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.     

Soil–pile–structure interaction under SH wave excitation

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

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.     

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

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

Probabilistic critical excitation for MDOF elastic–plastic structures on compliant ground

Earthquake ground motions and their effects on structural responses are very uncertain even with the present knowledge. It is therefore desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new random critical excitation method is proposed for MDOF elastic–plastic shear‐building structures on compliant ground. The power (area of power spectral density (PSD) function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. In contrast to linear elastic structures, transfer functions and simple expressions for response evaluation cannot be defined in elastic–plastic structures and difficulties arise in describing the peak responses except by laborious elastic–plastic time‐history response analysis. Statistical equivalent linearization is used to estimate the elastic–plastic stochastic peak responses approximately. The critical excitation responses are obtained for several examples and compared with those of the corresponding recorded earthquake ground motion. Copyright © 2001 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.     

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.     

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

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

Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion,site effects and soil–structure interaction phenomena. Part 2: Parametric study

The methodology for dealing with spatial variability of ground motion, site effects and soil–structure interaction phenomena in the context of inelastic dynamic analysis of bridge structures, and the associated analytical tools established and validated in a companion paper are used herein for a detailed parametric analysis, aiming to evaluate the importance of the above effects in seismic design. For a total of 20 bridge structures differing in terms of structural type (fundamental period, symmetry, regularity, abutment conditions, pier‐to‐deck connections), dimensions (span and overall length), and ground motion characteristics (earthquake frequency content and direction of excitation), the dynamic response corresponding to nine levels of increasing analysis complexity was calculated and compared with the ‘standard’ case of a fixed base, uniformly excited, elastic structure for which site effects were totally ignored. It is concluded that the dynamic response of RC bridges is indeed strongly affected by the coupling of the above phenomena that may adversely affect displacements and/or action effects under certain circumstances. Evidence is also presented that some bridge types are relatively more sensitive to the above phenomena, hence a more refined analysis approach should be considered in their case. Copyright @ 2003 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.     

Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion,site effects and soil–structure interaction phenomena. Part 1: Methodology and analytical tools

During strong ground motion it is expected that extended structures (such as bridges) are subjected to excitation that varies along their longitudinal axis in terms of arrival time, amplitude and frequency content, a fact primarily attributed to the wave passage effect, the loss of coherency and the role of local site conditions. Furthermore, the foundation interacts with the soil and the superstructure, thus significantly affecting the dynamic response of the bridge. A general methodology is therefore set up and implemented into a computer code for deriving sets of appropriately modified time histories and spring–dashpot coefficients at each support of a bridge with account for spatial variability, local site conditions and soil–foundation–superstructure interaction, for the purposes of inelastic dynamic analysis of RC bridges. In order to validate the methodology and code developed, each stage of the proposed procedure is verified using recorded data, finite‐element analyses, alternative computer programs, previous research studies, and closed‐form solutions wherever available. The results establish an adequate degree of confidence in the use of the proposed methodology and code in further parametric analyses and seismic design. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic effectiveness of tuned mass dampers considering soil–structure interaction

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

Influence of the soil–structure interaction on the fundamental period of buildings

This paper includes an investigation of the influence of the soil–structure interaction (SSI) on the fundamental period of buildings. The behaviour of both the soil and the structure is assumed to be elastic. The soil‐foundation system is modelled using translational and rotational discrete springs. Analysis is first conducted for one‐storey buildings. It shows that the influence of the SSI on the fundamental frequency of building depends on the soil–structure relative rigidity K_ss. Analysis is then extended for multi‐storey buildings. It allows the generalization of the soil–structure relative rigidity K_s to such complex structures. Charts are proposed for taking into account the influence of the SSI in the calculation of the fundamental frequency of a wide range of buildings. Copyright © 2007 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.     

Shinkansen high-speed train induced ground vibrations in view of viaduct–ground interaction

Train viaduct behavior and nearby ground motion under the high-speed train passage have been studied in this paper. First, the findings from the field measurement alongside the high-speed Shinkansen railway in Japan are interpreted. Then, the computer simulation is made based on the soil-foundation-viaduct interaction analysis under moving axle loads. The solution method is to apply the dynamic substructure method in the frequency domain. The viaduct girders including track structure and pier supports are modeled by the three-dimensional beam-column elements. The supporting pile foundation and nearby field are discretized by the axisymmetric three-dimensional finite elements and analyzed in a semi-analytical way, with a transmitting boundary replacing the far field based on the thin layer element method. Nearby ground motion during train passage on a viaduct have been calculated by superimposing the effects from neighboring pile foundations.The main parameters affecting viaduct vibrations are discussed by taking environmental vibration into consideration. The nearby ground motion along the viaduct is recomputed by applying the above determined forces to the foundation tops. The results from numerical studies are compared with the field test data, thus proving the present simulation to be effective and reliable.     

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.     

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.     

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.     

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 an interacting curved bridge–train system under frequent earthquakes

This paper establishes a scheme for the seismic analysis of interacting vehicle–bridge systems. The focus is on (horizontally) curved continuous railway bridges and frequent earthquakes. Main features of the proposed scheme are (i) the treatment of the dynamics in all three dimensions (3D), employing an additional rotating system of reference to describe the dynamics of the vehicles and a realistic 3D bridge model; (ii) the simulation of the creep interaction forces generated by the rolling contact between the wheel and the rail; and (iii) the integration of the proposed scheme with powerful commercial finite element software, during the pre‐processing and post‐processing phases of the analysis. The study brings forward the dynamics of a realistic vehicle–bridge (interacting) system during seismic shaking. For the (vehicle–bridge) case examined, the results verify the favorable damping effect the running vehicles have on the vibration of the deck. By contrast, the study stresses the adverse influence of the earthquake‐induced bridge vibration on the riding comfort but, more importantly, on the safety of the running vehicles. In this context, the paper unveils also a vehicle–bridge–earthquake timing problem, behind the most critical vehicle response, and underlines the need for a probabilistic treatment. Among the 20 sets of historic records examined, the most crucial for the safety of the vehicles are near‐fault ground motions. Finally, the study shows that even frequent earthquakes, of moderate intensity, can threaten the safety of vehicles running on bridges during the ground motion excitation, in accordance with recorded accidents. Copyright © 2016 John Wiley & Sons, Ltd.