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Zonal disintegration of surrounding rock mass around the diversion tunnels in Jinping II Hydropower Station, Southwestern China
Theoretical and Applied Fracture Mechanics 51 (2009) 129–138
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Theoretical and Applied Fracture Mechanics journal homepage: www.elsevier.com/locate/tafmec
Zonal disintegration of surrounding rock mass around the diversion tunnels in Jinping II Hydropower Station, Southwestern China Q.H. Qian a,b, X.P. Zhou a,*, H.Q. Yang a, Y.X. Zhang a, X.H. Li c a
School of Civil Engineering, Chongqing University, Chongqing 400045, China PLA University of Science and Technology, Nanjing 210007, China c Key Lab for the Exploitation of Southwestern Resources and the Environmental Disaster Control Engineering, Ministry of Education, Chongqing University, Chongqing 400044, China b
a r t i c l e
i n f o
Article history: Available online 10 April 2009 Keywords: Jinping II Hydropower Station Deep rock mass Zonal disintegration Numerical simulation
a b s t r a c t By means of numerical simulation, the special phenomenon of zonal disintegration of surrounding rock mass around the diversion tunnels of Jinping II Hydropower Station is analyzed in this paper. In order to model the growth and coalescence of cracks within rock mass in Jinping II Hydropower Station, the weakelement is adopted. When cracks coalesce, failure of deep crack-weakened rock masses occurs and fractured zone is formed. The present result is different from the one obtained by the traditional elasto-plastic theory. The numerical results show that the slip-line zonal fracture is created within rock mass around the diversion tunnels in Jinping II Hydropower Station. Meanwhile, the magnitude and distributions of fractured zones are determined by numerical simulation. It is shown that the present results are in good agreement with the one observed by model tests. Through sensitivity analysis, the effects of stress condition, cohesion and the angle of internal friction on the phenomenon of zonal disintegration is determined. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In shallow rock mass engineering, the excavation-affected rock around tunnel contains an excavation-damage zone and an excavation disturbed zone [1]. The excavation-damage zone (EDZ) refers to irreversible damage in the shallow crack-weakened rock resulting from the excavation of a tunnel. Damage occurs when the energy is dissipated in the frictional sliding along preexisting flaw and the growth of wing cracks. The excavation-damage zone can be further divided into loose zone and plastic zone. The loose zone is close to the tunnel wall and is delineated by a more rapid decrease in measured acoustic velocity and more rapid increase in hydraulic transmissivity than in the plastic zone of the EDZ. It is found from visual observations that macroscopic cracks exists in the loose zone. The loose zone is divided into failed and a nonfailed zones [2,3]. The failed zone occurs where cracks coalesce and rock has completely detached from the surrounding rock mass. The non-failed part of the loose zone, in contrast to the failed zone, may have visible macro-cracking but is not detached. The plastic zone displays a more gradual change in acoustic velocity and hydraulic transmissivity, which eventually return to background levels [1]. Beyond the EDZ itself, in situ stresses are disturbed in a range of several excavation radii [4] but not to such a degree that irreversible stress-induced changes to the rock properties have oc* Corresponding author. Tel./fax: +86 23 6512 3511. E-mail addresses: [email protected], [email protected] (X.P. Zhou). 0167-8442/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2009.04.006
curred. Therefore, the volume of stress-disturbed rock is referred to as the elastic zone, in which no microcrack propagates. The mechanical behaviors of deep rock mass are different from those of shallow rock mass. Zonal disintegration refers to the alternative occurrence of disintegration zone and non-disintegration zone around tunnel in deep rock mass engineering [5]. With the development of deep rock mass engineering, the special phenomenon of zonal disintegration, which is different from the traditional elasto-plastic theory, is observed in deep underground engineering. However, the mechanism of zonal disintegration is still not explicitly revealed. Better understanding of the mechanism of zonal fracture within deep rock mass promises benefit in many areas from rock mechanics to deep underground engineering and earthquake prediction. It is essential and important to understand how zonal fracture occurs under high geostress in order to provide better understanding of fracturing process of deep rock mass that occur in the deep engineering fields. At present, many approaches, such as in situ observations, model test and theoretical analysis, are applied to study the special phenomenon of zonal disintegration in deep rock mass. The phenomenon of zonal disintegration is initially observed in the mines of Talnakh-Oktyarb’ skiy deposit at depths up to 1050 m, in Russia. It was demonstrated that around the tunnel there are zones of fissured and non-fissured, propagating discretely into the depths of surrounding rock mass [6–9]. Similarly, zonal disintegration are observed by the in situ velocity tests of ultrasonic wave in the mine of Jinchuan, China [10]. Many model tests have also been
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conducted. For example, the results of layered fracture within surrounding rock have been obtained by Gu et al. [11]. It is obvious that both in situ test and model test are expensive and confined in certain condition. In the author’s previous work, the mechanism of zonal disintegration in deep rock mass is investigated, and the size and distributions of zonal disintegration are determined from theoretical point of view [12]. The theoretical results are more accurate, but the phenomenon of zonal disintegration is so complex that not every problem has explicit theoretical solution now. Usually, numerical simulation is effective in solving these problems. However, no numerical simulation of zonal disintegration is available now. In this paper, in order to take the growth and coalescence of cracks within rock mass into account, a new numerical simulation method, in which the weak-element is adopted, is proposed. It is shown that the present results are in good agreement with the one observed by model tests. Finally, the size and distributions of zonal disintegration in Jinping II Hydropower Station is obtained. Through sensitivity analysis, the effect of stress condition, cohesion and the angle of internal friction on the phenomenon of zonal disintegration are determined. 2. Comparison with the experimental observation To validate the weak-element model the weak-element method, the experiment observation on facture and failure around underground openings is chosen. Laboratory experiments were performed on the thick-walled hollow cylinders of Berea sandstone with a hole diameter of 25.4 mm, an external diameter of 89 mm, and a length of 152 mm [13,14]. The samples were subjected to axisymmetric pressures on outer diameter, internal pressure is zero. The sample were constrained to near zero axial deformation
(plane strain). Failure around the hole was caused by loading to a state of high external pressure (75 MPa). Uniaxial compressive strengths reported in the literature rang from 44–74 MPa for Berea sandstone. For Berea sandstone, Young’s modulus is 17 GPa, Poisson’s ratio is 0.32. The above parameters were applied to model facture and failure around the thick-walled hollow cylinders of Berea sandstone. The boundary conditions of numerical model is the same as those of experimental model. The experimental observation on the experiment observation on facture and failure around the thick-walled hollow cylinders of Berea sandstone is shown in Fig. 1a. The numerical result is depicted in Fig. 1b. Comparison between numerical and experimental results, it is found that the numerical simulation result is in good agreement with the experimental one on failure modes around the hole of Berea sandstone. It is implied that the present weak-element method can be applied to model failure modes around underground openings. 3. Background of Jinping II Hydropower Project Jinping II Hydropower Project at the upriver of the Yalong River is located in Sichuan Province, Southwest of China. The installed capacity of the project is 4800 MW. Four diversion tunnels with a diameter of 12–13 m and a total length of 16.67 km are constructed at depth of 1500–2000 m. In somewhere, the depth is up to 2525 m. There exist a series of difficulties, such as high geostress (max = 70 MPa), rock burst, karst, water flow, and instability of the surrounding rock mass [15,16]. Experience in dealing with some of these problems is still lacking. The main strata outcropping in this area consist of marble, limestone, sandstone and so on. There are three main sets of fractures within rock mass. One set of fractures is dominant. Dip angle of the dominant discontinuities is 60°, the length and spacing of the dominant discontinuities are 1 m and 0.5 m, respectively. The dominant discontinuities are filled with chip of rock whose thicknesses is equal to 2 mm. Both TBM and NATW are adopted in the construction of diversion tunnels. The No. 1 and No. 3 tunnels with a diameter of 13 m are constructed by TBM. However, the No. 2 and No. 4 tunnels are the four-arcs ones, which are constructed by NATW. The tests show that the maximum principal stress is about 70 MPa and the minimum principal stress is about 31 MPa. 4. Numerical simulation of zonal disintegration around diversion tunnel in Jinping II Hydropower Station
Fig. 1a. Typical failure around the thick-walled hollow cylinders of Berea sandston [13].
Fig. 1b. The numerical result of failure in Berea sandston.
In the middle of diversion tunnels, a cross-section, which is mainly composed of marble of the Zagu’nao stratum (T 2b ), is chosen as a representative section. The uniaxial compressive strength
Fig. 2. The complete stress–strain curves of marble with the confining pressure of 30 MPa.
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Fig. 3. Sketch of diversion tunnel in Jinping II Hydropower Station (plain strain). Table 1 Parameters of rock mass by tests. Cohesion Angle of Poisson’s Young’s Weight (MPa) internal ratio modulus density friction (°) (GPa) (kN m3) Intact rock element (marble) 10.6 Weak-element (faults) 2.1
34 34
0.23 0.23
18.9 10.9
27.20 25.16
of marble is about 75–85 MPa. The complete stress–strain curves of marble are shown in Fig. 2. 4.1. The numerical model A cross-section (300 m 90 m) with four diversion tunnels was analyzed by using multiscale simulation, as shown in Fig. 3. In order to model the growth and coalescence of cracks within rock
Fig. 4. The distributions of horizontal stress in the surrounding rock mass around diversion tunnel.
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Fig. 5. The distributions of vertical stress in the surrounding rock mass around diversion tunnel.
mass in Jinping II Hydropower Station, the weak-element method is applied to multiscale simulation. The present method is different from the traditional continuum mechanics-based approaches .The present method tries to consider the pre-existing crack from the microstructure level rather than the continuous level. The constitutive relation of the weak-element intersected by the pre-existing cracks, in which the nucleation, growth and coalescence of cracks are analyzed, is derived from mesomechanical theory [17]. This model is investigated under plane strain condition, in which there are 449,600 quadrangular elements. The cross-section in Fig. 3 is subjected to geostresses of rv ¼ 69:5 MPa and rh ¼ 23 MPa. It should be noted that the compressive stress is negative in this paper. The vertical displacement components of the bottom are restricted, and both left and right boundaries are loaded by geostress. All the material parameters are listed in Table 1.
around arch crown and sidewalls is subjected to tensile stress, which distributes in few region. It also shown in Fig. 4a that the horizontal stress is decreased at the distance of 2.2–4.2 m from the tunnel. This phenomenon of decrease of the horizontal stress can be observed more clearly in the enlarged photos, as shown in Fig. 4b–e. Fig. 5 illustrates the distributions of vertical stress around the diversion tunnel. The stress distributions obtained by the present numerical analysis are different from those obtained by traditional elasto-plastic theory. It is obvious that the stress field obtained by the present numerical analysis is not continuous, while the stress field obtained by traditional elasto-plastic theory is continuous. Fig. 6 shows the zonal disintegration around the diversion tunnel in Jinping II Hydropower Station. It is shown from the
4.2. Analysis of zonal disintegration around diversion tunnel in Jinping II Hydropower Station Horizontal and vertical stress are adopted, since horizontal and vertical stress can be monitored in the future. The distribution of horizontal stress around the diversion tunnel is depicted in Fig. 4. It is noted that the surrounding rock mass
Fig. 6. Distributions of zonal disintegration around four diversion tunnels.
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Fig. 7. The enlarged photo of the distributions of disintegration zone within the surrounding rock mass around diversion tunnel.
numerical results that there exist zones of fissured and non-fissured, extending discretely into surrounding rock mass around
the tunnel. Zonal disintegration, whose width is about 2 m, exists around sidewalls of the tunnel, but also some disintegration zones discretely distribute far from the tunnel. It is shown from Fig. 7 that the fractured zones look like slip-line. The enlarged photo of Fig. 6 is depicted in Figs. 7 and 8. Table 2 illustrates the sizes of disintegration zone which is far from diversion tunnel. It is suggested that the zonal disintegration is sensitive to tunnel shape. In this model, the magnitude of disintegration zones around circular tunnels is less than that of disintegration zones around the four-arcs ones. 5. Comparisons between presented method and traditional elasto-plastic theory
Fig. 8. Enlarged photo of disintegration zone.
Figs. 9 and 10 illustrate the stress distributions in surrounding rock mass around diversion tunnels. Material parameters applied in the elasto-plastic analysis are as follows: weight density c ¼ 27:2 kN m3 , Young’s modulus E ¼ 18:9 GPa, Poisson’s ratio t ¼ 0:23, cohesion C = 10.6 MPa, the angle of internal friction u ¼ 34 , vertical loading rv ¼ 69:5 MPa, horizontal loading rh ¼ 23 MPa. It is noted from Fig. 9 that the surrounding rock mass around the arch crown and sidewalls are subjected to tensile stress, which distributes in a little region. It is shown from Fig. 10 that the vertical stress is increased around diversion tunnel. Compared with Figs. 4 and 5, the maximum horizontal stress is larger in Fig. 4 than that in Fig. 9 and the maximum vertical stress in Fig. 5 is smaller than that in Fig. 10. Moreover, the stress distributions in Fig. 9 are more homogeneous than those in Fig. 4. It can be seen from single tunnel that the stress distributions obtained by elasto-plastic theory and by present method are distinct. Take No. 1 tunnel for example, it is revealed from Fig. 11a that the horizontal stress distribution is homogeneous
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Table 2 Magnitude and distribution of disintegration zones far from diversion tunnel. Diversion tunnel
Number of fracture
Location of fracture
Orientation of fracture
Distance from tunnel (m)
Length of fracture (m)
Width of fracture (cm)
No. 1 tunnel
ALU1 ALU2 ARU1 ALD1 ARD1 BLU1 BRU1 BLD1 CLU1 CLD1 CRU1 DLU1 DLU2 DLU3 DRU1 DRU2 DLD1 DRD1 DRD2
Top of left corner Top of left corner Top of right corner Bottom of left corner Bottom of right corner Top of left corner Top of right corner Bottom of left corner Top of left corner Bottom of left corner Top of right corner Top of left corner Top of left corner Top of left corner Top of right corner Top of right corner Bottom of left corner Bottom of right corner Bottom of right corner
Tangential Tangential Tangential Radial Tangential Tangential Tangential Tangential Tangential Radial Tangential Tangential Tangential Tangential Tangential Tangential Tangential Tangential Tangential
1.30 2.69 2.58 – 1.93 1.96 2.63 1.67 2.75 – 2.96 1.93 2.26 3.03 2.11 3.28 1.28 1.48 2.20
1.87 2.44 3.22 3.56 1.50 1.91 1.82 1.69 2.08 2.87 2.12 1.19 2.82 1.89 2.03 2.23 2.83 1.69 2.43
8–10 7–8 6–10 6–8 6–7 6–7 6–8 8–16 6–10 10–16 8–10 5–6 6–10 5–8 8–11 10–12 <6 <8 8–11
No. 2 tunnel
No. 3 tunnel
No. 4 tunnel
Fig. 9. The distributions of horizontal stress obtained by elasto-plastic theory.
Fig. 10. The distributions of vertical stress obtained by using elasto-plastic theory.
Fig. 11. Comparison of the distributions of horizontal stress near No. 1 tunnel between two different models.
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Fig. 12. Comparison of the distributions of vertical stress around No. 1 tunnel between two different models.
Fig. 13. Enlarged photo of disintegration zone around No. 3 tunnel.
and continuous, such as part A. However, in the zonal disintegration model in Fig. 11b, there exist some areas around No. 1 tunnel, in which the horizontal stress is decreased and nonhomogeneous and discontinuous after excavation, such as part B. The same distribution rule of vertical stress has been observed in Fig. 12a and b. The phenomenon of zonal disintegration only occur when the geostress and strength of rock mass satisfy certain relationship. According to experimental observation and theoretical analysis [13,14,17], under plane strain condition, when value of geostress is less than that of uniaxial compressive strength of rock mass, the phenomenon of zonal disintegration may occur. The present numerical results also show that (1) when value of geostress is less than that of uniaxial compressive strength of rock mass, the phenomenon of zonal disintegration may not occur, as depicted in
Fig. 14. Disintegration zone around four-arcs tunnel.
Fig. 13a; (2) when value of geostress is more than that of uniaxial compressive strength of rock mass, the phenomenon of zonal disintegration may occur, as shown in Fig. 13b. 6. Comparisons between presented method and model tests In order to compare with model tests, a four-arcs tunnel is chosen, as shown in Fig. 14. In Fig. 14a, material parameters applied in numerical simulation are as follows: for the intact rock, weight density c ¼ 27:2 kN m3 , Young’s modulus E ¼ 18:9 GPa, Poisson’s
Fig. 15. Model of an included four-arcs tunnel.
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ratio t ¼ 0:23, cohesion C = 10.6 MPa, the angle of internal friction u ¼ 30 . For the weak-element, weight density c ¼ 25:16 kN m3 , Young’s modulus E ¼ 10:9 GPa, Poisson’s ratio t ¼ 0:23, cohesion C = 4 MPa, the angle of internal friction u ¼ 30 , vertical geostress rv ¼ 70 MPa, horizontal geostress rh ¼ 40 MPa, The uniaxial compressive strength of rock mass is 31 MPa. It can be seen from Fig. 14 that the disintegration zones look like slip-line. The present results are in good agreement with model tests by Gu et al. [11], as shown in Figs. 1a and b.
Table 3 Material properties. Intact rock
Weak-element
Young’s modulus (GPa)
Poisson’s ratio
Weight density (kN m3)
Young’s modulus (GPa)
Poisson’s ratio
Weight density (kN m3)
18.9
0.23
27.2
10.9
0.23
25.16
7. Sensitivity analysis The mechanism of zonal disintegration is not clearly revealed in the previous analysis. In order to reveal the mechanism of zonal disintegration in depth rock masses. The numerical analysis is preformed. The mechanism of zonal disintegration in depth rock masses is revealed by using the present numerical analysis. Size of the fractured zone under different condition is also obtained from the present numerical analysis. In order to study the parameter sensitivity, a single tunnel is modeled under plain strain condition, as shown in Fig. 15. A cross-section (60 m 60 m) with an included diversion tunnel of 12–13 m in diameter was analyzed and the total number of elements is 122,240. Material properties of intact rock and weak-element are listed in Table 3. Fig. 16 illustrates influence of value of geostress on the fractured zone. Material parameters applied to numerical simulation are as follows: for intact rock, cohesion C = 16 MPa, the angle of internal friction u ¼ 30 . For weak-element, cohesion C = 4 MPa,
Fig. 16. Comparison of disintegration zone under different stress condition.
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Fig. 17. Comparison of disintegration zones in surrounding rock mass between different angle of internal friction.
Fig. 18. Comparison of disintegration zones in surrounding rock mass between different cohesion values.
the angle of internal friction u ¼ 30 , the uniaxial compressive strength of rock mass is about 55 MPa. It is observed from Fig. 16a and b that fractured zone, which causes apparent failure of rock mass around tunnel, exists around the sidewalls of tunnel, but also fractured zone discretely distributes far from the tunnel when value of the geostress is large enough. It is shown from Fig. 16c that zonal disintegration only exists around the sidewalls of tunnel since value of geostress is not large enough to lead to apparent failure of rock mass around tunnel. It is found from Fig. 16d that zonal disintegration does not occur when value of geostress is less than the uniaxial compressive strength of rock mass. It is suggested from Fig. 16 that zonal disintegration only occurs within rock mass around tunnel when value of geostress is larger than the uniaxial compressive strength of rock mass. In Fig. 16a and b, since the value of geostress is more than that of the uniaxial compressive strength of rock mass, zonal disintegration causes apparent failure of rock mass around tunnel. As a result, the phenomenon of disintegration zones transfers to the left and right corner far from the tunnel, which is founded first by authors. By comparison Fig. 16a with Fig. 16b, it is found that magnitude and size of fractured zone increases with increasing the vertical stress when value of the horizontal stress is smaller than that of the vertical stress. It is observed from Fig. 16e that zonal disintegration exists around the sidewalls and arch crown of tunnel when the vertical and horizontal stresses are nearly the same. Fig. 17 illustrates effect of the angle of internal friction on the fractured zone. Material parameters applied to numerical simulation are as follows: for intact rock, cohesion C = 16 MPa. For weak-element, cohesion C = 4 MPa. The vertical and horizontal geostress are 85 MPa and 50 MPa, respectively.
It can be concluded from Fig. 17 that zonal disintegration depends on the angle of internal friction of rock mass. Magnitude and size of fractured zone increase with decreasing the angle of internal friction of rock mass. Fig. 18 shows effect of magnitude of cohesion on disintegration zone. Material parameters applied to numerical simulation are as follows: for intact rock, the angle of internal friction of rock mass u ¼ 30 . For weak-element, the angle of internal friction u ¼ 30 , cohesion C = 4 MPa. The values of vertical and horizontal geostress are 85 MPa and 50 MPa, respectively. It is found from Fig. 18 that zonal disintegration is sensitive to the value of cohesion. It can be concluded from Fig. 18 that magnitude and size of the disintegration zones increase with decreasing the value of cohesion. In order to study the parameter sensitivity, an included circular tunnel is modeled under plain strain condition, as shown in Fig. 19. A cross-section (60 m 60 m) with an included circular tunnel of 13 m in diameter was analyzed. In numerical simulation, material parameters are as follows: for intact rock, the angle of internal friction of rock mass u ¼ 30 , C = 10 MPa. For weak-element, the angle of internal friction u ¼ 30 , cohesion C = 4 MPa. It is shown from Fig. 19 that zonal disintegration apparently exists around circular tunnel, but also fractured zone apparently distributes far from the tunnel when value of the geostress is large enough. In Fig. 19a, magnitude of fractured zone around left and right sidewall tunnel is about 3, respectively. magnitude of fractured zone around left and right upper corner of tunnel is about 2, respectively. In Fig. 19b, since the value of geostress is more than that of the uniaxial compressive strength of rock mass, zonal disintegration causes failure of parts of rock mass around circular tunnel. Magnitude of fractured zone around left and right sidewall
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sive strength of rock mass. Magnitude and size of the disintegration zones increase with decreasing the value of cohesion and the angle of internal friction.
Acknowledgement The authors would like to express their sincere thank to Professor G.C. Sih for his kind help and remarks. This work is supported by the National Natural Science Foundation of China (Nos. 50490275, 50679097, 50621403, 50778184). References
Fig. 19. Comparison of disintegration zone around circular tunnel under different stress condition.
tunnel is about 4, respectively. Magnitude of fractured zone around left and right upper corner of tunnel is about 3, respectively. 8. Conclusion By means of numerical simulation, the special phenomenon of zonal disintegration in surrounding rock mass around the diversion tunnels of Jinping II Hydropower Station is discussed in this paper. The conclusions are summarized as follows: (1) In order to model the growth and coalescence of cracks within rock mass in Jinping II Hydropower Station, the weak-element method is adopted. Meanwhile, the sizes and magnitudes of fractured zone around diversion tunnels are determined. (2) The present numerical results are different from the one obtained by the elasto-plastic theory. Zonal disintegration, which is in the slip-line pattern, is observed in the numerical simulation. The present numerical results are in good agreement with the model tests. (3) The effect of geostress condition, cohesion and the angle of internal friction on the phenomenon of zonal disintegration is determined. The phenomenon of zonal fracture may occur when value of geostress is larger than the uniaxial compres-
[1] J.B. Martion, N.A. Chandler, Excavation-induced damage studies at the underground research laboratory, International Journal of Rock Mechanics and Mining Sciences 41 (8) (2004) 1413–1426. [2] R.S. Read, Characterizing excavation damage in highly-stressed granite at AECL’s underground research laboratory, in: J.B. Martino, C.D. Martin (Eds.), Proceedings of the EDZ Workshop, Designing the Excavation Disturbed Zone for a Nuclear Repository in Hard Rock held at the International Conference on Deep Geological Disposal of Radioactive Waste, Winnipeg, MB, September 20, 1996. [3] C.D. Martino, R.S. Read, AECL’s mine-by experiment: a test tunnel in brittle rock, in: M. Aubertin, F. Hassani, H. Mitri (Eds.), Proceedings of the Second North American Rock Mechanics Symposium: Narms ’96, Rock Mechanics Tools and Techniques, June 19–21, Rotterdam, Balkema, 1996. [4] B.H.G. Brady, E.T. Brown, Rock Mechanics for Underground Mining, George Allen and Unwin, 1985. [5] Q.H. Qian, The characteristic scientific phenomena of engineering response to deep rock mass and the implication of deepness, Journal of East China Institute of Technology 27 (1) (2004) 1–5 (in Chinese). [6] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, et al., Zonal disintegration of rocks around underground workings, part I: data of in-situ observations, Journal of Mining Science 22 (3) (1986) 157–168. [7] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, et al., Zonal disintegration of rocks around underground workings, part II: rock fracture simulated in equivalent materials, Journal of Mining Science 22 (4) (1986) 223–232. [8] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, et al., Zonal disintegration of rocks around underground workings, part III: theoretical concepts, Journal of Mining Science 23 (1) (1987) 1–6. [9] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, et al., Journal of Mining Science 25 (4) (1989) 297–302. [10] Y.S. Pan, Y.J. Li, X. Tang, Z.H. Zhang, Study on zonal disintegration of rock, Chinese Journal of Rock Mechanics and Engineering 26 (s1) (2007) 3335–3341 (in Chinese). [11] J.C. Gu, L.Y. Gu, A.M. Chen, J.M. Xu, W. Chen, Model test study on mechanism of layered fracture within surrounding rock of tunnels in deep stratum, Chinese Journal of Rock Mechanics and Engineering 27 (3) (2008) 433–438 (in Chinese). [12] X.P. Zhou, Q.H. Qian, Zonal fracturing mechanism in deep tunnel, Chinese Journal of Rock Mechanics and Engineering 26 (5) (2007) 877–895 (in Chinese). [13] R.T. Ewy, N.G.W. Cook, Deformation fracture around cylindrical openings in rock. I. Observations analysis of deformations, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 27 (5) (1990) 387– 407. [14] R.T. Ewy, N.G.W. Cook, Deformation fracture around cylindrical openings in rock. II. Initiation growth and interaction of fractures, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 27 (5) (1990) 409–427. [15] G.Q. Chen, X.T. Feng, H. Zhou, B.R. Chen, S.L. Huang, C.Q. Zhang, Numerical analysis of the long-term stability of the seepage tunnel in Jinping II Hydropower Station, Rock and Soil Mechanics 28 (s2) (2007) 417–422 (in Chinese). [16] S.Y. Wu, X.H. Ren, X.R. Chen, et al., Stability analysis and supporting design of surrounding rocks of diversion tunnel for Jinping Hydropower Station, Chinese Journal of Rock Mechanics and Engineering 24 (20) (2005) 3777–3782 (in Chinese). [17] X.P. Zhou, F.H. Wang, Q.H. Qian, B.H. Zhang, Zonal fracturing mechanism in deep crack-weakened rock masses, Theoretical and Applied Fracture Mechanics 50 (1) (2008) 57–65.
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Theoretical and Applied Fracture Mechanics journal homepage: www.elsevier.com/locate/tafmec
Zonal disintegration of surrounding rock mass around the diversion tunnels in Jinping II Hydropower Station, Southwestern China Q.H. Qian a,b, X.P. Zhou a,*, H.Q. Yang a, Y.X. Zhang a, X.H. Li c a
School of Civil Engineering, Chongqing University, Chongqing 400045, China PLA University of Science and Technology, Nanjing 210007, China c Key Lab for the Exploitation of Southwestern Resources and the Environmental Disaster Control Engineering, Ministry of Education, Chongqing University, Chongqing 400044, China b
a r t i c l e
i n f o
Article history: Available online 10 April 2009 Keywords: Jinping II Hydropower Station Deep rock mass Zonal disintegration Numerical simulation
a b s t r a c t By means of numerical simulation, the special phenomenon of zonal disintegration of surrounding rock mass around the diversion tunnels of Jinping II Hydropower Station is analyzed in this paper. In order to model the growth and coalescence of cracks within rock mass in Jinping II Hydropower Station, the weakelement is adopted. When cracks coalesce, failure of deep crack-weakened rock masses occurs and fractured zone is formed. The present result is different from the one obtained by the traditional elasto-plastic theory. The numerical results show that the slip-line zonal fracture is created within rock mass around the diversion tunnels in Jinping II Hydropower Station. Meanwhile, the magnitude and distributions of fractured zones are determined by numerical simulation. It is shown that the present results are in good agreement with the one observed by model tests. Through sensitivity analysis, the effects of stress condition, cohesion and the angle of internal friction on the phenomenon of zonal disintegration is determined. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In shallow rock mass engineering, the excavation-affected rock around tunnel contains an excavation-damage zone and an excavation disturbed zone [1]. The excavation-damage zone (EDZ) refers to irreversible damage in the shallow crack-weakened rock resulting from the excavation of a tunnel. Damage occurs when the energy is dissipated in the frictional sliding along preexisting flaw and the growth of wing cracks. The excavation-damage zone can be further divided into loose zone and plastic zone. The loose zone is close to the tunnel wall and is delineated by a more rapid decrease in measured acoustic velocity and more rapid increase in hydraulic transmissivity than in the plastic zone of the EDZ. It is found from visual observations that macroscopic cracks exists in the loose zone. The loose zone is divided into failed and a nonfailed zones [2,3]. The failed zone occurs where cracks coalesce and rock has completely detached from the surrounding rock mass. The non-failed part of the loose zone, in contrast to the failed zone, may have visible macro-cracking but is not detached. The plastic zone displays a more gradual change in acoustic velocity and hydraulic transmissivity, which eventually return to background levels [1]. Beyond the EDZ itself, in situ stresses are disturbed in a range of several excavation radii [4] but not to such a degree that irreversible stress-induced changes to the rock properties have oc* Corresponding author. Tel./fax: +86 23 6512 3511. E-mail addresses: [email protected], [email protected] (X.P. Zhou). 0167-8442/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2009.04.006
curred. Therefore, the volume of stress-disturbed rock is referred to as the elastic zone, in which no microcrack propagates. The mechanical behaviors of deep rock mass are different from those of shallow rock mass. Zonal disintegration refers to the alternative occurrence of disintegration zone and non-disintegration zone around tunnel in deep rock mass engineering [5]. With the development of deep rock mass engineering, the special phenomenon of zonal disintegration, which is different from the traditional elasto-plastic theory, is observed in deep underground engineering. However, the mechanism of zonal disintegration is still not explicitly revealed. Better understanding of the mechanism of zonal fracture within deep rock mass promises benefit in many areas from rock mechanics to deep underground engineering and earthquake prediction. It is essential and important to understand how zonal fracture occurs under high geostress in order to provide better understanding of fracturing process of deep rock mass that occur in the deep engineering fields. At present, many approaches, such as in situ observations, model test and theoretical analysis, are applied to study the special phenomenon of zonal disintegration in deep rock mass. The phenomenon of zonal disintegration is initially observed in the mines of Talnakh-Oktyarb’ skiy deposit at depths up to 1050 m, in Russia. It was demonstrated that around the tunnel there are zones of fissured and non-fissured, propagating discretely into the depths of surrounding rock mass [6–9]. Similarly, zonal disintegration are observed by the in situ velocity tests of ultrasonic wave in the mine of Jinchuan, China [10]. Many model tests have also been
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conducted. For example, the results of layered fracture within surrounding rock have been obtained by Gu et al. [11]. It is obvious that both in situ test and model test are expensive and confined in certain condition. In the author’s previous work, the mechanism of zonal disintegration in deep rock mass is investigated, and the size and distributions of zonal disintegration are determined from theoretical point of view [12]. The theoretical results are more accurate, but the phenomenon of zonal disintegration is so complex that not every problem has explicit theoretical solution now. Usually, numerical simulation is effective in solving these problems. However, no numerical simulation of zonal disintegration is available now. In this paper, in order to take the growth and coalescence of cracks within rock mass into account, a new numerical simulation method, in which the weak-element is adopted, is proposed. It is shown that the present results are in good agreement with the one observed by model tests. Finally, the size and distributions of zonal disintegration in Jinping II Hydropower Station is obtained. Through sensitivity analysis, the effect of stress condition, cohesion and the angle of internal friction on the phenomenon of zonal disintegration are determined. 2. Comparison with the experimental observation To validate the weak-element model the weak-element method, the experiment observation on facture and failure around underground openings is chosen. Laboratory experiments were performed on the thick-walled hollow cylinders of Berea sandstone with a hole diameter of 25.4 mm, an external diameter of 89 mm, and a length of 152 mm [13,14]. The samples were subjected to axisymmetric pressures on outer diameter, internal pressure is zero. The sample were constrained to near zero axial deformation
(plane strain). Failure around the hole was caused by loading to a state of high external pressure (75 MPa). Uniaxial compressive strengths reported in the literature rang from 44–74 MPa for Berea sandstone. For Berea sandstone, Young’s modulus is 17 GPa, Poisson’s ratio is 0.32. The above parameters were applied to model facture and failure around the thick-walled hollow cylinders of Berea sandstone. The boundary conditions of numerical model is the same as those of experimental model. The experimental observation on the experiment observation on facture and failure around the thick-walled hollow cylinders of Berea sandstone is shown in Fig. 1a. The numerical result is depicted in Fig. 1b. Comparison between numerical and experimental results, it is found that the numerical simulation result is in good agreement with the experimental one on failure modes around the hole of Berea sandstone. It is implied that the present weak-element method can be applied to model failure modes around underground openings. 3. Background of Jinping II Hydropower Project Jinping II Hydropower Project at the upriver of the Yalong River is located in Sichuan Province, Southwest of China. The installed capacity of the project is 4800 MW. Four diversion tunnels with a diameter of 12–13 m and a total length of 16.67 km are constructed at depth of 1500–2000 m. In somewhere, the depth is up to 2525 m. There exist a series of difficulties, such as high geostress (max = 70 MPa), rock burst, karst, water flow, and instability of the surrounding rock mass [15,16]. Experience in dealing with some of these problems is still lacking. The main strata outcropping in this area consist of marble, limestone, sandstone and so on. There are three main sets of fractures within rock mass. One set of fractures is dominant. Dip angle of the dominant discontinuities is 60°, the length and spacing of the dominant discontinuities are 1 m and 0.5 m, respectively. The dominant discontinuities are filled with chip of rock whose thicknesses is equal to 2 mm. Both TBM and NATW are adopted in the construction of diversion tunnels. The No. 1 and No. 3 tunnels with a diameter of 13 m are constructed by TBM. However, the No. 2 and No. 4 tunnels are the four-arcs ones, which are constructed by NATW. The tests show that the maximum principal stress is about 70 MPa and the minimum principal stress is about 31 MPa. 4. Numerical simulation of zonal disintegration around diversion tunnel in Jinping II Hydropower Station
Fig. 1a. Typical failure around the thick-walled hollow cylinders of Berea sandston [13].
Fig. 1b. The numerical result of failure in Berea sandston.
In the middle of diversion tunnels, a cross-section, which is mainly composed of marble of the Zagu’nao stratum (T 2b ), is chosen as a representative section. The uniaxial compressive strength
Fig. 2. The complete stress–strain curves of marble with the confining pressure of 30 MPa.
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Fig. 3. Sketch of diversion tunnel in Jinping II Hydropower Station (plain strain). Table 1 Parameters of rock mass by tests. Cohesion Angle of Poisson’s Young’s Weight (MPa) internal ratio modulus density friction (°) (GPa) (kN m3) Intact rock element (marble) 10.6 Weak-element (faults) 2.1
34 34
0.23 0.23
18.9 10.9
27.20 25.16
of marble is about 75–85 MPa. The complete stress–strain curves of marble are shown in Fig. 2. 4.1. The numerical model A cross-section (300 m 90 m) with four diversion tunnels was analyzed by using multiscale simulation, as shown in Fig. 3. In order to model the growth and coalescence of cracks within rock
Fig. 4. The distributions of horizontal stress in the surrounding rock mass around diversion tunnel.
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Fig. 5. The distributions of vertical stress in the surrounding rock mass around diversion tunnel.
mass in Jinping II Hydropower Station, the weak-element method is applied to multiscale simulation. The present method is different from the traditional continuum mechanics-based approaches .The present method tries to consider the pre-existing crack from the microstructure level rather than the continuous level. The constitutive relation of the weak-element intersected by the pre-existing cracks, in which the nucleation, growth and coalescence of cracks are analyzed, is derived from mesomechanical theory [17]. This model is investigated under plane strain condition, in which there are 449,600 quadrangular elements. The cross-section in Fig. 3 is subjected to geostresses of rv ¼ 69:5 MPa and rh ¼ 23 MPa. It should be noted that the compressive stress is negative in this paper. The vertical displacement components of the bottom are restricted, and both left and right boundaries are loaded by geostress. All the material parameters are listed in Table 1.
around arch crown and sidewalls is subjected to tensile stress, which distributes in few region. It also shown in Fig. 4a that the horizontal stress is decreased at the distance of 2.2–4.2 m from the tunnel. This phenomenon of decrease of the horizontal stress can be observed more clearly in the enlarged photos, as shown in Fig. 4b–e. Fig. 5 illustrates the distributions of vertical stress around the diversion tunnel. The stress distributions obtained by the present numerical analysis are different from those obtained by traditional elasto-plastic theory. It is obvious that the stress field obtained by the present numerical analysis is not continuous, while the stress field obtained by traditional elasto-plastic theory is continuous. Fig. 6 shows the zonal disintegration around the diversion tunnel in Jinping II Hydropower Station. It is shown from the
4.2. Analysis of zonal disintegration around diversion tunnel in Jinping II Hydropower Station Horizontal and vertical stress are adopted, since horizontal and vertical stress can be monitored in the future. The distribution of horizontal stress around the diversion tunnel is depicted in Fig. 4. It is noted that the surrounding rock mass
Fig. 6. Distributions of zonal disintegration around four diversion tunnels.
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Fig. 7. The enlarged photo of the distributions of disintegration zone within the surrounding rock mass around diversion tunnel.
numerical results that there exist zones of fissured and non-fissured, extending discretely into surrounding rock mass around
the tunnel. Zonal disintegration, whose width is about 2 m, exists around sidewalls of the tunnel, but also some disintegration zones discretely distribute far from the tunnel. It is shown from Fig. 7 that the fractured zones look like slip-line. The enlarged photo of Fig. 6 is depicted in Figs. 7 and 8. Table 2 illustrates the sizes of disintegration zone which is far from diversion tunnel. It is suggested that the zonal disintegration is sensitive to tunnel shape. In this model, the magnitude of disintegration zones around circular tunnels is less than that of disintegration zones around the four-arcs ones. 5. Comparisons between presented method and traditional elasto-plastic theory
Fig. 8. Enlarged photo of disintegration zone.
Figs. 9 and 10 illustrate the stress distributions in surrounding rock mass around diversion tunnels. Material parameters applied in the elasto-plastic analysis are as follows: weight density c ¼ 27:2 kN m3 , Young’s modulus E ¼ 18:9 GPa, Poisson’s ratio t ¼ 0:23, cohesion C = 10.6 MPa, the angle of internal friction u ¼ 34 , vertical loading rv ¼ 69:5 MPa, horizontal loading rh ¼ 23 MPa. It is noted from Fig. 9 that the surrounding rock mass around the arch crown and sidewalls are subjected to tensile stress, which distributes in a little region. It is shown from Fig. 10 that the vertical stress is increased around diversion tunnel. Compared with Figs. 4 and 5, the maximum horizontal stress is larger in Fig. 4 than that in Fig. 9 and the maximum vertical stress in Fig. 5 is smaller than that in Fig. 10. Moreover, the stress distributions in Fig. 9 are more homogeneous than those in Fig. 4. It can be seen from single tunnel that the stress distributions obtained by elasto-plastic theory and by present method are distinct. Take No. 1 tunnel for example, it is revealed from Fig. 11a that the horizontal stress distribution is homogeneous
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Table 2 Magnitude and distribution of disintegration zones far from diversion tunnel. Diversion tunnel
Number of fracture
Location of fracture
Orientation of fracture
Distance from tunnel (m)
Length of fracture (m)
Width of fracture (cm)
No. 1 tunnel
ALU1 ALU2 ARU1 ALD1 ARD1 BLU1 BRU1 BLD1 CLU1 CLD1 CRU1 DLU1 DLU2 DLU3 DRU1 DRU2 DLD1 DRD1 DRD2
Top of left corner Top of left corner Top of right corner Bottom of left corner Bottom of right corner Top of left corner Top of right corner Bottom of left corner Top of left corner Bottom of left corner Top of right corner Top of left corner Top of left corner Top of left corner Top of right corner Top of right corner Bottom of left corner Bottom of right corner Bottom of right corner
Tangential Tangential Tangential Radial Tangential Tangential Tangential Tangential Tangential Radial Tangential Tangential Tangential Tangential Tangential Tangential Tangential Tangential Tangential
1.30 2.69 2.58 – 1.93 1.96 2.63 1.67 2.75 – 2.96 1.93 2.26 3.03 2.11 3.28 1.28 1.48 2.20
1.87 2.44 3.22 3.56 1.50 1.91 1.82 1.69 2.08 2.87 2.12 1.19 2.82 1.89 2.03 2.23 2.83 1.69 2.43
8–10 7–8 6–10 6–8 6–7 6–7 6–8 8–16 6–10 10–16 8–10 5–6 6–10 5–8 8–11 10–12 <6 <8 8–11
No. 2 tunnel
No. 3 tunnel
No. 4 tunnel
Fig. 9. The distributions of horizontal stress obtained by elasto-plastic theory.
Fig. 10. The distributions of vertical stress obtained by using elasto-plastic theory.
Fig. 11. Comparison of the distributions of horizontal stress near No. 1 tunnel between two different models.
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Fig. 12. Comparison of the distributions of vertical stress around No. 1 tunnel between two different models.
Fig. 13. Enlarged photo of disintegration zone around No. 3 tunnel.
and continuous, such as part A. However, in the zonal disintegration model in Fig. 11b, there exist some areas around No. 1 tunnel, in which the horizontal stress is decreased and nonhomogeneous and discontinuous after excavation, such as part B. The same distribution rule of vertical stress has been observed in Fig. 12a and b. The phenomenon of zonal disintegration only occur when the geostress and strength of rock mass satisfy certain relationship. According to experimental observation and theoretical analysis [13,14,17], under plane strain condition, when value of geostress is less than that of uniaxial compressive strength of rock mass, the phenomenon of zonal disintegration may occur. The present numerical results also show that (1) when value of geostress is less than that of uniaxial compressive strength of rock mass, the phenomenon of zonal disintegration may not occur, as depicted in
Fig. 14. Disintegration zone around four-arcs tunnel.
Fig. 13a; (2) when value of geostress is more than that of uniaxial compressive strength of rock mass, the phenomenon of zonal disintegration may occur, as shown in Fig. 13b. 6. Comparisons between presented method and model tests In order to compare with model tests, a four-arcs tunnel is chosen, as shown in Fig. 14. In Fig. 14a, material parameters applied in numerical simulation are as follows: for the intact rock, weight density c ¼ 27:2 kN m3 , Young’s modulus E ¼ 18:9 GPa, Poisson’s
Fig. 15. Model of an included four-arcs tunnel.
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ratio t ¼ 0:23, cohesion C = 10.6 MPa, the angle of internal friction u ¼ 30 . For the weak-element, weight density c ¼ 25:16 kN m3 , Young’s modulus E ¼ 10:9 GPa, Poisson’s ratio t ¼ 0:23, cohesion C = 4 MPa, the angle of internal friction u ¼ 30 , vertical geostress rv ¼ 70 MPa, horizontal geostress rh ¼ 40 MPa, The uniaxial compressive strength of rock mass is 31 MPa. It can be seen from Fig. 14 that the disintegration zones look like slip-line. The present results are in good agreement with model tests by Gu et al. [11], as shown in Figs. 1a and b.
Table 3 Material properties. Intact rock
Weak-element
Young’s modulus (GPa)
Poisson’s ratio
Weight density (kN m3)
Young’s modulus (GPa)
Poisson’s ratio
Weight density (kN m3)
18.9
0.23
27.2
10.9
0.23
25.16
7. Sensitivity analysis The mechanism of zonal disintegration is not clearly revealed in the previous analysis. In order to reveal the mechanism of zonal disintegration in depth rock masses. The numerical analysis is preformed. The mechanism of zonal disintegration in depth rock masses is revealed by using the present numerical analysis. Size of the fractured zone under different condition is also obtained from the present numerical analysis. In order to study the parameter sensitivity, a single tunnel is modeled under plain strain condition, as shown in Fig. 15. A cross-section (60 m 60 m) with an included diversion tunnel of 12–13 m in diameter was analyzed and the total number of elements is 122,240. Material properties of intact rock and weak-element are listed in Table 3. Fig. 16 illustrates influence of value of geostress on the fractured zone. Material parameters applied to numerical simulation are as follows: for intact rock, cohesion C = 16 MPa, the angle of internal friction u ¼ 30 . For weak-element, cohesion C = 4 MPa,
Fig. 16. Comparison of disintegration zone under different stress condition.
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Fig. 17. Comparison of disintegration zones in surrounding rock mass between different angle of internal friction.
Fig. 18. Comparison of disintegration zones in surrounding rock mass between different cohesion values.
the angle of internal friction u ¼ 30 , the uniaxial compressive strength of rock mass is about 55 MPa. It is observed from Fig. 16a and b that fractured zone, which causes apparent failure of rock mass around tunnel, exists around the sidewalls of tunnel, but also fractured zone discretely distributes far from the tunnel when value of the geostress is large enough. It is shown from Fig. 16c that zonal disintegration only exists around the sidewalls of tunnel since value of geostress is not large enough to lead to apparent failure of rock mass around tunnel. It is found from Fig. 16d that zonal disintegration does not occur when value of geostress is less than the uniaxial compressive strength of rock mass. It is suggested from Fig. 16 that zonal disintegration only occurs within rock mass around tunnel when value of geostress is larger than the uniaxial compressive strength of rock mass. In Fig. 16a and b, since the value of geostress is more than that of the uniaxial compressive strength of rock mass, zonal disintegration causes apparent failure of rock mass around tunnel. As a result, the phenomenon of disintegration zones transfers to the left and right corner far from the tunnel, which is founded first by authors. By comparison Fig. 16a with Fig. 16b, it is found that magnitude and size of fractured zone increases with increasing the vertical stress when value of the horizontal stress is smaller than that of the vertical stress. It is observed from Fig. 16e that zonal disintegration exists around the sidewalls and arch crown of tunnel when the vertical and horizontal stresses are nearly the same. Fig. 17 illustrates effect of the angle of internal friction on the fractured zone. Material parameters applied to numerical simulation are as follows: for intact rock, cohesion C = 16 MPa. For weak-element, cohesion C = 4 MPa. The vertical and horizontal geostress are 85 MPa and 50 MPa, respectively.
It can be concluded from Fig. 17 that zonal disintegration depends on the angle of internal friction of rock mass. Magnitude and size of fractured zone increase with decreasing the angle of internal friction of rock mass. Fig. 18 shows effect of magnitude of cohesion on disintegration zone. Material parameters applied to numerical simulation are as follows: for intact rock, the angle of internal friction of rock mass u ¼ 30 . For weak-element, the angle of internal friction u ¼ 30 , cohesion C = 4 MPa. The values of vertical and horizontal geostress are 85 MPa and 50 MPa, respectively. It is found from Fig. 18 that zonal disintegration is sensitive to the value of cohesion. It can be concluded from Fig. 18 that magnitude and size of the disintegration zones increase with decreasing the value of cohesion. In order to study the parameter sensitivity, an included circular tunnel is modeled under plain strain condition, as shown in Fig. 19. A cross-section (60 m 60 m) with an included circular tunnel of 13 m in diameter was analyzed. In numerical simulation, material parameters are as follows: for intact rock, the angle of internal friction of rock mass u ¼ 30 , C = 10 MPa. For weak-element, the angle of internal friction u ¼ 30 , cohesion C = 4 MPa. It is shown from Fig. 19 that zonal disintegration apparently exists around circular tunnel, but also fractured zone apparently distributes far from the tunnel when value of the geostress is large enough. In Fig. 19a, magnitude of fractured zone around left and right sidewall tunnel is about 3, respectively. magnitude of fractured zone around left and right upper corner of tunnel is about 2, respectively. In Fig. 19b, since the value of geostress is more than that of the uniaxial compressive strength of rock mass, zonal disintegration causes failure of parts of rock mass around circular tunnel. Magnitude of fractured zone around left and right sidewall
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sive strength of rock mass. Magnitude and size of the disintegration zones increase with decreasing the value of cohesion and the angle of internal friction.
Acknowledgement The authors would like to express their sincere thank to Professor G.C. Sih for his kind help and remarks. This work is supported by the National Natural Science Foundation of China (Nos. 50490275, 50679097, 50621403, 50778184). References
Fig. 19. Comparison of disintegration zone around circular tunnel under different stress condition.
tunnel is about 4, respectively. Magnitude of fractured zone around left and right upper corner of tunnel is about 3, respectively. 8. Conclusion By means of numerical simulation, the special phenomenon of zonal disintegration in surrounding rock mass around the diversion tunnels of Jinping II Hydropower Station is discussed in this paper. The conclusions are summarized as follows: (1) In order to model the growth and coalescence of cracks within rock mass in Jinping II Hydropower Station, the weak-element method is adopted. Meanwhile, the sizes and magnitudes of fractured zone around diversion tunnels are determined. (2) The present numerical results are different from the one obtained by the elasto-plastic theory. Zonal disintegration, which is in the slip-line pattern, is observed in the numerical simulation. The present numerical results are in good agreement with the model tests. (3) The effect of geostress condition, cohesion and the angle of internal friction on the phenomenon of zonal disintegration is determined. The phenomenon of zonal fracture may occur when value of geostress is larger than the uniaxial compres-
[1] J.B. Martion, N.A. Chandler, Excavation-induced damage studies at the underground research laboratory, International Journal of Rock Mechanics and Mining Sciences 41 (8) (2004) 1413–1426. [2] R.S. Read, Characterizing excavation damage in highly-stressed granite at AECL’s underground research laboratory, in: J.B. Martino, C.D. Martin (Eds.), Proceedings of the EDZ Workshop, Designing the Excavation Disturbed Zone for a Nuclear Repository in Hard Rock held at the International Conference on Deep Geological Disposal of Radioactive Waste, Winnipeg, MB, September 20, 1996. [3] C.D. Martino, R.S. Read, AECL’s mine-by experiment: a test tunnel in brittle rock, in: M. Aubertin, F. Hassani, H. Mitri (Eds.), Proceedings of the Second North American Rock Mechanics Symposium: Narms ’96, Rock Mechanics Tools and Techniques, June 19–21, Rotterdam, Balkema, 1996. [4] B.H.G. Brady, E.T. Brown, Rock Mechanics for Underground Mining, George Allen and Unwin, 1985. [5] Q.H. Qian, The characteristic scientific phenomena of engineering response to deep rock mass and the implication of deepness, Journal of East China Institute of Technology 27 (1) (2004) 1–5 (in Chinese). [6] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, et al., Zonal disintegration of rocks around underground workings, part I: data of in-situ observations, Journal of Mining Science 22 (3) (1986) 157–168. [7] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, et al., Zonal disintegration of rocks around underground workings, part II: rock fracture simulated in equivalent materials, Journal of Mining Science 22 (4) (1986) 223–232. [8] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, et al., Zonal disintegration of rocks around underground workings, part III: theoretical concepts, Journal of Mining Science 23 (1) (1987) 1–6. [9] E.I. Shemyakin, G.L. Fisenko, M.V. Kurlenya, et al., Journal of Mining Science 25 (4) (1989) 297–302. [10] Y.S. Pan, Y.J. Li, X. Tang, Z.H. Zhang, Study on zonal disintegration of rock, Chinese Journal of Rock Mechanics and Engineering 26 (s1) (2007) 3335–3341 (in Chinese). [11] J.C. Gu, L.Y. Gu, A.M. Chen, J.M. Xu, W. Chen, Model test study on mechanism of layered fracture within surrounding rock of tunnels in deep stratum, Chinese Journal of Rock Mechanics and Engineering 27 (3) (2008) 433–438 (in Chinese). [12] X.P. Zhou, Q.H. Qian, Zonal fracturing mechanism in deep tunnel, Chinese Journal of Rock Mechanics and Engineering 26 (5) (2007) 877–895 (in Chinese). [13] R.T. Ewy, N.G.W. Cook, Deformation fracture around cylindrical openings in rock. I. Observations analysis of deformations, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 27 (5) (1990) 387– 407. [14] R.T. Ewy, N.G.W. Cook, Deformation fracture around cylindrical openings in rock. II. Initiation growth and interaction of fractures, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 27 (5) (1990) 409–427. [15] G.Q. Chen, X.T. Feng, H. Zhou, B.R. Chen, S.L. Huang, C.Q. Zhang, Numerical analysis of the long-term stability of the seepage tunnel in Jinping II Hydropower Station, Rock and Soil Mechanics 28 (s2) (2007) 417–422 (in Chinese). [16] S.Y. Wu, X.H. Ren, X.R. Chen, et al., Stability analysis and supporting design of surrounding rocks of diversion tunnel for Jinping Hydropower Station, Chinese Journal of Rock Mechanics and Engineering 24 (20) (2005) 3777–3782 (in Chinese). [17] X.P. Zhou, F.H. Wang, Q.H. Qian, B.H. Zhang, Zonal fracturing mechanism in deep crack-weakened rock masses, Theoretical and Applied Fracture Mechanics 50 (1) (2008) 57–65.