Analytical approximations to the thermoelastic behavior of repository configurations

This report presents three different analytical solutions to approximate the surface uplift of a heated repository. The first solution assumes a temperature distribution which is a function only of the vertical coordinate (z) constant throughout the radius and the lateral strain is assumed to be zero. The second solution assumes a temperature distribution which is a function of the radial coordinate (r) constant throughout the height and assumes no radial displacement at the outer boundary. The third solution is similar to the second solution, the difference being that the outer boundary is assumed to be traction free. The second solution is subsequently derived from the third solution by superposing the elastic solution obtained from imposing a constant radial displacement at the outer boundary of a solid cylinder. The first solution consistently gives the highest vertical displacements due to the lateral constraints. The solutions are summarized and specific temperature distribution forms are used to formulate expressions for the vertical displacements. Some example problems are presented with comparisons to previous finite element analyses of various repository models (bedded and dome salt). Generally, the first and second solutions appear to bound the finite-element computations of the surface uplift