Evolutionary Characteristics and Mesoscopic Mechanisms of the Effective Stress Coefficient in Rock Fractures Under Complex Stress Paths

Accurately evaluating the effective stress coefficient (α) of rock fractures under hydro-mechanical (HM) coupling is paramount for assessing the stability of fractured rock in deep underground engineering. This study conducted triaxial HM tests under varying normal stresses and multi-stage fluid pressures on marble fractures from a deep-buried water transport tunnel. Coupled with numerical simulations, the dynamic evolution and mesoscopic physical mechanisms of α under complex stress paths were elucidated. Results demonstrate that α is highly stress-dependent and generally less than 0.4 for smooth marble fractures. Under low normal stress, α increases approximately linearly with elevated fluid pressure. Conversely, under high normal stress, α exhibits low sensitivity to fluid pressure variations until surpassing a critical threshold (10–12 MPa), after which it manifests a pronounced exponential increase. Mesoscopic analysis reveals that severe contact occlusion induced by high normal stress restricts fluid permeation, leading to a heterogeneous fluid pressure distribution. This heterogeneity restricts the applicability of the traditional effective stress principle under extreme conditions. Once fluid pressure crosses the threshold, a “wedging effect” triggered by high-pressure fluid forces rapid failure of contact spots, causing a precipitous reduction in the contact area ratio (Sc). This contact state evolution constitutes the physical essence underlying the exponential surge of α. Based on experimental and inverted data, an improved empirical model for fracture effective stress was established, incorporating the coupled influences of normal stress and fluid pressure. This model possesses explicit physical significance, providing a scientific theoretical basis for evaluating surrounding rock stability in deep-buried tunnels.