Multifactor analysis of roof deformation and reasonable determination of the unsupported distance of a coal roadway heading face based on response surface method

This paper is aimed at the problems of multiple factors influencing the roof stability near a heading face and unreasonable values of the unsupported distance leading to a slow excavation speed. The behavior of the direct roof subsidence in the unsupported area is analyzed, and numerical simulation and the response surface method are used to study the key factors affecting the roof deformation and their interaction relations. The results indicate that roof strength is the most critical factor affecting deformation and failure, followed by soft rock thickness, unsupported distance, and support strength. The interaction analysis in Zhaozhuang Coal Mine's 33082 lane shows that it is difficult to control the roof subsidence when the unsupported distance is more than 2 m and the soft rock thickness is more than 4 m. After the unsupported distance is set to about 2 m and the support strength is increased to 0.25 MPa, the excavation speed approximately doubles, and the overall roadway is stable and controllable. By implementing field applications, the rationality of the research approach was confirmed.


| INTRODUCTION
The total length of new roadways in China is more than 12,000 km/year, and the safe and rapid tunneling of underground roadways is required for efficient coal mining. [1][2][3] Roadway heading and supporting technologies have developed rapidly in recent years. Current commonly used coal roadway heading and supporting technology can be roughly divided into three types [4][5][6][7] : (i) continuous shearer and anchor trolley cross displacement tunneling; (ii) excavation and anchor unit integration tunneling; and (iii) cantilever tunneling machine and single drilling rig or anchor trolley combined tunneling. The first two processes limit the extension of the process in most mining areas because of roadway section or geological condition requirements. Because these roadways still use cantilever headers and monosomic anchor rig operation, the excavation speed is slow. [8][9][10] Engineering practice shows that there are two key factors affecting roadway excavation speed. First, the support speed is slow and does not match the cutting speed of the section. Second, the unsupported roof distance is often selected to be small because of limited roof stability. This results in increased boring and support cycle times, but low single-cycle efficiency. Therefore, the problem of slow excavation cannot be solved only by improving the supporting speed, and the maximum empty head distance must be reasonably determined to improve the efficiency of a single operation as much as possible. [11][12][13] Many investigators have researched methods for determining reasonable unsupported roof distances in heading faces. For example, Chen et al. 14 Ma, 15 Yang et al., [16][17][18] and Bi et al. 19 adopted mechanical models such as thin plates and rock beams to study the ultimate unsupported roof distance and the factors influencing the deformation and failure of the unsupported area. In the surrounding rock stress distribution and deformation of heading faces, Kang et al. 20,21 proposed the concept of a supporting stress field in surrounding rock stress distributions and heading face deformations. They analyzed the influence of the angle between the maximum horizontal principal stress and the heading face surrounding rock axial direction and bolt support in the empty area roof control. The analysis elucidated the excavation effect and the surrounding rock stress and heading face displacement distribution laws. Yi et al. 22 analyzed the laws of strain energy transfer and dissipation in deep roadways surrounding rock when considering the objective strain softening and dilatancy behavior, then analyzed the large deformation mechanism of surrounding rock. Guo et al. 23 analyzed the failure mechanics and energy characteristics of coal mass on the basis of confining pressure unloading and axial pressure loading experiments, and showed that rapid unloading was the key factor leading to lateral deformation and expansion failure of coal mass. Zhang et al. [24][25][26] based on the operating vibration signal acquisition system, studied the basic characteristics of microseismic events in the heading face, including the occurrence location, main frequency range, maximum amplitude range, event duration, and the relationship between stress and deformation in the heading face. Zhou et al. 27,28 studied the disturbance effects of deep well excavation through field measurements and numerical simulations. They suggested that the stress magnitude and direction changed significantly near the heading face and that the surrounding rock deformation experienced slow growth, rapid growth, and deformation stability with the advance of the excavation face. The influence of the type of stress field on the stress and plastic failure distributions of the heading surface was studied by Shu et al. 29,30 The roof stability of a heading face is affected by many factors, such as surrounding rock strength, support strength, stress level, and unsupported distance. Prior research has mainly considered the influence of a single factor but has rarely considered the combined effects of geological and technical factors. Therefore, this paper intends to employ the response surface method to analyze the roof deformation of a heading face for multiple factors to find a method to determine its maximum unsupported distance.

| ENGINEERING BACKGROUND
Jinneng Holding Group's Zhaozhuang Coal Mine faces serious connection problems between mining and heading, and improvements to the roadway excavation speed are urgently needed. Therefore, the heading face roof deformation of the well field 33082 lane was studied, and the unsupported distance of the heading face was optimized. As shown in Figure 1A, the Zhaozhuang Coal Mine is located in Changzhi City, Shanxi Province, with a designed production capacity of 8 million t/a mining the No. 3 coal seam. The study area is located at the 3308 working face of the mine's 3-panel area. Figure 1B shows the stratigraphic column of the 3308 working face.
Within the working face, the average thickness of the coal seam is 4.50 m, the thickness of mudstone in the direct roof is 4.80 m, the thickness of sandstone in the basic roof is 9.12 m, and the thickness of sandy mudstone in the floor is 7.20 m. The burial depth of the coal seam is 570-654 m, averaging 612 m. The inclination angle of the coal seam is 0.8-5.4°, with an average of 3.1°. Figure 1C shows the roadway layout of the 3308 working face, in which lane 33083 is the remaining roadway of the previous working face, lanes 33081 and 33082 adopt double roadway headings, and the width of the coal pillar between the roadways is 40 m. Because of the large size of the coal pillar retaining wall, it can be assumed that there is no mutual interference between the two roadways during heading. Figure 1D shows the original support scheme. Full cables with 17.8 mm diameters and 6300 mm lengths support the roof. There are five anchor cables in each row with 1100 × 1000 mm spacings. A cantilever tunneling machine and anchor trolley completed the lane 33082 tunneling and support. Cycle support is excavated and the maximum unsupported distance is 1 m.

| ANALYSIS OF STRESS ADJUSTMENT AND DEFORMATION LAW OF ROOF IN HEADING FACE
The Flac3D numerical software is used to study the stress adjustment and deformation of the heading face roof, providing a basis for the subsequent multifactor parameter analysis and the selection of response values. The  Table 1. The normal displacements of the four sides and the bottom surface of the model are fixed, and a stress boundary is adopted on the top surface. A 14.55 MPa vertical stress is applied to simulate the overburden pressure. The lateral pressure coefficient was set to 1.2. The roadway section is rectangular, with a width of 5.0 m and a height of 4.5 m. According to the size of the roadway section and the influence range of the tunneling face, the model size was width × height × thickness = 55 × 50 × 25 m. The numerical model is shown in Figure 2.
The tunnel is excavated and supported step by step using the FISH programming language. It is divided into 25 excavation and support steps, with 1 m excavation and 1 m support for each step. The bolts and cables are simulated with the Cable structure unit in Flac3D. The support scheme is shown in Figure 1D. The history command was used to monitor the displacement of the middle surface of the roof at section y = 13, and the three-way stress 1 m above the roof's middle surface was used to analyze the evolution of the roof stress and heading face deformation. Figure 3 shows the evolution of roof stress and displacement at the survey station for the heading face excavation. The abscissa of the figure takes the survey station position as the origin. The coordinate value of the surface is negative before it is excavated to the survey station and positive after it is excavated to the survey station.
The heading leads to stress redistribution. Stress adjustment begins to appear at about one hole diameter in front of the driving face (the hole diameter is the circumscribed circle diameter of the roadway, taken as 6 m in this paper), and the stress adjustment tends to be stable one hole diameter behind the heading face. The lateral and axial horizontal stresses 1 m above the middle of the roadway roof first increase and then decrease with increasing operation time step, while the vertical stress always has a downward trend. The roof subsidence begins to noticeably increase one hole diameter in front of the heading face, increasing continuously with distance from the heading face. The surrounding rock  The roof stability of the heading face is affected by the stress environment, surrounding rock strength, and heading support parameters. Therefore, four typical influencing factors, including roof mudstone cohesion, roof mudstone thickness, unsupported distance, and support strength, are selected to investigate the heading face roof stability. The values of each factor are given in Table 2.
Box-Behnken design in the Design-Expert experimental design software was used to study four factors and three experimental design levels, with a total of 29 groups of experimental points. The coding and level settings of each factor are shown in Table 2. Based on the numerical model in Section 3, the maximum subsidence in the middle of the roof section monitored by the model was selected to investigate the influencing factors. The results of the 29 scheme-setting groups and response values are shown in Table 3.
The response surface function of the maximum roof subsidence is obtained as follows using the Design-Expert software for multiple regression analysis: (1)

| Model verification
Goodness-of-fit tests can be used to evaluate the model's reliability, and the judgment index R 2 reflects the difference between the response values and the actual values with a value range is [0,1]. The closer R 2 is to 1, the smaller the difference between them, and the values are identical when R 2 = 1. 31 R 2 is defined as: where S R is the sum of the squares of the regression; S T is the sum of the squares of the total deviation, y* i , y i , and y are the measured and predicted values of the experimental results of group i and the mean value of all experimental results, and n is the sample size, equal to the number of experiments.
The p value reflects each factor's significant degree of influence on the experimental results. If p < 0.05, the factor significantly influences the experimental results. Analysis of variance was conducted on the regression model, and the results are shown in Table 4. p < 0.0001 indicates that the regression effect is very significant, and R 2 = 0.9978 indicates a good fit between the measured and predicted values of the experimental roof's maximum subsidence in each group. Scatter plots for each scheme's measured and predicted values of maximum   Table 4 shows that the roof subsidence of the heading face has significant sensitivity to all influencing factors. Among these, the sensitivity to support strength is the lowest but still significant. The influence of each factor on the subsidence is analyzed individually. For convenience, the median value of each influencing parameter is defined as the value when the coding value is zero, that is, the median values of the mudstone cohesion, mudstone thickness, unsupported roof distance, and support strength parameters, which are 3.0 MPa, 4 m, 2 m, and 0.15 MPa, respectively. The roof mudstone's strength and thickness significantly influence the roof subsidence. Figure 5A shows the change in roof subsidence with cohesion. When the median values of the other factors are fixed, roof subsidence is negatively correlated with mudstone strength (cohesion), and the subsidence decreases rapidly at first and then tends to be stable with increasing cohesion. Figure 5B shows the change in roof subsidence with mudstone thickness. The roof subsidence positively correlates with the mudstone thickness, but the growth rate slows with increasing thickness.

| Influence analysis of a single factor on roof subsidence
The heading and supporting parameters also affect the roof subsidence. Figure 5C shows the variation in roof subsidence with unsupported roof distance. When other factors are at their median value, roof subsidence positively correlates with unsupported roof distance. However, unlike the influence of the mudstone thickness on void roof distance, roof subsidence increases with the increasing unsupported roof distance, and its growth rate increases. Figure 5D shows the change in roof subsidence with support strength. Similar to the influence of mudstone strength on subsidence, roof subsidence is negatively correlated with support strength, and roof subsidence decreases with increasing support strength when the median values of other factors are fixed.

| Interaction analysis of multiple factors on roof subsidence
According to Equation (1) and Table 4, the heading face roof subsidence is affected not only by single factors such as mudstone strength, mudstone thickness, unsupported roof distance, and support strength but also by their interactions. The interactions of various influencing factors on the roof subsidence are analyzed as follows. Figure 6A-C shows the mutual interaction of mudstone roof strength (cohesion) with mudstone thickness, unsupported distance, and support strength of the heading face roof subsidence, respectively. The response surface projection contour focuses on the cohesion of smaller areas. When the cohesion is 5 MPa, the roof subsidence change is small, showing that when the strength of the mudstone roof is low, the interaction of the various influencing factors is even more significant. Therefore, the influence of roof mudstone strength on roof subsidence is much more significant than other factors when the other influencing factors have median values. The roof subsidence under the interaction of roof mudstone support strength and cohesion force is smaller than the other two interaction effects, indicating that increasing the support strength can improve the surrounding rock strength, and there is a coupling effect between them. Figure 6D,E shows the interaction effects between roof mudstone thickness, unsupported distance, and support strength on the heading face roof subsidence. When the soft rock thickness exceeds 4 m, roof subsidence increases noticeably with increasing unsupported distance, while a change in the support strength has little effect. Figure 6F shows the interaction effect between unsupported distance and support strength on roof subsidence. Increasing support strength has relatively little influence on roof subsidence for a fixed unsupported distance. Therefore, it is judged that the impact of the unsupported distance on roof subsidence is greater than the effect of support strength when the other conditions remain unchanged.

| Determination of a reasonable unsupported distance in the heading face
The preceding results show that mudstone strength is the most critical factor, followed by mudstone thickness, unsupported distance, and support strength. When the mudstone's strength is high or its thickness is small, the unsupported distance can be increased, and improving the support strength has little influence on determining the unsupported distance.
Roof deformation can be controlled by adjusting the unsupported distance and support strength while considering the influence of mudstone strength and thickness. Therefore, the response surface method is proposed to analyze the interaction of unsupported distance, support strength, and rock structure to determine the maximum unsupported distance. The roof deformation is analyzed by actively changing parameters such as support strength and unsupported distance and considering the rock structure to determine a reasonable maximum unsupported distance and support strength. The main process is as follows: the single-factor method of the numerical tests determines the key influencing factors → the response surface method is used to study the interaction of key factors → a reasonable parameter range is determined from the roof deformation law or allowable values → the reasonable unsupported distance and support strength are determined.
According to the simulated geological conditions, the roof subsidence increased significantly when the unsupported distance exceeds 2 m and the soft rock thickness exceeds 4 m, the change speed is fast, and control is difficult.

| ENGINEERING VERIFICATION
This research has optimized the unsupported distance and support parameters of roadway 33082 in the Zhaozhuang mine. The design adopts 22-mm-diameter high-strength roof anchor cables with a cable length of 6300 mm. The row spacing is 1000 mm, and each row has five anchor cables. The spacing is 1100 mm, the preload force is not less than 250 kN, and the calculated support strength is about 0.25 MPa, which is significantly improved compared with the original support strength of 0.15 MPa. According to the above analysis, the mudstone thickness is 4.80 m, and the maximum allowable unsupported distance of the roadway 33082 heading face can be set as 2 m, that is, support 2 m after a single cycle driving 2 m. Field observation was carried out on the heading face of lane 33082 to verify the scheme's feasibility. The new support scheme and monitoring scheme are shown in Figure 7.
There is almost no separation in the roof within 150 m from the heading face. The deformation behavior of the roadway roof is shown in Figure 8A, and the maximum deformation of the roadway roof from excavation to stability is less than 50 mm. The stress monitoring result of the roof anchor cable is shown in Figure 8B. The preloading force is 240-260 kN, and the stress is stable at about 250 kN during driving.
It can be seen that the roof anchor cable can effectively control the roof mudstone deformation. Within the scope of the anchor cable support, there is essentially no separation layer, the overall deformation is controllable, the anchor cable experiences a stable force, and the roadway is generally stable. According to the above method, the maximum unsupported roadway distance is determined to be about 2 m. After adopting the heading method of support 2 m after a single cycle driving 2 m and the high prestressed support to improve the support strength, the roadway excavation speed is increased from 180 m/month to F I G U R E 7 New support scheme and monitoring scheme. about 350 m/month on average, and the stability also is improved.

| CONCLUSION
The key factors and their interactions affecting heading face roof deformation are analyzed by numerical simulation and the response surface analysis method to address the problem of heading face roof deformation and unreasonable unsupported distances resulting in a slow excavation speed. The following conclusions are drawn from this study: 1) The stress and deformation evolution of heading face roofs are analyzed. The study found that stress adjustment began at about twice the hole diameter ahead of the heading faces. Heading face stress adjustment stabilized at twice the rear hole diameter. Roof subsidence increased significantly at the start of the position, ahead of twice the heading face hole diameter. The roof subsidence increases continuously with the distance away from the driving face, and the surrounding rock displacement is basically stable when it reaches twice the hole diameter.
2) The interaction between key factors is studied using the response surface method. It is shown that roof strength is the most critical factor, followed by soft rock thickness, unsupported distance, and support strength. When the strength of the soft rock is high or its thickness is small, the unsupported distance can be increased, and improving the support strength has little influence on determining the unsupported distance. Roof deformation can be controlled by adjusting the unsupported distance and support strength considering the influence of soft rock strength and thickness. A method for determining reasonable unsupported distance based on the interaction of key factors is proposed.
3) The maximum unsupported distance of lane 33082 was determined to be about 2 m, and the support strength was 0.25 MPa. Field monitoring shows that the roadway deformation is stable and controllable with increasing unsupported distance by improving the support strength, and the heading efficiency is greatly improved. It is demonstrated that the response surface method can effectively determine a reasonable unsupported distance and support strength of the heading face in practice under specified conditions.

AUTHOR CONTRIBUTIONS
All authors contributed to the study's conception and design. Chao Su and Peng Li performed the data collection and analysis. All authors have read and approved the final manuscript.