Improved Analytical Modeling of Brittle Shear Fractures in Deep Excavations under Hydrostatic Loading

ABSTRACT: Stress-induced brittle fractures pose significant hazards in deep underground excavations, releasing energy that can endanger personnel and equipment. Laboratory experiments have shown that localized, diffused spalling begins when hydrostatic stress near the tunnel wall exceeds the rock's peak shear strength - the stress-strength ratio. As this ratio increases, damage intensifies, forming fractures in a logarithmic spiral pattern. Theoretically, plastic slip line models can predict this shape based on material friction angles. At even higher stress-strength ratios, intersecting slip lines emerge, leading to broader specimen failure. Despite the critical risks posed by brittle failure instabilities, existing plastic slip line models using logarithmic spirals often fall short in capturing the specific behaviors of brittle fractures, primarily due to their reliance on a single friction angle. An enhanced analytical model is proposed to overcome the limitations of traditional plastic slip line models by employing Bézier curves to represent brittle shear slip lines with greater precision. This model incorporates additional factors, such as a damage factor and breakout width angle, allowing a more accurate depiction of brittle fractures. The damage factor reflects the stress-strength ratio, while the breakout width angle accounts for the earth pressure coefficient (horizontal to vertical stress) near the tunnel wall. Unlike theoretical slip lines that rely solely on material friction angles, the Bézier curve intersects the tunnel wall at a shallower angle, accommodating initial dilatational shear fracturing under low-confinement conditions. These Bézier slip lines provide a refined representation of brittle shear fractures across varying stress states, offering more profound insights into brittle failure mechanisms. Ultimately, this model leads to safer, more reliable design and mitigation strategies for high-stress underground excavation environments.