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The residual deformation of a goaf is studied to improve the foundation stability assessment for metro lines passing through the subsidence area of steeply inclined extra-thick coal seams. The variable mining influence propagation angle is introduced to describe the special form of the rock movement. Based on the modified parameters in the traditional probability integral model, a subsidence prediction model is established. Then, based on the idea of an equivalent mining thickness, Kelvin model is introduced to analyze the creep characteristics of the old goaf, and the dynamic prediction function of the residual subsidence is constructed to realize the dynamic analysis of the residual deformation. Moreover, a case study is used to evaluate the predictive effectiveness of the prediction model, and the results are compared with the monitoring data and numerical simulation results. The results show that the values with a relative error between the predicted value and measured value are in the range of ±7%, indicating that the prediction model based on the mining influence propagation angle is feasible. Thus, the residual deformation prediction model based on the mining influence propagation angle is considered to be suitable for predicting the subsidence of engineering projects crossing a goaf.

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