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Key Engineering Materials
ISSN: 1662-9795, Vol. 723, pp 782-788
doi:10.4028/www.scientific.net/KEM.723.782
© 2017 Trans Tech Publications, Switzerland
Submitted: 2016-06-08
Revised: 2016-08-09
Accepted: 2016-08-30
Online: 2016-12-12
Uplift Model Analysis for Shallow Overlaying Slurry Shield Tunnel Based
on Time-Varying Behavior of Cement Grouting Material
Yu Haung1, a *, Lin Li2, b, Jing Ni1, c, Leibiao Chen1, d
1
Department of Environment and Architecture, University of Shanghai for Science and Technology,
No. 516 Jungong Road, 200093 Shanghai, China
2
Shanghai Tunnel Engineering Co., Ltd, Shanghai 200082, China
a
* sunlitaurora@126.com, bl57488110@126.com, cwendy_1943@163.com,
d
1126033976@qq.com
Keywords: Slurry shield tunnel, Uplift, Shallow, Numerical analysis.
Abstract. As a necessary and key procedure of shield technology, synchronous grouting affects
ground layer deformation, and controls the tunnel uplift and ground subsidence, usually exerting
negative influence on underground engineering construction and surrounding buildings. This paper
establishes the 2D uplift model of the soil and lining by ABAQUS, based on a static buoyancy
varying with solidification of grout and dynamic buoyancy produced by grouting pressure. The effect
of buoyancy on lining is simulated in the lining and soil through a series of specific magnitude of
interference fit. Effectiveness of the model is validated by comparison of data measurement of South
Hongmei Rd. tunnel with predicted results for vertical displacement of ground surface. East line of
South Hongmei Rd. tunnel with super large diameter is chosen for the simulation and central burial
depths vary as a key parameter. The results show t4hat the differences between predictions and data
measurement are limited, hence providing a basis of numerical analysis for the design and
optimization of shallow slurry shield tunnel with super large diameter.
Introduction
Usually, shield tunnel lining is under buoyant stress composed of time dependent static buoyancy
due to setting and hardening of grouts and dynamic buoyancy produced by grouting pressure [3].
When the overlaying soil pressure and weight of lining cannot resist the buoyant stress, partial or
whole tunnel may float upward and cause soil failure and uplift of ground surface. Without proper
measures, tunnel may suffer cracking and leakage problems, Meanwhile, surrounding buildings and
underground pipelines may be under negative influence as well [4].
However, some part of tunnel can be under shallow overlaying soil during shield tunnel
construction, such as the portal section of the tunnel. With the increase of tunnel diameter, buoyancy
grows significantly. When the thickness of soil cover is less than 1~1.5 times of excavation diameter,
further research on safety problems caused by uplift of tunnel must be carried on [1, 2].
A lot of research work has been done on buoyancy in the recent year, Ye [5] presented that
buoyancy mainly consists of static buoyancy, such as underground water buoyancy, grout buoyancy,
and dynamic buoyancy, as well as grouting pressure, hydraulic pressure, jacking force, and unloading
rebound. Most of scholars believe that the value of static buoyancy is so small as to be ignored, which
would cause underestimation of practical devastation and inappropriate analysis of the safety of
shield tunneling.
Case Study
The South Hongmei Road Tunnel, a main project in this paper, which connects Fengxian and
Minhang is located in south region of Shanghai Huangpu River. Project is carried out by super large
diameter slurry balance shield at a diameter of 14.93 m. Tunnel diameter is 14.5m. The lining is 2m
wide and 0.6m thick made by C60P12 precast concrete. Average Grouting pressure is about 5.5 Bar.
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans
Tech Publications, www.scientific.net. (#103422207, Technische Universitaet Muenchen, Muenchen-13/11/17,04:17:06)
Key Engineering Materials Vol. 723
783
The construction of the shield tunnel for west line starts from Fengxian to Minghang. Then the
construction for east line starts from Minghang to Fengxian, indicating the completion of the whole
project. The shallow-buried section of the tunnel is located mainly at 14m~18m depth. Parameters of
the soil concerned are presented in Table 1.
Table 1. Parameters of soil.
Layer
②1
③
④1
⑤1-1
Soil name
Brown yellow silty clay
Grey muddy silty clay
Grey muddy clay
Grey clay
Dark green~straw yellow
silty clay
Gray yellow~ gray silt
Gray silt and silty clay
interbeded soil
⑥
⑦2
⑧2
unit
weight
γ
(kN/m3)
Compression
modulus
E(MPa)
Void
ratio
e
Poission
ratio
μ
Cohesion
C(kPa)
friction
angle
Φ( °)
19.2
17.1
17.0
17.6
5.83
2.90
2.51
3.40
0.782
1.275
1.303
1.118
0.30
0.38
0.39
0.32
26
11
11
15
18.5
17.0
13.0
16.5
19.6
7.80
0.692
0.29
45
16.5
18.9
13.04
0.770
0.32
4
35.0
19.0
9.13
0.772
0.28
3
34.0
Calculation of Buoyancy
Static Buoyancy. A generalized static buoyancy curve is acquired from the experiment based on the
buoyancy test of tunnel model which is proposed by Lin [6], Yang et al [7]. And generalized static
buoyancy can be expressed in terms of burial depth, tunnel volume, and solidification time of slurry
cement as Eq. 1:
-
()
-
(1)
where, is generalized static buoyancy (kN),  is solidification time of slurry cement(h) , is tunnel
volume (m3), is central burial depth (m).
Dynamic Buoyancy. The dynamic buoyancy is closely related to the movement of grouting slurry in
soil. The magnitude and distribution of dynamic buoyancy vary according to different diffusion
models. In this paper, the most disadvantaged compaction diffusion model of dynamic buoyancy is
considered [5] and proposed the following equation:
∫-
(
)
(2)
where,
is dynamic buoyancy (kN), is grouting pressure (kPa), is dynamic buoyancy effective
width (m),
is tunnel radius (m), is an angle between the boundary of the grouting slurry
distribution area and the vertical line.
Dynamic buoyancy effective width is taken as a homogeneous, uniformly thick and elastic
equivalent circular zone. According to the engineering experience, Poisson ratio of equivalent
circular zone is 0.2, and its width, , is given by [8]:
(3)
where, is a material coefficient, =0.7~0.9 for hard clay, =0.9~1.3 for dense sand, = 1.3~1.8 for
loose sand, =1.6~2.0 for soft clay, is void at shield tail. Based on Hongmei Rd.’s case,
, and
.
Resultant Force of Buoyancy As static buoyancy decreases over time and dynamic buoyancy only
exists during synchronous grouting, the resultant buoyancy is obtained by combining the static
buoyancy and dynamic buoyancy one hour after synchronous grouting starts.
The static buoyancy of unit length of tunnel lining is calculated for different depths (14m, 16m and
18m), with magnitude:
784
Proceedings of International Conference on Material Science and
Engineering 2016
{-
()
()
()
(4)
when,
, static buoyancy:
kN,
Then the resultant force of buoyancy can be obtained:
For H=14m,
For H=16m,
For H=16m,
kN,
kN,
;
;
.
Numerical Simulation
The model for analyzing the east line of South Hongmei Road Tunnel is established by finite
element software ABAQUS, and the hypotheses are expressed as followed:
(1) 2D model is established for simulation;
(2) All soil layers are horizontal;
(3) Effect of excavation of existing tunnel(west line) is not considered in this simulation;
(4) Grout is considered as a solid-like material which is called equivalent circular zone in
simulation;
(5) Resultant force of buoyancy acts through the interference fit between the equivalent circular
zone and the lining.
Materials. Concrete segments ,soil and grout(equivalent circular zone) are simulated in 2D planar.
Isotropic elastic material is used for lining and equivalent circular zone, while Drucker-Prager model
with non-associated flow rule is adopted for soil [9]. The lining is 2m wide and 0.6m thick. In order to
compare data measurement of ground surface displacement with predicted data, three different
central burial depths--14m, 16m and 18m are considered in numerical simulation. The center of the
east line is 25 meters away from the center of the existing west line. Material parameters used in
simulation model are given in Tables 2 and 3.
Table 2. Drucker-Prager model Parameters.
Layer
Soil name
③
⑤1-1
Grey muddy silty clay
Grey clay
Dark green~straw yellow
silty clay
Gray yellow~ gray silt
Gray silt and silty clay
interbeded soil
⑥
⑦2
⑧2
Non-associated flow rule
friction
Cohesion
angle
C(kPa)
Φ( °)
6.70
26.9
8.82
26.2
unit
weight
γ( / 3)
Compression
modulus
E(MPa)
Possion
ratio
μ
Layer
thickness
(m)
17.1
17.6
2.90
3.40
0.38
0.32
19.6
7.80
0.29
26.48
26.2
15
18.9
13.04
0.32
5.94
44.8
15
19.0
9.13
0.28
4.29
44.1
30
10
20
Table 3. Material parameters.
Material
Grouting slurry
(Equivalent circular zone)
Segment
Elastic modulus
(MPa)
Possion ratio
μ
unit weight
γ (kN/m3)
Thickness
(m)
3
0.2
20
0.387
30600
0.25
25
0.6
Soil and lining model is establish by FEM software ABAQUS. In this model, central burial depth
of tunnel H varies from 14m, 16m to 18m. East line of South Hongmei Road Tunnel with 14.5m
diameter is selected for simulation. Fig. 1 indicates that the odel di en ion i
The
horizontal constraints are imposed on both sides of the model. The bottom is fixed and the top is
unconstrained. Excavation area is inside of east tunnel lining. Element types of soil and 0.6m-thick
lining are CPE4I, CPE4 respectively.
Key Engineering Materials Vol. 723
785
H
260m
East Tunnel
14.5m
14.5m
Existing West Tunnel
90m
10.5m
Fig. 1 Model dimension.
Simulation Methods. Fig. 2 shows a procedure in detail for a numerical simulation [10].
Initial
geostress
calculation
The modulus of
excavation area
soil attenuate 30%
Activate
segment
Remove soil
of excavation
area
Applied
Interference
Fit
Fig. 2 Process of Simulate excavation.
Interference fit is conducted to simulate the complicated interaction between soil and lining, in
which outer edge of lining is set as master surface and inner edge of equivalent circle as slave surface.
When over-closure is applied between the lining and equivalent circle, contact force can be calculated.
Meantime, buoyancy is equal to the vertical component of contact force of semi-ring lining.
Case 1: For H=14m, magnitude of over-closure is -0.0230, and the vertical component of the
contact force of the unit length of lining is 5541.03kN; Case 2: For H=16m, magnitude of
over-closure is -0.0187, and the vertical component of the contact force of the unit length of lining is
5511.86kN; Case 3: For H=18m,magnitude of over-closure is -0.0172, and the vertical component of
the contact force of the unit length of lining is 5499.24kN.
Figs. 3, 4 and 5 respectively represent the contour of horizontal and vertical displacement of tunnel
lining in depths of 14m, 16m and 18m.
(b) soil vertical displacement
(a) soil horizontal displacement
Fig. 3 Soil displacement of 14m-burial-depth tunnel(m).
(a) soil horizontal displacement
(b) soil vertical displacement
Fig. 4 Soil displacement of 16m-burial-depth tunnel(m).
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Proceedings of International Conference on Material Science and
Engineering 2016
(a) soil horizontal displacement
(b) soil vertical displacement
Fig. 5 Soil displacement of 18m-burial-depth tunnel (m).
To verify the model, simulation of vertical displacement of ground surface for Case 2 and Case 3
are conducted and compared with data measurement of monitoring sections E1663 and E1687.
Monitoring section E1663 and E1687 are on the ground with burial depth of 18.3m and 15.8m
respectively. However, there is no measured data of ground surface for 14m depth in tunnel
construction. For this reason, Case 1 is not considered to compare. Fig. 6 represents the location of
monitoring points.
Monitoring section at E1678
tunnel maesured depth: 15.8m
Monitoring section at E1663
tunnel measured depth: 18.3m
E1678-1
E1678-2
E1678-3
E1678-4
E1678-5
E1678-6
E1663-6
E1663-5
E1663-4
E1663-3
E1663-2
E1663-1
East Tunnel Axis
West Tunnel Axis
Fig. 6 Monitoring point position.
Vertical surface displacement (mm)
Vertical surface diaplacement (mm)
Comparison of predicted results and data measurement are represented in Fig. 7. The difference of
vertical surface displacement between numerical simulation and data measurement is less than 3mm.
A “groove” is observed both in simulation profile and measurement profile. The minimum value of
the groove is at center of tunnel. It can be seen that the actual profiles of surface uplift are in a fair
agreement with those of numerical simulation. Therefore, this numerical model has a good reliability
to practical engineering project.
36
32
28
-15
Simulation value-Case 2
Masure value-Section E1678
-10
-5
0
5
10
Distance from the center of the East Tunnel (m)
15
35
30
25
Simulation value-Case 3
Masured value-Section E1663
20
-15
-10
-5
0
5
10
15
Distance from the center of the East Tunnel (m)
(b) Comparison of predicted and measured
(a) Comparison of predicted and measured
data at 18m-buried depth
data at 16m-buried depth
Fig. 7 Comparison of predicted and measured data.
Key Engineering Materials Vol. 723
787
Case1-burial depth 14m
Case2-burial depth 16m
Case3-burial depth 18m
40
Horizontal surface
displacement (mm)
Vertical surface
displacement (mm)
Fig. 8 shows the curve of vertical displacement of ground surface under different central burial
depths in the direction perpendicular to shield axis. The maximum upheaval value is on the left side of
axis of east tunnel when grouting finished. In Case 1, the maximum upheaval on the surface appears
at -6.53m, with a peak value of 38.34mm. In Case 2, the maximum upheaval on the surface appears at
-6.22m, with a peak value of 35.80mm. In Case 3, the maximum upheaval on the surface appears
-6.01m, with a peak value of 31.20mm.
The reduce of the uplifting value starts at the left side of east tunnel and then increases when
approaching to the existing tunnel, Therefore, there is the "groove" within the scope of 6 meters. The
minimum value of groove appears on the center of the tunnel. When the buried depth is 14m, 16m,
and 18m respectively, the minimum value for groove respectively is 35.18mm, 32.54mm, and
26.83 mm.
The magnitude of the peak near existing tunnel is less than the maximum value. Therefore, a
“di proportionate hump” is presented in Fig. 8. The maximum vertical displacement of surface
decreases when overlaying soil thickness increases. For burial depth changing from 18m to 16m, a
more reduced vertical displacement of ground surface at axis is observed when compared with that
for depth changing from 16m to 14m. This is largely due to the fact that with the overlaying soil
thickening, weight of overlaying soil increases, while resistance of buoyancy also increases,
Furthermore, the surface uplifting value decreases.
In Fig. 9, three simulated horizontal displacements of ground surface are indicated. The
horizontal displacement of center of east tunnel is zero in three cases. When central burial depth is
14m, 16m and 18m, the maximum horizontal displacements appear at 14.54m, 18.60m, and 20.21m
away from the center respectively, and corresponding values of maximum are 29.55mm, 25.76mm,
and 22.20mm.
30
20
-100
-50
40
30
20
10
0
-10
10
-20
-100
-50
0
Case1-burial depth 14m
Case2-burial depth 16m
Case3-burial depth 18m
0
50
100
150
Distance from the center of the
East Tunnel (m)
-30
0
50
100
Distance from the center of the East Tunnel (m)
Fig. 8 Stimulation data of vertical surface
displacement of different central burial depth.
-40
Fig. 9 Stimulation data of horizontal surface
displacement of different central burial depth.
Summary
Numerical analyses have been performed on a shield tunnel with super large diameter. The effect
of buoyancy which is taken as sum of static buoyancy based on one-hour consolidation and dynamic
buoyancy due to grouting pressure on the surface uplift response has been evaluated. The main
conclusions of this paper are summarized as follows:
(1) Before the hardening of grout, lining is subjected to static buoyancy caused by grout
buoyancy which is about 80% of dynamic buoyancy generated by grouting pressure and 44% of the
resultant. Therefore, the static buoyancy can not be ignored when buoyancy is considered in shield
tunnel floating and ground uplift problem.
(2) Tunnel burial depth has a significant influence on surface deformation. The maximum
vertical and horizontal displacement of surface decrease when overlaying soil thickness increases. As
788
Proceedings of International Conference on Material Science and
Engineering 2016
Fig. 8 and Fig. 9 show, the maximum vertical displacement of surface varies from 38.34mm to
35.80mm and to 31.20mm when depth changes from 14m to16m, and to 18m.
(3) For burial depth changing from 18m to 16m, a more reduced vertical displacement of ground
surface at axis is observed when compared with that for depth changing from 16m to 14m. Thus, the
overlaying thickness should be tightly controlled in shield tunnel construction.
(4) In the numerical simulation, uplift of ground surface occurs due to the buoyancy. The uplift
peaks are located in both sides of center of east line, and a “groove” is observed whose minimum is at
center of tunnel. The difference of vertical surface displacement between numerical simulation and
data measurement is less than 3mm.In this case, the prediction shows a good agreement with the
actual profiles of surface uplift.
(5) The maximum vertical displacement of ground surface appears away from existing tunnel
(west line), while the other peak near the existing tunnel (west line) is smaller when compared with
the maximum. This “di proportionate hump” demonstrates that existing tunnel restricts the surface
uplift of tunnel under construction.
References
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1041-1045+1056.
[3] K. Thomas, M. Gunther, A numerical study of effect of soil and grout material properties and
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[4] K. Thomas, M. Gunther, On the influence of face pressure, grouting pressure and TBM design in
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[5] F. Ye, C. He, S. M. Wang, Analysis of mechanical characteristic of shield tunnel segments lining
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[6] J. X. Lin, C. F. Duan, Y. P. Zhao, B. Xie, Study of new mortar anti-floating model experiment of
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[7] F. Q. Yang, Large diameter slurry shield funnel tests and theoretical studies of anti-floating,
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[8] H. Z. Zhang, J. W. Zhang, J. H. Zhai, ANSYS Method for Deduction of Parameters of Equivalent
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