A practical iterative procedure to estimate seismic-induced deformations of shallow rectangular structures

Abstract

An iterative procedure is proposed to estimate seismic-induced distortions of cut-and-cover rectangular structures. The procedure is based on an existing analytical solution for deep rectangular structures subjected to far-field shear stress which assumes elastic behavior of the soil and structure, tied contact at the soil–structure interface, and static loading. The new proposed procedure builds on the analytical solution and approximates dynamic response with a pseudo-static analysis and incorporates soil-stiffness degradation through an iterative scheme where the soil shear modulus is changed in each iteration based on the shear strain of the soil obtained in the previous iteration. The presence of the ground surface and slip at the soil–structure interface are neglected in the method proposed, but their effects are shown to be small and have compensating results when soil nonlinearity is introduced. Predictions obtained from the analytical solution have been verified by a series of numerical tests, which include the response of the Daikai subway station during the 1995 Kobe earthquake in Japan and the Los Angeles Civic Center subway station subjected to the 1994 Northridge earthquake in California. The relative errors in terms of deformation between analytical and numerical results are smaller than 15%. The procedure results in stresses on the structure that compare well with those obtained with the numerical method when there is no slip between soil and structure. If slip is allowed, the analytical solution overpredicts tensile normal stresses and underpredicts compressive normal stresses.