1. JING Chun-yan Tongji University 2006/10/21
The Stability Analysis of Inter-Space Rock of Closely-Spaced Tunnel with Altitude Difference
JING Chun-yan
Tongji University
2006/10/21

2. INTRODUCTION
In the expressway tunnel construction, as the restriction of landform geology, plane programming and regulation of land occupying plan, more and more closely-spaced tunnels are using these years. In this report, the definition of closely spaced tunnel is that the net distance between two tunnels is more than 10m and less than the distance of separation of tunnels.

3. INTRODUCTION
According to the code to design of highway tunnel(JTG D ), the definition of little distance tunnel is that the net distance between two tunnels is less than the suggestion valuation of the table below.
The smallest distance of separation tunnels
The class of surrounding rock Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ
The smallest distance（m）
1.0×B
1.5×B
2.0×B
2.5×B
3.5×B
4.0×B
Note: B means the widest dimension of tunnel.
The kind of tunnels are suitable for tunnels in the opening or the longitudinal length is short.

4. Report Framework 1.The background of study.
2.The FEM analysis of closely-spaced tunnel with altitude differences.
3.How to analyze the results of numerical simulation?
4.What are the conclusions?

5. 1. The background
There have been many achievements about it during these years.
Liu Yanqing and others analyze the mechanical characteristics of Zhaobaoshan road tunnels which are the first twin tunnels with small spacing in China. The mechanical characteristics are studied by FEM before design, and during construction, and systematic measures performed, include ground surface settlement, convergence, crown settlement, earth pressure, support structure deformation, loosen zone, and broken depth due to explosion.
In Tang Yixing’s paper, a 2-D visco-elasto-plastic FEM is used to analyze the stability of the excavation and lining structure of a nearby double tunnel in the national highway. The stress-deformation state and evolvement status of the plastic and tension zones of the surrounding rock and the lining structure are analyzed and compared on the basis of calculation under five different conditions.

6. 1. The background
Hu Yuanfang use the software of 2D-σ to studied the stability of surrounding rocks of double-hole urban tunnel with small interval, and the reference values of the minimum intervals are obtained.
Therefore, it is obviously the domestic analysis is emphasized on the tunnels with very small spacing. It is seldom seen about spacing over 10 meters, and two tunnels with altitude differences. This paper focuses on surrounding rocks of Ⅱ kind of a some expressway tunnel in Yunnan province. The stability of surrounding rocks influenced by altitude difference is analyzed here. The tunnel transect is circle with three centers and curve wall type. The designed net height is 7.1 meters, and net width is 11.2 meters. The method of construction is NATM.

7. 2.The FEM analysis
The FEM analysis tool for tunnels is PLAXIS which is developed by Delft University in the Netherlands. The based presumptions are:
<1>Because the longitudinal length is much longer than the excavation dimension, it is reasonable to consider the stress and deformation of surrounding rocks as plain strain although it is three-dimensional in fact.
<2> In order to simulate the reinforced zone of anchor pile and ductule, the physical parameters are properly enhanced.
<3> The calculation model is elasticoplastic model, and the yield condition is Mohr-Coulomb yield criterion.

8. 2.The FEM analysis
In this report, we take the typical section K7+439 for example, the net distance between two tunnels is 20 meters, and the distance between crown of right tunnel and ground surface is 23 meters. The partial press angle of ground surface is 13.1 degrees. Besides, the altitude of left tunnel is 4 meters higher than that of right tunnel. The surrounding rocks are Ⅱ kind. The FEM model is showed in figure 1. In order to satisfy the calculation request, the boundary size is big enough. All of restrictions are set for displacement, and the right and left sides are horizontal restriction, and bottom side is horizontal and vertical restriction.

9. Fig1. Model of the whole structure
2.The FEM analysis
Layer 1, yellow clayey soil, allowable bearing capacity is 200~250 kPa, SPT is 4.95~5.25 meter, N′=14
Layer 3, filemot silty mudstone, intensive weathering, allowable bearing capacity is 250~400 kPa
Layer 4, gray fine sand rock, the allowable bearing capacity of intensive weathering layer is 600~800 kPa, and weak weathering layer is 800~1200 kPa
STP means standard penetration test.标准贯入实验
Layer 3, filemot silty mudstone, weak weathering, the allowance bearing capacity is 400~600 kPa.
Fig1. Model of the whole structure

10. 2.The FEM analysis Table.1 Parameters of Surrounding Rocks and
Supporting Stuff in Numerical Simulation
Sorts
Model
Elastic modulus
Passion ratio
Cohesion
Angle of friction
Unit weight
Unit
kN/m2
kN/m3
Layer 1
Morh-Coulomb
3.75×105
0.4 60 22 18
Layer 3 and intensive weathering
5×105
0.37 50 26
26.2
Layer 4
1.5×106
0.34
100
26.9
Layer 3 and weak weathering
1.2×106
0.32 80 25
Enhanced zone of ductule
1×107
0.2
200 30 35
Secondary lining
Linear elastic
2.5×107
0.167
---
Enhance zone of anchor pile
2.2×106
0.25
550
27.8
The concreter of inverted arch
1.8×107

11. 2.The FEM analysis The cases of construction: Cases Altitude/m
Excavation sequence R4 4
Right tunnel first L4
Left tunnel first R0 L0

12. 2.The FEM analysis Construction process
The principle of tunnel construction is NATM. The close surface is formed with shotcrete as soon as the tunnel is excavated, and then the anchor and spouting structure is made. The secondary lining is made while the structure is comparatively steady according to the monitoring data. After excavating one tunnel for several days, the other tunnel can be excavated. We cannot take the distance of two excavation surface into account because of the two-dimensional numerical simulation.

13. 2.The FEM analysis Left tunnel Right tunnel
Step 1, producing gravity stress;
Step 2, making front ductule, and returning the displacement field to zero;
Step 3, excavating the upper semiannular rock of right tunnel;
Step 4, making the first lining of upper bench and enhancing surrounding rocks;
Step 5,excavating core rock of right tunnel;
Step 6, excavating the lower bench of right tunnel;
Step 7, supporting the lower bench with steel web and steel arch-frame of right tunnel, and shotcreting;
Step 8, excavating the inverted arch of right tunnel;
Step 9, making first lining;
Step 10, making secondary lining and casting concrete of inverted arch;
Step11~19, the same method as the left tunnel.

14. 3. Analyze the Results
Fig. 3 The horizontal displacement map when construction closed of case R4

15. 3. Analyze the Results
Fig.4 The horizontal displacement map when construction closed of case L4

16. 3. Analyze the Results
No matter which tunnel is excavated first, the maximum horizontal displacement is always appeared in the right side in the top of two tunnels. The phenomenon is possibly caused by partial press. Figure 3 and 4 respectively show horizontal displacement of case R4 and L4 when excavation is finished. So we choose the point in the red zone as delegate to study the influence of different cases.

17. 3. Analyze the Results
The displacement got in case R4 is 3 mm, which is the greatest. The least number is 2.5mm which is got in case R0. The displacement in R4 is greater by 11% than in case L4, which are both having altitude differences. When two tunnels are in the same horizontal line, it is better to excavate the right tunnel first under partial press, and it is consistent with conclusion of Liu Wei’s paper. In case R4, the displacement after excavating the first tunnel is about 50% of total displacement. However, in case L4, the percentage is about 30%. So it is better to excavate the left tunnel.

18. 3. Analyze the Results Stress analysis of inter-space rock
While analyzing the stress of rocks between two tunnels, it is usually emphasized of step 3 and 12, in which the upper semiannual sand are excavated and stress would change most. Figure 6 and 7 show the plastic zone in different cases.
(a) Step 3, 552 points
(b) Step12, 754 points
Fig.6 The Plastic Zone in Case R4

19. 3. Analyze the Results
(a) Step3, 649 points
(b) Step 12, 609points
Fig.7 The Plastic Zone in Case L4
From the plastic zone pictures in different cases, more plastic points will occurred when excavating left tunnel. So the surrounding rock of left tunnel should be enhanced more carefully when excavating it. And the finally plastic zone will be smaller.

20. 4.Conclusions
The partial pressed and closed-spaced tunnel is studied by software of PLAXIS. The conclusions can be got by different excavation sequences and altitudes:
(1) Whether from the point of displacement or stress, it is better to excavate the left tunnel for closely-spaced tunnel with different altitude and partial press;
(2) The different altitude has bad some influence to the steady of tunnels.
(3) When we excavate the left tunnel first, it should be given more attention to enhance this tunnel, in particular, the surrounding rock beside both shoulders. The rock will be steadier when the next tunnel is excavated.

21. Thanks for your attention!