Performance Evaluation of Submerged Floating Tunnel Subjected to ...

applied sciences Article

Performance Evaluation of Submerged Floating Tunnel Subjected to Hydrodynamic and Seismic Excitations Naik Muhammad

ID

, Zahid Ullah and Dong-Ho Choi *

Department of Civil and Environmental Engineering, Hanyang University, 222 Wangshimni-ro, Seoul 04763, Korea; [email protected] (N.M.); [email protected] (Z.U.) * Correspondence: [email protected]; Tel.: +82-222-20-4154 Received: 24 September 2017; Accepted: 27 October 2017; Published: 31 October 2017

Abstract: Submerged floating tunnels (SFTs) are innovative structural solutions to waterway crossings, such as sea-straits, fjords and lakes. As the width and depth of straits increase, the conventional structures such as cable-supported bridges, underground tunnels or immersed tunnels become uneconomical alternatives. For the realization of SFT, the structural response under extreme environmental conditions needs to be evaluated properly. This study evaluates the displacements and internal forces of SFT under hydrodynamic and three-dimensional seismic excitations to check the global performance of an SFT in order to conclude on the optimum design. The formulations incorporate modeling of ocean waves, currents and mooring cables. The SFT responses were evaluated using three different mooring cable arrangements to determine the stability of the mooring configuration, and the most promising configuration was then used for further investigations. A comparison of static, hydrodynamic and seismic response envelope curves of the SFT is provided to determine the dominant structural response. The study produces useful conclusions regarding the structural behavior of the SFT using a three-dimensional numerical model. Keywords: submerged floating tunnel (SFT); mooring cable configuration; dynamics of SFT; hydrodynamic response; seismic response

1. Introduction Submerged floating tunnels (SFTs) are tubular structures that float at a specified depth and are supported by mooring cables. The balance between pre-tensions in the mooring cables and net positive buoyancy (or residual buoyancy) maintains the structural stability of the SFT. The cost of an SFT per unit length remains almost constant with increasing length [1,2]. Therefore, it is considered an economical alternative for waterway crossings in comparison to cable-supported bridges, underground tunnels or immersed tunnels, especially for deep and wide crossings. In addition, SFT is more advantageous, because it is not bound to geographic terrain and does not interfere with water surface traffic. The research efforts for development of the SFT began in 1923 when the first Norwegian patent was issued for it. Since then, many case studies and proposals have been made for different proposed projects, such as Hogsfjord in Norway [3], Funka Bay in Japan [4,5], Messina Strait in Italy [6,7], Qiandao Lake in China [8,9] and Mokpo-Jeju SFT in South Korea [10]. The lack of experimental and model test results may be one of the reasons why an SFT has not yet been constructed. The work in [11] calculated the wave loads on a circular SFT using the boundary element method (BEM) and Morison’s equation and compared the results with model tests. Wave loads on an elliptical SFT were calculated similarly by [12] using Morison’s equation and compared with the test results. These studies indicated that both BEM and Morison’s equation gave reliable estimates of wave loads on SFT. Appl. Sci. 2017, 7, 1122; doi:10.3390/app7111122

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with the test results. These studies indicated that both BEM and Morison’s equation gave reliable 2 of 17 loads on SFT. Researchers have focused the research developments on the behavior of SFT for more than three decades. A formulation for the dynamic analysis of the SFT under seismic and sea waves effects was Researchers have focused the research developments on the behavior of SFT for more than three presented by [13]. A primary attempt to analyze the fluid-structure interaction (FSI) of the SFT using decades. A formulation for the dynamic analysis of the SFT under seismic and sea waves effects was a two-dimensional model was made by [14], followed by a more comprehensive presentation of FSI presented by [13]. A primary attempt to analyze the fluid-structure interaction (FSI) of the SFT using by [15] using the finite element implementation of the Navier–Stokes equation. The soil-structure a two-dimensional model was made by [14], followed by a more comprehensive presentation of FSI interaction of SFT is another issue that needs to be investigated properly. Some SFT numerical models by [15] using the finite element implementation of the Navier–Stokes equation. The soil-structure have idealized the soil-structure interaction as horizontal, vertical and rotational springs at the interaction of SFT is another issue that needs to be investigated properly. Some SFT numerical connecting points [16–18]. The vortex-induced vibrations of mooring cables caused by water currents models have idealized the soil-structure interaction as horizontal, vertical and rotational springs at the can produce fatigue damage to the cables [19–21]. Since SFT is considered an alternative solution for connecting points [16–18]. The vortex-induced vibrations of mooring cables caused by water currents transportation, moving load analysis or dynamic analysis under traffic loading is a key demand of can produce fatigue damage to the cables [19–21]. Since SFT is considered an alternative solution for the structure, but the research efforts are very limited regarding this problem. However, a primary transportation, moving load analysis or dynamic analysis under traffic loading is a key demand of attempt was made by [22], who investigated the effects of two- and three-dimensional added mass the structure, but the research efforts are very limited regarding this problem. However, a primary models on the response of SFT under single moving loads. attempt was made by [22], who investigated the effects of two- and three-dimensional added mass The numerical models described above focused on the dynamic response of SFT, including some models on the response of SFT under single moving loads. recent developments [10,23,24]. However, the global performance of the SFT under complex The numerical models described above focused on the dynamic response of SFT, including environmental conditions is not yet well understood. The determination of stable mooring cable some recent developments [10,23,24]. However, the global performance of the SFT under complex configurations for the SFT is one of the challenges for its realization [12,13]. Especially, the excessive environmental conditions is not yet well understood. The determination of stable mooring cable lateral displacement of the SFT due to waves and currents make it questionable for safe configurations for the SFT is one of the challenges for its realization [12,13]. Especially, the excessive lateral transportation. Three different cable configurations were analyzed numerically by displacement of the SFT due to waves and currents make it questionable for safe transportation. Three Mazzolani et al. [8] using the commercial software package ABAQUS/Aqua for the hydrodynamic different cable configurations were analyzed numerically by Mazzolani et al. [8] using the commercial conditions of Qiandao Lake (People’s Republic of China). Similar configurations are evaluated software package ABAQUS/Aqua for the hydrodynamic conditions of Qiandao Lake (People’s Republic further in the present study for an SFT with a cable inclination of 45°, in order to check the of China). Similar configurations are evaluated further in the present study for an SFT with a cable performance of SFT. The mooring cables with this inclination are more stable [21,25]. In addition, a inclination of 45◦ , in order to check the performance of SFT. The mooring cables with this inclination are comparison of the SFT responses for static, hydrodynamic and seismic loadings needs to be provided more stable [21,25]. In addition, a comparison of the SFT responses for static, hydrodynamic and seismic for SFT performance quantification under different conditions. loadings needs to be provided for SFT performance quantification under different conditions. More explicitly, this study evaluates the global performance of an SFT taking into account More explicitly, this study evaluates the global performance of an SFT taking into account hydrodynamic and seismic excitations. The formulation of the problem includes the modeling of hydrodynamic and seismic excitations. The formulation of the problem includes the modeling of cable element, hydrodynamics, ground motions and the SFT structure itself. A numerical model of cable element, hydrodynamics, ground motions and the SFT structure itself. A numerical model the SFT prototype to be built in Qindao Lake is used to evaluate the global performance under of the SFT prototype to be built in Qindao Lake is used to evaluate the global performance under different loadings, and some useful conclusions are drawn that can provide an initial step towards different loadings, and some useful conclusions are drawn that can provide an initial step towards the the realization of this innovative structural solution for waterway crossings. realization of this innovative structural solution for waterway crossings. Appl. Sci. 2017,of 7, wave 1122 estimates

2. Governing Equations of Motion 2. Governing Equations of Motion 2.1.Modeling ModelingofofWaves Wavesand andCurrents Currents 2.1. schematiclayout layoutofofthe thesubmerged submergedfloating floating tunnel (SFT) shown Figure The X-,Y-Y-and and AAschematic tunnel (SFT) is is shown inin Figure 1. 1. The X-, Z-axes are pointed along the axis of the tunnel, traverse and vertical to the tunnel axis, respectively. Z-axes are pointed along the axis of the tunnel, traverse and vertical to the tunnel axis, respectively. The tunnel supported vertical and inclined mooring cables. The tunnel is is supported byby vertical and inclined mooring cables. Free water surface

Z

Wave

X

Y

h1 Tunnel

Tunnel

Mooring cable

Mooring cable h

Seabed

(a)

(b)

Figure 1. Schematic layout of the submerged floating tunnel (SFT): (a) side view of the SFT and Figure 1. Schematic layout of the submerged floating tunnel (SFT): (a) side view of the SFT and (b) (b) cross-sectional the SFT. cross-sectional view view of theof SFT.

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Most of the wave theories used for the evaluation of wave forces on offshore structures are based on three parameters, i.e., water depth, wave height and wave period. The Airy wave theory, which holds for wave heights up to 10–15 m, covers a wide range and can consider significant waves of any actual sea states [13]. As the SFT is located at locations where the significant wave height is smaller than the water depth, the Airy wave theory can be used to model the sea states. According to the Airy wave theory, the first-order velocity potential Φ is given as follows [26]: gH cosh[k ( Z + h)] sin α 2ω cosh(kh)

Φ=

(1)

where α = k(Y ± ct) = kY ± ωt; k (= 2π/λ) is the wave number; ω (= 2π/T ) is the wave frequency; λ (= gT 2 /2π ) is the wavelength selected on the basis of deep-water criteria; H is the wave height; c is the wave speed; Y and Z are the vertical and transverse coordinates, respectively, having their origin at the free water surface; and h is the water depth. From the first-order velocity potential Φ, the water particle velocities in the transverse (Y) and vertical (Z) directions can be obtained as follows: .

dΦ gkH cosh[k ( Z + h)] = cos α dY 2ω cosh(kh)

(2)

.

dΦ gkH sinh[k ( Z + h)] = sin α dZ 2ω cosh(kh)

(3)

u=

v=

Differentiating the above equations with respect to time, the water particle accelerations in the transverse and vertical directions can be given as follows: ..

u= ..

gkH cosh[k( Z + h)] sin α 2 cosh(kh)

v=−

(4)

gkH sinh[k( Z + h)] cos α 2 cosh(kh)

(5)

The calculation of hydrodynamic forces on the SFT is one of the primary tasks in the design of the structure. It is also one of the most challenging tasks during numerical simulations due to the involvement of the fluid-structure interaction phenomena [27]. Morison’s equation can be used to evaluate the hydrodynamic forces on the SFT and gives reliable estimates as compared to experimental data [11,12]. The hydrodynamic forces from ocean waves and currents, acting per unit length of the SFT, are given by the modified Morison’s equation as follows [26].  n . o . . . . . 2  .. 2  .. + CM ρw πD wi − C A ρw πD qi (i = 1, 2) { f (qi , t)} = 12 CD ρw D wi ± W i − qi wi ± W i − qi 4 4 .

.

.

..

(6)

where subscript i denotes the Y or Z direction; wi is the water particle velocity (u or v); wi is the water . . . .. .. particle acceleration (u or v); W i is the velocity (U or V) of water currents acting at the centerline of the . . . . . . tunnel and is obtained by the linear equation: U = [(h − Z )/h]U c or V = [(h − Z )/h]V c ; U c and V c . .. are the velocities of surface currents in the Y and Z directions, respectively. qi and qi are the structural velocity and acceleration, respectively; ρw is the density of water; D is the external diameter of SFT; CD is the drag coefficient; C M is the inertia coefficient; and C A = C M − 1 is the added mass coefficient. In Equation (6), the first term on the right-hand side denotes the drag force; the second term denotes the inertia force; and the third term denotes the added mass effect. The drag force is much smaller than the inertia [12], so the drag force term is linearized by removing the structural velocity term for numerical simplification. Substituting Equations (2)–(5) into Equation (6), the horizontal and vertical components of hydrodynamic forces in the Y-direction and the Z-direction can be obtained as follows:

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. .  .  . FYD = 12 CD ρw D u ± U u ± U 2

..

FYI = C M ρw πD 4 u .  .  . . 1 FZD = 2 CD ρw D v ± V v ± V 2

(7)

..

FZI = C M ρw πD 4 v where the subscripts YD and YI represent the fluid drag and inertia forces in the Y-direction respectively; the subscripts ZD and ZI represent the fluid drag and inertia forces in the Z-direction, respectively. 2.2. Equations of Motion The equation of motion for the SFT moored by the mooring cables and subjected to gravity, hydrodynamic and seismic loads can be written in matrix form as follows: n .. o  .. . [ M + Ma ] q + [C ] q + [Ke + Km ]{q} = { f } + { f (q, t)} − [ M + Ma ]{ I } q g

(8)

where [ M] is the structural mass matrix of SFT; [ Ma ] is the added mass matrix, which is the mass contribution by water and is obtained from the third term on the right hand side of Equation (6). [C ] is the system damping matrix. [Ke ] and [Km ] are the elastic stiffness of the SFT and the mooring stiffness matrices, respectively. { f (q, t)} is the vector of time-dependent hydrodynamic forces. { f } is the vector n o ..

showing hydrostatic and live loads acting on the SFT. q g is the vector of ground motions acceleration.

{ I } is the influence coefficient vector, having one for elements corresponding to the degrees of freedom  ..  . in the direction of the applied ground motion and zero for the other degrees of freedom. q , q and {q} are the vectors representing structural acceleration, velocity and displacement, respectively. The vector {q} for an element is given as follows: {q} =

h

q X1

qY1

q Z1

θY1

θ Z1

q X2

qY2

q Z2

iT θY2

θ Z2

(9)

where q X , qY and q Z are the displacements along the X, Y and Z directions, respectively; while θY and θ Z are the rotations about the Y-axis and Z-axis, respectively. The subscripts 1 and 2 represent the first and second nodes of an element, respectively. The structural mass [ M] and the added mass [ Ma ] are lumped at the nodes. The added mass is applied in the traverse and vertical directions only. The elastic stiffness [Ke ] is calculated using the 3D beam element, and the nonlinear mooring stiffness [Km ] is calculated using the truss element. We used both cable elements and truss elements for modeling the mooring cables, and there was almost no difference in the response of the SFT due the fact that mooring cables always remain in tension under the input conditions of the present study. Therefore, we adopted the truss element. However, cable elements should be used in general when severe environmental conditions exist. In modeling the mooring cables, the residual buoyancy, which is the net hydrostatic force, was used as pretensions in the cable elements. The damping matrix [C ] is calculated using the Rayleigh damping model as follows:

[C ] = β 1 [ M + Ma ] + β 2 [ Ke + Km ] where:

(10)

β1 = ζ

2ωi ω j ωi + ω j

(11)

β2 = ζ

2 ωi + ω j

(12)

where β1 and β2 are the Rayleigh damping coefficients; ζ is the modal damping ratio; ωi and ω j are the ith and jth modal natural frequencies of the structure, respectively. The mass and stiffness proportional

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Appl. Sci. 2017, 7, 1122 Appl. Sci. 2017, 7, 1122 Z Z Appl. Sci. 2017, 7, 1122Z YZ X Y XX Y YZ X

Appl. Sci. 2017, 7, 1122 ZAppl. Sci. 2017, 7, 1122 Z X Y YZ

6 66ofof of1717 17 6 of 17 5 of 17 6 of 17

X

2A22mm m Z Xtwo AA A Cmodes BB B SFT, C the B modal2 m C Rayleigh damping coefficients are chosen of so that Abased on the B Yfirst C C 2Am and for the X same damping X for Y Y used damping ratio is 2.5%. The A ratios haveBbeen C the structure B cables C 2Am due to the fact that SFT is a tubular structure a pipeC[28]. A and resembles B B C The numerical procedure for the static and dynamic analysis is briefly described here. In the static analysis of SFT, the maximum wave and current 25.8 25.8 m as uniformly-distributed 25.8 m 25.8mm m forces were applied 25.8 static loads. In the dynamic analysis, the equations of motion were solved by Newmark’s time 25.8 m 25.8 direct m integration method. A computer program was 25.8 developed to perform the dynamic analysis of SFT m 25.8 m subjected to net residual buoyancy and time-dependent hydrodynamic and seismic forces. The tunnel was modeled using FEM with30 30 elements, torsional effect 30 was neglected it 2020 20 30 and m the 2020 mm 30 m 20 m 20 m because 20 30 m m 20mm m 30m3D-beam m 20 m 30mm m 30 m 30 was very small. 20 m 20 m 30 m 20 m 30 m 30 m 20 m

3. Numerical Example

20 m

30 m

(a) (a) (a) (a)

(a)

20 m

30 m

(a)

30 m

(a)

20 m

(a)

20 m

2

2

2

30 m 30 m 30 m

(a)

The performance evaluation of SFT needs to be carried out using a realistic model. Therefore, the prototype of the proposed SFT model, as shown in Figure 2 [8,9], which is planned to be built in Qiandao Lake, China, is evaluated in this 1 11 1 2 2study. The factored 1 2load combinations 2 used by [8] were used 2 3 33 3 for both static and hydrodynamic analyses in the present study. 1 1 2 2 3 Locations A, B and C Figure 2a shows the side view of the SFT model;1the SFT is supported at 1 2 2 by mooring cables. Figure 2b shows three different types of mooring cables arrangements. Figure 2c 3 (b) (b) (b) (b) (b) shows the material cross-section of the SFT. Three different SFT cases are analyzed based on three (b) (b)(t=0.1 m) Aluminum Aluminum (t=0.1Aluminum m) Aluminum (t=0.1m) m) different mooring cable arrangements defined in Table 1,(t=0.1 where the circled numbers represent the cable (b)(t=0.1 Aluminum m) tunnel, hydrodynamic Aluminum (t=0.1 m) arrangement shown in Figure 2b. The input parameters for SFT and(b) mooring

3 3 3

• •

3.553.55 m 3.55 m m

4.394.39 m 4.39 m m

3.55 m

4.39 m

3.553.55 m 3.55 m m 3.55 3.55 m m

•

4.394.39 m 4.39 m m 4.39 4.39 m m

cables are given in Table 2; the hydrodynamic parameters arem) those measured at Qindao Lake(t=0.1 [8]. m) Aluminum (t=0.1 Aluminum The assumptions made in this study and criteria are given as follows:

The cross-section of the SFT is hollow circular, consisting of an external aluminum layer followed by a sandwiched concrete layer and internal steel layer. The material’s thicknesses and tunnel diameters are shown in Figure 2c. A uniformly-distributed load of 125 kN/m, per unit length, was used for the tunnel. The Archimedes buoyancy was 160 kN/m (ρw gATunnel = 1050 × 10 × π × 4.42/4 = 160 kN/m), and the net residual buoyancy was 35 kN/m (160 − 125 = 35 kN/m). Concrete (t(t= =0.3 Concrete (t = 0.3 Concrete (t = 0.3 Concrete 0.3 Steel (t(t=kN/m Steel (t =to0.02 m)Steel = 0.02 m) A uniformly-distributed live load of 10 was be acting on(tthe tunnel; Steel =0.02 0.02m) m) assumed m) m) m) (t = 0.3 Concretem) (t = 0.3 Concrete Steel = 0.02point m) (seabed) and tunnelSteel = 0.02 m) The mooring cable connections at the (tanchor were(ttreated as pins; and m) (t = 0.3 (c) m) (t = 0.3 (c)(c) (c) Concrete (c)Concrete The tunnel displacements were restrained at one while the axial displacement was Steel (t = 0.02 m)end, Steel (t = 0.02 m)left free at m) m) (c) (c) the other end. The flexural rotations were allowed at both ends of the tunnel. Figure 2.2. layout Figure ofof Schematic submerged Figure layout floating 2. of Schematic the tunnel submerged layout (SFT): (a) of floating the side submerged view tunnel (SFT): the floating SFT (a) and side tunnel view (SFT): of the (a)SFT sidea Figure 2.Schematic Schematic layout of2.the the submerged floating tunnel (SFT): (a) side viewofof of the SFT and Figure Schematic layout the submerged floating tunnel (SFT): (a) side view the SFT and (c) (c) (b) cables (b) mooring cables (c)(c) (b) arrangements; mooring cables andarrangements; (c) ofmaterial cross-section and (c) material the cross-section SFT. of the SFT. (b)mooring mooring cablesarrangements; arrangements; and (c)material material cross-section ofthe theSFT. SFT. Figure 2. Schematic layout of theand submerged Figure floating 2.cross-section Schematic tunnel layout (SFT): (a) ofSFT. the side submerged view of of the floating SFT and tunnel (SFT): (a) side (b) mooring cables arrangements; and material cross-section of the

(b) mooring cables arrangements; (c) material (b) mooring cables arrangements; of the and (c) material cross-section of the SFT. Table 1. Three configurations used to support theSFT. Figure 2. Schematic layout of cable theand submerged Figure floating 2.cross-section Schematic tunnel layout (SFT): (a) ofSFT. the side submerged view of the floating SFT and tunnel (SFT): (a) side Table 1.1. Three cable configurations Table 1. Three used cable to Table support configurations 1. Three the SFT. cable used configurations to support theused SFT.to support the SFT Table 1. Three cable configurations used to support the SFT. Table Three cable configurations used to support the SFT. (b) mooring cables arrangements; and (c) material (b) mooring cross-section cables arrangements; of the SFT. and (c) material cross-section of the SFT. Table 1. Three cable configurations usedSection to Table support the SFT. cable configurations used to support the SFT Mooring configuration Section A B1. Three Section C

Mooring MooringSection configuration AA configuration Section Section Section Section Section A B CC Section Section B C Mooringconfiguration configuration SectionMooring SectionBA B Section Table 1. Three cable configurations used to Table support 1. Three the SFT. cable configurations used to support the SFT 1 11 1Mooring 1Section 1A1 11 C 1 Configuration 1 1(C1) Configuration 11 111(C1) Configuration 1 (C1) Mooring configuration Section A(C1) configuration Section B Section Section B1 Configuration (C1)Configuration 2 11 11 Configuration 21 2(C2) Configuration 2 11 11 2Mooring 11Section 12 (C1) 112 122(C2) (C1) Configuration 2 (C2) Mooring configuration Section A(C2) configuration Section B Section A C Section B1 Configuration (C2)Configuration 1 3 1 1 3 1 3 1 (C3) (C3) Configuration (C3)Configuration Configuration 213 3(C2) Configuration 2 11 11 3 (C3) 11 11 11 12 (C1) 1312 33(C2) (C1) Configuration 3 (C3)

11 11 11 32 Configuration 23 (C2) (C3) Configuration 2332 (C2) (C3) Table 2. Parameters of the Table SFT 2. tunnel, Parameters mooring Table of the cables 2. SFT Parameters tunnel, and hydrodynamics. mooring of the SFT cables tunnel, and mooring hydrodynamics. cables and hydrod Table 2. 2. Parameters of of the the 1SFT SFT tunnel, tunnel, mooring cables cables and hydrodynamics. hydrodynamics. 1 1 3 Table Parameters mooring Configuration 3 (C3) Configuration 33 (C3)and

Table 2. Parameters of the SFT tunnel, mooring Table cables 2. Parameters and hydrodynamics. of the SFT tunnel, mooring cables and hydrod

Element Element Parameter Element Parameter Unit Value ValueUn Element Parameter Unit Parameter Value Unit Table 2. Parameters of the SFT tunnel, mooring Table cables 2. Parameters and hydrodynamics. of the SFT tunnel, mooring cables and hydrod 3 3 equivalent 3 2451 2451 kg Tunnel equivalent density Tunnel equivalent kg/m Tunnel density density kg/m Element Parameter Element Unit Parameter Value Un 3 2451 Tunnel equivalent density kg/m 23Elastic 1010 2 10N/ 2 Elastic modulus Elastic modulus N/m 3 × modulus 10 N/m 3 × 10 2451 TunnelElastic equivalent density kg/m Tunnel equivalent kg Element Parameter Element Unit Value Un modulus N/m2 Parameter 3 × 1010 density Tunnel Tunnel Tunnel

Tunnel Mooring Mooringcables cables Mooring cables Mooring cables

2 2 Area Area kg/m mm m2 Tunnel Tunnel 5.1 23Elastic Area 5.110 density Elastic modulus N/m 3Area ×modulus 10 2451 Tunnel equivalent density Tunnel equivalent 24 Moment Moment ofof inertia mm of m4 12.3 10 442Elastic Area Tunnel 5.1 Elastic modulus N/m 3Area ×modulus 10inertia Moment inertia Moment of inertia 12.3 4 Length of tunnel mm Length 100 of tunnel 2 Moment Moment of inertia of inertia m 12.3 Area m Area 5.1 Length ofTunnel tunnel Length of tunnel 100 2Elastic 1111 N/m2 2 1.4 × 10 Mooring cables Elastic Mooring modulus cables Elastic modulus N/m modulus 4 2 Length of tunnel m Length 100 of tunnel Moment inertia m Moment of× inertia 12.3 1.4 1011 Elastic of modulus N/m

ElasticMooring modulus cables Length of tunnel ElasticMooring modulus cables

11 1.4100 × 10 N/m Elastic modulus m 2Length of tunnel 1.4modulus × 1011 N/m2Elastic

m 5.1 kg N/ m 12.3 N/ 100 m m 1.4 × 1011 N/ m m

N/m N/

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Z Y

X A

B

2m

C

25.8 m

20 m

30 m

20 m

30 m

(a)

1

2 3

(b)

3.55 m

4.39 m

Aluminum (t=0.1 m)

Steel (t = 0.02 m)

Concrete (t = 0.3 m)

(c) Figure 2. Schematic layout of the submerged floating tunnel (SFT): (a) side view of the SFT and Figure 2. Schematic layout of the submerged floating tunnel (SFT): (a) side view of the SFT and (b) (b) mooring cables arrangements; and (c) material cross-section of the SFT. mooring cables arrangements; and (c) material cross-section of the SFT. Table 1. Three cable configurations used to support the SFT. Table 2. Parameters of the SFT tunnel, mooring cables and hydrodynamics.

Mooring configuration Element Configuration 1 (C1) Configuration 2 (C2) Configuration 3 (C3)

Section A

Section B

Parameter 1

1

Section C Unit

1 Value

kg/m3

Tunnel equivalent density 1 2 1 2451 10 Elastic N/m2 1 modulus 3 1 3 × 10 Area 5.1 Tunnel m2 Moment of inertia 12.3 m4 Table 2. Parameters of the SFT tunnel, mooring cables and hydrodynamics. Length of tunnel m 100

Element Mooring cables

Tunnel

Mooring cables

ElasticParameter modulus Diameter of cable density Tunnel equivalent Moment of inertia Elastic modulus Cable density

Area Moment of inertia Length of tunnel Elastic modulus

2 N/mUnit m kg/m3 m4 N/m2 kg/m3

m2 m4 m N/m2

1.4 × 1011 Value 0.06 2451 −7 6 × 10 3 × 7850 1010

5.1 12.3 100 1.4 × 1011

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Element

Diameter of cable Moment of inertia Table 2. Cont. Cable density Wave height (H) Parameter Time period (T)

Wave height (H)

m m4 kg/m3 Unit m s

m s m/s . m/s m Surface Depth currentof velocity water(U (h)c ) Depth of water (h) m Distance of SFT from free surface (h1) m Distance of SFT from free surface (h1 ) m 3 w) kg/m Density of water (ρ 3 Density of water (ρw ) kg/m Drag coefficient Drag coefficient (CD )(CD) – -Inertia coefficient (CM )(CM) – -Inertia coefficient

Surface velocity ( U c ) Timecurrent period (T)

Hydrodynamics

Hydrodynamics

0.06 6 × 10−7 7850 1 Value 2.3 1

0.12.3 300.1 2 30 2 1050 1050 11 22

4. 4. Results Results Hydrodynamic Response 4.1. Hydrodynamic comparativestudy studyof ofthe theSFT SFTresponse responseusing usingthe thethree threedifferent differentcable cable configurations defined A comparative configurations defined in in Table presented. configuration that proves themost mostpromising promisingisis then then used used for Table 1 is1 is presented. TheThe configuration that proves totobebethe further investigations. The wave and current forces are obtained using the hydrodynamic conditions of Qiandao Lake (Table 2). acting on the using Morison’s equation.equation. During the numerical (Table 2).These Theseforces forces acting on SFT the are SFTcalculated are calculated using Morison’s During the simulations, the drag forces were considered distributed loadings and were converted numerical simulations, the and draginertia forcesforces and inertia forces were considered distributed loadings and to equivalent nodal forces using theforces work-equivalence method [29]. The time history oftime thesehistory forces were converted to equivalent nodal using the work-equivalence method [29]. The perthese unit forces lengthper of SFT shown Figure 3. The andtransverse vertical inertia forces are dominant of unitislength ofin SFT is shown intransverse Figure 3. The and vertical inertia forces hydrodynamic forces, while the dragwhile forcesthe aredrag veryforces small.are very small. are dominant hydrodynamic forces,

Figure Figure 3. 3. Hydrodynamic Hydrodynamic force force time time history history per per unit unit length length of of the the SFT. SFT.

4.1.1. of the the Numerical Numerical Model Model 4.1.1. Verification Verification of In the presented presented formulations formulations and In order order to to verify verify the and the the numerical numerical procedure, procedure, the the static static and and dynamic are compared compared with with finite finite element element results results from from ABAQUS/Aqua, ABAQUS/Aqua, dynamic responses responses of of the the SFT SFT are Mazzolani as follows: follows: Mazzolani et et al. al. [8]. [8]. For For comparison comparison purposes, purposes, the the absolute absolute displacement displacement is is defined defined as (13) DABS  qqY 2  qZ 2 (13) D ABS = qY 2 + q Z 2 where DABS is the absolute displacement. The same definition is valid for both static and dynamic where D ABS is In thethe absolute displacement. Themaximum same definition is valid for both static and used dynamic Y and Z displacements were for displacement. dynamic analysis, the displacement. the dynamic analysis, the maximum Y and Z displacements were used for calculating calculating theIn absolute displacements. the absolute displacements. Both static and dynamic absolute displacements based on the same input properties and cable Both static and dynamicwith absolute displacements onand the dynamic same input properties and cable configurations are compared [8]. The comparisonsbased of static absolute displacements configurations are compared with [8]. The comparisons of static and dynamic absolute displacements using mooring configurations C2 and C3 are shown in Figure 4a,b, respectively. The close agreement using configurations C2 of and are shown in Figure 4a,b, respectively. The close agreement of the mooring results shows the accuracy theC3presented model. of the results shows the accuracy of the presented model.

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DABS (m) DABS (m)

8 of 17 17 8 of 8 of 17

(a) (a)

(b) (b)

Figure 4. Comparison of absolute displacements with ABAQUS/Aqua [8]: (a) absolute static Figure Comparison of absolute absolute displacements with ABAQUS/Aqua ABAQUS/Aqua [8]: [8]: (a) (a) absolute absolute static static displacement and (b) absolute dynamic displacement. Figure 4.4. Comparison of displacements with displacementand and(b) (b)absolute absolutedynamic dynamicdisplacement. displacement. displacement

4.1.2. Static Response 4.1.2. Static Response 4.1.2. Static Response hydrodynamic forces in the transverse and vertical directions calculated from The maximum The maximum hydrodynamic forces in the transverse and vertical directions calculated from Equation (6) or (7) hydrodynamic were applied asforces equivalent nodal forces in the static analysis. The intensities The maximum in thestatic transverse and vertical directions calculated from Equation (6) or (7) were applied as equivalent static nodal forces in the static analysis. The intensities of these(6) forces the applied transverse (Y) and vertical (Z) directions 4.875 kN/m and kN/m, Equation or (7)inwere as equivalent static nodal forces in were the static analysis. The 4.858 intensities ofrespectively. these forcesThe in the transverse (of Y)the and vertical (Z) for directions were 4.875 kN/m and 4.858 kN/m, static analysis SFT is useful assessing the performance of the SFT for the of these forces in the transverse (Y) and vertical (Z) directions were 4.875 kN/m and 4.858 kN/m, respectively. The static analysis of the SFT is useful for assessing the performance of the SFT for the preliminaryThe design. respectively. static analysis of the SFT is useful for assessing the performance of the SFT for the preliminary design. Static displacements and internal forces envelope curves of the SFT are shown in Figure 5. The preliminary design. Static displacements and internal forces envelope curves of the(SFT shown in Figure(M 5.Z)The ), are bending moments and transverse response of the SFT, i.e., rotations ( Z ), displacements qY SFT Static displacements and internal forces envelope curves of the are shown in Figure 5. transverse response of the SFT, i.e., rotations ( Z ), displacements ( qY ), bending moments (MZ) and The transverse response of the when SFT, i.e., ), displacements (q ), bending moments (M Y) decreased therotations mooring(θcable configuration was changed from C1 to C3. shear forces (SF Z Z) Y Y ) decreased when the mooring cable configuration was changed from C1 to C3. shear forces (SF and shear forces (SFY ) decreased the rotations mooring cable configuration was C1 to C3. ( qZ ),changed bendingfrom moments (MY) However, the vertical response,when i.e., the ( Y ), displacements displacements (q ( qZZ),),bending bendingmoments moments(M (MYY)) However, the the vertical vertical response, response, i.e., i.e., the the rotations rotations (θ ( YY),),displacements However, and shear forces (SFZ), have different trends, where the response for configuration C2 is the greatest, and shear (SF where for C2 is different trends, where the the response for configuration configuration C2 Comparisons is the the greatest, greatest,of and shearforces forces (SFZZ), have different followed by configuration C3, and trends, configuration C1 response has the minimum response. followed by configuration C3, and configuration C1 has the minimum response. Comparisons of static followed by configuration C3, and configuration C1 has the minimum response. Comparisons ofB static displacements and internal forces of the SFT for three mooring configurations at Sections A, displacements and internal forces of the SFT for three mooring configurations at Sections A, B and C static displacements and internal forces of the SFT for three mooring configurations at Sections A, B and C (Figure 2a) are summarized in Table 3 to clearly show the trends described above. (Figure 2a) are summarized in Table to clearly the trends above. and C The (Figure 2a) are in3 Table 3 to show clearly show thedescribed trends described above. shape of summarized bending moment gives direct insight into the cable configurations and The shape of bending moment gives direct insight into the cable configurations and performances The shape of bending moment gives direct insight into the cable configurations and performances of mooring systems and reflects the uniqueness of the adopted mooring cable of mooring systems and the thethe adopted mooring cable can be performances of as mooring systems and reflects uniqueness thebeconfigurations, adopted mooring cable configurations, canreflects be seen inuniqueness Figure 5c. of From these results, itofcan concluded thatasthe static seen in Figureprovides 5c.asFrom these results, it can be the static response providesmooring an important configurations, can an be seen in Figure 5c.concluded From these results, it can be regarding concluded that the static response important benchmark for that decision-making cable benchmark for decision-making regarding mooring cable arrangements and configuration selection for response provides an important benchmark for decision-making regarding mooring arrangements and configuration selection for the preliminary design of SFT. However, thecable static the preliminary design of SFT. However, the static response is very small and could not be used for the arrangements andsmall configuration for for thethe preliminary designofofSFT, SFT. the static response is very and couldselection not be used practical design as However, shown in Figure 4, as practical design of SFT, as shown in Figure 4, as will be demonstrated further in the following sections. response is very small and could not be used for the practical design of SFT, as shown in Figure 4, as will be demonstrated further in the following sections. will be demonstrated further in the following sections.

(a) (a)

(b) (b) Figure 5. Cont.

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(c)

(d)

Figure Comparisonofof static displacementand andinternal internalforce forceenvelope envelopecurves curvesofofthe theSFT SFTfor for three Figure 5. 5. Comparison static displacement three mooring configurations: (a) vertical and transverse rotation; (b) vertical and transverse displacement; mooring configurations: (a) vertical and transverse rotation; (b) vertical and transverse displacement; vertical and transverse bending moment; and vertical and transverse shear force. (c)(c) vertical and transverse bending moment; and (d)(d) vertical and transverse shear force. Table Comparisonofofstatic staticdisplacements displacementsand andinternal internalforces forcesofofthe theSFT SFTfor forthree threemooring mooring Table 3. 3.Comparison configurations Sections B and configurations atat Sections A,A, B and C.C. C1 C1

θY (×10−3 rad)

−0.441

A C2

A C2

−0.585

B C3 C3

−0.512

C

B C2 C2

C1 C1

0.022

0.027

C3

C1

C3

0.024

C1

−0.441 −0.585 −0.512 0.022 0.027 0.024 θY (×10−3 rad) −3 rad) −13 −3 rad) 14 −14 −2.2 −13 10−13 −4.9−4.9 −2.2 0.312 0.312 0.1960.196 0.1340.134 −4 ×−4 θZ θ (×Z10(×10 10×−13 × 10×−10 × ×1010 1.395 0.918 0.663 1.716 1.114 0.791 qY (×10−2 m) q (×10−2 m) 2.264 1.395 2.7660.918 2.5110.663 2.6841.716 1.114 0.791 3.360 3.016 q Z (×Y10−2 m) 3 kN-m) 10.230 11.382 10.796 10.368 17.044 13.648 MY (× 10 −2 q (×10 m) 2.264 2.766 2.511 2.684 3.360 3.016 7.640 5.263 3.978 9.095 5.128 2.982 MZ (×Z103 kN-m) 2 kN) −12 3 1.459 0.659 0.231 − 0.800 − 1.228 SF ( × 10 − 6.2 × 10 MY Y (×10 kN-m) 10.230 11.382 10.796 10.368 17.044 13.648 −5.028 −4.645 −4.840 −5.552 −2.799 −4.200 SFZ (×102 kN)

M Z (×103 kN-m)

7.640

5.263

3.978

9.095

5.128

2.982

0.452

0.452 −0.312 −0.312 1.395 1.395 2.198 8.500 2.198 7.638 −1.459 8.500 −6.555

7.638

CC2 C2

0.599

C3 C3

0.524

0.599 0.524 −0.196 −0.134 −0.134 −0.196 0.918 0.663 0.918 2.437 0.663 2.685 9.269 8.878 2.685 2.437 5.262 3.977 −0.659 − 0.230 9.269 8.878 −9.500 −8.002

5.262

3.977

(×10 kN) 1.459 0.659 0.231 −6.2 × 10−12 −0.800 −1.228 −1.459 −0.659 −0.230 4.1.3.SF Dynamic Response Y 2 SFZ (×10 kN) −5.028 −4.645 −4.840 −5.552 −2.799 −4.200 −6.555 −9.500 −8.002 The modal analysis was performed, and the natural frequencies of the first 20 natural modes are listed in Table 4. The comparison of the natural frequencies of the SFT supported by different mooring 4.1.3.configurations Dynamic Response cable gives a direct measure of the cable system stiffness. The natural frequencies of the SFT increase the was cable configuration changed C1 to C3. Configuration C3 provides The modalwhen analysis performed, and is the natural from frequencies of the first 20 natural modes are more stiffness to the SFT than configurations C1 and C2, and similarly, configuration C2 provides listed in Table 4. The comparison of the natural frequencies of the SFT supported by different mooring more configuration C1. aHowever, the natural frequencies of the SFT forThe the natural three mooring cableof cablethan configurations gives direct measure of the cable system stiffness. frequencies configurations are when very close to each other for higher modes.from C1 to C3. Configuration C3 provides the SFT increase the cable configuration is changed 2

more stiffness to the SFT than configurations C1 and C2, and similarly, configuration C2 provides Table 4. Modal analysis of the SFT and comparison of the first 20 natural frequencies (Hz) for each more than configuration C1. However, the natural frequencies of the SFT for the three mooring cable cable configuration. configurations are very close to each other for higher modes. Mode C1 C2 C3 Mode Table 4. Modal analysis of the SFT and comparison of the 1 configuration. 0.5660 0.6997 0.824 11 cable 2 1.2825 1.1542 1.2144 12 Mode C1 C2 C3 Mode 3 2.2606 2.2606 2.2606 13 0.5660 0.6997 0.824 11 41 2.5041 2.5041 2.5041 14 1.2825 1.1542 1.2144 12 52 5.0739 5.0907 5.1103 15 2.2606 2.2606 2.2606 13 63 5.1324 5.1025 5.1160 16 2.5041 2.5041 2.5041 14 74 8.7454 8.7454 8.7454 17 5.0739 5.0907 5.1103 15 85 8.9895 8.9895 8.9895 18 5.1324 5.1025 5.1160 16 96 9.0143 9.0143 9.0143 19 8.7454 8.7454 8.7454 17 10 7 13.985 13.991 13.998 20 8 9 10

8.9895 9.0143 13.985

8.9895 9.0143 13.991

8.9895 9.0143 13.998

18 19 20

C1 C2 first 20 natural frequencies 14.0467 14.0359 20.0309 20.0309 C1 C2 20.0417 20.0417 14.0467 14.0359 26.2123 26.2123 20.0309 20.0309 27.0944 27.0975 20.0417 20.0417 27.1051 27.0996 26.2123 26.2123 35.1364 35.1364 27.0944 27.0975 35.1522 35.1522 27.1051 27.0996 43.6074 43.6074 35.1364 35.1364 44.1137 44.1155 35.1522 43.6074 44.1137

35.1522 43.6074 44.1155

C3 (Hz) for each 14.0408 20.0309 C3 20.0417 14.0408 26.2123 20.0309 27.1010 20.0417 27.1021 26.2123 35.1364 27.1010 35.1522 27.1021 43.6074 35.1364 44.1176 35.1522 43.6074 44.1176

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Y displacement (x10 -2 m)

Figure Figure66represents representsthe thecomparison comparisonofofthe thehydrodynamic hydrodynamicresponse responseofofthe theSFT SFTatatSection SectionA, A,using using three mooring cable configurations. Figure 6a shows the comparison of the SFT displacements three mooring cable configurations. Figure 6a shows the comparison of the SFT displacementsininthe the transverse direction: configuration C1 has the largest displacement, followed by configuration C2, transverse direction: configuration C1 has the largest displacement, followed by configuration C2, and andconfiguration configurationC3 C3has hasthe theminimum minimumdisplacement. displacement.The Themaximum maximumdisplacements displacementsof ofthe theSFT SFTfor for configuration C1, C2 and C3 are 0.046 m, 0.021 m and 0.011 m, respectively. The same trend occurs configuration C1, C2 and C3 are 0.046 m, 0.021 m and 0.011 m, respectively. The same trend occurs for as shown shownin inFigure Figure6b. 6b.The Themaximum maximumbending bendingmoments moments forthe thetransverse transverse bending bending moment moment (M (Mzz),), as of of SFT for configurations C1, C2 and C3 are 25,066.628 kN-m, 11,943.442 kN-m and 6838.661 SFT for configurations C1, C2 and C3 are 25,066.628 kN-m, 11,943.442 kN-m and 6838.661 kN-m, kN-m, respectively. respectively. Figure Figure 6c 6c shows shows the the comparison comparison of of the the SFT SFT displacement displacement in in the the vertical vertical direction; direction; configuration C2 has the largest displacement, followed by configuration C3, and configuration C1 has configuration C2 has the largest displacement, followed by configuration C3, and configuration C1 the minimum displacement. The maximum displacements of SFT for configurations C1, C2 and C3 and are has the minimum displacement. The maximum displacements of SFT for configurations C1, C2 0.029 m,0.029 0.035m, m and m, 0.032 respectively. The sameThe trend occurs foroccurs the vertical bending C3 are 0.0350.032 m and m, respectively. same trend for the verticalmoment bending (M ), as shown in Figure 6d. The maximum bending moments of SFT for configurations C1, C2 and Y moment (MY), as shown in Figure 6d. The maximum bending moments of SFT for configurations C1, C3 are 12,202.859 kN-m, 13,694.792 kN-m and 12,934.200 kN-m, respectively. C2 and C3 are 12,202.859 kN-m, 13,694.792 kN-m and 12,934.200 kN-m, respectively.

5 4 3 2 1 0 -1 -2 -3 -4 -5

C1

C2

3

C3

C1

C2

C3

2 1 0 -1

0

5

10

-2

C3

C1 C2

15 20 Time (s) (a)

25

30

0

5

10

3 Z displacement (x10-2 m)

C2

C1

-3

C1

MY (x104 kN-m)

2

C3

15 20 Time (s) (b)

25

C2

30

C3

C2

C3

1 C1

0 -1 -2 -3

(c)

0

5

10

15 20 Time (s) (d)

25

30

Figure6.6. Comparison Comparison of of the the hydrodynamic hydrodynamic response response of of the the SFT SFT at atSection SectionA: A:(a) (a)Y-displacement; Y-displacement; Figure Z; (c) Z-displacement; and (d) bending moment MY. (b) bending moment M (b) bending moment MZ ; (c) Z-displacement; and (d) bending moment MY .

Figure 7 represents the comparison of the hydrodynamic response of SFT at Section B. Figure 7 Figure 7 represents the comparison of the hydrodynamic response of SFT at Section B. Figure 7 shows the same trend as described to that of Section A. However, the general response at Section B shows the same trend as described to that of Section A. However, the general response at Section B is larger than that of Section A. In addition, the response shown by configuration C3 here is further is larger than that of Section A. In addition, the response shown by configuration C3 here is further reduced as compared to Section A, because Section B is supported by double inclined mooring cables. reduced as compared to Section A, because Section B is supported by double inclined mooring cables.

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4

C1

C2

C3

MZ (x104 kN-m)

3 2 1 0 -1 -2 -3 -4

C2

C1

0

5

10

(a)

15 20 Time (s) (b)

(c)

(d)

C3

25

30

Figure Figure7.7. Comparison Comparisonofofthe thehydrodynamic hydrodynamicresponse responseofofthe theSFT SFTatatSection SectionB:B:(a) (a)Y-displacement; Y-displacement; Z; (c) Z-displacement; and (d) bending moment MY. (b) bending moment M (b) bending moment MZ ; (c) Z-displacement; and (d) bending moment MY .

Both Figures 6 and 7 show that the transient motions of the SFT are small and decay quickly Both Figures 6 and 7 show that the transient motions of the SFT are small and decay quickly with with time, and the steady-state motions are more pronounced, especially in the traverse direction, as time, and the steady-state motions are more pronounced, especially in the traverse direction, as is is clear from the Y-displacement and bending moment MZ. In the vertical direction, the SFT vibrated clear from the Y-displacement and bending moment M . In the vertical direction, the SFT vibrated under the effect of inertial force and buoyancy force likeZ a beam on elastic supports, as shown by under the effect of inertial force and buoyancy force like a beam on elastic supports, as shown by the the Z-displacement and bending moment MY in Figures 6c,d and 7c,d, respectively. The SFT moored Z-displacement and bending moment MY in Figure 6c,d and Figure 7c,d, respectively. The SFT moored by tension leg mooring cables (C1) showed high peaks in the displacements and bending moments. by tension leg mooring cables (C1) showed high peaks in the displacements and bending moments. The SFT moored by a tension leg and a single inclined mooring cable at the center (C2) provided The SFT moored by a tension leg and a single inclined mooring cable at the center (C2) provided better better stiffness in the transverse direction, but lesser stiffness in the vertical direction. The SFT moored stiffness in the transverse direction, but lesser stiffness in the vertical direction. The SFT moored by by double inclined mooring cables at the center (C3) showed the minimum response in the transverse double inclined mooring cables at the center (C3) showed the minimum response in the transverse direction. The response of SFT moored by the C1 and C2 configurations showed large peaks, due to direction. The response of SFT moored by the C1 and C2 configurations showed large peaks, due to very small restraining in the transverse direction. Therefore, C3 type configurations should be used very small restraining in the transverse direction. Therefore, C3 type configurations should be used at at one or more locations at least, depending on the overall length of the SFT. It can be concluded that one or more locations at least, depending on the overall length of the SFT. It can be concluded that the the C3 type cable configuration is more stable. C3 type cable configuration is more stable. The SFT moored by mooring cable configuration C3 is used for the analysis hereafter. The SFT moored by mooring cable configuration C3 is used for the analysis hereafter. Three-dimensional visualization of the SFT response in both time and space gives a very clear Three-dimensional visualization of the SFT response in both time and space gives a very clear understating of the structural behavior of the SFT subjected to hydrodynamic waves and currents. understating of the structural behavior thedisplacements SFT subjectedand to hydrodynamic wavesare and currents. The three-dimensional time histories ofofthe bending moments shown in The three-dimensional time histories of the displacements and bending moments are shown in Figures 8 and 9. The response of the SFT is plotted along the Z-axis; the tunnel longitudinal Figures 8 and The response of the is plotted along the Z-axis; thethe tunnel longitudinal coordinates coordinates (x)9.are plotted along the SFT X-axis; and time is plotted along Y-axis. (x) are plotted along the X-axis; and time is plotted along the Y-axis. Figure 8 show the displacements along the length of the tunnel with time. Figure 8a illustrates Figure 8 show the displacements along the length ofin the with time. Figureextremities. 8a illustrates Y-direction both thetunnel positive and negative that the SFT vibrates harmonically in the that the SFT vibrates harmonically in the Y-direction both in the positive and negative extremities.

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(a) (a)

(b) Figure 8. Hydrodynamic displacements along the length of the SFT with time: (a) Y-displacement and

Figure 8. Hydrodynamic displacements along the(b length of the SFT with time: (a) Y-displacement and ) (b) Z-displacement. (b) Z-displacement. Figure 8. Hydrodynamic displacements along the length of the SFT with time: (a) Y-displacement and Figure 8b also shows a harmonic motion pattern, but only in the positive limit (this upward (b) Z-displacement.

Figure also shows harmonic only limit (this upward positive8b displacement is a caused by themotion residual pattern, buoyancybut acting onin thethe SFTpositive in this direction); which means that the were ainharmonic taut conditions and did notbut permit in this direction. Figure 8b cables also isshows motion pattern, only slackness in (this upward positive displacement caused by the residual buoyancy acting onthe thepositive SFT inlimit this direction); which Figure 9a shows the bending moment Mand Y distribution alongon the length ofinthis the tunnel withwhich time. positive displacement is in caused the residual buoyancy the SFT in direction); means that the cables were taut by conditions did not acting permit slackness this direction. The shape of bending moments gives a clear the mooring cables configuration (C3) with used. time. means that the cables in taut conditions and didof not permit slackness in this Figure 9a shows thewere bending moment MYpicture distribution along the length ofdirection. the tunnel The inclined mooring cables at themoment central location provided flexible elastic of bilateral restraint to the Figure 9a shows the bending M Y distribution along the length the tunnel with time. The shape of bending moments gives a clear picture of the mooring cables configuration (C3) used. transverse almost moments unilateral gives restraint to the vertical motion. The shape and of bending a clear picture of the mooring cables configuration (C3) used. The inclined mooring cables at the central location provided flexible elastic bilateral restraint to the Figure 9bmooring shows the bending MZ distribution along the length of the tunnel withto time, The inclined cables at themoment central location provided flexible elastic bilateral restraint the transverse and and almost unilateral restraint totothe vertical motion. and it is similar to the one relatedrestraint to a uniform beam vibrating in the first natural mode. It can be seen transverse almost unilateral the vertical motion. Figure 9binclined shows the bending moment M along length of the tunnel that Figure only cables, located at the center, provided along significant restraining in the transverse 9b shows the bending moment MZZ distribution distribution thethe length of the tunnel with with time, time, and itand is similar to the one related to a uniform beam vibrating in the first natural mode. It can be direction (i.e., M othertotwo groupsbeam of vertical cables andmode. right It ofcan thebe center it is similar toZ), theand onethe related a uniform vibrating in thefrom first left natural seen seen that onlyalmost inclined cables, located thecenter, center, provided significant restraining in transverse the transverse provided nocables, restraining in the transverse direction. that only inclined located atatthe provided significant restraining in the direction (i.e., M Z ), and the other two groups of vertical cables from left and right of the center direction (i.e., M ), and the other two groups of vertical cables from left and right of the center provided Z provided almost no restraining in the transverse direction. almost no restraining in the transverse direction.

(a) (a) Figure 9. Cont.

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(b)

(b) Figure 9. Hydrodynamic bending moments along the length of the SFT with time: (a) bending Figure 9. Hydrodynamic bending moments along the length of the SFT with time: (a) bending Figure 9. M Hydrodynamic bending moments along the length of the SFT with time: (a) bending moment moment Y and (b) bending moment moment MY and (b) bending momentM MZZ.. MY and (b) bending moment MZ .

4.2. Seismic Response 4.2. Seismic Response 4.2. Seismic Response As stated before, SFT massivetubular tubular structure, itsits structural response dramatically As stated before, thethe SFT is isa amassive structure,and and structural response dramatically As stated before, the SFT is a massive tubular structure, and its structural response dramatically increases external forcing.To Tocheck check the the maximum maximum orordominant structural response of SFT, increases withwith external forcing. dominant structural response of aSFT, a comparison of static, hydrodynamic andseismic seismic response toto bebe provided [16,23]. The El-Centro increases with external forcing. To and check the maximum or dominant structural response of SFT, comparison of static, hydrodynamic responseneeds needs provided [16,23]. The El-Centro (1940) ground motions are assumedand for the SFT numerical example tobe evaluate the [16,23]. dynamicThe behavior a(1940) comparison of static, hydrodynamic seismic response needs to provided El-Centro ground motions are assumed for the SFT numerical example to evaluate the dynamic behavior of the SFTmotions for the three-dimensional ground motion input.example Three components of the El-Centro ground (1940) are assumed forground the SFTmotion numerical to evaluate of the ground SFT for the three-dimensional input. Three components of dynamic El-Centrobehavior ground motions used as input motions are shown in Figure 10. The effective seismic forces using these of the SFT for the three-dimensional ground motion input. Three components of El-Centro ground motions usedmotions as input shown in Figure The points effective forces using these ground aremotions applied are simultaneously at the10. nodal in seismic the three-dimensional motions used as input motions aresimultaneously shown in Figureat 10. the The nodal effectivepoints seismicinforces using these ground ground motions are applied the three-dimensional numerical model. motions aremodel. applied simultaneously at the nodal points in the three-dimensional numerical model. numerical

(a)

(b)

(a)

(b)

(c) Figure 10. Ground motion input (El-Centro 1940 site Imperial Valley irrigation district): (a) S00E component; (b) S90W component; and (c) vertical component.

(c)

For the evaluation of the ground motion’s effects on the structural behavior of the SFT, two cases Figure 10. 10. Ground Ground motion motion input input (El-Centro (El-Centro 1940 1940 site site Imperial Imperial Valley Valley irrigation irrigation district): district): (a) (a) S00E S00E Figure are defined: Case (1): The ground motion component S00E was applied in the longitudinal direction component; (b) S90W component; and (c) vertical component. component; (b)component S90W component; and applied (c) vertical (X-direction); S90W was in component. the transverse; and the vertical component was applied in the vertical direction of the SFT, respectively; this case will be referred to as Load

For the evaluation of the ground motion’s effects on the structural behavior of the SFT, two cases For the evaluation of the ground motion’s effects on the structural behavior of the SFT, two are defined: Case (1): The ground motion component S00E was applied in the longitudinal direction cases are defined: Case (1): The ground motion component S00E was applied in the longitudinal (X-direction); component S90W was applied in the transverse; and the vertical component was direction (X-direction); component S90W was applied in the transverse; and the vertical component applied in the vertical direction of the SFT, respectively; this case will be referred to as Load was applied in the vertical direction of the SFT, respectively; this case will be referred to as Load

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Combination 1 (LC1). Case(2): (2):The Theground groundmotion motion component component S90W Combination 1 (LC1). Case S90Wwas wasapplied appliedininthe thelongitudinal longitudinal direction; component S00E was applied in the transverse direction; the vertical component applied direction; component S00E was applied in the transverse direction; the vertical componentwas was applied in the vertical direction of the SFT, respectively; this case will be referred to as Load Combination 2 2 in the vertical direction of the SFT, respectively; this case will be referred to as Load Combination (LC2). The ground motion component S00W is the maximum ground motion input having a peak (LC2). The ground motion component S00W is the maximum ground motion input having a peak ground acceleration (PGA) of 0.35 g. In contrast with the previous sections, the unfactored static and ground acceleration (PGA) of 0.35 g. In contrast with the previous sections, the unfactored static and hydrodynamic loads are used here for evaluating the structural behavior of the SFT. hydrodynamic loads are used here for evaluating the structural behavior of the SFT. A comparison of the static, hydrodynamic and seismic response envelope curves of the SFT is A comparison of the static, hydrodynamic and seismic response envelope curves of the SFT is shown in Figure 11. The maximum response of the tunnel is used to produce the envelope curves. shown in Figure 11. The maximum response of the tunnel is used to produce the envelope curves. The SFT response envelope curves of transverse and vertical displacements are shown in Figure 11a,b Therespectively; SFT response curves of transverse and displacements are shown in Figure 11a,b theenvelope longitudinal response of the SFT is vertical very small and is not shown. respectively; the longitudinal response of the SFT is very small and is not shown. The transverse displacements of SFT in Figure 11a show a large difference between the static The transverse displacements of SFTrelative in Figure 11a show large difference between the static and dynamic analysis. The approximate differences in amaximum transverse displacements andofdynamic analysis. The approximate relative differences in maximum transverse displacements the SFT from analysis cases LC2, LC1 and hydrodynamics to that of the static case are 95%, 94% of theand SFT42%, fromrespectively. analysis cases LC2, LC1 and hydrodynamics to that of the static case are 95%, 94% and 42%, respectively. The vertical displacements of the SFT are nearly the same for static and hydrodynamic analysis. Similarly, for LC1 and LC2, theofvertical the SFT almost same, as shown in The vertical displacements the SFTdisplacements are nearly theofsame for are static and the hydrodynamic analysis. Figure 11c. The approximate relative differences in maximum vertical displacements of the SFT from Similarly, for LC1 and LC2, the vertical displacements of the SFT are almost the same, as shown in analysis casesapproximate LC2, LC1 relative and hydrodynamics that of vertical the static case are 28%, 28% Figure 11c. The differences in to maximum displacements of the SFTand from 1.7%, cases respectively. analysis LC2, LC1 and hydrodynamics to that of the static case are 28%, 28% and 1.7%, respectively. The transverse responseisismore moreaffected affectedby by the the ground ground motions, is is The transverse response motions,while whilethe thevertical verticalresponse response more affected by gravity and hydrodynamic (waves and currents) actions. The transverse response more affected by gravity and hydrodynamic (waves and currents) actions. The transverse response is is extremely forseismic the seismic analysis as compared the vertical response; for instance, the extremely large large for the analysis as compared to theto vertical response; for instance, the relative relative difference in transverse and vertical displacements for LC1 and LC2 are 61% and difference in transverse and vertical displacements for LC1 and LC2 are 61% and 65%, respectively. 65%, respectively. Figure 11b,d represents the SFT bending moment MZ and bending moment MY envelope curves, Figure 11b,d represents the SFT bending moment MZ and bending moment MY envelope curves, respectively. Similar trends prevail for bending moments as described for displacements. The shape of respectively. Similar trends prevail for bending moments as described for displacements. The shape bending moments clearly demonstrates the effectiveness of the adopted mooring configuration. of bending moments clearly demonstrates the effectiveness of the adopted mooring configuration.

(a)

(b)

(c)

(d)

Figure 11. Comparison of static, hydrodynamic and seismic response envelope curves of the SFT: (a) Figure 11. Comparison of static, hydrodynamic and seismic response envelope curves of the SFT: Y-displacement; (b) bending moment MZ; (c) Z-displacement; and (d) bending moment MY. LC1, Load (a) Y-displacement; (b) bending moment MZ ; (c) Z-displacement; and (d) bending moment MY . LC1, Combination 1. Load Combination 1.

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To show a clear picture of the dynamic response of the SFT under seismic loadings, the To show clear picture of the dynamic response of the SFT under loadings, the comparison of amid-span displacements and bending moments forseismic hydrodynamic andcomparison seismic of mid-span displacements and bending moments for hydrodynamic and seismic analysis (LC2) are analysis (LC2) are shown in Figure 12. The hydrodynamic response is very small as compared to shown Figureload 12. The hydrodynamic is very small only as compared to whenscenario the seismic load when theinseismic is considered. The response comparison is shown for one seismic (LC2); is considered. The comparison is shown only for one seismic scenario (LC2); due to that, both seismic due to that, both seismic load combinations (LC1, LC2) produce very close responses in comparison combinations (LC1, LC2) produce very close responses comparison hydrodynamic toload hydrodynamic analysis. The hydrodynamic response of theinSFT resemblestothe shape of theanalysis. wave Themodel hydrodynamic response of theloading SFT resembles shape of the wave force used, while force used, while the seismic effect thethe transient motion of the SFT.model In addition, the the seismic loading effect the transient motion of the SFT. In addition, the transverse displacements transverse displacements (Figure 12a) and transverse bending moment (MZ, Figure 12b) are very large (Figure 12a) andaffected transverse bendingloading momentas(M 12b) are very large and significantly affected Z , Figure to and significantly by seismic compared vertical displacements (Figure 12c) and by seismic loading as compared to vertical displacements (Figureto12c) vertical vertical bending moment (MY, Figure 12d), and this is attributed theand small cable bending stiffness moment in the (MY , Figure 12d), and this is attributed to the small cable stiffness in the transverse direction. transverse direction.

(a)

(b)

(c)

(d)

Figure responsecomparison comparisonat at mid-span (Section B):Y-displacements; (a) Y-displacements; (b) Figure12. 12.SFT SFTdynamic dynamic response mid-span (Section B): (a) (b) bending Z; (c) Z-displacements; and (d) bending moment MY. bending moment moment M ; (c)M Z-displacements; and (d) bending moment M . Z

Y

5. Conclusions 5. Conclusions The submerged floating tunnel (SFT) is a new structural solution to waterway crossings. Despite The submerged floating tunnel (SFT) is a new structural solution to waterway crossings. Despite some valuable research having been accomplished, no SFT has been constructed in the world up to some valuable research having been accomplished, no SFT has been constructed in the world up to now. For the realization of SFT projects, the global performance in extreme environmental conditions now. For the realization of SFT projects, the global performance in extreme environmental conditions needs to be properly evaluated. This study evaluates the displacements and internal forces of an SFT needs to be properly evaluated. This study evaluates the displacements and internal forces of an SFT subjected to hydrodynamic and seismic loadings. The SFT tunnel was modeled by 3D beam elements; subjected to hydrodynamic and seismic loadings. The SFT tunnel was modeled by 3D beam elements; the mooring cables were modeled by truss elements; the ocean waves and currents were modeled by the mooring cables were modeled by truss elements; the ocean waves and currents were modeled by Airy wave theory. The SFT response subjected to hydrodynamic loading was evaluated using three Airy wave theory. The SFT response subjected to hydrodynamic loading was evaluated using three different mooring cable configurations; the suitable mooring cable configuration was then used for different mooring cable configurations; the suitable mooring cable configuration was then used for further evaluation. A comparison of response envelope curves for static, hydrodynamic and seismic further evaluation. A comparison of response envelope curves for static, hydrodynamic and seismic loadings was presented to evaluate the most effective structural response of SFT. loadings was presented to evaluate the most effective structural response of SFT. Based on the present study, the following conclusions can be drawn: Based on the present study, the following conclusions can be drawn:

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The static response can provide a benchmark for decision-making on mooring cable arrangements and configurations for the preliminary design. However, the static analysis underestimates the responses in comparison to those of dynamic analysis The SFT moored by tension leg mooring cables was least effective, because of lesser horizontal stiffness, and the SFT moored by such mooring cables undergoes extreme displacements in the transverse direction as compared to the one moored by inclined mooring cables. The SFT moored by a combination of tension legs and single inclined mooring cables was effective for moderate environmental conditions. For severe environmental conditions, the SFT should be moored either by a combination of tension legs and double inclined mooring cables or only by double inclined mooring cables. For hydrodynamic analysis, the transient motions of SFT were small and decayed quickly, and the steady-state motions mainly governed the structural response of SFT under the prescribed damping conditions. In the case of the seismic analysis, the transient motions are more pronounced as compared to the hydrodynamic response. In the hydrodynamic analysis, the vertical response of SFT was very small and mainly attributed to gravity and hydrodynamic forces; while the transverse response was very large for seismic analysis. The transverse displacements and internal forces were found to be larger than those of the vertical direction, which showed less restraining and lesser mooring cable stiffness in the transverse direction.

Acknowledgments: The Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education, Science and Technology (NRF-2015R1D1A1A09060113), supported this research. The authors wish to express their gratitude for this financial support. Author Contributions: Dong-Ho Choi supervised the research. Naik Muhammad contributed the idea, performed the numerical simulations and wrote the manuscript. Zahid Ullah helped with the simulations and the writing of the manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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