Methods of calculating infiltration of meltwaters into frozen soil

Abstract

Improvement and refinement of calculations and forecasts of the runoff of the spring flood are impossible without a detailed study of the infiltration capacity of soils in river basins during formation of the flood. Whereas the impermeability of thawed soils is determined mainly by their hydrophysical properties and degree of moistening, when estimating the infiltration of water into frozen soils it is necessary to know also its temperature and thermal properties.During thermal interaction of the infiltrating water with the frozen soil the permeability of the latter can change substantially. Phase transition of infiltrating water and soil moisture change not only the cross section of the flow but also the water and thermal properties of the soil. Meltwater, penetrating into soil, crystallizes, which causes the liberation of a considerable amount of heat and an increase of soil temperature. As a result a part of the soil moisture thaws. Mobile water in large pores freezes, and attached water, which is practically immobile during seepage, thaws. Crystallization of water in large pores is accompanied by a decrease of permeability of the soil, and in the case of complete plugging of the water-conducting pores infiltration of water into the soil stops and an impermeable layer forms.A decrease of the infiltration rate occurs not only due to a reduction of the cross section of the flow owing to plugging of the soil pores by precipitating ice crystals but also under the effect of a reduction at constant head of the piezometric gradient caused by lengthening of the seepage paths or of the head as a consequence of joining of the menisci of the infiltrating water and soll moisture.The problem of under what conditions ice forming from infiltrating water can plug all water-conducting pores in frozen soil is solved by the thermophysical method. From the condition of equality of the supply of cold in a unit volume of frozen soil and amount of heat brought into the soil by the infiltrating water and released upon its freezing, we derive the main equations by means of which we calculate the pertinent temperature and water content of the soil necessary and sufficient for complete plugging of the water-conducting pores.The negative temperature of the soil at which the supply of cold is sufficient for complete plugging of the pores is called the critical temperature Tcr and the soil moisture content corresponding to it is called the initial critical moisture content.The initial critical moisture content is calculated by the equation (L+Cwrin) pa!+aw~f t--a w + [cs+w~lcw--ct:J~-L~tw'~-Wnfl, (1) Win.== aw ~ + c w T m -" cl rcr where C w, Ci, C s are the heat capacity, respectively, of water, ice, and soil; L, specific latent heat of fusion; P, porosity; Tin , ini=ial temperature of the infiltrating water; Tcr, critical temperature of the soil; d i, d w, d, unit weight of ice, water, and soil; W~f, mass of nonfrozen water at O~ W~f, same at the critical temperature.It is necessary to take into account the initial water temperature T...