# Zonal Disintegration Mechanism of Deep Rock Masses under Coupled High Axial Geostress and Blasting Load

Authors: Pu Yuan; Ying Xu
Journal: Shock and Vibration
 (2018)

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## Abstract

Zonal disintegration phenomenon with alternative distribution of fracture zones and nonfracture zones is a characteristic failure in deep rock masses, especially for deep tunnel excavated by drill and blast method. To investigate the mechanism of zonal disintegration under coupled high axial geostress and blasting load, elastic stress field distribution for a circular tunnel in deep isotropic rock masses is obtained. Furthermore, Hoek-Brown criterion is amended by considering blast-induced damage effect. Both radial blasting load and blast-induced damage effect are assumed to decay in a negative exponential function. Taking the deep tunnel of Dingji coal mine in China as engineering background, the number and width of fracture zones are determined by deduced elastic stress field and modified Hoek-Brown criterion. Then numerical computation is conducted. Numerical computation results indicate that both the number and width of fracture zones mainly depend on high axial geostress and mechanical parameters of deep rock masses, and peak radial blasting load plays an important role in determining the width of fracture zone near the excavation.


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## Body

## 1. Introduction

With the ever-increasing demand of energy resources, deep mineral resources exploitation is inevitable and imperative due to the continuing consumption of shallow mineral resources [1], and deep mining has been identified as an important topic for research under China’s State Key Research and Development Program [2]. During deep mineral resources exploitation, some special rock failure phenomena, such as zonal disintegration and rockburst, are frequently reported and quite different from those in shallow rock Engineering [3–5]. Among these special rock failure phenomena, zonal disintegration is such a unique phenomenon with alternative distribution of fracture zones and nonfracture zones around an excavation in deep rock mass [6, 7].Zonal disintegration phenomenon is considered as one of the characteristics of deep rock masses. In 1970s, zonal disintegration phenomenon was firstly observed ahead of stope faces by periscope in Doornfontein gold mine of South Africa at about -2300 m level [8]. Then zonal disintegration phenomenon was also monitored around underground workings by electrometric techniques in Oktyabrsky Mine and Taymyrsky Mine of Russia at about -1000 m level [9]. However, an obvious zonal disintegration phenomenon in China was detected by bore TV video in Huainan mine at -910 m level [10].Formation condition and mechanism of zonal disintegration under in situ stresses have been studied subsequently by theoretical analysis, model experiment, numerical simulation, and in situ monitoring. Shemyakin et al. [11] considered that the fracture zone is the splitting failure in rock mass. Odintsev [12] found that zonal disintegration can be predicted by spatial periodicity of splitting failure around an excavation. Zhang et al. [13] established an elastic damage-softening model for zonal disintegration according to strain gradient theory and continuum damage mechanics. Chen et al. [5] revealed that the circulation of fracture zone is mainly caused by the peak stress intensity factor of a “new” plastic boundary. Jia et al. [14] stated that failure patterns of surrounding rock mass are influenced by multiaxial stress state and a high axial geostress is essential for zonal disintegration. Yuan and Gu [15] indicated that the major radial tension strain following tension breakage is the key factor of zonal disintegration. While traditional static mechanics theory cannot illustrate the formation of zonal disintegration well, therefore the unloading effect during excavation process is considered. Zhu et al. [16] indicated that a slowly unloading P-wave reflecting from a free surface may induce zonal disintegration. By assuming deep rock masses containing a set of parallel cracks, zonal disintegration mechanism was analyzed and fracture zone occurred when cracks satisfy the crack grown criterion or the strain energy density factor theory [17, 18].Based on non-Euclidean model, zonal disintegration mechanism around a deep circular tunnel was investigated and elastic stress field of surrounding rock was derived under various conditions, such as nonhydrostatic pressure state and dynamic unloading. In non-Euclidean model, radial stress and tangential stress around deep tunnel were obviously fluctuant, which was quite different with classic elastic solution [19, 20]. And zonal disintegration around an excavation is the result of the alternate appearance of stress wave crests and troughs [21, 22]. By establishing a new non-Euclidean model in a nonhydrostatic pressure state, it was found that the magnitude and position of fracture zones depend on the actual geostress state and non-Euclidean parameters [23]. Considering the characteristics of rock mass, both crack-weakened rock mass and cross-anisotropic rock mass were analyzed for zonal disintegration with a non-Euclidean model [24, 25]. Moreover, zonal disintegration around a deep circular tunnel under dynamic unloading condition was also studied with non-Euclidean model [26, 27]. When considering the excavation unloading effect, it was found that the magnitude and position of fracture zone mainly depend on unloading rate, and the quantity of fracture zones increases with decreasing excavation time [18, 22].In consideration of complex geological environment and blasting excavation, rock failure in deep rock mass can be induced by blasting load [28, 29]. General Particle Dynamics (GPD) method was put forward to study the zonal disintegration mechanism of deep rock mass in blasting excavation, and it was found that dynamic loads and high geostress are two dominant factors for occurrence of zonal disintegration [30]. Blasting excavation not only applies a dynamic load on deep rock masses but also induces blasting damage around an excavation [31, 32]. By considering both high axial geostress and blasting load in deep rock masses, failure mechanism of zonal disintegration is investigated by elastic stress field analyses and modified Hoek-Brown criterion. Then the effects of high axial geostress, mechanical parameters of deep rock masses, and radial blasting load on zonal disintegration are analyzed.


## 2. Elastic Stress Field under Coupled High Axial Geostress and Blasting Load

### 2.1. Decomposition of Elastic Stress Field

It is found that the axial stress of tunnel is vital for zonal disintegration [33]. Therefore, high axial geostress should be considered during elastic stress field analyses.It is assumed that a deep circular tunnel, whose radius isr0, is subjected to a vertical geostressp0, a horizontal geostressp0 at infinity, and a high axial geostress pz along the tunnel axis. Under coupled high axial geostress and blasting load, elastic stress field around a circular excavation in deep rock mass can be divided into two parts, elastic stress field caused by high axial geostress and transient elastic stress field induced by blasting load, which can be seen from Figure 1.Figure 1
Decomposition of elastic stress field under coupled high axial geostress and blasting load.


### 2.2. Elastic Stress Field Caused by High Axial Geostress

To simplify the analyses, three-dimensional problem is converted into a quasi-plane strain problem with an initial axial strainεz0 [34]. According to simplified quasi-plane strain state, axial stress component σz can be expressed as(1)σz=Eεz0+μσr+σθwhereE is Young’s modulus, μ is Poisson’s ratio, and σr and σθ are radial stress component and tangential stress component, respectively.Asr→∞, σz→pz, σr→p0, and σθ→p0, the initial axial strain εz0 can be obtained as(2)εz0=pz-2μp0EAccording to the research of Qian et al. [34], the first invariant of stress tensorI1 in surrounding rock with a distancer from tunnel center can be obtained as(3)I1=-E2ρ1-μAJ0ρ1/2r+BN0ρ1/2r-CK0ρ1/2r+pz+2p0(4)A=C2πρ1/2r0K0ρ1/2r0N1ρ1/2r0-K1ρ1/2r0N0ρ1/2r0(5)B=C2πρ1/2r0K0ρ1/2r0J1ρ1/2r0-K1ρ1/2r0J0ρ1/2r0(6)ρ2=Eμ2q1-μ2whereq in non-Euclidean model is the fitting parameter determined by experimental data,J0(ρ1/2r) andJ1(ρ1/2r) are zero-order and first-order Bessel function,N0(ρ1/2r) andN1(ρ1/2r) are zero-order and first-order Neumann function,K0(ρ1/2r) andK1(ρ1/2r) are zero-order and first-order modified Bessel function of second kind, andC coincides with the Wronskian of linearly independent solutionsJ0(ρ1/2r) andN0(ρ1/2r).According to elasticity mechanics, the first invariant of stress tensorI1 in surrounding rock with a distancer from tunnel center can also be written as(7)I1=σz1+σr1+σθ1=Eεz0+μσr1+σθ1+σr1+σθ1=Eεz0+1+μσr1+σθ1Then, the tangential stress componentσθ1 can be given as follows:(8)σθ1=I1-Eεz01+μ-σr1Under high axial geostress, the equation of equilibrium can be expressed as(9)∂σr∂r+2σrr-I1-Eεz01+μr=0Integrating (9), the radial stress component σr1 can be expressed as(10)σr1=1-r02r2p0-E2ρ3/21-μ2rAJ1ρ1/2r+BN1ρ1/2r-CK1ρ1/2rSubstituting (10) into (8), the tangential stress component σθ1 can be expressed as(11)σθ1=1+r02r2p0-E2ρ1-μ2AJ0ρ1/2r+BN0ρ1/2r-CK0ρ1/2r+E2ρ3/21-μ2rAJ1ρ1/2r+BN1ρ1/2r-CK1ρ1/2r


### 2.3. Transient Elastic Stress Field Induced by Radial Blasting Load

Elastic stress field induced by blasting load can be treated as an axial symmetric problem in plain strain state for long circular tunnel. As an impact load, blasting load usually increases firstly and then decreases. But the main cause of zonal disintegration phenomenon in deep rock mass is the tensile failure of surrounding rock in radial direction [15]. And the tensile failure in radial direction usually occurs in unloading stage rather than in loading stage. Therefore, a monotone decreasing radial blasting loadp(t) is applied on the boundary of circular tunnel in consideration of blasting load in excavation [35]. As shown in Figure 2, radial blasting load decays in a negative exponential function with action time. And the expression for time-varying radial blasting loadp(t) is shown as follows.(12)pt=pse-at0<t≤t0(13)ps=ρ0D2160where ps is the peak pressure of radial blasting load,a is exponential decay coefficient, andt0 is the action time of radial blasting load. ρ0 andD are density and detonation velocity of explosive.Figure 2
Time-varying radial blasting load.Under blasting load, the equations of equilibrium can be written as(14)∂2ur,t∂2r+1r∂ur,t∂r-ur,tr2=1Cp2∂2ur,t∂2twhere Cp is longitudinal wave velocity: Cp=E(1-μ)/[ρ0(1+μ)(1-2μ)].With the help ofLaplace transform, theLaplace transform ofu(r,t) can be expressed as(15)Ur,p=Lur,t=∫0∞ur,te-ptdtwherep is parameter ofLaplace transform.Then the equations of equilibrium can be written as(16)∂2Ur,p∂2r+1r∂Ur,p∂r-Ur,pr2=p2Cp2Ur,pAssuming thatη=pr/Cp, (16) can be obtained as(17)η2∂2Uη,p∂2η+η∂Uη,p∂η-η2+1Uη,p=0Equation (17) is modified Bessel equation, and its general solution is(18)Uη,p=MI1η+NK1η(19)I1η=∑k=0∞1k!Γk+2η22k+1(20)K1η=limα→1⁡I-αη-Iαηsin⁡αππ2whereI1(η) andK1(η) are first-order modified Bessel function of first kind and second kind andM andN are the parameters determined by boundary conditions.Asα→1, K1(η)→∞. WhileU(η,p) is bounded, the parameterN is equal to 0. According to the asymptotic property of Bessel function, the first-order modified Bessel function of first kindI1(η) can be expressed as(21)I1η=12πηeηTherefore, (18) can be written as(22)Uη,p=M2πηeηAccording to generalized Hooke’s law, the strain for plain strain problem in axisymmetric condition can be calculated as(23)εr=1-μ2Eσr2-μ1-μσθ2(24)εθ=1-μ2Eσθ2-μ1-μσr2By adding (23) multiplied by (1-μ)/μ with (24), the following can be obtained:(25)εr1-μμ+εθ=1-μ2E1-μμσr2-μ1-μσθ2+1-μ2Eσθ2-μ1-μσr2=1+μ1-2μEμσr2Then, the radial stress componentσr2 can be rewritten as(26)σr2=E1-μ1+μ1-2μεr+Eμ1+μ1-2μεθBy adding (23) multiplied by μ with (24) multiplied by (1-μ), the following can be obtained:(27)εrμ+εθ1-μ=1-μ2Eμσr2-μ1-μσθ2+1-μ2E1-μσθ2-μ1-μσr2=1+μ1-2μEσθ2Then, the tangential stress componentσθ2 can be rewritten as(28)σθ2=Eμ1+μ1-2μεr+E1-μ1+μ1-2μεθAssuming thatc1=E(1-μ)/[(1+μ)(1-2μ)] and c2=Eμ/[(1+μ)(1-2μ)], the stress-strain relation can be rewritten as(29)σr2=c1εr+c2εθ=c1∂ur,t∂r+c2ur,tr(30)σθ2=c2εr+c1εθ=c2∂ur,t∂r+c1ur,trOn the boundary of circular tunnel, the stress boundary condition can be expressed as(31)σr2r=r0=c1∂ur,t∂r+c2ur,trr=r0=ptWith the help ofLaplace transform, the stress boundary condition can be written as(32)c1∂Uη,p∂η+c2Uη,pηη=η0=Pp(33)Pp=Lpt=∫0∞pτe-ptdtwhere η0=pr0/Cp.Substituting (22) into (32), the parameterM can be obtained as(34)M=2Ppη0Cp2πη0peη0c12η0-1+2c2According toη=pr/Cp and (34), (22) can be expressed as(35)Ur,p=Ppr0/rCp/c1p-1/2-c2/c1Cp/r0er-r0/CppAccording to convolution theorem ofLaplace transform,(36)Lf1t∗f2t=F1p∗F2p(37)F1p=Pper-r0/Cpp(38)F2p=r0/rCp/c1p-1/2-c2/c1Cp/r0With the help of inverseLaplacetransform, the radial displacement u(r,t) around circular tunnel is obtained as(39)ur,t=Cppsr0/rc1ec1-2c2/2c1r0Cpt-at+r-r0/CpTherefore, according to (29) and (30), the radial stress component σr2 and tangential stress component σθ2 induced by radial blasting load can be obtained as(40)σr2=c1∂ur,t∂r+c2ur,tr=c2Cpc1-ar+Cp2psr0/rrec1-2c2/2c1r0Cpt-at+r-r0/Cp=μCp1-μ-ar+Cp2psr0/rre1-3μ/2r01-μCpt-at+r-r0/Cp(41)σθ2=c2∂ur,t∂r+c1ur,tr=Cp-c2c1ar+Cp2psr0/rrec1-2c2/2c1r0Cpt-at+r-r0/Cp=Cp-μ1-μar+Cp2psr0/rre1-3μ/2r01-μCpt-at+r-r0/Cp


### 2.4. Elastic Stress Field under Coupled High Axial Geostress and Blasting Load

Consequently, the radial stress componentσr and tangential stress component σθ under coupled high axial geostress and blasting load can be expressed as(42)σr=σr1+σr2=1-r02r2p0-E2ρ3/21-μ2rAJ1ρ1/2r+BN1ρ1/2r-CK1ρ1/2r+μCp1-μ-ar+Cp2psr0/rre1-3μ/2r01-μCpt-at+r-r0/Cp(43)σθ=σθ1+σθ2=1+r02r2p0+E2ρ3/21-μ2rAJ1ρ1/2r+BN1ρ1/2r-CK1ρ1/2r-E2ρ1-μ2AJ0ρ1/2r+BN0ρ1/2r-CK0ρ1/2r+Cp-μ1-μar+Cp2psr0/rre1-3μ/2r01-μCpt-at+r-r0/CpSubstituting (2), (42), and (43) into (1), the axial stress component σz can be expressed as(44)σz=Eεz0+μσr+σθ=pz-Eμ2ρ1-μ2AJ0ρ1/2r+BN0ρ1/2r-CK0ρ1/2r+Cp2-arμpsr0/rr1-μe1-3μ/2r01-μCpt-at+r-r0/Cp


## 2.1. Decomposition of Elastic Stress Field

It is found that the axial stress of tunnel is vital for zonal disintegration [33]. Therefore, high axial geostress should be considered during elastic stress field analyses.It is assumed that a deep circular tunnel, whose radius isr0, is subjected to a vertical geostressp0, a horizontal geostressp0 at infinity, and a high axial geostress pz along the tunnel axis. Under coupled high axial geostress and blasting load, elastic stress field around a circular excavation in deep rock mass can be divided into two parts, elastic stress field caused by high axial geostress and transient elastic stress field induced by blasting load, which can be seen from Figure 1.Figure 1
Decomposition of elastic stress field under coupled high axial geostress and blasting load.


## 2.2. Elastic Stress Field Caused by High Axial Geostress

To simplify the analyses, three-dimensional problem is converted into a quasi-plane strain problem with an initial axial strainεz0 [34]. According to simplified quasi-plane strain state, axial stress component σz can be expressed as(1)σz=Eεz0+μσr+σθwhereE is Young’s modulus, μ is Poisson’s ratio, and σr and σθ are radial stress component and tangential stress component, respectively.Asr→∞, σz→pz, σr→p0, and σθ→p0, the initial axial strain εz0 can be obtained as(2)εz0=pz-2μp0EAccording to the research of Qian et al. [34], the first invariant of stress tensorI1 in surrounding rock with a distancer from tunnel center can be obtained as(3)I1=-E2ρ1-μAJ0ρ1/2r+BN0ρ1/2r-CK0ρ1/2r+pz+2p0(4)A=C2πρ1/2r0K0ρ1/2r0N1ρ1/2r0-K1ρ1/2r0N0ρ1/2r0(5)B=C2πρ1/2r0K0ρ1/2r0J1ρ1/2r0-K1ρ1/2r0J0ρ1/2r0(6)ρ2=Eμ2q1-μ2whereq in non-Euclidean model is the fitting parameter determined by experimental data,J0(ρ1/2r) andJ1(ρ1/2r) are zero-order and first-order Bessel function,N0(ρ1/2r) andN1(ρ1/2r) are zero-order and first-order Neumann function,K0(ρ1/2r) andK1(ρ1/2r) are zero-order and first-order modified Bessel function of second kind, andC coincides with the Wronskian of linearly independent solutionsJ0(ρ1/2r) andN0(ρ1/2r).According to elasticity mechanics, the first invariant of stress tensorI1 in surrounding rock with a distancer from tunnel center can also be written as(7)I1=σz1+σr1+σθ1=Eεz0+μσr1+σθ1+σr1+σθ1=Eεz0+1+μσr1+σθ1Then, the tangential stress componentσθ1 can be given as follows:(8)σθ1=I1-Eεz01+μ-σr1Under high axial geostress, the equation of equilibrium can be expressed as(9)∂σr∂r+2σrr-I1-Eεz01+μr=0Integrating (9), the radial stress component σr1 can be expressed as(10)σr1=1-r02r2p0-E2ρ3/21-μ2rAJ1ρ1/2r+BN1ρ1/2r-CK1ρ1/2rSubstituting (10) into (8), the tangential stress component σθ1 can be expressed as(11)σθ1=1+r02r2p0-E2ρ1-μ2AJ0ρ1/2r+BN0ρ1/2r-CK0ρ1/2r+E2ρ3/21-μ2rAJ1ρ1/2r+BN1ρ1/2r-CK1ρ1/2r


## 2.3. Transient Elastic Stress Field Induced by Radial Blasting Load

Elastic stress field induced by blasting load can be treated as an axial symmetric problem in plain strain state for long circular tunnel. As an impact load, blasting load usually increases firstly and then decreases. But the main cause of zonal disintegration phenomenon in deep rock mass is the tensile failure of surrounding rock in radial direction [15]. And the tensile failure in radial direction usually occurs in unloading stage rather than in loading stage. Therefore, a monotone decreasing radial blasting loadp(t) is applied on the boundary of circular tunnel in consideration of blasting load in excavation [35]. As shown in Figure 2, radial blasting load decays in a negative exponential function with action time. And the expression for time-varying radial blasting loadp(t) is shown as follows.(12)pt=pse-at0<t≤t0(13)ps=ρ0D2160where ps is the peak pressure of radial blasting load,a is exponential decay coefficient, andt0 is the action time of radial blasting load. ρ0 andD are density and detonation velocity of explosive.Figure 2
Time-varying radial blasting load.Under blasting load, the equations of equilibrium can be written as(14)∂2ur,t∂2r+1r∂ur,t∂r-ur,tr2=1Cp2∂2ur,t∂2twhere Cp is longitudinal wave velocity: Cp=E(1-μ)/[ρ0(1+μ)(1-2μ)].With the help ofLaplace transform, theLaplace transform ofu(r,t) can be expressed as(15)Ur,p=Lur,t=∫0∞ur,te-ptdtwherep is parameter ofLaplace transform.Then the equations of equilibrium can be written as(16)∂2Ur,p∂2r+1r∂Ur,p∂r-Ur,pr2=p2Cp2Ur,pAssuming thatη=pr/Cp, (16) can be obtained as(17)η2∂2Uη,p∂2η+η∂Uη,p∂η-η2+1Uη,p=0Equation (17) is modified Bessel equation, and its general solution is(18)Uη,p=MI1η+NK1η(19)I1η=∑k=0∞1k!Γk+2η22k+1(20)K1η=limα→1⁡I-αη-Iαηsin⁡αππ2whereI1(η) andK1(η) are first-order modified Bessel function of first kind and second kind andM andN are the parameters determined by boundary conditions.Asα→1, K1(η)→∞. WhileU(η,p) is bounded, the parameterN is equal to 0. According to the asymptotic property of Bessel function, the first-order modified Bessel function of first kindI1(η) can be expressed as(21)I1η=12πηeηTherefore, (18) can be written as(22)Uη,p=M2πηeηAccording to generalized Hooke’s law, the strain for plain strain problem in axisymmetric condition can be calculated as(23)εr=1-μ2Eσr2-μ1-μσθ2(24)εθ=1-μ2Eσθ2-μ1-μσr2By adding (23) multiplied by (1-μ)/μ with (24), the following can be obtained:(25)εr1-μμ+εθ=1-μ2E1-μμσr2-μ1-μσθ2+1-μ2Eσθ2-μ1-μσr2=1+μ1-2μEμσr2Then, the radial stress componentσr2 can be rewritten as(26)σr2=E1-μ1+μ1-2μεr+Eμ1+μ1-2μεθBy adding (23) multiplied by μ with (24) multiplied by (1-μ), the following can be obtained:(27)εrμ+εθ1-μ=1-μ2Eμσr2-μ1-μσθ2+1-μ2E1-μσθ2-μ1-μσr2=1+μ1-2μEσθ2Then, the tangential stress componentσθ2 can be rewritten as(28)σθ2=Eμ1+μ1-2μεr+E1-μ1+μ1-2μεθAssuming thatc1=E(1-μ)/[(1+μ)(1-2μ)] and c2=Eμ/[(1+μ)(1-2μ)], the stress-strain relation can be rewritten as(29)σr2=c1εr+c2εθ=c1∂ur,t∂r+c2ur,tr(30)σθ2=c2εr+c1εθ=c2∂ur,t∂r+c1ur,trOn the boundary of circular tunnel, the stress boundary condition can be expressed as(31)σr2r=r0=c1∂ur,t∂r+c2ur,trr=r0=ptWith the help ofLaplace transform, the stress boundary condition can be written as(32)c1∂Uη,p∂η+c2Uη,pηη=η0=Pp(33)Pp=Lpt=∫0∞pτe-ptdtwhere η0=pr0/Cp.Substituting (22) into (32), the parameterM can be obtained as(34)M=2Ppη0Cp2πη0peη0c12η0-1+2c2According toη=pr/Cp and (34), (22) can be expressed as(35)Ur,p=Ppr0/rCp/c1p-1/2-c2/c1Cp/r0er-r0/CppAccording to convolution theorem ofLaplace transform,(36)Lf1t∗f2t=F1p∗F2p(37)F1p=Pper-r0/Cpp(38)F2p=r0/rCp/c1p-1/2-c2/c1Cp/r0With the help of inverseLaplacetransform, the radial displacement u(r,t) around circular tunnel is obtained as(39)ur,t=Cppsr0/rc1ec1-2c2/2c1r0Cpt-at+r-r0/CpTherefore, according to (29) and (30), the radial stress component σr2 and tangential stress component σθ2 induced by radial blasting load can be obtained as(40)σr2=c1∂ur,t∂r+c2ur,tr=c2Cpc1-ar+Cp2psr0/rrec1-2c2/2c1r0Cpt-at+r-r0/Cp=μCp1-μ-ar+Cp2psr0/rre1-3μ/2r01-μCpt-at+r-r0/Cp(41)σθ2=c2∂ur,t∂r+c1ur,tr=Cp-c2c1ar+Cp2psr0/rrec1-2c2/2c1r0Cpt-at+r-r0/Cp=Cp-μ1-μar+Cp2psr0/rre1-3μ/2r01-μCpt-at+r-r0/Cp


## 2.4. Elastic Stress Field under Coupled High Axial Geostress and Blasting Load

Consequently, the radial stress componentσr and tangential stress component σθ under coupled high axial geostress and blasting load can be expressed as(42)σr=σr1+σr2=1-r02r2p0-E2ρ3/21-μ2rAJ1ρ1/2r+BN1ρ1/2r-CK1ρ1/2r+μCp1-μ-ar+Cp2psr0/rre1-3μ/2r01-μCpt-at+r-r0/Cp(43)σθ=σθ1+σθ2=1+r02r2p0+E2ρ3/21-μ2rAJ1ρ1/2r+BN1ρ1/2r-CK1ρ1/2r-E2ρ1-μ2AJ0ρ1/2r+BN0ρ1/2r-CK0ρ1/2r+Cp-μ1-μar+Cp2psr0/rre1-3μ/2r01-μCpt-at+r-r0/CpSubstituting (2), (42), and (43) into (1), the axial stress component σz can be expressed as(44)σz=Eεz0+μσr+σθ=pz-Eμ2ρ1-μ2AJ0ρ1/2r+BN0ρ1/2r-CK0ρ1/2r+Cp2-arμpsr0/rr1-μe1-3μ/2r01-μCpt-at+r-r0/Cp


## 3. Hoek-Brown Criterion Considering Blast-Induced Damage Effect

Assume that when deep rock mass meets the nonlinear Hoek-Brown criterion, deep rock mass fracture occurs. And the size and location of fracture zone can be obtained according to principal stress components. The Hoek-Brown criterion can be expressed as [36, 37](45)σ1=σ3+mbσcσ3+sσc2where σ1 and σ3 are the maximum and minimum principal stress, σc is uniaxial compressive strength of intact rock, and mb ands are strength parameters.Strength parametersmb ands can be calculated byGSI (geological strength index). During blasting excavation, blast-induced damage plays down the integrity of rock mass and weakens the mechanical properties of rock mass. Hence, blast-induced damage factorD is introduced for cumulative damage effects of blasting excavation [38]. Then, the value of strength parameters mb ands can be obtained as(46)mb=miexp⁡GSI-10028-14D(47)s=exp⁡GSI-1009-3Dwhere mi is the value of mb for intact rock.With the increase of distance, blast-induced damage factorD decays in a negative exponential function [38], and it can be assumed as(48)D=e-r-r0/r0


## 4. Validation of Present Results

In China, an obvious zonal disintegration phenomenon was observed in Dingji coal mine at -910 m level. The distribution of facture zones is shown in Figure3 [10]. According to research of Zhang et al. [39], an essential condition for zonal disintegration is maximum principal stress parallel to tunnel axis, exceeding 1.5 times uniaxial compressive strength of surrounding rock mass.Figure 3
Zonal disintegration at Dingji mine [10].According to in situ condition, density of sandstone is 2620 kg/m3, Young’s modulus is 12.97 GPa, Poisson’s ratio is 0.268, and uniaxial compressive strength is 88.55 MPa. The height and width of straight wall arch tunnel are 3.88 m and 5.00 m, respectively. According to equivalent circular method [40], the equivalent circle radius is 2.54 m. In consideration of overburden rock mass, vertical geostress and horizontal geostressp0 at infinity are 25.10 MPa. High axial geostress pz is assumed to be uniaxial compressive strength of surrounding rock mass, 88.55 MPa. Non-Euclidean modelq = 3.28×107 N·m2;C = 50 m−2. Considering rock structure, joints, and initial cracks, Hoek-Brown parameter mi is 10, andGSI is 75. Density and detonation velocity of explosive are 1100 kg/m3 and 3262 m/s, respectively. Peak pressure, decay coefficient, and action time of radial blasting load are 73.15 MPa, 0.87, and 8 ms, respectively. Blast-induced damage factorD decays in a negative exponential function.Figure4 presents the number and location of fracture zones from present numerical computation results. As seen from Figure 4, zonal disintegration arises in both conditions, while the width of fracture zones is different. On one hand, radial blasting load leads to stress redistribution around the deep tunnel. Then the elastic stress field is changed. On the other hand, radial blasting load produces some microcracks in surrounding rock with deterioration of its mechanical properties and damage to its integrity. It can be found that blasting load plays an important role in determining the width of fracture zones near the excavation. Comparing Figure 3 with Figure 4, the number and location of fractured zones under coupled high axial geostress and blasting load are in good accordance with the results observed in Dingji coal mine.Figure 4
Zonal disintegration from present numerical computation result.
(a)
High axial geostress (b)
Coupled high axial geostress and blasting load


## 5. Numerical Computation Results

### 5.1. Effect of Geological Strength Index (GSI) on Distribution of Fracture Zones

Distribution of fractures zones under different geological strength index (GSI) conditions is shown in Figure 5. The other parameters are the same as mentioned in Section 4.Figure 5
Effect of geological strength index (GSI) on zonal disintegration.
(a)
GSI = 90 (b)
GSI = 80 (c)
GSI = 75 (d)
GSI = 70As seen from Figure5, both the number and the width of fracture zones increase with the reduction of geological strength index (GSI).


### 5.2. Effect of Hoek-Brown Parametermi on Distribution of Fracture Zones

Figure6 presents the distribution of fractures zones under various Hoek-Brown parameter mi conditions when geological strength index (GSI) is 80. The other parameters are the same as mentioned in Section 4.Figure 6
Effect of Hoek-Brown parametermi on zonal disintegration.
(a)
m i = 7 (b)
m i = 10 (c)
m i = 15 (d)
m i = 25It can be seen from Figure6 that when Hoek-Brown parameter mi is greater than 10, only the width of fracture zones increases with the reduction of Hoek-Brown parameter mi. While when Hoek-Brown parameter mi is less than 10, both the number and the width of fracture zones increase with the reduction of Hoek-Brown parameter mi.


### 5.3. Effect of High Axial Geostresspz on Distribution of Fracture Zones

As geological strength index (GSI) is 90 and Hoek-Brown parameter mi is equal to 15, the distribution of fractures zones under various high axial geostress pz conditions is shown in Figure 7. The other parameters are the same as mentioned in Section 4. High axial geostress pz varies from 1 times to 1.6 times of uniaxial compressive strength of surrounding rock mass.Figure 7
Effect of high axial geostresspz on zonal disintegration.
(a)
p z = 88.55 MPa (b)
p z = 106.26 MPa (c)
p z = 123.97 MPa (d)
p z = 141.68 MPaAs seen from Figure7, both the number and the width of fracture zones increase with the increase of high axial geostress pz.


### 5.4. Effect of Peak Radial Blasting Loadps on Distribution of Fracture Zones

When geological strength index (GSI) is equal to 80 and Hoek-Brown parameter mi is equal to 10, the distribution of fractures zones under various peak radial blasting load conditions is shown in Figure 8. The other parameters are the same as mentioned in Section 4.Figure 8
Effect of peak radial blasting loadps on zonal disintegration.
(a)
p s = 36.58 MPa (b)
p s = 73.15 MPa (c)
p s = 146.30 MPa (d)
p s = 219.45 MPaAs seen from Figure8, peak radial blasting load ps, which decays in a negative exponential function, shows a small influence on the number of fracture zones but a relatively big effect on the width of fracture zone near the excavation.


## 5.1. Effect of Geological Strength Index (GSI) on Distribution of Fracture Zones

Distribution of fractures zones under different geological strength index (GSI) conditions is shown in Figure 5. The other parameters are the same as mentioned in Section 4.Figure 5
Effect of geological strength index (GSI) on zonal disintegration.
(a)
GSI = 90 (b)
GSI = 80 (c)
GSI = 75 (d)
GSI = 70As seen from Figure5, both the number and the width of fracture zones increase with the reduction of geological strength index (GSI).


## 5.2. Effect of Hoek-Brown Parametermi on Distribution of Fracture Zones

Figure6 presents the distribution of fractures zones under various Hoek-Brown parameter mi conditions when geological strength index (GSI) is 80. The other parameters are the same as mentioned in Section 4.Figure 6
Effect of Hoek-Brown parametermi on zonal disintegration.
(a)
m i = 7 (b)
m i = 10 (c)
m i = 15 (d)
m i = 25It can be seen from Figure6 that when Hoek-Brown parameter mi is greater than 10, only the width of fracture zones increases with the reduction of Hoek-Brown parameter mi. While when Hoek-Brown parameter mi is less than 10, both the number and the width of fracture zones increase with the reduction of Hoek-Brown parameter mi.


## 5.3. Effect of High Axial Geostresspz on Distribution of Fracture Zones

As geological strength index (GSI) is 90 and Hoek-Brown parameter mi is equal to 15, the distribution of fractures zones under various high axial geostress pz conditions is shown in Figure 7. The other parameters are the same as mentioned in Section 4. High axial geostress pz varies from 1 times to 1.6 times of uniaxial compressive strength of surrounding rock mass.Figure 7
Effect of high axial geostresspz on zonal disintegration.
(a)
p z = 88.55 MPa (b)
p z = 106.26 MPa (c)
p z = 123.97 MPa (d)
p z = 141.68 MPaAs seen from Figure7, both the number and the width of fracture zones increase with the increase of high axial geostress pz.


## 5.4. Effect of Peak Radial Blasting Loadps on Distribution of Fracture Zones

When geological strength index (GSI) is equal to 80 and Hoek-Brown parameter mi is equal to 10, the distribution of fractures zones under various peak radial blasting load conditions is shown in Figure 8. The other parameters are the same as mentioned in Section 4.Figure 8
Effect of peak radial blasting loadps on zonal disintegration.
(a)
p s = 36.58 MPa (b)
p s = 73.15 MPa (c)
p s = 146.30 MPa (d)
p s = 219.45 MPaAs seen from Figure8, peak radial blasting load ps, which decays in a negative exponential function, shows a small influence on the number of fracture zones but a relatively big effect on the width of fracture zone near the excavation.


## 6. Conclusions

As a characteristic failure in deep rock masses, zonal disintegration phenomenon is such a unique failure phenomenon with alternative distribution of fracture zones and nonfracture zones. To study the formation mechanism of zonal disintegration under coupled high axial geostress and blasting load, the elastic stress field distribution for a circular tunnel in deep isotropic rock masses is deduced by assuming that radial blasting load decays in a negative exponential function. And Hoek-Brown criterion is modified by assuming that blast-induced damage effect decays in a negative exponential function. With the deep tunnel of Dingji coal mine in China as engineering background, the number and width of fracture zones are determined and they are in good accordance with the results observed in Dingji coal mine. Some numerical computations are carried out to study the effect of mechanical parameters of deep rock masses, high axial geo-stress, and radial blasting load on zonal disintegration. It is found that both the number and width of fracture zones mainly depend on high axial geostress and mechanical parameters of deep rock masses, and peak radial blasting load plays an important role in determining the width of fracture zone near the excavation. Both the number and the width of fracture zones increase with the increase of high axial geostress or with the deterioration of mechanical parameters of deep rock masses, while only the width of fracture zone near the excavation is extended with the increase of peak radial blasting load.



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*Source: 4957917-2018-07-04.xml*