THERMOELASTIC STRESS DUE TO A RECTANGULAR HEAT-SOURCE IN A SEMIINFINITE MEDIUM - PRESENTATION OF AN ANALYTICAL SOLUTION

The thermoelastic response due to a time-dependent rectangular heat so urce in a semi-infinite medium is analyzed. The problem originates fro m studies of nuclear waste repositories in rock. Canisters containing heal-emitting nuclear waste are deposited over a large rectangular are a deep below the ground surface. The solution for a time-dependent hea t source is obtained from the corresponding instantaneous heat source by superposition. The thermoelastic problem for the instantaneous rect angular heat source in an infinite surrounding is solved exactly. An i mportant step is the introduction of so-called quadrantal heat sources . The solution for the rectangle is obtained from four quadrantal solu tions. The solution for the quadrantal heal source depends on the thre e dimelasionless coordinates only. Time occurs in the scale factors on ly. The condition of zero normal and shear stresses at the ground surf ace is fulfilled by using a mirror heat source and a boundary solution . The boundary solution accounts for the residual normal stress at the ground surface. Using a Hertzian potential, a surprisingly simple sol ution is obtained. The final analytical solution is quite tractable co nsidering the complexity of the initial problem. The solution may be u sed to lest numerical models for coupled thermoelastic processes. It m ay also be used in more detailed numerical simulations of the process near the heat sources as boundary conditions to account for the three- dimensional global process. (C) 1998 Elsevier Science B.V. All rights reserved.