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The thaw front grows outward from the tunnel wall following a simplified cylindrical Stefan condition: the rate of advance is proportional to the net heat flux entering the frozen ground and inversely proportional to the current front radius (heat spreads over a larger circumference as the halo widens, so growth slows even under constant load). Net heat = heat load minus the fraction blocked by insulation, plus an advective term from groundwater flow, minus the rock's passive freezing capacity. When net heat drops below zero the front can recede (refreeze) back toward the lining. Support factor of safety falls as the thawed halo widens, since thawed ground carries far less strength than ice-bonded rock.