Theoretical frame for unsaturated freezing soil

Soil freezing involves complex processes of a multi-phaseporous medium and interactions with water, heat and deformation. The basictheoretical frame of the multi-phase porous medium is established in thispaper in order to mathematically predict the complex freezing or thawingprocesses for cold region engineering problems. Based on the authors'theoretical frame work of the saturated freezing soil, this paper focuses ona four-phase unsaturated porous medium consisting of soil particle, ice,water and air. Further consideration of the air phase in the unsaturatedfreezing soil is discussed in this paper for two ideal situations: air inthe soil is linked to the outside (the open porous medium), and air in thesoil is sealed from the outside (the sealed porous medium). Thecorresponding theoretical frame work for a multi-phase porous medium withinteraction of water, heat and deformation is proposed in this paper. Theproposed theoretical model is then extended to the general case (unsaturatedhalf-open and half-sealed porous medium), and a proper theoretical model forthe heat-moisture-deformation coupling behavior of the unsaturated freezingsoil is developed. And the software 3G2001 is also developed for theheat-moisture-deformation coupling behaviors. In-site measurements resultsfor Hua Shixia highway roadbed are introduced to compare to the numericalresults of the proposed model. The results indicate that numerical resultsof the temperature field variations along the roadbed depth at differenttime are with very good correlation to the measurements, and so do numericalresults of the relatively freezing deformations of road surface. Bothnumerical accuracy to the measurements are within 10\sim 20\%. Thecomparison analysis shows the proposed theoretical frame and its numericalmodeling for the temperature--moisture deformation coupling behaviors issuitable and acceptable.