A one dimensional frost heave model based upon simulation of simultaneous heat and water flux

Abstract A one-dimensional frost heave model is presented for unidirectional freezing in moist silts with a water table present. Frost heave is computed based upon a macrothermodynamic model that simulates heat and moisture transfer from an element of soil undergoing freezing. It is assumed that a portion of water in the element will not freeze, and all water in addition to this amount that freezes in excess of the soil porosity results in a corresponding heave. The freezing process is assumed to be isothermal. Simultaneous heat and water flux are simulated by a Galerkin finite element analog of the heat equation, including convective component, and the water flux equation based upon total energy head as the state variable. The dynamic component of the problem is simulated by the Crank-Nicholson procedure, and non-linear parameters are estimated on the basis of element centered state variable values which are generated by the quadratic shape functions used. To avoid instability, the moisture sink term in the water flux equation that arises as a result of water freezing is eliminated and handled as a thermodynamic bookkeeping quantity.