Modeling the Spatial and Temporal Evolution of Stress during Multiworking Face Mining in Close Distance Coal Seams

Mining in close distance coal seams (CDCSs) is frequently associated with engineering disasters because of the complicated nature of stress distribution within CDCSs. In order to establish a layout of a roadway to minimize the occurrence of disasters associated with mining CDCS, here the spatial and temporal evolution of stress distribution during the multiworking face mining of a CDCS was explored through numerical simulation based on the engineering and geological conditions of the Nantun Coal Mine. The numerical simulation results indicate that, after the extraction of adjacent multiple working faces, the spatial distribution of stress can be characterized with areas of increased, reduced, and intact stress. The superposed stress of inclined seams that are very close to each other propagates through coal pillars in the bottom floor, and this propagation follows neither the line along the axis of the coal pillar nor the line perpendicular to the direction of the floor. It instead propagates along a line angled with the axis of the coal pillar. The roadway can be arranged in the area with reduced stress, to improve its the stability. Based on the computed spatial and temporal evolution of stress, an optimized layout of roadway was proposed. This layout features a reasonable interval between the mining roadway and a minimal proportion of increased stress areas along the mining roadway and is aligned with geological structures.


Introduction
In recent years, as China's energy demand has continued to grow, coal mining activities in the country have continued to expand [1]. As a result, mining in close distance coal seams (CDCSs) has become increasingly important in many coal districts in China, such as Yanzhou, Datong, Pingdingshan, and Huainan. CDCSs are coal seams that are in close proximity to other seams, i.e., the distances between the different coal seams are very small [2,3]. e mining of CDCSs has been accompanied by frequent disastrous phenomena, such as large deformation of surrounding roadways, rock bursts, and coal and gas outbursts. ese phenomena are related to the multidimensional and dynamic redistribution of the stress of roadways in lower coal seams. It is therefore necessary to study the spatial and temporal evolution of stress in the roadways of CDCSs, in an effort to determine a general trend, so as to optimize their layout.
During several decades of CDCS mining, numerous researchers have investigated issues related to mining and roadway layout design [4][5][6][7][8]. Due to limitations in the available monitoring instruments and the engineering conditions, few investigations have focused on in situ stress distribution [9,10]. Recently, numerical simulations have increasingly been used to analyze the interactions of different extraction stages during CDCS mining. Wang et al. studied the mining interactions and reasonable positions between upper and lower mining faces using the discrete element simulation method [11]. Zhang et al. analyzed the distribution of coal pillar support pressure in the floor of a mine, using finite element numerical simulation. ey developed a method to determine the reasonable position of the roadway for ultraclose lower seams [12]. Liu et al. studied the deformation and stress redistribution of overlying coal seams above a doubleseam extraction, using a distinct element method based on a scaled modeling experiment [13]. Guo et al. performed a numerical investigation using a three-dimensional (3D) finite element code. ey used this approach to analyze the complex dynamic interaction between mining-induced strata stress changes and fractures in multiseam long wall mining at a Chinese colliery [14]. Suchowerska et al. developed a finite element model in conjunction with Wilson's equations to evaluate vertical stresses in the underlying strata. ey found that the abutment angle has a significantly greater effect on the magnitude of relative changes in vertical stress in the strata below a pillar than the overburden depth [15]. Adhikary et al. presented the results of a numerical simulation of the surface subsidence induced by multiseam longwall mining, obtained using both two-dimensional (2D) and 3D versions of a Cosserat continuum-based, finite element code called COSFLOW.
eir results highlighted deficiencies in 2D simulations. Other modeling studies have also focused on the stress evolution related to CSCD mining [16]. Zhu et al. studied the influence of vertical stress distribution to pillar stability during the extraction of a lower coal seam, using a 3D finite element model [17]. Zhang et al. utilized borehole imaging technology and a 2D numerical model to analyze the fissure evolution and distribution characteristics of both coal and rock, following the extraction of a lower coal seam [18]. Zhang et al. developed a 3D extraction model to explore the evolution of stresses and the effects of stress concentration and rock failure, during the extraction of an upper coal seam [19].
ese studies have mainly focused on stress evolution surrounding a single working face during CSCD mining. However, stress distribution has not yet been characterized during multiworking face CSCD mining. Based on the geological and mining conditions of Nantun Mine, a 3D numerical model was built to study stress distribution during CSCD mining. is model was used to explore the spatial and temporal evolution of stress during CSCD mining. rough the description of the geological conditions, setup of the numerical model, and analysis on the evaluation of the general trend of stress redistribution, an optimized roadway layout for the lower coal seam is presented.

Geological Description
Nantun Mine is located in center of Shandong Province, China. e mine field covers an area of 43.5 km 2 . e mine field is dominated by wide and gentle fold structures. e faults are relatively sparse, and the secondary folds are relatively developed. It is a medium-to-simple type; the faults are mainly normal faults with a small number of reverse faults. After 40 years of mining, the main working faces have become arranged using the descending mining method in coal seams no. 3 u and no. 3 l , at depths from 470 m to 590 m. As shown in Figure 1, the distance between coal seam no. 3 u and no. 3 l is less than 6 m, with a minimum of only 0.72 m, and coal seam no. 3 l is located below coal seam no. 3 u . e strata between coal seams no. 3 U and no. 3 L consist of sandstone. e thickness of coal seam no. 3 u varies from 1.4 to 5.7 m; its average thickness is 5.05 m. Coal seam no. 3 l is slightly thinner, ranging in thickness from 2.6 to 3.1 m; its average thickness is 2.98 m. e dip angles of these coal seams range from 6°to 20°; the average dip angle is 13°. e site engineering geological survey shows that the horizontal tectonic stress is small. In this study, the effects of gravity stress are considered according to the buried depth; they were calculated to be ∼11.75-14.75 MPa.
Four working faces were arranged in the research area, which is located in the east of the 9th Panel. Figure 2 shows a schematic diagram of the working faces' layout.

Numerical Model
It is important to understand the stress distribution of the coal-rock mass around the working face of 93 u 05 after the extraction of adjacent multiworking face and to provide guidelines for the extraction roadway arrangement and supporting method of selection for the 93 u 05 working face. Here, therefore, a 3D model was developed based on the engineering geological conditions of the site, using FLAC3D. e mesh used in the model is shown in Figure 3. e method of solution in FLAC3D is characterized by the following three approaches: (1) Finite difference approach (first-order space and time derivatives of a variable are approximated by finite differences, assuming linear variations of the variable over finite space and time intervals, respectively) (2) Discrete-model approach (the continuous medium is replaced by a discrete equivalent-one in which all forces involved and concentrated at the nodes of a three-dimensional mesh used in the medium representation) (3) Dynamic-solution approach (the inertial terms in the equations of motion are used as numerical means to reach the equilibrium state of the system under consideration) e laws of motion for the continuum are, by means of these approaches, transformed into discrete forms of Newton's law at the nodes. e resulting system of ordinary differential equations is then solved numerically using an explicit finite difference approach in time.
e maximum horizontal stress of the model is σ H � 26.5 MPa, the minimum horizontal stress of the model is σ h � 15.0 MPa, and the vertical stress of the model is σ V � 17.5 MPa. Boundary conditions and initial conditions are shown in Table 1. Material damage is calculated according to the Mohr-Coulomb strength criterion. e physical and mechanical parameters are listed in Table 2. Based on the experimental results of USBM (United States Bureau of Mines), the Salamon model was used to simulate the rock mass of the goaf [20,21].
In order to clearly delineate the impact of each working face to the mining stress distribution of the 93 l 05 working

Spatial and Temporal Evolution of Mine Stress.
According to the research results of Suchowerska et al. [15] and Zhang [22], the factor that has the greatest influence on the stress distribution of the lower coal during multi-coal mining is the safe coal column left after the upper coal is mined, mainly manifested as the significant change in vertical stress, and with the change of the inclination of the coal seam, the stress distribution in the lower coal will be more complicated. erefore, based on the abovementioned research results, this paper focuses on the stress distribution in the next coal seam after the vertical stress and the lateral stress are superimposed when the coal seam is mined at a close distance.    Advances in Civil Engineering Figure 5 shows the vertical stress distribution of the lateral bearing pressure of the 93 d 05 working face at each step. In Figure 5, the X and Y coordinates represent the transverse and longitudinal directions of the horizontal plane of the no. 3 l coal seam, respectively, and the Z coordinate corresponds to the vertical direction of the no. 3 l coal seam. Figure 5(a) shows the mine's stress distribution after the extraction of the 93 l 07 working face (Step 1). e distribution of vertical stress in the no. 3 l coal seam after the extraction of the 93 l 07 working face is similar to what is typically observed after the extraction of a single coal seam [23][24][25]. It exhibits the following features: (1) A zone affected by abutment pressure appears around the mining area after the extraction of the 93 l 07 working face. is zone can be divided into a subzone affected by the advanced abutment stress and a subzone affected by the lateral abutment stress. (2) e zone affected by the lateral abutment stress is located within the 93 l 05 working face. e horizontal distance from the edge of the 93 l 07 goaf to area of maximum lateral abutment stress (38 MPa) is 9.5 m. Considering an original rock stress of 13.5 MPa, the apparent stress concentration has a factor of 2.8. Figure 5 Step 3 concerns the extraction of the 93 u 05working face. Here, the lateral abutment stress of the 93 u 05 working face increases because the suspension area of the main roof of the 93 l 07 working face expands ( Figure 5(c)). e peak values of vertical stress between the 93 u 05 and 93 d 07 working faces both also increase, reaching 75 MPa (with a stress concentration factor of 4.3). In the area of the 93 l 07 goaf, the stress at the edge of goaf is relatively low. Here, the vertical stress increases due to the expansion of mining area, which leads to a continuous compaction of the internal rock, thereby increasing its strength. e stress transmits from the upper strata of rock to the bottom, and parts of the area recover to their original rock stress. Figure 5(d) shows the stress distribution after the extraction of the 93 u 03 working face in Step 4. e following observations can be made: (1) e vertical stress field in the no. 3 l coal seam can be divided into three zones: a zone with increased stress, a zone with reduced stress, and a zone with intact rock stress. e zone with increased stress includes zones with superposition of stress and without superposition of stress (i.e., a single working face).
(2) e vertical stress increases in each working face in the area around the no. 3 l coal seam. is is manifested in two kinds of zones with stress superposition: zones with superposed lateral abutment stress between two working faces and zones where the advanced abutment stress of a given working face superposes with the lateral abutment stress of the other working face. e latter type of zone has larger   Advances in Civil Engineering peak stress and subsequently has a more significant influence on the no. 3 l coal seam. (3) ough there are zones with raised stress, there are also zones with reduced vertical stresses, such as the unloading area of the excavation of mining roadway and the edge of the goaf. e mining roadway is arranged along the area with reduced stress so that the negative influence of vertical stress on the stability of the roadway is diminished. (4) As shown in Figure 5(d), because the 93 l 07 working face is located in the no. 3 l coal seam, the stress caused by the superposition of the abutment stress of the 93 l 07 working face and the abutment stress of the 93 u 05 working face is very high. As a result, if the upper mining roadway of the 93 l 05 working face is arranged as a gob-side entry, both its location and the supporting method used should be chosen carefully.

Vertical Stress Superposition.
Regarding the extraction of a multiworking face of a CDCS, the stress at the stopes of the surrounding rock mass evolves dynamically and superposes with each other. Figure 6 illustrates  Figure 7 shows that the superposed stress of the inclined seams is transmitted through the coal pillars in the bottom floor. is transmission path follows neither the line along the axis of the coal pillar, nor the line perpendicular to the direction of the floor, but instead follows along a line aligned with the axis of the coal pillar.

Optimization of the Roadway Layout.
After the coal seam is mined, affected by the redistribution of the mining stress field, the floor surrounding rock presents three different states: active limit zone, transition zone, and passive limit zone [26,27]. Taking the horizontal coal seam as an example, its distribution is shown in Figure 8.
Combining with the measured data in Nantun Coal Mine, firstly, the vformula [9] is used to calculate the depth of the floor fracture zone under horizontal conditions to be 7.6 m, which is greater than the thickness of the gangue between the two layers of coal.where L is the distance between the maximum support stress and the working surface  and φ is the internal friction angle between the two coal seams.
Secondly, analyze the approximate distribution of the failure area of the surrounding rock of the floor, taking the inclination of the coal seam into consideration, as shown in Figure 9.
Affected by the mining of the upper 3 coal seams and the 9307 working face, the damage depth of the surrounding rock at the lower mining roadway floor of the 93 l 05 working face is greater than that of the upper mining roadway floor of the 93 l 05 working face. erefore, when the working face is laid out, the distance between the two mining roadway s and the remaining coal columns of the upper layer should be arranged differently.
is section details an optimized roadway layout according to the computed spatial and temporal evolution of stress, especially the vertical stress curve shown in Figure 7. Due to the mining of the 93 l 07 working face and considering that the left side mining roadway of the 93 l 05 working face can avoid the stress concentration area formed by the upper coal columns in the lower coal, the left side mining roadway of the 93 l 05 working face can only be arranged under the goaf of the 93u05 working face and staggered a certain safe distance from the coal column in the spatial position; combined with the analysis of Figure 7, it can be seen that the stress concentration in the coal seam in this area is affected by the mining of the two working faces of the 3 upper coal seam. It tends to develop obliquely to the lower left. erefore, when arranging the right side mining roadway under 93 l 05, it should be spaced apart from the coal columns left by the upper coal. Comprehensive analysis shows that the best two of mining roadway s in the 93 l 05 working face should adopt the interior staggering type (note: the lower working face is drawn along the groove internal staggering layout).
Eventually, an arrangement for the mining roadway of the 93 l 05 working face is determined, which is shown in Figure 10. e upper mining roadway of the 93 l 05 working face is located in the lower stress zone of the 93 u 05 working face goaf. e distance between the top of the upper mining roadway of the 93 l 05 working face and the bottom of the mining roadway of the 93 l 07 working face is 6 m. e lower mining roadway of the 93 l 05 working face is located in the lower stress zone of the 93 u 05 working face goaf. e distance between the low side of the mining roadway of the 93 l 05 working face and the low side of the mining roadway of the 93 u 05 working face is 9 m.

Analysis of the Engineering Effect after Optimization of the
Roadway Layout. Two survey stations are set up to monitor the surface displacement of tunnel along the gob-side entry during the excavation. is allows for the layout optimization effect of the roadway to be examined. e location of each station is shown in Figure 11.
According to the results presented in Figures 12 and 13, the rock deformation surrounding the roadway obeys the    Advances in Civil Engineering following rule: during the excavation, the extent of roof subsidence in the tunnel along the goaf is 101 mm, the largest floor heave is 129 mm, and the largest extent of convergence on both sides of the tunnel is 163 mm. e changes in surface displacement over time monitored by stations 1 and 2 during the excavation are displayed in Figures 10 and 11. e results show that the optimization of the layout of the roadway, to enable stability control for the Nantun coal mine, is feasible.

Conclusion
CDCS has been accompanied by frequent disastrous phenomena, which are related to the multidimensional and dynamic redistribution of the stress of the roadway in lower coal seams. It is therefore necessary to study the spatial and temporal evolution of stress in these roadways and to optimize their layout so as to minimize the risks associated with CDCS mining. In this paper, based on analysis of the engineering and geological conditions of the Nantun Mine, China, a numerical model was developed to study the superposition and dynamic evolution of stress when multiple working faces were successively extracted. e model's results regarding the spatial and temporal evolution of mining     stress distribution during the extraction of the working face of the underlying coal seam were presented and analyzed. ese results show that there are areas with increased, reduced, and intact stress near the stope, after the extraction of the adjacent multiple working faces of a CDCS. e areas with increased stress include the mining stress zone of a single working face and superposed stress zone. e areas with reduced stress exist within the mining roadways and at the edge of the goaf. e mining roadway can therefore be arranged in the area with reduced stress to improve the stability of roadway. e stress superposition of inclined seams that are very close to each other propagates through coal pillars in the bottom floor, and the propagation path follows neither the line along the axis of the coal pillar, nor the line perpendicular to direction of the floor. is path instead follows a line aligned with the axis of the coal pillar.
Finally, based on the computed spatial and temporal evolution of stress, especially the vertical stress distribution, an optimized layout of roadway was proposed. is layout features a reasonable interval between the mining roadway and a minimal proportion of increased stress areas along the mining roadway and is aligned with geological structures.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.