Upper bound analysis of active and passive mechanisms of intermediate rock wall between two adjacent pressurised cavities

Abstract

The construction of adjacent cavities is important for deep oil storage and tunnel engineering. However, studies on the failure mechanisms of intermediate rock walls are scarce. Rock walls for underground cavities, such as oil reservoirs and tunnels built near concealed karst caves, are exposed to pressure variations. Because the magnitude of pressure imposed on the inner surface of two cavities varies, different kinematic mechanisms and failure extents of rock walls can be observed. To derive the analytical expressions of the failure surface for rock walls, limit analysis is conducted within the framework of the upper bound theorem. The active and passive failure modes of rock walls are defined based on the variation in the magnitude of pressure on both sides of the walls. Furthermore, two failure states of rock walls are summarised according to the relationship between the pressure difference and weight of rock walls. Moreover, based on the upper-bound solutions, thenon-linearoptimisations for critical pressure and thickness of rock walls are implemented by assuming that both cavities are cylindrical (rectangles in two dimensions). The results of the presented methods and numerical simulations indicate that the magnitude of pressure difference determines the failure modes and shape characteristics of rock walls. Evidently, the effects of internal pressures on the stability of rock walls must be intently considered in the design of two adjacent underground cavities filled with fluid.