One‐dimensional analysis of a poroelastic medium during freezing

A solution to the problem of freezing of a poroelastic material is derived and analysed in the case of one-dimensional deformation. The solution is sought within the framework of thermo-poroelasticity, with specific account of the behaviour of freezing materials. The governing equations of the problem can be combined into a pair of coupled partial differential equations for the temperature and the fluid pressure, with particular forms in the freezing and the unfrozen regions. In the freezing region, the equations are highly non-linear, partly due to the dependence of thermal and hydraulic properties on water saturation, which varies with temperature. Consequently, the solution is obtained through numerical methods, with special attention to the propagation of the freezing front boundary. The response to one-dimensional freezing is illustrated for the case of cement paste. Finally, the influence on the solution of varying selected parameters is analysed, such as the temperature boundary conditions, the parameters characterizing the geometry of the porous system, the ratio of fluid and thermal diffusivities, and the rate of cooling applied at the freezing end. Copyright (C) 2008 John Wiley & Sons, Ltd.

[1]  E. Schulson.  Brittle failure of ice , 2001 .

[2]  Vesa Penttala,et al.  Freezing-Induced Strains and Pressures in Wet Porous Materials and Especially in Concrete Mortars , 1998 .

[3]  Yuanming Lai,et al.  NONLINEAR ANALYSIS FOR THE COUPLED PROBLEM OF TEMPERATURE, SEEPAGE AND STRESS FIELDS IN COLD-REGION TUNNELS , 1998 .

[4]  Kevin O'Neill,et al.  Exploration of a Rigid Ice Model of Frost Heave , 1985 .

[5]  A. Fabbri,et al.  Freezing and thawing porous media: experimental study with a dielectric capacitive method , 2005 .

[6]  D. R. Nielsen,et al.  A consistent set of parametric models for the two‐phase flow of immiscible fluids in the subsurface , 1989 .

[7]  Olivier Coussy,et al.  Poromechanics of freezing materials , 2005 .

[8]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[9]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[10]  S. Taber.  The Mechanics of Frost Heaving , 1930, The Journal of Geology.

[11]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[12]  J. Murton,et al.  Bedrock Fracture by Ice Segregation in Cold Regions , 2006, Science.

[13]  K. M. Neaupane,et al.  Simulation of a fully coupled thermo–hydro–mechanical system in freezing and thawing rock , 1999 .

[14]  Jacques Marchand,et al.  Predicting the volume instability of hydrated cement systems upon freezing using poro-mechanics and local phase equilibria , 2004 .

[15]  D. F. McTigue,et al.  Thermoelastic response of fluid‐saturated porous rock , 1986 .