Design of Longwall Coal Pillar for the Prevention of Water Inrush from the Seam Floor with Through Fault

Setting up a waterproof coal pillar is an important measure to prevent water inrush from the Weibei mining through fault ﬂ oor. Based on the plastic slip line ﬁ eld theory, a mechanical model of ﬂ oor water inrush induced by con ﬁ ned water in the through fault zone was established. The mechanical expressions of con ﬁ ned water pressure and the width of the waterproof coal pillar under the state of limit equilibrium were derived. Combining the laws of ﬂ oor deformation, failure and fault activation under two kinds of coal pillar width, the safety width of the waterproof coal pillar was determined. Furthermore, the safety threshold is better than the empirical value mentioned in the “ coal mine safety regulations. ” Following this, grouting transformation was carried out on the K2 sand layer of the cut roadway ﬂ oor. This provided a theoretical basis and engineering practice for water disaster prevention and the control of the structural ﬂ oor under similar conditions in the Weibei mining area for future bene ﬁ t.


Introduction
The North China-type coalfield is rich in coal resources and accounts for about 90% of the total coal [1,2]. However, the complex hydrogeological conditions of minefields have caused the frequent occurrence of limestone karst water hazards [2,3]. With the large-scale development of coal resources in the recent decades, the shallow North China-type coalfield has gradually entered the stage of deep mining and lower group coal mining [4,5]. Furthermore, the coal seam floor is increasingly threatened by Ordovician ash highly confined water [6][7][8].
In some old mining areas, coal reserves threatened by karst water disasters account for 49%-87.6% of total mine reserves [9]. The Carboniferous-Permian coalfield in Weibei, known as the "Weibei black belt," is distributed in Tongchuan, Pubai, Chenghe, and Hancheng mining areas. Faults on the floor generally exist in the geological structure of the Weibei coalfield. Once mining induces fault activation, Ordovician confined water can easily rise along the fault zone and connected fractures. This results in water inrush from the floor.
Currently, remarkable theory and practice bases have been achieved by research carried out on the failure law, water inrush mechanism, and water inrush prediction [10][11][12][13][14][15][16][17][18]. Yin et al. [19] developed a numerical model to predict the time and the longwall locations of flood occurrences. Furthermore, Odintsev and Miletenko [20] studied the mine water inrush caused by spontaneous hydrofracturing of surrounding rocks and gave the influencing factors of spontaneous hydraulic fracturing. Additionally, Wang et al. [21] established an evaluation model for predicting water inrush in the Lu-an mining area based on fractal theory and improved the analytic hierarchy progress. This model provided a basis for water inrush research from the floor strata through faults. However, the study on the mechanism of water inrush and seepage from the through fault floor in the Weibei mining area has not yet taken a corresponding karst confined water prevention technology system and supporting measures. In the case of lower group coal resources through fault floors being blindly exploited, it is very easy for floor water inrush to proceed, endangering the safety of the construction of the mine and personnel safety.
The primary floor water inrush prevention and control measures include grouting transformation, water exploration, drainage, and setting of waterproof coal pillars [22][23][24][25][26][27]. Setting waterproof coal pillar measures is often adopted to prevent water inrush from the Weibei coal mine floor. However, the setting width of the waterproof coal pillar obtained from the empirical formula in "coal mine safety regulations" failed to consider the fault structure with complex conditions. Therefore, scientifically setting up a reasonable width of a waterproof coal pillar is one of the urgent problems to be solved through fault coal seam mining.
This paper established a mechanical model of floor water inrush induced by confined water in the through fault zone. Furthermore, this paper gave an analytical solution of the limit width of the waterproof coal pillar. By combining analysis of the floor's deformation, failure, and the law of fault activation under two kinds of coal pillar width with engineering examples and numerical simulation, it is proven that the mechanical model is reasonable. Moreover, the grouting of floor K2 sandstone can also be used as a reference for the treatment of other similar geological structures.  Figure 1 shows the abutment pressure distribution curve of coal in front of the working face. According to the failure degree, the coal body of the working face can be divided into the inelastic zone, the elastic zone, and the original rock stress zone under abutment pressure with the coal seam mining. Among them, the width of the inelastic zone is [28] x 0 =

Theoretical Analysis
where H 1 is the buried depth of the coal seam (m), H 2 is the mining height of the coal seam (m), k is the peak coefficient of abutment pressure, r is the average bulk density of the coal seam overlying rock (N/m 3 ), θ is the deformation angle of the coal seam (degree), C 1 is the cohesive force on the contact surface between the coal seam and the roof and floor (MPa),f 1 is the frictional force between the interface between the coal seam and the roof, k p = ð1 + sin φ 2 Þ/ð1 − sin φ 2 Þ, σ c is the ultimate compressive strength of the coal under uniaxial compression (MPa), and σ * c is the strength of the coal under uniaxial compression residual strength (MPa). Figure 2 shows the mechanical model of the plastic slip line for mining failure of floor rock mass caused by abutment pressure in front of the coal mining face [29], where O is the coal mining face position, OD is the goaf boundary, OA is the horizontal distance from the peak abutment pressure to the working face, and EF represents the maximum depth of mining failure of the floor. With the advancement of the working face, the maximum failure depth of floor mining is The horizontal distance between the maximum failure depth OE of the floor rock mass and the front end of the work is The maximum failure length of floor rock mass in the goaf along the horizontal plane is where x 0 is the width of the inelastic zone of the coal seam (m) and φ d is the weighted average internal friction angle of the floor rock mass.

Mechanical Analysis of the Activated Fault Floor
Structure. As the dip angle of the through fault is generally large in the Weibei mining area, this paper only discussed the fault with a large dip angle. For the convenience of derivation, the shaping slip line of the base plate is simplified to a straight line, as shown in Figure 3. Then, the angle between shaping slip line and coal seam can be expressed as The mechanical model in Figure 4 is taken from the triangular region in Figure 3. By analyzing the force of the triangular HGM rock block above fault, the upper rock mass pressure and confined water pressure of the rock block are regarded as a uniformly distributed load, as shown in Figure 4. Among them, q represents the confined water pressure, q 1 represents the uniformly distributed load of the upper rock mass acting on the rock block, and τ 1 , σ 1 represent the shear stress and normal stress provided by the lateral rock mass, respectively. The length of each segment can be expressed as By decomposing the forces in the diagram, the simplified force expression in the y-axis direction in the limit equilibrium state is

Plastic zone
Inelastic zone Crushed zone Hydraulic support     3 Geofluids where C d is the weighted average cohesion of floor rock mass. The mechanical model in Figure 5 is taken from the rectangular area in Figure 3. The force of rectangular MFGH rock above the triangle is analyzed, as shown in Figure 5. By taking any microelement d z in the z-axis direction, the expression of force acting on the z-axis in the equilibrium state is where σ x is the stress of the element in the x-axis direction (MPa).
Since the failure of the floor rock mass should conform to the principle of shear failure, the M-C criterion is selected as the yield criterion, and the limit ultimate equilibrium condition of the rock mass when it is about to fail is Let ð1 Substituting formulas (9) and (10) into formula (12), then solving the differential equation, and simplifying, one can obtain When z = 0, take the unit thickness as b. The following formula can be obtained: where r 1 is the average bulk density of the floor strata (kN/m 3 ). The z = 0 and formula (14) are substituted into formula (15) and simplified as Substituting equation (15) into the differential equation (13), we can get By substituting z = 0 into equation (16) and taking unit thickness as b, the simplified expression is Substituting equation (16) into equation (17), one can obtain In this limit state, H can be expressed as

Geofluids
where H is the width of the coal pillar corresponding to the direction of the working face (m). By substituting equations (8) and (19) into equation (18) and simplifying it, the expression of the confined water pressure of the through fault floor and the width of the corresponding coal pillar under the limit equilibrium state can be obtained: because this equation is transcendental and cannot be simplified to the H 3 = f ðqÞ form manually. However, it can be given a value by the method of a single variable solution by software. Therefore, the width of waterproof coal pillar H 4 in the through fault floor is 3. Engineering Practice and Application 3.1. Working Face Overview. The Dongjiahe coal mine is located 3.5 kilometers southwest of Chengcheng County, Weinan City, Shaanxi Province. This mine has a high terrain in the north and low terrain in the south ( Figure 6). It belongs to the Weibei Loess Plateau in geomorphology. The main coal seam of the mine is the no. 5 coal, which has a coal thickness of 2.9 m~4.7 m; the dip angle of the coal seam is 3°~15°. The 23503 working face is located in the second level and third mining area of the Dongjiahe coal mine, with a strike length of 1190 m and a dip length of 180 m. The terrain is lower than the static water level of Ordovician ash +370 m. This is classified as mining under pressure. The 23503 working face is near the eastern boundary of the mining area. It is only about 150 m away from the normal fault of Dongjiahe, which is a big fault outside the minefield. According to drilling, the floor fault structure of the working face is well developed, and the hydrogeological conditions are complex. The distance between the 5# coal seam floor and the top face of the Ordovician limestone is about 62.82 m (CH187)~31.47 m (DB6). There is a normal fault structure on the right boundary of the working face. This fault structure has a fault dip angle of 40°, and the fault crosses the K2 limestone. If mining starts at the working face, mining disturbances would affect the normal fault and result in fracture conduction. This will then cause floor water inrush. Therefore, in the mine, we decided to reduce the disturbance to the fault by setting up a waterproof coal pillar to avoid safety accidents.

Empirical Formula of "Coal Mine Safety Regulations."
In the "provisions on prevention and control of water in coal mine," when considering the pressure of fault water along the direction of the coal seam, the width of the waterproof coal pillar can be calculated by referring to the following empirical formula. This calculation applies in the case whereby coal seam is located above the aquifer and the fault is water-conducting.  Figure 6: Location of the Dongjiahe coal mine.

Geofluids
where L is the width of the coal pillar (m), M is the mining height (m), P is the hydrostatic pressure (MPa), K p is the tensile strength of coal (MPa), and K is the safety factor; take 2-5. Substitute the geological parameters of the 23503 working face in the Dongjiahe coal mine into the empirical formula (22), where the basic parameters are as follows: M is 3.8 m, K is 5, K p is 0.25 MPa, P is 1.4 MPa, and the minimum width of the waterproof coal pillar is 25 m.

Theoretical Solution of the Setting Width of the
Waterproof Coal Pillar. Based on the theoretical derivation in the previous section, the mechanical expressions of the confined water pressure with fault floor and the width of the retained waterproof coal pillar were obtained. By substituting the basic parameters of the 23503 working face in Table 1 into formulas (20) and (21), the minimum width theoretical solution of the waterproof coal pillar is 31.92 m.
In summary, the empirical and theoretical values of the waterproof coal pillar width in the 23503 working face were 25.13 m and 31.92 m, respectively. The empirical value was smaller than the theoretical value. Considering that some folds and small fault structures may exist in the actual mining of the working face, there will be unsafe factors in the empirical value of the regulations. Hence, in the mine, we initially proposed to set up a waterproof coal pillar of 28 m. To make a comprehensive study and judgment of the above results, a numerical simulation analysis was carried out on the lower cut mining at the distance of 28 m from the fault.  Table 2 shows some rock physical and mechanical parameters of the 23503 working face.

Geofluids
Step1-15-1 Step3-15-1 Step4-15-1 Step5 -   MPa was applied at the bottom to simulate the effect of Ordovician ash confined water on the floor. The original rock stress was a static stress field, and the rock stratum was a continuous medium. As shown in Figure 7, the fault of the model was normal with a distance of 28 m from the right fault (along the coal seam) and 334 m from the left boundary. By mining from right to left, there were a total of 10 steps. For the first and second steps of mining, each step was 32 m. For the third step to the tenth step, each step was 23 m, for a total of 248 m.

Analysis of Simulation Results of the Stress Field.
The picture shows the variation law of the vertical stress field (Figure 9). With the continuous advancement of the working face, the stress variation range of the cutting side was larger than that of the mining face, resulting in stress concentration on the cutting side. In the process of advancing to 110 m (step 4-15-1), it was evident that the stress on the left side of the fault continued to decrease due to failure of floor mining. Plastic failure occurred when the stress range exceeded the strength of the rock mass. This provided a water inrush channel for the confined water lift.

Analysis of Seepage Field Simulation
Results. By combining Figures 10 and 11, it can be seen that the pore water pressure in the fault increases slightly with the advancement of the working face to 64 m (step 2-15-1). Subsequently, when the working face advanced to 110 m (step 4-5-1), the fault zone was activated by disturbance and damage along the fault and confined water pressure continued to increase Step5-9-1 Simulation advancement steps Fault zone water pressure increased The water pressure has soared nearly fourfold The water inrush channel widens and water pressure is reduced 9 Geofluids and rose along the fault zone. When the simulation reached step 4-10-1, the development degree of the floor crack and the seepage vector near the mining failure area of the fault zone continued to increase. Until simulation to step 4-11-1, the cracks between the floor mining failure zone and the confined water guide zone developed and led to water inrush channels. The seepage vector in the water inrush channel was huge, and the water pressure increased sharply from the previous 0.23 MPa to 0.97 MPa. Then, in the process of simulation to step 4-14-1, water pressure decreased gradually and stabilized gradually. The change of water pressure in the fault zone is shown in Figure 11.

Comprehensive Comparison of Simulation and Theoretical
Results. It can be seen from the above simulation results that when the 28 m waterproof coal pillar is left, the fault confined water guide zone and floor mining failure zone are connected when the working face advances to 110 m. The rapid increase in seepage pressure leads to the inflow of confined water into the goaf, resulting in water inrush. Therefore, the calculation result of the coal pillar empirical formula for the 23503 working face is smaller than the actual situation. However, the theoretical calculation result is 32 m. Moreover, the normal fault of Dongjiahe is on the right side of the 23503 working face. The secondary fractures and structures of the floor are complicated. According to the theoretical calculation value of waterproof coal pillar with 2-3 times safety factor, the cut hole is arranged at 80 m from the fault. Step2-15-1

Hole Cutting Construction and Groove Wave Detection.
Based on the actual situation of the site and through comprehensive research, analysis, and expert meeting to exchange analysis, it was decided that according to the theoretical calculation value of the waterproof coal pillar with 2-3 times safety factor, the cut hole should be arranged at the distance of 80 m from the fault. During the open-cut roadway excavation, three fault structures were revealed, namely, Q1, Q2, and Q3, respectively. Because the Q1 fault was very small and the drop was less than 0.3 m, it did not affect the later excavation. On the other hand, the drops of the roadway where the Q2 and Q3 faults were located were relatively large, and the possible existence of other structures could not be ruled out. Therefore, the groove wave detection was carried out on the working face, and the groove wave observation results are shown in Figure 14.
There is no obvious change in water pressure The water pressure increases obviously  The hydrogeological conditions of the 23503 working face are complex, and the driving areas are all located below the Ordovician ash static water level. These areas belong to the pressure-bearing area. According to drilling data, there are different water gushing degrees in the drilling site. Judging from the amount of water gushing and its static pressure, the gushing water recharge had no hydraulic relationship with the underlying Ordovician limestone solution fissure water. It should be fracture water in the lower aquifer group (K2 quartz sandstone) of coal measure strata. However, it cannot be ruled out that the impact of mining causes Ordovician water to flow into the K2 sandstone layer. This forms a large amount of indirect replenishment to the water inrush source. To not affect the safe mining of the working face, the mine carried on the grouting transformation to the floor K2 sandstone. face. The specific gravity of the grout was between 1.13 and 1.30 g/cm 2 , and the total grouting volume was 7970.7 cubic meters ( Figure 15). The grouting reinforcement project of the working face starts from 28 November 2018 to 13 October 2019. After completing grouting, the whole working face was explored by the electrical method to meet water prevention and control requirements. Because the Q2 and Q3 faults exposed by the open-cut roadway have not developed to the Ordovician ash roof interface and are coupled with the previous floor grouting transformation, the water inflow of the open-cut roadway was reduced to 20 m 3 /h. It met the requirements of the detailed rules of water prevention and control and the existing drainage capacity of 200 m 3 /h of the mine. Currently, the 23503 working face has mined 700 m. From the observation data of the underground water inrush point, it can be seen that the average water inflow was maintained at 40-60 m 3 /h in the process of mining. The highest water inflow in the whole working face was over 105 m 3 /h. However, it still meets the existing drainage capacity of the mine and does not cause a water inrush accident.

Conclusions
Based on the plastic slip line field theory, this paper puts forward the analytical solution of the limit width of the waterproof coal pillar. Moreover, this paper analyzed the activation law of floor fault in the 23503 working face of the Dongjiahe coal mine. It also verified the theory by numerical simulation and engineering practice. The conclusions are as follows: (1) The numerical models under two different conditions of setting coal pillar width were established using the finite difference software. The laws of deformation and failure of the through fault floor and fault activation were obtained. It was determined that the safety width of the waterproof coal pillar is 80 m. This provided more reasonable data than the empirical value mentioned in the "coal mine safety regulations" for the location of new cut holes (2) When the waterproof coal pillar was set at 28 m, the existence of the through fault hindered the transmission of mining stress in the floor. This made the stress concentration in the floor rock mass between the goaf and the fault to increase, thereby deepening the floor failure depth near the fault. With the advancement of the working face, the fault zone continued to activate upward, and the seepage vector in the zone continued to grow and gradually extended to the failure depth of the floor (3) In the practical application of the research results, three fault structures were exposed during the process of open-hole excavation. Combining these results with grooving wave detection results in the 23503 working face, grouting transformation was carried out on the working face floor. This measure reduced the risk of floor water inrush and had a good effect of preventing water inrush. It also provided engineering references and practical experiences for water disaster prevention and for the control of structural floors under similar conditions in the Weibei mining area for future benefits

Data Availability
Some or all data, models, or codes generated or used during the study are available from the corresponding author by request.

Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.