Failure Mechanism for Surrounding Rock of Deep Circular Roadway in Coal Mine Based on Mining-Induced Plastic Zone

Work Safety Key Lab on Prevention and Control of Gas and Roof Disasters for Southern Coal Mines, Hunan University of Science and Technology, Xiangtan, Hunan, China Hunan Provincial Key Laboratory of Safe Mining Techniques of Coal Mines, Hunan University of Science and Technology, Xiangtan, Hunan, China School of Resource, Environment and Safety Engineering, Hunan University of Science and Technology, Xiangtan, Hunan, China


Introduction
With the increasing shortage of coal resources in shallow depth, the mining depth of coal mine in China is increasing at a speed of 10-25 m per year.Currently, China has 47 coal mines more than 1000 m deep [1][2][3].Deep coal mining at 1000 m in other countries like Poland, Germany, Britain, and Japan is also common [4].Compared with shallow mining, deep coal mining is confronted with some complicated problems such as large deformation, rockbursts, and water hazards [5][6][7][8].Among them, the large deformation and failure of deep roadways threaten seriously mining production and safety [9].
In order to minimize the disasters, the first thing to be solved is the clarity of the failure mechanism for deep roadways or deep rock.In recent years, scholars have carried out a lot of research on it by using numerical simulation, model testing, theoretic analysis, etc.For example, Dolezalova et al. [10][11][12][13][14][15][16] used FEM, FLAC 3D , FDEM, and 3EDC to simulate stress distribution and failure evolution of deep engineering, respectively.In view of the nonlinear problems of large deformation occurring in a deep soft rock roadway, He [17] adopted the material point method (MPM) to simulate the large deformation and failure process of deep rocks.Geomechanical model test is also an important way to investigate the failure behavior of deep surrounding rock.Sun et al. [18][19][20] conducted large-scale model tests.For theoretical analysis, Wang et al. [21] developed a dynamic failure constitutive model to computer deep large deformation, and Zareifard and Fahimifar [22] deduced an analytical solution for the stresses and deformations of deep tunnels considering the damaged zone.By field detection, the failure characteristics of the deep rock were also obtained [23,24].Zhao et al. [25][26][27][28] performed rock creep tests under multilevel load and revealed the nonlinear relationships between the instantaneous strain, viscoelastic strain, viscoplastic strain, and high deviatoric stress.
Large deformation and failure of deep roadways are not only related to high stress and weak rock masses but also closely associated with the mining-induced pressure (the side and front abutment pressure); thus, the influence of mining is sometimes a nonignorable factor [29,30], whereas limited research studies [31,32] have been carried out on the damage and failure of deep roadways subjected to mininginduced pressure.
Although the deformation and instability of deep roadways have been studied, the failure mechanism is still far from being complete and satisfactory.
e previous research [33,34] shows a close relation between the range and shape of the plastic zone and the stability of the roadway.Moreover, the plastic zone will be extended under the external extra load, which would result in the increase of unrestrained deformations and deterioration of the surrounding rock strength [35][36][37][38][39][40].erefore, the distribution and evolution of the plastic zone around the deep roadway under the secondary stress field is key to investigate its failure mechanism.In this work, the morphological evolution of the plastic zone and the relationship between the morphological indexes proposed and the stability of surrounding rock were explored.

Failure Characteristics of Deep Roadway under Mining-Induced Pressure in Coal Mine
For deep roadway, the high geostress and the intense mining activities nearby mainly lead to a quite nonuniform, complex stress field, which causes severe failure of the mininginfluenced deep roadway.e main failure characteristics of this kind of roadway are as follows: (1) e roadway roof subsides sharply, which can reach 500∼1200 mm, as shown in Figure 1

Evolutionary Laws of Morphology for Plastic Zone around Deep Roadways under
Mining-Induced Pressure e deep gate roadways are often subjected to mining influence from their own working face and adjacent excavation, which contributes to the superposition of the initial stress field, abutment pressure, and other dynamic loads.erefore, the regional stress field of deep gate roadways is quite complex.In order to solve problems conveniently, the following assumptions are made: (1) e length of the roadway along the horizontal direction is infinite, with a circular cross section, the radius R 0 , and the buried depth H ≥ 20R 0 .(2) e surrounding rock is considered the isotropic, homogeneous medium and an incompressible material in plasticity.(3) e initial maximum and minimum principal stresses of the roadway are P 1 and P 3 , respectively, which are parallel to the coordinate axes, without consideration of the supporting force.(4) Two parameters D ς1 and D ς3 (i.e., mining coefficients for the maximum and minimum principal stresses) that characterize the effect of mining on the initial principal stress are introduced.e principal stress field of the roadway changes with mining activities except for the stress direction.e mechanical model of the roadway is shown in Figure 2, and the surrounding rock can be divided into the plastic zone (radius equal to R p ) and elastic zone from inside to outside.

Boundary Equation of Plastic Zone (the Principle Stresses Parallel to Coordinate Axes).
e pressure (in Figure 2) acting on the surrounding rock is decomposed into two cases I and II, as shown in Figure 3.
For Case I, according to the theory of elasticity [17,21], the elastic stress field of the roadway surrounding rock subjected to uniform pressure is as follows: where σ r and σ θ are the radial stress and tangential stress at any point in surrounding rock under polar coordinates, respectively, and r represents the radial coordinate of this point.For Case II, the stress field of the surrounding rock is as follows:

Advances in Civil Engineering
where τ rθ is the shear stress in polar coordinates and θ is the tangential coordinate of the point.After superposition of the stress elds of surrounding rock in two di erent cases, the elastic stress eld of the circular roadway subjected to mining-induced pressure can be obtained as follows: In terms of the literatures [21,22], the polar expression of the Mohr-Coulomb yield criterion is where c denotes the cohesion of the surrounding rock and φ indicates the internal friction angle.Assuming that m D ς1 P 1 + D ς3 P 3 , n D ς3 P 3 − D ς1 P 1 , w R 2 0 /r 2 , and t n cos 2θ, substituting (3) into (4), the implicit function referred to r and θ is obtained as follows [41]: When f(r, θ) 0, it becomes the interface between the elastic and plastic zones of the deep roadway, i.e., the equation for boundary of the plastic zone.Especially for P 1 P 3 and D ς1 D ς3 1, the radius of the plastic zone around the circular roadway under uniform stress eld can be obtained from formula (5), which is

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Boundary Equation of Plastic Zone (the Principle
Stresses with a Certain Rotation Angle).e engineering practice shows that not only the magnitude of principal stress of the roadway but also the direction of that will be changed due to the nearby coal mining.It is assumed that the de ection angle of the maximum principal stress D ς1 P 1 is β relative to Figure 2, and the counterclockwise direction is positive.A new coordinate system x ′ − y ′ is established, as shown in Figure 4.
In the new and old coordinates, the polar coordinates of any point A in the surrounding rock are (r ′ , θ ′ ) and (r, θ), respectively.It is seen from Figure 4 that the rotation angle of the new coordinate axes relative to the old ones is β.
In the new coordinate system, the boundary equation of the plastic zone around the deep roadway under mininginduced pressure is similar to formula (5), given as follows: where m D ς1 P 1 + D ς3 P 3 , n D ς3 P 3 − D ς1 P 1 , w ′ R 2 0 /r ′ 2 , and t ′ n cos 2θ ′ .
Note that the relationship between the new and old polar coordinates of any point A is r ′ r and θ ′ θ − β; therefore, the implicit equation for the boundary of the plastic zone under de ection of the principal stress eld can be obtained from formula (7), given as follows: where w R 2 0 /r 2 and t 1 n cos 2(θ − β).

Morphological Evolution of Plastic Zone around Roadway
under Mining-Induced Pressure.Based on formula (5), the evolution of the plastic zone and the failure of surrounding rock of the deep roadway under mining-induced pressure were discussed.e diagrams of plastic zone distribution were drawn (Figure 5).In Figure 5, the parameters are set as follows: R 0 2 m, c 3 MPa, φ 25 °, and P 1 P 3 20 MPa.It is shown in Figure 5 that the pressure caused by coal mining has signi cant e ect on the distribution of the plastic zone around the deep roadway.
e shape of the plastic zone varies with the increase of the pressure di erence between horizontal and vertical direction, from circle to ellipse, rounded rectangle, and butter y shape.Except for the butter y shape, the dimension of the other three plastic zones is generally between 2.6 m and 3.2 m, without signi cant di erences.In contrast, the plastic radius of the butter yshaped plastic zone increases greatly in the inclined direction between the maximum and minimum principal stress due to the formation of the plastic wing, and the maximum plastic radius occurs nearby the bisector of the two directions.
Due to the in uence of mining, the butter y-shaped plastic zone around the deep roadway is more likely to occur.It is observed from Figure 5(a) that, with the increase of the vertical mining coe cient for the maximum principal stress, the plastic wings form and experience a rapid expansion, which present the slender type.For example, the size of the plastic wing grows exponentially during D ς1 changing from 2.5 to 2.8, with the maximum plastic radius (r p,max ) of 15 m. is demonstrates that the plastic damage of rock masses within this area is very sensitive to the mining coe cient.Even if the changes of mining in uence are small, it may also cause serious localized deformation and failure of the surrounding rock mass.e phenomenon that the shear deformation and failure often occur at the top or bottom corner of the deep roadway under the mining-induced pressure is proved theoretically by the formation and nonlinear extension of the plastic wings, which also shows that the deformation of the mining-in uenced roadway is larger than the ordinary one.us, it is quite di cult to ensure the stability of the roadway.If the direction of the principal stress eld for the miningin uenced roadway rotates, how the morphology of the plastic zone distributes and what is the relationship between the stability of surrounding rock and the morphological characteristics of the plastic zone should be investigated.e distribution diagram of the plastic-zone boundary around the circular roadway is plotted by formula (8), as shown in Figure 6.
It is found from Figure 6(a) that when the maximum principal stress D ς1 P 1 is perpendicular to the roof stratum of the roadway (i.e., β 0), the maximum depths of plastic damage mainly exist at the top and bottom corner, while the range of the plastic zone in the roof is quite small.With the increase of the de ection angle β of the maximum principal stress, the plastic damage of the roadway roof is gradually enlarged, and consequently, the stability of the roof is also deteriorated, as shown in Figure 6(b).
In Figure 6(c), the maximum principal stress is de ected at β 50 °, while the four plastic wings are just perpendicular to the sidewalls, oor, and roof.Under the ultrahigh stress eld (D ς1 P 1 42 MPa) caused by strong mining, the depth of the plastic wings can reach up to 14 m; therefore, oor heave, roof sinking, and side wall extrusion often occur in the deep mining-a ected roadway.It should be pointed out that if the rock mass structure of the roof is poor or the support is improper, the caving risk of the roof rock mass within the plastic wing will be very high.e plastic wings rotate with the continuous rotation of the maximum principal stress, and the area of the plastic zone in the roof decreases gradually, as shown in Figure 6(d).

Malignant Expansion of the Plastic
Zone around a Roadway.Figure 7 shows the e ect of D ς1 on the plastic radius r, and the necessary parameters are set as follows: R 0 2 m, c 3 MPa, φ 25 °, and D ς3 1. e values of r are all taken from the intersection of the plastic wing in the rst quartile and the direction of θ π/4 to represent the maximum plastic radius r p,max .It is seen from Figure 7 that whether, for low stress or for high stress, the curves all can be divided into two stages.During the rst stage, the plastic radius keeps increasing near-linearly as the mining coe cient for the maximum principal stress raises, and r can be stabilized at a certain value.When D ζ1 exceeds the critical value D ζc , the second stage starts.Clearly, the growth rate of r increases rapidly and r approaches to in nity nally, which shows that the malignant expansion of the plastic zone occurred.Here, D ζc is called the critical mining coe cient.e greater the initial stress, the smaller the value of D ζc , which indicates that the mining-in uenced roadway is more likely to produce malignant expansion of the plastic zone under high stress.
Figure 8 shows the relationship between the radius of the plastic zone and the mining coe cients for the maximum and minimum principal stresses under nonuniform high stress, where P 1 P 3 20 MPa.When D ζ3 takes a larger value (3∼5), the plastic radius r decreases from the in nite value to the minimum value (at the neutral line) with the rise of D ζ1 , and then it increases to a relatively small value.e neutral line indicates the congruent relationship between D ζ1 and D ζ3 when r takes the minimum value.It means that the radius of the plastic zone around the roadway reaches the minimum when the pressure distributes uniformly.e existence of the neutral line proves that one of the principles for the design and support of the deep roadway under mining-induced pressure is that the stress environment of surrounding rock should be improved, and its nonuniformity is required to be minimized for reducing the depth of plastic failure.6 Advances in Civil Engineering Based on the above analysis, the following de nitions are made: (1) e malignant expansion of the plastic zone (MEPZ): the radius r of the plastic zone increases rapidly with the increase of a certain variable ξ; nally, r cannot be stable at a certain magnitude but grows in nitely.is can be expressed as lim ξ → ξ e r(ξ) ∞, where r(ξ) is the function of the plastic radius and ξ e denotes the upper limit of the variable ξ.
(2) e criticality for the malignant expansion of the plastic zone (ξ c ): the plastic radius r increases gradually with the growth of the variable ξ; when ξ increases to a certain value ξ c , the growth rate of r increases rapidly, and eventually r is approaching in nity.Here, ξ c is called criticality for the malignant expansion of the plastic zone.

Index System for Morphological Characteristics of Plastic Zone around a Circular Roadway
In this section, the index system for characterizing the morphological features of the plastic zone around the circular roadway was established using the geometric morphology theory.

Main Indexes for Morphological Characteristics of the
Plastic Zone.Generally, the elastic or plastic solution for the underground roadway is treated as a plane problem, and the plastic failure eld obtained is also a 2D gure.erefore, the indexes established and related parameters are all for the 2D diagrams.

Uniformity Coe cient (U c ).
e uniformity coe cient U c is used to characterize the di erences in plastic failure depths on the plastic zone boundary around the circular roadway along any direction from 0 to 2π. e closer the value of U c is to 1, the smaller the di erences in plastic radius of the plastic zone in all directions are, the closer the shape of the plastic zone is to circle.Generally, the roadway with the circular plastic zone is more stable and has better integrity than those with the heteromorphic plastic zone with the same extension area.U c can be expressed as follows: where P b is the perimeter of the plastic zone boundary around the roadway and A p denotes the area enclosed by the plastic zone boundary.

Extension Factor (E f ).
e extension factor E f is de ned as the ratio of the area of the plastic zone of the surrounding rock to sectional area of the roadway.e extension factor re ects the relative size of the plastic zone extension.e larger the E f is, the larger the range of plastic failure of the surrounding rock is, i.e., the more unstable the surrounding rock mass is.e index of E f is not only related to the size of the plastic zone but also associated with the dimension of the tunnel.Hence, it is applicable to comparatively analyze the plastic zones around roadways with di erent sizes.E f can take the following form: where R 0 is the radius of the roadway section; A 0 is the sectional area of the roadway; and A p0 represents the area of the plastic zone, and it can be obtained from A p0 A p − A 0 .

Equivalent Radius (R eq,p ).
e equivalent size and range of the plastic zone can be described by the equivalent radius R eq,p that is one of the important geometric parameters for intuitively re ecting the macroscopic geometry of the plastic zone.e plastic zone with irregular shape can be transformed into an equivalent circular one in terms of the principle of the same area, shown as the dashed line in Figure 9.
e equivalent radius R eq,p is calculated by the following formula:

Extended Depth Coe cient (E dc ).
In order to characterize the relative size of the extended depth for plastic limit, the extended depth coe cient E dc is introduced.It can be written as follows: where d max is the maximum plastic radius of the roadway.e greater the E dc is, the more serious the plastic failure of surrounding rock is at the direction in which d max is located.8 Advances in Civil Engineering Although the di erent roadways have the same E dc values, the d max values are not equal.us, the local stability of the surrounding rock is also di erent.

Irregular Shape Coe cient (I sc ).
e shape of the plastic zone is closely related to the stability of the roadway.Usually, the roadways with an irregular plastic zone are less stable than those with the regular one due to weak regions in surrounding rock.en, the index I sc is used to characterize the degree of irregularity for the shape of the plastic zone.It is de ned as the ratio of the maximum plastic radius to the minimum one, given as follows: where d min is the minimum plastic radius of the roadway surrounding rock.e range of the irregular shape coe cient is I sc ∈ [1, +∞); the closer the value of I sc is to 1, the more regular the shape of the plastic zone in surrounding rock masses is.

Analysis for Indexes of Morphological Characteristics of the Plastic Zone.
In order to clarify the change of indexes with the evolution of the plastic zone, the plastic zones (Figure 10) with di erent shapes were analyzed.
e conditions for calculation are the same as given in Section 3.2.
e relationship between the indexes and η is shown in Figures 11-13.η is the ratio of the vertical principal stress to the horizontal one, i.e., η (D ς1 P 1 /D ς3 P 3 ).
It can be seen from Figures 10 and 11 that U c and I sc increase continuously with the increase of η.When η exceeds 1.9, the growth rate of U c and I sc becomes larger, which indicates that the di erences in the plastic extension depth at various directions are accelerating after the plastic zone evolved into the butter y shape.us, the shape of the plastic zone becomes more irregular, and the stability of the surrounding rock for the roadway is reduced greatly.Additionally, even if the change laws of U c and I sc are similar, I sc is more sensitive to the morphological changes than U c , which shows that the di erences in morphological changes can be better re ected by the index I sc .
e change process of E f and E dc with η can be all divided into two stages as shown in Figure 12. e rst stage is a slow growth period, and then the second stage of rapid growth starts, which shows that the area of the plastic zone and the limit of extended plastic depth will accelerate when the shape of the plastic zone changes into the butter y shape.For η > 2.2, the growth rate of the area of the plastic zone is much larger than that of the limit of extended plastic depth, and the overall stability of the surrounding rock will be decreased greatly.
In Figure 13, the equivalent radius R eq,p increases approximately at a constant acceleration during the initial stage (η ∈ [1.0, 2.2]); after that, the accelerating growth stage begins, in which the maximum equivalent radius of the plastic zone can be achieved (8.805 m).It is far beyond the anchorage range of the rock bolt, which indicates that the size of the plastic zone around the deep roadway under the Advances in Civil Engineering high deviatoric stress becomes quite large and that the size change of the plastic zone is more sensitive when the plastic zone enters into the stage of butter y-shaped evolution; therefore, the roadway tends to more easily fail.

Project Overview and Failure Status of the Roadway.
e #603 tailgate is located at the west second raise mining area of a coal mine in Jiangxi Province, China.B4 coal seam with the average thickness of 2.8 m is the main mining object.
e design length of #603 tailgate is 787 m with a buried depth of 806 m. e geological structure of coalmeasured strata is relatively simple.e immediate roof of this roadway is siltstone with a thickness of 8∼10 m, and the main roof with a thickness of 2∼4 m is the interbed of siltstone and ne sandstone.While the immediate oor is mudstone with a thickness of 2∼4 m, the main oor of sandstone is 12 m in thickness.
For the deep coal mining, it is very di cult to maintain the roadways, resulting in unbalance of the mining-drifting.
e gate roadways have to be tunneled along the unstable gob before nishing the #602 working face.erefore, the #603 tailgate is not only in uenced by the unstable gob but also by the present working face mining.e failure characteristics of #603 tailgate were obtained by eld investigation and testing: (1) Serious subsidence of the roof stratum and the extrusion of the sidewall occurred.As shown in Figure 14, during the recovery of #603 working face, the roof had an extremely serious subsidence, leading to large angle lean of the metal pillar, failure of bolts and cables, and localized roof fall.Both sidewalls squeezed out severely, the deformation of a single sidewall was up to 300∼700 mm, and the contraction rate of the roadway section was nearly 40%.(2) Serious oor heave occurred within the 60% length of the roadway, which hindered the use of roadway and the normal production of the coal mine.(3) e distribution characteristics of the failure eld in #603 tailgate surrounding rock were detected in boreholes by the recorder for strata detection, as shown in Figure 15.e results show that the damage depth of surrounding rock reaches nearly 8 m and the damage range is abnormally large; thus, the strength and integrity of internal rock masses around the roadway deteriorate.e failure depth of the roof and the sidewalls is signi cantly larger than that of the two top corners, while the failure depth of the roof is larger than that of the sidewalls.terms of the past monitoring data for ground pressure.en, the distribution diagram of the plastic zone around the roadway can be drawn by formula (8), as shown in Figure 16, and the magnitudes of morphological indexes are shown in Table 1.It can be seen from Figure 16 that the plastic zone of the surrounding rock shows an obvious butter y shape and the plastic wings extend greatly along the roof, oor, and sidewalls of the roadway.e indexes U c 3.46, I sc 4.98, E f 12.13, and R eq,p 8.33 m in Table 1 indicate that the shape of the plastic zone is quite irregular and that the area and dimension of plastic failure in the surrounding rock are very large, especially for the limit of extended depth for the plastic wings (d max � 13.24 m) which is 5.76 times the radius of the roadway so that it is extremely serious for the plastic deformation and failure of rock masses in these plastic wings grown along the roof, floor, and sidewalls.Based on the above analysis and the field situation, the failure mechanism of #603 tailgate is deemed that the soft surrounding rock produced notable deformation in the early stage due to insufficient strength and stiffness of support under high geostress.With the violent influence of roof caving in the gob and mining for #603 working face, the stress field around the roadway became the ultrahigh, nonuniform stress field; furthermore, the direction of the principal stress deflected, and consequently, a typical butterfly-shaped plastic zone formed (Figure 16).Since the plastic wings with great extended depths were nearly perpendicular to the roof, floor, or sidewalls and the fissures were more developed in surrounding rock, all of them caused nonlinear failure of the surrounding rock of the roadway.

Conclusions
(1) e analysis of the boundary equation for the plastic zone shows that when considering the influence of mining, the butterfly-shaped plastic zone in surrounding rock is more likely to occur, and the size of the plastic wing and the range of plastic failure are greater than those without consideration.If the plastic wings are approximately perpendicular to the roof, floor, or sidewall, large deformation and failure are very likely to occur for the deep roadway.(2) e definitions of malignant expansion of the plastic zone and its criticality were made.e effect of mining on the plastic zone around the deep roadway is more sensitive than that on the shallow one.Even if the changes of mining influence are small in short time, it may also cause serious deformation and plastic failure of surrounding rock masses, leading to the sudden instability of the roadway.
(3) e index system for morphological characteristics of the plastic zone around the circular tunnel was built, and the relationship between these indexes and the stability of surrounding rock were deeply analyzed.Compared with U c , I sc is more sensitive to the morphological changes; thus, the differences in morphological changes can be better reflected by the index I sc .(4) e failure characteristics of #603 tailgate were obtained from the field detection and geological conditions.After that, the mechanism of large deformation and failure for #603 tailgate under deep mining-induced pressure was revealed based on the principles for the formation and extension of the butterfly-shaped plastic zone around the mining-influenced roadway.
(a).Part of rock masses in the top anchorage region slides down.(2)e deformation of sidewalls is serious.Extruding magnitude of a single sidewall ranges from 400 mm to 800 mm.Besides, the phenomenon of sidewall caving appears in some regions (Figure1(b)).(3) e obvious floor heave causes cracking of shotcrete lining and serious inclination of the brace and track; thus, the roadway cannot be used properly (Figure1(c)).(4) Influenced by high geostress, repeated mining activities, and geological structures, the deformation of the roadway surrounding rock appears significantly asymmetry, which hinders the utilization of the roadway (Figure1(d)).

Figure 1 : 1 D ς3 P 3 D ς1 P 1 DFigure 2 :
Figure 1: Main characteristics of deformation and failure for the deep roadway under mining-induced pressure.

1 D ς3 P 3 D ς1 P 1 DFigure 4 :
Figure 4: Mechanical model of the roadway under de ection of the principal stress eld.

Figure 5 :
Figure 5: e plastic zone morphology of the deep roadway (a) in uenced by vertical mining-induced pressure and (b) in uenced by horizontal mining-induced pressure.

Figure 6 :
Figure 6: Distribution of the plastic zone around the circular roadway under de ection of the principal stress eld: (a) β 0 °; (b) β 30 °;

Figure 8 :Figure 7 :
Figure 8: e relationship between the radius of the plastic zone and mining coe cients.
Failure Mechanism of Roadway Based on the Mining-Induced Plastic Zone.According to the eld situations, the parameters for calculation are simpli ed as fol- lows: R 0 2.3 m, c 3.3 MPa, φ 27 °, P 1 20.2 MPa, and P 3 16 MPa.Additionally, D ς1 2.4, D ς3 1.0, and β 40 °in

Table 1 :
Magnitudes of morphological indexes for the plastic zone.