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Numerical Analysis of Rock Cover Thickness of Subsea Tunnel

Xiang-bo Qiu1,2, Shu-cai Li 1,3, Wei-zhong Chen1

1Key Laboratory of Rock and Soil Mechanics, Institute of Rock and Soil Mechanics,

Chinese Academy of Sciences, Wuhan 430071, P.R.China2School of Civil and Environmental Engineering, University of Southampton, U.K.

3School of Civil Engineering, Shandong University, P.R.China

ABSTRACTSince the first subsea tunnel-Kanmon tunnel was built in 1936 in Japan, nearly one hundred subsea

tunnels had been constructed all over the world. Under special environmental and geological

conditions, subsea tunnels are the safest and most economical scheme. But many problems still needed

to be resolved. Here we try to research the relationship between minimum thickness of rock cover and

tunnel stability by numerical method. The research combines with the engineering practice of Xiamen

subsea tunnel gives a recommendation of minimum safety rock cover thickness.

1. INTRODUCTION OF CONSTRUCTED SUBSEA TUNNELS IN THE WORLD

Countries that have constructed subsea tunnels include Japan, Norway, U.K, France, Denmark et. al.And the subsea rail-way tunnels and highway tunnels which were designed and constructed in

drill-blast method are mainly in Japan and Norway. According to the literature, the Kanmon tunnel in

Japan that began to be constructed at Sep. 1936 and finished at 1944 is the first subsea tunnel in the

world. The famous Japanese Sei-kan highway tunnel is the longest subsea tunnel which is constructed

by drill-blast method, and is 53.85 Km long. Some subsea tunnels are listed in Table 1.

In the earlier period, such as when the 2 Japanese tunnels were constructed, there was no rigorous

theory of the minimum rock cover thickness used in the designing and construction process. After then,

some special research was done and some common understanding had been realised:

a. The min. thickness of rock cover is one of the most important design parameters which can

influence the engineering safety and cost.

b. The min. thickness of rock cover is main factor that determine the length of the tunnel, after the

angle of inclination is determined.

c. The thinner the rock cover, the shorter the tunnel length, and the less the hydraulic pressure on the

lining.

d. To avoid accidentally rock fall and sea water ingress, the rock cover must be thick enough.

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e. To determine the rock cover thickness, two methods were always used, engineering analogical

analysis and stability analysis( numerical method)

Table 1. Main subsea tunnels in the world

Tunnel name National Year Use Length

km

Subsea

length

m

Area

m2

Deepth

m

Water

deepth

m

Rockcover

thichness

m

Rock type Construct

method

Kanmon Japan 1944 R 3.6 1.14 -40 14 11 Drill-Blast

Kanmon Japan 1958 H 3.5 95 -49 21 Drill-Blast

Shin Kanmon Japan 1974 R 18.7 90 -50 20 Drill-Blast

Vollsfjord Norway 1977 W 9.4 0.6 16 -80 26 Gneiss Drill-Blast

Frierfjord Norway 1977 L 3.6 3.1 16 -252 34 Gneiss Drill-Blast

Vard Norway 1981 H 2.6 53 -88 28 Sandstone

Shale

Drill-Blast

Sei-kan() Japan 1985 R 53.9 23.0 90 -250 140 100 Lava Drill-Blast

Ellingsy Norway 1987 H 3.5 1.1 68 -140 65 42 Gneiss Drill-Blast

Valdery Norway 1987 H 4.2 2.2 68 -137 70 34 Gneiss Drill-Blast

Kvalsund Norway 1988 H 1.5 43 -56 22 Gneiss Drill-Blast

Gody Norway 1989 H 3.8 48 -153 70 33 Gneiss Drill-Blast

Flekkery Norway 1989 H 2.3 46 -101 32 Gneiss Drill-Blast

Nappstrqumen Norway 1989 H 1.8 55 -63 27 Gneiss Drill-Blast

Hvaler Norway 1989 H 3.8 45 -120 29 Gneiss Drill-Blast

Storeblt Danmark 1990 H 7.9 28.5 -68 13 Marlite TBM

Nappstraumen Norway 1990 H 1.8 55 -60 27 Gneiss Drill-Blast

Maursundet Norway 1990 H 2.3 43 -93 27 Gneiss Drill-Blast

Fannefjord Norway 1990 H 2.7 43 -100 27 Gneiss Drill-Blast

Byfjord Norway 1992 H 5.8 70 -223 Phyllite Drill-Blast

Mastrefjord Norway 1992 H 4.4 70 -133 Gneiss Drill-Blast

Freifjord Norway 1992 H 5.2 70 -130 Gneiss Drill-Blast

Tromsysund Norway 1994 H 3.4 257 -101 Gneiss Drill-Blast

Hitra Norway 1994 H 5.3 70 -267 180 45 Gneiss Drill-Blast

England-France U.K,

France

1994 R 50.5 37.0 -105 60 40 Gneiss TBM

Troll Norway 1995 W 3.8 66 -260 Drill-Blast

Bjery Norway 1996 H 2.0 -88 Drill-Blast

Slverfjord Norway 1997 H 3.3 -120 Drill-Blast

Nordkapp Norway 1999 H 6.9 -150 Drill-Blast

Frya Norway 2000 H 5.3 -164 Drill-Blast

Oslofjord Norway 2000 H 7.3 -120 Drill-Blast

Bmlafjord Norway 2000 H 7.9 -262.5 Drill-Blast

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2. SUMMARY OF THE XIAMEN SUBSEA TUNNEL SCHEME

Xiamen is an island at south-east China, recently, its economics is developing quickly. By now, there

are only two entrances to Xiamen island, Xiamen bridge and Haichang bridge, the traffic is very

congested. So the third entrance-Xiamen Subsea Tunnel is very necessary and imperative. The tunnel

scheme was approved by State Development Planning Commission at the early 2003. After it is

constructed, it will be the first subsea tunnel in P.R.China. The highway tunnel will have double-lines,

each line will be about 6000 m long and have three running line. The cross section of each tunnel is

about 14.7m width and 9.85m high, the area is about 100m2, the maximum inclined angle is 3.5%, the

design altitude is -70m. The distance between the central lines of the two tunnels is about 50 m.

Drill-blast excavation method will be adopted.

The rock type in the tunnel area is mainly diorite granite. According to weathering grade, it can be

classified as 4 layers, fully weathered, strongly weathered, slightly weathered and fresh diorite granite.

The construction in the tunnel site is simple, basal rock is almost intact. Effected by the fault around

the site, there distribute joints in several orientations. The mechanical parameters are listed in table 2.

The geological section diagram is listed in Fig. 1.

Table 2. Parameters of rock mass

Shear strengthRock type D E

(GPa)

t

(Mpa) F(Degree) C(MPa)

Fully weathered granite 1950 0.45 0.05 0.1 23 0.033

Strongly weathered granite 2650 0.35 1.0 0.5 30 0.2

Slightly weathered granite 2650 0.25 15 1.0 39 1.0

Fresh granite 2650 0.25 20 1.5 42 1.2

D- density (Kn/m3);- Posssions ratio; E- Youngs modulus; t -Tension strength; f-friction; C-

cohesion

Tunnel

Slightly weathered granite

Strongly weathered granite

Fully weathered granite

K8+350 K8+750 K9+450 K10+000 K11+120

`

Fig.1 Geological sections diagram of Xiamen tunnel

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3. RESEARCH ON MIN. ROCK COVER THICKNESS OF XIAMEN TUNNEL

In the investigating process, governments and engineers have paid the most attention to its safety and

economy. For different design altitude, the rock cover thicknesses in several key cross sections are list

in table 3. Comparing with Norway subsea tunnel experience, formula is plotted in Fig.2.

Table 3. Rock cover thickness of different scheme

Min. rock cover thickness(m)Position Water

Depth

(mOriginal

Design

+2m +4m +6m +8m -2m -4m -6m

K8+350 27.5 35.0 33.0 31.0 29.0 27.0 37.0 39.0 41.0

K8+750 32.0 37.2 35.2 33.2 31.2 29.2 39.2 41.2 43.2

K9+450 32.5 41.0 39.0 37.0 35.0 33.0 43.0 45.0 47.0

K10+0.0 20.0 50.0 48.0 46.0 44.0 42.0 52.0 54.0 56.0

K10+500 22.5 42.5 40.5 38.5 36.5 34.5 44.5 46.5 48.5K11+120 5.0 42.5 40.5 38.5 36.5 34.5 44.5 46.5 48.5

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Mi n. r ock cover t hi ckness m

Waterd

epthm

Or i gi nal

0r i gi nal +2. 0m

Or i gi nal +4. 0

Or i gi anl +6. 0m

Or i gi anl +8. 0m

Or i gi anl -2. 0m

Or i gi anl -4. 0m

Or i gi anl -6. 0m

Fig.2 Comparison of Norway experience formula with the rock cover thickness in key cross sections

of different altitude scheme of Xiamen tunnel

Through Fig.2, its very clear that, for most cross sections, if the design altitude is elevated 8.0m, the

rock cover thickness still satisfy the Norway experience formula, but for position K8+750, special

reinforcement is needed. To ensure the suitable rock cover thickness, according to engineering

comparison analysis, different tunnel altitude models are adopted in numerical analysis. Different

initial geo-stress conditions are considered and three-dimension fast Lagrange method is used. A

solid-fluid model is adopted and construction progress is considered which include excavation and

For intact rock For cracked rock

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primary lining.

For simulating flow of fluid in saturated porous materials with FLAC-3D, fluid analysis is independent

of structural analysis. The variables involved in the description of fluid flow through porous media are

the pore pressure and the three components of the specific discharge vector. These variables are related

through the fluid mass-balance equation, Darcys law for fluid transport and a constitutive equation

specifying

the fluid response to changes in pore pressure, volumetric strains and temperature. For a homogeneous,

isotropic solid and constant fluid density, this law is given in the form of

ijjfi gxPkq ][ =

where kis the permeability (or mobility coefficient) in [m4/Ns], i is the fluid density in

[kg/m3], andgi , i = 1,3, are the three components of the gravity vector in [m/s2].

In theFLAC-3D formulation, changes in the variation of fluid content are related linearly to changes in

pore pressure,p, mechanical volumetric strains, e, and temperature, T . The fluid constitutive law is

expressed as:

t

T

t

e

t

p

Mt

+

=

1

where M is the Biot modulus in [N/m2], is the Biot coefficient, and is the undrained thermal

coefficient in [1 /C], which takes into account the fluid and grain thermal expansions.

Due to the paper length limited, only the calculation result of the scheme of original +4.0m is given.

The displacements in 4 key cross sections are listed in Table 4.

Table 4. Displacement of original +4.0m scheme

6.0/ =HV 9.0/ =HV Section Calculation

method

Settlement of

top

Uplift of

bottom

Settlement of

top

Uplift of

bottom

F-f -1.334 1.453 -1.244 1.412K8+350

E-P -1.113 1.396 -1.029 1.315

F-F -1.662 1.497 -1.549 1.452K8+750

E-P -1.233 1.467 -1.134 1.396

F-F -1.496 1.563 -1.401 1.516K9+450

E-P -1.122 1.486 -1.039 1.438

F-F -0.954 1.472 -0.880 1.432K11+12

0 E-P -0.937 1.284 -0.828 1.170

* F-F, mains Fluid flow analysis; E-P, mains Elastic-Plastic analysis.

For section K8+750, the pore pressure results after excavated 70 days are showed in Fig.3. The tension

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stress in K8+750 and K9+450 are little higher, the max. value is 0.366MPa, and locate at bottom of

tunnel.

FLAC3D 2.00

ItascaConsultingGroup,Inc.Minneapolis, Minnesota USA

Step308691 ModelPerspective10:01:20TueSep24 2002

Center:

X: 0.000e+000Y: 6.000e+000Z: 2.499e+001

Rotation:

X: 0.000Y: 0.000Z: 0.000

Dist:9.185e+002 Mag.: 3.81Ang.: 22.500

PlaneOrigin:X: 0.000e+000Y: 6.000e+000Z: 0.000e+000

PlaneNormal:X:0.000e+000Y:1.000e+000Z:0.000e+000

Job Title: FLUID - MECHANICAL INTERACTION

Contour of PorePressure

Plane:on0.0000e+000to 5.0000e+0041.0000e+005to 1.5000e+0052.0000e+005to 2.5000e+0053.0000e+005to 3.5000e+0054.0000e+005to 4.5000e+0055.0000e+005to 5.5000e+0056.0000e+005to 6.5000e+0057.0000e+005to 7.5000e+0058.0000e+005to 8.5000e+0059.0000e+005to 9.5000e+0051.0000e+006to 1.0500e+0061.0500e+006to 1.0553e+006

Interval= 5.0e+004

Fig.3 Pore pressure contour of K8+750 section ( 6.0/ =HV )

4. CONCLUSIONS

Through the above analysis, some concepts about Xiamen subsea tunnel are obtained.

1) The fluid flow tends to be stable in 70 days after excavation. Compared to elastic-plastic

analysis results, the max. tension stress increase and compression stress decrease.

2) The tunnel is on the whole stable if we adopt original +4.0m scheme, but in section

K8+750, there are thicker strongly weathered layer, the influence of fluid flow is notable. Inconstruction process, it will need special treatment such as grouting.

3) From the viewpoint of engineering analogical and numerical analysis, the min. rock cover

thickness is of original +4.0m scheme.

REFERENCE

Nilsen,B. Empirical analysis of minimum rock cover for subsea rock tunnels, Options for Tunnelling

1993 edited by H.Burger, 677~687, Amsterdam: Elsevier.

Akira Kitamura. Technical Development for the Seikan Tunnel, Tunneling and Underground Space

Technology, 1986, 1(3/4), 341~349.

Einar Broch. etr. Support of Large Rock Caverns in Norway Tunneling and Underground Space

Technology, 1996, 11(1): 11~19.

Z. D. Eisensteir, Large Undersea Tunnels and the progress of Tunnelling Technology. Tunnelling and

Underground Space Technology, 1994, 9 (3 ), 283~292.

Shogo Matsuo. An Overview of the Seikan Tunnel Project, Tunneling and Underground Space

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Technology, 1986, 1(3/4): 323~331.

T. S. Dahlo and B. Nilsen Stability and Rock Cover of Hard Rock Subsea Tunnels Tunneling and

Underground Space Technology 1994 9(2) 151~15.

Philippe Vandebrouck. The Channel Tunnel: The Dream Becomes RealityTunneling and Underground

Space Technology, 1995, 10(1) :17~21.

X.Qiu, D.Yang, B.Xu. et.al. 3-D FLAC Application in Stability Analysis of Ventilator Chamber of

Highway Tunnel, Rock and Soil Mech., 2003, 24(5): (in press)

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