Deformation and Failure Characteristics of the Roof in an Unsupported Area during Rapid Driving of Coal Roadway

In order to study the deflection and failure characteristics of the goaf roof, a mechanical model of the goaf thin plate is established and the deflection expression of the goaf roof is obtained. )e results show the following: (1) under the action of single factor, the roof deflection is more sensitive to the interaction of unsupported roof distance and load, but less sensitive to the support force. (2) )e influence degree of each factor on the deflection of the thin plate in the unsupported top area is as follows: unsupported roof distance and load interaction> unsupported roof distance and supporting force> supporting force and load. (3))e roof bending deformation is slow when the unsupported roof distance is within 0–2.3m. When the vacant distance of the roof is more than 2.3m, the bending deformation of the roof is accelerated. Using FLAC3D numerical simulation software, the distribution of vertical stress and displacement under different space distances is analyzed and the reasonable space distance is 2.0m.)rough the application of 150802 machine roadway in Liuzhuang coal mine, the driving speed of the coal roadway is improved and the monthly footage of coal roadway reaches 506m.


Introduction
In the recent years, with the development of roadway excavation and supporting technology and equipment, the speed of roadway excavation has been greatly improved. However, the efficiency and safety of roadway excavation are still low due to the limitation of geological conditions and various production processes of excavation [1,2]. e excavation and support affect the roadway driving speed at a time-consuming ratio of supporting and cutting of 3 : 1 [3]. Most coal mines often adopt cantilever roadheaders and single bolt drills for roadway excavation. e boring roadway operation involves frequent driving and exit of the roadheader, and workers moving the single bolt drill back and forth, which takes up a lot of tunneling time in a low roadway excavation efficiency [4,5].
Much research was conducted to solve the low roadway excavation efficiency. Most research focused on the tunneling of the coal mine roadway integrated unit, continuous mining unit, and related auxiliary equipment in terms of rapid excavation technology and equipment. For example, the study in [6] proposed an integrated excavation and anchoring unit. According to the high-efficiency tunneling and the integrated supporting technology, the parallel tunneling operation line of tunneling, support, transportation, and dust removal has been constructed. After the 1980s, most coal mines in the United States adopted continuous tunneling machines, increasing the advancing speed of the tunneling face [7][8][9].
China first applied bolt supporting technology to coal mine roadways in 1956, which was listed as a scientific and technological development project during the "Eighth Five-Year Plan" period, enabling the development and application of coal road bolt support [10,11]. Under the premises of ensuring the safety of driving roadways, the efficiency of roadway excavation has been improved. For example, the study in [12] established a low-damage continuous beam control roof theory according to the roof deformation instability and support time-effect characteristics of coal roadways and developed a flexible anchoring technology that was not restricted by the height of the roadway. e study in [13] proposed that the high strength, high prestress, and high system rigidity were the core technology, and the large-spaced high-performance bolt support system was suitable for the rapid excavation of coal roadways. e Beijing Mining Research Institute of the Central Coal Research Institute has developed high prestress and strong bolt supporting technology, realizing the safe and efficient support of the bolt with the timely, high initial anchoring force and active support [14,15]. e authors of [16,17] proposed a combined support method combining two or more basic support methods, and selected appropriate support parameters for coupling, so as to control roadway deformation.
In terms of tunneling technology theory, scholars mainly focused on researching the cyclic footage, i.e., the distance between the unsupported roofs. e limited unsupported roof distance and the roof deformation and failure in the unsupported roof area were studied by establishing mechanical models such as roof beams and thin plates [18][19][20]. For example, the study in [21] established a beam structure model, analyzed the key factors affecting the roof stability of the unsupported roof area and the interaction relationships, and simulated a reasonable distance between the roofs. e study in [22] established a thin plate mechanical model, analyzed the roof stability of the unsupported roof area, and determined the limit unsupported roof distance during the tunnel driving. e study in [23] established a mechanical model for roof stability analysis and adopted the difference method to calculate the roof stress distribution law and the unsupported roof distance. According to the conditions of roof stability, the limited unsupported roof distance was obtained. Besides, the reasonable unsupported roof distance was determined using the surplus roof safety factor during roadway excavation. e efficiency of roadway excavation is mainly reflected in the excavation and support. Realizing the parallel operation of excavation and support is the best way to improve the efficiency of roadway excavation. is paper analyzed the rules of roof deflection and subsidence under single factor and interaction through theoretical analysis and determined the size relationship of the factors that affected the roof stability. e reasonable void during the roadway excavation was determined by simulating the geological conditions of the 150802 machined roadway in the Liuzhuang Coal Mine. In terms of the supporting technology, the tunneling anchor was adopted to realize part of the bolt (cable) support. e field application showed that the fast excavation and fast support tunneling operation method greatly improved the tunneling efficiency of the roadway.

A Mechanics Model of the Roof.
After the roadway excavation, the stress of the surrounding rock changed from a three-dimensional stress state to a two-dimensional nonisostatic stress state, the bearing capacity of the rock mass at shallow decreased, and the surrounding rock gradually broke from shallow to deep [24][25][26]. erefore, the destruction of the surrounding rock during roadway excavation could be regarded as the destruction of rock mass at shallow (direct roof ). Figure 1 shows that the thickness of the direct roof is often much smaller than the width of the roadway for large-span roadways. e roof structure is similar to a plate, which can be analyzed using the plate theory [27,28]. For this reason, some assumptions are made for the direct roof of the goaf area and the support affected area: ① the ratio of the thickness of the direct roof to the width of the roadway needs to meet the thin plate condition; ② the two sides of the roadway and the coal body in front of the tunneling head provide sufficient support for the roof, while the supporting force of the bolt (cable) to the roof in the support area is small; and ③ the direct roof of the roadway is stable during the driving process. e direct roof of the unsupported roof area and the support affected area can be analyzed as a continuum, ignoring the discontinuous plastic failure.
According to the above assumptions, a thin plate model of the unsupported roof area is established with three sides fixed and one side simple supported and a direct roof support for the affected area, as shown in Figures 2 and 3 . Figure 3 shows that a is the width of the roadway, b is the unsupported length in the axial direction of the roof, c is the length of the support in the axial direction of the roof, and h is the thickness of the roof.
For a thin plate with three sides fixed and one side supported, the boundary conditions are According to the small deflection bending theory of thin plate in elasticity and the superposition principle [29][30][31], the mechanical model of the roof can be divided into two parts to calculate separately, and then the results of the two parts are superposed: Part 1: the thin plate only acts on a uniformly distributed load q 0 , and the deflection ω of the thin plate is set by the expression of the heavy triangular series, According to the differential equation of the elastic surface of the thin plate: D∇ 4 ω � q 0 , we get 2 Shock and Vibration (3) Substituting into equation (2), the expression for the deflection of the thin plate is Part 2: the thin plate is only affected by the upward bolt support force F in the supporting area. e upward distributed load on the thin plate is (F/dxdy) (m, n are the number of bolts in the x and y directions of the thin inner plate of the support, respectively). erefore, except for the bolt action point (ε, η), the distributed load of the thin plate is 0. Similarly, the deflection of the thin plate is supposed as a trigonometric series (equation (2)), which can be substituted into the thin plate balance differential equation to obtain Substituting into equation (2), the deflection expression of the thin plate is obtained as erefore, the deflection of the thin plate after superposition is expressed as In formula (7), D � (Eh 3 /12(1 − μ 2 )) and substituting formula (7) into the boundary mentioned above, conditions of the thin plate are all satisfied. When calculating the deflection of the thin plate, since the deflection of the thin plate is a heavy triangular series, the convergence is fast. erefore, the first three terms of the heavy triangular series can be selected to meet the accuracy of the thin plate deflection.

e Law of Roof Deformation under Different Influencing
Factors. According to formula (7), the roof deformation under different factors was analyzed. For the convenience of calculation, the roof length c, the roof width a, the roof thickness h, and Poisson's ratio μ of the support area were selected as 4.0 m, 5.0 m, 1.5 m, and 0.4, respectively. e modulus of elasticity is 500 MPa.

Supporting Force F in the Supporting Area.
Under the conditions of q 0 � 10 MPa, b � 4.0 m, Figure 4 shows the flexural deformation of the top plate when the supporting force F is 40 kN, 80 kN, and 120 kN, respectively. e results show that with the increase in the bolt support force, the roof deflection and sinking do not change much, and the peak position of the roof deflection is close to the heading direction of the tunneling in a small range.

A Load q 0 of Overlying Strata on the Direct Roof.
Under the conditions of F � 80 kN and b � 4.0 m, Figure 5 shows the flexural deformation of the top plate when the load q 0 is selected as 5 MPa, 10 MPa, and 15 MPa, respectively. e results show that the maximum deflection appears in the goaf area due to the absence of support. As the load of the overlying strata increases, the deflection and deformation of the roof increases, with the maximum deflection occurring at a position with equal head-on distance from the tunneling.

Unsupported Roof Distance b.
Under the conditions of q 0 � 10 MPa and F � 80 kN , Figure 6 shows the flexural deformation of the top plate when the unsupported roof distance b is selected as 2.0 m, 4.0 m, and 6.0 m, respectively. It can be seen from Figure 6 that when the unsupported roof distance is small, the peak deflection of the roof appears at the junction of the unsupported roof area and the support area because the tunneling head-on mainly controls the roof of the unsupported roof area. With the increase in the distance of the roof, the deflection and deformation of the roof in the roof area increase, and the peak deflection gradually shifts to the right, which in turn drives the roof in the support area to flex further and sink, leading to the decreased roof stability. Figures 4-6 show that the deflection deformation of the roadway roof is more sensitive to the unsupported roof Shock and Vibration 3 distance and the load interaction and less sensitive to the supporting force. If the load of the overlying rock layer has been determined, the distance of the unsupported roof and the supporting force should be determined reasonably to ensure the stability of the roof during the roadway excavation.
To further analyze the deflection and deformation of the roof under the interaction of the distance between the unsupported roof and the supporting force, and the overburden load, the unsupported roof distance and the supporting force, the unsupported roof distance and the overburden load and support are obtained according to formula (7). e response surface of the roof deflection and deformation under the supporting force and load interaction is shown in Figures 7-9 . Figures 7-9 show that the degree of influence on the deflection and deformation of the roof in the descending order is as follows: unsupported roof distance and load interaction > unsupported roof distance and supporting force interaction > supporting force and load interaction. When the unsupported roof distance is in the range of 0∼2.3 m, the top plate flexural deformation is slow. When the unsupported roof distance exceeds 2.3 m, the top plate flexural deformation accelerates. When the supporting force of the roadway roof exceeds 50 kN, the deflection and deformation of the roof decrease quickly. When the unsupported roof distance exceeds 2.3 m and the supporting force is less than 50 kN, the deflection and sinking speed of the roof are fast, leading to the increased control difficulty.   Table 1. e physical and mechanical parameters of the roof and floor of the roadway are shown in Table 1.
e bolt-net-cable support form is adopted in the roadway excavation. According to the bolt (cable) support parameters of Liuzhuang Coal Mine, left-hand threaded metal strong bolts are used for the bolts, and the row spacing between bolts is selected to be 900 × 900 mm, and the anchor preload must be greater than 50 kN. e anchor cable is made of prestressed steel strands with a diameter of 21.8 mm and a length of 9.2 m. e row spacing is 1600 × 1200 mm, and the anchor cable pretightening force is not less than 120 kN. e tunnel section support parameters are shown in Figure 11.

Influence of Unsupported Roof Distance on the Roadway
Roof Stability. In roadway excavation, the roof stability of the goaf area is controlled by the roof of the rear support area and the front coal wall. When the distance of the goaf roof is small, the coal wall in front of the roadway is important in controlling the roof stability of the goaf area. e supporting effect of the roof of the area is not obvious. When the distance of the unsupported roof is large, the roof of the unsupported roof area is controlled by the roof of the rear support area and the front coal wall. e support strength of the roof of the rear support area is greater than the support strength of the front coal wall. e deflection of the roof in the unsupported roof is distorted, showing that the axial roof in the unsupported roof area has a maximum value, which will increase the tensile stress of the roof. When the tensile stress reaches the tensile strength of the tensile roof rock mass, the roof will break and collapse.
To analyze the influence of the unsupported roof distance on the axial roof stability of the roadway, the vertical stress and vertical displacement of the axial roof of the roadway were analyzed using FLAC3D numerical simulation software with the unsupported roof distances at 1.0 m, 2.0 m, and 3.0 m, respectively. e characteristics of distribution evolution are given below.

Influence of Unsupported Roof Distance on the Vertical
Stress of the Surrounding Rock of the Roadway. Figure 12 shows the vertical stress distribution cloud diagram of the surrounding rock of the roadway when the distance of the unsupported roof is selected as 1 m, 2 m, and 3 m. e results show that there is an obvious end effect in the vertical stress distribution of the surrounding rock of the roadway after the excavation, leading to the large rock mass stress gradient near the tunneling face and a leading stress peak in front of the tunneling face. With the increase in the unsupported roof distance, the gradient change in roof rock mass stress is extremely small, and the peak stress decreases from 16.09 M Pa to 16.06 MPa, less than 2‰. erefore, the unsupported roof distance change does not affect the vertical stress distribution of the roadway roof. However, the change in the unsupported roof distance greatly influences the vertical stress of the roadway ledge. When the unsupported roof distance is increased from 1.0 m to 3.0 m, the peak high support stress of the ledge increases from 16.406 MPa to 16.624 MPa, an increase of nearly  Shock and Vibration 5 2%. However, due to the small space-top distance, the distribution of the high-supporting stress area of the siding does not change significantly. When the space-top distance increases from 2.0 m to 3.0 m, the distribution of the high-supporting stress area of the siding increases slightly, and the change in the speed of the peak stress increases, as shown in Figure 13. In order to analyze the radial and vertical stress distribution on different sections of the roadway, three types of roadway radial sections are selected: support area (15.0 m behind the heading), unsupported roof area (2.0 m behind the heading), and stress reduction (10.0 m in front of the heading), as shown in Figure 14. Figure 13 shows that, after the excavation, the magnitude and distribution range of the high stress in the shallow rock mass in the upper part of the roadway support area is large, and the magnitude and distribution range of the high stress of the rock mass in the upper part of the hollow roof area is small. e stress distribution in the range is consistent. e stress distribution in the front of the tunnel is increased due to the disturbance from tunneling.

Influence of Unsupported Roof Distance on the Vertical
Displacement of the Roof. Figure 15 shows the axial roof vertical displacement of the roadway with the unsupported roof distance at 1 m, 2 m, and 3 m. e results show that with the increase in the unsupported roof distance, the roof deformation in the unsupported roof area increases, leading to a further increase in the roof deformation in the support area behind the roadway. When the unsupported roof distance is in the range of 0-2.0 m, the roof does not exhibit obvious bending and sinking phenomenon, and the subsidence is lower than the roof subsidence of the last row of supports of the roadway. When the unsupported roof distance reaches 3.0 m, the inner roof exhibits obvious bending and sinking phenomenon, the maximum value appears at a position of 1.0 m from the tunnel head, and the sinking amount is 11.5% larger than that of the last row of supports of the roadway. erefore, to ensure the safe and efficient production of the excavation roadway, the unsupported roof distance is selected to be 2.0 m.

Geological Overview.
e 150802 machine lane is generally a monoclinic structure, with the belt going uphill in the 1508 mining area in the east, 150802 working face in the west, 150804 working face in the south, 150802 working face in the north, and 151101 working face and 151102 working face goaf up there. Figure 16 shows the 150802 machine lane layout.

Roadway Construction Technology and Process.
e 150802 roadway adopted the complete set of equipment of the rapid excavation system developed by the Taiyuan Coal Research Institute for excavations, as shown in Figure 17.
e specific construction process is as follows: anchor-net support process for roadheader construction: safety inspection (roof, gas, engineering quality, etc.) ⟶ roadheader excavation and shipment ⟶ safety inspection ⟶ net hanging, hanging H steel belt ⟶ temporary support ⟶ construction of Gable antipatch protection net ⟶ roofing anchor rod ⟶ brushing for shipment ⟶ hanging net and hitting two anchor rods (safety inspection runs through the whole process of operation). e 150802 roadway adopts the anchor-net-cable support form during tunneling. When the bolt is installed, each bolt hole requires one roll of MSK2850 and one roll of MSZ2850 anchoring agent. To ensure the     quality of the bolt support, the medium torque is not less than 300 N·m, the anchoring force is not less than 100 kN, the torque is not less than 200 N m when installing in the coal seam, and the anchoring force is not less than 50 kN. When installing the anchor cable, 1 roll of MSK2850 and 2 rolls of MSZ2850 resin anchoring agents for each anchor cable is used. e anchor end of the anchor cable should be anchored in the hard solid rock layer, and the pretightening force of the anchor cable should not be less than 120 kN/piece. In the process of construction anchoring, to increase the speed of the construction support, part of the construction work is carried out by using the on-board hydraulic rig of the tunneling anchorage part (Figure 18), which has the faster drilling speed, lower noise, and better construction environment compared with the manual hand-held pneumatic rig.

Mine Pressure Observation and Effect.
e unsupported roof distance of 2.0 m is applied to the 150802 belt along with the groove. To analyze the convergence and deformation of the roadway during tunneling, the "crosspoint method" is used for monitoring. e measuring station was arranged at 1100 m from the starting point of the roadway. After the station arrangement is completed, the initial monitoring of the roadway convergence and deformation is carried out at the position of the measuring station and then every 24 h. e monitoring results are shown in Figure 19, showing that when the roadway deformation in the rear support zone reaches a stable stage during the 150802 belt tunneling, the maximum relative movement of the roof and floor is 120 mm, and the maximum relative movement of the two sides is 105 mm. e overall roadway is relatively stable, as shown in Figure 20. Before process optimization, the average monthly footage of the roadway was 311 m. After the optimization, the monthly footage of the roadway tunneling reaches 506 m, and the tunneling speed is increased by 62.7%, realizing the safety and efficiency of coal mine tunneling, as shown in Figure 21.

Conclusions
(1) e expression of the deflection of the thin plate was calculated, and the influence of the single factor and the supporting force, the interaction of unsupported roof distance, and the load on the deflection of the thin plate were theoretically analyzed by the mechanical model of the thin plate of the roadway. e analysis results showed that the deflection deformation of the roadway roof under the single factor was more sensitive to the unsupported roof distance and the load interaction and less sensitive to the supporting force. e degree of influence of various factors on the deflection deformation of the thin plate in the unsupported roof area: unsupported roof distance and load interaction > unsupported roof distance and supporting force interaction > supporting force and load interaction. (2) FLAC3D numerical simulation software was used to analyze the influence of different unsupported roof distances on the vertical stress distribution and displacement of the roadway roof. ere was an obvious end effect in the vertical stress distribution of the roadway roof. e change in the unsupported roof distance as an effect of the vertical stress of the roadway roof is small. e position of the leading stress peak is the same (3.0 m head-on in tunneling). With the increase in the unsupported roof distance, the roadway roof subsidence increases. When the unsupported roof distance is greater than 3.0 m, the roof subsidence in the unsupported roof area is more obvious.
(3) e unsupported roof distance during roadway excavation is determined to be 2.0 m using theoretical analysis and numerical simulation calculations. e unsupported roof distance of 2 m is combined with the rapid excavation equipment and applied to the project site. e application shows that the roadway excavation speed is increased by 62.7%, and the monthly footage reaches 506 m.
Data Availability e data used in the field measurement can be obtained from the corresponding author upon request.

Conflicts of Interest
e authors declare no conflicts of interest with respect to the research, authorship, and/or publication of this article.

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Shock and Vibration