Monitoring and predicting mining area subsidence caused by coal mining help effectively control geological disasters. Information regarding small surface deformations can be obtained using a differential interferometric synthetic aperture radar (D-InSAR), which exhibits high monitoring accuracy and can cover large areas; thus, D-InSAR are being applied for mining area settlement monitoring. However, mining areas are prone to large gradient deformations in short durations; obtaining information regarding such deformations is outside the scope of D-InSAR monitoring. To adapt to the characteristics of D-InSAR monitoring, this study selected a Boltzmann function model with a slow boundary convergence rate to address the problem of probabilistic integration methods exhibiting a high boundary convergence rate. The three-dimensional surface deformation of the mining area can be accurately obtained. According to the projection relationship between D-InSAR line of sight (LOS) directional deformation, subsidence, and horizontal movement, a D-InSAR monitoring equation for mining subsidence assisted by Boltzmann is derived. This equation is combined with the shuffled frog leaping algorithm (SFLA) to obtain the parameters to be estimated from the equation. The D-InSAR LOS deformation information of the 13121 working face in the Huainan mining area was obtained from July 14 to October 30, 2019. The proposed method was then used to obtain the predicted parameters of the working face under insufficient mining. The predicted parameters of mining subsidence were calculated to obtain the predicted parameters when it was fully mined. Then, the revised parameters were used to predict the subsidence and horizontal movement of the mining area and compared with the actual leveling observations. The results show that the mean square error of predicted subsidence is 97.1 mm, which is about 3.09% of the maximum subsidence value; the mean square error of predicted horizontal movement is 46.1 mm, which is about 4.1% of the maximum horizontal movement value. The predicted results of the aforementioned method were used to analyze the damage to the buildings above the working face and determine the damage level of the buildings to provide a reference for the demolition and maintenance of the Zhaimiao village.

The mining subsidence in mining area could cause large-gradient deformation in a short period of time. When the deformation gradient exceeds the threshold value of the Differential Interferometry Synthetic Aperture Radar (D-InSAR) technology monitoring gradient, D-InSAR technology is likely to cause the failure of InSAR phase unwrapping algorithm. At this time, the InSAR technology is unable to monitor the 3D surface deformation. Aiming at these problems, an dynamic probability integral method (DPIM)-based InSAR phase unwrapping model and a method of extracting 3D surface deformation were proposed. The phase unwrapping model firstly used the empirical parameters of the probability integral of the mining face to predict the line of sight (LOS) direction deformation phase of the mining subsidence surface. Secondly, the phase of differential interferogram was unwrapped with the assist of the predicted LOS deformation phase under the constraint of DPIM, and the true LOS deformation phase was obtained, then the true LOS deformation phase transformed into LOS deformation. Finally, according to the geometric projection relationship between the LOS deformation and 3D deformation of mining subsidence surface, the probability integral prior model was brought into the equation of the geometric projection relationship. On the basis of relevant boundary conditions, the 3D surface deformation was extracted from the LOS direction deformation field of mining subsidence. The feasibility of the method was verified by the simulation experiment results. The differential interferogram of the subsidence basin was obtained by the differential interference processing of image data of Sentinel-1A on Nov. 16, 2017 and Dec. 10, 2017 of 1613 working face of Guqiao South Mine. By using the DPIM-based phase unwrapping model, the phase of differential interferogram was unwrapped and the 3D surface deformation during this period as well as the deformation extraction method were developed. The results showed that the maximum fitting error value of subsidence was 79 mm, about 8.33% of the maximum value of subsidence, and the fitting error of mean square of subsidence was ±33.5 mm. The results showed that the DPIM-based phase unwrapping model and the method of extracting 3D surface deformation proposed in this paper have certain engineering application values.

After underground coal resources are mined out in mining areas, large-gradient deformation is prone to occur on the ground surface during a short period of time. When the deformation gradient exceeds the threshold value of the gradient monitored by the D-InSAR (Differential Interferometry Synthetic Aperture Radar) technology, the conventional D-InSAR technology is likely to cause the failure of InSAR (Interferometry Synthetic Aperture Radar) phase unwrapping algorithms. In this case, neither the conventional D-InSAR technology nor the method of prior model + InSAR can obtain the 3D (three-dimensional) deformation field of mining-induced subsidence. Aiming at these problems, a method of monitoring 3D deformation of mining subsidence with large gradient was developed in this paper, which combines the improved dynamic prediction model and a single pair of D-InSAR. The probability integral method was firstly improved, and its problem of fast convergence at the edge of the subsidence basin was solved. Secondly, according to the geometric projection relationship between the LOS (Light Of Sight) deformation of D-InSAR in the mining area and the 3D surface deformation, the observation condition equation of the mining subsidence monitored by D-InSAR based on the improved dynamic model of PIM (Probability Integral Method) was established. Then, the solving model of prediction parameters of the improved dynamic model of PIM was constructed according to the GA (Genetic Algorithm) theory. Finally, based on the LOS deformation obtained by D-InSAR technology, the 3D deformation of mining subsidence is obtained by the 3D deformation predicting method proposed in this paper. The feasibility of the method was verified by the simulation experiment results. The LOS deformation at the edge of the subsidence basin was obtained by the differential interference processing of data from two images of Sentinel-1A on 16 November 2017 and 10 December 2017 of 1613 working face of Guqiao South Mine. The 3D deformation of the surface in the mining area during this period were obtained by using the method proposed in this paper. The predicted subsidence value was compared with the measured surface subsidence value. The result is as follow: the maximum error value of subsidence was 60 mm, about 9.1% of the maximum value of subsidence, and the fitting error of mean square of subsidence was ± 26.21 mm. The results show that the predicting 3D deformation method of D-InSAR for large gradient of mining subsidence based on constraints of improved dynamic prediction model proposed in this paper has certain engineering application values.