Numerical simulation of infiltration laws of grouts in random aperture based on multi-fractional Brownian motion

In order to study the influence of aperture distribution on the infiltration in a single fracture, based on the fractal theory of multi-fractional Brownian motion(MBM), four groups of fracture surfaces at different regularization dimensions are constructed, all of which more realistically reflect the asymptotic self-similarity of aperture distribution of natural fracture surface. From the numerical simulation of grouting in a single random aperture fracture, it is indicated that pressure contours show twists and turns spreading over time, which reflects the distinct non-uniform characteristics. The distribution of closed area has a tendency that is from dot-like scatter to focused plane with the regularization dimensions tending to reduce, and its spatial location has obvious influence on the pressure and grouting time. As the development of percolation, there appears a tendency that the node pressure is from monotonically rapid increase to stepwise stability, and the more the node approaching the percolation border, the shorter the grouting time used in the case of reaching the steady pressure. Moreover, there is a power relationship between the node pressure and the grouting time. In view of this rule, empirical equations with different parameters are also obtained by fitting curves.