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.     

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

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

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.     

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.     

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.     

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.     

Seismic analysis of infinite pile groups in liquefiable soil

Numerical analysis of an infinite pile group in a liquefiable soil was considered in order to investigate the influence of pile spacing on excess pore pressure distribution and liquefaction potential. It was found that an optimal pile spacing exists resulting in minimal excess pore pressure. It was also found that certain pile group configurations might reduce liquefaction potential, compared to free field conditions. It was observed that for closely spaced piles and low frequency of loading, pile spacing has little influence on the response of the superstructure.     

Response analysis of the Higashi–Kobe Bridge and surrounding soil in the 1995 Hyogoken–Nanbu Earthquake

This paper presents results of observation and analysis of the response of one of the longest cable-stayed bridges in the world to the Hyogoken–Nanbu (Kobe) Earthquake of 17 January 1995. It is determined that interaction of the foundations of the bridge towers with the supporting soil plays a decisive role in the overall structural behaviour. The key factor governing the changes of the soil properties at this site is pore-water pressure buildup, which results in liquefaction of the saturated surface soil layers under large dynamic loads. Models of the soil and structure are created and initially validated by accurately simulating the system response to a small earthquake. Soil parameters reflecting the pore-water pressure buildup in the strong earthquake are determined by an advanced non-linear effective stress analysis, combining the Ramberg–Osgood model of stress–strain dependence with a pore pressure model based on shear work concept. They are utilized to investigate and simulate the interaction of the foundation and the supporting soil using the program SASSI with the flexible volume substructuring approach. The results show a good agreement with the observations and have useful implications to the scientific and engineering practice. © 1998 John Wiley & Sons, Ltd.     

A practical method to transform frequency dependent impedance to time domain

In order to perform time history earthquake response analyses with consideration to both the dynamic soil–structure interaction and the non‐linear behaviour of the structure, it is important to transform the soil impedance in the frequency domain to the impulse response in the time domain. In this paper, a new transform method with high practicality is proposed. First, the formulation of the proposed transform method is described. Next, the validity of the method is examined using an example problem whose impulse response is analytically obtained. Then, the impedance of the rigid foundation on 2‐layered soil is transformed to the time domain, and the characteristics of the impulse response are investigated. Finally, time history earthquake response analyses of a structure on the soil using the obtained impulse response are carried out. The validity and the efficiency of the proposed method are confirmed through these investigations. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic soil–structure interaction of massive flexible strip-foundations embedded in layered soils by hybrid BEM–FEM

A study on the seismic response of massive flexible strip-foundations embedded in layered soils and subjected to seismic excitation is presented. Emphasis is placed on the investigation of the system response with the aid of a boundary element–finite element formulation proper for the treatment of such soil–structure interaction problems. In the formulation, the boundary element method (BEM) is employed to overcome the difficulties that arise from modeling the infinite soil domain, and the finite element method (FEM) is applied to model the embedded massive flexible strip-foundation. The numerical solution for the soil–foundation system is obtained by coupling the FEM with the BEM through compatibility and equilibrium conditions at the soil–foundation and soil layer interfaces. A parametric study is conducted to investigate the effects of foundation stiffness and embedment on the seismic response.     

Seismic analysis of lock–soil–fluid systems by hybrid BEM–FEM

A study of soil–structure–fluid interaction (SSFI) of a lock system subjected to harmonic seismic excitation is presented. The water contained lock is embedded in layered soils supported by a half-space bedrock. The ground excitation is prescribed at the soil–bedrock interface. The response is numerically obtained through a hybrid boundary element (BEM) finite element method (FEM) formulation. The semi-infinite soil and the fluid are modeled by the BEM and the lock is modeled by the FEM. The equilibrium equation for the lock system is obtained by enforcing compatibility and equilibrium conditions at the fluid–structure, soil–structure and soil–layer interfaces under conditions of plane strain. To the authors’ knowledge this is the first study of a lock system that considers the effects of dynamic soil–fluid–structure interaction through a BEM–FEM methodology. A numerical example and parametric studies are presented to examine the effects of the presence of water, lock stiffness, and lock embedment on the response.     

Response of seismically isolated structures to rocking‐type excitations

In this paper, the origin of rocking‐type excitations and their effects on the response of base isolated structures are studied. In particular, the role of kinematic interaction in the determination of the rocking excitation is highlighted. The cases of surface foundations subjected to horizontally propagating waves, as well as of embedded foundations under vertically incident shear waves are examined. The validity of the kinematic interaction based on the rigid base mat assumption is discussed. It is shown that, in the case of classical horizontal isolation, rocking input may amplify significantly the response of the lower non‐isolated modes. The examination of full three‐dimensional isolation and active and semi‐active control methods demonstrates the efficacy of these methods to improve the performance of seismically isolated structures subjected to rocking excitations. Copyright © 2009 John Wiley & Sons, Ltd.     

Horizontal impedance of square foundation in layered soil

This paper presents an extensive investigation into the influence of key mechanical and geometrical parameters on horizontal impedance of square foundations resting on or embedded in a two-layer soil deposit. The parameters investigated are the ratio of shear-wave velocities, the thickness of the top layer, the depth of embedment and the degree of contact between the footing-sidewall with backfill-soil. The results are presented in the form of simple and versatile dimensionless graphs, which should prove to be useful in understanding the steady-state harmonic response of square foundations in layered soils due to horizontal excitation. The investigation was conducted using a rigorous boundary element algorithm incorporating isoparametric boundary elements. Higher order quadratic elements were used since they can model the wavy nature of the dynamic problem investigated more accurately.     

A spatial windowing technique to account for finite dimensions in 2.5D dynamic soil–structure interaction problems

The dynamic interaction between a layered halfspace and quasi translationally invariant structures such as roads, railway tracks, tunnels, dams, and lifelines can be modelled using a computationally efficient 2.5D approach, assuming invariance of the geometry in the longitudinal direction. This assumption is not always fulfilled in practice, however. Even for elongated structures, full 3D computations may be required for an accurate solution of the dynamic soil–structure interaction problem. This paper presents a spatial windowing technique for elastodynamic transmission and radiation problems that allows accounting for the finite length of a structure, still maintaining the computational efficiency of a 2.5D formulation. The proposed technique accounts for the diffraction occurring at the structure's edges, but not for its modal behaviour resulting from reflections of waves at its boundaries. Numerical examples of a barrier for vibration transmission and a surface foundation are discussed to demonstrate the accuracy and applicability of the proposed methodology. Full 3D calculations are performed to provide a rigorous validation for each of these examples. It is demonstrated that the proposed technique is appropriate as long as the response is not dominated by the resonant behaviour of individual modes of the structure.     

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.     

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.     

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.     

A practical method for estimating dynamic soil stiffness on surface of multi‐layered soil

It is important to estimate the influence of layered soil in soil–structure interaction analyses. Although a great number of investigations have been carried out on this subject, there are very few practical methods that do not require complex calculations. In this paper, a simple and practical method for estimating the horizontal dynamic stiffness of a rigid foundation on the surface of multi‐layered soil is proposed. In this method, waves propagating in the soil are traced using the conception of the cone model, and the impulse response function can be calculated directly and easily in the time domain with a good degree of accuracy. The characteristics of the impedance, that is the transformed value to the frequency domain of the obtained impulse response, are studied using two‐ to four‐layered soil models. The cause of the fluctuation of impedance is expressed clearly from its relation to reflected waves from the lower layer boundary in the model. Copyright © 2005 John Wiley & Sons, Ltd.     

Local and global shape functions in a boundary element formulation for the calculation of traffic induced vibrations

This paper compares the use of local and global shape functions in a boundary element method that is used in a prediction model for traffic induced vibrations. The boundary element formulation describes the interaction problem between a linear elastic layered half-space and a longitudinally invariant structure representing a road or a railway track. The boundary element formulation in the frequency–wavenumber domain is obtained by means of a weighted residual method. Constant element shape functions, as well as Legendre and Chebyshev shape functions are considered. Their effect on both accuracy and computational effort is investigated. The presence of a singularity in the Chebyshev based shape functions allows to obtain a better approximation for the soil tractions. The theory is applied to road traffic induced vibrations where the response is calculated in a large number of output points.     

The role of soil in the collapse of 18 piers of Hanshin Expressway in the Kobe earthquake

An investigation is presented of the collapse of a 630 m segment (Fukae section) of the elevated Hanshin Expressway during the 1995 Kobe earthquake. The earthquake has, from a geotechnical viewpoint, been associated with extensive liquefactions, lateral soil spreading, and damage to waterfront structures. Evidence is presented that soil–structure interaction (SSI) in non‐liquefied ground played a detrimental role in the seismic performance of this major structure. The bridge consisted of single circular concrete piers monolithically connected to a concrete deck, founded on groups of 17 piles in layers of loose to dense sands and moderate to stiff clays. There were 18 spans in total, all of which suffered a spectacular pier failure and transverse overturning. Several factors associated with poor structural design have already been identified. The scope of this work is to extend the previous studies by investigating the role of soil in the collapse. The following issues are examined: (1) seismological and geotechnical information pertaining to the site; (2) free‐field soil response; (3) response of foundation‐superstructure system; (4) evaluation of results against earlier studies that did not consider SSI. Results indicate that the role of soil in the collapse was multiple: First, it modified the bedrock motion so that the frequency content of the resulting surface motion became disadvantageous for the particular structure. Second, the compliance of soil and foundation altered the vibrational characteristics of the bridge and moved it to a region of stronger response. Third, the compliance of the foundation increased the participation of the fundamental mode of the structure, inducing stronger response. It is shown that the increase in inelastic seismic demand in the piers may have exceeded 100% in comparison with piers fixed at the base. These conclusions contradict a widespread view of an always‐beneficial role of seismic SSI. Copyright © 2005 John Wiley & Sons, Ltd.