 Hydraulic control of frost heave

A porous sheet of thickness $d$ and permeability of a porous medium $\Pi$ supplies a thin premelting film. The Darcy flow law equates water supply to ice growth for equal densities. With equal film and ice conductivities, negligible latent heat relative to the through-going conductive flux, and $a\ll h$, phase equilibrium gives $p_T=(\rho L\Delta T/T_m{)}^{3/4}(A/(6\pi h^3){)}^{1/4}$. The increasing gravitational load limits growth. A quasi-steady temperature field alone does not imply the negligible-latent-heat approximation.