Numerical simulation of frozen wall formation in water-saturated rock mass by solving the Darcy-Stefan problem

Artificial ground freezing (AGF) is a common technology of shaft sinking through water-bearing strata. The AGF technique is used to create a frozen wall preventing shaft flooding. An additional factor that makes shaft sinking more complicated is associated with external groundwater flows occurred due to hydrostatic pressure gradients. In this paper, we study the influence of groundwater seepage on the frozen wall formation in fluid-saturated rock mass in the framework of the two-dimensional two-phase Darcy-Stefan problem. The results of numerical simulation of the thermal and hydraulic properties of the sandstone layer at the site of Petrikov Mining and Processing Plant are presented. It has been found that the external groundwater flow has a significant effect on the growth of a frozen wall in the case when the groundwater velocity magnitude is greater than or equal to 50 mm/day. This critical seepage velocity strongly depends on how quickly the water content and rock mass permeability decrease with decreasing temperature, or on the parameters of the rock mass freezing characteristic curve and permeability versus temperature curve. The proper setting of these parameters is a sine qua non for creating adequate mathematical models of heat and mass processes in the artificially frozen water-saturated rock mass.