Abstract: With regard to the near-field environment of deep geological repositories of high-level radioactive wastes, this study formulated a semi-analytical method for calculating the displacement and stress in the 3D processes of water flow and heat transfer in saturated sparsely fractured rocks. Goodier’s thermo-elastic displacement potential and Laplace transform are employed to calculate the temperature-gradient induced displacement and stress. Considering the case of a rock mass containing one single fracture, Boussinesq’s solution and Cerruti’s solution in the classic theory of elasticity are utilized to obtain the constraint-induced displacement and stress for complying with the boundary conditions, which supplement the temperature-gradient induced displacement and stress to arrive at the total thermal displacement and stress. The fracture is discretized into a set of rectangular elements, on which the integrals involving singularities are evaluated using an analytical method with polar coordinates, whereas numerical integration is employed for non-singular integrals and for the integral concerning the distributed heat source. Comparison with an analytical solution, which assumes one-dimensional heat conduction normal to the fracture walls, indicates that the semi-analytical results are essentially agreeable with minor differences only in the region where the effect of 3D heat conduction tends to be more significant. For a hypothetical 3D water flow and heat transfer process in a rock containing one single fracture, the distributions of temperature gradient induced, the constraint displacement induced, and the total displacements and stresses are calculated and examined, which reveal, among other things, that water flow and heat transfer may exert significant influences on the spatiotemporal variations of the displacements and stresses; and that the compressive stresses may occur in the region that is close to the distributed heat source due to constrained thermal expansion, while tensile stresses may exist in the region that is relatively further away from the distributed heat source due to constrained compatible contraction.

Key words: rock mass with a single fracture, saturated water flow, 3D heat transfer, thermo-elastic displacement potential, thermal stress