Coastal Engineering 55 (2008) 753–760

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Coastal Engineering
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o a s t a l e n g

Stability of an immersed tunnel in offshore conditions under deep water wave impact
T. Kasper a,⁎, J.S. Steenfelt a, L.M. Pedersen a, P.G. Jackson a, R.W.M.G. Heijmans b
a
COWI A/S, Parallelvej 2, 2800 Kongens Lyngby, Denmark
b
ARCADIS Infra BV, Piet Mondriaanlaan 26, 3800 AE Amersfoort, The Netherlands

a r t i c l e i n f o a b s t r a c t

Article history: One of the special design requirements for the immersed tunnel of the Busan–Geoje Fixed Link in South Korea
Received 19 April 2007 has been the stability of the tunnel under wave impact with up to 9.2 m significant wave height. A large part of
Received in revised form 10 February 2008 the tunnel is placed in a trench and is founded on soft marine clay which is reinforced by cement deep mixing
Accepted 14 February 2008
(CDM) columns to limit and control the settlements caused by the weight of the tunnel and its protection
Available online 22 April 2008
material. Being beyond the scope of any design standard the problem of the tunnel stability under wave
impact has been investigated and verified by a combination of physical model tests and numerical modelling.
Keywords:
This paper provides a detailed description of the methodology applied to solve this particular problem and a
Immersed tunnel
Deep water waves discussion of the results and consequences for the design of the tunnel.
Numerical modelling © 2008 Elsevier B.V. All rights reserved.
Hydraulic model test
Stability

1. Introduction of an immersed tunnel under wave impact with significant wave

heights of up to 5.3 m during its construction by means of model tests
The Busan–Geoje Fixed Link connects Busan, which is South Korea's and numerical simulations. A rapid stabilization method was proposed
second largest city, with the island of Geoje and comprises a 3.2 km consisting of a combination of backfilling at the sides, placement of
long immersed tunnel, two rock tunnels and two 1.7 and 1.9 km long concrete under the bottom of the tunnel to increase the friction and
cable-stayed bridges. The immersed tunnel is characterised by highly additional ballast weight in case of abnormal weather conditions. To
demanding design requirements such as a record water depth of 47 m, the authors' knowledge, this is the only available publication related to
foundation on soft marine clay and stability and serviceability under the stability of immersed tunnels under large waves after immersion.
earthquake and deep water wave impact. Several papers on different The stability of an immersed tunnel protected by backfill material
aspects of this unique immersed tunnel have been published and are at the sides and subject to waves represents an interdisciplinary
under preparation (Edvardsen et al., 2006; Jensen et al., 2006; Odgaard problem of hydraulics and geotechnics. The wave conditions for the
et al., 2006; Kasper and Jackson, 2008; Steenfelt et al., 2008). For about immersed tunnel of the Busan–Geoje Fixed Link have been deter-
2/3 of its length, the tunnel is placed in a trench and founded on the mined by means of numerical modelling as described in Section 2 of
marine clay improved with cement deep mixing (CDM) columns this paper. It is expected that during the 100 years service life of the
(Figs. 1 and 2). The deep mixing soil improvement technique (see e.g. tunnel, the fill material around the tunnel will silt up with fine
CDIT (1999) for an overview) has been developed in Scandinavia and sediment in the sections where the tunnel is located in a trench.
Japan in the 1970's. It is applied to the foundation of the tunnel in order Two potentially critical scenarios with regard to the stability of the
to limit its settlements and, in particular, the differential settlements tunnel under waves have been identified and addressed with physical
of the individual tunnel segments. Furthermore, it improves the model tests and numerical modelling:
behaviour of the tunnel under earthquake impact.
▪ Uplift problem: It has been found in the model tests and from
The area of the tunnel is prone to frequent raids of typhoons and
swell waves. Therefore, the stability of the tunnel under waves has numerical modelling that the largest wave induced uplift force on
been an important design issue. This is the first time that an immersed the tunnel occurs for sedimented (i.e. low-permeable) backfill,
tunnel has to be designed for deep water waves with significant wave when a deep wave trough is above the tunnel. In this case, the
heights of up to 9.2 m. Aono et al. (2003) have investigated the stability corresponding horizontal force on the tunnel is relatively small.
There has been some concern that this uplift force might lead to
instability of the tunnel.
⁎ Corresponding author. Tel.: +45 45972211; fax: +45 45972212. ▪ Horizontal stability problem: A steep gradient of a wave over the
E-mail address: tkas@cowi.dk (T. Kasper). tunnel together with highly permeable backfill on the inflow side

0378-3839/$ – see front matter © 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.coastaleng.2008.02.021
754 T. Kasper et al. / Coastal Engineering 55 (2008) 753–760

Fig. 1. Layout of the immersed tunnel.

and a lower permeability on the outflow side leads to the largest of waves due to the local wind, shoaling, refraction and breaking but
horizontal wave force together with a relatively large correspond- not diffraction and reflection. A very important part of the model basis
ing uplift force. is the bathymetry of the area as shown in Fig. 3. An analysis is
performed on statistical data of wind and waves in the area to form
The 2D hydraulic model tests and the verification of the uplift the basis for the modelling. Due to the free fetch towards south and
stability are described in Section 3 of this paper. The analysis of the the possibility of typhoons in the area, the offshore boundary wave
horizontal stability problem with finite element models is presented with a return period of 10,000 years is Hs = 16.6 m as shown in Table 1.
in Section 4. Extreme wind speeds 10 m above ground for the return periods 10,
100 and 10,000 years are 34.7, 45.0 and 57.9 m/s, respectively. Wave
2. Numerical wave modelling breaking is included in the model by the solution of Battjes and
Janssen (1978) where γ1 = 1.6, γ2 = 0.8 and α = 1. Bottom dissipation
The wave conditions in the area of the tunnel have been and wave–current interaction are not included. The model output is a
determined by numerical modelling with the program MIKE 21 stationary wave field represented by a significant wave height, Hs, a
Nearshore Spectral Wave (DHI Water & Environment, Denmark). It is a mean wave period, Tm, and a mean wave direction, MWD. Fig. 4 shows
two-dimensional spectral wave model that computes a stationary a typical output for the wave field for the return period of
wave field for the given input conditions specified as extreme wind 10,000 years. The alignment of the tunnel is shown by the dashed
speeds and extreme boundary waves. The model includes generation line. The results for the maximum wave conditions along the tunnel

Fig. 2. Typical cross-section of the tunnel on CDM foundation.

 T. Kasper et al. / Coastal Engineering 55 (2008) 753–760 755

Fig. 3. Numerical wave modelling: Bathymetry.

3. Uplift problem
Table 1
Extreme wave conditions at the boundary for three return periods and directions
2D wave flume tests at a model scale of 1:60 have been made at the
Wave Return period Significant wave height, Significant wave period, Danish Hydraulic Institute (DHI) to investigate the wave induced
direction (years) Hs (m) Ts (s) water pressures around the tunnel, the stability of the protective
SSE 10 7.4 13.6 armour and fill material and the risk of scour formation (Fig. 5). The
100 9.3 14.9 stability of the tunnel protection as well as the scour formation are
10,000 13.1 17.1
covered in Truelsen et al. (in preparation). A standard method for
S 10 8.0 12.0
100 10.9 15.0 correct scaling of the core materials has been adopted. This method
10,000 16.6 14.9 minimises the scale effects on the flow through granular materials by
SSW 10 7.0 11.0 ensuring similitude of the hydraulic gradients in the model and in
100 10.2 14.0
nature. Different gradings of the fill material have been applied to
10,000 16.6 14.9
simulate different degrees of siltation within the backfill. The test
conditions used in the model test were based on the wave results from
the numerical modelling, see Table 2. The wave flume was equipped
with a wave generator capable of generating arbitrary wave spectra
alignment for events with return periods of 10, 100 and 10,000 years and absorbing reflected waves. The water pressures have been
are summarised in Table 2. measured by 8 pressure sensors, 3 at the top, 3 at the bottom and 1
It can be seen from Figs.1 and 4 that the highest waves occur in the area on either side of the tunnel element, respectively.
of tunnel element E7. This element has therefore been the focus of all It has been found that the uplift force on the tunnel determined
further investigations. The fact that the waves approach from a southerly from the pressure signals increases for finer fill gradings, i.e. lower
direction and pass the tunnel almost perpendicularly (Table 1 and Fig. 4) permeabilities (Table 3): The decreasing permeability of the fill in
allows for a two-dimensional modelling of wave impact on element E7. combination with the compressibility of the water leads to increasing

Fig. 4. Numerical wave modelling: Significant wave heights for the extreme wave conditions with 10,000 years return period.
756 T. Kasper et al. / Coastal Engineering 55 (2008) 753–760

Table 2 Table 3
Extreme wave conditions along the tunnel alignment for three return periods Measured maximum uplift force (scaled to in situ) for different fill gradings in the model
tests
Return period
Fill grading (estimated permeability) Maximum measured uplift force
Wave conditions 10 years 100 years 10,000 years
Significant wave height, Hs (m) 6.2 8.0 9.2 A (k = 8 m/s) 408 kN/m
Mean wave period, Tm (s) 11.1 12.6 15.0 B (k = 5e−2 m/s) 593 kN/m
Wave direction, MWD (deg) 177 176 175 C (k = 2e−3 m/s) 679 kN/m

induced pore pressures and resulting wave forces on the tunnel for the
damping of the pressure propagation from the seabed to the bottom
case with uneven sedimentation (Fig. 7). The seepage analyses are
part of the tunnel. Therefore, the pressure decrease induced by a wave
based on Darcy's law for laminar flow in porous media and the
trough above the tunnel does not reach the bottom of the tunnel to the
continuity equation considering the compressibility of the pore water
same extent as for highly permeable fill and, consequently, the uplift
Kw = 1e+8 Pa). The assumption of Darcy flow represents a simplifica-
force increases.
tion, as predominant Forchheimer and local turbulent flow conditions
Numerical seepage analyses with the program PlaxFlow (Plaxis BV,
are actually expected in the tunnel protection material (Dybbs and
Netherlands) considering a compressibility of the water Kw = 1e+8 Pa
Edwards, 1984). However, simulations of the model tests with even
have confirmed the increase of the uplift force for the lower
sedimentation have shown that the wave force combinations obtained
permeability cases and have shown that it does not further increase
from the finite element model are actually conservative. The left, right
for permeabilities lower than 2e−3 m/s. While the uplift force increases
and lower boundaries of the model are assumed as impermeable. The
for lower permeability, the resistance against uplift movement of the
wave pressure boundary conditions along the seabed (along the blue
tunnel increases as well. This is due to the suction effect, i.e. the larger
line in Fig. 9) are p = γw · hw with the head hw and the unit weight of
resistance against the necessary inflow of water underneath the tunnel
water γw = 10 kN/m3. The wave, according to Fig. 6, is moved from left
required to lift it. The uplift problem has therefore been analysed with
to right across the tunnel with a velocity of 13 m/s in a series of steps
the program Plaxis (similar to the analyses presented in Section 4)
and steady-state analyses are made for each step. A steady-state
considering the largest uplift force of 679 kN/m together with the
condition is reached after a fraction of a second in the highly permeable
smallest corresponding resistance represented by a permeability of
material around the tunnel and is therefore an adequate assumption.
k = 2e−3 m/s. The calculated horizontal and vertical displacements of the
However, there is some uncertainty with regard to the penetration of
tunnel of 7.5 and 4 mm, respectively, do not represent a critical failure
the wave pressures into the low-permeable clay and CDM. This can be
scenario and have been considered as being acceptable for the
illustrated by solving Biot's equations of consolidation (Biot, 1941) for a
serviceability of the tunnel.
one-dimensional, saturated and low-permeable soil column with
oscillating pressure boundary conditions at the top. The penetration
4. Horizontal stability problem
depth of wave pressures varies significantly depending on the stiffness
relation between the soil skeleton and the water (which strongly
A head difference of a wave between the left and right hand side of
depends on the air content). Therefore, steady-state computations
the tunnel causes a water flow through the fill and the gravel bed
represent a simplified, conservative approach leading to full penetra-
from one side of the tunnel to the other. A steep gradient of the wave
tion of the wave pressures into the subsoil (cf. Fig. 10). The hydraulic
across the width of the tunnel together with a lower permeability of
characteristics for the seepage analysis are shown in Table 4. The
the fill on the outflow side lead to a large horizontal force and a
tunnel is modelled as impermeable. The wave forces, i.e. the integrals
vertical uplift force on the tunnel. This situation presents a potential
of the excess pore pressures around the tunnel, as obtained from the
horizontal stability problem for the tunnel. Although not very likely,
seepage analysis are shown in Fig. 8. The wave position and the pore
systematically uneven siltation of the fill material on the left and right
pressure distributions for the most critical wave force combination of
hand side of the tunnel cannot be excluded. It has been decided to
Fh/Fv =450/260 kN/m are shown in Figs. 9 and 10, respectively.
consider a difference in permeability of the fill on the left and right
The wave induced pore pressures are imported into a mechanical
hand side by a factor of 10 as a design situation. Fig. 6 shows the single
analysis with the program Plaxis to determine the corresponding
wave with the largest head gradient over the width of the tunnel out
displacements and stability of the tunnel. In this model, the complete
of 1500 waves in the model test of the 10,000 years wave event. This
construction and loading history is taken into account by the
wave has been chosen as the design wave for the horizontal stability
following modelling sequence:
problem.
Because only even sedimentation was modelled in the wave flume 1. Initial stress state in the clay and the underlying alluvium. Effective
tests, a finite element model has been set up to determine the wave horizontal stresses σh′ = K0 · σv′ are generated according to Jaky's

Fig. 5. Setup of the 2D hydraulic model tests of the tunnel made at DHI (Element 7).
 T. Kasper et al. / Coastal Engineering 55 (2008) 753–760 757

Fig. 6. Approximation of the most critical wave with the largest head gradient across the width of the tunnel, measured in the model test for the 10,000 years return period (scaled to
in situ).

Fig. 7. Plaxis/PlaxFlow finite element model (shown for a slope of the armour protection of 1:1.5).

formula K0 = 1 − sin φ′ and pore pressures are generated based on sponding to the conditions during wave impact. These increased
the still water level. values are shown in parentheses in Table 5.
2. Dredging of the trench. An additional force is applied to the tunnel in analysis step 5
3. Manufacturing of the CDM columns. representing the hydrodynamic force, which is motivated and estimated
4. Placement of the gravel bed, the tunnel, the fill and the armour as follows: Any obstruction in the flow field (to the orbital velocity) of
protection. the water in a wave is subject to a hydrodynamic force according to
5. Wave impact modelling. Mechanical analysis based on the wave Bernoulli's equation (Sumer and Fredsøe, 1997). The tunnel is situated in
induced pore pressures imported from the PlaxFlow seepage a trench and protrudes 5 m above the fill level at the sides of the tunnel.
analysis. Therefore, waves exert a hydrodynamic horizontal force on the tunnel,
which may conservatively be estimated as
Analysis steps 1 to 4 are modelled as drained for all materials,
while the behaviour of the clay and the CDM in analysis step 5 is 1 1
modelled as undrained. 15-node higher order triangular finite Phyd ¼ q m2 C ¼ d1000d 42 d 1 ¼ 8000 Pa
2 w 2
elements are used in the Plaxis calculation to obtain a good F hyd ¼8000d 5 ¼ 40000 N=m
approximation of the displacements and failure mechanisms. The
material models used in the analysis are summarised in Table 5.
It should be noted that this estimate is based on the assumption of a
Detailed information on the material models can be found in the
steady current. However, the protruding structure is about 50 m long,
Plaxis manuals. The parameters of the clay and alluvium have been
derived from geotechnical investigations, while all other parameters
are design parameters according to the project specifications. The
interface between the tunnel and the surrounding material is
modelled with a friction angle of 27°. The stiffness and strength
parameters of the clay correspond to strain ranges and strain rates of
normal laboratory test conditions. Increased values have been
conservatively estimated and are applied in analysis step 5 corre-

Table 4
Material parameters for the PlaxFlow seepage analysis

Material Permeability (m/s)

Armour stone layer 1

Fill left 0.1
Gravel bed 0.1
Fill right 0.01
Clay + alluvium 1e−9
CDM 1e−9
Fig. 8. Wave forces obtained from the PlaxFlow seepage analysis.
758 T. Kasper et al. / Coastal Engineering 55 (2008) 753–760

Fig. 9. Wave position resulting in the most critical wave force combination of Fh/Fv = 450/260 kN/m (For interpretation of the references to colour in this figure legend, the reader is
referred to the web version of this article.).

Fig. 10. Pore pressures (pressure head) obtained for the wave position resulting in the most critical wave force combination of Fh/Fv = 450/260 kN/m.

which is a substantial proportion of the wave length of about 200 – following can be observed and concluded from the results of the
250 m. Furthermore, the tunnel does not protrude above the normal numerical analyses:
sea bed, but only above the bottom of the trench. Therefore, the above
▪ Without consideration of the hydrodynamic force the horizontal
hydrodynamic force is regarded as a conservative upper estimate. By
tunnel displacements of 46 – 51 mm are within acceptable limits
means of a variation of the hydrodynamic force, the displacements and
for all considered slopes of the tunnel protection.
stability of the tunnel can be evaluated for different slopes (amounts)
of the tunnel protection as shown in Table 6, Fig. 11 and in Fig. 12. The
failure mechanism illustrated in Fig.12 consists of a wedge of fill sliding
down along the left hand side of the tunnel and a horizontal sliding
body consisting of the tunnel and the fill on the right hand side. The Table 6
Calculated horizontal displacements of the tunnel for different slopes of the tunnel
protection and different wave load levels

Slope of tunnel Hydrodynamic Total horizontal Load Horizontal

protection force (kN/m) force (kN/m) level displacement
Table 5 (mm)
Material models and parameters used in the mechanical analysis
1:1.5 0 450 1.00 51
50 500 1.11 122
Marine clay Alluvium CDM Gravel bed Fill + armour
100 550 1.22 172
Material Hardening soil Mohr– Linear elastic Mohr– Mohr– 1:2.0 0 450 1.00 49
model model Coulomb Coulomb Coulomb 50 500 1.11 56
γ (kN/m3) 14.7 20 20 20 20 100 550 1.22 67
Eref (kPa) 1200 (2400) 50,000 80,000 50,000 50,000 150 600 1.33 90
ν (−) 0.2 0.25 0.2 0.2 0.2 200 650 1.44 155
Eref
oed (kPa) 633 (1266) 1:2.5 0 450 1.00 46
Eref
ur (kPa) 8000 (30,000) 50 500 1.11 51
m (−) 1 100 550 1.22 59
pref (kPa) 100 150 600 1.33 69
c' (kPa) 3 0 0 0 200 650 1.44 101
φ' (°) 25 (30) 35 36 40 250 700 1.55 191
 T. Kasper et al. / Coastal Engineering 55 (2008) 753–760 759

5. Conclusions

The stability of the immersed tunnel of the Busan–Geoje Fixed Link

under wave loading has been subjected to detailed studies based on
model testing and numerical modelling. In this way it was possible to
identify the two most onerous scenarios. They correspond to uplift for
even sedimentation at medium low permeability and to horizontal
stability for consistent, uneven sedimentation with permeabilities
different by a factor ten on the two sides of the tunnel. It has been
found that the vertical uplift is not critical. For the horizontal
stability problem the transition from essentially elastic behaviour to
failure behaviour may take place for a relatively small increase in
the estimated horizontal wave load for the critical 10,000 years
wave. For the original design slope of the tunnel protection of 1:1.5
the limit of elastic behaviour is already reached for the characteristic
horizontal load. The slope of the tunnel protection has therefore
been changed to 1:2 for tunnel elements 3 to 9 to add robustness to
the design in that the elastic deformation range now corresponds
Fig. 11. Load – displacement diagram for different slopes of the tunnel protection. to roughly a 10 – 15% load increase (including hydrodynamic
forces) in load and an acceptable safety against failure of 1.4. At the
same time, the relatively small difference between 10,000 and
100 years waves in regard to horizontal stability is thereby taken
▪ With the originally designed slope of the tunnel protection of 1:1.5 into consideration.
(basic case) an increase of the horizontal force by 11% covering a
hydrodynamic force of 50 kN/m leads to an increase of the horizontal Acknowledgements
tunnel displacement from 51 to 122 mm. This corresponds to an
irrecoverable displacement of uhor,irr = 122 – 51 · 1.11 = 65 mm, which The authors gratefully acknowledge the permission from Daewoo
is deemed unacceptable. Engineering & Construction Co. Ltd. to publish this paper.
▪ With a less steep slope of 1:2.0 corresponding to an additional
amount of fill of totally 15 m3/m length of the tunnel the horizontal
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