Stability Analysis Model of Expressway Passing through Goaf Based on SBAS-InSAR Technology

Anhui Transport Consulting and Design Institute Co., Ltd., Hefei 230088, China School of Resources and Environmental Engineering, Hefei University of Technology, Hefei 230009, China Shaanxi Provincial Transport Planning Design and Research Institute Co. Ltd., Xi’an 710065, China School of Civil Engineering, Anhui University of Science and Technology, Huainan 232001, China Beijing Mass Transit Railway Operation Corp Ltd., Beijing 100044, China


Introduction
Construction projects above goaf deposits may lead to secondary movement and the deformation of goaf, which in turn may lead to the subsidence, local cracking, and tilting of structures at ground level. Goaf has become a major geological disaster that restricts the environment of mining area, sustainable development of the mining industry, and social economy. With the continuous expansion of mining intensity and scope, the subsidence areas around mines have become larger, thus greatly limiting the economic development of mining regions. Mining subsidence is reflected in the contradiction between the supply and demand of coal resource exploitation and economic development. At present, along with the rapid economic development in Nanjing, Hefei, and other surrounding cities, the pressure of highway construction has continued to increase. is amplifies the contradiction between soil and mines and has even led to a series of social problems. Also, troubles are often encountered during the quest to sustainably develop mining towns and resource-rich regions. If there is an expressway through the goaf and then highway subsidence and uneven subgrade subsidence, the subgrade and line may experience deformation, thus resulting in disastrous consequences. However, due to a lack of subsidence history data in goaf areas, only empirical evaluation methods can currently be used to assess stability in goaf areas. erefore, existing methods for the stability evaluation and residual subsidence prediction of goaf areas cannot meet the requirements of engineering practice. It is of great practical significance to evaluate goaf stability, which can be achieved by monitoring the subsidence of goaf.
InSAR technology combines synthetic aperture radar (SAR) and electromagnetic wave interference (EMI) technologies and is a method for the topographic survey and digital elevation inversion [1]. Since its creation, InSAR technology has been widely used for disaster warnings due to its ability to penetrate the atmosphere and obtain ground elevation and deformation information in all weather conditions and at any time of day. Besides, it possesses a deformation measurement accuracy up to the millimetre level [2,3]. Ye et al. [4] applied InSAR technology to landslide monitoring in the ree Gorges reservoir area to obtain deformation rate field. e Sentinel-1 SAR data were used by Dai et al. [5] for postdisaster assessment of the Xinmo landslide in Maoxian County, Sichuan Province in 2017. is confirmed the applicability of space-borne InSAR technology under complex weather and topographic conditions in mountainous areas. Based on the improved SBAS-InSAR technology, Wang et al. [6] established a local incident angle model that analysed the invalid areas of InSAR results.
is enabled them to determine the deformation rate of landslides and plot a distribution map of potential landslides. Besides, Li et al. [7] correlated landslide deformation with groundwater level and precipitation intensity, based on various InSAR data in Yizi village, Jin Shajiang. Xue and Lv [8] applied the unscented Kalman filter method and Sentinel-1 SAR data to predict landslide deformation in Maoxian County, Sichuan Province, China. Results indicated that the combined time series InSAR technology and unscented Kalman filter can be used to predict landslide deformation before large-scale landslides occur. InSAR technology also has great potential in surface deformation monitoring. Ma et al. [9] used Sentinel-1, COSMO-SkyMed, and TerraSAR-X data to monitor multiscale subsidence in the Guangdong-Hong Kong-Macao Greater Bay Area. ey discovered that sediment consolidation is the primary cause of subsidence, while groundwater extraction and artificial building loads are the trigger factors for deformation. Farolfi et al. [10] used the global navigation satellite system (GNSS) to correct the results of PSInSAR, which was applied to the monitoring of land subsidence in Ravenna and Ferrara, Italy. Also, Rateb and Kuo [11] utilised the Sentinel-1 SAR time series interferometry, hydrology, and weather experimental data to determine the relationship between land subsidence and groundwater storage decline near Baghdad, Iraq. Huang and He [12] obtained surface deformation field and velocity field data for the Hexi area in Nanjing by using SBAS technology, which confirms that this method is effective for extracting surface subsidence data. In the Hua Tugou oilfield in Northern Tibet, Li et al. [13] acquired a time series of surface deformation by using small baseline interference pairs and carried out accurate deformation monitoring on the surface. It can be seen that InSAR technology has already been widely used in surface subsidence monitoring, indicating that it also has strong practicability and generalization for surface subsidence inversion in coal mining areas.
In this study, we apply short baseline subset time series analysis technology (SBAS-InSAR) to monitor the history of goaf deformation in the Huaibei section of the Xu Huaifu Expressway. By minimising the influence of coherence removal and elevation error, we can obtain accurate data of goaf deformation and provide a basis for the stability assessment of goaf.

Project Overview and Field Investigation
e Xuzhou to Fuyang highway, which is about 215 km long, has helped to realise more convenient transportation between Anhui province and Jiangsu province and has enhanced the highway network in the region. e research area is located in the Huaibei section of Xu Huaifu Expressway. A diagram of the Huaibei section of the Xu Huaifu Expressway is shown in Figure 1. Huaibei City, Anhui Province, is one of the top ten coal bases in China, and coal mining has helped the urban economy to develop rapidly over the years. However, after long-term natural compaction of the underground goaf formed after coal mining, the separation layer and cracks in the rock mass are still under compaction, and the subsidence of goaf has continued to occur for a long time.

Investigation of Goaf Status.
ere are numerous mining areas along the Huaibei section of the Xu Huaifu Expressway. According to the field investigation, the Liuqiao 1 and Liudong mines, at a mileage of K48 + 000-K50 + 000, may influence the route stability. Goaf formations at Liuqiao 1 and Liudong mines affecting the route are labelled C1-C5 and the plane position diagram of expressway route and goaf is shown in Figure 2. Zone C1 is located to the west of the route. e surface of Zone C1 displays obvious mining subsidence, and serious cracks have formed on the surface. As Figure 3(a) illustrates, a subsidence basin has formed on the surface and a pond has appeared. e walls of the surrounding houses have cracked, and when the subsidence basin is formed, the surface tilted, the nearby village has been relocated, and the vegetation consists of mainly small plants.
Zone According to the field investigation, there is an obvious surface collapse in Zone C2, and whole block subsidence has occurred in the C3 area near the provincial highway, as shown in  erefore, the goaf mining time is between 4 and 12 years, meaning that a majority of the goaf formation time is more than five years. e coal mine belongs to a state-owned coal mining company, thus the coal seam recovery rate of the working face is higher and the collapse zone and fault zone are sufficiently developed. Compared with similar goaf sites and according to relevant experience, an empirical value of surface movement duration is shown in Figure 5(a), and we estimate that goaf subsidence has reached 80-90%. Because the active period of goaf subsidence has ended and it is now in the degeneration stage, the qualitative estimate of residual subsidence is smaller. However, due to the large buried depth of goaf and the long duration of surface deformation, residual deformation will continue for a long time in the future. erefore, the deformation is occurring slowly and the possibility of large-scale subsidence is small. Similarly, in the No. 10 coal seams in the Liudong coal mine, which is mined between 2007 and 2016 but most intensively towards the year 2016, the mining completion time is shorter, but the coal seam depth is shallower. According to a field investigation and visit, it is presumed that 80-90% of goaf subsidence has already occurred and that the active period of goaf subsidence has ended. Based on data collection and combined with the subsidence coefficient of remaining mobile deformation, we constructed a contour map of current mining and residual subsidence, as displayed in Figure 5(b).
In summary, the active stage of surface deformation caused by goaf in the main coal seams has ended. e goaf in the shallow coal seams (mining depth <400 m) is fundamentally stable, while the goaf that appears in the deep coal seams is in a declining subsidence period with little residual subsidence. However, the residual deformation in Zone C2 will continue for a certain period. Because part of the Huaibei section of the Xu Huaifu Expressway is planned to pass over the mining face, we must investigate the subsidence of the goaf to determine its stability and prevent the occurrence of potential risks.

Time Sequence Analysis of Surface Subsidence
In this study, using the latest interferometric synthetic aperture radar time series analysis method (SBAS-InSAR) and based on recent Sentinel-1 satellite SAR images from the European Space Agency, we monitored goaf deformation in the main areas surrounding the Huaibei section of the Xu Huaifu Expressway. is provided enough data to support the subsequent analysis of deformation genesis. e core concept of SBAS-InSAR is to network all images according to their time and space baselines. If the interference pairs of small baselines can be connected into a strongly connected graph, the deformation time series can be estimated by using phase changes and the least-squares method. e temporal deformation series of the surface can be obtained while DInSAR processing can reduce the influence of decorrelation and errors of elevation and atmosphere.
e deformation extraction process of SBAS-InSAR technology is shown in Figure 6 and includes the following steps: (1) generate connection diagrams, register the input Sentinel-1 data single view complex images, conduct interference pair combination with the set time and space baselines as thresholds, and carry out differential interference processing for each group of image pairs; (2) use ENVI SARscape radar interference processing software to complete the generated interference figure, interferogram deflattening effect, adaptive filtering, and phase unwrapping operation steps. Each interferogram operation generates interference results and unwrapping images to realize a preliminary understanding of the deformation of the study area. At the same time, transform the differential interferogram from a SAR coordinate system to a geographic coordinate system to confirm the location of suspicious deformation points. (3) Access to Variables: remove phase changes due to noise, atmospheric error, ground effect, and other factors to preserve only the deformation phase. After analysing geometrical relationships, perform a conversion on the variables to obtain the average annual figure for the deformation rate of the entire area. en, convert the annual average deformation rate grid file to vector points in the software to acquire the deformation rate and history of each vector point.
To accurately evaluate the stability of the study area, we extracted four consecutive years of deformation subsidence data from June 2017 to June 2021, which route station at K46 + 000 to K52 + 000. e SAR image data of goaf in the Huaibei section of the Xu Huaifu Expressway were preprocessed to obtain an interferogram of the study area, as shown in Figure 7. ere are differences between satellite remote sensing images in summer and winter of a year. rough the coherence analysis of satellite images in the project area, the image coherence is continuous. erefore, it can be seen that the settlement images of the study area are small in summer and winter.

Time Sequence Analysis of the Subsidence Risk Area
To facilitate analysis, the form variables of the obtained deformation map are accumulated to create a surface subsidence change map from June 2017 to June 2021, as shown in Figure 8. In the figure, the areas outlined in red designate zones with large subsidence deformation, while the blueoutlined areas show locations with smaller subsidence deformation. Figure 8 illustrates that the accumulative total goaf subsidence over the four years has generally been stable.
Considering the extent of subsidence, subsidence range, and influence on the route, the subsidence risk of the Y1-05 and Y1-09 areas is relatively high. Significantly, a traditional theoretical analysis did not locate the potential risk point of the Y1-05 area, and the stability judgement of this area is crucial for the selection of the route. According to the document "Technical Rules for the Design and Construction of Goaf Highways", the subsidence rate stability threshold at a goaf site is 60 mm/a. e maximum subsidence rate of Y1-05 is 54.7 mm/a-58.8 mm/a, while the subsidence rate at Y1-09 is 50.7 mm/a-54.8 mm/a. Based on the above data, our analysis will focus specifically on the Y1-05 and Y1-09 areas.

Time Sequence Analysis of the Deformation Area at Y1-05.
e closest distance between the Y1-05 area and the east side of route station at K46 to K47 of the expressway is about 273 m. e area Y1-05 is close to the east side of Da Miaogou Village, and its subsidence centre is located at the midpoint between Zhangdian Village and Da Lianglou Village, with a shape variable over 200 mm, as shown in Figure 9. e Y1-05 area is a potential risk point. To study the deformation trend of the entire area, eight monitoring points are selected to assess subsidence in the form of a "cross" distribution in the Y1-05 area. e distribution of the monitoring points and their deformation rates are presented in Figure 10. e subsidence at Points 1 and 2 are the most serious, and the subsidence at these points accelerated from August 2018. e subsidence at Point 1 slowed down in June 2020, exhibiting total subsidence of 191 mm from June 2017 to June 2021. e subsidence at Point 2 started to decelerate in December 2020, and there is no increase in subsidence at either point from the end of 2020. e subsidence at the outermost monitoring points (Points 5 and 8) is the smallest, and the other monitoring points present a similar trend, respectively experiencing the stage of acceleration-gentle-acceleration-gentle. e subsidence of all of the monitoring points tended to be stable in the final halfyear since December 2020. It can be seen that the centre of the Y1-05 sedimentation basin is located around Point 1 and Point 2 and gradually radiates outward in a funnel shape. e accumulated subsidence value at Point 1 is the greatest, but the subsidence in the past year is approximately 25 mm, and only about 10 mm in the most recent six months. In contrast, the subsidence at Point 2 reached 30 mm in the second half of 2020, which is at the threshold of Mathematical Problems in Engineering goaf stability evaluation. erefore, further analysis is still required to assess the overall stability of the area.

Time Sequence Analysis of the Deformation Area at Y1-09.
e Y1-09 deformation area is located to the west of the route station at K49 + 200 to K50 + 100, and the nearest distance to the centre line is 205 m. ere is discernible subsidence in the core of the area. According to the goaf distribution map, Y1-09 is situated in the C2 zone, which is consistent with the predictions of field investigations and theoretical analysis. Figure 11 shows the Y1-09 area subsidence distribution diagram.
By extracting the data from eight monitoring points in the Y1-09 deformation area for time-sequence analysis, we find that the subsidence at Points 6 and 8 is the smallest. Points    Mathematical Problems in Engineering points with similar subsidence are connected, it forms an obvious funnel shape with Point 3 at the core. In the past year, the subsidence rate at all monitoring points has become more stable. At Point 3, the subsidence is only 18 mm in the year from June 2020 to June 2021, and no obvious subsidence is observed at any other point from December 2020, indicating that this area is generally stable. Monitoring of subsidence in the Y1-09 area is shown in Figure 12.

Deformation Characteristics of the Subsidence Risk Area
To judge whether the study area may have an impact on the planned route, we conducted subsidence basin characteristic analysis and subsidence fitting of the study area according to the subsidence monitoring data, to predict potential subsidence.

Distribution Characteristics of the Subsidence Basin.
e subsidence observation lines are arranged in the middle of the Y1-05 and Y1-09 areas, and the bearing of the observation lines is perpendicular to the direction of the route. e study area runs from left to right with the subsidence centre as the midpoint.
As Figure 13 illustrates, the subsidence curve shows symmetrical distribution with the subsidence core as the symmetry point and it presents an inverted "convex" shape overall.
e subsidence curve can be divided into the accelerated subsidence zone, stable subsidence zone, and undisturbed zone from the centre to either side. As the distance from the subsidence centre grows, the subsidence decreases in a nonlinear manner. Figure 13(a) shows that from June 2017 to June 2018, a point 300 m away from the centre in the Y1-05 can be classified as the stable subsidence area. e subsidence boundary radius is 700 m-800 m, and the subsidence centre is about 1 km away from the centre line of the route. erefore, the subsidence basin will have little influence on the road. Over time, the Y1-05 basin has shown a trend of decreasing subsidence after initial growth in every year. e squat of all points of the Y1-05 area observation lines reaches a maximum between June 2018 and June 2019, and the maximum subsidence point is offset to the left. e zones of accelerated subsidence and stable subsidence increased accordingly, and the range of accelerated subsidence zone approaches 800 m away from the centre of subsidence. Since June 2019, the subsidence of each point in the observation line has gradually reduced, resulting in minimal subsidence in the past year. Although the Y1-05 subsidence area is not exhibiting accelerated subsidence, it is still slowly sinking, and the subsidence basin is experiencing gradient-type development. Figure 13(b) reveals that the Y1-09 subsidence basin is similar in shape to Y1-05. Subsidence has reduced year by year, and the rate of subsidence has displayed a decreasing trend; particularly, since June 2019, the subsidence curve has displayed a similar pattern over the last two years. And from June 2020 to June 2021, according to the subsidence curve, the stable subsidence area is significantly greater than from June 2019 to June 2020. is confirms that subsidence has entered a stage of stability, and because the expressway is about 500 m away from the subsidence centre, the subsidence basin will have a negligible influence on the route.

Residual Subsidence Risk Area Fitting Prediction.
Residual subsidence is also an important index that evaluates the stability of goaf. Combined with an analysis of the subsidence time sequence, the residual subsidence in the Y1-05 and Y1-09 areas can be determined. Based on the centre point data of the Y1-05 and Y1-09 areas from June 2017 to June 2021, the subsidence amount can be fitted: As Figure 14 illustrates, the similarity of the fitted curves is above 0.98 and the fitting results are very close to the measured values. Besides, the centre point subsidence of the two areas shows negative exponential attenuation. e Y1-05 area central subsidence amount is expected to be 720 mm, and the current subsidence is 245 mm. Over the next 15 years, the residual subsidence in the centre point of the Y1-05 area is predicted to be 475 mm, with annual average subsidence of 31.67 mm.
is confirms that the field is stable, although the Y1-05 area subsidence basin has a trend of subsidence with no subsidence mutation, it still needs stronger monitoring. e subsidence of centre point in the Y1-09 area is 340 mm, and the total remaining subsidence is only 50 mm. From Figure 14, it is obvious that the subsidence rate of the Y1-09 area has entered a stable stage and the residual subsidence will have a negligible influence on the expressway.

Prediction of Subsidence Risk Area Site Expansion.
In order to further evaluate the subsidence development range of the risk area sites, according to the shape of the subsidence basin, the model function is used to fit the shape of the subsidence basin in the Y1-05 area and Y1-09 area respectively. ere are four unknown numbers, namely, b 0 , A, x 0 , and w, where A determines the extreme value of function, x 0 determines the symmetry axis of the function, w 1 determines the opening amplitude of the function, and b 0 is the fine adjustment of the value of the function. e fitting results are shown in Figure 15 and Table 1.
From Table 1, we can see that the correlation coefficients of the fitting results are above 0.95, which indicates that the y � b 0 + A * exp(−0.5 * ((x − x 0 )/w) 2 ) function model can describe the shape of the subsidence basin well.
erefore, this function model, combined with the predicted value of central point subsidence, can predict the development of future subsidence basins.

Mathematical Problems in Engineering
Taking the Y1-05 area as an example to illustrate the solution process, it is assumed that the shape function of the subsidence basin within the next 15 years is y � b 1 + A 1 * exp(−0.5 * ((x − x 1 )/w 1 ) 2 ). As mentioned before, the basin has a significant range of accelerated subsidence, stable subsidence, and undisturbed areas. e subsidence basin in the Y1-05 area is sinking slowly, and the symmetry axis of the subsidence basin and the range of accelerated subsidence approaches a fixed value after June 2019. As shown in Figure 15(a), the subsidence slope is close to a  constant in the stable subsidence area of the subsidence basin, and the slope of the stable subsidence area in different years is approximately parallel. erefore, it can be assumed that the symmetry axis of the future subsidence basin and range of the accelerated subsidence area will remain unchanged, and the subsidence rate of the stable subsidence area will be close to a constant. Combined with the above fitting equation, we let the symmetry axis of the Y1-05 area subsidence basin x 0 is −30, and the following relationship is obtained: where x 0 is the position of the symmetrical axis of the subsidence basin, c 1 is the subsidence rate of the stable subsidence area at the left of the subsidence basin, c 2 is the subsidence rate of the stable subsidence area at the right of the subsidence basin, and y 1 is the predicted value of the subsidence central point within the next 15 years. Similarly, the shape function of the subsidence basin within the next 15 years in the Y1-09 area can be obtained. e shape functions of the subsidence basin in the Y1-05 area and Y1-09 area within the next 15 years, respectively, are as follows: e prediction of development subsidence basin in Y1-05 area and Y1-09 area is shown in Figure 16. e stable   subsidence area of the subsidence basin will be extended within the next 15 years. e most dangerous of these is the Y1-05 area, whose subsidence basin extends 100 metres from the edge of the line, despite the subsidence not affecting the stability of the route. However, in order to ensure the safety of the route and prevent uneven subsidence of the subsidence basin, which may lead to pavement tension shear failure in this section of the route, and it can be treated with flexible reinforced mesh.

Conclusion
(1) e SBAS-InSAR technology is utilised to rapidly obtain the ground surface subsidence of the goaf site in the Huaibei section of the Xu Huaifu Expressway from June 2017 to June 2021. Afterwards, the subsidence situation of the goaf site is accurately analysed, solving the problem of lacking historical data on surface subsidence in expressway route selection. (2) ere is still residual subsidence on the surface, even after underground mining has ceased in the Huaibei section of the Xu Huaifu Expressway. Using SBAS-InSAR technology, we find that Y1-05 and Y1-09 are two areas with high subsidence risk. e Y1-05 area is a potential risk point, while the settlement of Y1-09 area is affected by goaf. (3) e prediction of the subsidence boundary radius of the Y1-05 area is between 300 m and 350 m, and the residual subsidence is expected to be 475 mm, highlighting the need to strengthen monitoring. e residual subsidence of the Y1-09 area is 50 mm and has entered a gentle stage. (4) Based on the subsidence value of the centre subsidence point, the development trend of subsidence basin within the next 15 years is predicted. e shape function of subsidence basin is highly consistent with the subsidence data of the subsidence basin, which provides strong support for the prediction of the subsidence development of the subsidence basin.
Data Availability e datasets used in the experiments and discussed in the paper are available from the corresponding author on reasonable request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.