A model for the 3D kinematic interaction analysis of pile groups in layered soils

The paper presents a numerical model for the analysis of the soil–structure kinematic interaction of single piles and pile groups embedded in layered soil deposits during seismic actions. A finite element model is considered for the pile group and the soil is assumed to be a Winkler‐type medium. The pile–soil–pile interaction and the radiation problem are accounted for by means of elastodynamic Green's functions. Condensation of the problem permits a consistent and straightforward derivation of both the impedance functions and the foundation input motion, which are necessary to perform the inertial soil–structure interaction analyses. The model proposed allows calculating the internal forces induced by soil–pile and pile‐to‐pile interactions. Comparisons with data available in literature are made to study the convergence and validate the model. An application to a realistic pile foundation is given to demonstrate the potential of the model to catch the dynamic behaviour of the soil–foundation system and the stress resultants in each pile. Copyright © 2009 John Wiley & Sons, Ltd.     

A method for assessing kinematic bending moments at the pile head

The conventional design methods for seismically loaded piles still concentrate in providing adequate resistance from the pile to withstand only the inertial bending moments generated from the oscillation of the superstructure, thus neglecting the effect of kinematic interaction between pile and soil. By contrast there has been extensive research on kinematic effects induced by earthquakes and a number of simplified methods are available for a preliminary evaluation of kinematic bending moments at the interface between two soil layers. Less attention has been paid to the effects of kinematic interaction at the pile‐head. The paper summarizes recent research work on kinematic response analysis of fixed‐head piles aimed at the performance evaluation of a piled foundation. Results from an extensive parametric study, undertaken by means of three‐dimensional FE analyses, suggest a new criterion to predict kinematic bending effects at the pile head, where the combination of kinematic and inertial effect may be critical. Copyright © 2010 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.     

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.     

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.     

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.     

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.     

RESPONSE OF EARTH DAMS TO P AND SV WAVES USING COUPLED FE-BE FORMULATION

A study of the effects of dam–foundation interaction on the response of earth dams to obliquely incident P and SV waves is presented. Emphasis is placed on the effects of the foundation flexibility and the spatial variability of the ground motion. The study is based on a rigorous hybrid numerical formulation that combines the efficiency and versatility of the Finite Element Method (FEM) and the ability of Boundary Element Method (BEM) to account for the radiation conditions at the far field. The developed hybrid method is very powerful and can be used efficiently to obtain accurate solutions of problems of complex geometry, material heterogeneity and, for time-domain analyses, material nonlinearity. The 2-D frequency-domain formulation is used here to investigate the response of infinitely long earth dams to obliquely incident P and SV waves. By accounting rigorously for the energy radiated back into the half-space, the study demonstrates the dramatic effect of the flexibility of the foundation rock in reducing the overall response of the dam. The effects of the spatial variability of the ground motion for P and SV waves travelling across the width of the dam are also important, but somewhat less pronounced than those of the foundation flexibility.     

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.     

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.     

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.     

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.     

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.     

A discontinuous Galerkin method for seismic soil–structure interaction analysis in the time domain

A technique for modeling transient wave propagation in unbounded media is extended and applied to seismic soil–structure interaction analysis in the time domain. The technique, based on the discontinuous Galerkin method, requires lower computational cost and less storage than the boundary element method, and the time‐stepping scheme resulting from Newmark's method in conjunction with the technique is unconditionally stable, allowing for efficient and robust time‐domain computations. To extend the technique to cases characterized by seismic excitation, the free‐field motion is used to compute effective forces, which are introduced on the boundary of the computational domain containing the structure and the soil in the vicinity of the structure. A numerical example on a dam–foundation system subjected to seismic excitation demonstrates the performance of the method. Copyright © 2003 John Wiley & Sons, Ltd.     

Kinematic response of single piles to vertically incident P‐waves

Dynamic response of single piles to seismic waves is fundamentally different from the free‐field motion because of the interaction between the pile and the surrounding soil. Considering soil–pile interaction, this paper presents a new displacement model for the steady‐state kinematic response of single piles to vertically incident P‐waves on the basis of a continuum model. The governing equations and boundary conditions of the two undetermined functions in the model are obtained to be coupled by using Hamilton's principle. Then, the two unknown functions are decoupled and solved by an iterative algorithm numerically. A parametric study is performed to investigate the effects of the properties of the soil–pile system on the kinematic response of single piles. It is shown that the effects of the pile–soil modulus ratio, the slenderness ratio of the pile, and the frequency of the incident excitations are very significant. By contrast, the influence of soil damping on the kinematics of the system is slight and can be neglected. Copyright © 2013 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.     

A coupling model of FE–BE–IE–IBE for non-linear layered soil–structure interactions

A coupling model of Finite Elements (FEs), Boundary Elements (BEs), Infinite Elements (IEs) and Infinite Boundary Elements (IBEs) is presented for analysis of soil–structure interaction (SSI). The radiation effects of the infinite layered soil are taken into account by FE–IE coupling, while the underlying bed rock half-space is discretized into BE–IBE coupling whereby the non-horizontal bed rock surface can be accounted for. Displacement compatabilities are satisfied for all types of aforementioned elements. The equivalent linear approach is employed for approximation of nonlinearity of the near field soil. This model has some advantages over the current SSI program in considering the bed rock half-space and non-vertical wave incidence from the far field. Examples of verification demonstrate the applicability and accuracy of the method when compared with the FLUSH program. Finally, the effects of the relative modulus ratio E_r/E_s of rock and soil and the incident angles of non-vertical waves on the responses of the structure and the soil are examined. Copyright © 1999 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.     

Earthquake fault rupture—shallow foundation interaction in undrained soils: a simplified analytical approach

The interaction between normal or reverse fault ruptures and shallow foundations resting on a homogeneous undrained soil layer is investigated. After performing a thorough set of non‐linear finite element simulations, three simple kinematic mechanisms are proposed to predict the conditions for the fault rupture to be diverted by the foundation. The results obtained by both numerical and analytical approaches are in good agreement, and support the adequacy of the proposed mechanisms. A relationship is established for assessing the minimum foundation bearing load needed for diversion of the fault rupture trace, either normal or reverse. This relationship is proved to be independent of the fault type and dip angle, so that it can be applied easily for engineering applications, even in the absence of specific tectonic information. Copyright © 2006 John Wiley & Sons, Ltd.     

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.