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A new effective stress method for nonlinear site response analyses

A generic loosely coupled effective stress method is presented in this article for one‐, two‐ and three‐ dimensional (1D, 2D and 3D) nonlinear site response analyses. In this method, the 1D non‐Masing hysteretic constitutive model of Chen et al (2020) is extended into 2D and 3D stress conditions, by presenting a clever generalized formulation of equivalent shear strain (γeq). The element‐level simulation tests show that the proposed algorithm of γeq is conceptually simple with high precision to capture the strain reversals under complex multidirectional shakings. The coupling between the cyclic stiffness degradation and the excess pore water pressure (EPWP) generation during irregular cyclic loadings is established using the proposed algorithm of γeq in conjunction with the Chen et al (2019a) EPWP generation model and the extended non‐Masing hysteretic constitutive model. The simulations of the undrained cyclic triaxial tests using the new effective stress method reproduce excellently the observed response of the saturated sand specimens, demonstrating the ability to represent the undrained behavior of liquefiable sands during uniform cyclic loadings. The new effective stress method is then used to simulate the response of a downhole array liquefied site in Japan, which shows an excellent agreement between the simulations and the recordings in both horizontal and vertical components of ground motions at different depths.