Seismically induced stresses and stability of soil media

Most soil systems behave nonlinearly under dynamic loads. For design and safety evaluation of such nonlinearly behaving soil systems, a direct approach is presented in which seismic design inputs defined in the form of response spectra can be directly used. The proposed approach is essentially an equivalent linear approach in which an iterative analysis scheme is used. Though equivalent strain dependent soil properties are used, a linear analysis is performed in each iteration. The choice of shear modulus and damping values in each iteration is based on a stochastic linearization procedure. As smoothed design spectra are to be used as seismic inputs, the normal mode approach is employed in the analysis. Thus response quantities like stress and strains are obtained by the (modified) square-root-of-the-sum-of-the-squares procedure. The applicability of the approach for nonlinear dynamic analysis is verified by a numerical simulation study in which the numerical results obtained for an ensemble of time histories by a step-by-step nonlinear approach are compared with the results obtained by the proposed approach for an equivalent seismic input defined by response spectra. A favorable comparison is obtained in the calculated maximum stress and peak stress characteristics. The approach can be used to obtain a conservative estimate of factor of safety against cumulative damage type of failures.