Abstract:

In order to ensure the safety of the construction and operation of the karst water inrush tunnel, based on the elastic beam model, double cusp mutation model of the instability of the karst water inrush roof under dynamic disturbance was established by using the catastrophe theory. Considering the surrounding rock properties, hydrostatic pressure, dynamic disturbance and other factors, the instability mechanism and failure conditions of the roof of karst water inrush tunnel were analyzed, the discriminant equation of its instability mutation was established, and the minimum safe thickness of the roof was solved by Matlab software programming. At the same time, in order to avoid the irrationality of the theoretical formula of the mutation when the hydrostatic pressure was too large, the minimum safe thickness of the hydrostatic pressure was calculated separately, and the greater value of two calculated values was taken. The results show that whether the waterproof rock mass remains stable is determined by the factors the internal and external factors of rock mass. The minimum safe thickness of the rock mass increases with the increase of the span of the rock mass, and decreases with the increase of the elastic modulus of the rock mass. When the vibration frequency is constant, the greater the blasting load, the greater the minimum safe thickness of rock mass. When the blasting load is constant, the greater the frequency of blasting vibration, the smaller the minimum safe thickness of rock mass. The greater the hydrostatic pressure, the greater the minimum safe thickness of rock mass. The engineering example shows that this method of calculating the safety thickness of the roof of karst tunnel is feasible and highly accurate.

Key words: mutation theory, waterproof rock mass instability, safe thickness, dynamic loading, hydrostatic pressure