This study presents a practical design strategy for a large-size Submerged Floating Tunnel (SFT) under different target environments through global-performance simulations. A coupled time-domain simulation model for SFT is established to check hydro-elastic behaviors under the design random wave and earthquake excitations. The tunnel and mooring lines are modeled with a finite-element line model based on a series of lumped masses connected by axial, bending, and torsional springs, and thus the dynamic/structural deformability of the entire SFT is fully considered. The dummy-connection-mass method and constraint boundary conditions are employed to connect the tunnel and mooring lines in a convenient manner. Wave- and earthquake-induced hydrodynamic forces are evaluated by the Morison equation at instantaneous node positions. Several wave and earthquake conditions are selected to evaluate its global performance and sensitivity at different system parameters. Different Buoyancy-Weight Ratios (BWRs), submergence depths, and tunnel lengths (and mooring intervals) are chosen to establish a design strategy for reducing the maximum mooring tension. Both static and dynamic tensions are critical to find an acceptable design depending on the given target environmental condition. BWR plays a crucial role in preventing snap loading, and the corresponding static tension is a primary factor if the environmental condition is mild. The tunnel length can significantly be extended by reducing BWR when environmental force is not that substantial. Dynamic tension becomes important in harsh environmental conditions, for which high BWR and short mooring interval are required. It is underscored that the wet natural frequencies with mooring are located away from the spectral peaks of design waves or earthquakes.

The Submerged Floating Tunnel (SFT) has recently attracted significant attention as an alternative to conventional bridges and immersed tunnels for long-distance and deepwater crossing [

Active studies related to SFTs have been conducted with respect to a variety of environmental conditions for achieving the first real construction. Developing a robust and time-efficient simulation model is recognized as one of the essential tasks, especially for SFT research due to its potentially high deformability. There exist few experimental studies associated with the dynamics of SFT in waves [

Until now, most studies concentrated on theoretical investigations and parametric studies. For example, regarding wave excitations, Lu et al. [

There exist technical difficulties in the construction of the structure. One of the critical problems for the large diameter tunnel is considerable dynamic tension, which is usually due to snap loading. Higher BWR is recommended to resolve the snap loading, as also in [

In this study, a practical strategy for the SFT design is presented. Coupled time-domain hydro-elastic simulations for large SFT are conducted in wave and earthquake conditions. The tunnel and mooring lines are separately modeled with a finite-element line model based on the lumped mass method. Each component is divided into several finite elements to account for structural deformability. Their connection is completed by the dummy-connection-method [

A coupled time-domain model is established by OrcaFlex, a widely-used commercial program in the oil and gas industry [

All components in the Morison equation are considered under wave excitations. For the given wave spectrum with significant wave height (

The tunnel and mooring lines are modeled with separate line models while they are linked by employing the dummy-connection-mass method [

The earthquake effect is considered by inputting the time histories of seismic lateral and vertical displacements at each anchor location of the mooring line and both ends of the tunnel. The seismic effect then appears on the tunnel through

The present numerical simulation model has been validated against several experimental results in wave tanks [

SFT's basic configuration and design parameters are shown in

Studless chain mooring is chosen with a nominal diameter of 0.18 m, which is one of the largest sizes to handle large static and dynamic tensions. A mooring group consists of four mooring lines at the given tunnel cross section, and they are 60° inclined to the seabed. The same mooring group is distributed with equal interval along the tunnel length (see

Component | Parameter | Value | Unit |
---|---|---|---|

Tunnel | Length | 700, 1400, 2100, 4200 | m |

Outer diameter | 20 | m | |

End boundary condition | Fixed-fixed condition | -- | |

Material | High-density concrete | -- | |

BWR | 1.05, 1.10, 1.15, 1.20, 1.25, 1.30 | -- | |

Added mass coefficient | 1.0 | -- | |

Drag coefficient | 0.55 [ |
-- | |

Mooring lines |
Length | 50.2 (Line #1 and 2), |
m |

Mass/unit length | 644.8 | kg/m | |

Nominal diameter | 0.18 | m | |

Equivalent outer diameter | 0.324 | m | |

Axial stiffness | 2.77 × 10^{6} |
kN | |

Added mass coefficient | 1.0 | -- | |

Drag coefficient | 2.4 [ |
-- |

Waves and earthquakes are considered as environmental conditions. The JONSWAP wave spectrum is utilized to produce the time histories of random waves. As shown in

Three real seismic displacements are collected from USGS in a magnitude range of 3.8–8.4 in the moment magnitude (MM) scale, as summarized in

Number | Location | Year | Magnitude | { Peak lateral motion (cm)} | { Peak vertical motion (cm)} | { Duration (s)} |
---|---|---|---|---|---|---|

1 | California, USA | 2012 | 3.8 | −0.042 | −0.016 | 30 |

2 | Northern California, USA | 2010 | 6.5 | −3.306 | 2.145 | 126 |

3 | Indonesia | 2007 | 8.4 | 8.028 | −6.250 | 125 |

Modal analysis is carried out to obtain the natural frequencies and mode shapes of the SFT contacting water after the static simulation. The representative model shapes and natural frequencies are presented in

Item | { Tunnel length = 700 m, |
{ Tunnel length = 700 m, |
{ Tunnel length = 700 m, |
|||
---|---|---|---|---|---|---|

Mode # | { Horizontal NF (rad/s)} | { Vertical NF (rad/s)} | { Horizontal NF (rad/s)} | { Vertical NF (rad/s)} | { Horizontal NF (rad/s)} | { Vertical NF (rad/s)} |

1 | 1.604 | 2.493 | 1.663 | 2.640 | 1.686 | 2.694 |

2 | 2.606 | 3.115 | 2.643 | 3.309 | 2.641 | 3.356 |

3 | 4.556 | 5.163 | 4.566 | 5.104 | 4.507 | 5.039 |

Item | { Tunnel length = 1400 m, |
{ Tunnel length = 2100 m, |
{ Tunnel length = 4200 m, |
|||

Mode # | { Horizontal NF (rad/s)} | { Vertical NF (rad/s)} | { Horizontal NF (rad/s)} | { Vertical NF (rad/s)} | { Horizontal NF (rad/s)} | { Vertical NF (rad/s)} |

1 | 0.999 | 1.701 | 0.817 | 1.409 | 0.575 | 0.987 |

2 | 1.128 | 1.771 | 0.852 | 1.428 | 0.579 | 0.988 |

3 | 1.472 | 1.993 | 0.952 | 1.487 | 0.590 | 0.993 |

In this section, the tunnel's dynamic responses and mooring tensions are evaluated under wave excitations. As mentioned before, two different wave conditions (

First, BWR often plays a critical role in both static and dynamic responses, as demonstrated in

Mooring tension further demonstrates the snap loading phenomenon, as can be seen in

On the other hand, in the mild wave condition (_{S}

Second, the sensitivity with respect to submergence depth is checked, as shown in

Third, the effects of tunnel length and mooring interval on dynamic responses and mooring tensions are assessed, as shown in

As shown in

In this section, the tunnel's dynamic responses and the corresponding mooring tensions are evaluated under earthquake excitations. In the case of earthquake-induced dynamics, tunnel's submergence depth is almost irrelevant unless it is close to the free surface. Instead, mooring style and length become more relevant parameters. In this section, the submergence depth is fixed at 61.5 m. Three MM (moment magnitude)-scale time histories of earthquake excitations are obtained from USGS and employed in this study. Based on the spectral results in

First, the influences of BWR and earthquake magnitudes on dynamic responses and mooring tensions are checked, as reported in

As for the mooring tension, the maximum tension is governed by the static mooring tension, as shown in

Finally, the sensitivity test with respect to the tunnel length is carried out, as presented in

From the comparison between the 100-year storm condition in South Korea (

In this study, the practical design strategy for a large size SFT is investigated. A coupled time-domain dynamics simulation model for SFT is built considering wave and earthquake excitations. Tunnel and mooring lines are modeled by using a series of the finite-element line model. The line theory is based on a lumped mass method, where physical components are all lumped at nodes and they are connected by massless linear springs to represent elastic behaviors. The dummy-connection-mass method and the constraint boundary conditions are utilized to couple the tunnel and mooring lines. The Morison equation is employed to estimate the wave- and earthquake-induced hydrodynamic forces at instantaneous node positions. Various wave and earthquake conditions are tested to check the corresponding dynamic motions and mooring tensions at different system parameters. The wet natural frequencies are obtained through modal analysis for different BWRs, tunnel lengths, and mooring intervals. Systematic parametric studies are conducted under different BWRs, submergence depths, and tunnel lengths (and mooring interval) to build a cost-effective design strategy while satisfying the allowable mooring tension. The following design strategies are established according to the simulation results:

The primary wet natural frequencies with mooring need to be adjusted depending on the target wave and earthquake conditions to reduce the resonant motions.

Reducing BWR is generally beneficial when the dynamic environmental load is relatively small. In this case, the maximum tension is governed by the static tension by BWR. However, the possibility of snap loading at low BWRs should be carefully examined from the simulation.

The tunnel length or mooring interval can significantly be extended with increasing submergence depth since wave excitations decay exponentially with submergence depth.

The tunnel length or mooring interval can also be extended with appropriate BWR as storm-wave and seabed-earthquake conditions are relatively mild. In this case, the high static tension can be reduced with smaller BWR while dynamic tension plays relatively a minor role.

In the case of 100-yr severe storm condition at the South Sea of Korea, with 61.5-m submergence depth and 50-m mooring interval, BWR = 1.2 turns out to be the best case satisfying the mooring tension requirement. At a larger submergence depth of 101.5 m, no snap loading is observed, and the tension is governed by the static tension. In the case of 100-year storm at submergence depth 61.5 m of Norwegian Fjord or Indonesian earthquake of magnitude 8.4, tunnel length between two fixed stations as large as 4200 m (or mooring interval as large as 300 m) can be used with BWR = 1.05.

As given in

where _{0} and is the unstretched element length. The bending moment magnitude is then computed by the bending springs at either side of the node as:

where

The dummy-connection-mass method [