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Figure 1. Cross Section of the small spacing tunnel

Computation of tunnel structure:

The computation for metro tunnel structure means to operate finite element analysis for the strata and

support structure of the tunnel while the tunnel is being driven under both different geological

conditions and driving methods. The numerical simulation for the SST mainly includes the following

in this paper.

(1) Ground subsidence and displacement of tunnel clearance induced by excavation of the SST.

(2) Distribution and variation of internal forces of support structure of the SST.

(3) After excavation, the distribution of plastic zone in the surrounding soil around the tunnel.

A plane finite element model is set up, according to the feature that the longitudinal length of the SST

is much greater than its cross sectional area, and the distribution of internal forces of support structure

and deformation of surrounding soil just vary in the cross area perpendicular to the longitudinal length

of the SST. Therefore, a plane strain model is adopted in this computation. In order to reduce the

unfavorable influence of boundary constraints in the FEA model on the computation results, thedomain for computation of the tunnel model can be as follows. The limit length in the horizontal

direction is 4 times the span of tunnel, and the buried depth is 3 times the span of tunnel.

Determination of constitutive model for materials:

According to the physical and mechanical properties of soil and soil in the strata which the SST passes

through in the No.2 line of the Guangzhou Metro, the classification of strata can be classified into ,

,,and from the bottom boundary of the model to the surface. In this finite element

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computation and analysis, Drucker-Pragers elastoplastic nonlinear constitutive model is adopted.

According to Drucker-Prager modelthe equivalent stress for soil like materials can be as follows[3]

.

{ }[ ]{ }2

1

2

13

+= SMS

T

m

(1)

Where ,{ } { } [ ]TmS 000111 =

( )zyxm ++=

3

1

( )

sin33

sin2

= ,

( )

sin33

cos6

=

cy ;

Cis cohesion of materials, in MPa is internal friction angle of geo-materials.

Plastic yield criterion of Drucker-Prage is

{ }[ ]{ } 02

13

2

1

=

+= y

T

m SMSF

(2)

Computation parameters:

Physical and mechanical parameters of each layer of soil required in the finite element computation isadopted according to the Rock Classification Standard approved by Railway Ministry of China, and

they are shown in Table 1.

Table 1 Physical and mechanical parameters of surrounding soil

Rock

Classificatio

n

Elastic modulus Poisons ratio Weight density Cohesion Inter-friction angle

EMPa 10N/m3 ckPa

Grade 120 0.47 2100 10 20

Grade 400 0.41 2300 25 25

Grade 1000 0.35 2500 100 30

Grade 3000 0.29 2700 400 35

Grade 10000 0.23 2900 1700 40

Preliminarysupport C15

22000 0.20 2500

Inner lining

C20

28000 0.15 2500

The excavation process of the SST has been simulated while the structure is being modeled, and the

final state is considered after the completion of tunnel excavation in this paper. The surrounding soil

and primary support is simulated by solid element of Plane 82, and the inner lining is simulated by the

beam element Beam 3 in ANSYS V5.6.

Determination of load:

Strata load and hydrostatic pressure have been taken into account separately, and the load principle is

as follows. When the inner lining is not built, the preliminary support can stand 70% of earth pressure.

When the second lining is finished, the remained 30% of earth pressure can be applied to both the

second lining and the preliminary support. And as the tunnel is open to traffic, the inner lining can

bear 100% of hydrostatic pressure. Hydrostatic pressure can be calculated according to Eq.(3).

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hP ww = 3

Where, is the weight density of water, in kN/mw 3, his the depth of water table, in m.

As the net distance between the two tunnels just reaches 1.8m, so soil bolts, preceding grouting pipes

and pipe-roof protection have been adopted to strengthen the surrounding soil both on the top of roof

and between the two tunnels during the simulation of tunnel driving.

According to the construction process of the SST presented in preliminary design, the constructionprocedure is shown in Fig.2. Letters a, b, c, d, e and f in Fig.2 represent the driving sequence of the

SST. Comparison of driving sequence to the large and small cross section has also been carried out to

find out which kind of driving mode can cause minimum ground subsidence and deformation of

surrounding soil.

Figure 2 - Sketch map of driving procedure of the SST

Computation results and analysis

The ground subsidence, deformation of surrounding soil and distribution of internal forces of support

structure under different driving mode have been obtained through plane finite element computation

of the SST. The obtained results are stated as follows.

Ground subsidence induced by different driving mode

The early or late excavation sequence of the large and small tunnel has been compared in the

computation and the settlement under these two driving sequence is obtained. The results are shown in

Table 2.

Table 2 Maximum ground subsidence induced by different driving mode

Driving mode Maximum value of subsidencecm

Mode 1 2.0047

Mode 2 3.3680

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Figure 4 - Plastic zone around the surrounding soil

Internal forces of tunnel support structure:

The internal forces of support structure of the SST mainly include bending moment and axial force of

inner lining, and their state is obtained and shown in Fig.5 and Fig.6 respectively through numerical

simulation. According to bending moment in Fig.5, the moment of second lining of the left tunnel is

much greater because of its large span. Negative bending moment appears in the right and left

sidewall of large tunnel, and the maximum negative bending moment in the middle of both sidewalls

of large tunnel reaches 322.376 kNm. The maximum positive bending moment appears in the middle

of the invert of the left tunnel with a value of 365.956kNm. It can be obviously seen that the left

tunnel presses the right tunnel, and the positive bending moment appears in the both sidewalls of smalltunnel, but the negative moment appears in its crown. The axial forces of inner lining of the SST is

shown in Fig.6. Because the distance between the two tunnels is smaller, so the large tunnel presses

the small one and it can also be found out from their axial forces in Fig.6. The left tunnel has larger

axial forces in its sidewalls, but the small section tunnel has greater axial forces in its invert. The

maximum value of axial forces of the final lining of the SST reaches 2060kN.

Figure 5 - Bending moment of the inner lining

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Figure 6 - Internal forces of the inner lining

Conclusion

1It can be derived from the numerical simulation of driving sequence of the SST that the

ground settlement induced by prior excavation of right tunnel with single line is less than that caused

by the prior excavation of left tunnel with double line, and the ground subsidence caused by the

former can be controlled within the prescribed value. Therefore, driving sequence of mode 1 should beadopted during the construction of the SST so as to protect the safety of buildings on the ground.

2In view of the small distance between the two tunnels, the plastic zone induced by

excavation of large tunnel is reiterated with the one caused by prior excavation of right small tunnel inthe surrounding soil between them and this does not only enlarge the plastic zone in the strata but

increases the deformation of surrounding soil as well. Therefore, the surrounding soil between the two

tunnels must be pre-consolidated by taking measures such as rock bolts or pipe grouting during tunnelexcavation.

3During the construction of the SST, preliminary support should be closed as soon as

possible, and temporary support can not be removed until the preliminary support is closed. In order to

prevent greater subsidence induced by the early removal of temporary support, a certain distance must

be kept from the working face while they are dismantled.

(4) The construction of the SST has been conducted with the help of obtained numerical resultsby means of ANSYS, and the SST has been safely and successfully completed already.

Reference:

1) Zhou Xiaojun, Gao Bo. 2000, Numerical Analysis on the Design Program of Running

Tunnel in Guang Fang Lian Section between the Peoples Park and Zhong Shan Memorial

Hall of Guangzhou Metro. (in Chinese), West-China Exploration Engineering, Vol.12 No.1,

pp.66-68.

2) Zhou Xiaojun, Gao Bo. 2000, Three Dimensional Finite Element Analysis on Construction

Process of Large Span Tunnel of Guangzhou Metro. Tunnels and Underground Structures,

A.A.Balkema/Rotterdam Brookfield, Singapore, pp.335-342.

3) ANSYS manual for nonlinear analysis, ANSYS, Inc.

4) Shi Zhongheng.Design and Construction of Metro (in Chinese). 1997,Science & TechnologyPress of Shanxi, pp.376-377, Xian.