“Self-Burial of Radioactive Waste”, L. Ya. Kosachevskii, L. S. Syui1999-11-01 (self-sinking waste disposal)⁠:

The problem of the “self-burial” of radioactive waste into melting rock is solved for a spherical container of finite thickness.

The mathematical model constructed, unlike the existing ones, takes into account the thermal losses to the solid rock and to the melt behind the container, as well as the reverse evolution of heat upon solidification of the melt.

A calculation for the particular case of self-burial in granite shows that consideration of these factors substantially increases the maximum permissible radius at which the container will remain in the solid state and slows the burial rate.