Stability of Forcheimer's non-Darcy flow and probability of water inrush in coal mine

摘要

The instability of seepage flow of water in surrounding rock results in water inrush, and the mechanism of water inrush is controlled by the nonlinearity of the developing equations for this dynamic sytem. Forcheimer's non-Darcy flow system may be instable when both the control parameters and the boundary pressure are content with certain conditions, and the water inrush may take place. Especially, even if the system is in a steady state at initial moment, it evolves neither to a new steady state nor a periodic motion when a tiny turbulency of boundary pressure comes into being, and then the system may become instable. When the surrounding rock is affected by mining activities, its seepage properties will change remarkably, and the probability of water inrush increases remarkably too. Test results show that each of the seepage properties of rock is a stochastic variable satisfying a certain distribution, so the water inrush takes on randomicity evidently. In the current article, a test system, which can measure the seepage properties of Forcheimer's non-Darcy flow in fractured rock specimen, is constructed by combining a patent device with MTS815.02 Rock Mechanics Test System. The seepage properties-the permeability and the non-Darcy β factor of fractured rock specimen and their average values, E(k), E(β), and standard deviations σ(k), σ(β), under a set of preconcerted strain are worked out. Based on analyzing the control equations of the system, the conditions of water inrush are obtained, and the probability of water inrush is calculated. This study shows that the probability of water inrush increases rapidly as the increase of rock strain.