A model for calculating subgrade settlement over shallow old longwall goafs

This study addresses the calculation of subgrade settlement over shallow, old longwall goafs under traffic loads. Based on the spatial distribution characteristics of the additional stress field, the total settlement is first decoupled into four components: the subgrade settlement and foundation settlement directly induced by traffic loads, and the residual settlement and reactivated settlement specific to the old goaf. Subsequently, a comprehensive model for calculating the total subgrade settlement is developed by integrating the probability integration method, elasticity theory, and the layerwise summation method under a “component-based calculation and dynamic superposition” framework. The results indicate that the total subgrade settlement over shallow old longwall goafs consists of four components: subgrade settlement, foundation settlement, goaf residual settlement, and goaf reactivation settlement; neglecting traffic-load-induced subgrade settlement, foundation settlement, and goaf reactivation settlement will significantly underestimate the total settlement.The proposed model can dynamically combine the relevant settlement components according to varying load levels and structural stability states. This capability quantitatively characterizes the entire settlement response process, from a “structurally stable” state to a state of “progressive reactivation.” This model addresses the limitations of conventional methods, which often homogenize the old goaf and overlook these traffic-load-induced settlements. It significantly enhances the rationality and systematic nature of the calculations, offering a novel method for evaluating and predicting subgrade settlement over abandoned goaf areas beneath highways.