Study on the GenerationMechanism and Development Law of the Zonal Disintegration in Deep Burial Tunnels

In the development of underground spaces, we found that the mechanical properties of rock mass often demonstrate strong nonlinear characteristics. Some new phenomena emerge in deep rock mass engineering. .is includes zonal disintegration and rock burst. Zonal disintegration is very important in deep tunnels. In this paper, we start with the mechanical properties of deep rocks to understand the preconditions for zonal disintegration. Using the Failure Approach Index (FAI), the process of zonal disintegration can be modeled by FLAC (FISH language). Our results indicate that tensile failure in the Supporting Pressure Zone (SPZ) is a precondition for zonal disintegration. Various factors that affect the generation of zonal disintegration are studied. When the maximum stress is in the axial direction, zonal disintegration will be present in deep tunnels. .e high axial stress is necessary for zonal disintegration. We will present a zonal disintegration simulation in one coal mine for comparison with the borehole teleview data. We suggest some measures to prevent the development of zonal disintegration.


Introduction
e deep rock mass is situated in a unique environment with high stress, temperature, and water [1][2][3]. Zonal disintegration in this environment is important for stability, excavation, and design.
is is analogue to shallow tunnel loose, plastic, and elastic zones [4][5][6][7][8][9][10]. Understanding the rock mechanical behaviors in this environment prevents the impact pressure in the excavation and blasting process. Many works in this regard have been carried out in the past. In the 1980s, Shemyakin et al. [11] have found out that the annular fractured zone with interval distribution appears in the face of excavation. e fracture zones of width 1.0∼1.5 m often appear and their frequency depends on the stress. e shape of the fracture zone is similar to the shape of the tunnel. Using borehole periscope, Adams and Jager [12] have found that there are fractured zones of width 5∼150 mm in Witwatersrand mining, South Africa. ere is an intact rock zone of thickness about 1.0 m between interfracture zones. At the depth of 12 m, fracture and nonfracture zones alternate. Malan and Spottiswoode [13] have studied the influence of time and excavation methods on zonal disintegration based on field monitoring. ey found that the mine earthquake is a main factor for the development of zonal disintegration at the tunnel top. Metlov et al. [14] have simulated the process from elastic to failure using equilibrium thermodynamics theory. Li et al. [15] have discovered that zonal disintegration appears in the 6-1# auxiliary tunnel in Jingping hydropower station from the elastic wave data. Fang [16] has studied the mechanical properties of surrounding rock by field test in Jingchuan and Zhangjiawa mines and he found that tensile and compressive zones appear alternatively. is alternative tensile and compressive pattern develops over time.
Sellers and Klerck [17] have investigated the influence of discontinuities on the alternative patterns of zonal disintegration. In deep tunnels by experimental methods, they have shown that the discontinuities are crucial for zonal disintegration. Gu et al. [18] have verified the existence of zonal disintegration by high compressive test on cylinder with circular and arch rectangular hollow shapes in the center. e results indicate that slip line failure appears near the tunnel wall and circular failure appears at the deep section for the circular tunnel. e slip failure appears at the top and bottom of the tunnel and layered failure appears in the sidewall for the arch rectangular tunnel. When the curvature of tunnel wall is big or the sidewall is high, it expands towards the free face under high axial pressure and layered failure appears. Qian [19] has pointed out that zonal disintegration happens when the initial stress is bigger than uniaxial compressive strength of the rock. e number of fractured zones depends on initial stress. Zonal disintegration appears more often with drill blasting than machine excavation. is is because zonal disintegration is dependent on unloaded process. Wang et al. [20] can predict the whole process of deformation and failure by static models based on a relationship between stress and volume change. Layer failure will first appear, then a "new" tunnel is produced due to rapid unload. Many researchers [21] have investigated this process from theoretical analysis, field monitoring, lab experiment, and numerical simulation. However, we should have a good understanding of this process. Modeling of zonal disintegration requires the nonlinear properties of the rock mass. We still puzzle on failure criterion. In this paper, we present a zonal disintegration simulation in one coal mine for comparison with the borehole teleview data. Such comparison points out the future research direction.

Strain Softening Model
In this study, the zonal disintegration in the form of broken zone in the surrounding rock is not completely discontinuous. e rock mass fracture but not separation is considered to study the zonal rupture problem, so FLAC, which is usually used as a numerical simulation software for numerical analysis of continuous media, was chosen. Figure 1(a) shows the relationship between stress and strain in this model. e strain is constituted by both elastic and plastic strains after yield trend. e variation of some parameters, such as cohesion, internal friction, and dilatancy angle, can be viewed as plastic shear strain related. Tensile strength is a function of plastic tensile strain.

Failure Criterion.
e strain softening model in the software FLAC3D is based on Mohr-Coulomb with associated law of tensile flow and nonassociated law of shear flow. erefore, the yield function, potential function, and plastic flow law of the Mohr-Coulomb are consistent with the general one.
where f s is shear yield function; f t is tensile yield function; σ 1 is maximum principal stress; σ 3 is minimum principal stress; φ is internal friction angle; c is cohesion; N φ � (1 + sin φ)/(1 − sin φ)σ t is tensile strength. g s is the shear potential function corresponding to the nonassociated law of flow: g t is the tensile potential function corresponding to the associated law of flow: For strength criterion of zonal disintegration, we use the maximum tensile stress in the Mohr-Coulomb model of the software FLAC3D.

FAI Index.
Because FLAC3D is for continuum media mechanics, it is inconvenient to judge the failure state of rock mass. We introduce the YAI index to represent the degree of yield. e value of YAI is from 0 to 1. In plastic mechanics, the Mohr-Coulomb yield function is in which I 1 is the first invariant of stress tensor; J 2 is the second invariant of the deviatoric stress tensor; φ is internal friction angle; c is cohesion; θ σ is Lode angle. If we express formula (4) in terms of normal stress σ π and shear stress τ π , we have e stress state of arbitrary one-point Q on the π plane is shown in Figure 1(c). e coordinate of point Q is (σ π , τ π ). e coordinate of point C on the π plane is (σ π , τ π ′ ). We define YAI � QC/A 0 C � 1 − τ π /τ π ′ and apply formula (6) and denote τ π ′ as τ π ′ � (ασ π + c)/β. We obtain erefore, the expression of YAI in shear and tensile yield criterions is in which σ t is tensile strength; σ R � (σ t − c cos φ)/ (1 − sin φ). When (σ 1 + σ 3 )/2 ≤ σ R , the YAI is shear yield criterion. When (σ 1 + σ 3 )/2 > σ R , the YAI is tensile yield criterion. For rock material with main shear failure, the plastic shear strain is usually used to describe strain softening. is is also called Failure Degree (FD).
in which c r p is limit plastic shear strain, which is determined by the following formula: where e p ij is plastic deviator strain and determined by the following formula: And c p is plastic shear strain of rock material [22,23].
To analyze the numerical simulation results conveniently, we introduce the dangerous coefficient w(w � 1 − YAI). erefore, we can rewrite FAI as From formula (12), the dangerous coefficient w is used to evaluate dangerous degree before stress reaches yield state. e failure degree is represented as 1 + FD after rock mass reaches yield state. When FAI is between 0 and 1, it represents that rock mass does not yield. When FAI equals 1.0, rock mass starts to yield into a plastic state. When FAI is more than 2.0, it represents that plastic shear strain has reached its limit. Rock mass is damaged at this state. From equations (8) and (12) we can simulate the whole process of failure using FAI in software FLAC3D. To display the location and scope of fracture zones, the elements with FAI bigger than 2.0 will be put into the "shear-break" group in the program and their stress state will be displayed on the nephogram.

Realization of the Strain Softening
Mohr-Coulomb Model 3 e constraint conditions on other planes are modified simultaneously. We use the strain softening Mohr-Coulomb model as the constitutive model and the failure criterion of maximum tensile stress is used in this model. e sidewall is exerted with dynamic load to control the unload velocity to simulate the process of excavation. e calculation mode used is a dynamic one. e end calculation is controlled by the default displacement value. Figure 2 shows the simulation results. Many nephograms, such as cohesion, internal friction angle, YAI, FAI, maximum principal stress, minimum principal stress, plastic zone state, and fracture zone state, are shown.

Simulation Results.
Under high axial pressure, two fracture zones appear. From the cohesion and internal friction angle nephograms, the minimum value of cohesion and internal friction angle appear at certain distances from the tunnel. From the YAI nephogram, the YAI is between 0 and 0.2 at certain distances from the sidewall. We regard this as a fracture zone. e YAI increases gradually with the increase of the distance. With enough distance, the YAI decreases to the 0∼0.2 interval again. is indicates that another fracture zone is formed. From the FAI nephogram, the FAI is 0∼2.0 for distance interval of 4.64∼5.03 m. is indicates that one fracture zone is formed at a distance interval of 2.5∼4.64 m. Another fracture zone at a distance bigger than 5.03 m is also formed because FAI reaches more than 2.0 in this section. From the maximum and minimum principal stress nephograms, the maximum and minimum principal stresses increase gradually with the distance. e stress concentration emerges at the second fracture zone with the minimum principal stress demonstrating no change. It indicates that this location is very vulnerable to fracture. From the plastic and fracture zone nephograms, there is a nonfractured zone at the distance between 4.70 and 5.31 m. e plastic shear strain reaches its limit when FAI is equal to or larger than 2.0. To show the nonfractured zone and fractured zone clearly, the element with FAI equal or larger than 2.0 is marked as "shearbreak" group in Figure 2(h). e second small fractured zone emerges in a nonfractured zone. e nonfractured and fractured zone distributions are 2.5 m∼4.73 m, 4.73 m∼5.33 m, and 5.33 m∼6.93 m, respectively. e widths

Generation Process of Zonal
Disintegration. e failure of a deep tunnel appears at the sidewall in the initial stage of excavation due to stress concentration. e distribution of radial and tangential stresses is shown in Figure 3(a). e radial stress increases from zero to initial stress and tangential stress decreases from concentration stress to initial stress. is stress distribution is shown in Figure 3(b), in which R is the distance to the tunnel center and C is the distance from elastic/plastic interface to the tunnel center. When R is less than C, both radial and tangential stresses increase with R. When R is equal to C, the tangential stress reaches its maximum and it will decrease with the increase of R until it returns to the initial stress. e radial stress increases with R until it returns to the initial stress. is indicates that, at the location of elastic and plastic interface, a special zone exists to support the pressure of surrounding rock. We call this zone Pressure Support Zone (PSZ). ere are two stress states in PSZ. One is σ θ > σ z > σ r , where the tangential stress is the maximum principal stress, radial stress is the minimum principal stress, and the axial stress is the intermediate. e other is σ z > σ θ > σ r , where the axial stress is the maximum principal stress, the tangential stress is the intermediate principal stress, and the radial stress is the minimum principal stress. In SPZ, when the tensile stress reaches the tensile strength, failure and fracture will appear. e failure will form an annular tensile fissure because the circular tunnel stress distribution has axial symmetry. In essence, the failure makes a new tunnel of a bigger radius. e redistributed stress is shown in Figure 3(c). New fractured zones emerge under high tangential and axial stress and stress undergoes another redistribution as shown in Figure 3(d). is process pushes the PSZ zone outwards until the stress in the zone does not create tensile failures. e generation process of zonal disintegration is shown in Figure 3.
From Figure 2(f ), we can see that the minimum principal stress increases with R. It peaks between the first nonfractured zone and the second fractured zone. e maximum principal stress peaks at the interface of the first fractured zone and nonfractured zone as shown in Figure 2(e).

Influence Factors of Zonal Disintegration.
ere are many factors that influence zonal disintegration. In what follows, we will describe all major factors such as mechanical properties of the surrounding rock, unloading velocity, stress, and tunnel size and shape.
(1) Process of Unloading. Tunnel excavation is a process of unloading. To simulate this process, we use dynamic and static load of inverse direction applied to the tunnel sidewall. e control of unloading velocity is through exerting static load of inverse direction, which is shown in Figure 4.
From our modeling, the width of fractured zone created by fast unloading is bigger than that of slow unloading. Both fast and slow unloading can generate zonal disintegration.
(2) Direction of Maximum Principal Stress. We consider two cases where the direction of maximum principal stress is either parallel or perpendicular to the tunnel axis. Figure 5 shows the fractured and plastic zone for maximum principal stress perpendicular to tunnel axis. In comparison of Figures 5, 2(g), and 2(h), we found that the plastic zone scope at the top and bottom of the tunnel is less than that at the tunnel side.
ere is no zonal disintegration when the maximum principal stress is vertical to the tunnel axis. is proves that high horizontal stress is necessary for zonal disintegration generation. e main reason is that high axial stress causes the deformation towards the free face during excavation. e radial displacement of the sidewall causes big radial tensile strain. e tensile failure happens when the radial tensile strain reaches its limit.
(3) Axial Stress. To understand the influence of axial stress on zonal disintegration, we simulated three cases where the axial stress is two times, one time, and 0.8 times that of the compressive strength. Figure 6 shows the plastic and fractured zone for the last two axial stresses.
In comparison of Figures 6, 2(g), and 2(h), we can see that the width of fractured zone with axial stress of 1 time the uniaxial compressive strength is less than that of 2 times. For the axial stress of 0.8 times the uniaxial compressive strength, no zonal disintegration is generated. e width of fractured zone increases with that of the axial stress. e plastic circle around the tunnel with zonal disintegration is smaller than that without zonal disintegration. It demonstrates that zonal disintegration reduces the rock stability capacity. Zonal disintegration happens when axial stress is larger than the uniaxial compressive strength.
(4) Radius of Tunnel. In Section 3, we simulated the 2.5 m radius. In this section, the radii of 5.0 and 1.0 m are considered. Figure 7 shows the plastic and fractured zones for these two radiuses. e nonfractured and fractured zones for 5 m radius are 5.0 m∼6.8 m, 6.8∼7.1 m, and 7.1 m∼11.8 m, respectively. e widths of fractured zones are 1.8 m and 4.7 m, respectively, and the width of nonfractured zone is 0.3 m. e nonfractured and fractured zones for 1 m radius are 1.0 m∼1.9 m, 1.9∼2.7 m, and 2.7 m∼3.5 m, respectively. e widths of fractured zones are 0.9 m and 0.8 m, respectively, and the width of nonfractured zone is 0.8 m. e width of fractured zone increases gradually with the tunnel radius and the width of nonfractured zone decreases gradually.
(5) Tunnel Shape. We compare the arch rectangular tunnel to circular tunnel in this section. e arch radius is 2.5 m and the height of sidewall is 1.38 m. We keep the boundary conditions and parameters unchanged from the previous models. Figure 8 shows the plastic and fractured zones.
In comparison with the circular tunnel, though the scope of fractured zone becomes bigger, there is no zonal Shock and Vibration disintegration in the sidewall. e zonal disintegration at the arch is similar to that of the circular tunnel. e zonal disintegration at the tunnel bottom is less obvious than that at the arch. e scope of plastic zone at the sidewall is big. e shape of zonal disintegration is similar to that of the tunnel. We further conclude that the shape of zonal disintegration is similar to the shape of the tunnel.  Figure 9 shows the rock mass types. We used the medium sandstone's physical and mechanical parameters for simulation [21,24] Physical and mechanical parameters for simulation are shown in Table 2.

Case Studies
Four sections in a roadway are thoroughly investigated by Chen et al. [5] for zonal disintegration. ree to four bores are arranged in each section. e bore fracturing is observed by a TV imager and zonal disintegration distributions in four sections are obtained. e geostatic stress is about 25 MPa and lateral pressure coefficient is 1.5. e model is shown in Figures 10 and 11.

Model Construction.
e mesh is 60 m × 10 m × 60 m (X × Y × Z) and the geostatic stresses with different directions are applied on different faces of the model. e size of the excavation section is 5.00 m × 3.88 m, which is horseshoe shaped. In the initial geostress calculation, the normal constraint is applied only at the bottom (Z � − 30 m) to limit the displacement in the Z direction. A force σ z (25 MPa) is applied to the upper surface (Z � 30 m), which is used to simulate the effect of the upper load. e horizontal stress σ x , whose value is 37.5 MPa, is applied in the direction perpendicular to the axial direction of the cavern (X direction). Axial stress σ y , whose value is 177.1 MPa, is applied in the axial direction of the chamber (Y direction). Before excavation simulation, the surface pressure is removed and the axial pressure of 177.1 MPa is applied. e cohesion and internal friction angle are changeable with the plastic shear strain. e change law is shown in Figure 12. e calculation mode employed is a dynamic calculation one. e unload velocity is controlled by applying an inverse dynamic load on the tunnel sidewall. e period of unload is 2.5 ms and peak strength is 38.4 MPa. e relationship between unload strength and time is Figure 13 shows the failure development and principal stress. Shear failure first appears at the top section, and then junction between sidewall and bottom. As the fractured zone extends outside, the zonal        ere are three fractured zones on the top and two failure zones at the sidewall when the calculation reaches 65000 steps.

Zonal Disintegration.
e zonal disintegration at the bottom is remarkable. When calculation reaches 75000 steps, the fourth fractured zone at the top and the third fractured zone at the bottom are formed. Figure 14 shows the final state of the surrounding rock after tunnel excavation. It includes displacement vector, tensile strength, cohesion, internal friction angle, YAI, FAI, and plastic and fractured zones. e displacement of sidewall and junction between sidewall and bottom is small. e displacements at the middle section of top and bottom are big. e unload scope due to excavation can be seen from the nephogram. We mark the elements with FAI larger than 2.0 in red color. e number of fractured zones can be easily found from Figure 14(h). e FAI for every survey line is monitored during numerical simulation. ere are 75 elements traversed by each survey line. When the FAI of an element is more than 2.0, this element fails because its shear strain has reached the limit. Figure 16 shows FAI at each survey line. Table 3 shows the distribution scope of nonfractured zones for different survey lines. Inner Diameter (ID)  represents the distance from the fractured zone starting location to the sidewall and External Diameter (ED) represents the distance from the fractured zone ending location to the sidewall along the survey line.

Fractured Zones in the Surrounding
ere are four fractured zones based on the Table 3. Based on ID and ED of fractured zones, the scope and location of fractured zones can be obtained. e comparison between numerical simulation and field survey [5,23] is shown in Table 4.
For tunnel top, the number, scope, and location of zonal disintegration using numerical simulation have great agreement with those of field survey. e simulated width of the fourth fractured zone differs greatly from that of field survey. e reason is that the exceptional data point (16.

Conclusions
Strain softening Mohr-Coulomb Model is appropriate for zonal disintegration simulation. e FAI can be used to represent the rock failure. e location and scope of nonfractured and fractured zones can be obtained from FAI through simulation. High axial stress is necessary for zonal disintegration generation. e precondition for zonal disintegration generation is that tensile failure happens in the PSZ zone. e width of fractured zone caused by fast unloading is bigger than that of slow unloading. Only when the axial stress is more than the uniaxial compressive   strength, zonal disintegration appears. e width of fractured zone increases with the tunnel radius. For the arch rectangular tunnel, there is no zonal disintegration at the sidewall. e shape of zonal disintegration is similar to the shape of the tunnel. With a mine in China as an example, we demonstrated the validity of our numerical approach for zonal disintegration simulation.

Data Availability
In order to verify the results of this article, replicate the analysis, and conduct secondary analyses, for any reader or researcher who wishes to obtain the research data of this article, please contact the corresponding author via jin-liu920@163.com.

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