PROPERTY MATRICES IDENTIFICATION OF UNBOUNDED MEDIUM FROM UNIT-IMPULSE RESPONSE FUNCTIONS USING LEGENDRE POLYNOMIALS: FORMULATION

A systematic procedure to construct the (symmetric) static-stiffness, damping and mass matrices representing the unbounded medium is presented addressing the unit-impulse response matrix corresponding to the degrees of freedom on the structure–medium interface. The unit-impulse response matrix is first diagonalized which then permits each term to be modelled independently from the others using expansions in a series of Legendre polynomials in the time domain. This leads to a rational approximation in the frequency domain of the dynamic-stiffness coefficient. Using a lumped-parameter model which provides physical insight the property matrices are constructed.     

Time‐domain analysis of unbounded media using mixed‐variable formulations

Formulation of a matrix‐valued force–displacement relationship which can take radiation damping into account is of major importance when modelling unbounded domains. This can be done by means of fundamental solutions in space and time in connection with convolution integrals or by means of a frequency dependent boundary element representation, but for discrete frequencies Ω only. In this paper a method for interpolating discrete values of dynamic stiffness matrices by a continuous matrix valued rational function is proposed. The coupling between interface degrees of freedom is fully preserved. Another crucial point in soil–structure interaction analysis is how to implement an approximation in the spectral domain into a time‐domain analysis. Well‐known approaches for the scalar case are based on the partial‐fraction expansion of a scalar rational function. Here, a more general procedure, applicable to MDOF‐systems, for the transformation of spectral rational approximations into the time‐domain is introduced. Evaluation of the partial‐fraction expansion is avoided by using the so‐called mixed variables. Thus, unknowns in the time‐domain are displacements as well as forces. Copyright © 2001 John Wiley & Sons, Ltd.     

Effects of time series analysis protocols on transfer functions calculated from earthquake accelerograms

Transfer functions represent the ratio in the frequency domain of one ground motion to another. Transfer functions are a convenient way by which the variation of earthquake ground motions from the free-field to the foundation level of a structure can be quantified for studies of kinematic soil–structure interaction. Aside from ordinary filtering and baseline correction, substantial signal processing occurs in the computation of transfer functions, including windowing (to extract the S-wave portion of the record) and smoothing (to reduce scatter that can obscure physically significant trends). Utilizing several signal processing techniques on a sample data set, we find that detailed features of the transfer function ordinates (i.e., frequency-to-frequency variations) can be affected by the degree of smoothing and by the window length (e.g., whole record versus S-window). However, the overall shape and magnitude of the transfer functions are relatively consistent. More important than signal processing details is the frequency bandwidth over which the results are considered valid, because significant portions of the spectrum can be dominated by stochastic processes with little physical meaning. We argue that transfer functions should be interpreted over those portions of the spectrum having minimal noise impact, as indicated by high coherence.     

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.     

Seismic response and damage analysis of buildings supported on flexible soils

The investigation reported in this paper studies the effects of soil–structure interaction (SSI) on the seismic response and damage of building–foundation systems. A simple structural model is used for conducting a parametric study using a typical record obtained in the soft soil area of Mexico City during the 1985 earthquake. Peak response parameters chosen for this study were the roof displacement relative to the base and the hysteretic energy dissipated by the simple structural model. A damage parameter is also evaluated for investigating the SSI effects on the seismic damage of buildings. The results indicate that in most cases of inelastic response, SSI effects can be evaluated considering the rigid‐base case and the SSI period. Copyright © 2000 John Wiley & Sons, Ltd.     

Probabilistic evaluation of soil–foundation–structure interaction effects on seismic structural response

Complex seismic behaviour of soil–foundation–structure (SFS) systems together with uncertainties in system parameters and variability in earthquake ground motions result in a significant debate over the effects of soil–foundation–structure interaction (SFSI) on structural response. The aim of this study is to evaluate the influence of foundation flexibility on the structural seismic response by considering the variability in the system and uncertainties in the ground motion characteristics through comprehensive numerical simulations. An established rheological soil‐shallow foundation–structure model with equivalent linear soil behaviour and nonlinear behaviour of the superstructure has been used. A large number of models incorporating wide range of soil, foundation and structural parameters were generated using a robust Monte‐Carlo simulation. In total, 4.08 million time‐history analyses were performed over the adopted models using an ensemble of 40 earthquake ground motions as seismic input. The results of the analyses are used to rigorously quantify the effects of foundation flexibility on the structural distortion and total displacement of the superstructure through comparisons between the responses of SFS models and corresponding fixed‐base (FB) models. The effects of predominant period of the FB system, linear vs nonlinear modelling of the superstructure, type of nonlinear model used and key system parameters are quantified in terms of different probability levels for SFSI effects to cause an increase in the structural response and the level of amplification of the response in such cases. The results clearly illustrate the risk of underestimating the structural response associated with simplified approaches in which SFSI and nonlinear effects are ignored. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic response analysis of highway overcrossings including soil–structure interaction

This paper presents a systematic procedure for the seismic response analysis of highway overcrossings. The study employs an elementary stick model and a more sophisticated finite element formulation to compute response quantities. All dynamic stiffnesses of approach embankments and pile groups are approximated with frequency‐independent springs and dashpots that have been established elsewhere. A real eigenvalue analysis confirms the one‐to‐one correspondence between modal characteristics obtained with the three‐dimensional finite element solutions and the result of the simpler stick‐model idealization. A complex eigenvalue analysis yields modal damping values in the first six modes of interest and shows that modal damping ratios assume values much higher than those used by Caltrans. The validity of the proposed method is examined by comparing the computed time response quantities with records from the Meloland Road and Painter Street overcrossings located in southern and northern California, respectively. The proposed procedure allows for inexpensive parametric analysis that examines the importance of considering soil–structure interaction at the end abutments and centre bent. Results and recommendations presented by past investigations are revisited and integrated in comprehensive tables that improve our understanding of the dynamic characteristics and behaviour of freeway overcrossings. The study concludes with a step‐by‐step methodology that allows for a simple, yet dependable dynamic analysis of freeway overcrossings, that involves a stick model and frequency‐independent springs and dashpots. Copyright © 2002 John Wiley & Sons, Ltd.     

Dynamic soil–structure interaction effects on the seismic response of asymmetric buildings

An approach is formulated for the linear analysis of three-dimensional dynamic soil–structure interaction of asymmetric buildings in the time domain, in order to evaluate the seismic response behaviour of torsionally coupled buildings. The asymmetric building is idealized as a single-storey three-dimensional system resting on different soil conditions. The soil beneath the superstructure is modeled as linear elastic solid elements. The contact surface between foundation mat and solid elements of soil is discretised by linear plane interface elements with zero thickness. An interface element is further developed to function between the rigid foundation and soil. As an example, the response of soil–structure interaction of torsionally coupled system under two simultaneous lateral components of El Centro 1940 earthquake records has been evaluated and the effects of base flexibility on the response behaviour of the system are verified.     

Input and system identification of the Hualien soil–structure interaction system using earthquake response data

This paper presents an input and system identification technique for a soil–structure interaction system using earthquake response data. Identification is carried out on the Hualien large‐scale seismic test structure, which was built in Taiwan for international joint research. The identified quantities are the input ground acceleration as well as the shear wave velocities of the near‐field soil regions and Young's moduli of the shell sections of the structure. The earthquake response analysis on the soil–structure interaction system is carried out using the finite element method incorporating the infinite element formulation for the unbounded layered soil medium and the substructured wave input technique. The criterion function for the parameter estimation is constructed using the frequency response amplitude ratios of the earthquake responses measured at several points of the structure, so that the information on the input motion may be excluded. The constrained steepest descent method is employed to obtain the revised parameters. The simulated earthquake responses using the identified parameters and input ground motion show excellent agreement with the measured responses. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamic soil–structure interaction effects on the seismic response of suspension bridges

A stochastic approach has been formulated for the linear analysis of suspension bridges subjected to earthquake excitations. The transfer functions of various responses have been formulated while including the effects of dynamic Soil–Structure Interaction (SSI) via the use of the fixed-base modes of the structure. The excitation has been characterized by the ‘equivalent stationary’ processes corresponding to the free-field motions at each support and by an assumed coherency function between these motions. The proposed formulation considers the non-stationarity in the structural response due to sudden application of excitation by considering (i) the time-dependent frequency response functions, and (ii) the order statistics formulation for the peak factors in evolutionary response processes. The formulation has been illustrated by analysing the seismic response of the Golden Gate Bridge at San Francisco for two example excitations conforming to USNRC-specified design spectra. The significance of various governing parameters on the dynamic soil–structure interaction effects on the seismic response of suspension bridges has also been studied. It has been found that the contribution of the vertical component of ground motion to the bridge response increases with increasing soil compliance. Also, the extent to which the spatial variation of ground motion affects the bridge response depends on how significant the SSI effects are. Copyright © 1999 John Wiley & Sons Ltd.     

The influence of dynamic soil–structure interaction on traffic induced vibrations in buildings

This paper deals with the dynamic response of buildings due to traffic induced wave fields. The response of a two-storey single family dwelling due to the passage of a two-axle truck on a traffic plateau is computed with a model that fully accounts for the dynamic interaction between the soil and the structure. The results of three cases where the structure is founded on a slab foundation, a strip foundation and a box foundation are calculated and a comprehensive analysis of the dynamic structural response is performed. A methodology is also proposed to calculate the structural response, neglecting the effects of dynamic soil–structure interaction. A comparison with the results of calculations where dynamic soil–structure interaction is accounted for shows that a good approximation is obtained in the case of a rigid structure resting on a soft soil.     

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.     

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.     

Effect of non-linear soil–structure interaction on seismic response of tall slender structures

Some structures may be very massive and may have to be located on relatively soft soil. In such cases, the soil adjacent to the structure behaves in a non-linear fashion and affects the response of the structure to the dynamic loading. An approximate hybrid approach to analyse soil–structure systems accounting for soil non-linearities has been developed in this paper. The approach combines the consistent infinitesimal finite-element cell method (CIFECM) and the finite-element method (FEM). The CIFECM is employed to model the non-linear (near-field) zone of the soil supporting the structure as a series of bounded media. The material properties of the bounded media are selected so that they are compatible with the average effective strains over the whole bounded medium during the excitation. The linear zone of soil away from the foundation, the far-field, is modelled as an unbounded medium using the CIFECM for unbounded media. The structure itself is represented by the FEM. The proposed method is used to model the dynamic response of a one-mass structure and a TV-tower supported on a homogenous stratum and excited by an earthquake. It was found that the secondary soil non-linearity might increase or decrease the base forces of tall slender structures depending on the type of structure, frequency content of the input motion and the dynamic properties of the near-field soil.     

Three‐dimensional models of reservoir sediment and effects on the seismic response of arch dams

The important effects of bottom sediments on the seismic response of arch dams are studied in this paper. To do so, a three‐dimensional boundary element model is used. It includes the water reservoir as a compressible fluid, the dam and unbounded foundation rock as viscoelastic solids, and the bottom sediment as a two‐phase poroelastic domain with dynamic behaviour described by Biot's equations. Dynamic interaction among all those regions, local topography and travelling wave effects are taken into account. The results obtained show the important influence of sediment compressibility and permeability on the seismic response. The former is associated with a general change of the system response whereas the permeability has a significant influence on damping at resonance peaks. The analysis is carried out in the frequency domain considering time harmonic excitation due to P and S plane waves. The time‐domain results obtained by using the Fourier transform for a given earthquake accelerogram are also shown. The possibility of using simplified models to represent the bottom sediment effects is discussed in the paper. Two alternative models for porous sediment are tested. Simplified models are shown to be able to reproduce the effects of porous sediments except for very high permeability values. Copyright © 2004 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.     

Influence of free field variability on linear soil–structure interaction (SSI) by indirect integral representation

An integral equation for the representation of the response of a structure impinged by an incident wave field including soil–structure interaction is proposed. It requires the knowledge of the fundamental solution for the overall soil–structure domain when a unit load is applied to the structure. This fundamental solution is obtained by means of a substructuring technique and boundary integral equations using the Green tensors for homogeneous or horizontally stratified soil media. The effects of a non‐stationary modulated random incident field are addressed in terms of the instantaneous power spectral density of the structural response of interest for a given coherency function of the free field. Several applications of the proposed procedure are presented. The first one considers kinematic interaction of a rigid circular foundation and is used to validate the numerical implementation. The second one considers a complex structure on a stiff stratified soil and the last one considers the pounding effect between two adjacent, identical structures resting on a thin soft soil layer. Copyright © 2002 John Wiley & Sons, Ltd.     

Seismic response of a bridge–soil–foundation system under the combined effect of vertical and horizontal ground motions

Different levels of model sophistication have recently emerged to support seismic risk assessment of bridges, but mostly at the expense of neglecting the influence of vertical ground motions (VGMs). In this paper, the influence of VGMs on bridge seismic response is presented and the results are compared with the case of horizontal‐only excitations. An advanced finite element model that accounts for VGMs is first developed. Then, to investigate the effect of soil–structure interaction (SSI) including liquefaction potential, the same bridge with soil‐foundation and fixed boundary conditions is also analyzed. Results show that the inclusion of the VGMs has a significant influence on the seismic response, especially for the axial force in columns, normal force of bearings, and the vertical deck bending moments. However, VGMs do not have as much influence on the seismic demand of the pile cap displacements or pile maximum axial forces. Also, the significant fluctuation of the column axial force can reduce its shear and flexural capacity, and a heightened reversal of flexural effects may induce damage in the deck. In addition, relative to the fixed base case, SSI effects tend to reduce response quantities for certain ground motions while increasing demands for others. This phenomenon is explained as a function of the frequency content of the ground motions, the shift in natural vertical periods, and the VGM spectral accelerations at higher modes. Moreover, the mechanisms of liquefaction are isolated relative to SSI effects in nonliquefiable soils, revealing the influence of liquefaction on bridge response under VGMs. Copyright © 2012 John Wiley & Sons, Ltd.     

Structure, soil–structure response and effects of damage based on observations of horizontal-to-vertical spectral ratios of microtremors

The microtremor horizontal-to-vertical-spectral-ratio (HVSR) technique is widely used in the urban environment to assess the fundamental frequency response of the ground. Extensive literature exists about case histories using HVSR for microzonation in several cities, but no systematic studies have been devoted to check the presence of soil–structure interaction effects, and even less attention to study building behaviour after earthquake damage. To evaluate the above-mentioned effects, a series of experiments are reported in this article.We first made a series of microtremor measurements on buildings and civil structures to evaluate the reliability of fundamental frequency determinations. Then, we considered several case studies to evaluate the effect of soil–structure interaction in estimates of site response in the presence of tall buildings. Finally, an experiment on the frequency change due to damage was performed. It was possible to confirm that HVSR is able to detect building fundamental modes and once known the building frequency, it is also possible to detect the presence of soil–structure interaction. Thus, once the presence of the building natural frequency is identified, it is possible to infer the site response from free field measurements. We also found that the HVSR technique is equally useful for detecting structural damage by determining the frequency shift of the buildings.     

Influences of type of wave and angle of incidence on seismic bending moments in pile foundations

When analysing the seismic response of pile groups, a vertically‐incident wavefield is usually employed even though it does not necessarily correspond to the worst case scenario. This work aims to study the influences of both the type of seismic body wave and its angle of incidence on the dynamic response of pile foundations. To this end, the formulation of SV, SH and P obliquely‐incident waves is presented and implemented in a frequency‐domain boundary element‐finite element code for the dynamic analysis of pile foundations and piled structures. Results are presented in terms of bending moments at cap level of single piles and 3 × 3 pile groups, both in frequency and in time domains. It is found that, in general, the vertical incidence is not the most unfavourable situation. In particular, obliquely‐incident SV waves with angles of incidence smaller than the critical one, a situation in which the mechanism of propagation of the waves in the soil changes and surface waves appear, yield bending moments much larger than those obtained for vertically‐incident wavefields. It is also shown that the influence of pile‐to‐pile interaction on the kinematic bending moments becomes significant for non‐vertical incidence, especially for P and SV waves. Copyright © 2013 John Wiley & Sons, Ltd.