Quantitative characterization of fracture surface undulations and gas-guiding patterns in fractured rocks under steady loading

• The undulation degree of rock tensile fracture surfaces is critically influenced by the initial fracture angle, with a threshold at 45° separating high and low undulation intervals. • Quantitative indices for relative undulation degree, undulation frequency, and matching degree were developed to characterize fracture surface morphology. • A direct relationship was established between fracture surface undulation changes and gas flow guidance, enabling quantitative characterization of gas flow stability, tortuosity, and uniformity. • Numerical models validated the proposed indices, confirming their utility in predicting gas flow patterns in fractured rock strata.