Evaluating changes in the degree of saturation in excavation disturbed zones using a stochastic differential equation

Deformation characteristics of sedimentary rocks significantly change with water content during the drying process. Therefore, the proper evaluation of such drying deformation phenomena is necessary for tunnel construction in which extremely small displacements are allowed, such as geological disposal. Furthermore, it is also essential to accurately assess water content changes in the rock masses. The excavation disturbed zone (EDZ) spreads around the tunnel owing to the excavation process. The EDZ has a higher hydraulic conductivity than an intact rock mass. Therefore, it is essential to predict water content changes in the EDZ within the scope of the drying deformation phenomena. In this study, we derived the exact solution to the Richards’ equation at the Neumann boundary, which can describe the drying phenomena in sedimentary rocks. Using Japanese tuff, we conducted permeability test and mercury intrusion porosimetry tests to obtain the water diffusion coefficient and verify whether its drying behavior can be described using the exact solution. Using the verified exact solution, we propose a new stochastic differential equation that could be used to explain the local decrease in water content and the increase in variations in the EDZ, and we applied this stochastic differential equation to the 2D tunnel problem. •Exact solution to the Richards’ equation for rock drying deformation is derived.•Characteristics of the EDZ are modeled using Brownian motion.•A new stochastic differential equation for changes in water content in EDZs is derived.•Validity of the proposed methods is confirmed using experimental data.