Thermoelastic stress due to a rectangular heat source in a semi-infinite medium. Application for the KBS-3 repository

In the KBS-3 concept, canisters containing nuclear waste are deposited over a large rectangular area deep below the ground surface. The thermoelastic response due to such a time-dependent rectangular heat source in a semi-infinite medium is studied. An analytical solution for this problem for any heat source has been presented in a preceding paper. The complete solution is summarized in this paper. In this study the analytical solution is applied to the KBS-3 case. The temporal development of the stress field is calculated at points, along lines and in planes for KBS-3 data. The temperature field and in particular the stresses are illustrated in 56 figures for times up to 1500 years. Some stress components exhibit local maxima and minima near edges or corners of the repository. The largest tensile stress occurs at the ground surface directly above the repository centre. This stress is equal to 1.7 and 5.8 MPa after 50 and 500 years, respectively. The largest horizontal and vertical compressive stresses at the centre of the repository are 18 MPa for t=67 years and 3.7 MPa for t=680 years, respectively. A parameter sensitivity analysis is presented. The stress field at the repository centre is rather insensitive to 10% variations of the repository length, width and depth as well as the rock's volumetric heat capacity, heat conductivity and Poisson's number. This is also true for stresses at the ground surface with the exception of the depth parameter. The change in the stresses is at the most ±6% at the repository centre, and ±9% at the ground surface. The solution may be generalized to a repository that consists of several rectangular areas of different sizes and at different depths. The rectangular areas may be loaded at different times. An example is presented where two repositories are stacked, one on top of the other. The analytical solution for the stresses is compared with two other semi-analytical models. The agreement is good