随机结构动力可靠度估计算法的对比分析

对比分析了随机结构动力可靠度计算的三种估计算法.渐进展开法是基于Laplace算法对概率积分进行渐进估计的,此法通过计算最大被积分式值对应点,并将其代入概率积分的渐进估计表达式求解失效概率.由于概率积分的主要贡献来自于最大被积分式值对应点的周围,因此本文的重要抽样法假定重要抽样函数的最大似然值等于最大被积分式值对应点值.极值分布-泰勒展开法首先通过结构随机参数的极值分布函数给出失效概率的表达式,随后利用泰勒展开法对失效概率进行估计,其中采用中心差分法对极值分布函数的梯度进行估算.最后应用三种算法和Monte Carlo法对受高斯白噪声激励作用的单自由度随机结构进行了计算,结果表明三种方法不但运算简便,而且对比Monte Carlo法计算效率有显著提高.     

地震荷载作用下相关性对结构可靠度的影响

当一个结构系统承受偶发的不确定地震荷载时,其结构单元或元素失效无效的相关性在系统可靠度评估中的十分重要,该相关性的产生,是由于结构系统同时受某一基本随机变量的影响,如地震峰值地面加速度,荷载效应转换或构件承载力等,本文分析了考虑该相关的必要性,此外,还给出了一个考虑相关性的简单方法,可用于估计一个等关联性和等可靠度单元的并联系统的失效概率,该方法由拉斯渐进副近积分法导出。     

Improvements and Corrections to AT123D Code

Although based on exact analytical solutions, semi‐analytical solute transport models can have significant numerical error in applications with high frequency oscillatory source terms and when parameter value combinations cause series solution approximations to converge slowly. Methods for correcting these numerical errors are presented and implemented in the AT123D code, which employs Green's functions to represent point, linear, and rectangular prismatic source zones. In order to increase its computational accuracy, a Romberg numerical integration scheme was added to AT123D with prespecified error criteria, variable time stepping, and partitioning of the integral to handle rapidly changing source terms. More rapidly converging series solution approximations for the Green's functions were also incorporated to improve both accuracy and computational efficiency for finite‐depth aquifers. AT123D also has been modified to eliminate redundant calculations at points where approximate steady‐state conditions have been reached to improve computational efficiency during numerical integration. These modifications help to decrease computer run times that can be excessive for three‐dimensional problems with large numbers of computational points, small time steps, and/or long simulation time periods. Errors in the original AT123D code also were corrected in this modified version, AT123D‐AT, in order to accurately simulate finite‐duration (pulse) source releases.     

Closed‐Form Approximations for Two‐Dimensional Groundwater Age Patterns in a Fresh Water Lens

Simple closed‐form approximations are presented for calculating the steady‐state groundwater age distribution in two‐dimensional vertical cross sections of idealized fresh water lenses overlying salt water, for aquifers that are vertically semi‐infinite and of finite thickness. The approximations are developed on the basis of existing one‐dimensional analytical solutions for travel‐time calculation in fresh water lenses and approximate streamline formulations. The two‐dimensional age distributions based on the closed‐form solutions match convincingly with numerical simulations. As expected, notable deviations from the numerical solution are encountered at the groundwater flow divide and when submarine groundwater discharge occurs. Ratios of recharge over hydraulic conductivities are varied to explore how the magnitude of the deviations changes, and it is found that the approximate closed‐form solutions perform well over a range of conditions found in natural systems.     

Empirical Orthogonal Function (EOF) analysis of spatial random fields: Theory,accuracy of the numerical approximations and sampling effects

Empirical Orthogonal Function (EOF) analysis of spatial random fields involves calculation of the eigenfunctions of the covariance kernel of the field. For real-world applications, a numerical approximation is necessary because the process is spatially discretized. An approximation for two-dimensional fields is proposed and then, analytical solutions of the integral problem are derived and used to study the accuracy of the numerical approximations. Sampling effects are also considered.     

Application of saddlepoint approximation in reliability analysis of dynamic systems

The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function (CDF) of the performance variable. The failure probability is obtained as the value of the complement CDF at a specif ied threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function (CGF) of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and effi ciency of the proposed methodology.     

Reliability‐based robust control for uncertain dynamical systems using feedback of incomplete noisy response measurements

A reliability‐based output feedback control methodology is presented for controlling the dynamic response of systems that are represented by linear state‐space models. The design criterion is based on a robust failure probability for the system. This criterion provides robustness for the controlled system by considering a probability distribution over a set of possible system models with a stochastic model of the excitation so that robust performance is expected. The control command signal can be calculated using incomplete response measurements at previous time steps without requiring state estimation. Examples of robust structural control using an active mass driver on a shear building model and on a benchmark structure are presented to illustrate the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Traveltime approximation in vertical transversely isotropic layered media

The well‐known asymptotic fractional four‐parameter traveltime approximation and the five‐parameter generalised traveltime approximation in stratified multi‐layer transversely isotropic elastic media with a vertical axis of symmetry have been widely used for pure‐mode and converted waves. The first three parameters of these traveltime expansions are zero‐offset traveltime, normal moveout velocity, and quartic coefficient, ensuring high accuracy of traveltimes at short offsets. The additional parameter within the four‐parameter approximation is an effective horizontal velocity accounting for large offsets, which is important to avoid traveltime divergence at large offsets. The two additional parameters in the above‐mentioned five‐parameter approximation ensure higher accuracy up to a given large finite offset with an exact match at this offset. In this paper, we propose two alternative five‐parameter traveltime approximations, which can be considered extensions of the four‐parameter approximation and an alternative to the five‐parameter approximation previously mentioned. The first three short‐offset parameters are the same as before, but the two additional long‐offset parameters are different and have specific physical meaning. One of them describes the propagation in the high‐velocity layer of the overburden (nearly horizontal propagation in the case of very large offsets), and the other characterises the intercept time corresponding to the critical slowness that includes contributions of the lower velocity layers only. Unlike the above‐mentioned approximations, both of the proposed traveltime approximations converge to the theoretical (asymptotic) linear traveltime at the limit case of very large (“infinite”) offsets. Their accuracy for moderate to very large offsets, for quasi‐compressional waves, converted waves, and shear waves polarised in the horizontal plane, is extremely high in cases where the overburden model contains at least one layer with a dominant higher velocity compared with the other layers. We consider the implementation of the proposed traveltime approximations in all classes of problems in which the above‐mentioned approximations are used, such as reflection and diffraction analysis and imaging.     

A fast integral equation solver for 3D induction well logging in formations with large conductivity contrasts

Simulation of induction logging responses in formations with large conductivity contrasts is an important but challenging problem due to the singularity of a linear system caused by large contrasts. Also, three‐dimensional (3D) analysis of complex geophysical structures usually encounters high computational demands. In this paper, a pre‐corrected fast Fourier transform (pFFT)‐accelerated integral equation method is applied to overcome these difficulties. In the approach, the entire formation is included in the solution domain. The volume integral equation is set up in the region based on the fact that the total field is the summation of the excitation field and the secondary field. The emitted field by the transmitter coil (treated as a magnetic dipole) is regarded as the excitation of the system. Then the method of moments (MoM) is used to solve the integral equation. To reduce the high computational requirements of the MoM, the pFFT method is used to speed up the solution of the matrix equation and reduce the memory requirement as well. The resultant method is capable of computing induction logging problems involving large and complex formations. For problems with high conductivity contrasts, the solution of the matrix equation usually converges very slow or even fails to converge due to the large condition number of the coefficient matrix. To overcome this difficulty, an incomplete LU pre‐conditioner is used to significantly speed up the convergence of the matrix equation, thus further reducing the computation time. Numerical results show that the present method is efficient and flexible for 3D simulation of induction logging and is specifically superior for problems with high conductivity contrasts.     

Gravimetric survey terrain correction using linear analytical approximation

Various methods for computing the terrain correction in a high‐precision gravity survey are currently available. The present paper suggests a new method that uses linear analytical terrain approximations. In this method, digital terrain models for the near‐station topographic masses are obtained by vectorizing scan images of large‐scaled topographic maps, and the terrain correction computation is carried out using a Fourier series approximation of discrete height values. Distant topography data are represented with the help of digital GTOPO30 and Shuttle Radar Topography Mission cartographic information. We formulate linear analytical approximations of terrain corrections for the whole region using harmonic functions as the basis of our computational algorithm. Stochastic modelling allows effective assessment of the accuracy of terrain correction computation. The Perm Krai case study has shown that our method makes full use of all the terrain data available from topographic maps and digital terrain models and delivers a digital terrain correction computed to a priori precision. Our computer methodology can be successfully applied for the terrain correction computation in different survey areas.     

Modeling Variably Saturated Multispecies Reactive Groundwater Solute Transport with MODFLOW‐UZF and RT3D

A numerical model was developed that is capable of simulating multispecies reactive solute transport in variably saturated porous media. This model consists of a modified version of the reactive transport model RT3D (Reactive Transport in 3 Dimensions) that is linked to the Unsaturated‐Zone Flow (UZF1) package and MODFLOW. Referred to as UZF‐RT3D, the model is tested against published analytical benchmarks as well as other published contaminant transport models, including HYDRUS‐1D, VS2DT, and SUTRA, and the coupled flow and transport modeling system of CATHY and TRAN3D. Comparisons in one‐dimensional, two‐dimensional, and three‐dimensional variably saturated systems are explored. While several test cases are included to verify the correct implementation of variably saturated transport in UZF‐RT3D, other cases are included to demonstrate the usefulness of the code in terms of model run‐time and handling the reaction kinetics of multiple interacting species in variably saturated subsurface systems. As UZF1 relies on a kinematic‐wave approximation for unsaturated flow that neglects the diffusive terms in Richards equation, UZF‐RT3D can be used for large‐scale aquifer systems for which the UZF1 formulation is reasonable, that is, capillary‐pressure gradients can be neglected and soil parameters can be treated as homogeneous. Decreased model run‐time and the ability to include site‐specific chemical species and chemical reactions make UZF‐RT3D an attractive model for efficient simulation of multispecies reactive transport in variably saturated large‐scale subsurface systems.     

弹性波边界元法正演模拟

弹性波边界元地震模型方法（ＢＥＥＳＭ），实现了二维和三维问题的纵、横波及转换波的同时模拟，并且能模拟任意复杂构造的地震声波正演模型．根据地震模型的特点，本文发展了数值积分计算与矩阵消元同步进行的块状高斯消元法；用解析法处理奇异积分；用无限元法处理边界吸收问题；采用单元长度随介质速度和计算频率变化的变单元算法，及自动剖分单元等技术，提高了计算精度，节省了内存，缩短了计算时间．     

Probabilistic analysis of peak response of MDOF systems with uncertain PSD function

The use of uniform hazard spectra which have the same probability of exceedance at different frequencies has been proposed for the future version of the National Building Code of Canada. Commonly used combination rules to estimate the peak responses of multi‐degree‐of‐freedom (MDOF) systems are the square root of sum of squares rule and the complete quadratic combination rule. However, the probability that the peak response of a MDOF system exceeds the one estimated by using these rules with the peak modal responses from the uniform hazard spectra cannot be inferred directly. The assessment of the probability of exceedance of the peak response of MDOF systems is presented by considering that the uncertainty in seismic excitation due to all potential earthquakes can be lumped in the power spectral density function of the ground acceleration with uncertain model parameters. This probability is evaluated based on the random vibration of linear systems and the first‐order reliability method. It is found that the under‐ or over‐estimations are less than about 5 or 10% if the modal contributions are not within 10–90% of, or not within 20–80% of, the absolute sum of the effective modal peak responses, respectively. Otherwise, severe under‐ or over‐estimation could result. Copyright © 2002 John Wiley & Sons, Ltd.     

Seismic hybrid simulation of a nonductile RC building with severe damage to multiple columns

Reinforced concrete frame structures built prior to the mid‐1970s are susceptible to brittle column failure under seismic action, potentially leading to progressive collapse of the structure. The behavior of columns susceptible to brittle shear‐axial failure has been studied previously but rarely has the interaction between damaged columns and the surrounding three‐dimensional structure been investigated experimentally and at full scale. In this study, as the second in a series of hybrid simulations, two full‐scale reinforced concrete columns of a representative pre‐1970s structure were tested at the Multi‐axial Full‐scale Substructure Testing and Simulation (MUST‐SIM) laboratory. Through the use of hybrid simulation, the interaction of the columns with the surrounding structure is studied under a severe seismic motion including vertical excitation. The computational model representing the remainder of the representative 10‐story structure is created in the computer program OpenSees. During the hybrid simulation, both physical specimens experience significant loss of shear and axial strength, and the effects of these failures on the surrounding system are described. The three‐dimensional computational model in OpenSees allowed for analytical flexural‐axial failure of a third column in the structure to occur. The effects of these multiple failures on the response of a full structural system under seismic action are quantified, and the progressive collapse resistance mechanisms are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Effects of Multiscale Anisotropy on Basin and Hyporheic Groundwater Flow

Various subsurface flow systems exhibit a combination of small‐scale to large‐scale anisotropy in hydraulic conductivity (K). The large‐scale anisotropy results from systematic trends (e.g., exponential decrease or increase) of K with depth. We present a general two‐dimensional solution for calculation of topography‐driven groundwater flow considering both small‐ and large‐scale anisotropy in K. This solution can be applied to diverse systems with arbitrary head distribution and geometry of the water table boundary, such as basin or hyporheic flow. In a special case, this solution reduces to the well‐known Tóth model of uniform isotropic basin. We introduce an integral measure of flushing intensity that quantifies flushing at different depths. Using this solution, we simulate heads and streamlines and provide analyses of flow structure in the flow domain, relevant to basin analyses or hyporheic flow. It is shown that interactions between small‐scale anisotropy and large‐scale anisotropy strongly control the flow structure. In the classic Tóth flow model, the flushing intensity curves exhibit quasi‐exponential decrease with depth. The new measure is capable of capturing subtle changes in the flow structure. Our study shows that both small‐ and large‐scale anisotropy characteristics have substantial effects that need to be integrated into analysis of topography‐driven flow.     

钢框架结构的非线性静力抗震可靠性分析 II:可靠度指标及其灵敏度

将有限元反应及其灵敏度分析与结构可靠度分析的近似解析方法结合起来,可以进行具有隐式功能函数的大型复杂结构的可靠性分析。在基于位移的非线性纤维梁柱单元及其灵敏度直接微分表达式的基础上,通过力学变换、概率变换和反应灵敏度,将结构可靠度计算方法FORM和SORM与有限元方法有机地集成在一起。依据现行抗震设计规范,建立了钢框架结构典型构件承载能力和结构层间变形能力的抗震极限状态方程,利用地震作用的等效随机静力模型,采用非线性有限元静力可靠度方法,对一实际工程结构的抗震可靠度及其灵敏度进行了概率分析和评价,结果表明:尽管在大震作用下该结构的层间弹塑性变形可靠度较高,但是构件极限承载能力的可靠度指标较低,仍然存在失效的可能性。因此,仅验算"小震"作用下结构的承载能力可靠度和"大震"作用下结构的变形能力可靠度是不够的,还需要验算在"中震"和"大震"作用下结构的极限承载能力可靠度。     

钢框架结构的非线性静力抗震可靠性分析Ⅱ:可靠度指标及其灵敏度

将有限元反应及其灵敏度分析与结构可靠度分析的近似解析方法结合起来,可以进行具有隐式功能函数的大型复杂结构的可靠性分析。在基于位移的非线性纤维梁柱单元及其灵敏度直接微分表达式的基础上,通过力学变换、概率变换和反应灵敏度,将结构可靠度计算方法FORM和SORM与有限元方法有机地集成在一起。依据现行抗震设计规范,建立了钢框架结构典型构件承载能力和结构层间变形能力的抗震极限状态方程,利用地震作用的等效随机静力模型,采用非线性有限元静力可靠度方法,对一实际工程结构的抗震可靠度及其灵敏度进行了概率分析和评价,结果表明：尽管在大震作用下该结构的层间弹塑性变形可靠度较高,但是构件极限承载能力的可靠度指标较低,仍然存在失效的可能性。因此,仅验算“小震”作用下结构的承载能力可靠度和“大震”作用下结构的变形能力可靠度是不够的,还需要验算在“中震”和“大震”作用下结构的极限承载能力可靠度。     

在大震下 RC框架结构基于Pushover方法的失效相关性分析

目前,基于性能的建筑结构抗震设计成为世界各国土木工程界研究的热点之一.结构体系可靠度理论是进行结构性能分析的重要的理论基础.在结构体系可靠度的计算中,一个急待解决的问题是结构构件或截面间的失效相关性问题.本文基于pushover方法,采用Monte Carlo法和随机有限元法,在小震研究成果的基础上,进一步研究了钢筋混凝土框架结构在大震情况下的失效相关性问题,分别得出了框架梁、柱在大震作用下的部分失效相关性规律.