A distributed shear and flexural flexibility model with shear–flexure interaction for R/C members subjected to seismic loading

A beam–column‐type finite element for seismic assessment of reinforced concrete (R/C) frame structures is presented. This finite element consists of two interacting, distributed flexibility sub‐elements representing inelastic flexural and shear response. Following this formulation, the proposed model is able to capture spread of flexural yielding, as well as spread of shear cracking, in R/C members. The model accounts for shear strength degradation with inelastic curvature demand, as well as coupling between inelastic flexural and shear deformations after flexural yielding, observed in many experimental studies. An empirical relationship is proposed for evaluating the average shear distortion of R/C columns at the onset of stirrup yielding. The proposed numerical model is validated against experimental results involving R/C columns subjected to cyclic loading. It is shown that the model can predict well the hysteretic response of R/C columns with different failure modes, i.e. flexure‐critical elements, elements failing in shear after flexural yielding, and shear‐critical R/C members. Copyright © 2008 John Wiley & Sons, Ltd.     

Probabilistic estimation of inelastic displacement demands in soil–structure interaction systems on cohesive soils

Inelastic displacement ratios (IDRs) of nonlinear soil–structure interaction (SSI) systems located at sites with cohesive soils are investigated in this study. To capture the effects of inelastic cyclic behavior of the supporting soil, the Beam on Nonlinear Winkler Foundation (BNWF) model is used. The superstructure is modeled using an inelastic single-degree-of-freedom (SDOF) system model. Nonlinear SSI systems representing various combinations of unconfined compressive strengths and shear wave velocities are considered in the analysis. A set of strong ground motions recorded at sites with soft to stiff soils is used for considering the record-to-record variability of IDRs. It is observed that IDRs for nonlinear SSI systems are sensitive to the strength and the stiffness properties of both the soil and the structure. For the case of SSI systems on the top of cohesive soils, the compressive strength of the soil has a significant impact on the IDRs, which cannot be captured by considering only the shear wave velocity of the soil. Based on the results of nonlinear time-history analysis, a new equation is proposed for estimating the mean and the dispersion of IDRs of SSI systems depending on the characteristic properties of the supporting soil, dimensions of the foundation, and properties of the superstructure. A probabilistic framework is presented for the performance-based seismic design of SSI systems located at sites with cohesive soils.     

Inelastic displacement ratios for soil–structure systems allowed to uplift

The simultaneous effects of soil–structure interaction, foundation uplift and inelastic behavior of the superstructure on total displacement response of soil–structure systems are investigated. The superstructure is modeled as an equivalent single‐degree‐of‐freedom system with bilinear behavior mounted on a rigid foundation resting on distributed tensionless Winkler springs and dampers. It is well known that the behavior of soil–structure systems can be well described using a limited number of nondimensional parameters. Here, by introducing two new parameters, the concept is extended to inelastic soil–structure systems in which the foundation is allowed to uplift. An extensive parametric study is conducted for a wide range of the key parameters through nonlinear time history analyses. It is shown that while uplifting soil–structure systems experience excessive displacements, in comparison with systems that are not allowed to uplift, ductility demand in the superstructure generally decreases owing to foundation uplift. A new inelastic displacement ratio (IDR) is proposed in conjunction with a nonlinear static analysis of uplifting soil–structure systems. Simplified expressions are also provided to estimate the proposed IDR. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimation of monotonic behavior of reinforced concrete columns considering shear‐flexure‐axial load interaction

Reinforced concrete columns with insufficient transverse reinforcement and non‐seismic reinforcement details are vulnerable to brittle shear failure and to loss of axial load carrying capacity in the event of a strong earthquake. In this paper, a procedure is presented after examining the application of two macro models for displacement‐based analysis of reinforced concrete columns subjected to lateral loads. In the proposed model, lateral load‐deformation response of the column is simulated by estimating flexural and shear deformation components separately while considering their interaction and then combining these together according to a set of rules depending upon column's yield, flexural and shear strengths. In addition, lateral deformation caused by reinforcement slip in beam–column joint regions and buckling of compression bars are taken into account and considered in the analysis. Implementation of the proposed procedure produces satisfactory lateral load–displacement relationships, which are comparable with experimental data. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic interaction of bridge–train system under non‐uniform seismic ground motion

The probability that an earthquake occurs when a train is running over a bridge in earthquake‐prone regions is much higher than before, for high‐speed railway lines are rapidly developed to connect major cities worldwide. This paper presents a finite element method‐based framework for dynamic analysis of coupled bridge–train systems under non‐uniform seismic ground motion, in which rail–wheel interactions and possible separations between wheels and rails are taken into consideration. The governing equations of motion of the coupled bridge–train system are established in an absolute coordinate system. Without considering the decomposition of seismic responses into pseudo‐static and inertia‐dynamic components, the equations of motion of the coupled system are formed in terms of displacement seismic ground motions. The mode superposition method is applied to the bridge structure to make the problem manageable while the Newmark‐β method with an iterative computation scheme is used to find the best solution for the problem concerned. Eight high‐speed trains running over a multi‐span steel truss‐arch bridge subject to earthquakes are taken as a case study. The results from the case study demonstrate that the spatial variation of seismic ground motion affects dynamic responses of the bridge–train system. The ignorance of pseudo‐static component when using acceleration seismic ground motions as input may underestimate seismic responses of the bridge–train system. The probability of separation between wheels and rails becomes higher with increasing train speed. Copyright © 2011 John Wiley & Sons, Ltd.     

Bridge–embankment interaction under transverse ground excitation

Seismic performance and dynamic response of bridge–embankments during strong or moderate ground excitations are investigated through finite element (FE) modelling and detailed dynamic analysis. Previous research studies have established that bridge–embankments exhibit increasingly flexible performance under high‐shear deformation levels and that soil displacements at bridge abutment supports may be significant particularly in the transverse direction. The 2D equation of motion is solved for the embankment, in order to evaluate the dynamic characteristics and to describe explicitly the seismic performance and dynamic response under transverse excitations accounting for soil nonlinearities, soil–structure interaction and imposed boundary conditions (BCs). Using the proposed model, equivalent elastic analysis was performed so as to evaluate the dynamic response of approach embankments while accounting for soil–structure interaction. The analytical procedures were applied in the case of a well‐documented bridge with monolithic supports (Painter Street Overcrossing, PSO) which had been instrumented and embankment participation was identified from its response records after the 1971 San Fernando earthquake. The dynamic characteristics and dynamic response of the PSO embankments were evaluated for alternative BCs accounting for soil–structure interaction. Explicit expressions for the evaluation of the critical embankment length L_c are provided in order to quantify soil contribution to the overall bridge system under strong intensity ground excitations. The dynamic response of the entire bridge system (deck–abutments–embankments) was also evaluated through simplified models that considered soil–structure interaction. Results obtained from this analysis are correlated with those of detailed 3D FE models and field data with good agreement. Copyright © 2007 John Wiley & Sons, Ltd.     

Performance of base‐isolated reinforced concrete buildings under bidirectional seismic excitation considering pounding with retaining walls including friction effects

Seismic pounding of base‐isolated buildings has been mostly studied in the past assuming unidirectional excitation. Therefore, in this study, the effects of seismic pounding on the response of base‐isolated reinforced concrete buildings under bidirectional excitation are investigated. For this purpose, a three‐dimensional finite element model of a code‐compliant four‐story building is considered, where a newly developed contact element that accounts for friction and is capable of simulating pounding with retaining walls at the base, is used. Nonlinear behavior of the superstructure as well as the isolation system is considered. The performance of the building is evaluated separately for far‐fault non‐pulse‐like ground motions and near‐fault pulse‐like ground motions, which are weighted scaled to represent two levels of shaking viz. the design earthquake (DE) level and the risk‐targeted maximum considered earthquake (MCE_R) level. Nonlinear time‐history analyses are carried out considering lower bound as well as upper bound properties of isolators. The influence of separation distance between the building and the retaining walls at the base is also investigated. It is found that if pounding is avoided, the performance of the building is satisfactory in terms of limiting structural and nonstructural damage, under DE‐level motions and MCE_R‐level far‐fault motions, whereas unacceptably large demands are imposed by MCE_R‐level near‐fault motions. In the case of seismic pounding, MCE_R‐level near‐fault motions are found to be detrimental, where the effect of pounding is mostly concentrated at the first story. In addition, it is determined that considering unidirectional excitation instead of bidirectional excitation for MCE_R‐level near‐fault motions provides highly unconservative estimates of superstructure demands. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of pulse period of near‐field ground motions on the seismic demands of soil–MDOF structure systems using mathematical pulse models

In this paper, the effects of pulse period associated with near‐field ground motions on the seismic demands of soil–MDOF structure systems are investigated by using mathematical pulse models. Three non‐dimensional parameters are employed as the crucial parameters, which govern the responses of soil–structure systems: (1) non‐dimensional frequency as the structure‐to‐soil stiffness ratio; (2) aspect ratio of the superstructure; and (3) structural target ductility ratio. The soil beneath the superstructure is simulated on the basis of the Cone model concept. The superstructure is modeled as a nonlinear shear building. Interstory drift ratio is selected as the main engineering demand parameter for soil–structure systems. It is demonstrated that the contribution of higher modes to the response of soil–structure system depends on the pulse‐to‐interacting system period ratio instead of pulse‐to‐fixed‐base structure period ratio. Furthermore, results of the MDOF superstructures demonstrate that increasing structural target ductility ratio results in the first‐mode domination for both fixed‐base structure and soil–structure system. Additionally, increasing non‐dimensional frequency and aspect ratio of the superstructure respectively decrease and increase the structural responses. Moreover, comparison of the equivalent soil–SDOF structure system and the soil–MDOF structure system elucidates that higher‐mode effects are more significant, when soil–structure interaction is taken into account. In general, the effects of fling step and forward directivity pulses on activating higher modes of the superstructure are more sever in soil–structure systems, and in addition, the influences of forward directivity pulses are more considerable than fling step ones. Copyright © 2013 John Wiley & Sons, Ltd.     

A hybrid time frequency domain formulation for non-linear soil–structure interaction

Methods that combine frequency and time domain techniques offer an attractive alternative for solving Soil–Structure-interaction problems where the structure exhibits non-linear behaviour. In the hybrid-frequency-time-domain procedure a reference linear system is solved in the frequency domain and the difference between the actual restoring forces and those in the linear model are treated as pseudo-forces. In the solution scheme explored in this paper, designated as the hybrid-time-frequency-domain (HTFD) procedure, the equations of motion are solved in the time domain with due consideration for non-linearities and with the unbounded medium represented by frequency-independent springs and dampers. The frequency dependency of the impedance coefficients is introduced by means of pseudo-forces evaluated in the frequency domain at the end of each iteration. A criterion of stability for the HTFD approach is derived analytically and its validity is sustained numerically. As is often the case, the criterion takes the form of a limit of unity on the spectral radius of an appropriately defined matrix. Inspection of the terms in this matrix shows that convergence can be guaranteed by suitable selection of the reference impedance. The CPU times required to obtain converged solutions with the HTFD are found, in a number of numerical simulations, to be up to one order of magnitude less than those required by the alternative hybrid-frequency-time-domain approach. © 1998 John Wiley & Sons, Ltd.     

A static predictor of seismic demand on frames based on a post‐elastic deflected shape

Predictors of seismic structural demands (such as inter‐storey drift angles) that are less time‐consuming than nonlinear dynamic analysis have proven useful for structural performance assessment and for design. Luco and Cornell previously proposed a simple predictor that extends the idea of modal superposition (of the first two modes) with the square‐root‐of‐sum‐of‐squares (SRSS) rule by taking a first‐mode inelastic spectral displacement into account. This predictor achieved a significant improvement over simply using the response of an elastic oscillator; however, it cannot capture well large displacements caused by local yielding. A possible improvement of Luco's predictor is discussed in this paper, where it is proposed to consider three enhancements: (i) a post‐elastic first‐mode shape approximated by the deflected shape from a nonlinear static pushover analysis (NSPA) at the step corresponding to the maximum drift of an equivalent inelastic single‐degree‐of‐freedom (SDOF) system, (ii) a trilinear backbone curve for the SDOF system, and (iii) the elastic third‐mode response for long‐period buildings. Numerical examples demonstrate that the proposed predictor is less biased and results in less dispersion than Luco's original predictor. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Soil–pile–structure interaction under SH wave excitation

A continuum model for the interaction analysis of a fully coupled soil–pile–structure system under seismic excitation is presented in this paper. Only horizontal shaking induced by harmonic SH waves is considered so that the soil–pile–structure system is under anti‐plane deformation. The soil mass, pile and superstructure were all considered as elastic with hysteretic damping, while geometrically both pile and structures were simplified as a beam model. Buildings of various heights in Hong Kong designed to resist wind load were analysed using the present model. It was discovered that the acceleration of the piled‐structures at ground level can, in general, be larger than that of a free‐field shaking of the soil site, depending on the excitation frequency. For typical piled‐structures in Hong Kong, the amplification factor of shaking at the ground level does not show simple trends with the number of storeys of the superstructure, the thickness and the stiffness of soil, and the stiffness of the superstructure if number of storeys is fixed. The effect of pile stiffness on the amplification factor of shaking is, however, insignificant. Thus, simply increasing the pile size or the superstructure stiffness does not necessarily improve the seismic resistance of the soil–pile–structure system; on the contrary, it may lead to excessive amplification of shaking for the whole system. Copyright © 2003 John Wiley & Sons, Ltd.     

Linear analysis of concrete arch dams including dam–water–foundation rock interaction considering spatially varying ground motions

The available substructure method and computer program for earthquake response analysis of arch dams, including the effects of dam–water–foundation rock interaction and recognizing the semi‐unbounded size of the foundation rock and fluid domains, are extended to consider spatial variations in ground motions around the canyon. The response of Mauvoisin Dam in Switzerland to spatially varying ground motion recorded during a small earthquake is analyzed to illustrate the results from this analysis procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Analytical modelling of near‐source pulse‐like seismic demand for multi‐linear backbone oscillators

Nonlinear static procedures, which relate the seismic demand of a structure to that of an equivalent single‐degree‐of‐freedom oscillator, are well‐established tools in the performance‐based earthquake engineering paradigm. Initially, such procedures made recourse to inelastic spectra derived for simple elastic–plastic bilinear oscillators, but the request for demand estimates that delve deeper into the inelastic range, motivated investigating the seismic demand of oscillators with more complex backbone curves. Meanwhile, near‐source (NS) pulse‐like ground motions have been receiving increased attention, because they can induce a distinctive type of inelastic demand. Pulse‐like NS ground motions are usually the result of rupture directivity, where seismic waves generated at different points along the rupture front arrive at a site at the same time, leading to a double‐sided velocity pulse, which delivers most of the seismic energy. Recent research has led to a methodology for incorporating this NS effect in the implementation of nonlinear static procedures. Both of the previously mentioned lines of research motivate the present study on the ductility demands imposed by pulse‐like NS ground motions on oscillators that feature pinching hysteretic behaviour with trilinear backbone curves. Incremental dynamic analysis is used considering 130 pulse‐like‐identified ground motions. Median, 16% and 84% fractile incremental dynamic analysis curves are calculated and fitted by an analytical model. Least‐squares estimates are obtained for the model parameters, which importantly include pulse period T_p. The resulting equations effectively constitute an R ? μ ? T ? T_p relation for pulse‐like NS motions. Potential applications of this result towards estimation of NS seismic demand are also briefly discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Residual slip of sliding blocks induced by near‐fault ground motions

The response of a rigid block supported on a horizontally moving foundation through a dry‐friction contact is investigated to near‐fault ground motions. Such motions can be thought of as consisting of a coherent component (‘pulse’) and an incoherent component, which can be described as a band‐limited ‘random noise’. The equation of motion of this strongly nonlinear system is reduced to a normalized form that reveals important parameters of the problem such as the critical acceleration ratio. The response of the sliding block to a set of uniformly processed near‐fault motions, covering a sufficiently wide range of magnitudes, is evaluated numerically for selected discrete values of the acceleration ratio. For each value of the critical acceleration ratio, the numerically computed residual slips are fitted with a Weibull (Gumbel type III) extreme value probability distribution. This allows the establishment of regression equations that describe accurately design sliding curves corresponding to various levels of non‐exceedance probability. The analysis reveals that the coherent component of motion contributes significantly to the response of the sliding block. Furthermore, the relevant acceleration in specifying the critical acceleration ratio is the (normalized) amplitude, α_{H_pulse}, of the pulse and not the (normalized) amplitude of the incoherent component α_H. Finally, the incoherent component is described quantitatively in terms of the root‐mean‐square acceleration a_RMS, and an attempt is made to understand its influence on the response of the sliding block. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of train dynamics on seismic response of steel monorail bridges under moderate ground motion

This study is intended to investigate the seismic response of steel monorail bridges using three‐dimensional dynamic response analysis. We particularly consider monorail bridge–train interaction when subjected to ground motion that occurs with high probability. A monorail train car with two bogies with pneumatic tires for running, steering and stabilizing wheels is assumed to be represented sufficiently by a discrete rigid multi‐body system with 15 degrees of freedom (DOFs). Bridges are considered as an assemblage of beam elements with 6 DOFs at each node. Modal analysis is used for dynamic response analysis under moderate earthquakes. The seismic response of an advanced monorail bridge that adopts a simplified structural system and composite girders is investigated through comparison with seismic responses of a conventional bridge. The acceleration response of a monorail train is also calculated to investigate the effect of structural types of bridges on the train's dynamic response during earthquakes. Results show that the seismic responses of the advanced bridges are greater than those of the conventional monorail bridge because of the simplified structural system and increased girder weight that is attributable to composite girders of the advanced bridge. Moreover, the train on the advanced bridge shows greater dynamic response than that on the conventional bridge. Observations reveal that the dynamic monorail train system acts as a damper on the monorail bridge. That fact shows that the existing design, which considers a train as additional mass, yields a conservative result. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimum lateral load pattern for seismic design of elastic shear‐buildings incorporating soil–structure interaction effects

Recently, several new optimum loading patterns have been proposed by researchers for fixed‐base systems while their adequacy for soil–structure systems has not been evaluated yet. Through intensive dynamic analyses of multistory shear‐building models with soil–structure interaction subjected to a group of 21 artificial earthquakes adjusted to soft soil design spectrum, the adequacy of these optimum patterns is investigated. It is concluded that using these patterns the structures generally achieve near optimum performance in some range of periods. However, their efficiency reduces as soil flexibility increases especially when soil–structure interaction effects are significant. In the present paper, using the uniform distribution of damage over the height of structures, as the criterion, an optimization algorithm for seismic design of elastic soil–structure systems is developed. The effects of fundamental period, number of stories, earthquake excitation, soil flexibility, building aspect ratio, damping ratio and damping model on optimum distribution pattern are investigated. On the basis of 30,240 optimum load patterns derived from numerical simulations and nonlinear statistical regression analyses, a new lateral load pattern for elastic soil–structure systems is proposed. It is a function of the fundamental period of the structure, soil flexibility and structural slenderness ratio. It is shown that the seismic performance of such a structure is superior to those designed by code‐compliant or recently proposed patterns by researchers for fixed‐base structures. Using the proposed load pattern in this study, the designed structures experience up to 40% less structural weight as compared with the code‐compliant or optimum patterns developed based on fixed‐base structures. Copyright © 2012 John Wiley & Sons, Ltd.     

Non-linear dynamic earth dam–foundation interaction using a BE–FE method

A general, rigorous, coupled Boundary Element–Finite Element (BE–FE) formulation is presented for non-linear seismic soil–structure interaction in two dimensions. The BE–FE method is applied to investigate the inelastic response of earth dams to transient SV waves. The dam body, consisting of heterogeneous materials modelled with a simple non-linear hysteretic model, is discretized with finite elements, whereas the elastic half-space is discretized with boundary elements. The study focuses on the combined effects of the material non-linearity and foundation flexibility. The results show the significant effect of the foundation flexibility in reducing the response through radiation of energy. For excitations with peak ground accelerations from 0·2gto 0·6g, the crest acceleration amplification ranges from 2·5 to 1·4 and seems to be comparable with field observations and results from other studies. Deamplification increasing with strain is reported at the lower part of the dam. The method is computationally powerful and can be used for efficient non-linear analysis of complex soil–structure systems. The efficiency of the BE–FE method allows further improvements with incorporation of a more advanced constitutive model and consideration of the generation and dissipation of pore-water pressures during the earthquake. © 1998 John Wiley & Sons, Ltd.     

Seismic effectiveness of tuned mass dampers considering soil–structure interaction

This paper presents how soil–structure interaction affects the seismic performance of Tuned Mass Dampers (TMD) when installed on flexibly based structures. Previous studies on this subject have led to inconsistent conclusions since the soil and structure models employed considerably differ from each other. A generic frequency-independent model is used in this paper to represent a general soil–structure system, whose parameters cover a wide spectrum of soil and structural characteristics. The model structure is subjected to a stationary random excitation and the root-mean-square responses of engineering interest are used to measure the TMD's performance. Extensive parametric studies have shown that strong soil–structure interaction significantly defeats the seismic effectiveness of TMD systems. As the soil shear wave velocity decreases, TMD systems become less effective in reducing the maximum response of structures. For a structure resting on soft soil, the TMD system can hardly reduce the structural seismic response due to the high damping characteristics of soil–structure systems. The model structure is further subjected to the NS component of the 1940 El Centro, California earthquake to confirm the TMD's performance in a more realistic environment. Copyright © 1999 John Wiley & Sons Ltd.