-based fatigue design of wind-turbine rotor blades

A probabilistic model for analysis of the safety of a wind-turbine rotor blade against fatigue failure in flapwise bending is presented. The model is based on a Miner's rule approach to cumulative damage and capitalizes on a conventional S–N curve formulation for fatigue resistance in conjunction with a new ‘distorted Weibull' distribution for representation of wind-induced bending moment ranges. The model accounts for inherent variability and statistical uncertainty in load and resistance, and model uncertainties are also included. The model is applied to an analysis of the reliability of a site-specific wind turbine of a prescribed make. A 20-year design lifetime is considered. The probability of fatigue failure in flapwise bending of the rotor blade is calculated by means of a first-order reliability method. It is demonstrated how the reliability analysis results can be used to calibrate partial safety factors for load and resistance for use in conventional deterministic fatigue design.     

Dominant failure modes in stochastic structural systems

In an analysis of redundant structural systems in which either or both loading systems and/or member resistances are stochastic variables, all modes of failure are potentially of significance in the calculation of structural reliability. In practice, however, many modes do not contribute very much, and a problem has been to identify those modes which are stochastically dominant.In this paper a general, iterative procedure called the Truncates Enumeration Method [TEM] to determine the most stochastically dominant modes is derived from successive systematic curtailment of the results which would be obtained by complete enumeration. In this way, it is shown that the procedure presented has the capability to produce all dominant modes to within the accuracy of the criteria used for curtailment. The method is similar to that proposed by Murotsu et al.It is also shown that the incremental load method (ILM), proposed by Moses et al., has certain features common to TEM, that both techniques are essentially incremental in nature and that both methods produced the same mode failure probability statement, each using quite distinct procedures. It is finally argued that the methods are not restricted merely to the materials behaviour properties studied thus far by their proponents.