Geometry-dependent nonlinear flow behavior in mortar replicas with a single rough mismatched fracture

The oversimplification of fracture geometric features, such as roughness and aperture, is a prevalent issue in rock fluid flow studies, resulting in inaccurate characterization for nonlinear flow. To investigate the influence of complex fracture geometry on flow behavior, spectral method was employed to digitally generate 40 mismatched fracture-surface pairs, enabling a broader spectrum of roughness variables. The roughness and mechanical aperture of these digital surface pairs with central flow paths were described with surface roughness ( Z 2 ) and mechanical apertures normal to flow path ( e m_NMA ), respectively. Compared to the vertical traditional aperture ( e m_t ), the e m_NMA yields smaller values and also inherently captures the aperture directionality. Replicas with various mismatched-surface combinations were manufactured through 3D printing and mortar for constant-head flow tests under 6 different pressure gradients (1.01 × 10 4 –11.86 × 10 4 Pa m −1 ) to capture distinct nonlinear flow status. To address the limitations of single-parameter roughness descriptions and non-directional aperture models in hydraulic characterization, a new geometric parameter, G h , was developed by integrating multiple parameters from both individual and coupled fracture surfaces. Compared with the e m_t -based approach, the e m_NMA -based G h is more strongly correlated with both Forchheimer's and Izbash's coefficients and has potential for identifying critical flow regimes and assessing flow nonlinearity, as clearly revealed by its correlation with the critical Reynolds number (Re c ). Considering the robust correlations of the surface-pair geometry and Forchheimer–Izbash-modeled hydraulic properties, the superior hydraulic performances of e m_NMA and the composite geometry index G h were confirmed, thereby overcoming the limitations of the oversimplified geometric parameters commonly used in previous studies. The new index G h and related hydraulic performance presented herein are conducive to comprehending the morphology-hydromechanical coupled processes, quantitatively refining rock mass classifications before and after the excavation or drilling, informing hydraulic fracturing strategies in underground fluid resource exploration.