Numerical simulation is the most efficient way to investigate the mechanism of grout diffusion in jointed rocks

but one of the most critical challenges is to accurately track the grout flow in numerical simulation. This study was focused on the diffusion process of self-expanding grout in the flat fracture surface and considering characteristics of two-phase flow in the grout diffusing. Moreover

the VOF function was employed to describe the distribution of two-phase medium

and then was solved by Youngs method based on the principle of geometry. Thus

the tracking of grout moving interface was realised. Finally

the proposed method was examined by an example of the self-expanding grout with a known density freely diffusing with time in a plat fracture surface. The results showed that the analytical solutions were in good agreements with obtained locations and contours of the grout moving interface at different times in the example. Hence

the results verified that the proposed method had a high calculation precision and exhibited a sound effect of interface tracking. This study lays a solid foundation for developing the numerical method for simulating the diffusion processes of self-expanding grout flow.