#### Abstract

As the dangerous level of floor water inrush in Chinese coal field is becoming more and more serious annually, the widely used formulas of broken floor rock mass are belonged to nonlinear type or empirical type. However, they are not well conformed to the practical situation and including mining underground pressure. The biggest depth of broken floor rock mass and the length of gob-floor or mining-floor until the maximum broken floor location are expressed by theoretical formulas on integrity theory. Taking a mining face in Chinese Anhui Province as the object, the relationship between broken floor rock mass and mining underground pressure is studied by numerical simulation, the theoretical analysis, and the DC exploration. The peak and scope of broken floor rock mass will enlarge until reaching limit value with the increasingly advanced distance. The mining gob stress contour is saddle-shaped, and its growing speed is becoming slower, so the 180 m coal mining face has reached the sufficient mining stage. Wave velocity of broken floor rock mass from 0 m to 16 m is greatly decreased by the mining disturbance, and it is basically conformed to theoretical formula and practical situation. The results can be relatively better used in the pressure mining of the Ordovician limestone, because it can provide some safe guarantee for mining deep coal seam.

#### 1. Introduction

China is the country with the largest coal production and consumption than any other countries in the world. Water inrush from broken floor rock mass is one of difficult problems in Chinese coal field [1–5]. The statistical or the theoretical formulas of broken floor rock mass have made great achievement so far [6–10]. Shi et al. [11, 12] put forward some models using principal component analysis, fuzzy, particle swarm optimization algorithm, and support vector machine. Zhang et al. [13, 14] obtained some formulas by regression analysis fitting and built the model of Fisher’s discriminant analysis. Wu et al. [15–19] studied the vulnerable index method based on GIS, ANN, AHP, evidence weight, and logistic regression. Theoretical formulas of broken floor depth were the main consideration of fracture mechanics and plastic mechanics [20]. Relationship between broken floor depth and average mining depth, coal seam dip, mining face height, mining face length, floor resistance ability, and fault fractured zone was analyzed by statistical formula and regression analysis [21, 22]. Theoretical formulas of broken floor depth under stress-damage and flow-damage were derived, and floor damage variable was based on the rock test and floor index [23, 24]. The empirical formula of broken floor depth was analyzed by further error-correction and option-design [25]. Floor aquifuge thickness, weathered zone thickness, grouting section thickness, and broken floor depth were main factors of water inrush coefficient [26]. Weakening effect of acidic solution on the marble is much greater than that on amphibolite [27]. Broken floor depth and safely pressure mining were analyzed from aquifer structure, ecological water level, and water quality [28]. The equivalent Burgers model for revealing the rheological behavior was the combined action of hydraulic pressure and mining stress [29]. Floor rock mass with a fault can tolerate decreases with increasing fault dip and friction angle [30]. The revised shear strength model and experimental data indicated its capability in estimating the peak shear strength of unfilled rock joints [31]. When the inclined work face advanced to about 80 m, the depth of ﬂoor plastic failure zone reached over 15 m [32]. The shear-related roughness classification and strength model of natural rock joint based on fuzzy comprehensive evaluation can be explained objectively [33]. Double criteria for water inrush monitoring and early warning were established based on crack instability extension, water temperature, and water pressure [34]. The PSR model of ecosystem health evaluation and the risk evaluation indicator system were established to scientifically and reasonably assess water inrush risk [35]. Floor water inrush was comprehensively considered from the three aspects of the aquifer’s water yield, the hydraulic resistance characteristics of the aquitard, and the tectonic development of the study area [36].

Based on the broken floor rock mass integrity, the biggest depth of broken floor rock mass and the length of gob-floor or mining-floor until the maximum broken floor location are expressed by theoretical formulas. Taking a mining face in Chinese Anhui Province as an object, the relationship between broken floor rock mass and mining underground pressure is studied by numerical simulation, theoretical analysis, and DC exploration. The results will be used well in pressure mining of Ordovician limestone, which can provide some safe guarantee for deep coal mining.

#### 2. Solving Broken Floor Depth and Coal Plastic Scope in Mining-Floor by Integrity

##### 2.1. Solving the Maximum Floor Failure Depth in Mining-Floor by Integrity Theory

According to the slipping line field theory, the broken floor rock mass of mining face is shown in Figure 1, which is caused by advanced abutment pressure and changing underground pressure [37]. In Figure 1, *I* is in token of active stress, *II* is in token of transitional stress, *III* is in token of passive stress, is the length of broken gob-floor until maximum broken floor location, is the length of broken mining-floor until maximum broken floor location, is the length of yield zone in unmined coal seam, is the interior friction angle, is the coal mining location, is the maximum broken floor depth, is the maximum broken floor location, and is the broken floor mass curve. When the abutment pressure of floor rock mass exceeds its limit value, the plastic deformation and great failure area will appear in broken floor rock mass, and then they can change distribution of underground pressure. Due to the low normal stress and the fixed free surface, the plastic failure area of floor rock mass will move to the back gob by top caving method [38].

The initial broken floor depth in mining-floor rock mass is calculated in formulas (1)–(3), is the broken floor depth, is the radius of helix, is the angel of and , is the interior friction angle, and is the angel between and :

Taking formulas (2) and (3) into formula (1), the broken floor depth in mining-floor rock mass is calculated in formula (4) by :

When , the limit value of formula (4) is the maximum depth of broken floor rock mass by the following formulas:

The mining-floor integrity is measured by the borehole water quantity. In formula (7), is the floor rock mass integrity, is the borehole watertight length, and is the borehole total length, and the broken floor rock mass integrity is 7 by :

Taking formulas (2) and (7) into (4) to the broken floor rock mass integrity, the biggest depth of broken floor rock mass is calculated in formula (8) by :

Considering broken floor rock mass integrity, the length of broken gob-floor until maximum broken floor location is calculated in formula (9) by and the length of broken mining-floor until maximum broken floor location is calculated in formula (10) by :

##### 2.2. Solving Coal Plastic Scope in Central Mining-Floor by Integrity

Taking an element of unmined coal seam in equilibrium state, it is wide and high. The zero resultant force along *x* direction is measured in formulas (11) and (12) [39, 40], where *c* is the coal cohesive force, *σ*_{x} is the overburden weight stress, *φ*_{0} is the interior friction angle, d*x* is the coal element width, and *M* is the average mining height:

When differential element reached limit value, considering Mohr–Coulomb strength theory [37], formula (16) is taking formulas (14) and (15) into formula (13), where *σ*_{1} is the coal vertical stress, *σ*_{3} is the coal horizontal stress, *σ*_{z} is the coal interfacial stress, and *K*_{1} is the lateral pressure coefficient:

Defining the boundary condition ( and ), formula (16) can be solved and changed formula (17) by :

Taking formulas (7) and (16) into formula (17), the distance from peak abutment pressure to coal mining face on floor integrity is calculated in formula (18) by , where is the internal friction angle, is the coal cohesive force, and is the average mining height:

#### 3. Numerical Simulations of Broken Floor Shape and Different Advanced Distance

##### 3.1. Rock Mechanics Parameters of Numerical Simulation

Specific mechanic parameters of broken roof rock, coal seam, and floor rock are given Table 1, which are used in the numerical simulation of the mining face in Chinese Anhui Province.

##### 3.2. Numerical Simulation of Broken Floor Shape and Different Advanced Distance

Due to the limited space, when the coal seam work face advanced to about 180 m, the vertical stress distribution of broken floor rock mass is shown in Figure 2 and the mining failure features of broken floor rock mass are shown in Figure 3. Vertical stress distribution and mining failure features are little changed, but stress concentration in unmined coal seam is much changed, and front abutment pressure peak has reached more than 22 MPa. Stress contour in back gob is saddle-shaped, and its growing speed is becoming slower, so it fully proves that the 180 m coal mining face has been reached sufficient mining stage. With the advancing coal mining face, the limestone shear failure scope in broken floor rock mass is further increasing, but limestone shear failure depth is staying below less than 14 m.

**(a)**

**(b)**

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Abutment pressure distribution of floor rock mass and different advanced distance is shown in Figure 4, and the broken depth distribution of floor rock mass and different advanced distance is shown in Figure 5. The abutment pressure coefficient of floor rock mass is changed from 1.2 to 1.6 during the sufficient mining stage, and the peak abutment pressure is varied from 13.5 MPa to 22.7 MPa. Distance between peak abutment pressure and mining face is stayed about 5 m, and the affected length by advanced abutment pressure can reach 20 m. The broken depth of floor rock mass is changed from 8.1 m to 14.2 m, and the maximum was about 15 m. With the advancing working face, the peak and scope of broken floor rock mass will increase until reaching critical value and then basically remain stable.

#### 4. Calculating Broken Floor and Observing Wave Velocity of the Mining Face

##### 4.1. Calculating Broken Floor of the Mining Face

Taking a mining face of a colliery in Chinese Anhui Province as the research object, the average buried depth is 466 m, the average mining height is 3.4 m, the stratum bulk density is 2669 kg/m^{3}, the coal friction angle is 32°, the rock friction angle is 42.6°, static Poisson’s ratio is 0.19, the mean cohesive force is 12.5 MPa, and the mining-floor integrity is 0.9.

The biggest depth of broken floor rock mass is as follows by :

The length of broken gob-floor until maximum broken floor location is as follows by :

The length of broken mining-floor until maximum broken floor location is as follows by :

The distance from peak abutment pressure to coal mining face is as follows by :

Plastic destroyed area of floor rock mass of a colliery in Chinese Anhui Province is drawn in Figure 6.

##### 4.2. Measuring Wave Velocity of Broken Floor Rock Mass by DC Exploration

Figure 7 shows the schematic diagram of DC exploration technology. This method can constantly supply currents into electrodes, repeatedly measure the potential difference, and continuously record different apparent resistivity. So, it can form electric field penetration by *a*, *b*, *c*, and *d* in Figure 7. If floor rock mass is destroyed without water by mining disturbance, the rock conductivity will be weakened, and its resistivity will be gradually increased. If floor rock mass is destroyed with water by mining disturbance, the rock conductivity will be strengthened, and its resistivity will be relatively decreased. If rock resistivity is not obviously changed and basically remains stable, the floor rock mass can be undamaged during coal mining. The floor observed borehole in the ventilation roadway is about 21 m deep, 91 mm diameter, and vertical downward to floor rock mass. Background wave velocity of borehole is shown in Figure 8, and Ming wave velocity of borehole is shown in Figure 9. Floor wave velocity from 0 m to 8 m is 1.7 m/ms, floor wave velocity from 8 m to 16 m is 2.9 m/ms, and floor wave velocity from 16 m to 20 m is 3.2 m/ms. In general, the broken floor rock mass wave velocity from 0 m to 16 m is decreased by coal mining, and it is basically conformed to the calculation results and the actual situations.

#### 5. Conclusions

The biggest depth of broken floor rock mass, length of broken gob-floor or mining-floor until maximum broken floor location, and distance from peak abutment pressure to coal mining face are expressed by theoretical formulas. Stress contour in back gob is saddle-shaped, and its growing speed is becoming slower, so the 180 m mining coal mining face has reached sufficient mining stage. With the advancing coal mining face, limestone shear failure scope in broken floor rock mass is further increasing, but limestone shear failure depth is staying below less than 14 m.

Abutment pressure coefficient of floor rock mass is changed from 1.2 to 1.6 during sufficient mining stage. Because of increasingly advanced distance, the peak and scope of broken floor rack depth will increase until reaching its ultimate limit and then basically remain stable. The biggest depth of broken floor rock mass, length of broken gob-floor and mining-floor until biggest broken floor location, and distance from peak abutment pressure to coal mining face are calculated by a colliery in Chinese Anhui Province. Floor rock mass wave velocity from 0 m to 8 m and from 8 m to 16 m is 1.7 m/ms and 2.9 m/ms by DC, so floor rock from 0 m to 16 m is greatly changed by mining disturbance and basically conformed to theoretical calculation.

These calculation results are well consistent with the actual situation, which shows that the used models are feasible and reasonable. Dynamic evolution and disaster mechanism of broken floor rock mass and the increasingly mining advanced distance by underground pressure will be studied by water pressure and tectonic stress for future research direction. Locating the weak link of waterproof layers in broken ﬂoor rock mass and identifying the source of water hazards accurately are the key step in water inrush prevention and control.

#### Data Availability

The data used to support the findings of this study are included within the article.

#### Conflicts of Interest

The authors declare that there are no conﬂicts of interest regarding the publication of this paper.

#### Acknowledgments

This study was supported by the Inner Mongolia Autonomous Region Natural Science Foundation (2019MS05042 and 2019MS05053).