A note on a pseudo-natural SSI frequency for coupled soil–pile–structure systems

The notion of a pseudo-natural SSI frequency was introduced in a recent publication by the authors, as the frequency where foundation motion is minimized with respect to the free field surface motion. This frequency is determined analytically in this paper, for a single-degree-of-freedom structure supported on a pile foundation. The analytical solution is compared to numerical results from rigorous finite element analyses for different pile and structural configurations. The relationship between pseudo-natural (f_pSSI) and effective natural SSI frequency (f_SSI) of the coupled system is also analytically quantified. It is concluded that f_pSSI may deviate substantially from f_SSI when a stiff squatty structure is founded on a stiff and/or short end-bearing pile for which foundation translation prevails. Conversely, when a flexible tall structure is supported on a flexible pile, f_pSSI and f_SSI nearly coincide due to dominant base rocking effects. In the latter case the effective natural SSI frequency can be predicted by standard identification procedures even when free-field recordings are missing. Effective damping effects are also discussed.     

Natural vibration frequency and damping of slender structures founded on monopiles

Offshore wind turbine (OWT) is a typical example of a slender engineering structure founded on large diameter rigid piles (monopiles). The natural vibration characteristics of these structures are of primary interest since the dominant loading conditions are dynamic. A rigorous analytical solution of the modified SSI eigenfrequency and damping is presented, which accounts for the cross coupling stiffness and damping terms of the soil–pile system and is applicable but not restrictive to OWTs. A parametric study was performed to illustrate the sensitivity of the eigenfrequency and damping on the foundation properties, the latter being expressed using the notion of dimensionless parameters (slenderness ratio and flexibility factor). The application of the approximate solution that disregards the off diagonal terms of the dynamic impedance matrix was found to overestimate the eigenfrequency and underestimate the damping. The modified SSI eigenfrequency and damping was mostly affected by the soil–pile properties, when the structural eigenfrequency was set between the first and second eigenfrequency of the soil layer. Caution is suggested when selecting one of the popular design approaches for OWTs, since the dynamic SSI effects may drive even a conservative design to restrictive frequency ranges, nonetheless along with advantageous – from a designers perspective – increased damping.     

Influence of ground motion spatial variation,site condition and SSI on the required separation distances of bridge structures to avoid seismic pounding

It is commonly understood that earthquake ground excitations at multiple supports of large dimensional structures are not the same. These ground motion spatial variations may significantly influence the structural responses. Similarly, the interaction between the foundation and the surrounding soil during earthquake shaking also affects the dynamic response of the structure. Most previous studies on ground motion spatial variation effects on structural responses neglected soil–structure interaction (SSI) effect. This paper studies the combined effects of ground motion spatial variation, local site amplification and SSI on bridge responses, and estimates the required separation distances that modular expansion joints must provide to avoid seismic pounding. It is an extension of a previous study (Earthquake Engng Struct. Dyn. 2010; 39 (3):303–323), in which combined ground motion spatial variation and local site amplification effects on bridge responses were investigated. The present paper focuses on the simultaneous effect of SSI and ground motion spatial variation on structural responses. The soil surrounding the pile foundation is modelled by frequency‐dependent springs and dashpots in the horizontal and rotational directions. The peak structural responses are estimated by using the standard random vibration method. The minimum total gap between two adjacent bridge decks or between bridge deck and adjacent abutment to prevent seismic pounding is estimated. Numerical results show that SSI significantly affects the structural responses, and cannot be neglected. Copyright © 2010 John Wiley & Sons, Ltd.     

Dimensional analysis of structures with translating and rocking foundations under near-fault ground motions

This paper evaluates the inertial soil–structure interaction (SSI) effects on linear and bilinear structures supported on foundation that is able to translate and rock when subject to near-fault ground motions. Through rigorous dimensional analysis, the peak structural responses (e.g. structural drift and total acceleration) of the soil–foundation–structure interacting (SFSI) systems are characterized by a set of dimensionless Π-parameters, which can decisively describe the interactive behavior of SFSI systems. By comparing the normalized structural responses of various structure–foundation systems with their fixed-base counterparts, the study reveals that SSI effects highly depend on the structure-to-pulse frequency ratio, Π_ω, the foundation-to-structure stiffness ratio, Π_k, damping coefficient of foundation impedance, Π_c, the foundation rocking, and the development of nonlinearity in structures. For linear structures, the SSI effects are insignificant when the structure-to-pulse frequency ratio (Π_ω) is smaller than 1.5 and can amplify the structural responses when Π_ω is higher than 1.5. Foundation rocking can shift and enlarge the response amplification zone of SSI. For nonlinear structures, SSI tends to reduce the structural responses for Π_ω<3 while can increase the ductility demands for Π_ω≥3. The bilinear structures may experience more significant SSI effects than linear structures in certain frequency ranges. The numerical simulations on ten real building cases exhibiting significant rocking and a detailed case study on a nine-story frame structure demonstrate the applicability of dimensional analysis results to predict the SSI effects on realistic building structures. The study demonstrates that the dimensional analysis provides a concise and systematic way of evaluating SSI effects.     

分层土-基础-高层框架结构相互作用体系振动台模型试验研究

本文设计实现了分层土－基础－高层框架结构相互作用体系的振动台模型试验，再现了地震动激励下上部结构和基础的震害现象和砂质粉土的液化现象。通过试验，研究了相互作用体系地震动反应的主要规律：由于动力相互作用的影响，软土地基中相互作用体系的频率小于不考虑结构－地基相互作用的结构频率，而阻尼比则大于结构材料阻尼比；体系的振型曲线与刚性地基上结构的振型曲线明显不同，基础处存在平动和转动。土层传递振动的放大或减振作用与土层性质、激励大小等因素有关，砂土层一般起放大作用，砂质粉土层一般起减振隔振作用；由于土体的隔震作用，上部结构接受的振动能量较小，各层反应均较小。上部结构顶层加速度反应组成取决于基础转动刚度、平动刚度和上部结构刚度的相对大小。     

Transient kinematic pile bending in two-layer soil

The dynamic response of piles to seismic loading is explored by means of an extensive parametric study based on a properly calibrated Beam-on-Dynamic-Winkler-Foundation (BDWF) model. The investigated problem consists of a single vertical cylindrical pile, modelled as an Euler–Bernoulli beam, embedded in a subsoil consisting of two homogeneous viscoelastic layers of sharply different stiffness resting on a rigid stratum. The system is subjected to vertically propagating seismic S waves, in the form of a transient motion imposed on rock outcrop. Several accelerograms recorded in Italy are employed as input motions in the numerical analyses. The paper highlights the severity of kinematic pile bending in the vicinity of the interface separating the two soil layers. In addition to factors already investigated such as layer stiffness contrast, relative soil–pile stiffness, interface depth and intensity of ground excitation, the paper focuses on additional important factors, notably soil material damping, stiffness of Winkler springs and frequency content of earthquake excitation. Existing predictive equations for assessing kinematic pile bending at soil layer interfaces are revisited and new regression analyses are performed. A synthesis of findings in terms of a set of simple equations is provided. The use of these equations is discussed through examples.     

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.     

Simplified analysis of frame structures with viscoelastic dampers considering the effect of soil-structure interaction

In this study, simplified numerical models are developed to analyze the soil-structure interaction (SSI) effect on frame structures equipped with viscoelastic dampers (VEDs) based on pile group foundation. First, a single degree-of-freedom (SDOF) oscillator is successfully utilized to replace the SDOF energy dissipated structure considering the SSI effect. The equivalent period and damping ratio of the system are obtained through analogical analysis using the frequency transfer function with adoption of the modal strain energy (MSE) technique. A parametric analysis is carried out to study the SSI effect on the performance of VEDs. Then the equilibrium equations of the multi degree-of-freedom (MDOF) structure with VEDs considering SSI effect are established in the frequency domain. Based on the assumption that the superstructure of the coupled system possesses the classical normal mode, the MDOF superstructure is decoupled to a set of individual SDOF systems resting on a rigid foundation with adoption of the MSE technique through formula derivation. Numerical results demonstrate that the proposed methods have the advantage of reducing computational cost, however, retaining the satisfactory accuracy. The numerical method proposed herein can provide a fast evaluation of the efficiency of VEDs considering the SSI effect.     

结构-地基动力相互作用体系振动台模型试验研究

本文设计实现了结构－地基动力相互作用体系的振动台试验,通过试验研究了动力相互作用体系的地震动反应的主要规律,由于动力相互作用的影响,软土地基中相互作用体系的频率远小于刚性地基上不考虑结构－地基相互作用的结构频率,而阻尼比例则远大于结构材料阻尼比,软上地基对地震动走滤波和隔震作用,由于上部结构的振动反馈,基底地震动与自由场地震动不相同,上部结构柱顶加速度反应主要由基础转动引起的摆动分量组成,平均分量次之,而弹性变形分量很小,桩身应变幅值呈桩顶大,桩尖小的倒三角形分布,桩上接触压力幅值呈桩顶小,桩尖大的三角形分布,试验表明,结构－地基动力相互作用对体系地震反应的影响是很是显著的,本试验为验证理论与计算分析的研究成果,改进或提出合理的计算模型和分析方法,提出了丰富的试验数据,为进一步研究奠定的基础。     

The contribution of the built environment to the ‘free-field’ ground motion in Mexico City

Soil–structure interaction (SSI) effects on building dynamic behaviour have been studied extensively. In comparison, the radiation of waves away from the soil–foundation interface has received little attention. Recent studies point out that SSI in an urban environment can modify the ground motion recorded in the free-field. These modifications will be important when two conditions are met: structures founded on soft soils and coincidence between the vibration periods of the structure and those of the superficial layers. Both conditions are met in Mexico City lake zone. In this study, we investigate SSI effects on ‘free-field’ motion. The data we use consist of microtremors recorded on soft soils in Mexico City, a densely built environment. Our objective was to identify the modifications to free-field ground motion caused by neighbouring structures. Data were analysed using H/V spectral ratios. Large variations in the level of amplification and resonant frequency were determined from microtremors in very closely spaced stations. Our results suggest consistently that free-field ground motion is significantly affected by the presence of neighbouring structures.     

Structural control considering soil–structure interaction effects

A discussion of the effects of Soil-Structure Interaction (SSI) on the formulation of active structural control algorithms is presented. Two approaches for incorporating SSI effects in linear optimal control theory are developed: one which performs the control analysis on a structure with a fixed base and then considers the effects of SSI on the controlled structural response; and another which performs the control analysis using a structural equation of motion reformulated to include SSI effects. The two control formulations are studied and compared using a single-degree-of-freedom structure supported through a rigid foundation resting on a linear, elastic half-space. Results show that control effectiveness is affected by the approach used in formulating the equations of motion of the interacting system.     

土-结构相互作用效应对结构基底地震动影响的试验研究

利用土与结构动力相互作用振动台模型试验数据,通过各种试验工况下土层表面与基础表面加速度反应的比较,深入探讨了土与结构动力相互作用效应对高层建筑结构基底地震动的影响。从输入地震动频谱特性、输入地震动强度水平和上部结构动力特性3个方面详细分析了与SSI效应对高层建筑基底震动影响程度有关的一些因素。结果表明：SSI效应对高层建筑基底地震动的影响与输入地震波的动力特性有很大关系。在地震动的频谱成分方面,SSI效应对高层建筑基底地震动的影响主要体现为土层表面和基础表面在与输入地震动卓越频率相近处的频谱成分有较大差异;SSI效应对高层建筑基底地震动的影响程度随着输入加速度峰值水平的增加而减小;在某一特定地震波作用下,当上部结构的振动频率与地震地面运动的卓越频率相近时,SSI效应对高层建筑基底地震动的影响较为强烈。     

基于Simulink的桩-土-结构相互作用反应谱分析

在Simulink环境下对桩-土-结构相互作用系统进行了仿真计算分析,并利用反应谱理论研究了SSI效应对上部结构动力响应的影响.采用集中参数模型考虑桩-土对上部结构的影响,上部结构简化为单质点模型,给出了桩-土-结构系统的状态方程,根据模型状态方程在Simulink环境下建立系统的仿真模型,得到了不同场地条件下SSI效应对上部结构加速度谱与位移谱的影响规律.计算结果表明:位移谱基本保持着“刚性假定＜Ⅰ类场地＜Ⅱ类场地＜Ⅲ、Ⅳ类场地”的规律;加速度谱受场地影响的规律不太明显,但在场地较软、桩基刚度较大时,加速度比刚性假定下的要小,而在其他情况下,加速度则比刚性假定下的要大.     

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.     

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.     

Experimental and numerical investigation on the dynamic response of pile group in liquefying ground

The response of pile foundation in liquefiable sand reinforced by densification techniques remains a very complex problem during strong earthquakes. A shake-table experiment was carried out to investigate the behavior of a reinforced concrete low-cap pile group embedded in this type of ground. In this study, a three-dimensional (3D) finite element (FE) analysis of the experiment was conducted. The computed response of the soil-pile system was in reasonable agreement with the experimental results, highlighting some key characteristics. Then, a parametric study was performed to explore the influence of pile spacing, pile stiffness (EI), superstructure mass, sand permeability, and shaking characteristics of input motion on the behavior of the pile. The investigation demonstrated a stiffening behavior appearing in the liquefied mediumdense sand, and the pile group effect seemed negligible. Furthermore, the kinematic effect was closely connected with both EI and sand permeability. Nevertheless, the inertial effect was strongly influenced by the superstructure mass. Meanwhile, high frequency and large amplitude of the input motion could produced greater the pile’s moments. It is estimated that this case study could further enhance the current understanding of the behavior of low-cap pile foundations in liquefied dense sand.     

Time-domain representation of frequency-dependent foundation impedance functions

Foundation impedance functions provide a simple means to account for soil–structure interaction (SSI) when studying seismic response of structures. Impedance functions represent the dynamic stiffness of the soil media surrounding the foundation. The fact that impedance functions are frequency dependent makes it difficult to incorporate SSI in standard time-history analysis software. This paper introduces a simple method to convert frequency-dependent impedance functions into time-domain filters. The method is based on the least-squares approximation of impedance functions by ratios of two complex polynomials. Such ratios are equivalent, in the time-domain, to discrete-time recursive filters, which are simple finite-difference equations giving the relationship between foundation forces and displacements. These filters can easily be incorporated into standard time-history analysis programs. Three examples are presented to show the applications of the method.     

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.     

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.     

Effects of site dynamic characteristics on soil–structure interaction (II): Incident P and SV waves

In-plane, dynamic soil–structure interaction (SSI) for incident-plane P and SV waves is analyzed for a two-dimensional (2D) model of a shear wall on a rigid foundation that is embedded in a soil layer over bedrock. The indirect-boundary-element method (IBEM) and non-singular Green's functions of distributed loads on inclined lines are used to solve the problem. Although this in-plane, dynamic SSI problem displays characteristics similar to those of 2D, out-of-plane, dynamic SSI, which was studied in our previous work, there exist some significant differences. In analyses of the SSI of the full-scale structures, which recorded strong earthquake shaking, our interpretations are often based on the peaks in the transfer functions of observed structural response. It is shown in this paper how the amplitudes and the frequencies of those peaks are affected by the relative rigidity and thichness of the soil layer below the foundation.