面向设计应用的地震动空间相干函数模型

本文对现有的常用地震动空间相干模型进行了总结,提出了一个新的面向工程抗震设计应用的形式统一的地震动空间相干函数模型,在此基础上推导出了多点地震反应谱和功率谱计算所需要的振型组合系数的解析表达式,避免了耗费时间的数值积分运算。本文模型与计算方法使多点地震激励下结构响应的计算时间减低至积分方法的1/20以下,使多点地震反应谱方法和多点地震功率谱方法在计算时间方面实用化。     

A class of inhomogeneous shear models for seismic analysis of landfills

An analytical/numerical procedure is developed to calculate the shear elasto-plastic earthquake response of hill-shaped landfills. Landfill response is evaluated on the basis of newly developed one-dimensional inhomogeneous shear beam models. In these models, the nonhomogeneity of landfill materials is taken into account by assuming a specific variation of stiffness properties along the depth. Closed-form analytical expressions are derived for natural frequencies, modal displacements, modal participation factors, absolute accelerations and maximum shear strains. Parametric results are presented in graphical and tabular form and conclusions are drawn. Within a numerical implementation framework of the above formulation, the landfill materials may be modeled by an elasto-plastic hysteretic model following the principles of flow or incremental plasticity. The entire numerical procedure may be executed on a personal computer and consequently qualifies as a versatile tool for conducting preliminary design calculations or parametric-type investigations. Using this newly developed procedure, the seismic response of the Fresh Kills landfill in New York City is investigated.     

A modal combination rule for spatially varying seismic motions

The spatial variability of seismic ground motion is an important aspect for the earthquake resistant design of extended facilities. A modified response spectrum model, which addresses the problem of multiply supported structures subjected to imperfectly correlated seismic excitations, has already been developed (see References 1 and 2). The present paper proposes a modal combination rule for the case of non-uniform seismic input, which would be used together with the modified response spectrum model in order to compute physical responses. This rule, which accounts for modal cross-correlations, is an extension to an existing rule for the case of uniform seismic motions. It modifies the existing modal cross-correlation coefficients through a correction factor which depends on structural properties and on the characteristics of the wave propagation phenomenon. Finally, some practical considerations on the theoretical development are addressed. They aim at suggesting reasonable simplifications which render the modal combination rule more appealing for engineering purposes. The proposed practical combination rule is validated through a numerical experiment which also characterizes the effect of non-uniform seismic input on modal cross-correlation.     

Seismic behavior of a post-tensioned integral bridge including soil–structure interaction (SSI)

Current practice usually pays little attention to the effect of soil–structure interaction (SSI) on seismic analysis and design of bridges. The objective of this research study is to assess the significance of SSI on the modal with geometric stiffness and seismic response of a bridge with integral abutments that has been constructed using a new bridge system technology. Emphasis is placed on integral abutment behavior, since abutments together with piers are the most critical elements in securing the integrity of bridge superstructures during earthquakes. Comparison is made between analytical results and field measurements in order to establish the accuracy of the superstructure–abutment model. Sensitivity studies are conducted to investigate the effects of foundation stiffness on the overall dynamic and seismic response of the new bridge system.     

Analytical solution of seismic response of base-isolated structure with supplemental inerter

Closed-form solutions are derived for the modal characteristics and seismic response of a base-isolated structure equipped with additional inerters. By simplifying the structure-isolator-inerter system in terms of the two-degree-of-freedom (2DOF) model, the modal frequencies, mode shapes, damping ratios, and participation factors of the system are derived. Consequently, analytical seismic response solutions are formulated by the modal superposition method. Utilizing these analytical solutions, an extensive parametric study has been carried out to investigate the effect of supplement inerters on both the modal characteristics and seismic response of the structure-isolator-inerter system. There is a critical inertance leading to the zero second modal participation factor (ie, the disappearance of the second modal response). The associated critical inertance ratio is derived in closed form as well. Moreover, it is observed that the reduction of deformation of isolators by increasing the inertance may be offset by the increase in relative displacements of the superstructure. To circumvent this adverse effect, an optimal range of inertance is identified whereby both the deformation of isolators and the relative displacement of the superstructure are mitigated concurrently.     

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity- wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load- deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.     

A cantilever beam analogy for quantifying higher mode effects in multistorey buildings

This paper examines higher mode effects in systems where the ductile mechanism for seismic design is the base moment‐rotation response. The modal properties of flexural and shear beams with uniform mass and elasticity and with a variable amount of base rotational restraint are derived. As the base fixity is released, the first mode becomes the rigid body rotation of the beam about the base, but the higher modes change much less, particularly for the shear beam model. Most response quantities that are of interest in the seismic design of typical mid‐rise buildings are controlled by the first two lateral modes, except at locations along the height where the second mode contributes little. However, the third and higher lateral modes are more significant for high‐rise buildings. Based on the theory of uniform cantilever shear beams, expressions are developed to avoid the need for a modal analysis to estimate the overturning moment, storey shear, and floor acceleration envelopes. Considering the measured response from the shake table testing of a large‐scale eight‐storey controlled rocking steel braced frame, the proposed expressions are shown to be of similar or better accuracy to a modified modal superposition technique, which combines the higher mode response from an elastic modal analysis with the response associated with achieving the maximum base overturning moment according to an inverted triangular load distribution. Because the proposed method uses only parameters that are available at the initial design stage, avoiding the analysis of a structural model, it is likely to be especially useful for preliminary design. Copyright © 2015 John Wiley & Sons, Ltd.     

A method for stochastic seismic response analysis of non-classically damped structures

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain, The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response), Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy, This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy~     

Earthquake damage potential and critical scour depth of bridges exposed to flood and seismic hazards under lateral seismic loads

Many bridges located in seismic hazard regions suffer from serious foundation exposure caused by riverbed scour. Loss of surrounding soil significantly reduces the lateral strength of pile foundations. When the scour depth exceeds a critical level, the strength of the foundation is insufficient to withstand the imposed seismic demand, which induces the potential for unacceptable damage to the piles during an earthquake. This paper presents an analytical approach to assess the earthquake damage potential of bridges with foundation exposure and identify the critical scour depth that causes the seismic performance of a bridge to differ from the original design. The approach employs the well-accepted response spectrum analysis method to determine the maximum seismic response of a bridge. The damage potential of a bridge is assessed by comparing the imposed seismic demand with the strengths of the column and the foundation. The versatility of the analytical approach is illustrated with a numerical example and verified by the nonlinear finite element analysis. The analytical approach is also demonstrated to successfully determine the critical scour depth. Results highlight that relatively shallow scour depths can cause foundation damage during an earthquake, even for bridges designed to provide satisfactory seismic performance.     

The complete SRSS modal combination rule

The complete Square‐Root‐of‐Sum‐of‐Squares (c‐SRSS) modal combination rule is presented. It expresses the structural response in terms of uncoupled SDOF modal responses, yet accounting fully for modal response variances and cross‐covariances. Thus, it is an improvement over the classical SRSS rule which neglects contributions from modal cross‐covariances. In the c‐SRSS rule the spectral moments of the structural response are expressed rigorously in terms of the spectral moments of uncoupled modal responses and of some coefficients that can be computed straightforwardly as a function of modal frequencies and damping, without involving the computation of cross‐correlation coefficients between modal responses. An example shows an application of the c‐SRSS rule for structural systems with well separated and closely spaced modal frequencies, subjected to wide‐band and narrow‐band excitations. Comparisons with response calculations using the SRSS and the Complete Quadratic Combination rules are given and discussed in detail. Based on the c‐SRSS rule a response spectrum formulation is introduced to estimate the maximum structural response. An example considering a narrow‐band excitation from the great Mexico earthquake of September 19, 1985, is given and the accuracy of the response spectrum formulation is examined. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic dynamic response by approximate methods

Current seismic safety evaluation for earth dams relies on approximate methods of analysis for prediction of non-linear, transient, dynamic response. One of these approximate methods uses a Strain Reduction Factor (SRF), and has been widely applied in a variety of one-dimensional and two-dimensional soil structural analyses. A second method considered, Equivalent Temporal Damping (ETD), has been previously applied to several seismic dynamic analyses of earth dams. The relative accuracy of the two methods is assessed by comparing them with incremental plasticity, nearly exact numerical solutions. For a simple shear element subjected to deterministic and non-stationary random input accelerations, a serious overprediction of the maximum peak shear response occurs by the SRF method, whereas the ETD results agree very closely with the incremental plasticity solutions. The SRF and ETD methods are also applied to seismic dynamic response analysis of a Vertical Soil Column system, and the same trends as established in the previous case are observed. It is concluded that, in lieu of combined incremental plasticity and finite difference or finite element numerical solutions, the ETD approach is the more accurate of the methods tested for seismic dynamic response analysis of earth dams.     

Response analysis of flexible MDF systems for multiple-support seismic excitations

Two practical approaches, response spectrum and time-history methods, are developed to evaluate the response of flexible multi-degree-of-freedom (MDF) systems, notably long-span bridges, to multiple-support seismic excitations. For practical convenience, ground motions within a group of adjacent supports on continuous soil or rock are assumed to be uniform and synchronized, while those of different groups are treated as non-uniform and uncorrelated. The response spectrum analysis is extended to include the cross-correlation of modal responses, which prove important when closely spaced modal frequencies exist. An example of the significance of multiple-support excitations is illustrated by application to a suspension bridge. Qualitatively comparable effects can be expected for other bridges of similar type or dimensions.     

SEISMIC MONITORING OF A BRIDGE: ASSESSING DYNAMIC CHARACTERISTICS FROM BOTH WEAK AND STRONG GROUND EXCITATIONS

An array of 24 strong-motion accelerometers produced records for the New-Lian River Bridge, a five-span continuous bridge, during 25 February 1995 earthquake (weak motion) and 25 June 1995 earthquake (strong motion). This paper describes the application of linear discrete-time system identification methodology to the array of strong-motion measurements, in order to assess seismic response characteristics of the bridge. The structural system identification will concentrate not only on the global identification but also on the local structural system identification. Results of this application show that: (1) weak and strong ground excitation will induce significant differences on the dynamic response of the bridge; (2) linear models provide an excellent fit to the measured motions of the bridge from the records of these two seismic events; (3) the rigid-body rocking of the bridge pier during strong shaking is significant and cannot be ignored during identification; (4) the transverse motion at mid-span of the bridge is controlled by the quasi-static response from the boundary system and this phenomenon is quite significant during strong ground excitation. Also, systematic estimates of modal damping ratio and equivalent assessments of pier stiffness developed in the bridge during earthquake are discussed. © 1997 by John Wiley & Sons, Ltd.     

Seismic response of continuous span bridges through fiber-based finite element analysis

1 Introduction Older design codes based on equivalent elastic force approaches proved to be ineffective in preventing damage caused by destructive earthquakes. After recent major earthquakes (e.g. Northridge 1994, Kobe 1995, and Kocaeli 1999 etc.), the necessity for using more accurate methods, which explicitly account for geometrical nonlinearities and material inelasticity, to evaluate seismic demand on structures, became evident. Within this framework, two analysis tools are currently offe…     

强震区非对称连续梁桥地震响应及性能评价

为研究高烈度地区不等跨连续梁桥的抗震性能，依托某高速公路上一座主跨为（40+60+35）m的典型不等跨连续梁桥，建立其动力分析有限元模型，获得该桥的模态特性。在E1概率和E2概率两种地震水平作用下，同时采用反应谱分析和时程分析法，对不等跨桥梁结构的地震响应进行分析。最后根据桥墩验算截面的弯矩-曲率关系曲线，探讨该桥梁的抗震性能。研究结果表明：动态时程反应分析与反应谱分析所得的结果基本吻合，由于反应谱分析假定结构线弹性状态而时程反应分析考虑了材料的弹塑性，在E2概率水平下，两者个别响应值有较大差别；由于反应谱法是对各阶模态下最大响应的组合，动态时程反应分析是同一时刻各地震波引起的结构响应的组合，因而时域和频域计算结果会存在一些误差，频域结果偏于保守；E1、E2概率地震作用下，主桥桥墩检算截面仍然在弹性范围内工作，满足弹性设计要求。     

土石坝地震响应的非线性剪切条模型与对比分析

对一维剪切条计算模型进行改进,提出了土石坝非线性地震反应的简化计算方法。首先将坝体沿坝高离散为一系列的具有不同剪切刚度与阻尼比等参数特性的层状体系,建立了各层的振动控制方程及其边值条件,进而采用数学物理方程方法进行了求解,确定了体系的振动特性,并根据振型叠加原理和Duhamel积分确定了坝体地震反应的线弹性解。采用等价线性化方法考虑坝料的动力非线性性质,通过对线弹性地震响应的反复迭代计算,使得各层土的模量和阻尼比与其相应的剪应变水平相协调,确定出与非线性坝体系统相等效的线性解答,并将所得到的地震响应作为非线性地震响应的近似解。最后,以均质坝和心墙坝作为算例进行了具体的数值计算,将所得结果与有限元数值解进行对比分析,论证了所提方法的适用性和合理性。     

Structural response for six correlated earthquake components

The paper examines the effect on the structural response of the inevitable correlation which exists between the six earthquake components acting along a set of structural axes. The rotational components are expressed in terms of the spatial derivatives of the translational components. For the calculation of response, modal analysis is employed so that ground response spectra can also be used as seismic input. A methodology is developed to obtain the maximum mean square response which can occur in a structure, irrespective of its orientation with respect to the impinging seismic waves. The application of this methodology for the calculation of design response is advocated, especially for asymmetric structures. For the assumed model of seismic wave motion, the numerical results show a significant contribution to the response from the rotational components. This contribution is, however, expected to be reduced by structural foundation averaging and interaction effects. Further studies with more complete models of seismic wave motions, and their interaction with structural foundations, are thus warranted for a realistic evaluation and characterization of the rotational inputs for design purposes.     

多点地震动激励下的高效反应谱方法

在多点地震动激励下,结构的反应谱分析计算非常耗时。结构的地震谱响应可以用若干个相关系数来表示,如果相关系数使用解析形式来表示,可以大大减少计算时间。本文提出了空间相干函数的近似表达式,并对其系数进行积分,得到了相关系数的解析式。该解析表达式根据克拉夫-彭津（Clough-Penzien）和胡聿贤自功率谱密度函数模型推导得出。案例桥梁的计算结果表明,相关系数的近似解析表达式具有足够的工程精度,用于多点地震反应谱计算具有极高的效率。      

Quasi‐static and pseudo‐dynamic testing of unbonded post‐tensioned rocking bridge piers with external replaceable dissipaters

It has been well documented that following a major earthquake a substantial percentage of economic loss results from downtime of essential lifelines in and out of major urban centres. This has thus led to an improvement of both performance‐based seismic design philosophies and to the development of cost‐effective seismic structural systems capable of guaranteeing a high level of protection, low structural damage and reduced downtime after a design‐level seismic event. An example of such technology is the development of unbonded post‐tensioned techniques in combination with rocking–dissipating connections. In this contribution, further advances in the development of high‐performance seismic‐resistant bridge piers are achieved through the experimental validation of unbonded post‐tensioned bridge piers with external, fully replaceable, mild steel hysteretic dissipaters. The experimental response of three 1 : 3 scale unbonded, post‐tensioned cantilever bridge piers, subjected to quasi‐static and pseudo‐dynamic loading protocols, are presented and compared with an equivalently reinforced monolithic benchmark. Minimal physical damage is observed for the post‐tensioned systems, which exhibit very stable energy dissipation and re‐centring properties. Furthermore, the external dissipaters can be easily replaced if severely damaged under a major (higher than expected) earthquake event. Thus, negligible residual deformations, limited repair costs and downtime can be achieved for critical lifeline components. Satisfactory analytical–experimental comparisons are also presented as a further confirmation of the reliability of the design procedure and of the modelling techniques. Copyright © 2008 John Wiley & Sons, Ltd.