Adjustment of Thermophysical Rock Mass Properties in Modeling Frozen Wall Formation in Mine Shafts under Construction

Analysis of Temperature Anomalies during Thermal Monitoring of Frozen Wall Formation

“…The temperature distributions along the depth of the TM wells are used to restore the temperature field in the entire soil volume under the action of AGF. This is usually performed by solving the inverse Stefan problem [8,22] in the enthalpy formulation [2,23].…”

“…This additional condition causes the transition from the direct to the inverse Stefan problem. The inverse problems are considered to be ill-posed, and, for this reason, the solutions to Equations ( 1)-( 8) can be obtained by Tikhonov's natural regularization method described in [24] and implemented in our previous works [8,25]. Additional unknown parameters appear in Equations ( 1)- (8), which are to be determined, namely, the thermophysical properties of soils (i.e., thermal conductivities λ lq , λ sd and initial moisture content w).…”

“…The inverse problems are considered to be ill-posed, and, for this reason, the solutions to Equations ( 1)-( 8) can be obtained by Tikhonov's natural regularization method described in [24] and implemented in our previous works [8,25]. Additional unknown parameters appear in Equations ( 1)- (8), which are to be determined, namely, the thermophysical properties of soils (i.e., thermal conductivities λ lq , λ sd and initial moisture content w). In this sense, solving the inverse Stefan problem allows us to adjust the thermophysical parameters of the model so that the calculated temperature distribution matches the measured temperatures in the TM wells as closely as possible.…”

“…Within the framework of the enthalpy-porosity approach, all information on the phase transition of pore water is contained in the function of specific enthalpy on temperature-H = H(T). In this case, there is no need to explicitly track the front of the phase transition, which greatly simplifies the procedure for the numerical implementation of the model in Equations ( 1)- (8). From the form of the function included in the model, it follows that the front of the phase transition is blurred in a finite temperature range [T sd ; T lq ].…”

“…Experimental monitoring of the FW state is a mandatory procedure prescribed by many countries' regulations. On the basis of the data from experimentally measured temperatures in TM wells, the mathematical models of heat and mass transfer processes in soils during artificial ground freezing (AGF) are usually adjusted [6][7][8]. These adjusted mathematical models allow for the correct calculation of the temperature distribution over the entire soil volume and the FW thickness at the current time and are necessary to make predictions for FW evolution in the future.…”