Hydraulic Brittle Fracture in a Rock Mass

This paper presents a novel method on the hydraulic brittle fracture propagation in a rock mass forced by high-frequency fluctuating pressures due to the turbulence phenomena that occur in unlined dissipation structures and spillways. This type of brittle fracture analysis allows the risk assessment related to the design of unlined emergency spillways and in pre-excavated plunge pools and stilling basins, with reference to small duration flood events that are larger than the design ones. These peaks in dam spillway discharge could be caused by the clime change, or imposed by new regulatory requirements for managing the Probable Maximum Flood (PMF). The fluctuating pressures propagating inside the rock fissures generate zones of alternative stress at the tip of fractures. If the stress exceeds the limited toughness of the rock, it generates brittle fractures. This increments the fracture length in a stable manner, with a finite crack velocity propagation, which differs from the catastrophic behaviours of tensile cracks in structural engineering as assumed in the previous studies on rock scour. The finite crack velocity propagation, for these peak flood events, implies the rock scour depth could be mainly defined by the profoundness of the brittle fractured area. The hydraulic brittle fracturing also has application in the oil and gas industry for waste injection and unconventional gas production wells. In the literature, these cases are analysed in quasi-steady conditions neglecting the inertial terms in the flux equations, because these terms are considered negligible in all cases for a fracturing liquid except at extremely early time. On the contrary, in this investigation, these terms become more and more important when the frequency of the fluctuating pressures increases and they cannot be neglected in the design of the hydraulic structures. This is because these terms outline the resonance conditions where the strongest stress in the rock matrix occurs. Modelling hydraulic fractures requires considerations of both fluid and solid mechanics. This study considers the fissure lengthening in time by coupling the geological and hydraulic aspects of the phenomena via reformulation of the classical water hammer equation. The water hammer equation takes into account both the inertial term and dissipative term in the fluid equation. It allows evaluating the advancement of the disintegration zone in a rock matrix, starting from the pre-existing rock fissure system inferred by geological surveys, during flood events. The outcomes of the paper include a sensitivity analysis changing the rock mechanical characteristics, fissure geometry and the air concentration in the air-water mixture inside the fissure. The results of this novel study also improve the Discrete Fracture Network Software for application in dams and hydropower engineering.