Evolution of Characteristics of the Zone of Rock Loosening with Cross-Sectional Area

Because of the large deformation of surrounding rock mass and the di ﬀ erent deformation characteristics of roadways with di ﬀ erent cross-sectional areas, it is di ﬃ cult to determine the means of support of roadways and the hole-sealing depth of extraction boreholes, which will cause serious roadway deformation and reduce the gas drainage rate. In order to solve these problems, this paper studies the evolution law of the zone of rock loosening around the roadway at four di ﬀ erent cross-sectional areas (15 m 2 , 20 m 2 , 25m 2 , 30m 2 ) by means of the acoustic ﬁ eld tests and numerical simulation. The results revealed three key points: ﬁ rst, the zone of rock loosening around the roadway is symmetrically distributed around the center of the roadway, and its shape is approximately that of a “ butter ﬂ y. ” Second, ﬁ eld tests results indicate that the rock loose zone of 1302 North ﬂ oor mining roadway is in the range of 2.3 – 2.4 m on the side of the roadway and is 2.7 – 2.9 m on the central auxiliary transportation roadway. The simulation results show that the rock loose zone of 1302 North ﬂ oor mining roadway is 2.5m on the side of the roadway and is 3.0m on the central auxiliary transportation roadway. The simulation results under four di ﬀ erent section areas matched the ﬁ eld test results well, and the range of the surrounding rock loosening zone increases with the increased cross-sectional area. Third, the loose zone at the top corner and side of the roadway has a linear relationship with the cross-sectional area, and the loose zone at the bottom corner of the roadway does not change signi ﬁ cantly with the cross-sectional area. These results have signi ﬁ cance for determining the cross-sectional area of mine roadways in the same geological conditions, the sealing depth of the borehole, and the surrounding rock support.


Introduction
During the process of roadway excavation, the original stress equilibrium state of surrounding coal and rock mass is destroyed, and the surrounding rock mass changes from the original state of three-dimensional stress equilibrium to a two-dimensional stress state, resulting in an increase of tangential stress and a decrease of radial stress [1]. The stress of surrounding rock will be redistributed in a short time, and the stress will be concentrated around the roadway. If the concentrated stress value does not exceed the rock's strength, the surrounding rock will be in a state of elastic self-stability. In contrast, if the value of concentrated stress exceeds the strength of rock after falling, the surrounding rock will break, and this will gradually extend from the periphery to deeper layers, until reaching another new state of three-dimensional stress equilibrium [2]. During this process, a range of damage and looseness is initiated in the surrounding rock this is called the roadway-surrounding rock loosening zone.
Because of the requirements of the detailed rules for prevention and control of coal and gas outbursts, regional-outburst prevention measures must be taken in outburst mines. Predrainage of coal seam gas is the most commonly used regional method of prevention of outburst in China. The sealing length of gas drainage boreholes is an important parameter determining the effect of gas drainage. The determination of the reasonable sealing depth and distance of gas drainage boreholes is closely related to the size of the zone of rock loosening. At the same time, the type of roadway support and the length of anchor cable/anchor bolts are directly related to the size of the zone of rock loosening. Therefore, it is important to determine the distribution law of the zone of rock loosening for improving the efficiency of gas drainage, maintaining the stability of the surrounding rock, preventing accidental coal and gas outbursts and deformation of the surrounding rock, and ensuring the safe production of the coal mine [3].
Considerable research has been carried out on the distribution of the loose zone of the surrounding rock. Xie et al. simulated the distribution of fractures of the mining rock mass, using model tests on similar materials, thereby deriving the evolution law of the fracture network and provided insights to the design of deep roadway supports [4][5][6]. Wen et al. studied the influence of weak intercalation on the progressive failure mode of rock surrounding tunnels by using similar material in a simulation experiment and found that weak intercalation increased the range of the failure zone, and this made the stress distribution uneven, which affected the stability of rock surrounding the tunnel [7,8]. Moreover, the location, dip angle, thickness of the weak interlayer, and the distance between the interlayer and the tunnel were important factors affecting the stability of the tunnel. By applying elastic mechanics, Chen et al. derived the distribution of the displacement and stress fields after tunnel excavation and derived the calculation formula for the radius of the zone of rock loosening. Furthermore, they analyzed the influence of the earth stress, support stress, and the firmness coefficient of the surrounding rock on the distribution of the zone of rock loosening [9][10][11][12]. Li revised the theory of a balanced arch, put forward an analysis method to predict the loose pressure of surrounding rock of deep buried double tunnels, compared the results with field monitoring data, and achieved good consistency [13]. He et al. studied rock stability around a site tunnel by using the geological radar method, borehole image method, and infrared imaging technology. They obtained the propagation direction of the stress wave caused by excavation and the range of the zone of rock loosening, so that the site support scheme had the data to support the design of a reliable ground structure [14][15][16][17][18]. Shen carried out a detailed numerical simulation of the stability and deformation of a roadway under different roof support schemes through simulation, taking a deep mine as the experimental background, and proposed a new roadway support scheme, which significantly improved the stability of the surrounding rock of the roadway [19][20][21]. Yu et al. studied the permeability and deformation behaviors of soft rock and sandstones through the experimental method and numerical calculation [22,23]. Based on the M-C criterion, Wang et al. [24] deduced the analytical solutions of stress and surrounding rock in the broken zone and plastic zone of the circular roadway. Zhao et al. [25] studied the distribution of the deviatoric stress field and strain energy density of the surrounding rock under triaxial stress, and the results showed that for the σ z dominant stress field, it is necessary to pay attention to the "X"-shaped expansion of the surrounding rock plastic zone. These previous studies mainly focused on one kind of roadway and determined the range of the zone of rock loosening in their theoretical analysis, utilizing similar experiments, numerical simulations, and field measurements. In contrast, research on the evolution law of the zone of rock loosening under different cross-sectional areas is less common.
The acoustic field tests were conducted on the central auxiliary transportation roadway and the North bottom extraction roadway from the Yuxi coal mine to study the evolution law of the zone of rock loosening around the roadway under different cross-sectional areas. In addition, the rock roadway with different section areas was used to perform numerical simulations, and the relationship between different positions and cross-sectional areas around the roadway is analyzed. Our results have significance for the determination of the cross-sectional area of a roadway, the sealing of extraction boreholes, and the support of surrounding rock.

Theoretical Analysis of Surrounding Rock
Zone of Rock Loosening The rock around the roadway is in one of three states: a zone of rock loosening, a plastic zone, and an elastic zone ( Figure 1; in the figure, b represents the zone of rock loosening, p represents plastic zone and e represents the elastic zone). The roadway cross-sectional area is r 0 , the roadway support stress is Pz, and the original surrounding rock stress of the roadway at infinity is P 0 . The radii of the surrounding zone of rock loosening and plastic zone around the roadway are (R b − r 0 ) and (R p − R b ), respectively. In order to facilitate the calculation, the following assumptions were made: (1) the surrounding rock around the roadway is uniform and isotropic; (2) the roadway is in the hydrostatic stress field, and the lateral pressure coefficient is 1; and (3) the roadway is infinitely long, which can be solved as a plane strain problem.
In the rock surrounding a roadway, the deformation of the elastic zone meets Hooke's law, and the stress of the rock mass meets the following formulae [26].
where p 0 is the original surrounding rock stress of the roadway, R p is the radius of the plastic zone, andσ re is the radial stress at the junction of the elastic zone and the plastic zone. According to the Mohr Coulomb yield criterion, it meets the following formula: where ζ is the slope of the strength line, which can be calculated according to ð1 − sin φÞ/ð1 + sin φÞ;φ is the internal friction angle of the rock mass; and σ c is the uniaxial compressive strength.

Geofluids
Combined with the physical and geometric equations [27], the radial displacement of the elastic region is given by where e is the elastic modulus. For ease of calculation, A is defined asA = ð1 + μÞðσ re − p 0 Þ/r. At the junction of the elastic and plastic zones, the geometric equation can be obtained as follows: In the rock surrounding the tunnel, the total strain in the plastic zone is given by For the rock surrounding the roadway, the volume deformation of the rock mass in the elastic area is small and can therefore be ignored. In the plastic softening and failure areas, there are expansion characteristics. Considering the flow rule of the volume expansion of the rock mass [28], in the plastic area where Δε p r and Δε p θ are the radial and tangential strain increments in the plastic zone, respectively; η 1 is the coefficients related to the expansion of rock mass in the plastic zone, η 1 ≥1, and meets η 1 = ζ = ð1 − sin φÞ/ð1 + sin φÞ.
According to the geometric equation, we get Combined with the radial displacement u e j r=R p = AR p at the junction of elastic and plastic zones, the flow rule in plas-tic zone, and the Mohr Coulomb yield rule, we get According to the static equilibrium equation and boundary condition ðσ e r Þ r=R p = ðσ p r Þ r=R p , the stress expression of the plastic zone can be obtained as follows: In rock surrounding the roadway, the total strain in the zone of rock loosening satisfies the following formula: Considering the flow rule of volume expansion of rock mass, the zone of rock loosening is as follows: where Δε p r and Δε p θ are the radial and tangential strain increments in the zone of rock loosening, respectively; η 2 is the coefficient related to the expansion of rock mass in the zone of rock loosening, η 1 ≥1, generally taken as 1.3-1.5.
According to the geometric equation, we get Combined with the Radial displacement u e j r=R b = AR b f 1 + ð2/1 + η 1 Þ½ðR p /R b Þ 1+η 1 − 1g at the junction of the elastic and plastic zone, the flow rule of the zone of rock loosening [29], the Mohr Coulomb yield rule [30], and the boundary conditions, the stress expression of the zone of rock 3 Geofluids loosening is obtained as follows: In the expression of the zone of rock loosening stress, r is equal to the tunnel radius, and the radial stress of zone of rock loosening is equal to the support stress, P Z . The analytical solution for the zone of rock loosening radius is obtained as follows: Through the above analysis, it can be concluded that the cross-sectional area of the roadway is closely related to the range of the loosening zone of the rock surrounding the roadway. However, in practice, the cross-sectional shape of the roadway is not a regular circle but is mainly an arched cross-section. Rectangular and trapezoid cross-sections are also widely used. Consequently, this paper analyzes and studies the different sectional areas of an arched crosssection.

Field Measurement of Rock Surrounding the
Zone of Rock Loosening 3.1. Overview of the Mine. Shanxi Lanhua Kechuang Yuxi Coal Mine Co., Ltd. (hereinafter referred to as the "Yuxi coal mine") is located in the south Shanxi Province and is southeast of the Fanzhuang general survey area. The shape of the well field is stepped, being 5.1 km wide from north to south, 6.78 km long from east to west, and 29.79 km 2 in area. Its geographical location is shown in Figure 2. The Yuxi coal mine is a coal and gas outburst mine with high outburst risk, a designed production capacity of 2.40 Mt/a, and a service life of 50.7 years. Coal seam 3 is mainly mined within the mine, which is located in the lower part of the Shanxi formation, with a thickness ranging between 5.12 and 7.20 m and an average thickness of 5.85 m. The roof of the coal seam is mudstone, sandy mudstone, and siltstone; the local part is fine-grained sandstone, and the floor is mudstone. The structure of the coal seam is simple, and it is a stable and minable coal seam in the whole area. Geological exploration and observation of the exposed area have established that the buried depth of coal seam 3 is 505-862 m, the permeability coefficient of the coal seam is 0.1032~26.58 m 2 /MPa 2 d, the maximum original gas content is 25.59 m 3 /t, and the maximum original gas pressure is 2.90 MPa.
3.2. Field Test Methods. At present, the commonly used testing methods of rock surrounding a zone of rock loosening in China are [15,31,32] (1) acoustic wave analyses, (2) multipoint displacement meter analyses, (3) seismic waves and geological radar analyses, and (4) borehole camera analyses. At present, the acoustic method is generally recognized as a suitable method for measuring the rock surrounding the zone of rock loosening, and a large number of engineering practices have proved the feasibility of this method.
According to elastic theory, and from the wave equation of elastic wave to the static equation of elastic space problem, the relationship between the velocity of ultrasonic P-wave and S-wave and the elastic parameters of the medium can be obtained [33].
where V p is the longitudinal wave velocity of coal (m/s), V s is the shear wave velocity of coal (m/s), E is the elastic modulus of coal (MPa), μ is the Poisson's ratio of coal, and ρ is the density of coal (kg/m 3 ).
From the above formula, the propagation speed of an ultrasonic wave in the coal body is related to the elastic modulus, Poisson's ratio, and density of the coal body, while the elastic modulus, Poisson's ratio, and density of the coal body are directly related to its compressive strength and compactness. Therefore, the wave speed of the coal body can indirectly reflect the condition of cracking in the coal body, and the change rule of the acoustic time and wave speed at different depths of the roadway can determine the size of the zone of rock loosening around the roadway [34]. Meanwhile, the ground stress reaches the breaking strength of the rock layer, where the roadway is located; therefore, the loose zone starts to develop gradually on the side of the roadway. When the sound wave propagates in rock or the coal seam, its speed will decrease due to the development of fractures, the decrease of density, and the increase of acoustic impedance. In contrast, if the integrity of rock mass is good, the force (stress) is large and density is large, then the propagation speed is also large. Therefore, for a rock mass of the same class, a high measured acoustic wave velocity is indicative of a good integrity of the rock mass and conversely, a low wave velocity indicates that there are cracks in the rock and the rock mass is damaged. The wave velocity of rock mass at different depths from the surface of the surrounding rock is measured by acoustic testing instruments. The depth 4 Geofluids and wave velocity curve are then constructed and the thickness of rock surrounding the zone of rock loosening of the roadway is inferred, using relevant geological data [35].  Figure 3.
The measurement steps of the zone of rock loosening by the acoustic method are as follows: (1) Drilling was undertaken at the field test site perpendicular to the side of the roadway, to a drilling depth of 5 m. Subsequent to the drilling, the hole was cleared of debris and the hole was cleaned with clear water until the discharge water was clear of rock slag (2) The battery was installed in the instrument, the display and circuit of the instrument were checked and the push-pull measuring rod and transceiver were connected. The receiving and transmitting probes were installed at the bottom of the drilling hole through the measuring rod. Additional accessories were inserted into the appropriate position in the   5 Geofluids hole and a water stop plug was used to block the drilling hole, followed by injection of the coupling agent (water) to the end of the measuring rod. There was a continuous water outflow (3) The instrument was initiated to measure the wave velocity of the surrounding rock at different depths using the copper metal measuring rod; four groups of data at each depth were recorded. Data at depth increments of 0.1 m were recorded until the test was completed (4) The average of the four groups of data measured at each depth was calculated. Taking the wave velocity as the ordinate and the distance from the roadway side as the abscissa, the relationship between wave velocity and distance from the roadway side was plotted 3.3. Site Measurement Location. The central auxiliary transportation roadway and the North bottom extraction roadway 1302 in the Yuxi coal mine were selected as the test sites for the analyses of roadway zones of rock loosening (Figures 4-6). The central auxiliary transportation roadway is located in the rock stratum under the floor of coal seam 3. The roadway cross-section is a straight wall semicircular arch, 5.4 m wide, 4.3 m high, and the roadway excavation crosssectional is 20.1 m 2 . The surrounding rock is mainly grayish black mudstone. The core is a long or short column, prone to scaly and fragmentary cracking, shell fracture, and containing plant fossils, pyrite, and chert nodules; the largest nodule is 5 cm.
The North bottom extraction roadway 1302 and its transport roadway are located in the rock floor stratum of 3# coal seam. The roadway section is a straight wall semicircular arch section with a width of 4 m, a height of 3.5 m, and a cross-sectional area of 12.6 m 2 . Gas drainage utilizes an anchor mesh cable support, with a design length of 2157 m. The surrounding rock is mainly black mudstone.
The core is a long or short column, scaly or fragmentary, and the shell fracture contains plant fossils and pyrite nodules, with the largest nodule of 5 cm.

Numerical Simulation of the Evolution of the Zone of Rock Loosening with Different Section Area
During the process of field testing of the zone of rock loosening, due to the limitation of local experimental conditions, only 12.6 m 2 and 20.1 m 2 of the zone of rock loosening were obtained from the side of the roadway. According to the change rule of the range of the zone of rock loosening of rock around the roadway with the change of crosssectional area, simulation software is required to verify the rule obtained from the field data. Consequently, in this paper, the field test results were supplemented and verified by numerical simulation.

Derivation of the Mathematical Model.
Because of the influence of geological conditions, the rock mass surrounding the roadway is heterogeneous and discontinuous and exhibits a complex stress field, with bedding and joints. However, a large area was chosen which can be approximately regarded as an isotropic, homogeneous, body. To simplify the problem, the following assumptions were made: (1) The rock surrounding the roadway is an ideal elasticplastic body, which meets the Mohr Coulomb yield criterion (2) Each rock stratum has a layered distribution, and the rock mass is an homogeneous isotropic body (3) Because the dip angle of the rock stratum is small, it is treated as a horizontal rock stratum (4) The influence of groundwater seepage is not considered

Geofluids
The equilibrium equation of elasticity with solid deformation is where L is the differential operator, σ is the stress, and F is the volume force.

Initial and Boundary
Conditions. The rock failure criterion is taken as the Mohr Coulomb criterion, and the corresponding in situ stress (the average density of rock is taken as 2500 kg/m 3 ), i.e., 16.5 MPa, was loaded on the upper part of the model. A rolling boundary condition was adopted for the left and right sides of the model, and the fixed boundary condition was adopted for the lower part. The initial and boundary conditions of the P Figure 9: The physical model.   Figure 10). Meanwhile, Figure 11 shows the distribution of the stress under different cross-sectional areas. Figure 10(a) shows the results of the numerical simulation of cross-section 15 m 2 , in which the length of the loosened area of the roadside is 2.5 m. Figure 10 Analysis of Figures 10 and 11 shows (1) With the excavation of the roadway, the zone of rock loosening around the roadway is symmetrically distributed around the center of the roadway, and the shape is approximately that of a "butterfly." There are no obvious zones of rock loosening in the floor and roof of the roadway  10 Geofluids the range of the zone of rock loosening of the top and bottom corner is larger than that of the side of the roadway. The range of the zone of rock loosening at different positions with different cross-sectional areas is shown in Table 2 (3) The maximum stress is 8.61 MPa, 8.87 MPa, 9.21 MPa, and 9.34 MPa, respectively, under the cross-sectional area of 15 m 2 , 20m 2 , 25m 2 , and 30 m 2 . The comparison shows that under the same conditions, as the cross-sectional area increases, the maximum stress gradually increases Figure 12 shows the change curve of the zone of rock loosening at different positions as a function of the crosssectional area.

Discussion
Analyses of Table 2, Figures 10-12 lead to the following conclusions: (1) The range of rock loose zone is the largest at the apex angle of roadway and the bottom angle of roadway, and it is roughly symmetrical. Therefore, it can be seen that as the cross-sectional area increases, the loose rock zone tends to develop on the "butterfly wings" (the largest at the apex angle of roadway and the bottom angle of roadway) (2) The linear relationship between the range of the zone of rock loosening and cross-sectional area for the side of the road is y = 1 + 0:1x, and the correlation coefficient is 0.99. For the top angle of the roadway, the linear relationship between the range of the zone of rock loosening and cross-sectional area is y = 3:31 + 0:154x, and the correlation coefficient is 0.95. Therefore, with increased cross-sectional area, the zone of rock loosening of the top angle and the side of the roadway increased (3) With respect to the bottom corner of the road, the range of the zone of rock loosening did not change significantly with increased cross-sectional area. This was because the lithology of rock layer 1 is a finegrained sandstone, and its rock strength exceeds that of other rock layers. Consequently, fractures cannot continue to extend to large depths; they only continue to develop along the stratum until it is in equilibrium

Conclusions
We conducted the acoustic field tests to study the evolution law of the zone of rock loosening around the roadway under different cross-sectional areas. In addition, the rock roadway with different section area was used to perform numerical simulations. The simulation results under four different section areas matched the field tests results well, and the relationship between different positions and cross-sectional areas around the roadway is analyzed. Our conclusions are as follows: (1) In order to measure the range of rock roadway loose circle, the acoustic method is used to test the surrounding rock crack detector CT-2 in the field. According to the changing law of wave velocity, the range of loosening zone can be determined. Among them, the rock loose zone of 1302 North floor mining roadway is in the range of 2.3-2.4 m on the side of the roadway, and in the central auxiliary transportation roadway, the rock loose zone is in the range of 2.7-2.9 m on the side of the roadway (2) The loose rock area around the roadway is symmetrically distributed around the center of the roadway, and its shape is similar to the "butterfly" shape, and the loose rock zone tends to develop on the "butterfly wings." The range of the zone of rock loosening surrounding the roadway increased with increased cross-sectional area. For the side of the roadway, the linear relationship between the range of the zone of rock loosening and cross-sectional area was y = a + BX (a, B are coefficients), and the correlation coefficient was 0.99. For the roadway top angle, the linear  11 Geofluids relationship between the range of the zone of rock loosening and cross-sectional area was y = C + DX (C, D are coefficients), and the correlation coefficient was 0.95 (3) Through the study of the influence of different crosssection area on the range of surrounding rock loose area, the basis for determining the effective sealing distance of the borehole is provided. Through numerical simulation, the results show that: with the increase of cross-sectional area, the range of rock loose zone increases linearly with the increase of cross-sectional area. Therefore, in order to ensure the effectiveness of the sealing effect, it is necessary to change the sealing distance according to the size of the roadway section area, so as to achieve the distance outside the loose area

Data Availability
The data that support the findings of this study are tested by authors. It is provided in the supplementary material.

Conflicts of Interest
The authors declare that they have no conflicts of interest.