Thermoelastic and thermoplastic response of a double-layer porous space containing a decaying heat source

Abstract

Solutions are presented for the behaviour of a layered porous space which contains a decaying heat source. Such a problem arises when high-level nuclear waste is placed in deep underground depositories in deep clayey formations of sedimentary basins. The geometry of the problem is one dimensional and the porous space is constituted by two layers: a deep low permeability layer which contains the nuclear waste disposal and a superficial layer. The solution is used to examine the effects of contrasts of permeability, thermal conductivity and specific heat capacities between the two layers on the large-scale behaviour of the porous space. Results are presented, using realistic data, for the pore pressure and temperature evolution at the heat source centre, and for the vertical displacement of the ground level. The superficial layer has no significant effects on pore pressure, temperature and stress evolution near the heat source centre. The vertical displacement of the ground level is mainly due to the thermal dilatation of the pore water, so it decreases with an increasing of permeability of the superficial layer. The solution of the time-dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical methods to invert the transformed solutions. Comparisons with numerical simulations taking into account the non-linear and non-reversible behaviour of the rock mass are presented. © 1998 John Wiley & Sons, Ltd.