Some analytical results on lateral dynamic stiffness for footings supported on hysteretic soil medium

The nonlinearity of the soil affects soil–structure interaction to a considerable extent. For a reliable and safe analysis of soil interaction effects on the dynamic response of structures, a more realistic and relatively straightforward method incorporating the nonlinear hysteretic nature of the underlying soil–foundation system needs to be developed. The present paper models the soil–foundation system as a single degree of freedom spring–dashpot system with nonlinear hysteresis in form of elasto-perfectly plastic behavior. Analytical results for the lateral dynamic stiffness on footing have been presented. An example study has been carried out in case of circular footings. It is shown how the analytical results can be used to get a preliminary idea of the lateral dynamic stiffness of footings on a soil medium prior to a detailed computational geo-mechanics analysis provided the static nonlinear load–deformation characteristic of the soil medium is known and can be modeled by a hysteretic elasto-plastic behavior. The corresponding results are presented in a graphical form. The results have been computed showing parametric variations with the change in the amplitude and dimensionless frequency of the non-dimensional excitation force. Analytical results are also presented for the asymptotic cases at low and very high values of dimensionless frequency parameter.     

Kinematic soil–structure interaction for long-span cable-supported bridges

A general procedure is presented to study the dynamic soil–structure interaction effects on the response of long-span suspension and cable-stayed bridges subjected to spatially varying ground motion at the supporting foundations. The foundation system is represented by multiple embedded cassion foundations and the frequency-dependent impedance matrix for the multiple foundations system takes into account also the cross-interaction among adjacent foundations through the soil. To illustrate the potential implementation of the analysis, a numerical example is presented in which the dynamic response of the Vincent–Thomas suspension bridge (Los Angeles, CA) subjected to the 1987 Whittier earthquake is investigated. Although both kinematic and inertial effects are included in the general procedure, only the kinematic effects of the soil–structure interaction are considered in the analysis of the test case. The results show the importance of the kinematic soil–foundation interaction on the structural response. These effects are related to the type, i.e. SH-, SV-, P- or Rayleigh waves and to the inclination of the seismic wave excitation. Moreover, rocking components of the foundation motion are emphasized by the embedment of the foundation system and greatly alter the structural response.     

Seismic soil–structure interaction in multi‐span bridges: Application to a railway bridge

The effects of soil‐structure interaction on the seismic response of multi‐span bridges are investigated by means of a modelling strategy based on the domain decomposition technique. First, the analysis methodology is presented: kinematic interaction analysis is performed in the frequency domain by means of a procedure accounting for radiation damping, soil–pile and pile‐to‐pile interaction; the seismic response of the superstructure is evaluated in the time domain by means of user‐friendly finite element programs introducing suitable lumped parameter models take into account the frequency‐dependent impedances of the soil–foundation system. Second, a real multi‐span railway bridge longitudinally restrained at one abutment is analyzed. The input motion is represented by two sets of real accelerograms: one consistent with the Italian seismic code and the other constituted by five records characterized by different frequency contents. The seismic response of the compliant‐base model is compared with that obtained from a fixed‐base model. Pile stress resultants due to kinematic and inertial interactions are also evaluated. The application demonstrates the importance of performing a comprehensive analysis of the soil–foundation–structure system in the design process, in order to capture the effects of soil‐structure interaction in each structural element that may be beneficial or detrimental. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic behavior of a post-tensioned integral bridge including soil–structure interaction (SSI)

Current practice usually pays little attention to the effect of soil–structure interaction (SSI) on seismic analysis and design of bridges. The objective of this research study is to assess the significance of SSI on the modal with geometric stiffness and seismic response of a bridge with integral abutments that has been constructed using a new bridge system technology. Emphasis is placed on integral abutment behavior, since abutments together with piers are the most critical elements in securing the integrity of bridge superstructures during earthquakes. Comparison is made between analytical results and field measurements in order to establish the accuracy of the superstructure–abutment model. Sensitivity studies are conducted to investigate the effects of foundation stiffness on the overall dynamic and seismic response of the new bridge system.     

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 isolated bridges with soil–structure interaction

The modern transportation facilities demand that the bridges are to be constructed across the gorges that are located in seismically active areas and at the same time the site conditions compel the engineers to rest the pier foundation on soil. The purpose of this study is to assess the effects of soil–structure interaction (SSI) on the peak responses of three-span continuous deck bridge seismically isolated by the elastomeric bearings. The emphasis has been placed on gauging the significance of physical parameters that affect the response of the system and identify the circumstances under which it is necessary to include the SSI effects in the design of seismically isolated bridges. The soil surrounding the foundation of pier is modelled by frequency independent coefficients and the complete dynamic analysis is carried out in time domain using complex modal analysis method. In order to quantify the effects of SSI, the peak responses of isolated and non-isolated bridge (i.e. bridge without isolation device) are compared with the corresponding bridge ignoring these effects. A parametric study is also conducted to investigate the effects of soil flexibility and bearing parameters (such as stiffness and damping) on the response of isolated bridge system. It is observed that the soil surrounding the pier has significant effects on the response of the isolated bridges and under certain circumstances the bearing displacements at abutment locations may be underestimated if the SSI effects are not considered in the response analysis of the system.     

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.     

Dynamic soil–structure interaction of a single-span bridge

Experimental and analytical studies were conducted to determine dynamic soil–structure interaction characteristics of a single-span, prestressed-concrete bridge with monolithic abutments supported by spread footings. The experimental programme, consisting of harmonic forced vibration excitation of the bridge in the transverse and longitudinal directions, revealed the presence of four modes in the frequency band, 0 to 11 Hz, and the onset of a fifth mode at 14 Hz, the highest frequency attained during the tests. The fundamental mode at 4.7 Hz was the primary longitudinal bending mode of the deck and had a relatively low damping ratio (ζ₁), that was approximately 0.025 of critical. The second and third modes at 6.4 Hz and 8.2 Hz were the primary twisting modes of the deck which involved substantial transverse rocking, transverse translation and torsion of the footings. As expected, the damping ratios associated with these two modes, ζ₂ = 0.035 and ζ₃ = 0.15, were directly related to the relative amounts of deck and footing motion. The fourth mode at 10.6 Hz was the second twisting mode of the deck and involved relatively little motion of the footings and abutment walls, which was consistent with the low damping, ζ₄ = 0.02, observed in this mode. The response data at 14 Hz suggested that the fifth mode beyond this frequency was the second longitudinal bending mode of the deck involving longitudinal translation and bending of the abutment walls. A three-dimensional finite element model of the bridge, with Winkler springs attached to the footings and abutment walls to represent the soil–structure interaction, was able to reproduce the experimental data (natural frequencies, mode shapes and bridge response) reasonably well. Although the stiffnesses assigned to the Winkler springs were based largely on the application of a form of Rayleigh's principle to the experimental data, these stiffnesses were similar to theoretical foundation stiffnesses of the same size footings on a linearly elastic half space and theoretical lateral stiffnesses of a rigid retaining wall against a linearly elastic backfill.     

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。     

Identification of soil–structure interaction effect in base-isolated bridges from earthquake records

Identification of system parameters with the help of records made on base-isolated bridge during earthquakes provides an excellent opportunity to study the performance of the various components of such bridge systems. Using a two-stage system identification methodology for non-classically damped systems, modal and structural parameters of four base-isolated bridges are reliably identified using acceleration data recorded during 18 earthquakes. Physical stiffness of reinforced concrete columns, dynamic properties of soil and foundation impedance are found by available theoretical models in conjunction with pertinent information from the recorded accelerographs. Soil–structure interaction (SSI) effect in these bridges is examined by comparing the identified and physical stiffness of the sub-structure components. It is found that SSI is relatively pronounced in bridges founded in weaker soils and is more strongly related to the ratio of pier flexural stiffness and horizontal foundation stiffness than soil shear modulus, G_s, alone. However, substantial reduction in G_s is observed for moderate seismic excitation and this effect should be taken into account while computing foundation impedance.     

SOIL–PILE–BRIDGE SEISMIC INTERACTION: KINEMATIC AND INERTIAL EFFECTS. PART I: SOFT SOIL

A substructuring method has been implemented for the seismic analysis of bridge piers founded on vertical piles and pile groups in multi-layered soil. The method reproduces semi-analytically both the kinematic and inertial soil–structure interaction, in a simple realistic way. Vertical S-wave propagation and the pile-to-pile interplay are treated with sufficient rigor, within the realm of equivalent-linear soil behaviour, while a variety of support conditions of the bridge deck on the pier can be studied with the method. Analyses are performed in both frequency and time domains, with the excitation specified at the surface of the outcropping (‘elastic’) rock. A parameter study explores the role of soil–structure interaction by elucidating, for typical bridge piers founded on soft soil, the key phenomena and parameters associated with the interplay between seismic excitation, soil profile, pile–foundation, and superstructure. Results illustrate the potential errors from ignoring: (i) the radiation damping generated from the oscillating piles, and (ii) the rotational component of motion at the head of the single pile or the pile-group cap. Results are obtained for accelerations of bridge deck and foundation points, as well as for bending moments along the piles. © 1997 by John Wiley & Sons, Ltd.     

公路简支梁桥的地震能量响应分析

利用有限元软件SAP2000建立了某公路简支梁桥的有限元模型,以7条典型强震记录为输入,研究了公路简支梁桥的地震能量响应及其分配规律。结果表明:①地基柔性效应对公路简支梁桥的地震能量响应及其分配规律的影响较小;②当场地土质变软时,地震总输入能、结构阻尼耗能和结构阻尼耗能比均呈递增趋势,而结构滞回耗能和结构滞回耗能比则不断减小,即地基土体作为桥梁动力系统的一部分,增大了系统阻尼,并分担了部分非弹性变形;③随着PGA增大,输入结构的地震能量也增加,导致塑性铰的非弹性变形增加,即结构滞回耗能和结构阻尼耗能增大。     

Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.     

Seismic analysis of coupled soil-pile-structure systems leading to the definition of a pseudo-natural SSI frequency

The elastodynamic response of coupled soil-pile-structure systems to seismic loading is studied using rigorous three-dimentional (3D) finite element models. The system under investigation comprises of a single pile supporting a single degree of freedom (SDOF) structure founded on a homogeneous viscoelastic soil layer over rigid rock. Parametric analyses are carried out in the frequency domain, focusing on the dynamic characteristics of the structure, as affected by typical foundation properties such as pile slenderness and soil-pile relative stiffness. Numerical results demonstrate the strong influence on effective natural SSI period of the foundation properties and the crucial importance of cross swaying-rocking stiffness of the pile. Furthermore, the notion of a pseudo-natural SSI frequency is introduced, as the frequency where pile-head motion is minimized with respect to free field surface motion. Dynamic pile bending is examined and the relative contributions of kinematic and inertial interaction, as affected by the frequency content of input motion, are elucidated.     

System identification estimation of soil properties at the Lotung site

Dynamic properties of the soils at the Lotung test site, Lotung, Taiwan, are estimated from seismic vertical array measurements (input–output data sets) using both time-invariant and time-variant parametric modeling methods (system identification). Soil properties are directly mapped from model parameters to an equivalent lumped mass model of the soil interval. Shear stiffness and damping ratios were calculated for 8 events with M_L ranging from 4.5 to 7.0. Shear stiffness ranged between 0.5 and 6 MN/m, inversely proportional to PGA. The equivalent viscous damping ratio varied from 2 to 30% of critical damping, proportional to PGA. Degradation of soil behavior, while less pronounced with increasing depth, consistently occurs above a peak input acceleration of 0.07 g. Although “non-linear” behavior is evident above 0.17 g, Event 7 (0.21 g) is accurately predicted using a linear constant parameter model estimated from the smaller Event 8 aftershock ground motions.     

Development of fragility functions for geotechnical constructions: Application to cantilever retaining walls

Fragility curves constitute an emerging tool for the seismic risk assessment of all constructions at risk. They describe the probability of a structure being damaged beyond a specific damage state for various levels of ground shaking. They are usually represented as two-parameter (median and log-standard deviation) cumulative lognormal distributions. In this paper a numerical approach is proposed for the construction of fragility curves for geotechnical constructions. The methodology is applied to cantilever bridge abutments on surface foundation often used in road and railway networks. The response of the abutment to increasing levels of seismic intensity is evaluated using a 2D nonlinear FE model, with an elasto-plastic criterion to simulate the soil behavior. A calibration procedure is followed in order to account for the dependency of both the stiffness and the damping on the soil strain level. The effect of soil conditions and ground motion characteristics on the global soil and structural response is taken into account considering different typical soil profiles and seismic input motions. The objective is to assess the vulnerability of the road network as regards the performance of the bridge abutments; therefore, the level of damage, is described in terms of the range of settlement that is observed on the backfill. The effect of backfill material to the overall response of the abutment wall is also examined. The fragility curves are estimated based on the evolution of damage with increasing earthquake intensity. The proposed approach allows the evaluation of new fragility curves considering the distinctive features of the structure geometry, the input motion and the soil properties as well as the associated uncertainties. The proposed fragility curves are verified based on observed damage during the 2007 Niigata-Chuetsu Oki earthquake.     

Strain effects on kinematic pile bending in layered soil

The kinematic bending of single piles in two-layer soil is explored to account for soil stiffness degradation and associated damping increase with increasing levels of shear strain, a fundamental aspect of soil behaviour which is not incorporated in current simplified seismic design methodologies for pile foundations.A parametric study of a vertical cylindrical pile embedded in a two-layer soil profile to vertically-propagating S waves, carried out in the time domain by a pertinent beam-on-dynamic-Winkler-foundation (BDWF) model, is reported. Strain effects are treated by means of the equivalent-linear procedure which provides soil stiffness and damping ratio as function of shear strain level. Whereas the approach still represents a crude representation of the actual soil behaviour to dynamic loading, it is more realistic than elementary solutions based on linear visco-elasticity adopted in earlier studies.The paper highlights that soil nonlinearity may have either a detrimental or a beneficial effect on kinematic pile bending depending on the circumstances. The predictive equations for kinematic pile bending in visco-elastic soil recently developed by the Authors are extended to encompass strain effects. Numerical examples and comparisons against experimental data from case histories and shaking table tests are presented.     

Research on Dynamic Interaction Characteristics of Soil-pile-steel Frame Structure

利用振动台模型试验和有限元数值模拟的方法对土质地基-群桩-钢框架结构体系动力相互作用的规律和特征进行研究,并讨论了基桩长径比对于体系动力相互作用特征的影响。试验地基土体模型为均匀粉质黏土,剪切波速约为213 m/s;群桩基础由9根长2.0 m、直径0.1 m的基桩3×3对称布置;上部结构模型简化为三层钢框架结构。本文研究结果表明:土-桩-钢框架结构体系的阻尼比相较固定基础情形有所增加,输入相同地震动时其地震反应小于固定基础情形;动力相互作用体系中运动相互作用的贡献与惯性相互作用相当,不应忽略;随着基桩长径比的增大,运动相互作用增大,钢框架结构的加速度反应增大。     

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.     

A Study of Piles during Earthquakes: Issues of Design and Analysis

The seismic response of pile foundations is a very complex process involving inertial interaction between structure and pile foundation, kinematic interaction between piles and soils, seismically induced pore-water pressures (PWP) and the non-linear response of soils to strong earthquake motions. In contrast, very simple pseudo-static methods are used in engineering practice to determine response parameters for design. These methods neglect several of the factors cited above that can strongly affect pile response. Also soil–pile interaction is modelled using either linear or non-linear springs in a Winkler computational model for pile response. The reliability of this constitutive model has been questioned. In the case of pile groups, the Winkler model for analysis of a single pile is adjusted in various ways by empirical factors to yield a computational model for group response. Can the results of such a simplified analysis be adequate for design in all situations?The lecture will present a critical evaluation of general engineering practice for estimating the response of pile foundations in liquefiable and non-liquefiable soils during earthquakes. The evaluation is part of a major research study on the seismic design of pile foundations sponsored by a Japanese construction company with interests in performance based design and the seismic response of piles in reclaimed land. The evaluation of practice is based on results from field tests, centrifuge tests on model piles and comprehensive non-linear dynamic analyses of pile foundations consisting of both single piles and pile groups. Studies of particular aspects of pile–soil interaction were made. Piles in layered liquefiable soils were analysed in detail as case histories show that these conditions increase the seismic demand on pile foundations. These studies demonstrate the importance of kinematic interaction, usually neglected in simple pseudo-static methods. Recent developments in designing piles to resist lateral spreading of the ground after liquefaction are presented. A comprehensive study of the evaluation of pile cap stiffness coefficients was undertaken and a reliable method of selecting the single value stiffnesses demanded by mainstream commercial structural software was developed. Some other important findings from the study are: the relative effects of inertial and kinematic interactions between foundation and soil on acceleration and displacement spectra of the super-structure; a method for estimating whether inertial interaction is likely to be important or not in a given situation and so when a structure may be treated as a fixed based structure for estimating inertial loads; the occurrence of large kinematic moments when a liquefied layer or naturally occurring soft layer is sandwiched between two hard layers; and the role of rotational stiffness in controlling pile head displacements, especially in liquefiable soils. The lecture concludes with some recommendations for practice that recognize that design, especially preliminary design, will always be based on simplified procedures.