Roles of soil-structure interaction and damping in base-isolated structures built on numerous soil layers overlying a half-space

This study examines the roles of soil-structure interaction (SSI), higher modes, and damping in a base-isolated structure built on multiple layers of soil overlying a half space. Closed-form solutions for the entire system, including a superstructure, seismic isolator, and numerous soil layers overlying a half-space, were obtained. The formulations obtained in this study simply in terms of well-known frequencies and mechanical impedance ratios can explicitly interpret the dynamic behavior of a base-isolated structure interacting with multiple soil layers overlying a half-space. The key factors influencing the performance of the isolation system are the damping ratio of the isolator and the ratio of the natural frequency of the fixed-base structure to that of the isolated structure by assuming that the superstructure moves as a rigid body. This study reveals that higher damping in the base isolator is unfavorable to higher mode responses that usually dominate the responses of the superstructure and that the damping mechanism plays an important role in transmitting energy in addition to absorbing energy. It is also concluded that it is possible to design a soft soil layer as an isolation system for isolating vibration energy.     

Wave energy in surface layers for energy-based damage evaluation

Seismic wave energy in surface layers is calculated based on vertical array records at four sites during the 1995 Hyogo-ken Nambu earthquake by assuming vertical propagation of SH waves. The upward energy generally tends to decrease as it goes up from the base layer to the ground surface particularly in soft soil sites. Theoretical study on 1D multi-layers model to investigate the basic energy flow mechanism indicates that the energy at the ground surface can be smaller on softer soils due to high soil damping during strong shaking even if resonance effect is considered. A simple calculation for a shear-vibrating structure resting on foundation ground shows that induced strain in the structure is directly related to the energy or the energy flux of surface layers. Hence, a general perception that soft soil sites tend to suffer heavier damage than stiff sites should be explained not by greater incident energy but by other reasons such as degree of resonance. Furthermore, it is recommended that not only acceleration or velocity but also S-wave velocity should be specified at a layer where a design seismic motion is given, so that the seismic wave energy can clearly be quantified in seismic design practice.     

Characterization of seismic hazard and structural response by energy flux

Seismic safety of structures depends on the structure's ability to absorb the seismic energy that is transmitted from ground to structure. One parameter that can be used to characterize seismic energy is the energy flux. Energy flux is defined as the amount of energy transmitted per unit time through a cross-section of a medium, and is equal to kinetic energy multiplied by the propagation velocity of seismic waves. The peak or the integral of energy flux can be used to characterize ground motions. By definition, energy flux automatically accounts for site amplification. Energy flux in a structure can be studied by formulating the problem as a wave propagation problem. For buildings founded on layered soil media and subjected to vertically incident plane shear waves, energy flux equations are derived by modeling the building as an extension of the layered soil medium, and considering each story as another layer. The propagation of energy flux in the layers is described in terms of the upgoing and downgoing energy flux in each layer, and the energy reflection and transmission coefficients at each interface. The formulation results in a pair of simple finite-difference equations for each layer, which can be solved recursively starting from the bedrock. The upgoing and downgoing energy flux in the layers allows calculation of the energy demand and energy dissipation in each layer. The methodology is applicable to linear, as well as nonlinear structures.     

Mechanism and bounding of earthquake energy input to building structure on surface ground subjected to engineering bedrock motion

The mechanism of earthquake energy input to building structures is clarified by considering the surface ground amplification and soil–structure interaction. The earthquake input energies to superstructures, soil–foundation systems and total swaying–rocking system are obtained by taking the corresponding appropriate free bodies into account and defining the energy transfer functions. It has been made clear that, when the ground surface motion is white, the input energy to the swaying–rocking model is constant regardless of the soil property (input energy constant property). The upper bound of earthquake input energy to the swaying–rocking model is derived for the model including the surface ground amplification by taking full advantage of the above-mentioned input energy constant property and introducing the envelope function for the transfer function of the surface ground amplification. Extension of the theory to a general earthquake ground motion model at the engineering bedrock is also made by taking full advantage of the above-mentioned input energy constant property.     

Lumped-parameter model for a rigid cylindrical foundation embedded in a soil layer on rigid rock

To represent a cylindrical rigid foundation vibrating in horizontal, vertical, rocking or torsional motions embedded in a soil layer resting on rigid rock, a lumped-parameter model is described. The coupling between the horizontal and rocking degrees of freedom is considered. For each degree of freedom eight frequency-independent real coefficients determine the springs, dashpots and the mass of the lumped-parameter model with two internal degrees of freedom. These coefficients are specified for various ratios of the radius of the foundation to the depth of the layer and lateral contact ratios. To derive the mechanical properties of the lumped-parameter model a systematic procedure of curvefitting of the dynamic-stiffness coefficient up to, in general, twice the fundamental frequency of the layer is applied, capturing the fact that below the (horizontal) fundamental frequency (cutoff frequency) no radiation of energy occurs. The lumped-parameter model can be used to represent the soil in a standard finite-element program for structural dynamics working in the time domain, whereby the structure can exhibit non-linear behaviour. Stability of the unbounded soil-layer model and of the total system is guaranteed. A hammer foundation with partial uplift of the anvil is analysed for illustration.     

In-plane soil–structure interaction in layered,fluid-saturated,poroelastic half-space I: Structural response

Linear in-plane soil–structure interaction in two dimensions (2D) is studied in fluid-saturated, poroelastic, layered half-space using the Indirect Boundary Element Method (IBEM). The structure is a shear wall supported by a rigid embedded foundation. Exact stiffness matrices for the soil layer and half-space, and Green׳s functions of uniformly distributed loads and pore pressure on an inclined line are derived. Results of the system response in the frequency domain are presented for the special case of single soil layer over bedrock, semi-circular foundation and zero seepage force. The effects of water saturation, soil porosity, depth of soil layer, rigidity contrast between layer and bedrock are investigated in the frequency domain for incident plane P- and SV waves. The results suggest that water saturation may cause increase of the system frequency by more than 10%.     

Soil‐structure system frequency and damping: Estimation from eigenvalues and results for a 2D model in layered half‐space

This paper presents a formulation for estimation of the frequency and damping of a soil‐structure interaction system based on the classical modal analysis and solving the system eigenvalue problem. Without loss of generality, the structure is represented by a single degree of freedom oscillator, while the soil effects are included through impedance functions for in‐plane motion of a 2D rigid foundation. For the results presented in this paper, the impedance functions were computed by the indirect boundary element method for a rectangular foundation embedded in a soil layer over elastic bedrock. The study shows that the classical modal‐analysis approach works well, with the exception of squat, stiff structures, even though the impedance functions are frequency‐dependent and the soil‐structure interaction system does not possess normal modes. The study also shows that system frequency and damping are independent of the wave passage effects, contrary to findings of some previous studies, and that the site conditions, represented by the soil‐layer thickness and stiffness contrast between bedrock and soil layer, have significant influences on both system frequency and system damping. Finally, the paper examines the accuracy of some of the simple methods for estimation of these two system parameters and comments on some conflicting conclusions of previous studies about the effects of foundation embedment.     

THE SPECTRAL FUNCTION OF A LAYERED SYSTEM AND THE DETERMINATION OF THE WAVEFORMS AT DEPTH*

Consider the mathematical model of a horizontally layered system subject to an initial downgoing source pulse in the upper layer and to the condition that no upgoing waveforms enter the layered system from below the deepest interface. The downgoing waveform (as measured from its first arrival) in each layer is necessarily minimum-phase. The net downgoing energy in any layer, defined as the difference of the energy spectrum of the downgoing wave minus the energy spectrum of the upgoing wave, is itself in the form of an energy spectrum, that is, it is non-negative for all frequencies. The z-transform of the autocorrelation function corresponding to the net downgoing energy spectrum is called the net downgoing spectral function for the layer in question. The net downgoing spectral functions of any two layers A and B are related as follows: the product of the net downgoing spectral function of layer A times the overall transmission coefficient from A to B equals the product of the net downgoing spectral function of layer B times the overall transmission coefficient from B to A. The net downgoing spectral function for the upper layer is called simply the spectral function of the system. In the case of a marine seismogram, the autocorrelation function corresponding to the spectral function can be used to recursively generate prediction error operators of successively increasing lengths, and at the same time the reflection coefficients at successively increasing depths. This recursive method is mathematically equivalent to that used in solving the normal equations in the case of Toeplitz forms. The upgoing wave-form in any given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding prediction error operator with the surface seismogram. The downgoing waveform in this given layer multiplied by the direct transmission coefficient from that layer to the surface is equal to the convolution of the corresponding hindsight error operator (i.e., the time reverse of the prediction error operator) with the surface seismogram.     

1D harmonic response of layered inhomogeneous soil: Analytical investigation

The seismic response of inhomogeneous soil deposits is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The problem under investigation comprises of a continuously inhomogeneous stratum over a homogeneous layer of higher stiffness, with the excitation defined in terms of vertically propagating harmonic S waves imposed at the base of the system. A generalized parabolic function is employed to describe the variable shear wave propagation velocity in the inhomogeneous layer. The problem is treated analytically leading to an exact solution of the Bessel type for the natural frequencies, mode shapes and base-to-surface response transfer function. The model is validated using available theoretical solutions and finite-element analyses. Results are presented in the form of normalized graphs demonstrating the effect of salient model parameters such as layer thickness, impedance contrast between surface and base layer, rate of inhomogeneity and hysteretic damping ratio. Equivalent homogeneous soil approximations are examined. The effect of vanishing shear wave propagation velocity near soil surface on shear strains and displacements is explored by asymptotic analyses.     

Impact of soil moisture heterogeneity length scale and gradients on daytime coupled land‐cloudy boundary layer interactions

Using a coupled large‐eddy simulation–land surface model framework, the impact of two‐dimensional soil moisture heterogeneity on the cloudy boundary layer under varied free‐atmosphere stabilities is investigated. Specifically, the impacts of soil moisture heterogeneity length scale and heterogeneity in terms of soil moisture gradients on micrometeorological states, surface fluxes, boundary layer characteristics, and cloud development are examined. The results show that mesoscale circulations due to surface heterogeneity in soil moisture play an important role in transferring water vapour within the boundary layer and in regulating cloud distribution at the entrainment zone, which, in turn, provides feedbacks on boundary layer/surface energy budgets. The initial domain‐averaged soil moisture is identical for all homogenous and heterogeneous cases; however, the soil moisture heterogeneity in gradient and length scale between dry and wet regions has a significant impact on the estimates of near‐surface micrometeorological properties and surface fluxes, which further affect the boundary layer states and characteristics. Both liquid water potential temperature and liquid water mixing ratio increase with an increasing soil moisture gradient, whereas the amount of specific humidity decreases. Heterogeneity length scale and free atmosphere stability also amplify these impacts on the boundary layer structure and cloud formation. In a low atmospheric stability condition that potentially allows for a deeper boundary layer and a higher entrainment rate, cloud base height and cloud thickness significantly increase as the soil moisture gradient and length scale increase. Analysis to differentiate the influences of surface heterogeneity type (i.e. length scale vs gradient) shows that in general soil moisture gradient provides a larger impact than heterogeneity length scale, although the heterogeneity length scale is large enough to initiate circulation features responsible for differences in the coupled system between homogeneous and heterogeneous soil moisture cases. Copyright © 2012 John Wiley & Sons, Ltd.     

Non-linear modeling of seismic isolation systems made of recycled tire-rubber

This article considers the effectiveness of a seismic isolation system composed of a shallow layer of soil mixed with sand and rubber from shredded tires. A thorough review of past work is first provided, which is then followed by an evaluation of the constitutive properties of sand-rubber soil mixtures when these undergo large states of deformation and slip. Finally, a comprehensive set of simulations that involve a structure underlain by a strongly non-linear, seismic isolating layer when subjected to a variety of actual earthquakes scaled to various peak accelerations, are considered in detail. It is shown that the concept of using soil-rubber mixtures for the purposes of seismic isolation appears promising. A thickness for the rubber–soil mixture of just 2–3 m is likely to be enough to achieve good levels of reductions in the seismic response of the structure. This suggests the desirability of following these analyses with large-scale experimental verifications, not only to fully validate the concept, but also to quantify and assess the numerical predictions with our simple even if non-linear mechanical models, and verify the large-strain constitutive properties of the soil mixtures inferred from laboratory analyses.     

Effects of the site dynamic characteristics on soil–structure interaction (I): Incident SH-Waves

In this paper, the role that the site dynamic characteristics play in soil–structure interaction is studied on a simple model in which the site is represented as a soil layer over bedrock (half-space), and using the indirect boundary-element method (IBEM). For the purpose of comparison with published analytical solutions, the structure is represented as a shear wall supported by a semi-circular rigid foundation, subjected to incident plane SH waves. The accuracy of the method is verified, numerical results are analyzed, and the model response is compared with earthquake observations at the Hollywood Storage Building. It is shown that the effects of dynamic soil–structure interaction may become more significant near the characteristic frequencies of the site, and that the resonance of the system shifts to lower frequencies. The thickness of the soil layer, the stiffness of the bedrock, and the mass and the stiffness of the superstructure all influence the values of the system frequencies and system amplitudes.     

土-桩-钢结构相互作用体系的振动台模型试验

本项试验是研究土-结构相互作用对结构TLD减震控制影响的系列振动台模型试验的组成部分,主要目的是提供相应的对比试验数据。在这组试验中,突出的问题是TLD、上部被控结构和土层三个子系统模型基频间的协调。为了尽可能降低土层模型基频,文中采用了一种具有低剪切波速特性的土层模拟介质。最后,通过土-桩-钢结构系统的振动台模型试验,研究了土-结构相互作用对钢结构动力特性和地震反应的影响。     

MODAL ANALYSIS OF SOFT-SOIL SITES INCLUDING RADIATION DAMPING

For the one-dimensional analysis of soft-soil layers on an elastic half-space, a general form of analytical solution is developed for converting radiation damping due to energy leaking back to the half-space into equivalent modal damping, allowing the modal analysis technique to be extended to a site where radiation damping has to be accounted for. Closed-form solutions for equivalent modal damping ratios and effective modal participation factors are developed for a single layer with a shear wave velocity distribution varying from constant to linearly increasing with depth. Compact and recursive forms of solutions for equivalent modal damping ratios are developed for a system with an arbitrary number of homogeneous layers on an elastic half-space. Comparisons with numerical solutions show that the modal solutions are accurate. The nominal frequency of a site, i.e. the inverse of four times the total shear wave travel time through the layers, is an important parameter for estimating the high mode frequencies. A parameter study shows that for the same impedance ratio of the bottom layer to the elastic half-space, a system of soil layers with an increasing soil rigidity with depth has, in general, larger peak modal amplifications at the ground surface than does a single homogeneous layer on an elastic half-space, while a system with a decreasing soil rigidity with depth has smaller modal peak amplifications. © 1997 by John Wiley & Sons, Ltd.     

A pattern recognition approach to evaluation of soil liquefaction potential using piezocone data

A pattern recognition approach to liquefacation evaluation is propoesed. The state of any soil layer at a level ground site subject to seismic loads is represented by a pattern in a seven-dimensional feature space and can be classified into one of three classes: liquefiable cohesive soil, and non-liquefiable cohesionless soil. The liquefaction potential of the soil layer can be assessed according to the probabilities of the pattern belonging to the three classes. Training patterns derived from field data (piezocone (CPTU) data and maximum ground acceleration) from sites which liquefied or did not liquefy during earthquakes in New Zealand are randomly chosen to design a pattern recognition system to provide an optimal estimation of the liquefaction potential of any soil stratum of interest. Two recognition systems have been set up to estimate the state-conditional probability density function. One is based on a Parzen window approach in which no knowledge of the probabilistic structure of the training patterns is assumed; the other is based on a parameter estimation approach assuming a multivariate normal distribution. The error rate of recognition by the Parzen window approach is 6·9% when taking the window size as 1·5, and the error rate by the parameter estimation approach, which can be easily, is 7·7%. implemented without reference to our training patterns     

Modal identification of a centrifuge soil model using subspace state space method

In this paper, modal parameters of a layered soil system comprising of a soft clay layer overlying a dense sand layer are identified from accelerometer recordings in a centrifuge test. For the first time, the subspace state space system identification (4SID) method was employed to identify the natural frequencies, damping ratios, and complex valued mode shapes while considering the non-proportional damping in a soil system. A brief review of system identification concepts needed for application of the 4SID techniques to structural modal identification is provided in the paper. The identified natural frequencies were validated against those estimated by transfer function spectra. The computed normal mode shapes were compared with closed-form solutions obtained from the one-dimensional shear wave propagation equation. The identified modal parameters were then employed to synthesize state space prediction models which were subsequently used to simulate the soil response to three successive base motions. The identified models captured acceleration time-histories and corresponding Fourier spectra reasonably well in the small and moderate shaking events. In the stronger third shaking event, the model performed well at greater soil depths, but was less accurate near the surface where nonlinearities dominated.     

Ambient noise energy bursts observation and modeling: Trapping of harmonic structure-soil induced–waves in a topmost sedimentary layer

We study the nature of energy bursts that appeared in the frequency range 3–5 Hz in ambient seismic noise recorded in the Grenoble basin (French Alps) during a seismological array experiment. A close agreement is found between the identified azimuths of such noise bursts with the location of an industrial chimney. In-situ measurements of the chimney dynamic characteristics show a coincidence between the frequency of the first harmonic mode of the chimney and the fundamental frequency of a thin surficial layer that overlay the deep sediment fill. The interaction between the chimney and the surficial layer is then numerically simulated using simple impedance models and two soil profiles. Simulations exhibit a satisfactory agreement with observations and suggest that energy bursts result of inertial structure-soil interaction favored by resonance effects between the first harmonic mode of the structure and the fundamental frequency of the topmost layer.     

Modeling of soil heterogeneity and its effects on seismic response of multi-support structures

This paper addresses the analytical evaluation of soil lateral heterogeneity effects,especially the random fluctuations of the soil layer's predominant frequency,on the spatial coherency of ground motion and the seismic response of multi-support structures.A coherency probabilistic model is proposed.In this model,the spatial variation of motion is attributed to wave passage effects,effects of loss of coherence in the bedrock motion and particularly site response effects(based on the assumption of vertically propagating shear-waves through a horizontal layer with random characteristics).The results indicate that soil lateral heterogeneity effects tend to cause diminution of the values of the total coherency function.This diminution is not limited to the vicinity of the mean resonant frequency of the layer,but reaches considerably high frequencies even for relatively low values of coefficient of variation(CV of 5 to 15%).Therefore,the trend of the total coherency function(exponential decay) can be influenced significantly by site effects.Finally,the proposed coherency model is applied for two different support seismic excitations.Study results indicate that the greater the soil heterogeneity,the larger are the dynamic displacements and shear forces in the columns of the oscillator(i.e.,support structure).Furthermore,these two components of the response are influenced differently by soil heterogeneity effects.     

Damping/global energy balance in FE model of bridge foundation lateral response

A global energy analysis is presented of three static unloading–reloading foundation lateral loading cycles, calculated using the nonlinear finite element (FE) program DYNAFLOW. This simulates seismic action on an offshore pier foundation in the Rion-Antirion Bridge in Greece, located in deep-sea water (65 m). A cyclic horizontal force is applied at a height of 30 m to a rigid raft 78 m in width placed on the surface of an idealized 2-layer soil profile consisting of a 3.5 m man-made gravel layer over soft deep natural clay, with elastic vertical steel inclusions reinforcing the soil. Results of the two-dimensional FE run are used for the energy analysis. It is verified that for the three cycles, the sum of energies associated with the external forces and moments, mostly dissipated through hysteresis loops, is about equal to the sum of the total internal energies dissipated or stored in the system. For the smaller loops almost all energy is dissipated in the soil, while for the largest loop about half of the energy is dissipated by horizontal sliding at the raft-soil interface. Global damping ratios obtained from the areas of the horizontal and rocking moment hysteresis loops are about double of those computed from the corresponding static backbone curves using the Masing criterion.     

Soil amplification of plane seismic waves

Amplitudes of surface particle velocities are calculated when time-harmonic seismic waves of uniform amplitude are incident upon an arbitrary stratified elastic soil layer from the underlying bedrock. Whereas previous workers have mainly treated normally incident S waves, we allow the waves to be of SV, P, or SH types and to have arbitrary angles of incidence. Following standard practice the problem is set up as a matrix differential system, but in such a way that incident SV and P waves may be treated together (the system for SH decoupling). Though complicated, the 4 × 4 SVP system has considerable structure which is elucidated in Appendices 1 and 2. These results, though not altogether new, are of independent interest, and are gathered together in concise form for reference. The theory for low- and for high-frequency approximations is given. The main results of the work are illustrated by two numerical examples: Model 1 where the soil layer is homogeneous; and Model 2 where the soil layer has a linear velocity profile.