Liquefaction Response of Partially Saturated Sands. II: Empirical Model

Partial saturation in sands attributable to the presence of gas bubbles (not capillarity) can be encountered naturally in the field because of the decomposition of organic matter, or it can be induced for liquefaction mitigation. An empirical model (RuPSS) was developed to predict the excess pore pressure ratio ($r_u$) in partially saturated sands subjected to earthquake-induced shear strains. The model is based on experimental test results on partially saturated sands. Cyclic simple shear strain tests were performed on specimens prepared and tested in a special liquefaction box. Excess pore pressures were measured for a range of degrees of saturation $40\%<S<90\%$, relative densities $D_r=20-67\%$, and cyclic shear strains $\gamma =0.01-0.2\%$. The test results demonstrated that partially saturated sands achieved a maximum excess pore pressure ratio ($r_{u,\text{max}}$) when large enough cycles of shear strain were applied. The excess pore pressure ratio ($r_u$) that partially saturated sand can achieve under a given earthquake-induced peak shear strain and the number of equivalent cycles of application can be significantly smaller than $r_{u,\text{max}}$. Therefore, the empirical model was developed in two stages. In the first stage, $r_{u,\text{max}}$ was related to $S$, $D_r$, and shear strain ($\gamma$). In the second stage, a model was developed relating $r_u$ to $r_{u,\text{max}}$, shear strain amplitude ($\gamma$), effective stress (${\sigma }_v^{\prime }$), and earthquake magnitude ($M$). This paper presents the equations that define the predictive models for $r_{u,\text{max}}$ and $r_u$. Through these equations, plots for $r_{u,\text{max}}$ and $r_u$ are provided for ranges of soil and earthquake parameters for ease of use in engineering applications. To illustrate the implementation of the empirical model for predicting $r_{u,\text{max}}$ and $r_u$, an example is presented in which a partially saturated sand layer experiencing a peak earthquake-induced shear strain was analyzed, and the pore pressure response of the sand was evaluated using both the predictive equations and the plots.