An Extension of the InSAR-Based Probability Integral Method and Its Application for Predicting 3-D Mining-Induced Displacements Under Different Extraction Conditions

Underground extraction can be roughly classified into three types, i.e., subcritical, critical, and supercritical extraction, in accordance with the geological conditions in the overburden and the geometry of mined-out areas. In 2016, we proposed an approach based on the interferometric synthetic aperture radar (InSAR) technique and the probability integral method (PIM) for the cost-effective prediction of 3-D mining-induced displacements (abbreviated as InSAR-PIM). Due to the inherent assumption of critical extraction in the PIM, the InSAR-PIM method performs well in predicting the 3-D displacements caused by critical and/or supercritical extraction, but poorly for subcritical extraction. In this paper, we first propose a generalized PIM (GPIM) by modifying the traditional PIM with a simplified Boltzmann function. We then replace the PIM of the InSAR-PIM with the proposed GPIM to develop an extension of InSAR-PIM (referred as to InSAR-GPIM). The InSAR-GPIM was tested in the Qianyingzi coal mining area, China. The results show that the InSAR-GPIM-predicted horizontal and vertical displacements caused by subcritical, critical, and supercritical extraction agree well with the in situ observations, with average root-mean-square errors of about 0.032 and 0.050 m, respectively. These accuracies represent improvements of 60.9% and 59% when compared with the accuracies predicted by the InSAR-PIM in the horizontal and vertical directions. The results indicate that the InSAR-GPIM is capable of accurately predicting 3-D mining-induced displacements under different extraction conditions (i.e., subcritical, critical, and supercritical extraction), and it performs much better than the InSAR-PIM in the case of subcritical extraction. It is therefore believed that InSAR-GPIM will have a wider scope of applications than the previous InSAR-PIM.