Study on Gas Enrichment Mechanism of Coal Seam Influenced by Vertical Stress on Mountainous Region Condition

State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Beijing 10083, China School of Civil and Architecture Engineering, China University of Mining and Technology, Beijing 100083, China Shandong Energy Yanzhou Coal Mining Company Limited, Jining, Shandong 273500, China Transportation Institute, Inner Mongolia University, Hohhot, Inner Mongolia 010070, China China Coal Technology Engineering Group Chongqing Research Institute, Chongqing 400037, China


Introduction
e coal reservoir permeability affected by pressure, pores, cracks, and other factors is of great significance to coal-bed methane occurrence, gas development and utilization, and safe mining of coal resources. Recently, there has been growing interest in the mechanical relationship between permeability and stress state in mining engineering. It is well known that permeability is an important parameter characterizing the flow capacity of gas in coal mass. Coal porosity and permeability are key petrophysical parameters, pivotal in facilitating coal-bed methane extraction and CO 2 sequestration [1]. e gas flow capacity of coal seam increases with the rise of permeability. Some researchers have found that the coal seam permeability is closely related to its stress state [2,3]. In the elastic deformation stage, permeability generally reduces with increasing pressure [4][5][6], which plays a restrictive role on the flow of gas. In the southern margin of the Junggar Basin, researchers found that permeability gradually decreases from the reservoir top to the base due to depth-increasing stress while gas content gradually increases due to permeability [7]. Meanwhile, the permeability often increases with decrease in pressure [8][9][10][11]. e permeability-strain curve of coal has a similar change rule for the stress-strain curve. e cracks in surrounding rock are also closed by increasing pressure, resulting in the reduction in rock permeability [5,12]. Generally, burial depth of the coal seam can directly control its stress, which indirectly controls the permeability for predictable reasons. To further clarify the relationship between the three, more studies have been published by scholars in the field of rock mechanics. For ground stress increases with the increase in burial depth, the permeability of the coal seam decreases gradually [13][14][15] and the gas content of the coal body increases as burial depth of coal seam increases [16][17][18]. e influence mechanism of burial depth on gas content can be expressed as follows according to the above investigations: the permeability of the coal seam is controlled directly by the stress associated with burial depth, which has strong correlation with gas flow. It implies that the high ground stress and low permeability might induce gas enrichment of the coal seam in complex coalforming and geology movement process. e more detailed logical relationships among burial depth, stress, permeability, and gas enrichment are shown in Figure 1. Figure 1 implies that gas flow might be affected by the permeability at a certain place. e result of [19] indicates that the permeability also affects the gas flow, with the larger permeability regions having the higher daily production. On this basis, we can indirectly evaluate the permeability via gas flow laws.
On condition of mountainous topography, the surface elevation often changes dramatically, causing huge changes in the burial depth of the coal seam. us, the burial depth, stress, and permeability of the coal seam change simultaneously, resulting in the great difference in gas reservation on the identical coal seam. It will be reflected on gas content of the coal seam and the amount of gas emission in the process of coal roadway excavation. At present, there is less research on this important phenomenon, which needs to be analyzed and studied. e aim of the investigation here was to analyze the inner mechanism of mountainous topography to gas enrichment. e Winkler elastic foundation beam theory was used to establish the mechanical model so as to analyze the stress and permeability change rules of the coal seam pressurised by the overlying mountain. Also, we carried out several sets of case experiments to test the validity of the research results.
is pioneer work might contribute to our present understanding of gas enrichment mechanism and is of great significance for the development and utilization of coal-bed gas and the safe exploitation of coal resources.

Establishment of the Mechanical Model.
In underground mines, the thickness of the coal seam is extremely thin compared with overburden strata and thus it can be simplified as a beam. To study the characteristics of the coal seam pressurised by overlying mountains, the coal seam was simplified to an infinite long beam and a mechanical model under the action of a single mountain was established. e typical model is shown in Figure 2.
Some hypotheses should be proposed as follows: (1) e weight of overlying rock except for the part of the mountain can be simplified as a uniform load q � ch, where c is the rock mass bulk and h is the distance from the coal seam to the surface. (2) e effect of the mountain on the coal seam is equivalent to a trapezoidal-distributed load m � bx + c + ch, wherein b is the slope and the c + ch is the vertical pressure of the overlying rock layers and the peak of the mountain at the O point. (3) Tectonic stress is not considered here.

eoretical Solution of the Mechanical Model.
e width of the beam can be assumed as 1, and the establishment of a rectangular coordinate system is shown in Figure 2. According to the Winkler elastic foundation beam theory, the model deflection curve can be expressed with [20,21] w � e ax (A cos ax + B sin ax) + e −ax (C cos ax + D sin ax) where e is the nature base; a is the characteristic coefficient; in a 4 � K/4EI, K is the foundation stiffness; the EI is the flexural section stiffness; A, B, C, and D are the undetermined coefficients; and w 0 (x) represents the special solution of the equation.   e model is axisymmetric, and only the analysis range of the right part of the w axis of the model was studied, and the pressure on the coal seam can be represented by segmented functions as follows: Any microsegment dx was taken; based on the mechanical equilibrium relation, the deflection differential equation of the model can be expressed with Equation (3) is a four-order constant-coefficient nonhomogeneous linear differential equation, the solution of which is composed of the common solution to the homogeneous equation and the special solutions to the nonhomogeneous equation.
ere are two nonhomogeneous items in equation (3), which can be written as w 01 (x) and w 02 (x). e first special solution w 01 (x) and the second special solution w 02 (x) to the right side of equation 3 can be solved. en, use the superposition principle to obtain w 0 (x). e expressions of w 01 (x) and w 02 (x) were obtained by mathematical knowledge as follows: Expression w 0 (x) was the sum of w 01 (x) and w 02 (x): erefore, the deflection equation of the coal seam can be expressed as According to the Winkler elastic foundation beam theory, nominal stress on the coal seams can be expressed as Equation (8) can be obtained by inserting equation (6) into equation (7): (1) When 0 ≤ x < 1, the coal seam is only subject to the trapezoidal distribution load. It can be known by natural boundary conditions and continuous deformation conditions: the expressions of A 1 , B 1 , C 1 , and D 1 can be obtained by using it: , Shock and Vibration 3 e nominal stress equation of the infinite long beam when 0 ≤ x < 1 can be obtained conveniently by inserting equation (9) into equation (8).
(2) When x ≥ 1, bx + c � 0 in the third item in equation (6), and the following can be known from natural boundary conditions and continuity conditions: obtained by using it. Equation (10) can be obtained by inserting it into equation (8): en, the nominal stress of the coal seam can be expressed with the segmented functions as follows: From equations (9) and (11) e study [22] showed that the nominal stress σ was related to gas pressure p, effective stress σ T , and porosity ϕ: Considering the compression deformation characteristics of the solid skeleton of the porous media, the porosity state equation can be introduced: where ϕ 0 is the initial porosity, %; c ϕ is the pore compressibility, 10 −3 MPa −1 ; p is the gas pressure, MPa; and p o is the initial gas pressure, MPa. Based on the experimental study [23], permeability is generally exponentially related to effective stress, which can be expressed as follows: where k is the permeability, m 2 ; k 0 is the initial permeability, m 2 ; and e and d are constants. Let u � ek 0 exp(d); the following equation can be obtained according to Equations (12)- (14): Equation (15) is an equation containing nominal stress, gas pressure, and permeability. Compared with other research results, equation (15) (9), (11), and (15). Given the length of the paper, the formula is omitted in the section. ose researchers who are interested in that can obtain the formula easily by taking equation (9) and equation (15) into equation (11). It is easy to see that the formula contains stress controlled by the burial depth and permeability affected by porosity of the coal seam. e relationships among burial depth, stress, and permeability will be studied in the following section.

Stress Characteristics of the Coal Seam Pressurised by the
Overlying Mountain. According to the above mechanical analysis, the stress characteristics of the mountain pressurised by the coal seam would be studied by an example analysis method. Coal seam thickness was taken as 8 m, and its elastic modulus E � 3.38 GPa; thus, EI � 144.21 × 10 9 N·m 2 . e stiffness K of coal seam foundation was 0.25-1.00 GPa [24], where K � 0.5 GPa was taken in here and l � 50 m, the ch � 5, 10, 15 MPa, c � 7, 10, 15 MPa, and b � −0.1 were taken for the convenience to research.
Based on the above values and equation (11), the stress characteristics of the coal seam were studied as follows.  Figure 2). And the farther away the point is, the lower the stress concentration is. e stress concentration continues to the edge of the mountain impact.
To further represent and verify the above phenomenon between stress and burial depth of the coal seam, the numerical modeling technology based on Flac 3D was used in the Mechanical Model section. Compared to the previous study, two mountain peaks with heights of 60 m and 35 m to rock mass stress were considered in this model. e length, width, and height of this model were set as 200 m, 80 m, and 260 m, respectively. e dip angle of rock mass was 23°according to geological conditions in the Shabatai coal mine where the mechanical parameters used in calculation were picked up. e applied parameters are listed in Table 1. Moreover, different boundary conditions were conducted to the model. e upper part of the model was free boundary, and the front, back, left, and right were horizontal displacement constraints. e vertical displacement restriction was applied on the bottom. Besides, the Mohr-Coulomb theory was used to calculate the model. A simulating result describing the SZZ contour map is shown in Figure 5.
e SZZ stress contour map obtained by numerical analysis and above studies exhibits good consistency in terms of the trend. It can be observed that the SZZ stress shows noteworthy nonlinear characteristics with change of burial depth. e SZZ stress under the peak is the largest, while it gets the smallest value at the edge. Compared to the higher peak, the value of SZZ stress under the lower peak is relatively small at a certain burial depth.
Although the results obtained through numerical simulation are slightly different from the above theoretical analysis, the results can still reflect the major mechanical behaviors of the relationship between burial depth and stress. erefore, the numerical simulation and theoretical analysis are verified by each other. (9), (11), and (15), parameters EI, K, and l were selected according to Section 3.1. e porosity ϕ 0 was given the value of 1.5%, the initial gas pressure p 0 was 1 MPa, and the pore compressibility c ϕ was 0.5 × 10 −3 MPa −1 . Let ch � 5 MPa, p � 3 MPa, and c � 7, 10, and 15 MPa. Change curves of the value of k/u in a different parameter c are shown in Figure 6.

Permeability Change Laws of the Coal Seam on Mountainous Region Condition. Based on equations
(1) e permeability of the coal seam and the change in trend of nominal stress showed a good correlation, and with the increase in nominal stress, the permeability decreased significantly. (2) e larger the value of parameter c, the smaller the permeability of the coal seam under the same distance from the original point and then the greater the difficulty of gas flows and release. (3) e permeability at the original point reached the minimum value, and with the distance increasing from the point, the permeability increased gradually.
In view of the control effect of coal permeability on gas flow, the synergistic relationship between permeability and stress/strain of coal, the positive correlation between permeability and burial depth, the positive correlation between burial depth and gas content, and the positive correlation between permeability and gas content, many scholars have done a lot of research by means of laboratory tests and have obtained a series of beneficial results.
In this paper, the stress characteristics and permeability of the mountain pressurised by the coal seam were studied by means of mechanical analysis. e results showed that the burial depth, stress, and permeability of the coal seam pressurised by the overlying mountain have changed significantly, which can inevitably lead to the change of gas content. As our theoretical support, the similar results had been obtained in [2] and [3] by different study methods.

Gas Enrichment Laws of the Coal Seam on Mountainous Region Condition
We have obtained the gas enrichment mechanism influenced by vertical stress on mountainous region condition by the aforementioned study. It is well known that the gas emission rate and gas content are characteristic parameters to express gas enrichment which was mainly affected by stress and permeability.

Gas Emission Rate during the Ventilation Roadway
Tunneling. For accurately studying the absolute gas emission rate on condition, the coal-bed methane was not the adopted measures of premining drainage before tunneling. No fold, fault, and other geological structures were found during tunneling, which excluded the influence of the geological structure on gas emission. In order to minimize the impact of driving speed on gas emission, we adopted a smaller excavation speed, namely, 2-3 m per day. e absolute gas emission rate is shown in Figure 8.
It can be divided into four regions according to surface elevation. We can see that there are great disparities in the gas emission rate for different regions. And the gas emission rate during tunneling corresponds to the changes of surface elevation. (1) Specifically, the absolute gas emission rate shows an increasing trend in region 1# with surface elevation increasing from 1540 m to 1550 m. (2) e growth trend of absolute gas emission is obvious mild in region 2# when the surface elevation increases from 1550 m to 1610 m slowly. (3) e absolute gas emission rate keeps oscillating at high values in region 3# when surface elevation is kept at 1610 m. (4) ereafter, as the surface elevation drops rapidly from 1610 m to 1556 m in region 4#, the absolute gas emission rate    significantly decreases accordingly. Also, the similar trend appears in the mean value of the gas emission rate at different regions. e quantities of that are 1.17 m 3 /min, 3.00 m 3 /min, 3.30 m 3 /min, and 2.30 m 3 /min, respectively, from regions 1# to 4#. device consists of 7 parts: the underground coring and desorption system, ground gas desorption system, weighing system, coal sample crushing system, moisture measurement system, gas composition measurement system, and data processing system. e method has the advantages of short determination period, low cost, small laboratory workload, and higher success rate. Particularly, the gas content determination work can be completed within 8 hours. e device is shown in Figure 9, and the measuring process is shown in Figure 10. e borehole for the determination of gas content was set perpendicular to the ventilation roadway, one every 50 meters. e samplings were all taken at 70 m depth. And, 19 holes were set in the roadway in total. e sketch map of gas content measurement drilling in the ventilation roadway is shown in Figure 11. e determination results of gas content of the coal seam are shown in Figure 12. While, at region 2#, the changes of gas content maintain a certain balance and fluctuate around the mean. For region 3#, the value of gas content implies a degree of increase with the surface elevation rising from 1550 m to 1558 m.   Particularly, gas content at region 4# shows a significant decline as the drop of surface elevation. us, Figure 12 reveals that there has been a sharp correlation between methane content of the coal seam and changes of surface elevation under mountainous condition. e similar conclusion can be obtained for the changing trends of the mean gas content of the four regions. e values of those are 4.75 m 3 /t, 5.54 m 3 /t, 5.90 m 3 /t, and 5.74 m 3 /t, respectively.

Conclusion
Gas occurrence of coal seam is closely related to the overlying mountain, which has always been ignored. Based on the Winkler elastic foundation beam theory, seepage theory, and the method of field observation, the change rules of stress and permeability of the coal seam pressurised by the overlying mountain were studied. en, the relationship between burial depth, stress, permeability, and gas content was analyzed. As a result, the gas enrichment mechanism of the coal seam pressurised by the overlying mountain was studied: (1) e mechanical model of the coal seam pressurised by the overlying mountain was established and analyzed based on the Winkler elastic foundation beam theory and seepage theory. e theoretical solution to nominal stress was derived. en, the theoretical solution to permeability with nominal stress and gas pressure as variables was obtained. (2) e change rules of stress and permeability of the coal seam pressurised by the overlying mountain were studied based on the method of example analysis. e results showed that the changes of the stress and permeability are significantly consistent with the changes of burial depth and surface elevation. (3) It shows a strong correlation between surface elevation, depth, stress, and permeability on the condition of the coal seam pressurised by the overlying mountain. e initial gas content is controlled by the permeability and the stress of the coal seam. Also, the field practice showed that there was a significant positive correlation between the initial gas content, surface elevation, and burial depth. At the same time, the absolute gas emission rate during roadway driving showed the same characteristics. (4) is new finding is helpful to understand the essential mechanism of the increase of coal-bed methane occurrence under mountainous area condition and gives the implication of solving the gas disaster. Under this condition, we can take measures such as increasing the density of the gas drainage borehole and extracting time so as to further reduce the gas disaster and obtain coal-bed methane resources as much as possible.
Data Availability e data supporting the findings of this study are included within the article and its supplementary materials. Shock and Vibration 9 field tests; B. C., S. S., and C. H. provided theoretical and technical guidance; R. H. analyzed the data and wrote the paper.