Modeling cement distribution evolution during permeation grouting

Permeation grouting is a proper technique for strengthening dry sand before a tunnel construction in it. In the fifties of the past century, N. N. Verygin modeled this technique with 1-dimensional problems formulated in domains with a free moving boundary and came up with their analytical solutions. As for the 2-dimensional set ups, respective problems are formulated in domains that have complicated shapes and contain free moving boundaries. Until recently these difficulties seemed to be insuperable and all 2-dimensional grouting models in the framework of the continuum approach were based on the convective dispersion equation. They can be classified as the ones that describe pollution propagation. Nevertheless, M. B. Demchuk has lately come up with numerical solutions of 2-dimensional problems with free moving boundaries which set ups correspond to in situ grouting. Moreover, he has shown the following: adoption of the continuum approach is relevant for the set of input parameters used, among the curvilinear grids the calculations are performed on there are the ones that have chaotic dispositions of their nodes in space on some time layers. In this work, rough estimates are performed that indicate that the use of problems with free moving boundaries in the numerical modeling in hand is relevant.