Mathematical Principles in Prediction of Lateral Ground Displacement Induced by Seismic Liquefaction

Abstract

ABSTRACT The present paper aims at developing a mathematical theory for prediction of the lateral soil displacement induced by seismic liquefaction. By using the knowledge obtained from shaking table tests together with the principle of the minimum potential energy at force equilibrium, the theory of maximum possible displacement was developed, and is described in detail. Boundary conditions as well as irregular topography were also considered using the principle of the minimum potential energy. Prediction of the increase of displacement with time was also attempted. This aim was achieved by using a scalar function of time, denoted by λ, that stands for the increase of displacement from zero towards the maximum possible one. An equation of motion in terms of λ was derived by using the theory of Lagrangean equation of motion together with the Hamiltonian principle. By combining the maximum possible displacement and λ, it is possible to predict the variation of displacement with time. The proposed method is characterized by its need for a limited number of input data.