Parametric Study on the Ground Control Effects of Rock Bolt Parameters under Dynamic and Static Coupling Loads

State Key Laboratory of Mining Disaster Prevention and Control, Shandong University of Science and Technology, Qingdao 266590, China Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao 266590, China Jiaozuo Coal Company, Henan Energy and Chemical Group Corporation, Jiaozuo 266590, China Tengdong Coal Company, Zaozhuang Mining Group Corporation, Zaozhuang 277519, China


Introduction
With the increase in energy demand and the increasing intensity of mining, shallow resources are decreasing, and the geological and geotechnical conditions of deep mining have become common in mines worldwide. Due to the high ground stress, high ground temperature, and high osmotic pressure, the geomechanical environment of the deep surrounding rock is significantly different from that in the shallow parts of the mine. As mining and underground constructions migrate to deeper levels, stress-induced rock fracturing and failure are inevitable. In some cases, rocks can fail, violently releasing a large amount of seismic energy and causing damage in the form of dynamic disasters [1]. With the expansion of deep coal mining, dynamic disasters such as mine seismicity and rock bursts caused by mining are becoming increasingly prevalent. In deep underground excavations, high stress is the dominant feature for dynamic disaster conditions. However, geological factors can also be a significant contributor [2,3]. Driad-Lebeau et al. [4,5] analyzed the cause of a mine dynamic disaster in France. ey found that the shock wave released the impact energy, indicating the correlation between the impact energy and the stress and elastic energy release rate. e research mentioned above has drawn a series of conclusions by analyzing the causes of dynamic disasters, the stress environment, and the transformation of the mechanical properties of deep rock masses. In deep engineering, the excavation of roadways and working faces will damage the integrity of surrounding rock. e stress environment is changed, and the considerable mining space subjects deep roadways to high ground stress. e stress state and stability of roadways are significantly affected by the mining-induced stress distribution. e above factors have aggravated the occurrence of dynamic disasters in deep roadways.
In a deep roadway, under the joint action of the in situ stress and the mining-induced stress, the mining area and surrounding stress are in an extremely chaotic and unstable state [6][7][8][9]. When a certain amount of energy accumulates, a high-stress concentration zone will form. Cyclic operations at the working face, rock formation breakage, fault slip, and other dynamic events release shock waves that trigger the sudden release of elastic energy in the high-stress concentration zone, which induces large-area vibration of the rock formation and unstable failure. In the process of dynamic disasters, strong disturbance energy will be released, as well as complex original rock stress fields caused by deep mining. e abovementioned stresses jointly constitute the surrounding rock stress field of "high static load + strong disturbance" [10,11]. erefore, the energy type of most deep roadways is dynamic and static coupling loads. e dynamic load (D) comes from the strong disturbance energy released by the dynamic load. ere are three main types of dynamic load in coal mines: (1) the energy generated by the propagation of shock waves in rock strata; (2) instantaneous load (passive dynamic load) generated by dynamic events such as rock formation breaking and fault slip; and (3) shock load generated by high-pressure gas in the center of explosive blasting. While the static load (S) comes from the stress field of the original rock caused by the strata overlying the deep roadway, the dynamic and static coupling loads are the most common stress environments in deep roadways. erefore, the study of the mechanical response of surrounding rock in deep roadways under DSLs is of great significance for deep engineering. Some scholars have deeply divided the sources of deep dynamic loads in coal mines. Dou et al. proposed the principle and prevention of dynamic and static superimposed loads of coal mine [12]. He et al. conducted a numerical simulation study on rock burst induced by a hard roof [13,14]. e main roadway serving the mining face is always located in the coal seam, which generally has relatively weak properties compared to those of the roof and floor rock strata. A database of coal mine rock mechanical properties, which consists of over 4,000 samples from fifty coal seams in ninety mines, was developed by Sun and Peng [15]. According to their work, most coal seams have a uniaxial compressive strength of less than 34 MPa and tensile strength of less than 2.7 MPa. us, it can be expected that the weak properties of coal contribute significantly to the stability of the surrounding rock (or it can be expected that the weak properties of coal are of great significance). e strata structure of the roadway in most coal mines is that the roof or floor is the weak strata, or the roadway is in the coal seam. erefore, such a strata structure has far-reaching significance for the study of the surrounding rock mechanical response of deep roadways under the loading of the DSLs.
With the further study of the bolting of deep roadways, new conclusions have been reached about the mechanical response of the deep roadway support under the DSL bolt. Mortazavi and Alavi [16] studied the response of the bolt with full grouting length under dynamic load. In this study, changes in bolt displacement acceleration and bolt pressure were recorded. Furthermore, the variation mechanism under the dynamic load was analyzed. Li et al. [17] proposed a dynamic simulation model for a cone bolt based on an experimental study; they performed drop weight tests on resin-based cone bolts. eir experiments revealed that the bolt has two energy absorption mechanisms: sliding in the resin and plastic deformation. ese theories reveal the mechanical response of the bolt under the DSLs in detail and explain the mechanical method of the surrounding rock deformation controlled by the bolt in the dynamic load roadway. ese theories reveal the mechanical response of one single bolt under the DSLs. For deep engineering scales, the response of the complete bolt support system can better reflect the mechanics of the surrounding rock in a deep roadway response.
To investigate the causes of the different ground control effects of the different support designs, a roadway-wide numerical model with a fine mesh was built, and the mechanism was analyzed from the perspective of supportinduced tensile failure distributions and roof subsidence. In this study, the roadway stability with 16 different support designs under DSLs was investigated to determine the controlling effect of the four support parameters on ground deformation and failure. Further analysis of the simulation results has been conducted, which contributes to the stability analysis, support design, and optimization under DSL conditions.

Geology and Geotechnical Overview of Zhaogu No. 2 Mine.
Zhaogu No. 2 mine is located in Xinxiang City, Henan Province, China, was chosen as the study site because of the poor stability of its roadways. All panels in this mine are using retreating longwall method to extract coal seams. e coal seam is nearly horizontal with a mean thickness of 6.12 m. e target gateroad for this case study is the roadway in 11050 panel at a depth of 800 m. e panel is approximately 180 m wide along the dip and 2000 m long along the strike as illustrated in Figure 1. A typical geological column based on core logging is shown in Figure 2. e roof strata of this panel are mainly composed of mudstone, sandy mudstone, and sandstone. e immediate roof is a layer of less than 2 m thick mudstone, which would cave and fall into the goaf, following the advance of coal extraction and shield support.
Bolt support simulates the method of prestressed bolts and strengthens the end support. e material of the bolt is high-strength steel bar, and the support scheme is shown in Figure 3. Density is 7500 kg/cm 3 , tensile strength is 225 kN, and Young's modulus is 2.06 GPa. e bolt material elongation is 15%. e breaking load of the bolt material is 170 kN.

Establishment of a Numerical Model.
In this study, the mining operations, including entry development, support installation, and coal-rock mass release energy, are simulated with FLAC 3D , a finite difference numerical simulation software suitable for rock support modeling with embedded structural elements. e numerical simulation model is shown in Figure 4. Currently, the nearly horizontal seam being mined is at a depth of approximately 800 m. As determined by model sensitivity analysis with regard to size and mesh density, the boundary conditions are set according to a previous numerical study of the same mine [18,19]. e immediate roof and main roof of the target entry are composed of mudstone and sandy mudstone, respectively; two ribs and the floor are composed of coal because the entry was driven along the coal seam roofline. e roadway is 50 m long, 4 m wide, and 3 m high, as shown in Figure 1. e model top boundary is loaded by a 20 MPa vertical stress to simulate the overburden pressure by assuming the overlying unit weight is 0.025 MN/m 3 , and no displacement is allowed

Advances in Civil Engineering
in the direction perpendicular to the side boundaries. e in situ stress is simulated by applying stresses of 22 and 16 MPa in the x-and y-directions, respectively. e model rock mass properties [20] are shown in Table 1.
After the completion of the support, the iterative calculation started again. After the simulation reaches the equilibrium, the dynamic analysis will proceed by applying dynamic load to the top of the model. According to previous scholars' modeling methods of dynamic load being only applied on the top surface of the model, the other surfaces of the model were set to static boundary conditions to absorb the stress waves of the dynamic load [21].
is process avoided the secondary dynamic destruction of the model by the internal refraction of the stress wave. en, the dynamic calculation was used, and the model results were recorded when T = 0 s, T = 0.02 s, T = 0.04 s, T = 0.06 s, T = 0.08 s, and T = 0.1 s. e calculation was completed until the dynamic load was applied to 0.1 s. e numerical simulation process is shown in Figure 5.
e four factors of bolt length, bolt diameter, bolt spacing, and grouting length have a significant impact on the support effect. Four levels were set up under each factor, and 16 schemes were generated after optimizing the combination. e four factors were bolt length: 1800 mm, 2000 mm, 2200 mm, and 2400 mm; bolt diameter: 16 mm, 18 mm, 20 mm, and 22 mm; bolt spacing: 600 mm, 800 mm, 1000 mm, and 1200 mm; and grouting length: 600 mm, 1000 mm, 1400 mm, and 1800 mm (corresponding to grouting percentages of 30%, 50%, 70%, and 90%). In this study, the influence of a single bolt factor on the mechanical response of the surrounding rock was analyzed, thus providing a data analysis basis for the optimization of the DSL soft rock roadway support. e support schemes are shown in Table 2.

Determination of the Dynamic Load.
In underground mining activities, the determination of the location of the dynamic load source has specific technical difficulties. e location selection of the source has a significant influence on the surrounding rock of the roadway [20,21]. It is better to choose the simulated dynamic vibration wave to transmit energy in the surrounding rock. Most deep engineering dynamic disasters are mainly caused by the transmission of shock waves in the rock formation. erefore, the model selects the dynamic load application method as a surface application instead of the point-source application. e dynamic load damping is mainly caused by the internal friction of the material and the possible sliding of the contact surface. To reproduce the damping of the natural system under the dynamic load in the numerical simulation, the model adopts the Rayleigh damping setting method. According to previous scholars' calculation methods of QUAD4 Rayleigh damping, we can know that when the damping ratio is 5%, the damping ratio at this time is a damping ratio independent of the dynamic frequency of the dynamic load. e damping ratio of 5% was chosen to offset the uncontrollable energy transfer caused by the different depths of the model rock layer and the frequency of the dynamic load [22][23][24]. e effect of the dynamic load has periodicity, and the dynamic energy of the simulated dynamic load derives from the periodic disturbance of mining at the working face. us, the other parameters of the experimental dynamic load are determined by taking the working face mining disturbance as an example to determine the relevant parameters of the dynamic load. First, the dynamic load of the mining activity is regarded as a shock wave, which is added to the internal nodes of the model in a speed-time course. It can be seen from the theory of an elastic wave that any shock wave can be synthesized by Fourier transformation using several sine waves. Hence, the sine wave is the basic form of the shock wave.
For the sinusoidal shock wave transmitted in the z direction, the particle velocity v(z, t) is from the following equation: where v 0 is the maximum vibration velocity of the particle (maximum amplitude of peak velocity), f is the shock wave frequency, and C is the shock wave velocity. t is the time it takes for the shock wave to cycle once, and z is the propagation speed of the shock wave in the z-axis direction. Some research has calculated and analyzed the microseism events of coal mines with different energy levels [25] and found a larger maximum peak velocity but a lower vibration frequency. When the vibration energy is 1e 4 -1e 5 , the vibration frequency is 2-15; when the vibration energy is 1e 5 -1e 6 , the vibration frequency is 0.5-12; and when the vibration energy is greater than 1e 6 , the vibration frequency is 0.4-5. e action time of the shock wave takes one cycle of the simple harmonic, which is T �1/f. Because f � 10 Hz in the simulation, the corresponding energy level is 1e 4 -1e 5 , which meets the range of the dynamic load energy level in the literature [25]. e magnitude of T is 0.1 s in one cycle. e action time is 0.1 s for one cycle. From [25], we can determine the strain rate of coal mine dynamic disasters, as shown in Table 3. Because the corresponding energy level of the shock wave is 1e 4 -1e 5 and 3, 4, and 5 in Table 3 are all within this energy level range, the middle value of the wave speed range of the three experimental groups is selected to determine the wave speed to 2.5 m/s.

Influence of Bolt Length on the Response of Roadway
Rock. e plastic zone distribution scope of the roadway and subsidence of the roof are the most common and direct indicators for the evaluation of roof stability and roof support design. e parameters of the support bolt are L (bolt length), φ (bolt diameter), Lg (bolt spacing), and S (grouting length). In this simulation, four levels were selected for the support parameters and the impact of variation in the parameters on the surrounding rock of the roadway under dynamic and static loading was studied. e simulated parameters are shown in Table 4. Figure 6 and Table 5 show that Design L 1 and Design L 2 (L = 1800 mm and L = 2000 mm, respectively) have the widest distribution of tensile failure zones. By applying an increase in L, the number of tensile failure zones in the roadway decreases dramatically: 13.1% failure reduction for Design L 3 and 13.8% reduction for Design L 4 under the static

Stratum
Lithology σ t is the tensile strength, Φ is the friction angle, E i is the elastic modulus, V is Poisson's ratio, c is the density of rock, and K is the bulk modulus.
Strain-so ening model establishment   E is the energy, F is the frequency, Pv is the peak velocity, and SR is the strain rate.     Figure 6, the scope of the tensile failure between the roof and two ribs is controlled by enhancing L. Similar to the subsidence results, Design L 3 and Design L 4 show certain control of the tensile failure scope in the roof and two ribs. In addition to the control of the tensile failure scope, as shown in Table 6, the roof subsidence was also reduced by enhancing L. In comparison to the results of Design L 1 , the roof subsidence of Design L 3 and Design L 4 is reduced by 5.18 mm and 9.02 mm, respectively, under the DSLs, and roof subsidence exhibits no significant effect under the static load.

Influence of Bolt Diameter on the Response of the Rock
Surrounding the Roadway. By using the diameter of the bolt as the simulated variable, the bolt diameter simulation was established for four sets. e bolt diameters of the four sets were 16 mm, 18 mm, 20 mm, and 22 mm. e support parameters are shown in Table 7. Figure 7 and Table 8 show all the simulated results of Design φ. By increasing φ, the number of tensile failure zones in the roadway did not decrease dramatically. e results of the four sets of simulations are highly similar. As shown in Figure 7, the roadway tensile failure distribution is highly consistent under the static load or DSLs. Table 8 shows that the differences in the support effects of the four sets of simulations under the DSLs or static load were all within 100. Table 9 shows that the differences in the four sets of roof subsidence simulations under the DSLs or static load were all within 1 mm. Changing the diameter of the bolt has less impact on the roof subsidence.

Influence of the Bolt Spacing on the Response of the Rock
Surrounding the Roadway. By using the spacing of the bolt as the simulated variable, the bolt spacing simulation was established for four sets. e bolt spacings of the four sets were 600 mm, 800 mm, 1000 mm, and 1200 mm. e support parameters are shown in Table 10. Figure 8 and Table 11 show that Design Lg 3 and Design Lg 4 (Lg � 1000 mm and Lg � 12000 mm) have the widest distribution of tensile failure zones. By shortening Lg, the number of tensile failure zones in the roadway decreases dramatically: 31.9% reduction in failures for Design Lg 1 and 29.3% reduction for Design Lg 2 under the static load. Under the DSLs, the number of tensile failure zones in the roadway similarly decreases with a 41.1% failure reduction for Design Lg 1 and 39.9% reduction for Design Lg 2 . In addition to the control effects in the number of tensile failures, as shown in Figure 8, the scope of the tensile failure between the roof and two ribs is controlled by shortening Lg. Similar to the subsidence results, Design Lg 1 and Design Lg 2 show certain control of the extent of tensile failure in the roof and two ribs.
In addition to the control of the scope of tensile failure, as shown in Table 12, the roof subsidence was also reduced by shortening Lg. In comparison to the results of Design Lg 4 , the roof subsidence values of Design Lg 1 and Design Lg 2 are reduced by 35.59 mm (20.5%) and 18.53 mm (10.7%) under the DSLs, respectively, and by 29.56 mm (38.0%) and 24.18 mm (31.1%) under the static load, respectively. Regardless of the type of load, the Lg has a significant effect on roof subsidence.

Influence of the Grouting Length on the Response of the
Rock Surrounding the Roadway. By using the grouting length as the simulated variable, the grouting length simulation was established for four sets. e bolt grouting lengths of the four sets were 600 mm, 1000 mm, 1400 mm, and 1800 mm. e support parameters are shown in Table 13. Figure 9 and Table 14 show that Design S 1 (S � 600 mm) has the widest distribution of tensile failure zones under the static load. By increasing S, the number of the tensile failure zones in the roadway decreases dramatically: a 20.3% reduction in failures unit obtained for Design S 4 under the static load. In addition, new simulation results indicate that Design S 2 and Design S 3 (S � 1000 mm and S � 1400 mm) have the widest distribution of tensile failure zones under the DSLs. In comparison to the results of Design S 2 , the number of tensile failure zones in the roadway of Design S 1 and Design S 4 is reduced by 319 (14.2%) and 203 (9.0%), respectively, under the DSLs. e roof subsidence was also reduced by enhancing S. In comparison to the results of Design S 1 , the roof subsidence of Design S 4 was reduced by 25.84 mm (31.59%) under the static load. Table 15 shows that the roof subsidence decreases with increasing grouting length under static load. However, when the stress condition becomes DSLs, the variation in roof deformation is the same as that of the tensile failure zone. Design S 2 (S � 1000 mm) has the largest roof subsidence under the DSLs. In comparison to the results of Design S 2 , the roof subsidence values of Design S 1 and Design S 4 are reduced by 7.04 mm (4.1%) and 11.61 mm (6.8%), respectively, under the DSLs.

Analysis of the Support Designs
It can be concluded from the simulation results in Section 3 that the difference between Design L and Design φ is not significant in terms of the control effects on the roof subsidence and the tensile failure distribution and quantities. However, one interesting point worth noting is that although L and φ do not have significant control effects on the roof subsidence and the tensile failure distribution and quantities, in this simulation of four factors, the tensile failure is closely associated with roof subsidence. Roadways with small amounts of roof subsidence usually have small numbers of tensile failures and small distribution scopes.
Design Lg has a significant effect on the roof subsidence and the tensile failure quantities and distribution under the static load or DSLs. Shortening Lg is an effective way to increase the stability of the roadway under both static and DSL conditions. According to the suspension theory [26], the purpose of the bolt is to suspend the weak or severely Advances in Civil Engineering broken rock on the overlying hard rock to maintain the integrity of the surrounding rock. After shortening Lg, the number of bolts suspended in the hard rock strata increases, which dramatically increases the strength of the surrounding rock grouting area, and the maximum load limit of the supporting system is significantly increased, thereby controlling the surrounding rock deformation and increasing the stability of the roadway.  φ is the bolt diameter, L is the bolt length, Lg is the bolt spacing, and S is the grouting length.    Lg is the bolt spacing, L is the bolt length, φ is the bolt diameter, and S is the grouting length.   Advances in Civil Engineering 9

Lg
Design S provides an interesting simulation result on the DSLs. e roof subsidence values of Design S 1 is 32 mm more than that of Design S 2 under static load, but the roof subsidence value of Design S 1 under DSLs has decreased by nearly 10 mm compared to the Design S 2 . And, under the DSLs, Design S 2 has the most tensile failure zones and largest roof subsidence. In comparison to the results of Design S 2 , the roof subsidence values of Design S 1 and Design S 4 are reduced by 7.04 mm (4.1%) and 11.61 mm (6.8%) under DSLs. In this simulation, Design S 1 has the worst stability under the static load. In contrast, when the dynamic load acts on the roadway, Design S 1 has the minimum amount of roof subsidence, number of tensile failures, and smallest distribution. When S = 600 mm, the roof has massive settlement subsidence under the static load. In addition, the roof cannot bear a high-stress concentration, and a mass of the stress shifts to the deep part of the surrounding rock to achieve a specific effect of surrounding rock pressure relief [26]. Moreover, when subjected to dynamic load, the lengthening of the steel bar leads to a decrease in diameter whereby the outer end of the bolt is free to yield. e rock bolt has a weak plastic deformation capacity when fully grouted in cement. erefore, the low grouting design creates plastic deformation in the bolt. In a laboratory, rock bolts in concrete cylinders were subjected to free tests to achieve a loading velocity of 10 m/s. e tests demonstrated that the distribution of plastic strain along the length of a grouted rock bolt is not constant when dynamically loaded. e section where plastic yielding was allowed was not fully utilized in any of the cases, opposite to the results in previous static tests that show almost constant elongation of the bolts. e tests also verified that the load-carrying components of the bolt, the nut, and the grouting are reliable when S is the grouting length, L is the bolt length, φ is the bolt diameter, and Lg is the bolt spacing.

Conclusions
In this study, the roadway stability with 16 different support designs under DSLs was investigated with a roadway-wide numerical model. A parametric study was conducted to investigate the controlling effects of the four support parameters on ground deformation and failure. Further analysis of the simulation results has been conducted, which contributes to the stability analysis, support design, and optimization under DSL conditions. According to the simulation results, both Design S and Lg can reduce the extent of the failure of the surrounding rock mass. After shortening Lg, the number of bolts suspended in the hard rock strata increases, which dramatically increases the strength of the surrounding rock grouting area, and the maximum load limit of the supporting system is significantly increased, thereby controlling the surrounding rock deformation and increasing the stability of the roadway. In Design S, under static load, Design S 1 has the most tensile failure zones and largest roof subsidence. Design S 4 is to increase the upper limit of the load of the surrounding rock support system by increasing the anchor length. Design S 1 is to enhance the stability of surrounding rocks through flexible support and timely pressure relief. All two support designs have obtained good simulation results under DSLs. Simulation results of Design S 1 show that flexible support and timely pressure relief can be used as effective control measures for surrounding rock deformation of DSL roadway.
To investigate the causes of the different ground control effects of the different support designs, a roadway-wide numerical model with a fine mesh was built, and the mechanism was analyzed from the perspective of supportinduced tensile failure distributions and roof subsidence. First, all simulation results indicate that tensile failure and roof subsidence have a consanguineous correlation. Roadways with small amounts of roof subsidence usually have small numbers of tensile failures and small distribution scopes. ese two indicators reflect the stability of the rock surrounding the roadway. In addition, Lg (bolt spacing) and S (grouting length) have significant control effects on the roadway rock mass. Lg has significant control effects under both stress conditions. Shortening Lg is an effective way to increase the stability of the roadway and control rock deformation. All the Design S simulation results under the DSLs indicate that the rock pressure relief and the bolt plastic deformation capacity are important factors that affect the stability of roadway under DSL conditions. In the process of support design optimization under the DSLs, the rock pressure relief and the bolt plastic deformation capacity should be considered. ese four factors (shortening bolt spacing, high grouting length, rock pressure relief, and bolt plastic deformation capacity) significantly influence the DSL roadway. ese factors can provide a basis for determining a reasonable support scheme for the DSL roadway.
Data Availability e processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.

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