Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions

Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions

Dec. 2007 Journal of China University of Mining & Technology J China Univ Mining & Technol Vol.17 No.4 2007, 17(4): 0552 – 0556 Numerical Simula...

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Dec. 2007

Journal of China University of Mining & Technology

J China Univ Mining & Technol

Vol.17

No.4

2007, 17(4): 0552 – 0556

Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions SUN Jin-shan, ZHU Qi-hu, LU Wen-bo State Key Laboratory of Water Resource and Hydropower Engineering Science, Wuhan University, Wuhan, Hubei 430072, China Abstract: Rock burst in a circular tunnel under high in-situ stress conditions was investigated with a numerical method coupled the rock failure process theory (RFPA) and discontinuous deformation theory (DDA). Some numerical tests were carraied out to investigate the failuer patterns of circular tunnel under unloading conditions. Compared the results under loading conditions, the shapes of failure zones are more regular under the unloading conditions. The failure patterns in the same type of rock mass are clearly different because of non-homogeneity of the rock material. The extension of cracks shows some predictability with an increasing of in-situ stress. When the homogeneity index of rocks (m) is either relatively high or low and lateral pressure coefficients (λ) is high, the number of regular shear slide cracks decreases and the probability of a rock burst also becomes lower. Our numerical simulation results show that the stability of surface rock and the natural bedding stratification of rock material greatly affect rock bursts. Installing bolts with due diligence and suitably can effectively prevent rock bursts. However, it is not effective to control rock bursts by releasing the strain energy with normal pre-boreholes. Key words: circular tunnel; unloading; rock burst; numerical simulation; RFPA; DDA CLC number: TU 45

1

Introduction

Rock burst is a typical geologic phenomenon caused by excavation. Many scholars have investigated the complex geological hazard from different points of view. However, the essential reasons of this phenomenon have not been understood. Rock burst gestates in the rock masses and there never is any warning that it is about to happen. So files that record the entire process of rock burst are hard to find, which includes the process from gestation to burst. By model tests and investigating rock bursts records, some scholars proposed some ratiocinations about rock burst processes[1–3]. Rock burst contains the emerging and extension process of cracks on the meso-scale and the macroscopic loss of stability. It is very difficult to study this phenomenon with classical theories of mechanics. As well, only one single process of it can be studied by some numerical methods. Hence, in our investigation we have analyzed rock burst with a method coupled the rock failure process analysis theory (RFPA) on a meso-scale and the discontinuous deformation analy-

sis theory (DDA) on a macro-scale.

2 Numerical Simulation Method of Rock Bursts Rock burst is caused by the excavation of underground caves which unload the in-situ stress. It can be divided into two basic phases. One is the gestation process of rock burst, in which rock materials crack gradually. The other is the dynamic burst of rock blocks which release vast strain energy of the surrounding rock masses. Given this classification it also can be divided into two processes when rock burst is simulated with numerical methods. In the first step, the numerical mode could be studied by RFPA that considers the non-homogeneity of rock materials. A given load should be specified for numerical models in order to simulate the in-situ stress in rock masses. Then, elements in a circular opening will be deleted to simulate the excavation. The processes of cracks emerging and extending can be simulated with the RFPA2D program. Based on the results of RFPA2D, the failure pat-

Received 25 March 2007; accepted 15 June 2007 Projects 50639100 supported by the National Natural Science Foundation of China and 50539100 by the New Century Talents Plan of Education Department Corresponding author. Tel: +86-27-68772232; E-mail address: [email protected]

SUN Jin-shan et al

Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions

terns of surrounding rock masses can be judged. If a large number of failure points are distributed densely or dispersed widely and there are no long cracks, the rock mass may go into the plastic flow state (e.g. relaxation and squeezing) and releases a mass of strain energy. However, if there are some long cracks and a small quantity of dispersed failure points and the elastic module of rock blocks has not changed fundamentally, much of the strain energy may be released through rock bursts. When the surrounding rock mass is partioned into blocks it becomes a discontinuous deformation system which can be analyzed by DDA method. Based on the results of failure analysis a DDA model of the circular tunnel can be made, in which the mechanical parameters and load conditions are equal to those of the RFPA model. When the rock mass is meshed in rock blocks and structure faces, the cracks caused by stress unloading are simplified to the structure faces. Some potential crack faces are set in the model. Then the failure process of rock mass can be simulated with the DDA2D program.

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Simulation of Rock Burst Gestation

According to the slip-line theory, the surrounding rock mass will crack along the slip-line. Many rock Table 1 Loading conditions

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burst records and analyses of fractured faces show, with a scanning electron microscope, that the shearing-dislocation rock burst is one of the most common patterns, especially in circular tunnels[4–6]. Hence, the shearing-dislocation rock burst is most often investigated. Considering the characteristic structure of the tunnel, this problem is converted to a plane strain problem. 3.1 Unloading failure simulation The numerical models have dimensions of 400 mm ×400 mm. The diameter of the circular opening is 80 mm. The elements have dimensions of 1 mm×1 mm. The objects to be analyzed are the brittle, hard and intact rock masses. The mechanical properties of rock masses are specified as: elastic modulus E=60 GPa, poisson ratio µ=0.25, uniaxial compressive strength σ ci = 200 MPa, tensile strength τ = 5 MPa, internal friction angle φ=40º and homogeneity index m=3.0. In the calculation procedure, the horizontal and vertical press is specified for the model, initially to simulate the in-situ stress. Then the elements in the location of the opening are deleted to simulate the tunnel excavation. Subsequently, the failure patterns of the tunnel are simulated. The results are shown in Table 1.

Failure patterns of circular tunnel with different lateral pressure coefficients (λ)

In-situ stress (MPa)

Failure patterns

Vertical

Horizontal

λ=8

5

40

Tensile failure zone appears at top and bottom arch

λ=4

12.5

50

Shearing failure zones appear at both lateral arches; a few tensile failure zones appear at top and bottom arch

λ=1.25

33

44

Shearing failure zones appear at both lateral arches

λ=1.0

48

48

Splitting failure zones distributed around the opening

The calculation results indicate that the failure patterns of the surrounding rock masses are similar to those by Zhu which were conducted under the loading conditions[7]. However, the shape of the failure zone is more regular and the failure points are more cen-

(a) Horizontal in-situ stress is 40 MPa and vertical in-situ stress is 10 MPa

Fig. 1

(b)Horizontal in-situ stress is 44 MPa and vertical in-situ stress is 11 MPa

tralized. When λ=1.25 or 4, shear failure is the main failure pattern. In these cases, shear cracks would release less strain energy and make rock burst gestate easily. With λ=4, the failure patterns under different in-situ stress are shown in Fig. 1.

(c) Horizontal in-situ stress is 48 MPa and vertical in-situ stress is 12 MPa

(d) Horizontal in-situ stress is 50 MPa and vertical in-situ stress is 12.5 MPa

Distribution of shear stress and cracks in different in-situ stress fields

The results show that when λ=1.25 or 4, the failure depth will increase nonlinearly when the in-situ stress

becomes higher (Fig. 2).

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failure zones are clearly different because of the non-homogeneity of the rock material. As shown in Fig. 1, cracks extend much more regularly in the top zones than in the bottom zones. In the bottom zones the failure points are dispersed and are probably enter into the plastic flow state, which will release the great mass of strain energy of rock masses. Therefore, rock bursts will likely occur in the top failure zones. Fig. 2

Failure depth of rock mass (h is failure depth, D is the diameter of tunnel)

The failure zone extends in a regular fashion along with the increase of in-situ stress. And it shows some predictability: when the in-situ stress is low, cracks emerge in the shallow zone, parallel to the major principal stress orientation; when the in-situ stress increases, cracks emerge in the deep zone and extend towards the tunnel surface. When λ=1.25 or 4, the failure zones show the shear failure characteristics. In addition, the failure patterns of the top and bottom

(a) m=1

(b) m=3

Fig. 3

The microstructure of rock material is generally in one of two states: failure or intact. This makes different types of rock show different mechanical characteristics. The same type of rock, such as granite, coming from different producing areas may have a different non-homogeneity, so that the probability of a rock burst might be different too. With the model in 3.1, the failure patterns of rock masses are analyzed when the Weibull homogeneity index m is 1, 3, 5 or 8, λ=4, σ H = 50 (horizontal in-situ stress) and σ V = 12.5 (vertical in-situ stress) (Fig. 3).

(c) m=5

(d) m=8

Distributions of cracks for different homogeneity (m)

It shows that non-homogeneity of rock effects the failure pattern considerably. When m decreases, the number of failure points increases, however, the number of long cracks decreases. This means the rock mass goes into plastic flow state. Therefore, when the homogeneity index of rock material (m) is relatively high or low, the number of regular shear sliding cracks and the probability of rock burst will both decrease.

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3.2 Effect of non-homogeneity on rock bursts

Simulation of Dynamic Rock Burst Process

With the model in 3.1, the rock burst process can be simulated with the DDA method. It is assumed that the failure process does not release any strain energy[8–9]. Based on the results of the RFPA analysis, some initial structure faces (thick lines) are set in the DDA model and some potential crack faces (thin lines) are set along the potential failure directions. Other rock masses are divided into blocks, which helps to set stress filed after excavation. Then, the possibility of rock burst after excavation can be observed (Fig. 4).

Fig. 4

Sketch of RFPA model to DDA model

The mechanical properties of the initial structure faces are specified as: c=0 (cohesion), φ=40° (internal friction angle) and τ=0 (tensile strength). The mechanical properties of the potential crack faces are specified as: c=1.0 MPaˈφ=40° and τ=10 MPa. In order to guarantee the stability of computing, the properties of other rock masses are specified as: c=100 MPa, φ=80° and τ=500 MPa. The spring stiffness is 50 times elastic module of rock material. The simulation results show that the direction of the potential crack faces affects the rock burst process greatly. When the direction of potential crack faces is almost normal to the slip-line and cut the failure zone into square blocks, the crack faces will interlock and

SUN Jin-shan et al

Numerical Simulation of Rock Burst in Circular Tunnels Under Unloading Conditions

reduce the odds of rock bursts. When the direction of potential joints is almost parallel to the slip-line and cut the failure zone into wedge-shaped blocks, the crack faces will slide. Hence, when there are natural bedding stratifications in rock materials, their direction should be considered. As shown in Fig. 5, when the rock burst happens, the surface rock blocks initially burst at a high speed

(a) Step 300

(b) Step 500

Fig. 5

In practice, there are several measures can be taken to prevent rock bursts, such as spraying cool water on the rock surface, drilling energy release boreholes, softening the rock by injecting water, setting anchor bolts and steel bar nets[10]. In our study, we investigated the mechanism of preventing rock bursts by setting grouted rock bolts and energy release preboreholes. With λ=4, the in-situ stress σv =48 MPa

Fig. 6

and then a great number of blocks burst at lower speeds. Finally, a failure zone is formed. It suggests that loss of stability of the surface rock mass is an omen or the beginning of a rock burst. Hence, it is important to control the stability of the tunnel surface. For the new formed tunnel, setting shotcrete and anchor bolts will control the rock burst.

(c) Step 1000

(d) Step 2000

Simulation of dynamic processes of rock burst with DDA

5 Investigations of the Measures Preventing Rock Burst

(a) Initial status

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(b) After setting bolts

and σH=12 MPa, the possibility of rock burst was analyzed before and after setting anchor bolts and pre-boreholes. The mechanical properties of the bolts are specified as follows: E=210 GPa, τ˙400 MPa and their length is half of tunnel diameter (D). It is assumed that the bolts and rocks are glued as an integral whole. The diameter of the pre-boreholes is 6 mm; the distance between holes center and tunnel wall is D/8 and the distance between holes is D/8 (Fig. 6).

(c) Pre-borehole

(d) After setting pre-boreholes

Failure patterns of tunnel before and after installing mortar bolts and pre-boreholes

Compared with the rock mass without bolts, the number of cracks in the failure zone decreased significantly, especially surrounding the bolts. It means that the possibility of rock burst will be greatly reduced. Therefore, in tunnel constructions, installing grouted rock bolts suitably and as required will prevent the occurrence of rock bursts. After setting energy release pre-boreholes, the number of cracks clearly increases. The cracks mainly expand around the holes. However, the graph of the acoustic emission (AE) count and load step curve shows that in step 9 the AE count is 0 when pre-boreholes are set. It implies that there is almost no strain energy released by the holes. Therefore,

considering our numerical results, the mechanism of this measure should be investigated in advance (Fig. 7).

Fig. 7

Acoustic emission and load step curve after setting pre-borehole

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Conclusions

1) With a numerical simulation method coupled to RFPA and DDA theories, the gestation of rock burst was investigated when high in-situ stress was unloaded. The shape of the failure zone was more regular than those under loading conditions. The extension of cracks showed some predictability when the in-situ stress increased. The failure patterns in the same type of rock mass were clearly different because of the non-homogeneity of rock materials. When the homogeneity index of rock material is either relatively high or low and λ˙4, the number of regular shear slide cracks decreases and the probability of a rock burst becomes lower. 2) The dynamic process of rock bursts was simulated. The results show that the stability of the surface rock and the natural bedding stratification of rock

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material greatly affect rock bursts. 3) The failure patterns of the surrounding rock masses were investigated before and after setting grouted rock bolts and energy release pre-boreholes. It suggests that installing the grouted rock bolts with due diligence and suitably will control the rock burst significantly. However, the effect of pre-boreholes was not significant and its mechanism should be investigated further. 4) Obviously, it is difficult to simulate the failure process of the surrounding rock mass under real conditions. In the DDA model, the rock mass will have to be discretized artificially. The released strain energy is ignored in the DDA model. The rock burst involves continuous and discontinuous mechanics. Therefore, a perfect simulation of rock bursts needs further investigation.

References [1]

Tan Y A. Analysis of fractured face of rockburst with scanning electron microscope and its progressive failure process. Journal of Chinese Electron Microscopy, 1989, 21(2): 41–48. (In Chinese) [2] Miao X X, An L Q, Zhai M H, et al. Model of rockburst for extension of slip fracture in palisades. Journal of China University of Mining & Technology, 1999, 28(2): 113–117. (In Chinese) [3] Xu D J, Zhang G, Li T J. On the stress state in rock burst. Chinese Journal of Rock Mechanics and Engineering, 2000, 19(2): 169–172. (In Chinese) [4] Tang C A, Kaiser P K. Numerical simulation of cumulative damage and seismic energy release during brittle rock failurHü Part I: fundamentals. International Journal of Rock Mechanics and Mining Sciences, 1998, 35(2): 113–121. [5] Shi G H. Numerical Analysis Methods and Discontinuous Deformation Analysis. Beijing: Qinghua University Press, 1997. (In Chinese) [6] Fakhimia F, Carvalhoc T, Ishidad J F. Simulation of failure around a circular opening in rock. International Journal of Rock Mechanics & Mining Sciences, 2002, 39: 507–515. [7] Zhu W C, Liu J, Tang C A, et al. Simulation of progressive fracturing processes around underground excavations under biaxial compression. Tunneling and Underground Space Technology, 2005, 20: 231–247. [8] Huang R Q, Wang X N, Chan L S. Triaxial unloading test of rocks and its implication for rock burst. Bull Eng Geol Env, 2001, 60: 37–417. [9] Sahouryeh E, Dyskin A V, Germanovich L N. Crack growth under biaxial compression. Engineering Fracture Mechanics, 2002, 69: 2187–2198. [10] William D O. The behavior of tunnels at great depth under large static and dynamic pressures. Tunneling and Underground Space Technology, 2001, 16: 41–48.