A semi-analytical method and its application for calculating the thermal stress and displacement of sparsely fractured rocks with water flow and heat transfer

Abstract

Using Goodier’s thermo-elastic displacement potential and Laplace transform, a semi-analytical method is developed for calculating the displacement and stress induced by heat transfer in sparsely fractured granitic rocks with saturated water flow and distributed heat sources. An integral equation of the thermo-elastic displacement potential is formulated in the Laplace-transformed domain. The fractures are discretized into rectangular elements, and the elemental integrals that involve singularities are calculated analytically. The numerical solutions of the potential are calculated using numerical Laplace inversion, and the temperature-gradient-induced displacements and stresses are calculated using central differences. The method is employed to examine the characteristics of the temperature-gradient-induced displacement and stress for a hypothetical problem that is intended to mimic the near-field environment of deep geological repositories of high-level radioactive wastes. Among other things, the results reveal the following: (1) In early time of operation of the repository, the region of rock under thermal expansion and compressive is limited; (2) As the intensity of the heat source gets smaller with time, only a small portion of the rock expands whereas the remaining portion contracts; (3) Downstream peak temperatures may be higher due to the supply of thermal energy by the water-flow-facilitated heat transfer, and patterns of influences of the water velocities on the thermal stress and displacement are similar; (4) Sufficiently close heat sources would cause superposition of the heating effects and make the near-field temperature increase significantly.