A simplified method to determine seismic responses of reinforced concrete moment resisting building frames under influence of soil–structure interaction

As the Iranian seismic code does not address the soil–structure interaction (SSI) explicitly, the effects of SSI on RC-MRFs are studied using the direct method. Four types of structures on three types of soils, with and without the soil interaction, are modeled and subjected to different earthquake records. The results led to a criterion indicating that considering SSI in seismic design, for buildings higher than three and seven stories on soil with V_s<175 m/s and 175<V_s<375 m/s, respectively, is essential. A simplified procedure has been presented, on the basis that lateral displacement increments could be applied to the fixed-base models using simple factors.     

Effects of soil cracking on the seismic response of soil–structure systems

A numerical study on the influence that cracks and discontinuities (closed cracks) can have on the seismic response of a hypothetical soil–structure system is presented and discussed. A 2-D finite-difference model of the soil was developed, considering a bilinear failure surface using a Mohr–Coulomb model. The cracks are simulated with interface elements. The soil stiffness is used to characterize the contact force that is generated when the crack closes. For the cases studied herein, it was considered that the crack does not propagate during the dynamic event. Both cases, open and closed cracks, are considered. The nonlinear behavior was accounted for approximately using equivalent linear properties calibrated against several 1-D wave propagation analyses of selected soil columns with variable depth to account for changes in depth to bed rock. Free field boundaries were used at the edges of the 2-D finite-difference model to allow for energy dissipation of the reflected waves. The effect of cracking on the seismic response was evaluated by comparing the results of site response analysis with and without crack, for several lengths and orientations. The changes in the response obtained for a single crack and a family of cracks were also evaluated. Finally, the impact that a crack may have on the structural response of nearby structures was investigated by solving the seismic-soil–structure interaction of two structures, one flexible and one rigid to bracket the response. From the results of this investigation, insight was gained regarding the effect that discontinuities may have both on the seismic response of soil deposits and on nearby soil–structure systems.     

Dynamic response of structures subjected to pounding and structure–soil–structure interaction

During strong earthquakes, adjacent structures with non-sufficient clear distances collide with each other. In addition to such a pounding, cross interaction of adjacent structures through soil can exchange the vibration energy between buildings and make the problem even more complex. In this paper, effects of both of the mentioned phenomena on the inelastic response of selected steel structures are studied. Number of stories varied between 3 and 12 and different clear distances up to the seismic codes prescribed value are considered. The pounding element is modeled within Opensees. A coupled model of springs and dashpots is utilized for through-the-soil interaction of the adjacent structures, for two types of soft soils. The pounding force, relative displacements of stories, story shears, and plastic hinge rotations are compared for different conditions as the maximum responses averaged between seven consistent earthquakes. As a result, simultaneous effects of pounding and structure–soil–structure interaction are discussed.     

Inelastic seismic behavior of soil–pile raft–structure system under bi-directional ground motion

Performance based design of structure requires a reasonably accurate prediction of displacement or ductility demand. Generally, displacement demand of structure is estimated assuming fixity at base and considering base motion in one direction. In reality, ground motions occur in two orthogonal directions simultaneously resulting in bidirectional interaction in inelastic range, and soil–structure interaction (SSI) may change structural response too. Present study is an attempt to develop insight on the influence of bi-directional interaction and soil–pile raft–structure interaction for predicting the inelastic response of soil–pile raft–structure system in a more reasonably accurate manner. A recently developed hysteresis model capable to simulate biaxial interaction between deformations in two principal directions of any structural member under two orthogonal components of ground motion has been used. This study primarily shows that a considerable change may occur in inelastic demand of structures due to the combined effect of such phenomena.     

The effect of soil–structure interaction on the seismic risk to buildings

This paper studies the effect of soil–structure interaction (SSI) on the seismic risk estimates of buildings. Risk, in this context, denotes the probability distribution of seismic monetary loss due to structural and nonstructural damage. The risk analysis here uncovers the probability that SSI is beneficial, detrimental, or uninfluential on seismic losses. The analyses are conducted for a wide range of buildings with different structural systems, numbers of stories, and foundation sizes on various soil types. A probabilistic approach is employed to account for prevailing sources of uncertainty, i.e., those in ground motion and in the properties of the soil–structure system. In this approach, probabilistic models are employed to predict the response, damage, and repair cost of buildings. To properly account for the ground motion uncertainty, a suite of nearly 7000 accelerograms recorded on soil is employed. It is concluded that structures on very soft soils are extremely likely to incur smaller losses due to SSI, which is in line with the common belief that SSI is a favorable effect for such systems. However, the results for buildings on moderately soft soils reveal a considerable probability, up to 0.4, that SSI has an adverse effect on the structure and increases the seismic losses.     

Effects of soil–structure interaction on the dynamic properties and seismic response of piled structures

This paper presents a simple and stable procedure for the estimation of periods and dampings of piled shear buildings taking soil–structure interaction into account. A substructuring methodology that includes the three-dimensional character of the foundations is used. The structure is analyzed as founded on an elastic homogeneous half-space and excited by vertically incident S waves. The strategies proposed in the literature to estimate the period and damping are revised, and a modified strategy is proposed including crossed impedances and all damping terms. Ready-to-use graphs are presented for the estimation of flexible-base period and damping in terms of their fixed-base values and the system configuration. Maximum shear forces together with base displacement and rocking peak response are also provided. It is shown that cross-coupled impedances and kinematic interaction factors need to be taken into account to obtain accurate results for piled buildings.     

Effects of soil–structure interaction on seismic base isolation

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

Influence of plasticity on the seismic soil–micropiles–structure interaction

This paper includes an analysis of the influence of soil plasticity on the seismic response of micropiles. Analysis is carried out using a global three-dimensional modeling in the time domain. The soil behavior is described using the non-associated Mohr–Coulomb criterion. Both the micropiles and the superstructure are modeled as three-dimensional beam elements. Proper boundary conditions are used to ensure waves transmission through the lateral boundaries of the soil mass. Analyses are first conducted for harmonic loadings and then for real earthquake records. They show that plasticity could have a significant influence on the seismic response of the soil–micropiles–structure systems. This influence depends on the amplitude of the seismic loading and the dominant frequencies of both the input motion and the soil–piles–structure system.     

Simplified seismic analysis of soil–well–pier system for bridges

Seismic analysis of soil–well–pier system was carried out using three different approaches to evaluate their comparative performance and associated complexities. These approaches were (a) two-dimensional nonlinear (2D-NL), (b) two-dimensional equivalent-linear (2D-EqL), and (c) one-dimensional spring–dashpot (1D). Soil was modeled as 2D plane-strain elements in the 2D-NL and 2D-EqL approaches, and as springs and dashpots in the 1D approach. Nonlinear behavior of soil was captured rigorously in the 2D-NL approach and approximately in the remaining two approaches. Results of the two approximate analyses (i.e., 2D-EqL and 1D) were compared with those of the 2D-NL analysis with the objective to assess suitability of approximate analysis for practical purposes. In the 1D approach, several combinations of Novak's and Veletsos' springs were used to come up with a simplified 1D model using three types of spring–dashpots. The proposed model estimates the displacement and force resultants relatively better than the other 1D models available in literature.     

Soil–structure interaction effects on seismic inelastic analysis of 3-D tunnels

This paper investigates the importance of seismic soil–structure interaction in three-dimensional lined tunnels, assuming inelastic material behaviour for both the concrete liner and the soft rock type of soil. The seismic response of the soil–structure system is determined by the finite element method (FEM) in the time domain. Viscous absorbing boundaries are used in conjunction with the discretization of the rock medium. Both the rock medium and the concrete liner are assumed to behave inelastically on the basis of the continuum damage mechanics theory. The seismic waves are assumed to have any arbitrary time variation and direction of propagation. The system is analysed with and without soil–structure interaction in order to assess its importance on the response of the system. Through parametric studies, the influence of the most critical parameters affecting the structural response is determined and critically discussed.     

Seismic response of base-isolated buildings including soil–structure interaction

This study investigates the effect of soil–structure interaction (SSI) on the response of base-isolated buildings. The equations of motion are formulated in the frequency domain, assuming frequency-independent soil stiffness and damping constants. An equivalent fixed-base system is developed that accounts for soil compliance and damping characteristics of the base-isolated building. Closed-form expressions are derived, followed by a thorough parametric study involving the pertinent system parameters. For preliminary design, the methodology can serve as a means to assess effective use of base isolation on building structures accounting for SSI. This study concludes that the effects of SSI are more pronounced on the modal properties of the system, especially for the case of squat and stiff base-isolated structures.     

Probabilistic seismic performance and loss assessment of a bridge–foundation–soil system

This paper presents the probabilistic seismic performance and loss assessment of an actual bridge–foundation–soil system, the Fitzgerald Avenue twin bridges in Christchurch, New Zealand. A two-dimensional finite element model of the longitudinal direction of the system is modelled using advanced soil and structural constitutive models. Ground motions at multiple levels of intensity are selected based on the seismic hazard deaggregation at the site. Based on rigorous examination of several deterministic analyses, engineering demand parameters (EDP's), which capture the global and local demand, and consequent damage to the bridge and foundation are determined. A probabilistic seismic loss assessment of the structure considering both direct repair and loss of functionality consequences was performed to holistically assess the seismic risk of the system.It was found that the non-horizontal stratification of the soils, liquefaction, and soil–structure interaction had pronounced effects on the seismic demand distribution of the bridge components, of which the north abutment piles and central pier were critical in the systems seismic performance. The consequences due to loss of functionality of the bridge during repair were significantly larger than the direct repair costs, with over a 2% in 50 year probability of the total loss exceeding twice the book-value of the structure.     

Nonlinear seismic behaviour of wall-frame dual systems accounting for soil–structure interaction

The aim of this paper is to study the effects of soil–structure interaction on the seismic response of coupled wall-frame structures on pile foundations designed according to modern seismic provisions. The analysis methodology based on the substructure method is recalled focusing on the modelling of pile group foundations. The nonlinear inertial interaction analysis is performed in the time domain by using a finite element model of the superstructure. Suitable lumped parameter models are implemented to reproduce the frequency-dependent compliance of the soil-foundation systems. The effects of soil–structure interaction are evaluated by considering a realistic case study consisting of a 6-storey 4-bay wall-frame structure founded on piles. Different two-layered soil deposits are investigated by varying the layer thicknesses and properties. Artificial earthquakes are employed to simulate the earthquake input. Comparisons of the results obtained considering compliant base and fixed base models are presented by addressing the effects of soil–structure interaction on displacements, base shears, and ductility demand. The evolution of dissipative mechanisms and the relevant redistribution of shear between the wall and the frame are investigated by considering earthquakes with increasing intensity. Effects on the foundations are also shown by pointing out the importance of both kinematic and inertial interaction. Finally, the response of the structure to some real near-fault records is studied. Copyright © 2012 John Wiley & Sons, Ltd.     

The effect of foundation flexibility variation on system response of dynamic soil–structure interaction: an analytical solution

A closed-form analytical solution is presented for the dynamic response of a SDOF oscillator, supported by a flexible composite foundation embedded in an elastic half-space, and excited by plane SH waves. The solution is obtained by the wave function expansion method. The solution is verified for the two limiting cases of a rigid–flexible composite foundation and a homogeneous flexible foundation by comparison with published results. The model is used to investigate the effect of the foundation flexibility variation on the system response. The results show that the effect is significant for both foundation response and structural relative response. For a system with larger foundation flexibility variation, the peak of the foundation effective input motion is smaller, while the amplitude of structural relative response less changes. When foundation flexibility variation decreases, system frequency will shift to lower frequency, and the shift value is also highly dependent on the foundation flexibility variation.     

Simulation of soil–foundation–structure interaction of Hualien large-scale seismic test using dynamic centrifuge test

Understanding the soil–structure interaction (SSI) mechanism is crucial in the seismic design of nuclear power plant (NPP) containment systems. Although the numerical analysis method is generally used in seismic design, there is a need for experimental verification for the reliable estimation of SSI behavior. In this study a dynamic centrifuge test was performed to simulate the SSI behavior of a Hualien large-scale seismic test (LSST) during the Chi-Chi earthquake. To simulate the soil profile and dynamic soil properties of the Hualien site, a series of resonant column (RC) tests was performed to determine the model soil preparation conditions, such as the compaction density and the ratio of soil–gravel contents. The variations in the shear wave velocity (V_S) profiles of the sand, gravel, and backfill layers in the model were estimated using the RC test results. During the centrifuge test, the V_S profiles of the model were evaluated using in-flight bender element tests and compared with the in-situ V_S profile at Hualien. The containment building model was modeled using aluminum and the proper scaling laws. A series of dynamic centrifuge tests was performed with a 1/50 scale model using the base motion recorded during the Chi-Chi-earthquake. In the soil layer and foundation level, the centrifuge test results were similar to the LSST data in both the time and frequency domains, but there were differences in the structure owing to the complex structural response as well as the material damping difference between the concrete in the prototype and aluminum in the model. In addition, as the input base motion amplitude was increased to a maximum value of 0.4g (prototype scale), the responses of the soil and containment model were measured. This study shows the potential of utilizing dynamic centrifuge tests as an experimental modeling tool for site specific SSI analyses of soil–foundation–NPP containment system.     

Nonlinear response analyses of a soil–structure interaction system using transformed energy transmitting boundary in the time domain

The energy transmitting boundary used in programs such as FLUSH and ALUSH is a very accurate and useful technique for the earthquake response analysis of soil–structure interaction systems. However, it is applicable only to linear analyses or equivalent linear analyses, because it can be calculated only in the frequency domain. The author has proposed methods for transforming frequency-dependent impedance into the time domain. In this paper, an earthquake response analysis method for a soil–structure interaction system, using the energy transmitting boundary in the time domain, is proposed. First, the transform of the transmitting boundary matrices to the time domain using the methods proposed by the author is studied. Then, linear and nonlinear time history earthquake response analyses using the boundary are performed. Through these studies, the validity and efficiency of the proposed methods are confirmed.     

Nonlinear 3D finite element analysis of soil–pile–structure interaction system subjected to horizontal earthquake excitation

The dynamic response of a seismic soil–pile–structure interaction (SSPSI) system is investigated in this paper by conducting nonlinear 3D finite element numerical simulations. Nonlinear behaviors such as non-reflecting boundary condition and soil–pile–structure interaction modeled by the penalty method have been taken into account. An equivalent linear model developed from the ground response analysis and the modified Drucker–Prager model are separately used for soil ground. A comparison of the two models shows that the equivalent linear soil model results in an underestimated acceleration response of the structure under this ground shaking and the soil behavior should be considered as a fully-nonlinear constitutive model in the design process of the SSPSI system. It was also observed that the dynamic response of the system is greatly affected by the nonlinearity of soil–pile interface and is not sensitive to the dilation angle of the soil. Furthermore, the effect of the presence of pile foundations on SSPSI response is also analyzed and discussed.     

Early history of soil–structure interaction

Soil–structure interaction is an interdisciplinary field of endeavor which lies at the intersection of soil and structural mechanics, soil and structural dynamics, earthquake engineering, geophysics and geomechanics, material science, computational and numerical methods, and diverse other technical disciplines. Its origins trace back to the late 19th century, evolved and matured gradually in the ensuing decades and during the first half of the 20th century, and progressed rapidly in the second half stimulated mainly by the needs of the nuclear power and offshore industries, by the debut of powerful computers and simulation tools such as finite elements, and by the needs for improvements in seismic safety. The pages that follow provide a concise review of some of the leading developments that paved the way for the state of the art as it is known today. Inasmuch as static foundation stiffnesses are also widely used in engineering analyses and code formulas for SSI effects, this work includes a brief survey of such static solutions.     

Blind identification of soil–structure systems

Surrounding soil can drastically influence the dynamic response of buildings during strong ground shaking. Soil’s flexibility decreases the natural frequencies of the system; and in most cases, soil provides additional damping due to material hysteresis and radiation. The additional damping forces, which are in non-classical form, render the mode shapes of the soil–structure system complex-valued. The response of a soil-foundation system can be compactly represented through impedance functions that have real and imaginary parts representing the stiffness and damping of the system, respectively. These impedance functions are frequency-dependent, and their determination for different configurations been the subject of a considerable number of analytical, numerical, and experimental studies. In this paper, we first develop a new identification technique that is capable of extracting complex mode shapes from the recorded free or ambient vibrations of a system. This technique is an extension of the second-order blind identification (SOBI) method, which is fairly well established in a number of other areas including sound separation, image processing, and mechanical system identification. The relative ease of implementation of this output-only identification technique has been the primary source of its appeal. We assess the accuracy and the utility of this extended SOBI technique by applying it to both synthetic and experimental data. We also present a secondary procedure, through which the frequency-dependent soil-foundation impedance functions can be easily extracted. The said procedure has a practical appeal as it uses only free or ambient responses of the structure to extract the foundation impedance functions, whereas current techniques require expensive and time-consuming forced-vibration tests.