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Accurately tracking the moving interface is one of the most critical challenges in numerically modeling grout diffusion in fractures. The traditional Youngs method does not consider fluid transport to the oblique adjacent cell, which leads to repeated calculation and error accumulation. Based on the interface reconstruction technology, this paper introduced the idea of the unsplit algorithm to capture the grout-air interface. The unsplit interface advancement formulas were derived considering the fluid fluxes from the central cell to the oblique adjacent cells in the structured cell system. The numerical method based on the unsplit algorithm was validated by examples of predicting the propagation of expansible grout in a fracture. Results show that the diffusion pattern and grout front position calculated by the proposed method are in better agreement with the analytical solution compared with the traditional split algorithm. The new method can effectively improve the grout-air interface tracking accuracy.

Unsplit Youngs Method for Tracking the Moving Interface of Expansible Grout