| Abstract: | Solutions are presented for the behaviour of layered soil or rock deposits which contain a heat source. Such a problem arises when high level nuclear waste is placed in deep underground depositaries, as the waste continues to generate heat for many years after placement. This heating of the surrounding soil or rock may lead to expansion and cracking with subsequent contamination of ground water. Results are presented for heat soureces with different decay rates and for heat sources in layers of material with different coefficients of expansion. An example using realistic data for rock is also given. The solution method involves applying Fourier or Hankel transforms to the field quantities and this reduces the two-dimensional or axisymmetric problem to one involving a single spatial dimension. In cases where the soil or rock is horizontally layered, the method has great advantages over other numerical methods such as finite element or finite difference techniques, since little computer storage and data preparation time is required. Solution of the time-dependent problem is carried out by applying Laplace transforms to the field variables, obtaining solutions and then using numerical means to invert the transformed solutions. This enables easy solution of problems involving time-dependent (i.e. decaying) heat sources. |
