Centrifugal modelling of dynamic soil-structure interaction

This paper presents a centrifuge model that is capable of realistically representing soil-structure systems subjected to earthquake-like excitation. The model is validated by performing (i) free field soil tests, (ii) dynamic soil-structure interaction tests and (iii) a numerical analysis of the experimental results. The free field experiments show that the simulated earthquake, which is generated by the hammer-exciter plate method, is similar in amplitude and frequency content to a real earthquake. The experiments also demonstrate that a confined soil sample can satisfactorily model a horizontal soil stratum of infinite lateral extent when the containment walls are lined with an absorptive material to attenuate wave reflections that would otherwise occur. Measurements of the acceleration at different locations on the free soil surface indicate that the surface motion is fairly uniform over a relatively large area. This is further confirmed by a comparison made between the measured free and scattered field motions for a surface foundation. Next, a series of soil-structure interaction tests are performed which examine the dependence of radiation damping on the natural frequencies of the structure relative to the fundamental frequency of the soil stratum. The experimental results are shown to be consistent with established theories. Finally, the experimental results are used to compute the stiffness and damping parameters of a two degree of freedom numerical model of the soil-structure system. The experimental parameters are shown to be in good agreement with calssical text book formulae. This study demonstrates that the centrifuge model consistently behaves as expected for simple, but realistic, dynamic soil and soil-structure systems, and can, therefore, be used with confidence to examine more complicated systems that are not yet fully understood.     

软土地基核电厂房动力响应振动台试验

为了分析软土地基－筏基础核电厂房结构地震反应规律和特征,利用地震模拟振动台开展了软土地基－筏基础－核电厂房动力相互作用问题的试验研究。分别进行了表面水平土体模型和表面凹陷土体模型的运动相互作用试验、地基土－筏基础－核电厂房振动台相互作用试验、核电厂房直接固定在振动台面上的刚性基底振动台试验。试验采用圆形叠层剪切模型箱,地基土模型为某工程场地的均匀粉质粘土,其剪切波速为213 m/s;核电厂房简化为3层框架剪力墙结构模型。试验输入波形为美国核电规范常用的RG1.60反应谱合成得到的人工地震动时程。振动台试验结果对比分析表明:土－结构体系中系统的振动周期和阻尼明显大于刚性基底下结构的振动周期和阻尼;相同地震作用下在土－结构动力相互作用体系中结构加速度明显小于刚性基底下的结构加速度反应;而位移明显大于刚性基底下结构的位移。本文的研究成果可为软土地基建立核岛厂房的适应研究提供参考。     

Seismic response of bridge pier on rigid caisson foundation in soil stratum

An analytical method to study the seismic response of a bridge pier supported on a rigid caisson foundation embedded in a deep soil stratum underlain by a homogeneous half space is developed. The method reproduces the kinematic and inertial responses, using translational and rotational distributed Winkler springs and dashpots to simulate the soil-caisson interaction. Closed-form solutions are given in the frequency domain for vertical harmonic S-wave excitation. Comparison with results from finite element （FE） analysis and other available solutions demonstrates the reliability of the model. Results from parametric studies are given for the kinematic and inertial responses. The modification of the fundamental period and damping ratio of the bridge due to soil-structure interaction is graphically illustrated.     

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.     

基于土-结构体系对建筑结构响应的减震效果评估

提出一种基于土-结构体系地震记录的土-结构相互作用(SSI)的减震评估方法。该方法采用简化的SSI模型,通过系统辨识确定模型参数。将上部建筑结构地震反应的SSI减震效应分解为惯性相互作用和运动相互作用,同时还提出由惯性相互作用和运动相互作用单独降低结构响应的方法。将2011年东北地震太平洋沿岸期间两栋中层建筑用此方法进行分析,结果表明:当建筑物结构响应进入非弹性范围时,惯性相互作用的减震效果降低。     

Dynamic response of non-linear building-foundation systems

An analysis is made of the steady-state response of a bilinear hysteretic structure supported on the surface of a viscoelastic half-space. The method of equivalent linearization is used to solve the equations of motion, and simplified approximate formulas are obtained for the fundamental resonant frequency of the system and for an effective critical damping ratio. Numerical results indicate that for non-linear hysteretic structures compliance of the soil foundation may lead to larger displacements than would occur if the base were rigid. This behaviour differs from that generally observed for linear systems, for which the effect of soil-structure interaction is to reduce the rigid-base response.     

Frequency-independent impedances of soil-structure systems in horizontal and rocking modes

The frequency-independent foundation impedances, commonly used in soil-structure dynamic interaction problems, are developed for a circular footing resting on a homogeneous halfspace. As they ignore the structure attached to the foundation, the error introduced in the structural response may be 50 per cent or more in the neighbourhood of the fundamental frequency of the soil-structure system. The present study proposes a new method developed for most dynamic soil-structure interaction problems. The key idea is to retain for the frequency-independent impedances values computed for the fundamental frequency of the soil-structure system; thus these values include the dynamic characteristics of the whole soil-structure system and lead to a satisfactory approximation of the exact solution over a wide frequency range. The method is developed here for the horizontal and rocking modes of a structure with a circular base resting on a homogeneous halfspace. Numerical applications are given for a simple linear oscillator in order to make possible a thorough parametric study. The response of some idealized building-foundation systems to harmonic excitation or to a seismic input is next examined in order to illustrate the efficiency of the proposed model.     

The system damping,the system frequency and the system response peak amplitudes during in-plane building-soil interaction

The system damping, the system frequency, the relative building response and the base rocking response peak amplitudes are studied, as those depend on the building mass and height, the flexibility of the soil, the structural damping, the type of incident waves and their angle of incidence. A linear two-dimensional model is used, which assumes the soil to be a homogeneous isotropic half-space, the foundation supporting the building to be a rigid embedded cylinder, and in which the building model is an equivalent single-degree-of-freedom oscillator. The system frequency and the system damping ratio are determined by measuring the width and the frequency of the peak in the transfer function of the oscillator relative response, using the analogy with the half-power method for a single-degree-of-freedom fixed-base oscillator. Previous similar studies are for dynamic soil-structure interaction only, and for simplified models in which the stiffness of the soil and the damping due to radiation are represented by springs and dashpots. The study in this paper differs from the previous studies in that the wave passage effects (or the kinematic interaction) are also included, and that no additional simplifications of the model are made. Results are shown for excitation by plane P- and SV-waves.     

Deflection modification factors of multistory buildings considering soil-structure interaction

In this investigation,attempts are made to examine the effects of soil-structure interaction on the deflection modification factor of multistory buildings and to clarify the role of deformable soil on this factor.A comprehensive study is conducted to investigate the effect of inertial interaction on displacement demand ratios in soil-structure systems with different structural characteristics and various non-dimensional parameters,using a simplified interacting model.A two-step regression analysis of the nonlinear,dynamic computer simulation results obtained,leads to a reliable and accurate formula for predicting deflection modification factors that incorporate foundation flexibility.The results illustrate that the application of deflection modification factors derived from fixed-base structures can lead to unsafe evaluation of the structures on soft soil.The proposed formula provides a useful tool for design engineers to incorporate the effect of soil-structure interaction into the evaluation of structural deformations.     

Antiplane response of a dike on flexible embedded foundation to incident SH-waves

The response of an elastic circular wedge on a flexible foundation embedded into a half-space is investigated in the frequency domain for incident pane SH-waves. The problem is solved by expansion of the motion in all three media (wedge, foundation and half-space) in cylindrical wave functions (Fourier-Bessel series). The structural model is simple, but accounts for both differential motions of the base and for the effects of soil-structure interaction. Usually, structural models in earthquake engineering consider either differential ground motion, but ignore soil-structure interaction, or consider soil-structure interaction, but for a rigid foundation, thus ignoring differential ground motion. The purpose of the study is to find how stiff the foundation should be relative to the soil so that the rigid foundation assumption in soil-structure interaction models is valid. The shortest wavelength of the incident waves considered in this study is one equal to the width of the base of the wedge. It is concluded that, for this model, a foundation with same mass density as the soil but 50 times larger shear modulus behaves as ‘rigid’. For ratio of shear moduli less than 16, the rigid foundation assumption is not valid. Considering differential motions is important because of additional stresses in structures that are not predicted by fixed-base and rigid foundation models.     

Evaluation of the half‐power bandwidth method to estimate damping in systems without real modes

The objective of this work was to assess the significance of the values of damping obtained applying the half‐power bandwidth method to the frequency response records of the steady‐state response of a system that does not possess real modes either because the damping matrix does not satisfy the orthogonality condition or because its parameters are functions of frequency. A multi‐degree of freedom system with real modes and different types of damping is considered first. A two degree of freedom system with an arbitrary damping matrix, a rigid mass on an elastic foundation subjected to vertical and coupled horizontal/rocking vibrations, and a single degree of freedom model of a building accounting for inertial soil structure interaction effects are considered next in more detail. The results show that the predictions of the method, when applicable compare very well with those provided by approximate formulae and procedures used in practice. Copyright © 2010 John Wiley & Sons, Ltd.     

Centrifuge modeling of seismic response of layered soft clay

Centrifuge modeling is a valuable tool used to study the response of geotechnical structures to infrequent or extreme events such as earthquakes. A series of centrifuge model tests was conducted at 80g using an electro-hydraulic earthquake simulator mounted on the C-CORE geotechnical centrifuge to study the dynamic response of soft soils and seismic soil–structure interaction (SSI). The acceleration records at different locations within the soil bed and at its surface along with the settlement records at the surface were used to analyze the soft soil seismic response. In addition, the records of acceleration at the surface of a foundation model partially embedded in the soil were used to investigate the seismic SSI. Centrifuge data was used to evaluate the variation of shear modulus and damping ratio with shear strain amplitude and confining pressure, and to assess their effects on site response. Site response analysis using the measured shear wave velocity, estimated modulus reduction and damping ratio as input parameters produced good agreement with the measured site response. A spectral analysis of the results showed that the stiffness of the soil deposits had a significant effect on the characteristics of the input motions and the overall behavior of the structure. The peak surface acceleration measured in the centrifuge was significantly amplified, especially for low amplitude base acceleration. The amplification of the earthquake shaking as well as the frequency of the response spectra decreased with increasing earthquake intensity. The results clearly demonstrate that the layering system has to be considered, and not just the average shear wave velocity, when evaluating the local site effects.     

Dynamic soil–structure interaction of coupled shear walls by boundary element method

For a class of civil engineering structures, that can be accurately represented by ‘coupled shear walls’ (CSWs), a discrete model for the analysis of the dynamic interaction with the underlying soil is proposed. The CSWs, with one or more rows of openings, rest on a rigid foundation embedded in the elastic or viscoelastic half-space. A hierarchical finite element model based on an equivalent continuum approach is adopted for the structure. A frequency-domain boundary element method is used to represent the half-space. Finally, the set of equations governing the response of the coupled soil-structure system to harmonic lateral loads acting on the structure is also given. The frequency deviation effect with respect to the fixed-base structure and the effects of radiation and material damping in the soil are presented for different characteristics of the structure and different soil properties.     

Centrifuge modelling of structures with oil dampers under seismic loading

Experimental research into the seismic performance of buildings with passive oil dampers has so far been restricted to large-scale testing of frames erected on laboratory shaking tables that ignore the foundation soil below. This simplification of the problem falls short of replicating dynamic soil-structure interaction that would occur in the field. This paper presents the first experimental attempt at utilising high gravity dynamic centrifuge testing to replicate the response of a damped building at a reduced model scale. The paper compares the dynamic response of two similar two-degree-of-freedom model sway frames, one control (bare) frame and one frame equipped with miniature oil dampers, both structures founded on shallow raft foundations in dry dense sand. The miniature oil dampers successfully mitigate floor accelerations, drifts, and storey shear forces in the damped frame with minor modification to the frame stiffness. For strong, near resonance motions, global rocking of the undamped frame associated with physical uplifting of the foundation from the soil surface and subsequent yielding of sand beneath has led to floor acceleration levels, which are comparable to those obtained in the damped building fitted with miniature oil dampers. Assessment of the instrumentation installed on the miniature oil dampers reveals a viscoelastic damper behaviour with a dependency on stroke magnitude and on velocity.     

Shear wave velocity measurements and soil–pile system identifications in dynamic centrifuge tests

This paper presents a pre-shaking technique for measuring the $V_{s}$ profile of sand deposits and determining the natural frequencies of the sand bed and soil-structure system in a centrifuge model at an acceleration of 80 g. The pre-shaking technique is a non-destructive test. It uses a shaker as a wave generation source and a vertical array of accelerometers embedded in the sand bed and the accelerometers attached to the pile head as receivers. The pre-shaking method can be easily used for in-flight subsurface exploration ( $V_{s}$ profile measurements) and in-flight system identification of soil-structure systems (natural frequency measurements). A soil–pile centrifuge model is used to demonstrate the versatility of pre-shaking during a routine centrifuge shaking table test. This paper discusses the testing setup, testing procedures, related SI techniques, and signal processing for the soil–pile system. The natural frequencies measured by the pre-shaking tests are consistent with theory-based results. This technique can be conducted at any time before and after major earthquake events occur in a test.     

Rosenblueth's modal combination rule for systems with non-classical damping

A simple rule is derived to combine, within the framework of a complex mode superposition, the maximum modal responses of systems such as soil-structure and structure-equipment systems, for which closely spaced natural frequencies are likely, and for which, because of the large difference in the damping values of their various components, the assumption of an orthogonal damping matrix may lead to significant errors. The rule constitutes the generalization of Rosenblueth's rule for systems with closely spaced natural frequencies and classical modes, and is expressed in terms of their complex mode shapes and natural frequencies. Its derivation is based on the theory of a complex modal analysis for systems with non-classical modes of vibration and on Rosenblueth's original derivation. As in this original derivation, earthquake ground motions are modelled as a stationary white noise process, but the formulae obtained under this assumption are modified later on to account for the transient nature of actual earthquakes. A numerical example is presented to illustrate the application of the rule, and a comparative study with numerical integration solutions is performed to assess its accuracy. In this comparative study, it predicts the numerical integration solutions with an average error of 0.3 per cent.     

Significance of small strain damping and dilation parameters in numerical modeling of free-field lateral spreading centrifuge tests

Lateral spreads are complex dynamic phenomena that are challenging to represent numerically. In this paper numerical models are developed and calibrated using the displacement, acceleration, and pore water pressure time histories recorded in a free-field lateral spreading centrifuge test. The calibrated numerical model then is used to predict another free-field lateral spreading centrifuge test using the same soil profile but different input acceleration time history. The computed response shows good agreement with the centrifuge test measurements. This paper demonstrates that even in a large strain problem, such as lateral spreading, small strain damping plays an important role in numerical simulation results; it also shows the need to have pressure dependent dilation parameters in the employed soil constitutive model implemented in order to simultaneously reproduce measurements of pore water pressure, acceleration and lateral displacement.     

Equivalent linearization of non-linear soil-structure systems

The concept of equivalent linearization, in which the actual nonlinear structure is replaced by an equivalent linear single-degree-of-freedom (SDOF) system, is extended for soil-structure systems in order to consider the simultaneous effects of soil-structure interaction (SSI) and inelastic behavior of the structure on equivalent linear parameters (ELP). This is carried out by searching over a two-dimensional equivalent period–equivalent damping space for the best pair, which can predict the earthquake response of the inelastic soil-structure system with sufficient accuracy. The super-structure is modeled as an elasto-plastic SDOF system whereas the soil beneath the structure is considered as a homogeneous half-space and is replaced by a discrete model. An extensive parametric study is carried out for a wide range of soil-structure systems subjected to a suite of 59 ground motions. The effect of SSI on ELP is studied through introducing a set of non-dimensional key parameters, which define the soil-structure system. It is shown that ELP of soil-structure systems result from a trade-off between SSI effect and nonlinear behavior of the structure. The contribution of each of these two factors depends on the characteristics of the soil-structure system which, in turn, are defined by the introduced non-dimensional key parameters. Moreover, the reliability of the predicted response of soil-structure systems and its sensitivity to deviation from optimal ELP is studied in detail, which sheds light on the consequences of using improper pairs of ELP for interacting systems in the framework of performance-based design of structures. Copyright © 2012 John Wiley & Sons, Ltd.     

Site-dependent strength reduction factors for soil-structure systems

The effect of soil conditions on strength reduction factors (SRFs) is investigated. Both site effect and soil-structure interaction (SSI) effect are considered in the study with special emphasis on the latter effect. The structure is modeled as an elasto-plastic single degree of freedom (SDOF) system, whereas the underlying soil is considered as a homogeneous half-space. The half-space is also replaced by a simplified 3DOF system, based on the concept of Cone Models. The whole 4DOF model is then analyzed under a total of 54 strong motions recorded on different soil types. A parametric study is done for a wide range of non-dimensional parameters, which completely define the problem. It is concluded that SSI reduces the SRF values, especially for the case of buildings located on soft soil. Consequently, using the fixed-base SRFs for soil-structure systems lead to non-conservative design forces. Simplified expressions are proposed to estimate SRF for soil-structure systems.     

Effect of soil-structure interaction on damping of structures

Damping of structures resting on flexible foundations is affected by soil-structure interaction in two ways: (1) the structure gains damping through energy dissipation in soil, and (2) the damping the structure would have on a rigid foundation is reduced. These effects are evaluated using two approaches: an energy consideration which is a simple but approximate approach, and the complex eigenvalue analysis which is mathematically accurate but uses damped, non-classical vibration modes. These two methods are compared and the accuracy of the more convenient energy approach is assessed. Examples of modal damping are given for rigid structures, buildings and towers.