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The effect of model scope on numerical results for deep-buried tunnel Naifei Liu1 and Ning Li2, Bianyuan Deng1, Xiaofan An1 1
School of Civil Engineering and Architecture, Xi’an University of Technology, No. 5 South JinhuaRoad, Xi’an, 710048 P.R. China;
[email protected] 2 School of Civil Engineering and Architecture, Xi’an University of Technology, No. 5 South JinhuaRoad, Xi’an, 710048 P.R. China; E-mail:
[email protected] ABSTRACT: Numerical simulation method has become one of the most important assistant approaches for engineering design. But for the model scope of the overlying strata of deep-buried tunnel, there's no consensus which could be accepted by the whole geotechnical engineering industry, and in most cases, the boundary of the model is determined by experience. In this paper, the influence of overlying strata’ simulation on stress and deformation field of surrounding rock mass is studied through the method of 2D and 3D finite element method. The diameter, depth and section shape are all taken into account. Finally, a reasonable simulating scope of the overlying strata is proposed which may provide some reference for deep-buried tunnel’s numerical simulation. INTRODUCTION Numerical Analysis is an analysis method developed with the widespread use of computer technology which is a powerful and effective complement for the experiment and theory. In geotechnical engineering, only a very few problems can be solved by structural or elastic mechanics method while most problems could not get an analytic solution for the geometrical and material nonlinearity. In this case, numerical computation method was emerged, which can obtain approximation solution compared with the actual situation. For the numerical analysis method can complete a large number of computing tasks in a short time with low cost and high efficiency, so it is widely used in safety evaluation and designs of the civil, mining and hydraulic rock engineering, and so on. Many people investigate the stability of tunnel with numerical method. Zhu (2011) using the FLAC software to simulate the creep effect of Hanjialing large-span road tunnel to access the long-term stability. Li (2006) studied the in-situ stress distribution in the engineering region by the three-dimensional finite element method. Dynamic responses of subway tunnel section were studied by using LS-DYNA under different yields of surface explosion for evaluation the blast-induced effects (Luo,
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Tunneling and Underground Construction GSP 242 © ASCE 2014
2007). High-speed train moving into a railway tunnel is studied by the computation of the compressible Navier-Stokes equations with the zonal method (Zhao, 2003). Finite difference method (FLAC 3D) was widely used in high-speed railway tunnel, tunnels in high field stress areas, subway tunnel and cross-river tunnel(Huang, 2005; Zhao, 2007; Li, 2004; Wang, 2012).Yang (2006), Zhang (2012) and Ji (2011) investigated the stability of tunnel with coupled analysis method. Numerical analysis method was also used in fire, water inrush, burst, et al (Yu, 2007; F.Y. Hsiao, 2009; Wang, 2011; Lu, 2011, S.Y. Wang, 2012). Overall, numerical analysis method is a very important tool for the tunneling analysis. However, there still are some people who doubt about the correctness of numerical analysis results for the overburden is reduced to linear load. For deep-buried tunnel, it is crucial to fix the boundary condition when simulation it with numerical method. But for the model scope of deep-buried tunnel’s overlying strata, nowadays, there's no uniform approach which could be accepted by the whole geotechnical engineering industry. In this study, a series of two or three dimension numerical tests are conducted to investigate the simulation method of the overlying strata of a deep-buried tunnel, with particular attention being paid to the stress and strain of the surrounding rock. As the main affecting factors, the diameter, depth and section shape are taken into account in numerical simulation. Finally, a reasonable simulating scope of the overlying strata has been proposed which could provide some reference for the tunnel’s numerical simulation. ANALYSIS PARAMETERS AND SCHEME In the following simulation, deep-buried tunnels are considered with different rock types. The rocks themselves are assumed to obey the Mohr-Coulomb criterion, and the analysis parameters of the rock and concrete are listed in Table 1, which are based upon the “Specifications for bolt-shotcrete support GB 50086-2001”. To simplify the analysis, the effects of the excavation process and reinforcement are not considered. The geometry and boundary conditions are shown in Fig.1. In order to simulate the real situation, the overlying strata are treated as a linear load. The span ratio of the arched section models is 1.0. Table 2 describes the scheme use to study the influence of boundary scope. THE NUMERICAL ANALYSIS RESULTS OF TWO-DIMENSION The results of the arched sections In this section, total 32 simulations with various rock types, diameters, tunnel shapes and different model scopes are carried out (see Table 2). They aim here is to study the influence of the model scope on the numerical simulation’s results of deepburied tunnel. For the two-dimensional simulation, the FIANL soft ware was used in this paper, which is well suited for the analysis of geotechnical engineering.
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l:m:n=5:4:3
Fig. 1. Key point’s position and the geometry and boundary conditions Table 1. Mechanical properties of surrounding rock and concrete Young’s modulus (GPa) 8.0 2.0 0.6 21.0
Materials Rock Ⅲ Rock Ⅳ Rock Ⅴ C20 Concrete
Poisson’s ratio 0.280 0.320 0.400 0.167
Cohesion force (MPa) 1.00 0.40 0.08 -
Friction angle (°) 40.0 33.0 25.0 -
Unit weight (×103KN/m3) 24.0 23.0 18.0 -
Table 2. The analysis scheme of two-dimensional numerical simulation Rock type
Buried depth (m)
Ⅲ
400
Ⅳ
300
Ⅴ
200
Diameter (m) 5 10 15 5 10 15 5 10
Tunnel shape
Spray layer (cm)
Circular, Arched
10
Circular, Arched
15
Circular, Arched
20
Model scope 5.0D, 10.0D, 40.0D, 80.0D 5.0D, 10.0D, 20.0D, 40.0D 5.0D, 8.30D, 13.3D, 26.7D 5.0D, 10.0D, 40.0D, 60.0D 5.0D, 10.0D, 20.0D, 30.0D 5.0D, 8.30D, 13.3D, 20.0D 5.0D, 10.0D, 20.0D, 40.0D 5.0D, 10.0D, 15.0D, 20.0D
* D is the diameter of the tunnel and model scope is the distance between model’s upper boundary and tunnels’ outline, the same below.
Rock Ⅲ Fig.2 shows the vertical deformation curves for different diameters (5m. 10m, 15m) and different model scopes. As expected, the deformation curves for the cases with a model scope of 5D lie above these for the cases with other model scopes for a certain diameter. However, the deformation increments are very small, which are only 0.78mm with a diameter of 5m, and that for 10m and 15m are 1.53mm and 2.24mm, respectively. Here the increment value is the numerical results of 5D model scope compared with the real depth model. Fig. 3 shows the vertical stress curves of deep tunnel under different model scopes. From this figure, it is clear that the stress around
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the tunnel also decrease with the model scopes increase from 5D to ground surface, however, the increment is very small as well. This indicates that, even for the 5D model, the boundary influence for the numerical results are still acceptable to real engineering. 1 First principal stresses /MPa
8 Displacement/mm
5D 40D
4
10D 80D
2 Key points
0 1
-2
2
3
4
5
6
7
8
9
D=5m
-4 -6 -8
5D 20D
5
First principal stresses /MPa
Displacement/mm
-1
1
2
3
4
5
6
7
8
9
-2 5D 10D 40D 80D
-3 -4
D=5m
-5
1
10
10D 40D Key points
0 1
2
3
4
5
6
7
8
9
-5 D=10m -10 -15
Key points 0 -1
1
2
3
4
5
6
7
8
9
-2 5D 10D 20D 40D
-3 -4
D=10m
-5 -6
1 5D 13.3D
First principal stresses /MPa
25 20 15 10 5 0 -5 -10 -15 -20 -25
Key points 0
-6
15
Displacement/mm
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6
8.30D 26.7D Key points
1
2
3
4
5
6
7
8
9
D=15m
Fig. 2. Vertical deformation for rock
Key points 0 -1
1
2
3
4
5
6
7
8
9
-2 -3 -4
5D 8.30D 13.3D 26.7D
D=15m
-5 -6
Fig. 3. First principal stress for rock
Rock Ⅳ Fig. 4 shows the vertical displacement of rock type Ⅳ tunnel with different model scope (D=5m), while Fig. 5 shows the corresponding vertical stress.
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60 Displacement/mm
5D 13.3D
20
8.30D 20.0D Key points
0 1
2
3
4
5
6
7
8
9
-20 D=15m -40
First principal stresses /MPa
1
40
-60
Key points
0 -1
1
2
3
4
5
6
7
8
9
-2 -3 5D 8.30D 13.3D 20.0D
-4 -5 -6
D=15m
-7 -8
Fig. 4. Vertical deformation for rock
Fig. 5. First principal stress for rock
From these two figures, it is clear that rock type Ⅳ show the same changing rule of vertical deformation and first principal stresses as that of rock type Ⅲ. From these results, it appears that the deformation increment is 1.76mm, 3.44mm, 5.55mm as the diameter increases from 5m to 10m to 15m, respectively. It is worth noting that for the case of rock type Ⅳ, although the deformation increment along the tunnel outline is bigger than that of type Ⅲ, the numerical results of 5D are still acceptable to real engineering. RockⅤ 1
5D 20D
10
10D 40D
5
Key points
0 -5
1
2
3
4
5
6
7
8
9
-10 -15 -20
D=5m
-25 -30
First principal stresses /MPa
15 Displacement/mm
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Key points 0 1
2
3
4
5
6
7
8
9
-1 -2 -3 -4
5D 10D 20D 40D
D=5m
-5
Fig. 6. Vertical deformation for rock
Fig. 7. First principal stress for rock
In this section, the diameter only include 5m and 10m since the rock Ⅴ is too weak to construct larger diameter tunnel. Fig. 6 shows the vertical deformation of deeply buried tunnel under different model scopes. Fig. 7 shows the corresponding first principal stress. It is clear that the numerical result shows the same changing rule under different scope as that of rock Ⅲ and Ⅳ. The deformation increment is 1.95mm, 4.72mm for the diameter of 5m and 10m, respectively. The results of the circular sections To investigate the influence of the shapes of tunnel section on the numerical results of deep-buried tunnel, rock types, diameters, and different model scopes are varied as parameters (see Table 2). To save space, it is just present the numerical
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results of maxi-mum and minimum model scope. The cover depth of these tunnels are 400m, 300m, 200m for the rock type of Ⅲ, Ⅳ, Ⅴ, respectively. 1
30
Displacement/mm
10
Key points
0 1
2
3
4
5
6
7
8
9
-10 -20 -30
2
0.0
3
4
Ⅲ-5D Ⅳ-30D
-0.5
5
6
Ⅲ-40D Ⅴ-5D
7
8
9
Ⅳ-5D Ⅴ-20D
-1.0 -1.5 -2.0 -2.5 Key points -3.0
Fig. 8. Vertical deformation for all rocks
Fig. 9. First principal stress for rocks
Fig. 8 shows the vertical deformation for different rock types with 5D and the real depth model scope. It is clear that the deformation increased with the model scope decreased form maximum to 5D and the rock types weaken form to . But for a given rock type the deformation increments are not obvious. The increment for different rock types are 1.2mm, 2.50mm, 1.90mm, respectively. Fig. 9 shows the first principal stress curves of the tunnel under different rock types and depth. The 5D curves are almost coincided with that of real depth scope for a certain rock type, which again proves that the usual boundary conditions (5D) are fully satisfactory to the need of engineering. THE NUMERICAL ANALYSIS RESULTS OF THREE-DIMENSION In this section, the dimensions of the numerical model of the deep-buried tunnel are considered. The key points’ position, boundary conditions and the geometry are showed in Fig.1. In order to lessen the calculation workload, only the rock is investigated in this section using ANSYS soft ware (see Table 2). Key points First principal stresses /MPa
40 30 Displacement/mm
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20
Ⅲ-40D Ⅳ-30D Ⅴ-20D
First principal stresses /MPa
Ⅲ-5D Ⅳ-5D Ⅴ-5D
5D 20D
20
10D 30D
10 Key points
0 -10 -20
1
2
3
4
5
6
7
8
9
D=10m
-30 -40
Fig. 10. Vertical deformation for rock
0 1
2
-5
3
4 5D 20D
5
6
7 10D 30D
8
9
-10 -15 D=10m -20 -25
Fig. 11. Vertical stress for rock
Fig. 10 shows the vertical displacement of the deep-buried tunnel with different model scope under several kinds diameters (D=10m), while Fig. 11 shows the corresponding vertical stress. It can be seen that the change rule of vertical
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deformation is exactly the same when the diameter increases from 5m, 10m, 15m. Similarly, the vertical stress decreases when the diameter increases from 5m, 10m to 15m. Here the vertical deformation of surrounding cavern decreases as the model scope increase from 5D to ground surface. Mean deformation increment is 2.60mm, 4.22mm and 6.49mm, respectively, when the diameter increases from 5m, 10m to 15m. Based on the numerical results, the vertical deformation under usual scope (5D) is greater than real value, which is more conservative and advantageous to the safety of real engineering. CONCLUSIONS Using the software of FINAL and ANSYS, this paper has investigated the influence of model scope for deep tunnel’s numerical simulation results under different rock types, section shape and diameters. The result from the common model scope (5D) appears to be quite close to the real depth model. Although there are some minor differences, but it’s good for the stability of the deep cover tunnel. Here the numerical results of real depth model scope are slightly smaller than that of common model scope (5D) which are more conservative. We also studied the influence under circle section, as expected, the same rules were accepted. Lastly, to investigate if the same conclusion could be got under the condition of three-dimensional, a meaningful simulation is carried out using ANSYS software under rock type , which also got the same results. So the simulation results of common model scope (5D) are basically able to meet the engineering needs and can be widely used in engineering practice. ACKNOWLEDGMENTS We would like to express our gratitude to the two anonymous reviewers for their constructive comments and suggestions. This research was supported by the National Natural Science Foundation of China (Grant No. 51179153), Exceptional PhD Innovation Foundation (Grant No. 207-002J1306) and the National Natural Science Foundation of China (Grant No. 11002108). REFERENCES Chengyuan Zhang, Xiaoyan Liu and Quansheng Liu. (2013). " A thermo-hydromechano-chemical formulation for modeling water transport around a ventilated tunnel in an argillaceous rock." J. Journal of Rock Mechanics and Geotechnical Engineering, Vol. 5 (2): 145-155. F.Y. Hsiao, C.L. Wang and J.C. Chern (2009). " Numerical simulation of rock deformation for support design in tunnel intersection area." J. Tunnelling and Underground Space Technology, Vol. 24 (1): 14-21. HUANG Jun and ZHANG Ding-li (2005). " Mumerical simulation of stratum deformation above overlapping metro tunnel." J. Chinese Journal of Rock Mechanics and Engineering, Vol. 24 (6): 2076-2182.
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