A predictive model for asymmetric surface subsidence above inclined metal mines considering coupled discontinuity slip and stress-arch restraint

Surface subsidence induced by underground mining of inclined metal orebodies is commonly characterised by pronounced asymmetry and slow far-field convergence. Conventional predictive methods, such as the probability integral method, are founded on assumptions of layered continua and stochastic media and therefore have difficulty reproducing this behaviour. Evidence from steeply inclined orebodies confirms that stress redistribution drives structural damage within the overburden, whereas dominant geological discontinuities govern the kinematic path of stratal movement. The neglect of this stress–structure coupling is a fundamental limitation of conventional models. This study therefore proposes a structural influence model based on Cauchy kernels. The model employs a negative peak to represent gravity-driven overburden subsidence and a positive peak to represent the restraining effect of volumetric expansion in caved rock under stress arching. A structural-offset parameter explicitly incorporates the geometric constraint imposed by discontinuities. The model was validated by combining Interferometric Synthetic Aperture Radar and Global Positioning System observations from an inclined iron mine. Compared with a conventional Gaussian model, the double-Cauchy model reproduced both the hanging-wall offset and the long-tailed far-field deformation induced by the steeply inclined orebody. For the 19 tabulated observation–prediction pairs, root-mean-square error decreased from 0.088 to 0.021 m (approximately 76.2%), R 2 increased from 0.130 to 0.951, and the absolute peak-location error on the 20 m grid decreased from 40 to 20 m.