A Unified Analytical Model for Undrained Compressibility Behavior of Foam-Conditioned Coarse-Grained Soils Based on Effective Stress Analysis

During the tunneling process of earth pressure balance (EPB) shield machines, the undrained compressibility of foam-conditioned soils in the excavation chamber is essential for reducing the fluctuation of chamber pressure and guaranteeing effective tunnel face support. As conditioned soil is simplified to be radially constrained by the shield shell and in a quasi-one-dimensional compression state under the face pressure along the tunneling direction, a mechanism-inspired analytical model was developed to estimate the void ratio and pore pressure of foam-conditioned coarse-grained soils (FCS) in one-dimensional compression based on effective stress analysis. In the model, an expansion coefficient was proposed to characterize the filling state of foam bubbles in pores and a void ratio threshold (e(th)) was defined as the transition point of the FCS with and without effective stress. The variation of void ratio and pore pressure with total stress of FCS in two distinct stages of the void ratio (e), either greater or smaller than its threshold, were calculated based on Boyle's law and the hyperbolic assumption of the effective stress-strain relation of soil. A good agreement between the analytical and experimental results verified the reliability of the proposed analytical method. Furthermore, a parametric study indicated that the compressibility increases with an increase in the expansion coefficient and foam injection ratio (FIR). Increasing additional water content leads to a decrease in compressibility under low pressure (sigma(v) <= 20 kPa), but an increase in compressibility under high pressure (sigma(v) > 20 kPa). Meanwhile, the pore pressure in FCS in the stage of e < eth also positively correlates with the expansion coefficient, FIR, and additional water content. The research findings would provide a convenient method to estimate the undrained compressibility behavior of FCS and theoretically guide the soil conditioning optimization in EPB tunneling.