多年冻土区桩基础桥墩随机地震反应分析

将随机振动理论、粘弹性边界条件的二维波动法以及结构动力分析有限元法结合起来，考虑场地地震动为零均值的高斯平稳随机过程，对青藏铁路多年冻土区桩基础桥墩进行了随机地震反应分析，计算了9度地震作用下桥墩随机地震响应最大值的均值和均方差，分析了冻土层及桥墩高度对桥墩随机地震响应的影响。     

Analysis of tubular steel bridge piers

A one‐dimensional model is proposed for the static and dynamic analysis of tubular steel bridge piers subjected to strong ground motions. The present formulation does not require experimental results nor shell analysis to obtain the constitutive equation of the model, which shows strength deterioration. The material properties and dimensions of bridge piers are required for static and dynamic analysis of the present model. The present analysis consists of two steps. The first step is to obtain the stress and strain relationship of the base plastic‐hinge region, where local inelastic buckling is observed. The modified Shanley's model and fiber elements are used to establish the compressive skeleton curve. The strength deterioration is taken into account in the resulting constitutive model. The second step is to analyze static and dynamic responses of tubular steel bridge piers. For overall analysis, the base plastic‐hinge region is discretized in the circumferential direction by using fiber elements whose constitutive equation was obtained in the first step. The validity of the present model has been confirmed through comparisons with existing experimental results. Copyright © 2005 John Wiley & Sons, Ltd.     

青藏铁路多年冻土区桥墩随机地震反应分析

利用随机振动理论和动力分析的有限元方法,将场地地震动考虑为均值为零的高斯平稳随机过程,对青藏铁路多年冻土区典型桥墩进行了随机地震反应分析,计算了9度地震作用下桥墩随机地震响应的统计特性,分析了冻土层对桥墩地震反应的影响。研究结果表明,冻土层对桥墩地震反应具有显著影响。     

A computational procedure for the implementation of equivalent linearization in finite element analysis

This paper deals with the practical implementation of the statistical equivalent linearization method (EQL) in conjunction with general FE‐analysis to evaluate non‐linear structural response under random excitation. A computational procedure is presented which requires the non‐linear part of the system to be subdivided into suitable sub‐domains (elements). Each element is independently linearized using only a minimum number of co‐ordinates. A local co‐ordinate system is introduced using linear transformations of the global (master) degrees of freedom. Restoring forces and non‐linear constitutive laws are defined by the local co‐ordinates of each element. The linearization coefficients are further transformed back to establish the global linearized system. The procedure has, on one hand, the ability to use any desired linearization criterion and, on the other hand, it can be combined with highly developed procedures to determine the response of arbitrary large FE‐models. To illustrate the applicability of the procedure, two different non‐linear systems are analysed under bi‐directional earthquake excitation. Copyright © 2000 John Wiley & Sons, Ltd.     

大跨度斜拉管线桥地震反应分析

首先利用Newmark-β法和修正的Newton-Raphson法，提出并推导了一种求解几何非线性地震反应方程的方法。利用该方法对大跨度斜拉管线桥进行了线性和非线性地震响应分析。通过结果比较，得出一些有意义的结论：几何非线性效应对斜拉管线桥的地震反应分析影响很大，在分析中不能忽略，尤其是恒载初始内力。     

An experimental study on the rocking response of bridge piers with spread footing foundations

Some spread footing foundations from real retrofitting practices in Taiwan were extended to be uneconomically large due to the restriction of foundation uplift regulated in the design code. Although rocking mode of spread footings induced from foundation uplift is not favorable in current design code, recent studies have shown that the rocking of a spread footing may have a beneficial effect on the dynamic performance of piers by reducing the earthquake forces that can be transmitted to the pier base. This implies that the plastic deformation that occurs at the pier's plastic zone can be decreased and as a result the ductility demand of piers can possibly be reduced. In order to gain a better understanding of the structural behavior related to rocking and to clarify that if the widening and strengthening of the foundations to limit the rocking mechanism of spread footing is necessary for the retrofitting work, a series of preliminary rocking experiments were performed. A total of three circular reinforced concrete columns with spread footing foundations were tested. Using pseudo‐dynamic tests and a cyclic loading test, these columns were subjected to different levels of earthquake accelerations, including a near field ground motion. The results of the tests and the rocking behavior of the footings are discussed in this paper. From the benchmark test, the difference between the response behavior of a rocking base and a fixed base foundation was highlighted. By comparing the experimental responses of the retrofitted column with the responses of the original one, the effect of the rocking mechanism on the ductility demand and strength demand of the columns was also identified. Copyright © 2010 John Wiley & Sons, Ltd.     

EQUIVALENT LINEARIZATION OF GENERALLY PINCHING HYSTERETIC,DEGRADING SYSTEMS

Many types of structural systems that undergo cycles of inelastic deformation under severe natural hazard loadings exhibit ‘pinching’ of hysteresis loops. In this paper, a generally pinching hysteretic restoring force model—an extension of the Bouc–Wen differential hysteresis model—is used in stochastic equivalent linearization of single-degree-of-freedom structural systems. The severity and rate of pinching are controlled by the hysteretic energy dissipation and the pinching level can be specified to match experimental data. Under white noise excitations, estimates of reponse statistics from linearization are shown to compare favourably with those from Monte Carlo simulation. Numerical studies on the sensitivity of the accuracy of response statistics obtained by linearization to changes in the hysteresis parameters showed that, for a range of practical cases, the linearization method can be used in lieu of simulation and that, in low-frequency systems, some hysteresis parameters may be set to a constant value a priori to reduce the number of model parameters that needs to be estimated or identified, and to simplify further random vibration analysis and/or performance evaluation studies.     

Bivariate Gaussian mixture–based equivalent linearization method for stochastic seismic analysis of nonlinear structures

To address challenges in stochastic seismic analysis of nonlinear structures, this paper further develops a recently proposed Gaussian mixture–based equivalent linearization method (GM‐ELM). The GM‐ELM uses a Gaussian mixture distribution model to approximate the probabilistic distribution of a nonlinear system response. Using properties of the Gaussian mixture model, GM‐ELM can decompose the non‐Gaussian response of a nonlinear system into multiple Gaussian responses of linear single–degree of freedom oscillators. With the set of the equivalent linear systems identified by GM‐ELM, response statistics as crossing rate and first‐passage probability can be computed conveniently using theories of linear random vibration analysis. However, the original version of GM‐ELM may lead to an inaccurate estimate because of the heuristic parameters of the linear system introduced to supplement insufficient information. To overcome this limitation and define unique equivalent linear systems, this paper proposes a further developed version of GM‐ELM, which uses a mixture of bivariate Gaussian densities instead of univariate models. Moreover, to facilitate the use of elastic response spectra for estimating the mean peak responses of a nonlinear structure, a new response spectrum combination rule is proposed for GM‐ELM. Two numerical examples of hysteretic structural systems are presented in this paper to illustrate the application of the bivariate GM‐ELM to nonlinear stochastic seismic analysis. The analysis results obtained by the bivariate GM‐ELM are compared with those obtained by the univariate GM‐ELM, the conventional equivalent linearization method, the tail equivalent linearization method, and Monte Carlo simulation. The supporting source code and data are available for download at https://github.com/yisangri/GitHub‐bGM‐ELM‐code.git     

考虑基础提离与塑性的桥墩地震反应

浅平基桥墩在承受强震作用时,其基础与地基之间会发生提离,地基土会进入塑性状态.精确模拟上述两个问题是非常困难的.本文分析中地基采用了能考虑基础提离及地基塑性的弹塑性Winkler地基模型,采用1940年El Centro(NS)地震记录作为输入,对三个不同高度的双柱式浅平基桥墩进行了非线性时程分析.研究结果表明,基础提离和地基塑性对双柱式桥墩的地震反应有很大影响.考虑地基非线性后,墩顶位移增大,剪力减小,对保护桥墩减小震害是有利的.     

高墩梁桥地震响应分析

本文将对两座高墩桥梁的地震响应进行分析,一座是连续-刚构组合梁桥,另一座是刚构桥。这两种是高墩桥梁普遍采用的桥型,对其进行详细的动力分析对此类桥梁的抗震设计具有一定的指导作用。针对这两种桥梁结构,本文首先分析直接影响结构动力响应的自振特性,从中总结高墩桥梁的特点,然后采用反应谱法、时程分析法分析结构地震响应,并对其结果进行比较,同时讨论桩-土相互作用对高墩桥梁地震响应的影响。     

Experimental research and finite element analysis of bridge piers failed in flexure-shear modes

In recent earthquakes, a large number of reinforced concrete （RC） bridges were severely damaged due to mixed flexure-shear failure modes of the bridge piers. An integrated experimental and finite element （FE） analysis study is described in this paper to study the seismic performance of the bridge piers that failed in flexure-shear modes. In the first part, a nonlinear cyclic loading test on six RC bridge piers with circular cross sections is carried out experimentally. The damage states, ductility and energy dissipation parameters, stiffness degradation and shear strength of the piers are studied and compared with each other. The experimental results suggest that all the piers exhibit stable flexural response at displacement ductilities up to four before exhibiting brittle shear failure. The ultimate performance of the piers is dominated by shear capacity due to significant shear cracking, and in some cases, rupturing of spiral bars. In the second part, modeling approaches describing the hysteretic behavior of the piers are investigated by using ANSYS software. A set of models with different parameters is selected and evaluated through comparison with experimental results. The influences of the shear retention coefficients between concrete cracks, the Bauschinger effect in longitudinal reinforcement, the bond-slip relationship between the longitudinal reinforcement and the concrete and the concrete failure surface on the simulated hysteretic curves are discussed. Then, a modified analysis model is presented and its accuracy is verified by comparing the simulated results with experimental ones. This research uses models available in commercial FE codes and is intended for researchers and engineers interested in using ANSYS software to predict the hysteretic behavior of reinforced concrete structures.     

多维地震激励作用下大跨度钢管混凝土提篮拱桥的随机响应

以某大跨度钢管混凝土提篮拱桥为例,分别研究了大跨度钢管混凝土提篮拱桥的自振特性及其在纵向激励、纵 竖向激励、纵 横向激励、纵 竖 横向激励作用下的地震响应特性。结果表明,横向激励对提篮拱桥地震响应特性有较大影响,对于多维激励情况,提篮拱桥的抗震性能并不优于平行拱,并进一步分析了原因。     

两结构高效阻尼控制系统随机动力反应分析

对由高效阻尼装置(HEDMS)连接的两单自由度相邻结构在过滤白噪声激励下的相对位移响应进行了随机分析。在对阻尼装置滞变位移等价线性化的基础上，采用虚拟激励法计算结构响应的谱密度和互谱密度，研究了该阻尼装置各参数对位移响应方差的影响以及该装置的适用范围。     

Bidirectional loading hybrid tests of square cross‐sections of steel bridge piers

Steel rectangular section columns with stiffened plates are commonly used for elevated highway bridges in the urban areas of Japan. The seismic design of bridge piers is usually performed by dynamic analysis in the horizontal direction using various independent directional seismic acceleration data. However, this simple treatment does not reflect the effect of bilateral loading as a structural response to inelastic interaction. In this study, unidirectional and bidirectional loading hybrid tests were conducted to examine the seismic response and performance of square cross‐sections of steel bridge piers subjected to bidirectional seismic accelerations. Comparison of the results of unidirectional and bidirectional loading tests revealed that the maximum load is the same as the average of unidirectional loading in the NS and EW directions; however, the maximum response displacement and residual displacement increase in proportion with hard to soft ground types. Moreover, a modified seismic design is proposed considering these bidirectional loading effects. Copyright © 2012 John Wiley & Sons, Ltd.     

平稳随机激励下随机结构非线性动力响应分析

为了在结构强震灾变过程模拟中正确反映结构参数的随机性并准确界定结构失效模式,提出一种平稳随机激励下随机结构非线性动力响应分析的简化方法.首先运用点估计法将复合非线性随机系统转化为一系列平稳随机激励下的确定性非线性结构,然后再应用成熟的等效线性化方法计算出平稳随机激励下非线性结构动力响应的各阶矩.文末进行了算例分析与验证...     

Rapid repair of severely earthquake-damaged bridge piers with flexural-shear failure mode

An experimental study was conducted to investigate the feasibility of a proposed rapid repair technique for severely earthquake-damaged bridge piers with flexural-shear failure mode. Six circular pier specimens were first tested to severe damage in flexural-shear mode and repaired using early-strength concrete with high-fluidity and carbon fiber reinforced polymers (CFRP). After about four days, the repaired specimens were tested to failure again. The seismic behavior of the repaired specimens was evaluated and compared to the original specimens. Test results indicate that the proposed repair technique is highly effective. Both shear strength and lateral displacement of the repaired piers increased when compared to the original specimens, and the failure mechanism of the piers shifted from flexural-shear failure to ductile flexural failure. Finally, a simple design model based on the Seible formulation for post-earthquake repair design was compared to the experimental results. It is concluded that the design equation for bridge pier strengthening before an earthquake could be applicable to seismic repairs after an earthquake if the shear strength contribution of the spiral bars in the repaired piers is disregarded and 1.5 times more FRP sheets is provided.     

Seismic response of bridge piers on pile groups for different soil damping models and lumped parameter representations of the foundation

This paper presents a wide parametric study aimed at elucidating the influence, on the computed seismic response of bridge piers, of two related aspects of the model: (1) the adoption of the classical hysteretic or the causal Biot's damping models for the soil and (2) the use of two different lumped parameter models of different complexity and accuracy to approximate the impedances of the pile foundation. A total of 2072 cases, including different superstructures, pile foundations, soil deposits, and seismic input signals, are studied. The results are presented so that the influence of the different parameters involved in the analysis can be assessed. From an engineering point of view, both lumped parameter models provide, in general, sufficiently low errors. The choice of the most adequate model for each case will depend not only on the configuration of the structure and the soil-foundation system but also on the assumed soil damping model, whose influence on the computed seismic responses is relevant in many cases. The nonphysical behaviour provided by the classical hysteretic damping model for the soil at zero frequency generates issues in the process of fitting the impedance functions. It is also found that larger deck displacements are predicted by Biot's model due to the higher damping at low frequencies provided by the classical hysteretic damping model.     

Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation

Fragility curves express the probability of structural damage due to earthquakes as a function of ground motion indices, e.g., PGA, PGV. Based on the actual damage data of highway bridges from the 1995 Hyogoken‐Nanbu (Kobe) earthquake, a set of empirical fragility curves was constructed. However, the type of structure, structural performance (static and dynamic) and variation of input ground motion were not considered to construct the empirical fragility curves. In this study, an analytical approach was adopted to construct fragility curves for highway bridge piers of specific bridges. A typical bridge structure was considered and its piers were designed according to the seismic design codes in Japan. Using the strong motion records from Japan and the United States, non‐linear dynamic response analyses were performed, and the damage indices for the bridge piers were obtained. Using the damage indices and ground motion indices, fragility curves for the bridge piers were constructed assuming a lognormal distribution. The analytical fragility curves were compared with the empirical ones. The proposed approach may be used in constructing the fragility curves for highway bridge structures. Copyright © 2001 John Wiley & Sons, Ltd.     

波形钢腹板混凝土箱拱地震响应分析

采用时程分析法,对三向地震动作用下的波形钢腹板混凝土箱拱新型结构的地震特性进行分析,通过与混凝土腹板的混凝土箱拱动力特性和地震响应特点的对比,得出该新型拱圈结构具有较优越的抗震性能。同时,把三向地震作用的结果与在两个主方向(纵桥向和横桥向)同时施加地震动的计算结果进行比较,得到竖向地震动对波形板箱拱地震响应的影响程度。