Foundation Impedance Functions Research Articles

Impedance functions of rigid rectangular foundations bonded on layered transversely isotropic elastic/poroelastic half-space

This paper explores a complete set of impedance functions including vertical, torsional, horizontal, rocking, and coupling impedances for a surface rigid rectangular foundation bonded on a multilayered transversely isotropic half-space composed of alternatively elastic and poroelastic layers with the use of boundary element method. The slow convergence issue of Green's functions in numerical evaluation is remedied by a simple asymptotic approach presented in this paper. To evaluate the impedances accurately and efficiently, new finite elements namely exponentially-gradient elements are employed to consider the singular behavior of tractions that happens at the edges and corners of the foundation. The validity and accuracy of the solutions are verified by comparing the results with some simpler existing cases. The impedance functions are presented for different aspect ratios of the foundation to be applicable for a variety of structures. The effects of anisotropy, inhomogeneity, layer thickness, underground water level, and soil damping are assessed.

Dynamic behavior of soil-foundation-structure systems subjected to scour

Earthquake and scouring are the leading causes of bridge failure worldwide, resulting not only in casualties and fatalities but also in enormous societal and economic losses. A great number of bridges in earthquake-prone countries cross rivers and have shallow foundations, which renders them highly vulnerable to the combined effects of earthquake and flood-induced scour. Thus, the research on the dynamic response of bridges with shallow foundations under scour and earthquake hazards is timely and imperative. This study investigates the problem through the development of a numerical model for evaluating the effect of scour on the impedance functions of a massless rigid strip foundation resting on a homogenous elastic half-space. The developed impedance functions are then used in an extensive parametric study analyzing the changes of the fundamental frequency of bridge piers for different combinations of the geometrical and mechanical properties of the soil-structure-foundation system. The study results shed light on the effects of scour on the dynamic properties and fundamental frequency of vibration of bridges with shallow foundations and have important implications on the development of inverse techniques for scour identification based on the evaluation of the changes in the bridge modal properties.

Sensitivity of translational impedance functions of surface foundation to the parameters of soil and applied load

ABSTRACT The effect of soil and loading parameters on the impedance function of a circular disk on homogeneous half space under translational motion is studied. The soil parameters are Poisson’s ratio (ν) and damping ratio (ξ), whereas the loading parameter is the dimensionless frequency (a 0). The impedance functions (spring coefficients and damping coefficients) are initially calculated using the Cone model, for vertical and horizontal modes of vibration. Then, the effect of material damping is observed using three material damping models, namely, Hysteretic model, Voigt model and Kelvin model. The material damping is incorporated using the correspondence principle. Finally, a parameter importance analysis has been carried out to observe the significance of all the parameters considered. The analysis of results suggests that in most of the cases, the spring and damping coefficients are primarily controlled by dimensionless frequency (a 0 and damping ratio (ξ) of soil, respectively

Foundation impedance functions from full-scale soil-structure interaction tests

The paper presents and discusses the dynamic foundation impedance functions calculated from full-scale field tests on soil-structure interaction at the prototype facility of EuroProteas at Euroseistest in Greece. The experimental campaign included ambient noise, free- and forced-vibration tests throughout a wide frequency and amplitude range. The response of the soil-structure system was observed to be dominated by rocking. Hence, the impedances were derived under two hypotheses, i.e. considering or neglecting the foundation swaying in the dynamic equilibrium of the soil-structure system. The trend of the back-calculated impedance at high frequencies was observed to vary depending on the interpretation model and turned out to be in satisfying agreement with the available analytical solutions. Conversely, values at resonance were found almost independent of the test type and of the interpretation model. These findings imply that i) the currently widespread non-destructive tests (for instance ambient noise tests) can be effectively used to derive impedance functions; ii) the uncertainties are minimized for the resonance frequency traditionally used to calibrate the flexible-base models for soil-structure interaction analyses.

The Influence of Model Assumptions on the Dynamic Impedance Functions of Shallow Foundations

The influence of model assumptions on the dynamic impedance functions of shallow foundations is investigated using finite elements in two studies. The first investigates the effects of model assumptions in different combinations including embedment of the foundation, variation of modulus with depth, and permanent load acting on the foundation. The second study is a parametric analysis investigating the effects of permanent load at varying soil depths and with different soil modulus coefficients. Shallow foundations in strata of frictional soil on top of bedrock are considered. Small-strain modulus and modulus reduction relationships are used in an iterative process to update the modulus due to the permanent load. The results show that model assumptions can have a large influence on impedance functions. The static stiffness coefficients differ, in some instances by more than 100%. The impedance functions, normalized with the static stiffness coefficients match each other well in the pre-resonance frequency range. However, in the frequency range above the fundamental frequency, the normalized impedance functions show a large variation. Further, the results show that the influence of the permanent load is largest in the case of shallow and stiff soil strata, both regarding normalized impedance functions as well as the static stiffness coefficient, which can be increased up to 67%. The change in fundamental frequency was however minimal.

Soil-Structure Dynamic Interaction under Field-Simulated Ground Motion Tests

To study the soil-structure dynamic interaction, field-simulated ground motion tests of a 15-storey reinforced concrete frame structure are designed and performed. The response records of the structure and ground motion near the foundation are processed and analyzed. The fixed-base natural frequencies and modal damping ratios of the superstructure are determined and compared with the results obtained by the pulsating test. At the fundamental system frequency, the relative roof displacement is almost caused by the rigid-body motion of the foundation. The foundation impedance functions can also be derived from the response data. The test results show an improvement in the accuracy of the amplitude-frequency and phase-frequency characteristic curves and effective reduction in the measurement errors of the phase difference.

Evaluation of two-stage scaling for physical modelling of soil−foundation−structure systems

Several factors, such as the payload capacity of a geotechnical centrifuge, performance of an in-flight shake table and a maximum achievable centrifugal acceleration, limit the size of a structure that can be modelled to study soil−foundation−structure interaction (SFSI) effects using centrifuge modelling. The two-stage scaling method is an innovative technique to model larger prototypes in currently available centrifuge facilities. In this study, two sets of dynamic centrifuge experiments were conducted to evaluate the applicability of the method for SFSI studies. Two physical models, representing a target structure placed on dry sandy soil, were designed based on the scaling factors of conventional centrifuge modelling at 50g and the two-stage scaling method at 25g. The models were excited under different realistic earthquake motions. The results showed good agreements for the estimation of flexible-base natural frequencies of the physical models. The performance of the method for estimation of seismic amplification factors, kinematic incoherence parameters and foundation impedance functions was fair. Poor and fair agreements were observed for the estimation of seismic soil settlement recorded beneath the physical models and free field, respectively. Overall, the method can be used for SFSI studies in the centrifuge modelling while considering its strengths and weaknesses.

Application of Spectral Element Method for Dynamic Analysis of Plane Frame Structures

The paper presents a methodology to analyze plane frame structures using the Spectral Element Method (SEM) with and without considering Soil-Structure Interaction (SSI). The formulation of spectral element matrices based on higher-order element theories and the assemblage procedure of arbitrarily oriented members are outlined. It is shown that SEM gives more accurate results with much smaller computational cost, especially at high frequencies. Since the formulation is in the frequency domain, the frequency-dependent foundation impedance functions and SSI effects can easily be incorporated in the analysis. As an example, the dynamic response of a plane frame structure is calculated based on the Finite Element Method (FEM) and SEM. FEM and SEM results are compared at different frequency bands, and the effects of SSI on the dynamic response are discussed.

A Simplified Method to Assess the Dynamic Properties of First-Order Mode Dominated Structures on Pile Foundations

A simplified analysis was performed to investigate the influence of soil–pilestructure interaction (SPSI) on the dynamic characteristics of structures. Superstructures were modeled as generalized single degree-of-freedom sys­tems using the virtual displacement principle, and the impedance functions of pile foundations were solved based on the thin-layer method. Extensive para­metric analyses of simplified shear-type structures were carried out, and the results were used to obtain simple relationships, which can be utilized to per­form a preliminary estimation of the SPSI effects. The proposed method, which was verified by experimental data, could be used to solve the dynamic characteristics of shear-type structures immediately without performing com­plex analysis.

Impedance functions of three-dimensional rectangular foundations embedded in multi-layered half-space

Although most of the building foundations are approximate to embedded three-dimensional rectangular foundations of different length-to-width ratios, the two-dimensional models or axis-symmetric models which ignore the influence of length-to-width ratios, are usually used for dynamic analysis due to less computational effort on impedance functions. The impedance functions of foundations characterized by different length-to-width ratios and depth-to-width ratios embedded in multi-layered half-space, are obtained by a boundary element method, combined with non-singular Green's functions of high efficiency. Results of high precision based on dense element meshing are presented on complete eight impedance functions (two horizontal, two coupled, two rocking, vertical and torsional impedance functions) for the practical values in the dynamic analysis of the buildings.

Dynamic vertical impedance of a submarine strip foundation in ocean engineering: Water wave pressure effect

Many papers in the literature present studies of the interaction of sea waves, structures, and soil; however, most of these studies focus on the pore pressures and stresses in the soil around structures. Very little knowledge has been obtained regarding the impedance of a foundation considering the coupling of the water wave pressure effect (WPE) and dynamic soil-structure interaction (DSSI), as classical impedance functions are obtained based on a foundation on an elastic half-space with a stress-free surface. Impedance functions can be used to study the dynamic responses of a structure using the substructure method during the serviceability limit state design. This paper studies the forced vertical vibration of a strip foundation on a poro-elastic seabed with surface subjected to water wave pressures. The strip foundation on the seabed is simultaneously excited by water wave and other external forces at the same frequencies as water waves (with WPE-DSSI coupled). Three new impedance functions for foundations in ocean engineering are defined. Selected results for the new impedance functions are examined based on different water depth, wave height, wave frequency, and poroelastic material. The results show that for a rigid strip foundation in ocean engineering, both its total impedance and effective impedance are displacement dependent.

Implementation and stability analysis of discrete-time filters for approximating frequency-dependent impedance functions in the time domain

This work presents the implementation and stability analysis of a method to account for inertial soil-structure interaction (SSI) in time-history analyses, which is achieved by approximating nominally frequency-dependent foundation impedance functions in the time domain using discrete-time digital filters. The method is demonstrated using a multi-story shear building supported by a rigid disk foundation resting atop a uniform soil half-space and subjected to a horizontal ground motion. The soil-foundation-structure system's equations of motion are numerically integrated to determine its time-history response. The results are verified through comparison to those obtained both through frequency domain analyses and through sampling of the foundation impedance functions at a representative frequency. Numerical stability of the method is examined both analytically and numerically; and it was determined that the stability of the filter and the stability of the time-stepping method adopted do not guarantee that their combination will be stable as well.

Implementation of the consistent lumped-parameter model for the computation of the seismic response of nonlinear piled structures

The computation of the nonlinear response of piled structures taking soil-structure interaction into account is tackled in this paper. The structure is assumed to be founded on a group of piles, whose impedance and kinematic interaction functions are computed, in the frequency domain, through a boundary elements-finite elements coupled formulation. On the other hand, the response of the system is computed using a time-stepping procedure for the integration of the equations of motion for an inelastic superstructure, which requires a time-domain representation of the above-mentioned impedance and kinematic interaction functions. This can be achieved by the use of different methodologies, such as standard lumped-parameter models, higher-order consistent lumped-parameter models, or hidden state variable models, among others. In this paper, the use of high-order consistent lumped-parameter models for the deterministic representation of the impedance functions of deep foundations will be discussed together with different aspects of the resulting equivalent systems such as degree of accuracy, physical representation of parameters or arising numerical stability issues. Then, the use of this approach for the computation of the inelastic response of piled structures subject to seismic excitation will be explored.

An Investigation of Soil-Structure Interaction Effects Observed at the MIT Green Building

The soil-foundation impedance function of the MIT Green Building is identified from its response signals recorded during an earthquake. Estimation of foundation impedance functions from seismic response signals is a challenging task, because: (1) the foundation input motions (FIMs) are not directly measurable, (2) the as-built properties of the super-structure are only approximately known, and (3) the soil-foundation impedance functions are inherently frequency-dependent. In the present study, aforementioned difficulties are circumvented by using, in succession, a blind modal identification (BMID) method, a simplified Timoshenko beam model (TBM), and a parametric updating of transfer functions (TFs). First, the flexible-base modal properties of the building are identified from response signals using the BMID method. Then, a flexible-base TBM is updated using the identified modal data. Finally, the frequency-dependent soil-foundation impedance function is estimated by minimizing the discrepancy between TFs (of pairs instrumented floors) that are (1) obtained experimentally from earthquake data and (2) analytically from the updated TBM. Using the fully identified flexible-base TBM, the FIMs as well as building responses at locations without instruments can be predicted, as demonstrated in the present study.

Foundation impedance and tower transfer functions for offshore wind turbines

This article investigates the dynamic interaction between a horizontal-axis wind turbine, modelled as a discrete Euler–Lagrangian system, and the soil–foundation system, modelled in a finite element framework. The model comprises a rotor blade system, a nacelle and a flexible tower connected to the soil–foundation system using a substructuring approach. The aerodynamic loading on the rotor blades is modelled using blade element momentum theory. The offshore wind turbine is founded on a monopod suction caisson foundation. The soil–foundation system is modelled using a finite element method (Plaxis 3D dynamics) and a 1D strength of materials based on wave propagation approach (cone method) for comparison. A dynamic-stiffness matrix and a static stiffness matrix formulation are used to represent the soil–foundation behaviour at the mudline. Tower displacement response transfer functions are generated using each soil–foundation model at various soil stiffness. The effects of the soil stiffness on the displacement transfer functions and the wind turbine dynamics are discussed. Results from a static stiffness formulation (with coupling) are seen to match those given by frequency-dependent models, indicating that such simplified models maybe used for analysis under certain conditions.

Blind identification of soil–structure systems

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

Impedance Functions of Slab Foundations with Rigid Piles

The earthquake resistant design of structures depends upon the soil-structure interaction during seismic excitation. The dynamic behavior of surface foundations and deep foundations has been investigated by several authors (Gazetas in Soil Dyn Earthq Eng 2(1):2–42, 1983; Pecker in Dynamique des sols. Presses de l’Ecole Nationale des Ponts et Chaussees, Paris, 1984; Sieffert and Cevaer in Manuel des fonctions d’impedance. Ouest-Editions, Nantes, 1992, etc.) but the dynamic behavior of pile-reinforced soils has not been sufficiently studied yet. The design of pile-reinforced soils comprises the design of the rigid piles and the design of the earth-platform. The foundation system studied in this article consists of an earth-platform over a soft ground reinforced by deep piles. In order to understand the dynamic behavior of a rigid pile, a series of dynamic tests is conducted on an experimental site. The vertical and horizontal impedances of the slab foundation are obtained with and without rigid piles. The numerical models are developed to interpret these dynamic tests. The numerical and experimental impedance functions are compared in both the vertical and the horizontal directions. A sensitivity analysis on the influence of the physical and geometrical properties of rigid piles on the impedance functions is presented.

Dynamic stiffness of deep foundations with inclined piles

AbstractThe influence of inclined piles on the dynamic response of deep foundations and superstructures is still not well understood and needs further research. For this reason, impedance functions of deep foundations with inclined piles, obtained numerically from a boundary element–finite element coupling model, are provided in this paper. More precisely, vertical, horizontal, rocking and horizontal–rocking crossed dynamic stiffness and damping functions of single inclined piles and 2 × 2 and 3 × 3 pile groups with battered elements are presented in a set of plots. The soil is assumed to be a homogeneous viscoelastic isotropic half‐space and the piles are modeled as elastic compressible Euler–Bernoulli beams. The results for different pile group configurations, pile–soil stiffness ratios and rake angles are presented. Copyright © 2010 John Wiley & Sons, Ltd.

DİKDÖRTGEN RİJİT TEMELLERİN DİNAMİK EMPEDANS FONKSİYONLARI

Dynamic Impedance Functions for Rectangular Rigid Foundations In the analysis of soil-structure interaction problems, the soil medium can be considered as a discrete system based on the substructure approach. The main step in this method is to determine the complex dynamic-stiffness coefficients defined on the interface of soilfoundation system. In this study, the discrete values of impedance functions over a wide range of frequency-factor are presented for both surface-supported and embedded

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.