In this study, a numerical procedure is described for the transient response analysis of a submerged\ud
floating tunnel with reference of a designed tunnel in Japan. Tension legs seizing the tunnel are simply modeled by a\ud
spring elements and the tunnel itself is assumed by two rigid bodies between which a flexible joint is used. A recorded\ud
seismic excitation is used while the wave load is calculated under a specific design condition. Hydro-damping and\ud
added mass are considered for numerically modeling the underwater condition. A numerical procedure is validated with\ud
compared to the previous results of the designed tunnel. Some modifications are proposed through the validating\ud
process in terms of modeling and analysis procedure. Eventually, the modified numerical procedure will be used in\ud
analyzing the transient response of a newly designed tunnel

Han, I.S.

Han, S.H.

Ko, K.H.

Lee, K.S.

Park, W.S.

Hasanuddin University Repository

 831 
 
 
Proceedings of the 7th International Conference on Asian and Pacific Coasts  
(APAC 2013) Bali, Indonesia, September 24-26, 2013 
 
 
TRANSIENT RESPONSE ANALYSIS OF A SUBMERGED FLOATING TUNNEL UNDER 
SEISMIC AND WAVE EXCITATIONS 
 
J.H. Ko 
1
, I.S. Han 
1
, S.H. Han 
1
, W.S Park
1
 and K.S. Lee
1 
 
 
ABSTRACT: In this study, a numerical procedure is described for the transient response analysis of a submerged 
floating tunnel with reference of a designed tunnel in Japan. Tension legs seizing the tunnel are simply modeled by a 
spring elements and the tunnel itself is assumed by two rigid bodies between which a flexible joint is used. A recorded 
seismic excitation is used while the wave load is calculated under a specific design condition. Hydro-damping and 
added mass are considered for numerically modeling the underwater condition. A numerical procedure is validated with 
compared to the previous results of the designed tunnel. Some modifications are proposed through the validating 
process in terms of modeling and analysis procedure. Eventually, the modified numerical procedure will be used in 
analyzing the transient response of a newly designed tunnel. 
 
Keywords: Submerged floating tunnel, transient response analysis, seismic excitation, wave load. 
 
                                                 
1 Korea Institute of Ocean Science & Technology, 787 Haean-ro(st). Sangnok-gu, Ansan-si, Gyeonggi-do, South Korea 
INTRODUCTION  
Submerged floating tunnels (SFT) have been 
researched as a new promising technology for strait 
crossing since it is superior to conventional crossing 
structures. The research society of SFT in Hokkaido, 
Japan was established in 1991 to realize SFT through 
experimental and analytical researches with feasibility 
studies. Funka bay crossing was the first feasibility study 
for the society (Kanie, 2010). The research group in 
KIOST, Korea has started the study of SFT since 2010 
supported by a project "Development of core techniques 
for submerged floating tunnels". China and Italy have 
also been interest in the study on SFT.  
Transient analysis is a powerful approach in estimating 
the dynamic responses of structures under seismic and 
wave load, which are critical in judging the safety of the 
structures. In this study, a numerical procedure is 
described for the transient response analysis of a 
submerged floating tunnel with reference of a designed 
tunnel in Funka bay.  
 
PROBLEM DEFINITION & MODELING 
The total length of a targeted tunnel, which is designed 
in Funka Bay, Japan, is 7km and it is consist of 200m 
tubes. The tubes are located at 30m below a water 
surface. The water depth is 90m in the first domain from 
0m to 2km, 80m in the second domain from 2km to 
3.8km, and 70m in the third domain from 3.8km to 7km. 
The outer diameter of the tube is 23m and its inner 
diameter is 21m.  So, the length of the tension leg in the 
first domain is 48.5m, that in the second domain is 
38.5m, and that in the third domain is 28.5m. The both 
ends of the tunnel are connected to a ventilation structure.   
   The tubes of the tunnel are floating and strained by the 
tension legs. Among the types of tension legs, a simplest 
type is utilized and it is consisted of single cable and 
straightly aligned along vertical axis to an anchor on the 
ground. The initial tension of the tension leg is 4.9e7 N 
and its area is 0.1120m2 (RS-SFT). 
   Recovery forces in horizontal and vertical axes are 
calculated by  
                                                   (1)
  
in which  Lv is the length of  the tension leg, Pv is initial 
tension, E is young's modulus, and A is the area of the 
section of the tension leg. The tension leg is coupled 
with another one, so the final values are doubled. From 
the equation, (Kx, Ky, Kz) for each domain are calculated 
as follows.  
First domain: (2.02e6 N/m, 2.02e6N/m, 9.0e8 N/m) 
Second domain: (2.55e6 N/m, 2.55e6 N/m, 11.4e8 N/m) 
Third domain: (3.44e6 N/m, 3.44e6 N/m, 15.5e8 N/m) 
  In order to analyze the dynamic response of the whole 
tunnel quickly, the real model is simplified as shown in 
the Fig. 1. 
 
 
J.H. Ko., et al. 
832 
 
 
Fig. 1 Simplified model and corresponding 
terminologies. 
As a further simplification, the tube is separated into 
two rigid bodies and the joint of the tube is used for 
connecting between them as shown in the Fig. 2. The 
tension leg and the joints are actually modeled by a 
spring element in a corresponding finite element model.  
 
Fig. 2 Further simplified model and corresponding 
terminologies. 
Properties of the rigid body and joints are listed in 
Table 1. Highlighted values indicate that original values 
are modified.  
Table 1 Properties of each part (RS-SFT). 
Part  Properties  Value  
Rigid 
body  
Mass (ton) 33670 
Rotational inertia moment 
(x axis: ton-㎡) 
8360 
Rotational inertia moment 
(y axis: ton-㎡)  
2.80E+06 
Rotational inertia moment 
(z axis: ton-㎡)  
2.80E+06 
Joint  
 Shear spring (tf/m) 1.01E+06 
 Rotational spring (tf-m) 
4.33E+08(y, z) 
1.01E+08(x) 
Axial spring (tf/m) 3.57E+06 
Joint of 
tube  
 Shear spring (tf/m) 1.01E+06 
 Rotational spring (tf-m) 1.30E+08 
Finite element model, in which the high stiffness is 
given for implementing the rigid body model, is depicted 
in Fig. 3.  
MSC/NASTRAN is used for the transient analysis from 
seismic and wave dynamic loads.  
A Rigid body is modeled by two NASTRAN CBAR 
linear elements, and the middle node is then connected to 
spring element. The section of the tube is defined in 
NASTRAN PBAR.  
So the bar element has 50m length and the number of 
the elements is 140. Mass in the table 1 is adjusted by 
giving a corresponding density, but inertia moments are 
not adjusted well because of the fore-mentioned 
simplifications. The middle node of the rigid body is 
connected to ground by using NASTRAN CELAS1 
elements of which number is 70. The joint and joint of 
the tube are also modeled by NASTRAN CELAS1 
elements of which number are 70 and 69, respectively. 
Fixed point constraints are imposed to the both ends of 
the tunnel, which are connected to the ventilation 
structure, and the low end of every spring for modeling 
the tension legs. In case of seismic analysis, the loading 
is imposed at the end of every spring for the tension legs 
as well.  
 
Fig. 3 Finite element model and boundary condition. 
Added mass and hydrodynamic damping should be 
considered in analyzing an underwater structure because 
of high density water effect in a transient analysis.  
Newmark et al. (1971) introduced a simple calculation of 
the added mass in water as  
  ,     (2)       
in which w  is the water density, r is a radius of object, 
and   is angle between flow direction and longitudinal 
direction of the tunnel. Calculated added mass is applied 
in imposing the material properties. The hydrodynamic 
damping is calculated by following 4 terms.  
 
Transient Response Analysis of A Submerged Floating Tunnel Under Seismic and Wave Excitations 
 
 
833 
 
 
Cook (1982) introduces the ranges or the values of the 
four terms as follows:  
  
Hence, the additional offshore damping is included in 
the following range for a pile supporting structure 
(Schmidt, 2010) 
 
The tunnel is supported by a tension leg-anchor instead 
of the pile, thus  is a little bit decreased but the 
damping of a concrete is larger than that of steel. Thus, 
we use 1% as damping ratio, D. In MSC/NASTRAN, the 
structural damping G is used in giving damping ratio: G 
= 2D = 0.02 and is calculated by the following equation 
(Rose, 2001). 
    , 
in which w3 is dominant frequency of the response in 
radians per second. In the equation, [B] is viscous 
damping matrix, [K] is global stiffness matrix, [Ke] is 
element stiffness matrix, Ge is element structural 
damping, and W4 is the dominant frequency of each 
element. w3 is obtained as 0.178 from the eigensolution 
in Fig. 4. Ge is given by zero.  
 
Fig. 4 First natural frequency and normal mode. 
 
DYNAMIC LOAD 
 
 (1) Seismic load 
The seismic load is assumed to be same at all 
supporting points. In our model, the both ends of the 
tunnel and the low ends of the tension legs are 
considered as the supporting points. The seismic loads 
are reproduced from the previous work (RS-SFT) as 
shown in Fig. 5. 
 
 
Fig. 5 Horizontal(top) and vertical(bottom) seismic loads. 
(2) Wave load 
 
A worst condition, in which the wave height is 23.4m 
and the period is 13 second, is chosen for design purpose. 
The wave loads are calculated in an in-house code, 
CADMAS-SURF 3D for every domain of the tunnel. Fig. 
6 shows the horizontal and vertical loads in the third 
domain where water depth is 70m.  
 
 
 
Fig. 6 Horizontal(top) and vertical(bottom) wave loads 
in 70m depth.  
 
ANALYSIS RESULTS 
The structural responses for the given seismic loads 
are extracted on center nodes of all rigid bodies in Fig. 2. 
In this paper, we showed only our results due to a 
copyright issue. The further information and 
 
J.H. Ko., et al. 
834 
 
supplementary data will be given in the presentation.  
 
(1) Seismic load 
  From the dynamic response, the peak values in 
acceleration curves along in axial direction are plotted in 
Fig. 7. Maximum acceleration in the horizontal direction 
is observed in the both ends of the tunnel and its value is 
similar to the previous work. Maximum acceleration in 
vertical direction is also observed in the both ends of the 
tunnel as well. Its value is lower than the values in the 
previous work.  
 
 
 
Fig. 7 Maximum horizontal(top) and vertical(bottom) 
accelerations along axial direction. 
 
(2) Wave load 
    From the dynamic responses, the peak values in 
displacement and acceleration curves along in vertical 
direction are plotted in Fig. 8. Maximum displacement 
and acceleration are observed near the left end of the 
tunnel as same as the previous work. Their values are 
also similar to the previous work.  
 
CONCLUSION 
In this study, a numerical procedure is investigated for 
the transient response analysis of a submerged floating 
tunnel with reference of a designed tunnel in Japan. The 
chosen results from our model by using the numerical 
procedure are similar to those of the previous model. 
However, the model is constructed based on the two-
level simplifications, thus detail modeling will be 
required for acquiring more reliable results. Our future 
work is a flexible modeling for satisfying it and quick 
solution techniques.    
 
 
 
 
Fig. 8 Maximum displacement(top) and 
acceleration(bottom) in the vertical axis. 
 
ACKNOWLEDGEMENTS 
This research was supported by the project 
‘Development of core techniques for submerged floating 
tunnels (PE98941)’ funded by Korea Institute of Ocean 
Science and Technology 
REFERENCES 
Kanie, S., 2010, Feasibility studies on various SFT in 
Japan and their technological evaluation, Procedia 
Engineering 4, 13–20 
Research Society of Submerged Floating Tunnel (RS-
SFT), Underwater submerged tunnel: case study, 
research report.  
Cook, M.F., Vandiver, J.K., 1982, Measured and 
predicted dynamic response of a single pile platform 
to random wave excitation, MIT, OTC(Offshore 
Technology Conference report) 4285.  
 Schmidt, B., 2010, Overall Damping for Piled Offshore 
Support Structures, DWL-Scmi-extern-001 
Newmark, N. M., Rosenblueth, E., 1971, Fundamentals 
of Earthquake Engineering, Prentice-Hall, 
Englewood Cliffs, NJ. 
 Rose, T., 2001, An Approach to Properly Account for 
Structural Damping, Frequency-Dependent 
Stiffness/Damping, and to Use Complex Matrices in 
Transient Response, MSC. Software Corporation 
2001 Aerospace Conference and Technology 
Showcase. 


Transient response analysis of a submerged floating tunnel under seismic and wave excitations

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Transient response analysis of a submerged floating tunnel under seismic and wave excitations

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