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.