Exact solution of Richards’ equation using heat transfer boundary and application to dry-induced deformation behavior of Tage tuff

In geological disposal of radioactive waste and tunnel construction of high-speed railways, it is important to minimize the deformation of the rock to be excavated. When constructing such rock structures at sedimentary rock sites, it is important to consider the dry deformation of the rock masses. The authors have investigated changes in mechanical properties associated with continuous changes in the water content of green tuffs originating from submarine volcanoes widely distributed in eastern Japan (called Tage tuff). On the other hand, it is widely known that the water content in rock mass changes non-uniformly from the surface in contact with the atmosphere. Considering that the mechanical properties of rock mass change according to the water content, it is important to obtain the water content distribution. In this study, we show a method of linearizing the Richards’ equation of a nonlinear partial differential equation by adding two conditions that the water diffusion coefficient is constant and the permeability coefficient does not depend on the coordinates, and the exact solution in which saturation changes depending on coordinates and time is obtained. Using the obtained exact solution, we simulated the drying experiment of Tage tuff conducted by the authors and examined some conditions based on the heat transfer boundary.