An alternative empirical function to predict air–water mixture bulk modulus for numerical modeling of liquefaction behavior of induced partially saturated sands

During the past decades, various soil improvement techniques have been developed to mitigate liquefaction hazards. One of the most newfound techniques is induced partial saturation (IPS). The capability of this method in liquefaction mitigation has been demonstrated through experimental and analytical research studies. This technique's main objective is to reduce the degree of saturation to convert fully saturated liquefiable sands into a partially saturated state and consequently reduce the potential of liquefaction occurrence. For numerical modeling of partially saturated sands' liquefaction behavior, the sand's main parameter that should be carefully determined is air–water mixture bulk modulus. A numerical model of a cyclic simple shear liquefaction box (CSSLB) on a shaking table was built to study the liquefaction response of induced partially saturated sands in the presented research. Primarily, a conventional equation was employed to predict air–water mixture bulk modulus of induced partially saturated sands, and the results of numerical liquefaction analysis were not much in accordance with those obtained from shaking table experiments. Then, experimental test results obtained from CSSLB were used to propose an empirical function to predict air–water mixture bulk modulus of induced partially saturated sands. It was shown that the new empirical function could predict the effect of entrapped air in excess pore water pressure generated in induced partially saturated sands during cyclic loading. Finally, this empirical function was validated with experimental results obtained from a laminar box on a shaking table and a centrifuge test. The results showed that the proposed empirical function could be considered as an alternative function in the numerical analysis of liquefaction response of induced partially saturated sands.