Coupling between pressure and opening during fluid injection into a fracture—implication for fracture normal stiffness

Our study aims to demonstrate the control of fracture aperture opening on the apparent normal stiffness of fractures during fluid injection, a key factor governing the hydro-mechanical behavior of impermeable rock formations containing highly permeable fractures. Using the Distinct Element Method (DEM) implemented in 3DEC, we simulate fluid injection into a 100 m planar fracture through a line source under constant overpressure. By systematically varying the assigned fracture normal stiffness, we perform a sensitivity analysis on how aperture changes affect the apparent stiffness. For theoretical validation, we adopt a semi-analytical approach, which includes two governing equations: one assuming a negligible aperture gradient and another without this assumption. Numerical results closely match these semi-analytical solutions. In the “soft” fracture regime, the apparent stiffness decreases over time, eventually falling below the nominal stiffness assigned at a small-scale as the aperture grows. Conversely, in the “rigid” regime—where the aperture gradient is negligible—this effect is not observed. These findings underscore the role of time-dependent aperture evolution in controlling fracture stiffness during fluid injection.