Modeling permanent strains of granular soil under cyclic loading with variable confining pressure

Previous experimental studies showed that variable confining pressure (VCP) promoted the development of permanent strains of granular soils in most cases and indicated VCP should not be ignored. However, existing empirical formulas do not fully account for the effect of VCP on permanent strains. Therefore, three series of cyclic triaxial tests with constant confining pressure (CCP) and VCP are performed on saturated sand at three relative densities. These tests aim at investigating the influential factors which could reflect the effect of VCP on permanent strains and should be considered in establishing the empirical formula. Test results show that an increasing initial void ratio has great effect on the permanent strains of sand. The permanent strains increase with an increase in the stress ratio of maximum deviatoric stress to average confining pressure qmax/σ3av\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{q^{\hbox{max} } } \mathord{\left/ {\vphantom {{q^{\hbox{max} } } {\sigma_{3}^{\text{av}} }}} \right. \kern-0pt} {\sigma_{3}^{\text{av}} }}$$\end{document} and the length of stress path L in both CCP and VCP tests. Based on that, a four-parameter equation considering the initial void ratio, stress ratio, length of stress path, and number of loading cycles is proposed to predict the permanent strains under cyclic loading with VCP. Comparison between the measured and predicted permanent strains shows that the equation can well capture the permanent strain response in tests with CCP and VCP.