Determination and application of the unsupported roof distance in coal roadway driving with the thick and hard main roof

The present study was envisaged to explore the relationship between the stress distribution law of the roof in the unsupported roof area and the unsupported roof distance. In this pursuit, a mechanical model of the immediate roof rock beam under the condition of the thick and hard main roof was established, and the functional relationship between the tensile stress of the roof in the unsupported area and the unsupported roof distance was calculated. Combined with the geological conditions of the 150802 roadway in Liuzhuang Coal Mine, the distribution law of the tensile stress of the roof support end in the unsupported roof area under different supporting forces and the distribution characteristics of the roof stress in the vertical direction were analyzed. From the relationship between the tensile stress and the tensile strength of the roof, the maximum unsupported roof distance during the roadway driving was determined. In order to select the reasonable unsupported roof distance, considering the surplus safety factor of the roof in the unsupported roof area during roadway driving, the unsupported roof distance of the 150802 roadway was found to be 2.0 m finally, and the field application was conducted. Based on the calculation results of this mechanical model, a reasonable unsupported roof distance was selected during the driving, the comprehensive driving speed of the coal roadway in the working face was improved, and the monthly footage was more than 400 m.


Introduction
In recent years, the roadway driving speed not only depends on the modernization of the boring equipment, but also is closely associated with the various production processes (Zhao 2007;Yang 2008;Bai et al. 2011;Xue and Li. 2017). At present, the bolter miner, a newly developed key equipment with the integrated technology of excavation and anchor at home and abroad, needs to be much adaptive in the selection. In particular, the driving speed and safety are still at lower level due to the geological conditions (roof and floor conditions, coal seam pitch, rock hardness, gas, water, etc.), and the roadway driving is still the shortcoming for safe, green and efficient coal mining (Wang 2014;Obeida et al.2006;Wang 2014;Wang et al. 2018). Therefore, after working for a cycle, the boring machine in most coal mines has to retreat to about 5 m behind the driving face to start the manual support operation, which results in the increase of the number of advancing, retreating and manual support operations of the driving machine. Furthermore, it increases the supporting time of the construction bolt, and slows the driving speed. Therefore, the main factors affecting the roadway driving speed are as follows: (1) small distance of the unsupported roof, and low driving cycle efficiency; (2) large time consumption of the roadway support, and low start-up rate of the boring machine. The driving speed of the coal roadway cannot be fully improved by solely optimizing the support technology. In order to alleviate the contradiction between the excavation and replacement, it is also necessary to reasonably select the unsupported roof distance, so as to improve the single operation efficiency of the coal roadway (Ma 2003;Esterhuizen and Tulu.2016).
In order to improve the driving speed of the coal roadway, researchers at home and abroad have mainly aimed at optimizing the roadway support technology, reducing the support time and then improving the driving speed (Lv et al.2016;Ren 2015;Liu and Yang 2019;Zhang et al.2019;Tang et al.2020). The reasonable determination of the unsupported roof distance during the roadway driving has been studied by few researchers. Among them, (Wu 2017) analyzed the mechanical behavior of the thin plate model in the unsupported roof area of the layered rectangular roadway with the thin plate theory as the starting point. He revealed the self-stability evolution law of the roof in the unsupported area of the rapid driving, and studied the influence characteristics of the stress environment on the limit unsupported roof distance. With the roof rock beam in the unsupported roof area of the rapid driving roadway as the main research object, (Ma 2016) studied the limit unsupported roof distance and the factors influencing the deformation and failure of the unsupported roof area using theoretical analysis, numerical simulation and field measurement. In order to determine the unsupported roof distance of roadway driving when the roof is broken, (Tang et al. 2013) put forward a test method to determine the unsupported roof distance, and obtained the reasonable data of the unsupported roof distance of the roadway driving by combination of the numerical calculation and industrial test. (Yan et al. 2020) established the roadway roof stability model using the finite difference method (FDM), and proposed a new method to determine the unsupported roof distance of the coal mine roadway. (Fan 2016) analyzed the influence of the unsupported roof area on the roadway stability with the numerical calculation method, and determined the reasonable unsupported roof distance.
The consideration of the influencing factors for roof stability in the unsupported roof area is relatively singular in the above research results. Based on the existing research results, the present study proposed a method to determine the unsupported roof distance. By establishing the mechanical model of roof rock beam stability analysis based on the thick and hard main roof, a relationship between the friction resistance and the support strength between the support area and the immediate roof in the unsupported roof area was established. Subsequently, according to the judging conditions of the tensile stress and tensile strength of the roof, the maximum unsupported roof distance under the different support force conditions was obtained, and the reasonable unsupported roof distance was determined by considering the surplus safety factor of the immediate roof during roadway driving. The method was verified by an example and a field industrial test.
The results show that it was feasible to calculate the unsupported roof distance using this method, which provides an important theoretical basis for the rapid excavation of the coal roadway.

Mechanical model of roof in driving face
After roadway excavation, the stress of the surrounding rock is redistributed. The surrounding rock on the roadway surface changes from the three-way stress state to the two-way stress state. The strength of rock mass is greatly reduced and the bearing capacity is weakened (Chen et al.2011;Zhang 2018;M. Cai and P. K. Kaiser 2014). Therefore, the immediate roof of the roadway is prone to collapse under the action of overlying rock load. However, when the basic roof has a large thickness and strength, the roadway span and the length of roof in the unsupported roof area are relatively less, when compared with the bearing capacity of the basic roof, and it is difficult to collapse. Therefore, the immediate roof is the key to control the surrounding rock of the roof in an unsupported roof area during the excavation. In the theoretical calculation process, the overlying rock load was not considered, and the section was made along the axial direction of the roadway driving. The headward influence area was divided into support area, unsupported roof area and coal wall support area. The immediate roof of the middle section of the roadway width in the driving face area was selected as the research object. The mechanical model of the immediate roof is shown in Fig. 1 . Since the mechanical properties of the roof rock were improved after the bolt (cable) support was applied to the roof of the support area, the bearing capacity and anti-deformation capacity of the roof in the support area and the unsupported roof area were different. Under the immediate roof weight, it was easy to cause a vertical upward static friction resistance S F between the support area and the unsupported roof area, so as to ensure the stability of the roof in the unsupported roof area. In order to calculate the relationship between the roof stress distribution and the unsupported roof distance, the length of the support area and the support section of the coal wall in the mechanical model in Fig. 1 was regarded as the unit length, and the static friction resistance S F was regarded as the upward tangential force on the support end of the roof in the unsupported roof area, and it can be represented as a beam structure with the right end fixed and the left end subjected to the tangential force, as shown in Fig. 2. According to the static balance, the static friction resistance of the roof support end in the unsupported roof area is given by Equation (1).
where, G q is the uniform load of the immediate roof, f q the force provided by the bolt (cable) in the support area (regarded as the pre-tightening force), and L and h are the length and thickness, respectively, of the immediate roof in the unsupported roof area.  Fig. 2, according to elastic mechanics, the stress function is given by Equation (2).
where, f1(y) and f2(y) are arbitrary functions related to y.
Substitute (2) The stress component can be obtained from Eq. (6): According to the boundary condition: On substituting Eq. (7) into the above boundary condition, then: The inertia moment of the beam section is Considering the mechanical characteristics of the rock materials that are subjected to compression instead of tension, the stability of the immediate roof is mainly controlled by the tensile stress. When the tensile stress exceeds the tensile strength, the immediate roof is subjected to the tensile failure and instability (Liu et al.2019;Yao et al.2007;Ma 2014;Ju 2018). Therefore, in order to ensure that the roof will not experience the tension damage during the driving, the tensile stress of the roof should not exceed the tensile strength, according to the roof stability condition: In order to analyze the relationship between the roof stress and the unsupported roof distance, the axial stress According to the judging conditions of the roof stability, the tensile failure occurs, when the tensile stress of the roof exceeds the tensile strength. Therefore, in order to obtain the maximum unsupported roof distance under the action of the roof support end f q in the unsupported roof area, the condition that the tensile stress and the tensile strength of the roof are equal is taken as the condition for the maximum unsupported roof distance. Eq. (11) is substituted into Eq. (9) to calculate the distance from the support end, when the tensile stress of the roof reaches the tensile strength as given by Equation (12).
where, the supporting force of the roof support end shall meet the following conditions: At this time, the tensile stress of the roof exceeds the tensile strength, since the distance from the support end of the roof in the unsupported roof area reaches . In order to ensure that the roof in the unsupported roof area will not be damaged during the roadway driving, the maximum unsupported roof distance is given by Equation (13).  As shown in the Figure 3, the distribution of tensile stress curve of the immediate roof and the distance from the support end of the roof was of quadratic function type. With the increase in the distance from the roof support end in the unsupported roof area, the distribution of the tensile stress increased initially and subsequently decreased. The tensile stress of the roof reached the peak at the symmetry axis. In the area, where the tensile stress of the roof increased, when the distance from the support end `increased, the tensile stress of the roof increased nonlinearly and the surplus safety factor decreased. When the force f q at the support end of the roof in the unsupported roof area increased, there was a decrease in the peak value of the tensile stress of the roof and the symmetrical axis shifted to the left; the distribution characteristics of the tensile stress curve were "wide range of left shift on the right side of the symmetry axis" and "small range of right shift on the left side of the symmetry axis", and the critical unsupported roof distance increased.
In order to further reasonably determine the unsupported roof distance during the roadway driving, the relationship between the support end force f q of the roof in the unsupported roof area and the corresponding maximum unsupported roof distance lm was calculated by using the roof stability criterion (Table 1), and the relationship curve between these two was obtained by fitting (Fig. 4). As shown in Fig. 4, with the increase in the support end force f q , the maximum unsupported roof distance during the roadway driving increased nonlinearly. Therefore, it was necessary to select the unsupported roof distance reasonably considering to the engineering geological conditions of the roadway. Overlying strata breaking and mining-induced stress evolution in the working face…    Therefore, when the unsupported roof distance was 3.4 m, tension damage could possibly occur on the immediate roof of the mudstone; when the distance was 2.7 m, the immediate roof of the mudstone would not experience the tension damage, but the surplus safety factor was small. The unsupported roof distance was finally determined to be 2.0 m, considering the roof stability and the convenience of labor construction organization.
In order to analyze the convergence of the roadway deformation, when the unsupported roof distance was 2.0 m, the "cross measuring point method" was used to observe the roadway convergence during the during of the 150802 working face. The observation results are shown in Figure 8. As revealed by the deformation convergence curve of the roadway, the relative displacement of the roof and floor was 58 mm, the relative displacement of two sides was 83 mm, and the immediate roof and two sides of the roadway were relatively stable (Fig. 9).The maximum unsupported roof distance of the roadway is 2.0m, which increases the speed of fully mechanized coal roadway excavation at the working face and achieves a monthly footage of more than 400m (Fig. 10). (1)In the roadway excavation, the roof stability in the unsupported roof area is mainly controlled by the support force of the front coal wall and the bolt support force of rear support area. When the unsupported roof distance is large, the roof stability mainly depends on the bolt supporting force. Therefore, in order to improve the driving speed of the coal roadway and reduce the start-up rate of the boring machine during the driving (less advance and more retreat), increasing the unsupported roof distance, i.e. the cyclical footage, is an important way to realize the rapid driving of the coal roadway, while selecting the high preload bolt for support.
(2)By establishing the mechanical model of roof rock beam, the immediate roof stress in the unsupported roof area was solved, and the distribution law of the immediate roof stress in the unsupported roof area was obtained.
Subsequently, the relationship between the unsupported roof distance and the position of the roof depth under different supporting forces was obtained. The stability of the roof in the unsupported roof area was determined according to the comparison of the roof stress and the tensile strength, and the corresponding maximum unsupported roof distance was determined. Combined with the surplus safety factor of the roof under different unsupported roof distances, the reasonable unsupported roof distance during roadway driving was selected.
(3)The results of engineering application show that this mechanical model can be used to calculate the reasonable unsupported roof distance. During the roadway driving, the roadway roof and floor and two sides exhibited a sound stability as suggested by the monitoring of the roadway convergence. This can effectively improve the driving speed of the coal roadway and alleviate the contradiction between the excavation and the replacement.