Eduardo Kausel

Approximate formulas for dynamic stiffnesses of rigid foundations

Approximate formulas are proposed to describe the variation with frequency of the dynamic stiffnesses of rigid embedded foundations. These formulas are obtained by fitting mathematical expressions to accurate numerical solutions. Because of the restricted data available at the present time, only cylindrical and rectangular embedded foundations are analysed herein; this is not a serious restriction, since these are the more common shapes used in practice. The imaginary part of the stiffnesses are approximated, for high frequencies, by their asymptotic values, which give excellent results in that range. These asymptotic values are computed assuming simple one-dimensional wave propagation theory. The approximate formulas provide a good approximation of the foundation stiffnesses and their use is very simple. Although the soil is assumed to have no internal damping, it can be incorporated by using the Correspondence Principle, if so desired.

The spring method for embedded foundations

Abstract The paper presents simplified rules to account for embedment and soil layering in the soil-structure interaction problem, to be used in dynamic analyses. The relationship between the spring method, and a direct solution (in which both soil and structure are modeled with finite elements and linear members) is first presented. It is shown that for consistency of the results obtained with the two solution methods, the spring method should be performed in three steps. The first two steps require, in general, finite element methods, which would make the procedure unattractive. It is shown, however, that good approximations can be obtained, on the basis of one-dimensional wave propagation theory for the solution of step 1, and correction factors modifying for embedment the corresponding springs of a surface footing on a layered stratum, for the solution of step 2. Use of these rules not only provides remarkable agreement with the results obtained from a full finite element analysis, but results in substantial savings of computer execution and storage requirements. This frees the engineer to perform extensive studies, varying the input properties over a wide range to account for uncertainties, in particular with respect to the soil properties.

Dynamics of piles and pile groups in layered soil media

Abstract A general formulation is presented for the dynamic response analysis of piles and pile groups in a layered halfspace. Greens functions for layered media, evaluated numerically by the application of Integral transform techniques, along with analytical solutions for the dynamic response of piles are the ingedients of this formulation. The analytical derivations are presented in this paper and the extension of the formulation to seismic analyses is described. In addition, a limited number of representative results on the dynamic stiffnesses and seismic response of pile groups are presented.

Effects of Local Soil Conditions on the Topographic Aggravation of Seismic Motion: Parametric Investigation and Recorded Field Evidence from the 1999 Athens Earthquake

During the 1999 Athens earthquake, the town of Adames, located on the eastern side of the Kifissos river canyon, experienced unexpectedly heavy damage. Despite the particular geometry of the slope that caused significant motion amplification, topography effects alone cannot explain the uneven damage distribution within a 300-m zone parallel to the canyon’s crest, which is characterized by a rather uniform structural quality. In this article, we illustrate the important role of soil stratigraphy and material heterogeneity on the topographic aggravation of surface ground motion. For this purpose, we first conduct an extensive time-domain parametric study using idealized stratified profiles and Gaussian stochastic fields to characterize the spatial distribution of soil properties, and using Ricker wavelets to describe the seismic input motion; the results show that both topography and local soil conditions significantly affect the spatial variability of seismic motion. We next perform elastic two-dimensional wave propagation analyses based on available local geotechnical and seismological data and validate our results by comparison with aftershock recordings.

Closed-form integration of singular terms for constant, linear and quadratic boundary elements. Part 1. SH wave propagation

One of the most important aspects in the application of boundary element techniques to wave propagation problems is the accurate representation of the singular terms at the points of application of the virtual loads. It is current practice to carry out this task by means of numerical quadrature. This paper presents an analytical evaluation of the singular integrals for constant, linear and quadratic boundary elements involving SH waves, the results of which are then used to model inclusions in a two-dimensional acoustic medium illuminated by dynamic anti-plane line sources. Finally, the BEM results are compared with the known analytical solutions for cylindrical inclusions.

An equivalent linear algorithm with frequency- and pressure-dependent moduli and damping for the seismic analysis of deep sites

The seismic analysis of soil deposits is most often carried out with an iterative computational scheme, proposed by Seed and Idriss, in which inelastic effects are only approximately modeled through soil degradation curves. Laboratory experimental data indicate that for highly confined materials, the standardized reduction curves commonly used overestimate the capacity of soils to dissipate energy. This paper first presents the results obtained with a simple four-parameter constitutive soil model, which when used to simulate cyclic loading, produces results that agree well with available laboratory experiments for soils under arbitrarily large confining pressures. Thereafter, a frequency- and pressure-dependent iterative algorithm for seismic amplification is proposed, which provides time histories that match well the results obtained with a true non-linear model. Finally, the modified linear iterative analysis is successfully used for the seismic analysis of a 1 km deep model for the Mississippi embayment near Memphis, Tennessee, and a class-A prediction of the seismic amplification in Treasure Island during the Loma Prieta earthquake.

Fundamental Solutions in Elastodynamics

Preface Part I. Preliminaries: 1. Fundamentals 2. Dipoles Part II. Full Space Problems: 3. Two-dimensional problems in full, homogeneous spaces 4. Three-dimensional problems in full, homogeneous spaces Part III. Half-Space Problems: 5. Two-dimensional problems in homogeneous half-spaces 6. Three-dimensional problems in homogeneous half-spaces Part IV. Plates and Strata: 7. Two-dimensional problems in homogeneous plates and strata Part V. Analytical and Numerical Methods: 8. Solutions to the Helmholtz and wave equations 9. Integral transform method 10. Stiffness (impedance) matrix method Part VI. Appendices: 11. Basic properties of mathematical functions 12. Brief table of integral transforms 13. MATLAB(R) program listings.

Soil-Dependent Topographic Effects: A Case Study from the 1999 Athens Earthquake

In the Ms 5.9 Athens, Greece, earthquake, surprisingly heavy damage occurred on the eastern bank of the Kifissos River canyon. To explore whether the particular topographic relief and/or the local soil conditions have contributed to the observed concentration and non-uniform damage distribution within a 300-m zone from the canyon crest, we conduct finite-element analyses in one and two dimensions, using Ricker wavelets and six realistic accelerograms as excitation. The nonlinear soil response is simulated in the time-domain using a hyperbolic stress-strain model, and also approximated using a modified equivalent-linear algorithm; results obtained by means of the two methods are discussed in detail. Our simulations show that topographic effects are substantial only within about 50 m from the canyon ridge, materializing primarily because of the presence of relatively soft soil layers near the surface of the profile. We then introduce the concept of two-dimensional/one-dimensional response spectral ratio to describe the effects of topography as a function of local soil conditions, and suggest a frequency- and location-dependent topographic aggravation factor to be introduced for the modification of design spectra in a seismic code.

Lamb's problem at its simplest

This article revisits the classical problem of horizontal and vertical point loads suddenly applied onto the surface of a homogeneous, elastic half-space, and provides a complete set of exact, explicit formulae which are cast in the most compact format and with the simplest possible structure. The formulae given are valid for the full range of Poissons ratios from 0 to 0.5, and they treat real and complex poles alike, as a result of which a single set of formulae suffices and also exact formulae for dipoles can be given.

Dynamic point sources in laminated media via the thin-layer method

Abstract This paper presents closed-form expressions for the Greens functions associated with harmonic point sources acting within horizontally layered media. These expressions are intended for use with the highly efficient Thin-Layer Method (TLM) described elsewhere, which is now being used widely for diverse engineering purposes. Among the dynamic sources considered are point forces, force dipoles (cracks and moments) , blast loads, seismic double couples with no net resultant, and bimoments (moment dipoles) . Comparisons with known analytical solutionsfor homogenous media demonstrate the accuracy of the formulation. However, the main field ofapplication is laminated media, for which no analytical solutions can be obtained. On the otherhand, it should be noted that the computational effort in this method does not depend on whetherthe system is layered. The resulting Greens functions could be used to efficiently model elasticwaves in complex media by means of the Boundary Integral Method.