Centrifuge modeling of rocking‐isolated inelastic RC bridge piers

Experimental proof is provided of an unconventional seismic design concept, which is based on deliberately underdesigning shallow foundations to promote intense rocking oscillations and thereby to dramatically improve the seismic resilience of structures. Termed rocking isolation, this new seismic design philosophy is investigated through a series of dynamic centrifuge experiments on properly scaled models of a modern reinforced concrete (RC) bridge pier. The experimental method reproduces the nonlinear and inelastic response of both the soil‐footing interface and the structure. To this end, a novel scale model RC (1:50 scale) that simulates reasonably well the elastic response and the failure of prototype RC elements is utilized, along with realistic representation of the soil behavior in a geotechnical centrifuge. A variety of seismic ground motions are considered as excitations. They result in consistent demonstrably beneficial performance of the rocking‐isolated pier in comparison with the one designed conventionally. Seismic demand is reduced in terms of both inertial load and deck drift. Furthermore, foundation uplifting has a self‐centering potential, whereas soil yielding is shown to provide a particularly effective energy dissipation mechanism, exhibiting significant resistance to cumulative damage. Thanks to such mechanisms, the rocking pier survived, with no signs of structural distress, a deleterious sequence of seismic motions that caused collapse of the conventionally designed pier. © 2014 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.     

Sensitivity of seismically isolated structures

In this paper we study the sensitivity of seismically isolated structures to a small variability of the earthquake excitation and of some structural properties with respect to the probability of failure and floor spectra. In particular, the influence of the nonlinear behaviour of the isolated superstructure on the vulnerability and on the floor spectra is investigated by means of a series of Monte Carlo simulations of simple two degrees‐of‐freedom systems. Several types of passive and active isolation systems are examined and three different idealized nonlinear constitutive laws are considered for the superstructure. It is found that, in general, the probability of failure does not depend on the specific cyclic behaviour of the assumed constitutive law and general trends regarding the impact of different isolation devices on vulnerability are established. As for the floor spectra, the influence of moderate nonlinear behaviour of isolated superstructures, with the exception of the case of a non‐dissipative elastic nonlinear law, is negligible, contrary to the case of conventional structures. Copyright © 2008 John Wiley & Sons, Ltd.     

Simplified analysis of mid‐story seismically isolated buildings

The mid‐story isolation design method is recently gaining popularity for the seismic protective design of buildings located in the areas of high population. In a mid‐story isolated building, the isolation system is incorporated into the mid‐story rather than the base of the building. In this paper, the dynamic characteristics and seismic responses of mid‐story isolated buildings are investigated using a simplified three‐lumped‐mass structural model for which equivalent linear properties are formulated. From the parametric study, it is found that the nominal frequencies of the superstructure and the substructure, respectively, above and below the isolation system have significant influences on the isolation frequency and equivalent damping ratio of a mid‐story isolated building. Moreover, the mass and stiffness of the substructure are of greater significance than the superstructure in affecting the dynamic characteristics of the isolated building. Besides, based on the response spectrum analysis, it is noted that the higher mode responses may contribute significantly to the story shear force of the substructure. Consequently, the equivalent lateral force procedure of design codes should carefully include the effects of higher modes. Copyright © 2010 John Wiley & Sons, Ltd.     

Response of seismically isolated buildings considering poundings

Numerical simulations and parametric studies have been used to investigate the influence of potential poundings of seismically isolated buildings with adjacent structures on the effectiveness of seismic isolation. Poundings are assumed to occur at the isolation level between the seismically isolated building and the surrounding moat wall. After assessing some common force‐based impact models, a variation of the linear viscoelastic impact model is proposed to avoid tensile impact forces during detachment, while enabling the consideration of permanent plastic deformations at the vicinity of the impact. A large number of numerical simulations of seismically isolated buildings with different characteristics have been conducted under six earthquake excitations in order to investigate the influence of various design parameters and conditions on the peak floor accelerations and interstorey deflections during poundings. The numerical simulations demonstrate that poundings may substantially increase floor accelerations, especially t the base floor where impacts occur. Higher modes of vibration are excided during poundings, increasing the interstorey deflections, instead of retaining an almost rigid‐body motion of the superstructure, which is aimed with seismic isolation. Impact stiffness seems to affect significantly the acceleration response at the isolation level, while the displacement response is more insensitive to the variation of the impact stiffness. Finally, the results indicate that providing excessive flexibility at the isolation system to minimize the floor accelerations may lead to a building vulnerable to poundings, if the available seismic gap is limited. Copyright © 2007 John Wiley & Sons, Ltd.     

Pile‐head kinematic bending in layered soil

Kinematic effects at the head of a flexible vertical pile embedded in a two‐layer soil deposit are investigated by means of rigorous three‐dimensional elastodynamic finite‐element analyses. Both pile and soil are idealized as linearly viscoelastic materials, modelled by solid elements, without the restrictions associated with the use of strength‐of‐materials approximations. The system is analyzed by a time‐Fourier approach in conjunction with a modal expansion in space. Constant viscous damping is considered for each natural mode, and an FFT algorithm is employed to switch from frequency to time domain and vice versa in natural or generalized coordinates. The scope of the paper is to: (a) elucidate the role of a number of key phenomena controlling the amplitude of kinematic bending moments at the pile head; (b) propose a simplified semi‐analytical formula for evaluating such moments; and (c) provide some remarks about the role of kinematic bending in the seismic design of pile foundations. The results of the study provide a new interpretation of the interplay between interface kinematic moments and corresponding head moments, as a function of layer thickness, pile‐to‐soil stiffness ratio, and stiffness contrast between the soil layers. In addition, the role of diameter in designing against kinematic action, with or without the presence of an inertial counterpart, is discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

The effect of foundation embedment on inelastic response of structures

In this research, a parametric study is carried out on the effect of soil–structure interaction on the ductility and strength demand of buildings with embedded foundation. Both kinematic interaction (KI) and inertial interaction effects are considered. The sub‐structure method is used in which the structure is modeled by a simplified single degree of freedom system with idealized bilinear behavior. Besides, the soil sub‐structure is considered as a homogeneous half‐space and is modeled by a discrete model based on the concept of cone models. The foundation is modeled as a rigid cylinder embedded in the soil with different embedment ratios. The soil–structure system is then analyzed subjected to a suit of 24 selected accelerograms recorded on alluvium deposits. An extensive parametric study is performed for a wide range of the introduced non‐dimensional key parameters, which control the problem. It is concluded that foundation embedment may increase the structural demands for slender buildings especially for the case of relatively soft soils. However, the increase in ductility demands may not be significant for shallow foundations with embedment depth to radius of foundation ratios up to one. Comparing the results with and without inclusion of KI reveals that the rocking input motion due to KI plays the main role in this phenomenon. Copyright © 2008 John Wiley & Sons, Ltd.     

System identification for evaluating soil–structure interaction effects in buildings from strong motion recordings

Parametric system identification is used to evaluate seismic soil–structure interaction effects in buildings. The input–output strong motion data pairs needed for evaluations of flexible- and fixed-base fundamental mode parameters are derived. Recordings of lateral free-field, foundation, and roof motions, as well as foundation rocking, are found to be necessary for direct evaluations of modal parameters for both cases of base fixity. For the common situation of missing free-field or base rocking motions, procedures are developed for estimating the modal parameters that cannot be directly evaluated. The accuracy of these estimation procedures for fundamental mode vibration period and damping is verified for eleven sites with complete instrumentation of the structure, foundation, and free-field. © 1998 John Wiley & Sons, Ltd.     

Discrete model for dynamic through-the-soil coupling of 3-D foundations and structures

An efficient discrete model for predicting the dynamic through-the-soil interaction between adjacent rigid, surface foundations supported by a homogeneous, isotropic and linear elastic half-space is presented. The model utilizes frequency-independent springs and dashpots, and the foundation mass, for the consideration of soil–foundation interaction. The through-the-soil coupling of the foundations is attained by frequency-independent stiffness and damping functions, developed in this work, that interconnect the degrees of freedom of the entire system of foundations. The dynamic analysis of the resulting coupled system is performed in the time domain and includes the time lagging effects of coupled dynamic input due to wave propagation using an appropriate modification of the Wilson-θ method. The basic foundation interaction model is also extended to the evaluation of coupled building-foundation systems. © 1998 John Wiley & Sons, Ltd.     

Development and validation of p‐y modeling approach for seismic response predictions of highway bridges

This study aims to realistically simulate the seismic responses of typical highway bridges in California with considerations of soil–structure interaction effects. The p‐y modeling approaches are developed and validated for embankments and pile foundations of bridges. The p‐y approach models the lateral and vertical foundation flexibility with distributed p‐y springs and associated t‐z and q‐z springs. Building upon the existing p‐y models for pile foundations, the study develops the nonlinear p‐y springs for embankments based on nonlinear 2D and 3D continuum finite element analysis under passive loading condition along both longitudinal and transverse directions. Closed‐form expressions are developed for two key parameters, the ultimate resistant force p_ult and the displacement y₅₀, where 0.5p_ult is reached, of embankment p‐y models as functions of abutment geometry (wall width and height, embankment fill height, etc.) and soil material properties (wall‐soil friction angle, soil friction angle, and cohesion). In order to account for the kinematic and site responses, depth‐varying ground motions are derived and applied at the free‐end of p‐y springs, which reflects the amplified embankment crest motion. The modeling approach is applied to simulate the seismic responses of the Painter Street Bridge and validated through comparisons with the recorded responses during the 1992 Petrolia earthquake. It is demonstrated that the flexibility and motion amplification at end abutments are the most crucial modeling aspects. The developed p‐y models and the modeling approach can effectively predict the seismic responses of highway bridges. Copyright © 2016 John Wiley & Sons, Ltd.     

Discrete‐time variable structure control of seismically excited building structures

Generally, the active structural control system belongs to the discrete‐time control system, and the sampling period is one of the most important factors that would directly affect the performance of the control system. In this paper, active control approaches by using the discrete‐time variable structure control theory are studied for reducing the dynamic responses of seismically excited building structures. Based on the discrete reaching law method, a feedback controller which includes the sampling period is presented. The controller is extended by introducing the saturated control method to avoid the adverse effect when the actuators are saturated due to unexpected extreme earthquakes. The simulation results are obtained for a single‐degree‐of‐freedom (SDOF) system and a MDOF shear building equipped with active brace system (ABS) under seismic excitations. It is found that the discrete variable structure control approach and its saturated control method presented in this paper are quite effective. Copyright © 2001 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.     

Response simulation and seismic assessment of highway overcrossings

Interaction of bridge structures with the adjacent embankment fills and pile foundations is generally responsible for response modification of the system to strong ground excitations, to a degree that depends on soil compliance, support conditions, and soil mass mobilized in dynamic response. This paper presents a general modeling and assessment procedure specifically targeted for simulation of the dynamic response of short bridges such as highway overcrossings, where the embankment soil–structure interaction is the most prevalent. From previous studies it has been shown that in this type of interaction, seismic displacement demands are magnified in the critical bridge components such as the central piers. This issue is of particular relevance not only in new design but also in the assessment of the existing infrastructure. Among a wide range of issues relevant to soil–structure interaction, typical highway overcrossings that have flexible abutments supported on earth embankments were investigated extensively in the paper. Simulation procedures are proposed for consideration of bridge‐embankment interaction effects in practical analysis of these structures for estimation of their seismic performance. Results are extrapolated after extensive parametric studies and are used to extract ready‐to‐use, general, and parameterized capacity curves for a wide range of possible material properties and geometric characteristics of the bridge‐embankment assembly. Using two instrumented highway overpasses as benchmark examples, the capacity curves estimated using the proposed practical procedures are correlated successfully with the results of explicit incremental dynamic analysis, verifying the applicability of the simple tools developed herein, in seismic assessment of existing short bridges. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic design of yielding structures on flexible foundations

This paper introduces a simple method to consider the effects of inertial soil–structure interaction (SSI) on the seismic demands of a yielding single‐degree‐of‐freedom structure. This involves idealizing the yielding soil–structure system as an effective substitute oscillator having a modified period, damping ratio, and ductility. A parametric study is conducted to obtain the ratio between the displacement ductility demand of a flexible‐base system and that of the corresponding fixed‐base system. It is shown that while additional foundation damping can reduce the overall response, the effects of SSI may also increase the ductility demand of some structures, mostly being ductile and having large structural aspect ratio, up to 15%. Finally, a design procedure is provided for incorporation of the SSI effects on structural response. Copyright © 2015 John Wiley & Sons, Ltd.     

On poundings of a seismically isolated building with adjacent structures during strong earthquakes

This paper presents selected indicative results from an extensive parametric investigation that has been performed in order to assess the effects of potential earthquake‐induced poundings on the overall dynamic response of seismically isolated buildings. In particular, a seismically isolated building and its adjacent fixed‐supported buildings are subjected to various earthquake excitations that induce structural impact among the buildings in series. The results indicate that the seismically isolated building may hit against the adjacent buildings at the upper floor levels before the occurrence of any pounding at the isolation level with the surrounding moat wall. The severity of the impact depends on the dynamic properties of the adjacent buildings, in combination with the earthquake characteristics. Copyright © 2009 John Wiley & Sons, Ltd.     

Extraction of hysteretic properties of seismically isolated bridges from quick‐release field tests

A simple procedure for identifying hysteretic properties of seismically isolated bridges from full‐scale quick‐release tests is presented in this paper. An analytical solution for the quick‐release response of a SDOF system with a bilinear spring is derived. Based on the solution, some characteristics of such systems are obtained. A time domain optimization method is employed to identify the hysteretic properties of the lead–rubber bearings installed in seismically isolated bridges. The total damping effects of the isolation system are expressed as a combination of the rate‐independent (hysteretic) damping and the linear viscous damping. The Menegotto–Pinto (MP) model and bilinear model are used to represent the force–displacement relation of the lead–rubber bearings. In both the longitudinal and transverse directions the bridges have been idealized as single degree of freedom (SDOF) systems. Time histories recorded from the field quick‐release tests on two bridges are used for the examples presented herein. The hysteretic loops of the isolators obtained from laboratory tests are compared with those obtained using the optimization method, and they agree well. In conclusion, the procedure shown in this paper can be used to identify the essential in situ hysteretic characteristics of isolation bearings from quick‐release field testing. Copyright © 2001 John Wiley & Sons, Ltd.     

On the response of yielding seismically isolated structures

This paper investigates the seismic response of yielding isolated structures. To establish a general understanding of the nonlinear response of seismically isolated structures, this study first investigates the nonlinear response of isolated structures subjected to steady‐state harmonic motion and nonlinear transient ground excitation. The response of both viscously damped and hysteretically damped isolation systems is investigated in three phases. Initially, basic insights are gained through simple nonlinear two degrees of freedom (2‐DOF) models subjected to harmonic motion of varying frequencies. Next, the transient response analysis of the nonlinear 2‐DOF model is investigated for a wide range of isolation system and superstructure properties. The results obtained from both approaches indicate that the yielding behavior of a structure on an isolation system is significantly different from that of the comparable fixed‐base structure. Finally, the response of the nonlinear 2‐DOF system model is compared with that of a 15‐story, three‐dimensional model. Based on the results of these analytical investigations, some important considerations for the design of seismically isolated structures are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental and analytical studies of structures seismically isolated with an uplift‐restraining friction pendulum system

This paper presents findings from a comprehensive analytical and experimental study on the uplift‐restraining XY‐FP sliding isolation system. To investigate the effectiveness of the XY‐FP isolator and provide a rational basis for evaluating the efficacy of the developed mathematical model, an extensive experimental program was conducted on the earthquake simulator at the University at Buffalo. The experimental program involved a slender, five‐storey, scale‐model frame seismically isolated with four XY‐FP isolators subjected to simulations of historical horizontal and vertical ground motions. The experimental response demonstrates the validity of the concept and provides evidence for the effectiveness of the XY‐FP isolator in preventing uplift. A comprehensive analytical model capable of emulating the mechanical behaviour of the XY‐FP isolator is developed and implemented in program 3D‐BASIS‐ME. The newly enhanced program is used to predict the dynamic response of the seismically‐isolated model structure. Comparison of analytical predictions with experimental results attests to the efficacy of the analytical model for simulating the response of the XY‐FP isolator. With its appealing conceptual simplicity and its proven effectiveness, the new uplift‐restraining isolator has the potential to facilitate the application of seismic isolation even under the most extreme of conditions, including but not limited to near‐fault strong ground motions and uplift‐prone structural systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Modified sliding‐mode bang–bang control for seismically excited linear structures

Recently, sliding‐mode control (SMC) methods have been investigated for application to seismically excited civil engineering structures and have proved to be effective control strategic methods. On the other hand, although another class of well‐known optimal control laws, the so‐called ‘bang–bang’ control, has been investigated for several decades, their potential in civil engineering structural control has not been fully exploited. The purpose of this paper is to present a new control law for civil engineering structures, which is the sliding‐mode bang–bang control (SMBBC). The SMBBC method is a combination of the SMC and the bang–bang control. In consideration of actuators not suitable for high‐speed switching of control forces in the SMBBC in practice, modified sliding‐mode bang–bang control (MSMBBC) law is proposed and demonstrated to be able to provide the same control effects as the SMBBC case. Condition modified sliding‐mode bang–bang control (CMSMBBC) law is also investigated in this paper. In the CMSMBBC case, actuators act only when response quantities exceed some designated threshold values. The determination method of maximum control‐forces for actuators is investigated through example computation. The performance and robustness of the proposed control methods are all demonstrated by numerical simulation. Simulation results demonstrate that the presented methods are viable and an attractive control strategy for application to seismically excited linear structures. Copyright © 2000 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.     

Effects of foundation embedment during building–soil interaction

A numerical solution for evaluating the effects of foundation embedment on the effective period and damping and the response of soil–structure systems is presented. A simple system similar to that used in practice to account for inertial interaction effects is investigated, with the inclusion of kinematic interaction effects for the important special case of vertically incident shear waves. The effective period and damping are obtained by establishing an equivalence between the interacting system excited by the foundation input motion and a replacement oscillator excited by the free-field ground motion. In this way, the use of standard free-field response spectra applicable to the effective period and damping of the system is permitted. Also, an approximate solution for total soil–structure interaction is presented, which indicates that the system period is insensitive to kinematic interaction and the system damping may be expressed as that for inertial interaction but modified by a factor due to kinematic interaction. Results involving both kinematic and inertial effects are compared with those obtained for no soil–structure interaction and inertial interaction only. The more important parameters involved are identified and their influences are examined over practical ranges of interest. © 1998 John Wiley & Sons, Ltd.