Parametric analysis of eccentric structure–soil interaction system based on branch mode decoupling method

In order to carry out parametric analysis of eccentric structure–soil interaction system, an analytical model based on branch mode decoupling method is presented in this paper. The solution of system equations is implemented in the frequency domain by assuming that the superstructure maintains classic normal modes. The transfer functions of translational and torsional response are derived later. The influence of eccentricity ratio, torsional to translational frequency ratio, height-to-base ratio and foundation flexibility on the curve and peak value of transfer functions and torsionally coupled degree are analyzed and discussed systematically. Results of analysis indicate that the flexibility of foundation soil can weaken the torsional response of superstructure substantially, and the natural frequencies of interaction system reduce as the flexibility of foundation soil increase. The influence of eccentricity ratio on the peak values of transfer functions varies with the torsional to translational frequency ratio, which can be summarized as the decrease of translational component and the increase of torsional component. The translational displacement of SSI system is larger than that of fixed-base condition, while the deformation amplitude is notably reduced. The torsional response decreases as well. As the height-to-base ratio increase, the varying tendency of response is further enhanced. The torsionally coupled degree of eccentric structure is remarkably affected by the torsional to translational frequency ratio, which is significantly reduced under soft soil condition.     

Code design provisions for torsionally coupled buildings on elastic foundation

The effectiveness of the design recommendations made by various major building codes to account for torsional coupling effects is evaluated with respect to the parametric responses to earthquake ground motion of a simple single-storey asymmetric building model supported on an elastic foundation. The objectives are to determine the extent to which the response trends observed in previous studies of asymmetric rigidly based buildings are affected by changes in the flexibility of the foundation medium and to comment on and suggest necessary amendments to the design recommendations in order that suitable allowance be made for the resultant changes in the magnitude of torsional coupling effects. It is concluded that whilst the qualitative effects of torsional coupling are not affected by soil–structure interaction, their magnitude depends significantly on the frequency content of the free-field motion. The response to the El Centro earthquake record is conservatively accounted for by assuming the structure to be supported on a rigid foundation. An allowance for increased response effects due to soil–structure interaction is suggested for incorporation in the torsional design recommendations when European earthquake records are employed.     

Accidental eccentricity in symmetric buildings due to wave passage effects arising from near‐fault pulse‐like ground motions

This article investigates the characteristics of the accidental eccentricity in symmetric buildings due to torsional response arising from wave passage effects in the near‐fault region. The soil–foundation–structure system is modeled as a symmetric cylinder placed on a rigid circular foundation supported on an elastic halfspace and subjected to obliquely incident plane SH waves simulating the action of near‐fault pulse‐like ground motions. The translational response is computed assuming that the superstructure behaves as a shear beam under the action of translational and rocking base excitations, whereas the torsional response is calculated using the mathematical formulation proposed in a previous study. A broad range of properties of the soil–foundation–structure system and ground motion input are considered in the analysis, thus facilitating a detailed parametric investigation of the structural response. It is demonstrated that the normalized accidental eccentricity is most sensitive to the pulse period (T_P) of the near‐fault ground motions and to the uncoupled torsional‐to‐translational fundamental frequency ratio (Ω) of the structure. Furthermore, the normalized accidental eccentricities due to simplified pulse‐like and broadband ground motions in the near‐fault region are computed and compared against each other. The results show that the normalized accidental eccentricity due to the broadband ground motion is well approximated by the simplified pulse for longer period buildings, while it is underestimated for shorter period buildings. For symmetric buildings with values of Ω commonly used in design practice, the normalized accidental eccentricity due to wave passage effects is less than the typical code‐prescribed value of 5%, except for buildings with very large foundation radius. Copyright © 2017 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.     

Response‐only modal identification of structures using strong motion data

Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd.     

Parametric earthquake response of torsionally coupled buildings with foundation interaction

A study is made of the effect of soil-structure interaction on the coupled lateral and torsional responses of asymmetric buildings subjected to a series of historical free-field earthquake base motions. It sh shown that for particular classes of actual buildings the equivalent rigid-base responses are significantly increased for structures founded on medium-stiff soils, and hence the assumption of the major building codes that a conservative estimate of response is obtained by considering the structure to be fixed rigidly at its base is shown to be inconsistent with the presented dynamic results. It is shown that foundation interaction produces greatest amplification of torsional coupling effects for structures subjected to a particular class of European strong-motion earthquake records, identified by similarities in their spectral shape, for which the vibrational energy of the ground motion is distributed approximately uniformly over the range of frequencies which are of interest for real structures. It is recommended that provision be made in the torsional design procedures of building codes for the increase in the coupled torsional response due to soil-structure interaction as indicated in this study. Such provision should be based on the results of comprehensive parametric studies employing a wide selection of earthquake records and accounting for expected variations in localized soil conditions.     

Effects of soil–structure interaction on seismic base isolation

The effects of soil–structure interaction on the performance of a nonlinear seismic base isolation system for a simple elastic structure are examined. The steady-state response of the system to harmonic excitation is obtained by use of the equivalent linearization method. Simple analytical expressions for the deformation of the base isolation system and of the superstructure at resonance are obtained in terms of an effective replacement oscillator characterized by amplitude-dependent frequency, damping ratio, and excitation. Numerical results suggest that the seismic response of a structure resting on an inelastic base isolation system may be larger when the flexibility of the soil is considered than the corresponding response obtained by ignoring the effects of soil–structure interaction. It is shown that, in the undamped case and in the absence of soil–structure interaction effects, a critical harmonic excitation exists beyond which the steady-state resonant response of the isolators and structure become unbounded.     

Identification of structural and soil properties from vibration tests of the Hualien containment model

Measurements of the response of the ¼‐scale reinforced concrete Hualien (Taiwan) containment model obtained during forced vibration tests are used to identify some of the characteristics of the superstructure and the soil. In particular, attempts are made to determine the fixed‐base modal frequencies, modal damping ratios, modal masses and participation factors associated with translation and rocking of the base. The shell superstructure appears to be softer than could have been predicted on the basis of the given geometry and of test data for the properties of concrete. Estimates of the shear‐wave velocity and damping ratio in the top layer of soil are obtained by matching the observed and theoretical system frequency and peak amplitude of the response at the top of the structure. The resulting models for the superstructure and the soil lead to theoretical results for the displacement and rotations at the base and top of the structure which closely match the observed response. Copyright © 2004 John Wiley & Sons, Ltd.     

Simplified seismic analysis of asymmetric building systems

The paper reviews the uncoupled modal response history analysis (UMRHA) and modal pushover analysis (MPA) procedure in the analysis of asymmetric structures. From the pushover curves in ADRS format, showing the relationships of base shear versus roof translation and base torque versus roof rotation, a bifurcating characteristic of the pushover curves of an asymmetric structure is observed. A two‐degree‐of‐freedom (2DOF) modal stick is constructed using lump mass eccentrically placed at the end of beam which is connected with the column by a rotational spring. By converting the equation of motion of a whole structure into 2DOF modal equations, all of the elastic properties in the 2DOF modal sticks can be determined accurately. A mathematical proof is carried out to demonstrate that the 2DOF modal stick is consistent with the single‐degree‐of‐freedom (SDOF) modal stick at elastic state. The bifurcating characteristic of modal pushover curves and the interaction of modal translation and rotation can be considered rationally by this 2DOF modal stick. In order to verify the effectiveness of this proposed 2DOF modal stick, a two‐storey asymmetric building structure was analysed by the UMRHA procedure incorporating this novel 2DOF modal sticks (2DMPA) and conventional SDOF modal sticks (SDMPA), respectively. The analytical results are compared with those obtained by nonlinear response history analysis (RHA). It is illustrated that the accuracy of the rotational response histories obtained by 2DMPA is much better than those obtained by SDMPA. Consequently, the estimations of translational response histories on flexible side (FS) and stiff side (SS) of the building structure are also improved. Copyright © 2006 John Wiley & Sons, Ltd.     

Free‐vibration analysis of a three‐dimensional soil–structure system

A procedure which involves a non‐linear eigenvalue problem and is based on the substructure method is proposed for the free‐vibration analysis of a soil–structure system. In this procedure, the structure is modelled by the standard finite element method, while the unbounded soil is modelled by the scaled boundary finite element method. The fundamental frequency, and the corresponding radiation damping ratio as well as the modal shape are obtained by using inverse iteration. The free vibration of a dam–foundation system, a hemispherical cavity and a hemispherical deposit are analysed in detail. The numerical results are compared with available results and are also verified by the Fourier transform of the impulsive response calculated in the time domain by the three‐dimensional soil–structure–wave interaction analysis procedure proposed in our previous paper. The fundamental frequency obtained by the present procedure is very close to that obtained by Touhei and Ohmachi, but the damping ratio and the imaginary part of modal shape are significantly different due to the different definition of damping ratio. This study shows that although the classical mode‐superposition method is not applicable to a soil–structure system due to the frequency dependence of the radiation damping, it is still of interest in earthquake engineering to evaluate the fundamental frequency and the corresponding radiation damping ratio of the soil–structure system. Copyright © 2001 John Wiley & Sons, Ltd.     

Coupled lateral-torsional behaviour of frame structures under earthquake loading

A series of parametrically defined experimental model structures has been tested under earthquake base loading using the SERC national U.K. earthquake simulator. The models have been designed with variable ratios of torsional to lateral stiffness, and with both symmetric and asymmetric mass distributions. This paper first describes the tests carried out to determine the basic dynamic model properties and the establishment of idealized analytical models which give accurate predictions of model behaviour under steady-state loading and free-vibration conditions. Secondly, a detailed discussion is made of the two highly coupled structural models having uncoupled torsional to lateral frequency ratio R_f = 1.2, commenting on the ability of the modal analysis procedures to predict accurately the maximum recorded responses. It is concluded that the theory underestimates the significance of the fundamental torsional mode of vibration in the combined structural response, and overestimates the contribution of the first lateral mode. These effects compensate each other on the side of the structure which is most severely affected by torsional response, but produce large inaccuracies on the side of the building which is commonly assumed to be affected beneficially by torsional coupling.     

Seismic soil–structure interaction in multi‐span bridges: Application to a railway bridge

The effects of soil‐structure interaction on the seismic response of multi‐span bridges are investigated by means of a modelling strategy based on the domain decomposition technique. First, the analysis methodology is presented: kinematic interaction analysis is performed in the frequency domain by means of a procedure accounting for radiation damping, soil–pile and pile‐to‐pile interaction; the seismic response of the superstructure is evaluated in the time domain by means of user‐friendly finite element programs introducing suitable lumped parameter models take into account the frequency‐dependent impedances of the soil–foundation system. Second, a real multi‐span railway bridge longitudinally restrained at one abutment is analyzed. The input motion is represented by two sets of real accelerograms: one consistent with the Italian seismic code and the other constituted by five records characterized by different frequency contents. The seismic response of the compliant‐base model is compared with that obtained from a fixed‐base model. Pile stress resultants due to kinematic and inertial interactions are also evaluated. The application demonstrates the importance of performing a comprehensive analysis of the soil–foundation–structure system in the design process, in order to capture the effects of soil‐structure interaction in each structural element that may be beneficial or detrimental. Copyright © 2011 John Wiley & Sons, Ltd.     

Wavelet‐based non‐stationary seismic rocking response of flexibly supported tanks

The non‐stationary rocking response of liquid storage tanks under seismic base excitations including soil interaction has been developed based on the wavelet domain random vibration theory. The ground motion has been characterized through statistical functionals of wavelet coefficients of the ground acceleration history. The tank–liquid–foundation system is modelled as a multi‐degree‐of‐freedom (MDOF) system with both lateral and rocking motions of vibration of the foundation. The impulsive and convective modes of vibration of the liquid in the tank have been considered. The wavelet domain coupled dynamic equations are formulated and then solved to get the expressions of instantaneous power spectral density function (PSDF) in terms of functionals of input wavelet coefficients. The moments of the instantaneous PSDF are used to obtain the stochastic responses of the tank in the form of coefficients of hydrodynamic pressure, base shear and overturning base moment for the largest expected peak responses. Parametric variations are carried out to study the effects of various governing parameters like height of liquid in the tank, height–radius ratio of the tank, ratio of total liquid mass to mass of foundation, and shear wave velocity in the soil medium, on the responses of the tank. Copyright © 2003 John Wiley & Sons, Ltd.     

Shake table tests on a mass eccentric model with base isolation

A mass eccentric structure is usually more seismically vulnerable than its concentric counterpart because of the coupled torsional–translational response of such structures. In this work, dynamic characteristics and response of a five‐storey benchmark model with moderate mass eccentricity were investigated using a shake table, simulating four different ground motions. The effectiveness of laminated rubber bearings (LRB) and lead‐core rubber bearings (LCRB) in protecting eccentric structures was examined and evaluated in relation to translational and torsional responses of the benchmark model. It was observed that both translational and torsional responses were significantly reduced with the addition of either a LRB or LCRB isolated system regardless of the nature of ground motion input. The LRB were identified to be more effective than LCRB in reducing model relative displacements, the relative torsional angle as well as accelerations, and therefore provided a better protection of the superstructure and its contents. On the other hand, LCRB rendered a smaller torsional angle and absolute displacement of the base isolation system, hence a more stable structural system. Copyright © 2003 John Wiley & Sons, Ltd.     

Appropriate viscous damping for nonlinear time‐history analysis of base‐isolated reinforced concrete buildings

There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.     

Evaluation of the effect of earthquake frequency content on seismic behavior of cantilever retaining wall including soil–structure interaction

A three-dimensional backfill–structure–soil/foundation interaction phenomenon is simulated using the finite element method in order to analyze the dynamic behavior of cantilever retaining wall subjected to different ground motions. Effects of both earthquake frequency content and soil–structure interaction are evaluated by using five different seismic motions and six different soil types. The study mainly consists of three parts. In the first part, following a brief review of the problem, the finite element model with viscous boundary is proposed under fixed-base condition. In the second part, analytical formulations are presented by using modal analysis technique to provide the finite element model verification, and reasonable agreement is found between numerical and analytical results. Finally, the method is extended to further investigate parametrically the effects of not only earthquake frequency content but also soil/foundation interaction, and nonlinear time history analyzes are carried out. By means of changing the soil properties, some comparisons are made on lateral displacements and stress responses under different ground motions. It is concluded that the dynamic response of the cantilever wall is highly sensitive to frequency characteristics of the earthquake record and soil–structure interaction.     

Stochastic seismic response of multiply-supported secondary systems in flexible-base structures

A formulation has been proposed for the transfer function of a secondary system response while the primary system is supported on a compliant soil and the excitation comprises of translational ground motion at its base. For this purpose, the earlier formulation of the authors for the fixed-base case, which exactly considers the interaction between the two sub-systems and is based on the use of their individual modal properties, has been extended. Also, the concept of modifying the input excitation for the interaction accelerations (associated with the soil–structure interaction) has been used. An example P–S system and three example earthquake excitations have been considered to illustrate the proposed formulation and to estimate the expected response peak amplitudes in the secondary system. This study shows that ‘detuning’ of the tuned systems may occur in case of significant soil–structure interaction. Further, for the reasons of both safety and economy, ignoring the interaction effects in designing the secondary systems may not always be justified. Copyright © 1999 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.     

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.     

Influence of dynamic soil–structure interaction on the nonlinear response and seismic reliability of multistorey systems

A set of reinforced concrete structures with gravitational loads and mechanical properties (strength and stiffness) representative of systems designed for earthquake resistance in accordance with current criteria and methods is selected to study the influence of dynamic soil–structure interaction on seismic response, ductility demands and reliability levels. The buildings are considered located at soft soil sites in the Valley of Mexico and subjected to ground motion time histories simulated in accordance with characteristic parameters of the maximum probable earthquake likely to occur during the system's expected life. For the near‐resonance condition the effects of soil–structure interaction on the ductility demands depend mainly on radiation damping. According to the geometry of the structures studied this damping is strongly correlated with the aspect ratio, obtained by dividing the building height by its width. In this way, for structures with aspect ratio greater than 1.4 the storey and global ductility demands increase with respect to those obtained with the same structures but on rigid base, while for structures with aspect ratio less than 1.4 the ductility demands decrease with respect to those for the structures on rigid base. For the cases when the fundamental period of the structure has values very different from the dominant ground period, soil–structure interaction leads in all cases to a reduction of the ductility demands, independently of the aspect ratio. The reliability index β is obtained as a function of the base shear ratio and of the seismic intensity acting on the nonlinear systems subjected to the simulated motions. The resulting reliability functions are very similar for systems on rigid or on flexible foundation, provided that in the latter case the base rotation and the lateral displacement are removed from the total response of the system. Copyright © 2006 John Wiley & Sons, Ltd.