Nonlinear surface ground analysis via statistical approach

Abstract

A statistical approach is proposed for nonlinear surface ground analysis. In contrast to the conventional method which deals with only a single ground motion for equivalent linearization of soil properties, a design response spectrum defined at the upper level (bottom of the surface ground) of an engineering bedrock can be handled as the target design earthquake in the present paper. The effective shear strain in each soil layer is evaluated by means of a statistical procedure in which the mean peak shear strain is computed in terms of its standard deviation and the corresponding peak factor. The stiffness and damping ratio of each soil layer are obtained iteratively from the nonlinear relation of stiffness reduction factors and damping ratios with respect to the strain level. After the evaluation of the equivalent stiffness and damping ratio of every soil layer, the ground surface response spectrum is transformed from the design response spectrum defined at the upper level of the engineering bedrock via the one-dimensional wave propagation theory. The reliability and accuracy of the proposed analysis method is examined through the comparison with the results by the conventional method (represented by the shake program) for many simulated spectrum-compatible ground motions.