A New Residual Subsidence Prediction Method of Short Working Face Goaf for Safety Construction of Urban Viaduct

The planned viaduct in Jining, Shandong is a priority project in the city, but the 63 working face of a mine in Jining is only 3m away from the planned viaduct, which poses the serios threat to safety construction of the viaduct. Therefore, it is necessary to evaluate the stability of the planned viaduct goaf area under the in�uence of 63 working face. However, the 63 working face is a short face, and the corresponding prediction of surface residual subsidence is lacking. For this purpose, the theoretical analysis and numerical simulation were employed in this paper to reveal the foundation deformation mechanism and characteristics of fractured rock and soil mass of short goaf. It was concluded that the main source of residual subsidence was the stripping and yield softening of the coal wall on both sides of short goaf. Then, the residual subsidence prediction method of short goaf was proposed for viaduct mined-out area. The new method was applied to the planned viaduct of Jining, and the effectiveness of the method was proved by InSAR and leveling monitoring results. The research results provided the technical support for viaduct construction under the in�uence of underground mining.


Introduction
The long-periodic large-scale coal mining has guaranteed the global energy security, which also formed large tracts of goaf subsidence areas.Although the coal mine goaf and the fractured rock mass above the goaf are in a relatively balanced state after a long period of natural compaction, cracks, separation layers and cavities still exist in the overburden rock of the goaf.Under the action of various internal and external loads (building load, vibration load, seismic force, groundwater, etc.), the relative balance state of the overburden rock will be broken again, causing the secondary settlement of the surface, which calls the "activation" of old goaf (Han et  Shandong Jining is a typical coal resource-based city, there are many coal mines and mined-outed areas, resulting in urban infrastructure inevitably through the goaf.For example, Jining city 2021 priority project-north extension viaduct, the straight distance from mine 63 working face goaf to the planned viaduct is only 3m, which poses a serios threat to the safety construction of the viaduct.Therefore, it is necessary to evaluate the stability of the mined-out area of planned viaduct.The prediction of surface residual deformation is the key for evaluating the stability of mined-out area. At present, the commonly used surface residual deformation prediction models for goaf sites are mainly divided into two categories: one is using the probability integral prediction method based on the limit thought to establish the surface residual deformation prediction model, which is the most commonly used method in engineering at present (Li et  samples, which assumes that there must be some functional relationship between the time series of surface residual subsidence of the goaf, and then establishes the corresponding prediction model (Guo et al. 2021;Du et al. 2020;Hamdi et al. 2018).The existing research around the prediction method of surface residual deformation is mainly aimed at the goaf of conventional longwall working face (face length ≥ 60m).The prediction method of surface residual deformation of conventional longwall goaf site facing different geological and mining conditions has been established and incorporated into the corresponding industry speci cations, which has basically solved the problem of surface residual deformation prediction of the conventional longwall goaf site.
The working width of 63 mined-out area near planned viaduct is 45m.However, the prediction method of residual surface deformation of short mined-out area (25m ≤ face length ≤ 50m) has not been established, resulting in a lack of scienti c basis for stability evaluation of short working face goaf.A relatively stable secondary structure system existing in the form of natural balanced arch may be formed in the overburden rock of the short working face goaf, which is signi cantly different from the overburden rock structure of the goaf of the conventional long wall working face, thus causing a large difference in the residual deformation of the ground surface between the short working face and the conventional long wall working face (Chen et Yin et al. 2022).In general, the migration mechanism and characteristics of overburden rock of short working face goaf are not clear, and there is also a lack of corresponding prediction methods for residual surface deformation.
Therefore, the deformation mechanism and characteristics of the fractured rock soil foundation of short working face goaf were studied and analyzed by combining the method of theoretical analysis and numerical simulation.Then, the prediction method of surface residual deformation of short working face goaf was proposed, which takes into account the yield and stripping of coal walls on both sides of goaf.The research results provided the technical support for viaduct construction under the in uence of underground mining.

Engineering Background and Overview
The planned north extension viaduct is the priority project of Jining, Shandong, which has great signi cance for urban development, as shown in Fig. 1.The grade of viaduct is urban main road, two-way 6 lanes, and design speed 60km/h and the load level was BZZ-100 standard vehicle.The viaduct used simply supported beam structure.
However, the 63 working face of a mine is only 3m away from the planned north extension viaduct.The 63 working face was mined from April 17 to May 13, 2021.The mining width of 63 short working face is 45m and the advance length is 260m; The upper coal seam 3 of Shanxi Formation is mined with an average mining thickness of 2.47m, an average mining depth of 462m and an average dip angle of 3°.
Inclined short mining and full caving method are adopted to manage the working face roof.The elevated road is on the east side of the short working face as shown in Fig. 2.
The mining of 63 working face can cause surface movement and deformation, which poses the serious threat for viaduct safety construction.In order to ensure the viaduct safety construction, it is necessary to scienti cally analyze the stability of mined-out area of the planned north extension viaduct.The prediction of surface residual deformation is the key for evaluating the stability of mined-out area.However, the foundation deformation mechanism of fractured rock and soil mass in the goaf of short working face is still unclear and the corresponding prediction method of surface residual subsidence is lacking, leading the lack of basis for the stability evaluation of short goaf.

Deformation mechanism and characteristics of fractured rock soil foundation of short goaf
The deformation mechanism and characteristics of the fractured rock and soil foundation in the short working face goaf are the basis for establishing the prediction method of its surface residual deformation.As the deformation mechanism of the broken rock and soil foundation in the short working face goaf is not clear at present, this section mainly uses the method of combining numerical simulation and theoretical analysis to analyze the deformation mechanism and characteristics of the broken rock and soil foundation in the short working face goaf.

Establishment of numerical model
The numerical model based on the geological and mining conditions of the working face is established after simplifying the stratum information with the drilling data of a short working face in Shandong and using FLAC®3D to reconstruct terrain.The average mining thickness of the coal seam is 2.47m, and the average mining depth is 462m, which is a nearly horizontal coal seam.The model size is 1500m × 650m × 486m, the length and width of each unit are xed as 10 meters, and the height varies with the rock stratum.There are 253500 units in total in this model.The left and right boundaries of the model are xed with x-direction displacement, the front and rear sides are xed with y-direction displacement, the lower boundary is xed with z-direction displacement, and the upper boundary is a free boundary.The numerical model is shown in Fig. 3.The model parameters are determined according to the indoor experimental results.
The distribution and simulation mechanical parameters of each rock stratum in the mining area are shown in Table 1.
There are 12 kinds of geotechnical constitutive models built in FLAC®3D, including an empty model, 3 elastic models and 8 plastic models.Rock and soil are closer to plastic body rather than ideally elastic.Among plastic models, the Moore Coulomb model is the most common constitutive model of geotechnical material, which has the advantages of few criteria parameters, easy access, etc.It can simulate the strength of rock and land better, and is widely used in the simulation of rock strata movement in mining (Shi et  The face length of the short working face in the model is 50m, and the strike length is 270m.On the corresponding model, 615-885m in the x direction and 300-350m in the y direction are taken, and the corresponding cells are excavated.Figure 4 shows the relative position relationship between the goaf and the ground viaduct after the excavation of the short goaf.

Stress distribution and surface subsidence characteristics of overburden strata in short working face mining
(1) Stress distribution characteristics of overburden strata in short working face goaf According to the numerical simulation results, the stress distribution cloud diagram of the inclination main section in the short working face is obtained through data processing as shown in Fig. 5.According to the theoretical analysis and Fig. 5, the tensile stress borne by the rock mass above the caving mining face is greater than the maximum tensile strength of the rock mass, which leads to the rock fracture and collapse, then forming a caving zone during the mining of short working face.A stable arch shell structure is formed between the rock stratum above the solid coal on both sides of the goaf and the main structural rock stratum above the collapse zone, namely, the stress balanced arch.Due to the unloading and transfer of overburden stress above the short type goaf, the load of the upper rock stratum is transferred to the solid coal on both sides through the stress balanced arch, and the stress concentration phenomenon occurs.The maximum vertical stress of the solid coal on both sides reaches 9.29MPa.
In order to further analyze the change characteristics of the internal stress of the main section rock stratum after the short face mining, 24 stress monitoring points are arranged at different heights above the goaf, above the goaf boundary and above the solid coal 40m from the goaf boundary respectively.Through processing the simulation results, the stress distribution curve in the main section rock stratum after the short working face mining is obtained as shown in Fig. 6.It can be seen from the gure that the overall stress above the goaf shows a trend of increasing rst and then decreasing, while the stress above the goaf boundary and above the solid coal continuously decreases with the upward direction of the rock stratum; At a height of about 140m from the coal seam, the internal stress of the rock stratum is basically equal, decreases with the increase of the height of the rock stratum, and is consistent at the same height.
Figure 5 and Fig. 6 show that a stable arch shell structure can be formed above the goaf after the short working face is mined.The development height of the stress balanced arch is limited, which is less than the thickness of the overlying bedrock.At the same time, the rock stratum above the coal seam height of 140m is mainly slightly bent and deformed, leading to small ground subsidence.
In the literature (Jiang et al. 2016), the overburden is divided into "immediate loading zone", "time-delay loading zone" and "static loading zone" according to the in uence of rock strata on the surrounding stress.Because of the relatively short length of the working face, the stress structure of overburden in this paper degenerates into a two-band structure of "instant loading zone + static loading zone", so the position of the stress arch should be consistent with the height of the instant loading zone.The calculation formula in this reference is listed: Where h is the mining height and H is the height of the immediate loading zone.
According to the above formula, the position of stress arch should be 25m above the coal seam, which is more consistent with the results of numerical simulation (about 30m).
(2) Surface deformation characteristics above goaf of short working face The key to establish the prediction method is to analyze the surface deformation characteristics above the goaf of short working face.In order to analyze the surface deformation characteristics of short working face mining, this paper processed the simulation results, extracted the surface subsidence value along the strike main section, and drew the surface subsidence curve of the strike main section as shown in Fig. 7.
The position of the maximum surface subsidence value after the mining of the short working face is directly above the center of the goaf as shown in Fig. 5.The subsidence value gradually decreases from the center of the subsidence basin to the edge until 0 mm when the position reaches the boundary of the basin.Meanwhile, the surface movement and deformation are continuous and gentle, which conforms to the surface subsidence prediction model using the probability integral method.
3.3 Features of overburden failure and surface subsidence after coal wall stripping on both sides of goaf in short working face Under the high stress, long-term groundwater and weathering, the coal walls on both sides of the short goaf may be stripped and yield softened, which will lead to progressive destruction of the coal pillar.Considering that the coal walls on both sides of the goaf are stripped along with the stopping mining time, it is assumed that the maximum yield and stripping width of the coal walls on both sides of the short working face is 7m.Therefore, the above established model will be further excavated for 7m along both sides of the coal wall to study the overburden stress distribution and surface subsidence characteristics after the coal wall was stripped on both sides of the short working face goaf (the most unfavorable working condition).
(1) Analysis on the distribution characteristics of overburden stress caused by coal wall stripping on both sides of goaf The stress distribution cloud diagram of the inclined main section after the stripping of the coal walls on both sides of the short working face goaf is obtained as shown in Fig. 8 after processing the simulation results.The negative sign indicates the compressive stress in the gure.It can be seen from the gure that after the stripping of coal walls on both sides of the short working face goaf, the overburden can still form a stable stress balanced arch structure.After the stripping of coal walls on both sides of the goaf, the stress arch height and arch foot width increase by 20m compared with those before stripping.
Twenty-four stress monitoring points are arranged at different heights above the goaf, above the goaf boundary and above the solid coal at 40m from the goaf boundary respectively.The stress distribution curve in the main section rock stratum after stripping of coal walls on both sides of the goaf is obtained as shown in Fig. 9 after processing the simulation results.After analyzing Fig. 9, it can be known that the changes of the internal stress of the rock stratum before and after the stripping of the coal walls on both sides of the goaf are basically the same.The stress above the goaf and the boundary of the goaf increases rst and then decreases with the increase of the height, while the stress above the solid coal on both sides of the goaf decreases continuously with the increase of the height.The maximum vertical stress the rock stratum can bear is about 9.42MPa, which is 0.12MPa higher than that before the stripping of the coal wall.
Combined with the comparative analysis of numerical simulation results before and after the coal wall yield and stripping on both sides of the short working face goaf, it can be seen that the overburden before and after the coal wall yield stripping on both sides of the short working face can form a relatively stable equilibrium arch structure, and the development height of the stress equilibrium arch is limited.
From the perspective of the distribution characteristics of overburden stress, the yield and stripping of coal walls on both sides of the goaf of the short working face have little impact on the movement of the overburden, and will not lead to signi cant "activation" of the overlying strata when the stress arch is not destabilized by seismic force, tectonic stress caused by regional geological tectonic activity, nearby mining or explosion and other external forces.
(2) Deformation characteristics of the upper surface after coal wall stripping in short working face goaf In order to analyze the surface deformation characteristics after the stripping of the coal walls on both sides in the goaf of the short working face, the surface subsidence value along the strike main section of the short working face is extracted after processing the simulation results, and the surface subsidence curve of the strike main section is made as shown in Fig. 10.
The maximum ground subsidence value after the stripping of coal walls on both sides of the short working face goaf is 214mm after analyzing Fig. 10, which is 70mm higher than that before the stripping of coal walls on both sides of the goaf, and the position of this value is located right above the center of the goaf; The subsidence value gradually decreases from the center of the subsidence basin to the edge until 0 mm when the position reaches the basin boundary.The surface movement and deformation are continuous and gentle, which conforms to the probability integral method surface subsidence prediction model.

Deformation mechanism of fractured rock soil foundation in short working face goaf
Based on the above general characteristics of short working face overburden stress distribution, surface subsidence simulation results, short working face ground pressure behavior, and overburden failure, the analysis shows that the mechanism of the overburden failure in short working face goaf and the deformation of ground foundation is as follows: (1) The damage degree and development characteristics of the overlying strata of the short working face are closely related to the length of the working face.Generally, when the length of the short working face exceeds a certain size (such as more than 25m), the roof of the goaf will break, collapse and fracture; The longer the working face is, the closer its overburden failure characteristics are to those of the longwall working face.As the length of short working face generally does not exceed 50m, the degree of overburden collapse and fracture development is not su cient; The direct and basic roof caving rock blocks are stacked in the goaf, and the upper fracture zone rock stratum is easy to form a masonry beam structure.And usually within a certain height a natural balanced arch balance system can be formed.The overburden load above the natural balanced arch structure up to the surface above the goaf is transferred to the coal pillars on both sides of the goaf through the natural balanced arch, and an obvious vertical stress rise zone is formed in the coal pillars on both sides.
(2) Under the action of high stress, long-term groundwater and weathering, the coal walls on both sides of the short working face goaf may be stripped and yield softened, resulting in the expansion of the support pressure area of the coal pillars on both sides and the collapse of the rock mass in the goaf eating into the coal pillars on both sides, which further leads to the expansion of the overburden fracture area in the goaf and the further development of the secondary structure of the natural balanced arch (increase in arch height).To some extent, the stripping and yield softening will increase the displacement and deformation of the surface above the goaf, and the law of surface movement and deformation conforms to the surface subsidence prediction model of probability integral method.
(3) Although a relatively stable natural balanced arch secondary structure system can be formed in the overlying strata of the short goaf, under the action of external forces such as seismic force, tectonic stress caused by regional geological tectonic activity, and disturbance caused by nearby mining or explosion, the overlying natural balanced arch secondary structure of the stope may become instable and delamination cracks may be compacted, resulting in the recurrence of surface subsidence.
(4) The collapse fractured rock mass in the middle of the short goaf bears a small vertical compressive stress under the protection of the natural balance arch, and the compaction effect of the vertical compressive stress on the collapse fractured rock mass in the middle of the short goaf has basically occurred during the mining process; With the extension of time, the risk of re-compaction of the middlecollapsed fault rock mass and the consequent overburden movement and deformation is low.Only when the natural balanced arch is unstable can the collapse fracture rock mass be recompacted.
To sum up, the main cause of the subsidence of the goaf ground caused by the "activation" of the old goaf in the short working face is that the stripping and yield softening of the coal walls on both sides of the goaf cause the natural balanced arch foot of the overburden to move outward and the arch height to increase, resulting in the instability of the original natural balanced arch until a new natural balanced arch is formed at a higher height, and to some extent, the movement and deformation of the surface above the goaf are increased.
Moreover, the surface movement and deformation laws before and after the coal wall yield stripping on both sides of the short working face goaf conform to the surface subsidence prediction model of probability integral method.
4 Prediction method of surface residual settlement and deformation in goaf of short working face Combined with the mechanism and characteristics of the ground deformation of the fractured rock and soil mass in goaf of the short working face, the surface movement and deformation of the goaf site of the short working face are mainly caused by the local yield and stripping effect of the solid coal pillars on both sides in the long-term high stress and groundwater erosion process, causing the instability of the natural balanced arch formed in the mining process until a new natural balanced arch is formed at a higher position.The effect further causes the increase of the surface movement and deformation of the goaf site, which is the limit value of the surface residual settlement and deformation of the short working face goaf.Therefore, the prediction value of surface movement and deformation before and after the yield and stripping of coal walls on both sides of the working face can be calculated based on the probability integral method, and the difference between the two values can be used as the maximum estimate of the residual surface deformation in the goaf of the short working face.It is worth noting that the key is how to calculate the maximum yield and stripping width of coal walls on both sides of the goaf of the short working face.
(1) Calculation method of maximum yield width of coal wall on both sides of short goaf based on Wilson strength theory Referring to A.H. Wilson strip coal pillar stability calculation method, under the action of long-term high stress, groundwater erosion and overlying rock lamination stress, yield areas appear in the coal walls on both sides of the short working face goaf.The stress zoning of the coal pillar is shown in Fig. 11.The relationship between the width of yield zone Y of coal pillars on both sides and the mining depth m and thickness H is as follows: .
(2) Calculation method of maximum yield width of coal wall on both sides of short goaf based on uni ed strength theory Under the action of overlying strata pressure, the coal pillar extrudes to the goaf on both sides and gradually yields to the interior of the coal pillar until the boundary of the elastic zone inside the coal pillar.During this process, the slip surface between the coal pillar and the rock mass is subject to the action of overburden stress and shear force, and the yield part of the coal pillar is in the state of stress limit equilibrium.Considering the stress characteristics of the coal pillar, the coal pillar is considered as an ideal elastic plastic material that is uniform, continuous and isotropic, and the stress of the coal pillar can be considered to symmetrical with respect to the neutral plane of the coal pillar.Mechanical model is shown in Fig. 12.
According to the above model, under the stress limit equilibrium state, the calculation formula for the width of the coal pillar yield zone is as follows (Nianjie et al. 1989): 1 Where, x 0 is the width of yield zone; m is the mining thickness of the coal seam; A is the coe cient of lateral pressure; is the internal friction angle between the coal seam and the top and bottom slate; C is cohesion; K is the stress concentration factor; is the average unit weight of rock stratum; H is the mining depth; P is the support resistance of support to coal wall.
(3) Calculation method of maximum stripping width of coal wall on both sides of goaf in short working face The coal pillars on both sides of the short working face may be stripped due to weathering, groundwater immersion or wall slicing in a long period of time, especially when the underground water lls the goaf after the well is shut in, so the stripping model of the coal pillars on both sides of the short working face is built as shown in Fig. 13.
Considering the most unfavorable conditions, the width of the goaf is increased by the stripping of solid coal walls on both sides of the short working face, so the calculation method of the width of the goaf after stripping is as follows (Yu et al. 2017; Yu et al 2018) : Where, b is the width of the goaf after the stripping failure of the coal pillar (m); d m is the maximum stripping depth of coal pillar (m); is the angle of repose of the accumulation body, generally 45°; k is the coe cient of crushing expansion, generally 1.1.
(4) Prediction steps of surface residual settlement and deformation in goaf of short working face To sum up, the steps to predict the extreme value of ground residual settlement and deformation in goaf of short working face are as follows: Calculate the sum of the maximum yield and stripping width of coal walls on both sides of goaf of short working face; Use the probability integral method to predict the surface movement and deformation value of short working face goaf before the yield and stripping of coal walls on both sides; Calculate the sum of the width of the short working face goaf and the maximum yield and stripping width of the coal walls on both sides of the goaf; Use the probability integral method to predict the surface movement and deformation value of the goaf after the yield and stripping of the coal walls on both sides according to the sum width in ; Get the difference between the predicted surface movement and deformation values before and after the coal wall yielding and stripping on both sides of the goaf of the short working face, which is the residual deformation of the short working face for extremely insu cient mining.Then, the prediction of the surface residual deformation of the short working face goaf is realized.
5 Example application

Prediction of surface residual deformation of 63 working face goaf
According to the measured and empirical data, the parameters of the calculation method for the maximum buckling width of the coal walls on both sides of the goaf in the short working face based on the uni ed strength theory are selected as follows: It is calculated by substituting the above parameters into formula (2) that the maximum yield width of coal walls on both sides of goaf in short face based on uni ed strength theory is 4.95m.
According to the calculation of the mining depth and thickness of the working face, the maximum yield width of the coal walls on both sides of the goaf of the short working face based on Wilson strength theory is 5.59m.
For safety reasons, the maximum yield width of coal walls on both sides of the goaf of the working face takes 5.59m if the maximum value is taken for calculation.
According to the calculation formula of stripping width of coal pillar, the stripping width of coal pillar is 1.15m.
To sum up, it is considered that the total width of the coal pillar without bearing capacity on one side is the sum of the stripping width and the yield zone width of the coal pillar, that is, 1.15m + 5.59 = 6.74m.
According to the geological and mining conditions of the goaf of the short working face, the future residual settlement and deformation of the surface in the viaduct area are calculated by using the above-mentioned prediction method for the residual settlement and deformation of the surface in the goaf of the short working face.The maximum value of residual settlement and deformation of the surface in the viaduct area above the short working face are calculated and demonstrated in Table 3; Contours of residual surface movement and deformation distribution at the site and nearby areas are also drawn in Fig. 14.For space reasons, only contour lines of residual surface subsidence are provided.3, it can be determined that the site of the viaduct area above the short working face is stable, providing technical support for the evaluation of the site stability and construction suitability of the viaduct area.

Field measurement of surface residual deformation in goaf of short working face
Two Sentinel-1A satellite interferometric wide swath (IW) SAR images are selected for the monitoring of residual surface deformation in the goaf of the short working face.The images are acquired on September 20, 2021 and January 6, 2022, respectively.The orbits are elevated.At the same time, ASTER GDEM V2 data with a spatial resolution of 30m is used to assist in interferogram registration and remove the terrain phase information in the interference phase; The precise orbit data of Sentinel-1A satellite corresponding to SAR images are used to reduce the orbit error in the interference phase.
D-InSAR technology was used to process the above images, and the surface deformation above the working face was obtained from September 20, 2021 to January 6, 2022, as shown in Fig. 14.According to the analysis of Fig. 14, the maximum vertical displacement of the viaduct site above the short working face is within 20mm during the period from September 20, 2021 to January 6, 2022.At the same time, the third order leveling was used to monitor the viaduct site, and the surface subsidence of the viaduct site was 6 mm from September 18, 2021 to December 30, 2021.
As the surface deformation of the short working face is still in the initial stage of residual deformation during this leveling and InSAR monitoring, that is, the surface deformation value obtained by monitoring should be less than the residual subsidence value of the short working face predicted by the proposed method (62mm).However, the surface residual deformation of the short working face will continue to occur, and the difference between the two will decrease with the increase of monitoring time; On the other hand, the surface residual deformation prediction method proposed for short working face is based on the most unfavorable conditions (for engineering safety), so the theoretical prediction results should also be greater than the measured data.
6 Conclusion (1) The main source of the "activated" subsidence of the short working face goaf is that the natural balanced arch foot of the overburden rock moves outward and the arch height increases due to the stripping and yield softening of the coal walls on both sides of the goaf, which causes the instability of the original natural balanced arch until a new natural balanced arch is formed at a higher height, thus causing the increase of the displacement and deformation of the surface above the goaf.This increase represents the limit value of the surface residual settlement and deformation of the short working face goaf.
(2) After calculating the maximum yield and stripping width of the coal walls on both sides of the short face goaf, the width of the goaf after the yield and stripping of the coal walls on both sides of the short face can be obtained.Then, the surface movement and deformation values before and after the yield and stripping of the coal walls on both sides of the face can be calculated based on the probability integral method.The maximum estimation value of the residual surface deformation of the short working face goaf can be obtained by making a difference between the two.Thus, the prediction of surface residual deformation of short goaf can be realized.The monitoring results of InSAR and leveling show that the method is effective.
(3) The proposed method was applied to the stability evaluation of the viaduct mined-out area in Jining, Shandong.It is concluded that the goaf of 63 working face will not affect the safety construction of planned north extension viaduct.Stress distribution of main inclined section before and after coal wall stripping in short working face/Pa Internal stress variation curve of rock mass after coal wall stripping on both sides of goaf in short goaf al. 2022; Du et al. 2022; Liu et al. 2019; Qu et al. 2021).The poor foundation site of the large mined-out region has posed a serious restriction and potential safety hazard to the construction land needed for the transformation and upgrading of mining cities (Ma et al. 2022; Wojtecki et al. 2021; Zhang et al. 2019; Pal et al. 2020).
al.2022; Zhao et al.2020; Huang et al.2020; Luan et al.2020; Hescock et al.2018; Chi et al.2021) ; The other is a mathematical model based on the learning of previous measured data

Figures
Figures Figure 1

Figure 4 Relative
Figure 4

Figure 5 Stress
Figure 5

Figure 10 Surface
Figure 10

Figure 11 Schematic diagram of coal pillar stress zoning Figure 12 Mechanical model of coal pillar Page 20 / 21
Figure 11

Table 3
Extreme value of surface residual subsidence and deformation prediction in viaduct area above short goaf