Prediction of time of liquefaction using kinetic and strain energy

Abstract

The time of liquefaction triggering during a strong ground motion can have a large influence on the expected level of foundation and superstructure damage. To enable simple, yet accurate estimates of the triggering time, the build-up of pore pressure needs to be understood in terms of cumulative measures of ground motion intensity. This paper develops a theoretical framework and simple procedure to predict the build-up of excess pore pressure based on the principles of conservation of energy. The liquefaction resistance is first quantified in terms of cumulative absolute change in strain energy, which is shown through the evaluation of experimental cyclic simple shear tests to be insensitive to loading amplitude. A ground motion intensity measure is presented that uniquely calculates the cumulative absolute change in kinetic energy. This intensity measure is then used to provide an exact analytical solution for the cumulative absolute change in strain energy at any depth in a homogenous linear elastic soil deposit using the novel, nodal surface energy spectrum (NSES). A simple reduction to the NSES is proposed for viscous and nonlinear soil deposits, as well as a correction for changes in stiffness between layers of soil. The estimation of strain energy and build-up of pore pressure using the simple NSES method was applied to 500 randomly generated soil deposits using a range of different ground motions and validated against nonlinear total stress and nonlinear effective stress time-history analyses, with the NSES method providing a high level of accuracy. The proposed spectrum based solution provides an efficient and physically consistent procedure for the prediction of excess pore pressure build-up.