Optimization of the Passive Regime of Artificial Freezing of a Water-Saturated Rock Mass

Abstract

An iteration computational algorithm is presented for optimization of the passive regime of artificial freezing of a water-saturated rock mass, which is the longest and most cost-intensive stage in the process of shaft excavation and carriage installation. The optimization is implemented by solving the inverse problem of determination of the heat flux on the boundary of a freezing well in a horizontal rock layer. Heat transfer in the rock layer is considered with account taken of the phase transition of the first kind on the basis of the Stefan problem in a two-dimensional formulation. The developed algorithm is based on the principle of descriptive regularization and the optimization method of steepest descent. In the algorithm, the target functional gradient and the parameters of optimization of the problem′s solution are determined from the solution of a conjugate problem for temperature increment. Using the proposed algorithm, optimum regimes of passive freezing for rock layers with different thermal and physical characteristics under varied initial conditions have been obtained.