Analytical Solutions Under Cylinder Condition

This chapter develops an analytical method to explore the thermal consolidation of a saturated porous hollow cylinder of infinite-length. Initially, solutions are obtained in the Laplace transform space, and numerical inversion is performed using the Stehfest method. Two different boundary conditions are explored. In the first case, variable thermal loading is applied to the outer and inner pervious lateral boundaries of the hollow cylinder, and a time-dependent mechanical load is imposed on the outer surface, while the inner boundary remains fixed. The second case involves variable mechanical and thermal loading on the outer pervious surface, and yet the inner surface is both insulated and fixed. The governing equations for thermal consolidation in an isotropic homogeneous material are subsequently derived, considering the interdependencies of stress, temperature, and displacement fields. This analysis focuses on a saturated medium with a long cylindrical cavity subjected to both variable thermal loading and a time-dependent radial water flux or hydrostatic pressure. Furthermore, hollow cylindrical geometries are applied for determining material properties and understanding consolidation formation. Finally, the behavior of a cylinder containing a heat source with an exponentially increasing temperature on the inner surface is explored.