Exact seismic response of smooth rigid retaining walls resting on stiff soil

Joaquin Garcia‐Suarez,Domniki Asimaki

doi:10.1002/nag.3082

Abstract

SummaryThe assessment of forces exerted on walls by the backfill is a recurrent problem in geotechnical engineering, owing to its relevance for both retaining systems and underground structures. In particular, the work by Arias and colleagues, and later also the one by Veletsos and Younan, among others, becomes pertinent when considering pressure increments on underground structures triggered by seismic events. As a first step, they studied the response of a rigid retaining wall resting on rigid bedrock subjected to SV waves, introducing some simplifying assumptions. This paper presents the exact solution to this reference problem. The solution is given in horizontal wavenumber domain; hence, it comes in terms of inverse Fourier transforms, which can be approximated numerically in Mathematica, which in turn are verified against finite‐element simulations. Specific features of this exact solution that were not captured by prior engineering approximations are highlighted and discussed.

Highlights

The study of the forces that soil exerts over retaining structures dates back centuries
In this text we derive the exact solution of the Younan-Veletsos problem in terms of elementary functions in the horizontal wavenunber space
By evaluating the solution numerically, it has been shown that there exist resonance phenomena that current simplified models do not capture, as the latter presuppose that the natural frequencies of the displacement field close to the wall resemble those of the displacement at the far-field

Summary

Funding information

The assessment of forces exerted on walls by the backfill is a recurrent problem in Geotechnical Engineering, owing to its relevance for both retaining systems and underground structures. The work by Veletsos and Younan becomes pertinent when considering pressure increments on underground structures triggered by seismic events. These scholars furnished the first satisfactory engineering solution corresponding to a simple configuration, which has become a milestone in the field. The solution is given in horizontal wavenumber domain, it comes in terms of inverse Fourier transforms, which in turn are verified against finite-element simulations. Specific features of this exact solution that were not captured by prior engineering approximations are highlighted and discussed. KEYWORDS Geotechnical Engineering , Retaining Walls , Elastodynamics , Mathematical Modelling , Exact Solution

| INTRODUCTION

| Introduction of relative displacements

Findings

| CONCLUSIONS AND FUTURE WORK