Modelling of Transient Ground Surface Displacements Due to a Point Heat Source

Abstract

Using Laplace-Hankel integral transformations, transient closed-form solutions of the thermally induced ground surface displacements, excess pore water pressure and temperature increment due to an instantaneous point heat source buried in an isothermal permeable half space are presented and discussed. The basic formulations of the governing equations are on the basis of Biot’s three-dimensional consolidation theory of porous media. Numerical results show that the maximum ground surface horizontal displacement is around 38.5% of the maximum ground surface vertical displacement. The study concludes that the thermally induced horizontal displacement is significant. The solutions can be used to test numerical models and numerical simulations of the thermoelastic processes near the heat sources. Heat source buried in the stratum leads to thermo-mechanical responses of fluid saturated porous medium. The heat source such as a canister of radioactive waste can cause temperature rise in the soil. The solid skeleton and pore fluid expand due to the heat source, and the volume increase of pore fluid is greater than that of the voids of solid matrix. This leads to an increase in pore fluid pressure and a reduction in effective stress. Therefore, thermal failure of soil will occur as a result of losing shear resistance due to the decrease in effective stress. Attention is focused on the analytical solutions of the transient thermoelastic responses of an isotropic stratum due to an instantaneous point heat source. The responses of the stratum were satisfactorily modeled by assuming it as a thermoelastic porous continuum (Booker & Savvidou, 1985). It suggested that linear theory was adequate for a repository design based on technical conservatism. For example, Hueckel and Peano (1987) indicated that European guidelines require that temperature increments in the soil close to the heat source should not exceed 80C while the temperature increments at the ground surface are limited to less than 1C. Given these modest temperature increments, Hollister et al. (1981) observed that any significant non-linear behavior and/or plastic deformation of the soil would be confined to a relatively small volume of soil around the waste canister itself. In this case, a linear model can provide a reasonable approximation to the assessment of a proposed design (Smith & Booker, 1996). Hudson et al. (2005) given advices on how to incorporate thermo-hydro14