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Using an analogy to the classical Stefan problem, we construct evolution equations for the fluid pore pressure on both sides of a propagating stress-induced damage front. Closed form expressions are derived for the position of the damage front as a function of time for the cases of thermally-induced damage as well as damage induced by over-pressure. We derive expressions for the flow rate during constant pressure fluid injection from the surface corresponding to a spherically shaped subsurface damage front. Finally, our model results suggest an interpretation of field data obtained during constant pressure fluid injection over the course of 16 days at an injection site near Desert Peak, NV.