Research ArticleResponse Analysis of Submerged Floating Tunnel Hit bySubmarine Based on Smoothed-Particle Hydrodynamics

Gang Luo 1 Shaokang Pan 1 Yulong Zhang1 and Liang Chen2

1School of Highway Changrsquoan University Xirsquoan Shaanxi 710064 China2Guangxi Communications Investment Group Co Ltd Nanning Guangxi 530000 China

Correspondence should be addressed to Gang Luo luogangchdeducn

Received 9 April 2019 Accepted 20 May 2019 Published 9 June 2019

Academic Editor Luca Landi

Copyright copy 2019 Gang Luo et al $is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

$is paper presents the theoretical investigation on the damage of the submerged floating tunnel (SFT) under extreme loadsWater was modeled by smoothed-particle hydrodynamics (SPH) Anchor cables SFT and submarine were modeled by the finiteelement method (FEM) Penetrating phenomenon in the calculation process was achieved by the penalty function and the fluid-solid coupling effect was also considered in the simulation $e process of a submarine striking on the SFTwas studied based onthe commercial software $e relationships between the energy of the water submarine and SFTwere studied $e structural andhuman damages were evaluated using the kinematics and kinetic parameters of the SFT according to the relevant criterion $eresults indicate that the SPH-FEM coupling method is suitable to investigate the impact of the SFT in the water $e initial kineticenergy of the submarine is mainly converted into kinetic energy of the water and internal energy of the tunnel $e kinematicparameters at the impact point reach a peak value$e kinematic parameters at the anchor cables reach the minimum value so theanchor cables can inhibit the development of disaster significantly $e SPH-FEM coupling method can be helpful for collisionand explosion analysis of the SFT

1 Introduction

A submerged floating tunnel (SFT) also known as anArchimedes bridge is mainly composed of pipe bodies andfixtures (including fixed supports anchor cables or buoys)and bulkhead joints suspended at a certain depth below thewater surface As a result of limited influence of weathersmall longitudinal slope and no influence on surface trafficthe SFT has become a preferred traffic structure across longand deep water [1ndash3]

SFTs may be subjected to extreme loads such as earth-quakes and explosions inside and outside the pipelinewrecks or collisions with underwater submersibles duringoperation which should be involved as a necessary processfor the structural safety Morita et al [4] Carpaneto [5]Fogazzi and Perotti [6] Chen andHuang [7] Martinelli et al[8] Dong et al [9] and Lee et al [10] analyzed the responseof a submerged floating tunnel and an anchor system underthe action of an earthquake using the Green function large

mass method response spectrum method pseudoexcitationmethod and finite element method (FEM) Seo et al [11 12]and Luo et al [13] used ANSYSLS-DYNA software toanalyze the dynamic response of an SFT under the un-derwater explosion condition Hong and Lee [14] Zhanget al [15] and Xiang and Yang [16 17] studied the responseanalysis of an SFTunder impact and collision loads based ona simplified elastic support beam model of FEM Wu andMei [18] discussed the effects of hydrodynamics earth-quakes and structural parameters on the dynamic responseof tunnel anchors under seismic conditions Because a fewstudies have been conducted on SFTs under submarinecollision conditions and a numerical analysis based on thearbitrary LagrangendashEulerian is inefficient due to the modelsize and calculation cost smoothed-particle hydrodynamics(SPH) and FEM coupling methods were proposed to analyzethe collision response of an SFT

$e SPH program was applied to simulate the impactissue [19] Two impact models which included a frontal

HindawiShock and VibrationVolume 2019 Article ID 9056416 12 pageshttpsdoiorg10115520199056416

impact and an oblique impact were simulated $e resultsshowed that the SPHmethodwas suitable for dealingwith largedeformation problems It was demonstrated that the SPHmethod could be applied to solving impact mechanics prob-lems Xu et al [20] used the SPH method to simulate thecollision process of projectiles on thin target plates $e shapeand characteristics of the debris cloud coincide with the ex-periment results indicating the effectiveness of the SPHmethod on the simulation of this mechanics problem Based onSPH theory Yang et al [21] studied the influence of watersurface explosion $e results verified that the SPH method issuitable for the evaluation of the compressiblemultimedia flow

In summary some conditions of the SFTunder extremeenvironments have been focused all over the world in-cluding the overall response of the tunnel and the influenceof different anchor cable forms However research on hu-man safety in tunnels after collision is still limited$ereforeit will be very interesting to conduct further study on theimpact of SFT according to the SPH

2 Basic Principle of the SPH Method

21 SPH Method $e SPH method differs from traditionalnumerical methods based on a discrete grid (such as thefinite difference and FEM) $e SPH method was firstproposed in 1977 [22] and is a pure Lagrangian form of ameshless particle method $e method discretizes a con-tinuum into a group of particles with a certain mass andspeed$e field function value of all particles was assessed byan interpolation function and the spatial derivative wasdeduced without relying on the grid $e phenomenon ofgrid entanglement and distortion was avoided and acomputational overflow was from a large interface de-formation $erefore the SPH method has significant ad-vantages in evaluation of the large deformations

22 Calculation Principle of SPH Method $e SPH methodis mainly based on interpolation theory Each particlerepresents an interpolation point of an available physicalproperty Using a specific interpolation function W(x h)macro f(x) (such as the speed and displacement) is obtainedfrom the form of integral estimation In solving domain Dthe values of the relative variables at space x are calculated byfield function

f(x) 1113946D

f xprime( 1113857W xminusxprime h( 1113857dxprime (1)

where W is a smoothing function and h is the smoothinglength which stipulates the influence domain of W $eweight functions include Gaussian and cubic spline func-tions which meet the conditions of regularization and acompact support Formula (1) is an approximate expressionof the continuous form of particles which can be rewrittenas the discrete form [23] of particle j in the influence domainof particle i at x

f(x) 1113944N

j1

mj

ρj

f xj1113872 1113873W xminusxj h1113872 1113873 (2)

where N is the amount of particles within the influencedomain of particle i andm and ρ correspond to the mass anddensity of the particle respectively

3 Calculation Model and Parameters

31 Calculation Model $e parameters of an SFT in theSonnen Strait Norway are presented in this paper $erelevant indicators of the pipe body anchor cables andsubmarine are shown in Table 1 $e geometry diagram ofthe analytical model is shown in Figure 1 which included606139 elements 696443 nodes and 331719 SPH particles$e SFT submarine and anchor cables were modeled by theFEM Figure 2 is the image of the finite element model inwhich a large number of particles are removed so as toimprove the quality Figure 3 is the modelrsquos cutaway view$e water was modeled by SPH where the diameter of theSPH particles was set to 1m $e boundary of the watermodel and the entire model were considered as the radiationboundary which came from the SFT suspended in the seaand usually corresponded to the sea surface [24] $e wholemodel was built using HyperMesh $e dimension of themesh was smaller than 30meters of the impact of the tunneland the mesh size of this part was 02m $e rest of thetunnel was made by graded meshing Farther away from theimpact area the size of the mesh was larger $e reason forthis meshing method was that if the deformation of theimpact zone is large refining the mesh can improve theaccuracy of the solution and if the deformation of the rest isrelatively small the solution efficiency could be improved byincreasing the mesh size appropriately $e bow and stern ofthe submarine are both hemispherical with a radius of 8mand 4m respectively $e tunnel submarine and anchorcables were made of Q345 based on the solid elements $etwo ends of the tunnel were fixed and the anchor cables were25meters from the ends As Figure 2 shows the directionlongitudinally along the tunnel was the Z-direction thevertical direction was the Y-direction and the direction ofthe submarine movement (impact direction) was the X-direction $e impact point was located in the middle of thetunnel

32CalculationMethod In the calculation process the forcebetween the particles and the meshes was transmitted byusing the penalty function constraint therefore the fluid-structure interaction was realized Figure 4 shows the in-terface diagram of meshes and particles

$e contact coupling algorithm allows the mesh andparticles to interact without penetrating $e particlesshould be checked for whether the penetration behaviorhappened to the master surface before each step If there wasno penetration no treatment was required Otherwise thepenetration distance l was calculated using the particle ra-dius and the distance from the center of the particle to theinterface In order to eliminate the penetration the contactforce f was calculated according to the size of l to act on theparticles [25]$e direction of fwas opposite to the directionof penetration $e f was named the penalty function value

2 Shock and Vibration

which could limit the penetration of particles and achievethe 13uid-structure interaction

d m

2π2ρr

radic

fn fskl nrarr

ft fs∣∣∣∣∣∣∣∣μ

(3)

where d is the particle radius r is the radial coordinate fn isthe normal contact force of the interface k is the mastersurface stiness fs is the scale factor of k n is the normal unitvector of the grid unit ft is the tangential contact force of theinterface and μ is the coecient of friction of the particles atthe contact surface

33 Constitutive Parameters e submarine and anchorcables were made of an elastic material the tunnel was made

Anchor cables

35m (graded mesh)

35m (graded mesh)

35m (02m grid)

Submarine

X

Y

Z

Submerged floating tunnel

Figure 2 Finite element method model

Table 1 Parameters of the models

Parts Parameters Values

Pipe body

Length (m) 10000Outer diameter (m) 1204Wall thickness (m) 026

Depth (m) 3000Quality (tm) 7600

Anchor cable

Length (m) 7000Diameter (m) 040Poissonrsquos ratio 030

Elastic modulus (Pa) 207E11Density (kgm3) 790000

Submarine

Quality (t) 86000Length (m) 1500

Distance from the tunnel (m) 250Wall thickness (m) 040Initial speed (ms) 500

25m 50m 25m 30m

70m

Water surface

Submarine

25m

Anchor cable

1204m

Anchor cable

15m

SubmarineSFT

Figure 1 Geometric model

Shock and Vibration 3

of an elastoplastic material and the CowperndashSymondsmodel was used to illustrate the in13uence of the strain rateon the yield stress e model equation is as follows

σy 1 +εC( )

1p[ ] σ0 + βEpε

effp( ) (4)

where σy is the yield stress σ0 is the initial yield stress ε is thestrain rate β is the hardening parameter C and P are thestrain rate parameters (C 40 P 5 for steel) εeffp is theeective plastic strain and Ep is the plastic hardeningmodulus [26]

e water is dened using the empty material model andthe equation of state is as follows

P ρ0c2μ 1 + 1minus c02( )( )μminus(a2)μ2[ ]

1minus S1 minus 1( )μminus S2 μ2(μ + 1)( )minus S3 μ3(μ + 1)2( )[ ]2

+ c0 + aμ( )E(5)

where P is the pressure ρ0 is the density of water at normaltemperature c is the intercept of μsndashμp (shock wavespeedndashparticle speed) curve S1 S2 and S3 are the slope

coecients of the μsndashμp curve μ is the initial relative specicvolume ρ is the density of water after an explosion c0 is theGruneisen coecient a is the rst-order volume correctioncoecient of c0 and E is the material internal energy Someparameters of which are shown in Table 2 [27]

4 Response Analysis of SFT

41Analysis ofEnergy Figure 5 shows the time history of thekinetic energy internal energy total energy and hourglassenergy of the system It was generally considered that whenthe hourglass energy was less than 5 of the peak internalenergy the calculation result was stable [28] In the gurethe peak internal energy was 753times106 J and the maximumhourglass energy was 031times 106 J which accounted for 4 ofthe peak internal energy erefore from the perspective ofenergy conservation and hourglass energy control thesimulation results were considered reasonable

Figure 6 shows the energy relation among the watersubmarine and tunnel e energy of the anchor cable is toosmall to be analyzed in the gure It was found that the frontpart of the submarine was 25m away from the tunnel at thebeginning of the calculation e total energy of the systemwas the initial kinetic energy of the submarine the value ofwhich was 108times106 J Prior to collision (055 s) owing tothe resistance of water the kinetic energy of the submarinewas attenuated at 75times106 J and the total energy was reducedby 31 At this time the kinetic energy and internal energyof the water are 26times106 J and 06times106 J respectively etotal energy of the water was almost the same as the decreaseof the kinetic energy of the submarine After the collisionsystem was stabilized the total energy of the water was

Anchor cables

Submerged floating tunnel

Submarine

SPH particles

X

Y

Z

Figure 3 Cutaway view of the model

ld

Interface

FEM meshes

SPH particlesf

Figure 4 Interface diagram of mesh and particle

4 Shock and Vibration

32times106 J accounting for 30 of the initial kinetic energy ofthe submarine which showed that the resistance of the waterin the impact process cannot be ignored In same time thekinetic energy of the submarine was 44times106 J Most of thiskinetic energy was converted into internal energy(22times106 J) and kinetic energy (08times106 J) of the tunnel Inthe collision process the tunnel absorbed 40 of the total

energy as the main form of absorption which was theinternal energy generated by the deformation of the tunnelwall

42Analysis ofKinematicResults Safety Limits for the Eshyectsof Surface Ship Shock on Man [29] (GJB 2689-96) proposedsome regulations about safety In this standard the humanbody is in a standing posture

e time when the shiprsquos specic part got the maximumspeed was set to T after the ship was hit If T was less than15ms the injury of the passengers would be induced by theimpact speed and the degree about passengersrsquo injury wouldbe determined by the average impact accelerationAccording to the speed and acceleration the areas can bedivided into a safety zone light injury zone moderate injuryzone and severe injury zone the specic standards of whichare listed in Table 3

Figure 7 shows the maximum displacement of the im-pact direction (which in the following is simply referred asthe X-direction) at dierent positions along the longitudinaldirection of the tunnel and Figure 8 shows a time-historycurve for the displacement of the tunnel impact point in theX-direction

In Figure 7 the maximum displacement at impact pointA (longitudinal position of 0m) was 1188mm and themaximum displacement from the impact point along thelongitudinal direction of the tunnel to both ends of thetunnel (50m) generally attenuated in an inverted ldquoVrdquo-shaped trend with the two sides being symmetric eanchor cable was connected to the tunnel at point B (C) andthe displacement of the two points was 114mm in the X-direction Since the tunnel was pulled by the anchor cablefurther deformation of the tunnel was restrained andminimum value occurred at point B (C) Both ends of thetunnel were xed causing the displacement to be zero

In Figure 8 after a collision at 055 s the displacement ofpoint A increases obviously At 060 s the displacement inthe X-direction reached the maximum value e dis-placement then decreased signicantly After the submarineseparated from the tunnel at 068 s the displacement of thepoint A reciprocated with time and the amplitude graduallydecreased Figure 9 shows the displacement nephograms ofthe tunnel at 055 and 060 s

In Figure 10 the speed of point A was the largest with avalue of 318ms e maximum speed in the X-directionfrom point A to the tunnel ends gradually decreased sym-metrically Point B (C) got the local minimum of 045ms

Table 2 Material parameters and coecients in Gruneisenequation of state of water

ρ0 (kgm3) c (ms) c0 a S1 S2 S31000 1480 04934 13937 256 minus1986 02268

12

Kinetic energyInternal energy

Total energyHourglass energy

10

8

6

4

2

0

00 02 04 06Time (s)

Ener

gy (times

106 J)

08 10

Figure 5 Global energy

Kinetic energy of waterInternal energy of waterInternal energy ofsubmarine

Kinetic energy of tunnel

Kinetic energy ofsubmarine

Internal energy of tunnel

12

10

8

6

4

2

0

Ener

gy (times

106 J)

00 02 04 06Time (s)

08 10

Figure 6 Energy relationship between the tunnel and submarine

Table 3 Division of physical injury areas

Area determinantsImpact maxspeed (ms)(Tlt 15ms)

Impact averageacceleration (ms2)

(Tgt 15ms)Safety area lt22 lt140Light injury area 22sim30 140sim200Moderate injury area 30sim40 200sim250Severe injury area gt40 gt250

Shock and Vibration 5

25m120

ndash50 ndash40 ndash30 ndash20 ndash10 0 10

C (25 114)CB

CAB

Submarine

Longitudinal positions (m)

Maximum displacement in the X-direction

Anchorcables

Tunnel A (0 1188)

20 30 40 50

100

80

ndash25m 0m

50m

60

40

20

0Max

imum

disp

lace

men

t in

the X

-dire

ctio

n (m

m)

ndash50m

Figure 7 Maximum X-direction displacement at dierent longitudinal positions

Displacement in the X-direction

(068 ndash168)

(06 1188)120

100

80

60

40

20

ndash20

0

Disp

lace

men

t in

the X

-dire

ctio

n (m

m)

00 02 04 06Time (s)

08 10

Figure 8 Time-history curve of X-direction displacement at point A

1254e + 01

1115e + 01

9764e + 00

8374e + 00

6984e + 00

5593e + 00

4203e + 00

2813e + 00

1422e + 00

3193e ndash 02

ndash1358e + 00

Fringe levels

(a)

1242e + 02

1095e + 02

9487e + 01

8020e + 01

6554e + 01

5087e + 01

3621e + 01

2154e + 01

6873e + 00

ndash7793e + 00

ndash2246e + 01

Fringe levels

(b)

Figure 9 Displacement nephograms of point A within 10m (a) 055 s nephogram (b) 060 s nephogram

6 Shock and Vibration

As shown in Figure 11 after collision the speed of pointA increased signicantly At 056 s the X-direction speedreached a maximum value of 318ms (which was earlierthan the time that maximum displacement occurred) enthe speed of point A reciprocated with time and the am-plitude decreased gradually Figure 12 shows the speednephograms at 056 and 062 s

Referring to the evaluation criteria of the eects ofimpact on the human body in Table 3 the safety of thehuman body when the submarine impacted the tunnel wasanalyzed ere was T10ms between the start of theimpact process (055 s) and the time when speed reachingthe maximum (056 s) less than 15ms Accordingly theimpact speed played a decisive role in estimating thehumanrsquos injury e maximum speed of point A at thismoment (056 s) was 318ms A human body of 22m nearthe point acquired moderate injury According to themaximum speed at dierent areas along the longitudinaldirection of the tunnel the dierent degrees of the humanrsquosinjury were classied into three categories (Figure 13)

Please note that the displacement and velocity of thecollision point cannot represent the motion state of the pipe ofthe SFT Pedestrian walkways and maintenance passages onboth sides may be reserved during the design of the SFTPedestrians and maintenance workers will appear on bothsides of the side walls of the tunnel Based on the mostdangerous and worst conditions the parameters of the colli-sion point are applied to evaluate the injury of the human body

In Figure 14 the acceleration at point A reached1483ms2 Meanwhile the acceleration gradually decreasedat positions farther from the impact point where the localminimum acceleration at B (C) was 26ms2 e accelera-tion of segments A to B and A to C gradually decreased andthen increased slightly before decreasing to zero emaximum acceleration occurred at 068 s (Figure 15)

43 Analysis of Kinetic Results e impulse could beresponded by impact and time e impact force and

impulse are important parameters for evaluating an impactinjury e time-history curve of the impact force is shownin Figure 16 e curve of impact force against penetrationdepth is shown in Figure 17

As shown in Figure 16 the impact force rapidly reachedthe peak value of 723times106N at the moment of collision andthen decreased sharply e collision process from the start(055 s) to separation (068 s) lasted for 013 s According tothe time history of the impact force the impulse was618times106Nmiddots As shown by the arrow in Figure 17 theimpact force in the early stage (section ①sim②) was pro-portional to the penetration depth e impact force andpenetration depth of the impact at point②were 551times 106Nand 435mm respectively When the impact force reachedthe maximum value at point③ of 723times106N it decreasedgradually As the tunnel recovered its shape gradually thesubmarine moved in the opposite direction and the pene-tration depth fell back

Figure 18 shows a longitudinal stress nephogram of thetunnel at 059 s Figure 19 shows a distribution diagram ofthe stress peak at dierent longitudinal positions Figures 20and 21 indicate the stress and strain time-history curves ofpoint A

As shown in Figure 19 the stress at point A was thelargest and the stress at joint B (C) between the anchor cableand the tunnel was the second largest e maximum stressat point A was 0541GPa and the value exceeded the yieldstress (345MPa) of the Q345 steel and the area (red area ofFigure 17) of point A within 54m had already yielded ejoints and the ends of point B (C) (0284GPa) and D (E)suered a maximum stress value due to the stress con-centration e results from Figure 19 indicate that for thelarge stress the key parts (such as the joints between anchorcables and tunnels the connections between two tunnel pipesections and the connection between tunnel and coastal)should be taken special care except the impact pointStructural damage might happen when the tunnel en-counters an extreme load which endangers the safety of thetunnel

(72 22)

B

(11 30)

A (0 318)

Safety area

Safety area

Moderate injuryarea

Submarine

Tunnel

Anchorcables

B A C

Light injury area

C (25 045)

ndash50 m ndash25 m 0 m 25 m 50 m

00

05

10

15

25

25

30

35

Max

imum

spee

d in

the X

-dire

ctio

n (m

s)

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50

Lomgitudinal positions (m)

Maximum speed in the X-direction

Figure 10 Maximum X-direction speed at dierent longitudinalpositions

(056 318)

(071 189) (084 187)

(095 ndash023)

(092 ndash17)

(067 ndash264)

Speed in the X-direction

ndash3

ndash2

ndash1

0

1

2

3

Spee

d in

the X

-dire

ctio

n (m

s)

02 04 06 08 1000Time (s)

Figure 11 Time-history curve of X-direction speed at point A

Shock and Vibration 7

In Figure 20 the stress of point A reached the maximumstress of 0541GPa at 055 s With the development of theimpact process the stress decreased sharply e moment atwhich the tunnel and submarine were separated (066 s) theminimum stress value of point A was 0143GPa After theseparation the stress value was restored approximately to0427GPa and 13uctuated in the trend of declination In

Fig 21 055 s was the moment of impact and the initialstrain was 000326 As the submarine moved continually thestrain increased rapidly and maintained a large value of00218 during the impact process (055sim068 s) After sep-aration (068 s) the strain was increased slightly to 00231Figure 22 shows stress nephograms at 055 and 058 sFigure 23 shows strain nephograms at 055 and 066 s

2987e + 00

2630e + 00

2274e + 00

1917e + 00

1560e + 00

1203e + 00

8467e + 01

4900e + 01

1332e + 01

ndash2235e + 01

ndash5802e + 01

Fringe levels

(a)

6377e ndash 01

4349e ndash 01

2321e ndash 01

2929e ndash 01

ndash1735e ndash 01

ndash3763e ndash 01

ndash5791e ndash 01

ndash7819e ndash 01

ndash9847e ndash 01

ndash1187e + 00

ndash1390e + 00

Fringe levels

(b)

Figure 12 Speed nephograms of point A within 10m (a) 056 s nephogram (b) 062 s nephogram

428m 428m61m61m 22m

Safety area

Moderate injury areaLight injury area

1 2 3

3

2

2

1

1

Figure 13 Division of physical injury along the tunnel

B (ndash25 26) C (25 26)

Submarine

Tunnel

B A Cndash25m 0m 25m50mndash50m

Anchor cables

A (0 1483)

Maximum acceleration in the X-direction

0

20

40

60

80

100

120

140

160

Max

imum

acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50Longitudinal positions (m)

Figure 14 Maximum X-direction acceleration at dierent longi-tudinal positions

(068 1483)

Acceleration in the X-direction

02 04 06 08 1000Time (s)

ndash100

ndash50

0

50

100

150

Acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

Figure 15 Time-history curve of X-direction acceleration at pointA

8 Shock and Vibration

5 Conclusions

Based on the principles of the SPH and FEM methods amodel of the SFT impacted by the submarine was estab-lished e variation relationship of related physical quan-tities of the submarine and tunnel was analyzed based on theANSYSLS-DYNA software e conclusions could bedrawn as follows

e tunnel absorbed 40 of the total energy and mainlyin the form of internal energy generated by the tunnel walldeformation

e kinematic parameters such as the displacementspeed and acceleration of the impact point reached the peakvalue during the impact process e impacted parametersgenerally show an inverted ldquoVrdquo-shaped attenuation trendMoreover the anchor cables could inhibit the movement ofthe tunnel to prevent the expansion of a collision disaster

(068 125 times 106)

(058 723 times 106)

Impact force

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

02 04 06 08 1000Time (s)

Figure 16 Time-history curve of the impact force

1

Impact force

(ndash168 125 times 106)

(980 367 times 106)

5

2

4

3

(435 551 times 106)

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

0 20 40 60 80 100 120ndash20Penetration depth (mm)

Figure 17 Relationship between impact force and penetrationdepth

Anchor cable(point B)

Impact point(point A)

Anchor cable (point C)

5106e ndash 014596e ndash 014086e ndash 013575e ndash 013065e ndash 012555e ndash 012045e ndash 011534e ndash 011024e ndash 015138e ndash 023545e ndash 04

Fringe levels

Figure 18 Nephogram of stress along the tunnel at 059 s

Stress peak

The stress of this areagt345 MPa

D (50 0049)

C (25 0284)(27 0345)

B (ndash25 0284)

A (0 0541)

E (ndash50 0049)

00

01

02

03

04

05

06

Stre

ss p

eak

(GPa

)

ndash45ndash40ndash35ndash30ndash25ndash20ndash15ndash10 ndash5 0 5 10 15 20 25 30 35 40 45 50ndash50

Longitudinal positions (m)

Figure 19 Peak of stress at dierent longitudinal positions

(066 0143)

(068 0427)

(058 0537)(055 0541)

Stress

00

01

02

03

04

05

06St

ress

(GPa

)

02 04 06 08 1000Time (s)

Figure 20 Time-history curve of the stress at impact A

Shock and Vibration 9

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

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Shock and Vibration

Hindawiwwwhindawicom Volume 2018

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Submit your manuscripts atwwwhindawicom

which could limit the penetration of particles and achievethe 13uid-structure interaction

d m

2π2ρr

radic

fn fskl nrarr

ft fs∣∣∣∣∣∣∣∣μ

(3)

where d is the particle radius r is the radial coordinate fn isthe normal contact force of the interface k is the mastersurface stiness fs is the scale factor of k n is the normal unitvector of the grid unit ft is the tangential contact force of theinterface and μ is the coecient of friction of the particles atthe contact surface

33 Constitutive Parameters e submarine and anchorcables were made of an elastic material the tunnel was made

Anchor cables

35m (graded mesh)

35m (graded mesh)

35m (02m grid)

Submarine

X

Y

Z

Submerged floating tunnel

Figure 2 Finite element method model

Table 1 Parameters of the models

Parts Parameters Values

Pipe body

Length (m) 10000Outer diameter (m) 1204Wall thickness (m) 026

Depth (m) 3000Quality (tm) 7600

Anchor cable

Length (m) 7000Diameter (m) 040Poissonrsquos ratio 030

Elastic modulus (Pa) 207E11Density (kgm3) 790000

Submarine

Quality (t) 86000Length (m) 1500

Distance from the tunnel (m) 250Wall thickness (m) 040Initial speed (ms) 500

25m 50m 25m 30m

70m

Water surface

Submarine

25m

Anchor cable

1204m

Anchor cable

15m

SubmarineSFT

Figure 1 Geometric model

Shock and Vibration 3

of an elastoplastic material and the CowperndashSymondsmodel was used to illustrate the in13uence of the strain rateon the yield stress e model equation is as follows

σy 1 +εC( )

1p[ ] σ0 + βEpε

effp( ) (4)

where σy is the yield stress σ0 is the initial yield stress ε is thestrain rate β is the hardening parameter C and P are thestrain rate parameters (C 40 P 5 for steel) εeffp is theeective plastic strain and Ep is the plastic hardeningmodulus [26]

e water is dened using the empty material model andthe equation of state is as follows

P ρ0c2μ 1 + 1minus c02( )( )μminus(a2)μ2[ ]

1minus S1 minus 1( )μminus S2 μ2(μ + 1)( )minus S3 μ3(μ + 1)2( )[ ]2

+ c0 + aμ( )E(5)

where P is the pressure ρ0 is the density of water at normaltemperature c is the intercept of μsndashμp (shock wavespeedndashparticle speed) curve S1 S2 and S3 are the slope

coecients of the μsndashμp curve μ is the initial relative specicvolume ρ is the density of water after an explosion c0 is theGruneisen coecient a is the rst-order volume correctioncoecient of c0 and E is the material internal energy Someparameters of which are shown in Table 2 [27]

4 Response Analysis of SFT

41Analysis ofEnergy Figure 5 shows the time history of thekinetic energy internal energy total energy and hourglassenergy of the system It was generally considered that whenthe hourglass energy was less than 5 of the peak internalenergy the calculation result was stable [28] In the gurethe peak internal energy was 753times106 J and the maximumhourglass energy was 031times 106 J which accounted for 4 ofthe peak internal energy erefore from the perspective ofenergy conservation and hourglass energy control thesimulation results were considered reasonable

Figure 6 shows the energy relation among the watersubmarine and tunnel e energy of the anchor cable is toosmall to be analyzed in the gure It was found that the frontpart of the submarine was 25m away from the tunnel at thebeginning of the calculation e total energy of the systemwas the initial kinetic energy of the submarine the value ofwhich was 108times106 J Prior to collision (055 s) owing tothe resistance of water the kinetic energy of the submarinewas attenuated at 75times106 J and the total energy was reducedby 31 At this time the kinetic energy and internal energyof the water are 26times106 J and 06times106 J respectively etotal energy of the water was almost the same as the decreaseof the kinetic energy of the submarine After the collisionsystem was stabilized the total energy of the water was

Anchor cables

Submerged floating tunnel

Submarine

SPH particles

X

Y

Z

Figure 3 Cutaway view of the model

ld

Interface

FEM meshes

SPH particlesf

Figure 4 Interface diagram of mesh and particle

4 Shock and Vibration

32times106 J accounting for 30 of the initial kinetic energy ofthe submarine which showed that the resistance of the waterin the impact process cannot be ignored In same time thekinetic energy of the submarine was 44times106 J Most of thiskinetic energy was converted into internal energy(22times106 J) and kinetic energy (08times106 J) of the tunnel Inthe collision process the tunnel absorbed 40 of the total

energy as the main form of absorption which was theinternal energy generated by the deformation of the tunnelwall

42Analysis ofKinematicResults Safety Limits for the Eshyectsof Surface Ship Shock on Man [29] (GJB 2689-96) proposedsome regulations about safety In this standard the humanbody is in a standing posture

e time when the shiprsquos specic part got the maximumspeed was set to T after the ship was hit If T was less than15ms the injury of the passengers would be induced by theimpact speed and the degree about passengersrsquo injury wouldbe determined by the average impact accelerationAccording to the speed and acceleration the areas can bedivided into a safety zone light injury zone moderate injuryzone and severe injury zone the specic standards of whichare listed in Table 3

Figure 7 shows the maximum displacement of the im-pact direction (which in the following is simply referred asthe X-direction) at dierent positions along the longitudinaldirection of the tunnel and Figure 8 shows a time-historycurve for the displacement of the tunnel impact point in theX-direction

In Figure 7 the maximum displacement at impact pointA (longitudinal position of 0m) was 1188mm and themaximum displacement from the impact point along thelongitudinal direction of the tunnel to both ends of thetunnel (50m) generally attenuated in an inverted ldquoVrdquo-shaped trend with the two sides being symmetric eanchor cable was connected to the tunnel at point B (C) andthe displacement of the two points was 114mm in the X-direction Since the tunnel was pulled by the anchor cablefurther deformation of the tunnel was restrained andminimum value occurred at point B (C) Both ends of thetunnel were xed causing the displacement to be zero

In Figure 8 after a collision at 055 s the displacement ofpoint A increases obviously At 060 s the displacement inthe X-direction reached the maximum value e dis-placement then decreased signicantly After the submarineseparated from the tunnel at 068 s the displacement of thepoint A reciprocated with time and the amplitude graduallydecreased Figure 9 shows the displacement nephograms ofthe tunnel at 055 and 060 s

In Figure 10 the speed of point A was the largest with avalue of 318ms e maximum speed in the X-directionfrom point A to the tunnel ends gradually decreased sym-metrically Point B (C) got the local minimum of 045ms

Table 2 Material parameters and coecients in Gruneisenequation of state of water

ρ0 (kgm3) c (ms) c0 a S1 S2 S31000 1480 04934 13937 256 minus1986 02268

12

Kinetic energyInternal energy

Total energyHourglass energy

10

8

6

4

2

0

00 02 04 06Time (s)

Ener

gy (times

106 J)

08 10

Figure 5 Global energy

Kinetic energy of waterInternal energy of waterInternal energy ofsubmarine

Kinetic energy of tunnel

Kinetic energy ofsubmarine

Internal energy of tunnel

12

10

8

6

4

2

0

Ener

gy (times

106 J)

00 02 04 06Time (s)

08 10

Figure 6 Energy relationship between the tunnel and submarine

Table 3 Division of physical injury areas

Area determinantsImpact maxspeed (ms)(Tlt 15ms)

Impact averageacceleration (ms2)

(Tgt 15ms)Safety area lt22 lt140Light injury area 22sim30 140sim200Moderate injury area 30sim40 200sim250Severe injury area gt40 gt250

Shock and Vibration 5

25m120

ndash50 ndash40 ndash30 ndash20 ndash10 0 10

C (25 114)CB

CAB

Submarine

Longitudinal positions (m)

Maximum displacement in the X-direction

Anchorcables

Tunnel A (0 1188)

20 30 40 50

100

80

ndash25m 0m

50m

60

40

20

0Max

imum

disp

lace

men

t in

the X

-dire

ctio

n (m

m)

ndash50m

Figure 7 Maximum X-direction displacement at dierent longitudinal positions

Displacement in the X-direction

(068 ndash168)

(06 1188)120

100

80

60

40

20

ndash20

0

Disp

lace

men

t in

the X

-dire

ctio

n (m

m)

00 02 04 06Time (s)

08 10

Figure 8 Time-history curve of X-direction displacement at point A

1254e + 01

1115e + 01

9764e + 00

8374e + 00

6984e + 00

5593e + 00

4203e + 00

2813e + 00

1422e + 00

3193e ndash 02

ndash1358e + 00

Fringe levels

(a)

1242e + 02

1095e + 02

9487e + 01

8020e + 01

6554e + 01

5087e + 01

3621e + 01

2154e + 01

6873e + 00

ndash7793e + 00

ndash2246e + 01

Fringe levels

(b)

Figure 9 Displacement nephograms of point A within 10m (a) 055 s nephogram (b) 060 s nephogram

6 Shock and Vibration

As shown in Figure 11 after collision the speed of pointA increased signicantly At 056 s the X-direction speedreached a maximum value of 318ms (which was earlierthan the time that maximum displacement occurred) enthe speed of point A reciprocated with time and the am-plitude decreased gradually Figure 12 shows the speednephograms at 056 and 062 s

Referring to the evaluation criteria of the eects ofimpact on the human body in Table 3 the safety of thehuman body when the submarine impacted the tunnel wasanalyzed ere was T10ms between the start of theimpact process (055 s) and the time when speed reachingthe maximum (056 s) less than 15ms Accordingly theimpact speed played a decisive role in estimating thehumanrsquos injury e maximum speed of point A at thismoment (056 s) was 318ms A human body of 22m nearthe point acquired moderate injury According to themaximum speed at dierent areas along the longitudinaldirection of the tunnel the dierent degrees of the humanrsquosinjury were classied into three categories (Figure 13)

Please note that the displacement and velocity of thecollision point cannot represent the motion state of the pipe ofthe SFT Pedestrian walkways and maintenance passages onboth sides may be reserved during the design of the SFTPedestrians and maintenance workers will appear on bothsides of the side walls of the tunnel Based on the mostdangerous and worst conditions the parameters of the colli-sion point are applied to evaluate the injury of the human body

In Figure 14 the acceleration at point A reached1483ms2 Meanwhile the acceleration gradually decreasedat positions farther from the impact point where the localminimum acceleration at B (C) was 26ms2 e accelera-tion of segments A to B and A to C gradually decreased andthen increased slightly before decreasing to zero emaximum acceleration occurred at 068 s (Figure 15)

43 Analysis of Kinetic Results e impulse could beresponded by impact and time e impact force and

impulse are important parameters for evaluating an impactinjury e time-history curve of the impact force is shownin Figure 16 e curve of impact force against penetrationdepth is shown in Figure 17

As shown in Figure 16 the impact force rapidly reachedthe peak value of 723times106N at the moment of collision andthen decreased sharply e collision process from the start(055 s) to separation (068 s) lasted for 013 s According tothe time history of the impact force the impulse was618times106Nmiddots As shown by the arrow in Figure 17 theimpact force in the early stage (section ①sim②) was pro-portional to the penetration depth e impact force andpenetration depth of the impact at point②were 551times 106Nand 435mm respectively When the impact force reachedthe maximum value at point③ of 723times106N it decreasedgradually As the tunnel recovered its shape gradually thesubmarine moved in the opposite direction and the pene-tration depth fell back

Figure 18 shows a longitudinal stress nephogram of thetunnel at 059 s Figure 19 shows a distribution diagram ofthe stress peak at dierent longitudinal positions Figures 20and 21 indicate the stress and strain time-history curves ofpoint A

As shown in Figure 19 the stress at point A was thelargest and the stress at joint B (C) between the anchor cableand the tunnel was the second largest e maximum stressat point A was 0541GPa and the value exceeded the yieldstress (345MPa) of the Q345 steel and the area (red area ofFigure 17) of point A within 54m had already yielded ejoints and the ends of point B (C) (0284GPa) and D (E)suered a maximum stress value due to the stress con-centration e results from Figure 19 indicate that for thelarge stress the key parts (such as the joints between anchorcables and tunnels the connections between two tunnel pipesections and the connection between tunnel and coastal)should be taken special care except the impact pointStructural damage might happen when the tunnel en-counters an extreme load which endangers the safety of thetunnel

(72 22)

B

(11 30)

A (0 318)

Safety area

Safety area

Moderate injuryarea

Submarine

Tunnel

Anchorcables

B A C

Light injury area

C (25 045)

ndash50 m ndash25 m 0 m 25 m 50 m

00

05

10

15

25

25

30

35

Max

imum

spee

d in

the X

-dire

ctio

n (m

s)

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50

Lomgitudinal positions (m)

Maximum speed in the X-direction

Figure 10 Maximum X-direction speed at dierent longitudinalpositions

(056 318)

(071 189) (084 187)

(095 ndash023)

(092 ndash17)

(067 ndash264)

Speed in the X-direction

ndash3

ndash2

ndash1

0

1

2

3

Spee

d in

the X

-dire

ctio

n (m

s)

02 04 06 08 1000Time (s)

Figure 11 Time-history curve of X-direction speed at point A

Shock and Vibration 7

In Figure 20 the stress of point A reached the maximumstress of 0541GPa at 055 s With the development of theimpact process the stress decreased sharply e moment atwhich the tunnel and submarine were separated (066 s) theminimum stress value of point A was 0143GPa After theseparation the stress value was restored approximately to0427GPa and 13uctuated in the trend of declination In

Fig 21 055 s was the moment of impact and the initialstrain was 000326 As the submarine moved continually thestrain increased rapidly and maintained a large value of00218 during the impact process (055sim068 s) After sep-aration (068 s) the strain was increased slightly to 00231Figure 22 shows stress nephograms at 055 and 058 sFigure 23 shows strain nephograms at 055 and 066 s

2987e + 00

2630e + 00

2274e + 00

1917e + 00

1560e + 00

1203e + 00

8467e + 01

4900e + 01

1332e + 01

ndash2235e + 01

ndash5802e + 01

Fringe levels

(a)

6377e ndash 01

4349e ndash 01

2321e ndash 01

2929e ndash 01

ndash1735e ndash 01

ndash3763e ndash 01

ndash5791e ndash 01

ndash7819e ndash 01

ndash9847e ndash 01

ndash1187e + 00

ndash1390e + 00

Fringe levels

(b)

Figure 12 Speed nephograms of point A within 10m (a) 056 s nephogram (b) 062 s nephogram

428m 428m61m61m 22m

Safety area

Moderate injury areaLight injury area

1 2 3

3

2

2

1

1

Figure 13 Division of physical injury along the tunnel

B (ndash25 26) C (25 26)

Submarine

Tunnel

B A Cndash25m 0m 25m50mndash50m

Anchor cables

A (0 1483)

Maximum acceleration in the X-direction

0

20

40

60

80

100

120

140

160

Max

imum

acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50Longitudinal positions (m)

Figure 14 Maximum X-direction acceleration at dierent longi-tudinal positions

(068 1483)

Acceleration in the X-direction

02 04 06 08 1000Time (s)

ndash100

ndash50

0

50

100

150

Acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

Figure 15 Time-history curve of X-direction acceleration at pointA

8 Shock and Vibration

5 Conclusions

Based on the principles of the SPH and FEM methods amodel of the SFT impacted by the submarine was estab-lished e variation relationship of related physical quan-tities of the submarine and tunnel was analyzed based on theANSYSLS-DYNA software e conclusions could bedrawn as follows

e tunnel absorbed 40 of the total energy and mainlyin the form of internal energy generated by the tunnel walldeformation

e kinematic parameters such as the displacementspeed and acceleration of the impact point reached the peakvalue during the impact process e impacted parametersgenerally show an inverted ldquoVrdquo-shaped attenuation trendMoreover the anchor cables could inhibit the movement ofthe tunnel to prevent the expansion of a collision disaster

(068 125 times 106)

(058 723 times 106)

Impact force

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

02 04 06 08 1000Time (s)

Figure 16 Time-history curve of the impact force

1

Impact force

(ndash168 125 times 106)

(980 367 times 106)

5

2

4

3

(435 551 times 106)

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

0 20 40 60 80 100 120ndash20Penetration depth (mm)

Figure 17 Relationship between impact force and penetrationdepth

Anchor cable(point B)

Impact point(point A)

Anchor cable (point C)

5106e ndash 014596e ndash 014086e ndash 013575e ndash 013065e ndash 012555e ndash 012045e ndash 011534e ndash 011024e ndash 015138e ndash 023545e ndash 04

Fringe levels

Figure 18 Nephogram of stress along the tunnel at 059 s

Stress peak

The stress of this areagt345 MPa

D (50 0049)

C (25 0284)(27 0345)

B (ndash25 0284)

A (0 0541)

E (ndash50 0049)

00

01

02

03

04

05

06

Stre

ss p

eak

(GPa

)

ndash45ndash40ndash35ndash30ndash25ndash20ndash15ndash10 ndash5 0 5 10 15 20 25 30 35 40 45 50ndash50

Longitudinal positions (m)

Figure 19 Peak of stress at dierent longitudinal positions

(066 0143)

(068 0427)

(058 0537)(055 0541)

Stress

00

01

02

03

04

05

06St

ress

(GPa

)

02 04 06 08 1000Time (s)

Figure 20 Time-history curve of the stress at impact A

Shock and Vibration 9

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

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of an elastoplastic material and the CowperndashSymondsmodel was used to illustrate the in13uence of the strain rateon the yield stress e model equation is as follows

σy 1 +εC( )

1p[ ] σ0 + βEpε

effp( ) (4)

where σy is the yield stress σ0 is the initial yield stress ε is thestrain rate β is the hardening parameter C and P are thestrain rate parameters (C 40 P 5 for steel) εeffp is theeective plastic strain and Ep is the plastic hardeningmodulus [26]

e water is dened using the empty material model andthe equation of state is as follows

P ρ0c2μ 1 + 1minus c02( )( )μminus(a2)μ2[ ]

1minus S1 minus 1( )μminus S2 μ2(μ + 1)( )minus S3 μ3(μ + 1)2( )[ ]2

+ c0 + aμ( )E(5)

where P is the pressure ρ0 is the density of water at normaltemperature c is the intercept of μsndashμp (shock wavespeedndashparticle speed) curve S1 S2 and S3 are the slope

coecients of the μsndashμp curve μ is the initial relative specicvolume ρ is the density of water after an explosion c0 is theGruneisen coecient a is the rst-order volume correctioncoecient of c0 and E is the material internal energy Someparameters of which are shown in Table 2 [27]

4 Response Analysis of SFT

41Analysis ofEnergy Figure 5 shows the time history of thekinetic energy internal energy total energy and hourglassenergy of the system It was generally considered that whenthe hourglass energy was less than 5 of the peak internalenergy the calculation result was stable [28] In the gurethe peak internal energy was 753times106 J and the maximumhourglass energy was 031times 106 J which accounted for 4 ofthe peak internal energy erefore from the perspective ofenergy conservation and hourglass energy control thesimulation results were considered reasonable

Figure 6 shows the energy relation among the watersubmarine and tunnel e energy of the anchor cable is toosmall to be analyzed in the gure It was found that the frontpart of the submarine was 25m away from the tunnel at thebeginning of the calculation e total energy of the systemwas the initial kinetic energy of the submarine the value ofwhich was 108times106 J Prior to collision (055 s) owing tothe resistance of water the kinetic energy of the submarinewas attenuated at 75times106 J and the total energy was reducedby 31 At this time the kinetic energy and internal energyof the water are 26times106 J and 06times106 J respectively etotal energy of the water was almost the same as the decreaseof the kinetic energy of the submarine After the collisionsystem was stabilized the total energy of the water was

Anchor cables

Submerged floating tunnel

Submarine

SPH particles

X

Y

Z

Figure 3 Cutaway view of the model

ld

Interface

FEM meshes

SPH particlesf

Figure 4 Interface diagram of mesh and particle

4 Shock and Vibration

32times106 J accounting for 30 of the initial kinetic energy ofthe submarine which showed that the resistance of the waterin the impact process cannot be ignored In same time thekinetic energy of the submarine was 44times106 J Most of thiskinetic energy was converted into internal energy(22times106 J) and kinetic energy (08times106 J) of the tunnel Inthe collision process the tunnel absorbed 40 of the total

energy as the main form of absorption which was theinternal energy generated by the deformation of the tunnelwall

42Analysis ofKinematicResults Safety Limits for the Eshyectsof Surface Ship Shock on Man [29] (GJB 2689-96) proposedsome regulations about safety In this standard the humanbody is in a standing posture

e time when the shiprsquos specic part got the maximumspeed was set to T after the ship was hit If T was less than15ms the injury of the passengers would be induced by theimpact speed and the degree about passengersrsquo injury wouldbe determined by the average impact accelerationAccording to the speed and acceleration the areas can bedivided into a safety zone light injury zone moderate injuryzone and severe injury zone the specic standards of whichare listed in Table 3

Figure 7 shows the maximum displacement of the im-pact direction (which in the following is simply referred asthe X-direction) at dierent positions along the longitudinaldirection of the tunnel and Figure 8 shows a time-historycurve for the displacement of the tunnel impact point in theX-direction

In Figure 7 the maximum displacement at impact pointA (longitudinal position of 0m) was 1188mm and themaximum displacement from the impact point along thelongitudinal direction of the tunnel to both ends of thetunnel (50m) generally attenuated in an inverted ldquoVrdquo-shaped trend with the two sides being symmetric eanchor cable was connected to the tunnel at point B (C) andthe displacement of the two points was 114mm in the X-direction Since the tunnel was pulled by the anchor cablefurther deformation of the tunnel was restrained andminimum value occurred at point B (C) Both ends of thetunnel were xed causing the displacement to be zero

In Figure 8 after a collision at 055 s the displacement ofpoint A increases obviously At 060 s the displacement inthe X-direction reached the maximum value e dis-placement then decreased signicantly After the submarineseparated from the tunnel at 068 s the displacement of thepoint A reciprocated with time and the amplitude graduallydecreased Figure 9 shows the displacement nephograms ofthe tunnel at 055 and 060 s

In Figure 10 the speed of point A was the largest with avalue of 318ms e maximum speed in the X-directionfrom point A to the tunnel ends gradually decreased sym-metrically Point B (C) got the local minimum of 045ms

Table 2 Material parameters and coecients in Gruneisenequation of state of water

ρ0 (kgm3) c (ms) c0 a S1 S2 S31000 1480 04934 13937 256 minus1986 02268

12

Kinetic energyInternal energy

Total energyHourglass energy

10

8

6

4

2

0

00 02 04 06Time (s)

Ener

gy (times

106 J)

08 10

Figure 5 Global energy

Kinetic energy of waterInternal energy of waterInternal energy ofsubmarine

Kinetic energy of tunnel

Kinetic energy ofsubmarine

Internal energy of tunnel

12

10

8

6

4

2

0

Ener

gy (times

106 J)

00 02 04 06Time (s)

08 10

Figure 6 Energy relationship between the tunnel and submarine

Table 3 Division of physical injury areas

Area determinantsImpact maxspeed (ms)(Tlt 15ms)

Impact averageacceleration (ms2)

(Tgt 15ms)Safety area lt22 lt140Light injury area 22sim30 140sim200Moderate injury area 30sim40 200sim250Severe injury area gt40 gt250

Shock and Vibration 5

25m120

ndash50 ndash40 ndash30 ndash20 ndash10 0 10

C (25 114)CB

CAB

Submarine

Longitudinal positions (m)

Maximum displacement in the X-direction

Anchorcables

Tunnel A (0 1188)

20 30 40 50

100

80

ndash25m 0m

50m

60

40

20

0Max

imum

disp

lace

men

t in

the X

-dire

ctio

n (m

m)

ndash50m

Figure 7 Maximum X-direction displacement at dierent longitudinal positions

Displacement in the X-direction

(068 ndash168)

(06 1188)120

100

80

60

40

20

ndash20

0

Disp

lace

men

t in

the X

-dire

ctio

n (m

m)

00 02 04 06Time (s)

08 10

Figure 8 Time-history curve of X-direction displacement at point A

1254e + 01

1115e + 01

9764e + 00

8374e + 00

6984e + 00

5593e + 00

4203e + 00

2813e + 00

1422e + 00

3193e ndash 02

ndash1358e + 00

Fringe levels

(a)

1242e + 02

1095e + 02

9487e + 01

8020e + 01

6554e + 01

5087e + 01

3621e + 01

2154e + 01

6873e + 00

ndash7793e + 00

ndash2246e + 01

Fringe levels

(b)

Figure 9 Displacement nephograms of point A within 10m (a) 055 s nephogram (b) 060 s nephogram

6 Shock and Vibration

As shown in Figure 11 after collision the speed of pointA increased signicantly At 056 s the X-direction speedreached a maximum value of 318ms (which was earlierthan the time that maximum displacement occurred) enthe speed of point A reciprocated with time and the am-plitude decreased gradually Figure 12 shows the speednephograms at 056 and 062 s

Referring to the evaluation criteria of the eects ofimpact on the human body in Table 3 the safety of thehuman body when the submarine impacted the tunnel wasanalyzed ere was T10ms between the start of theimpact process (055 s) and the time when speed reachingthe maximum (056 s) less than 15ms Accordingly theimpact speed played a decisive role in estimating thehumanrsquos injury e maximum speed of point A at thismoment (056 s) was 318ms A human body of 22m nearthe point acquired moderate injury According to themaximum speed at dierent areas along the longitudinaldirection of the tunnel the dierent degrees of the humanrsquosinjury were classied into three categories (Figure 13)

Please note that the displacement and velocity of thecollision point cannot represent the motion state of the pipe ofthe SFT Pedestrian walkways and maintenance passages onboth sides may be reserved during the design of the SFTPedestrians and maintenance workers will appear on bothsides of the side walls of the tunnel Based on the mostdangerous and worst conditions the parameters of the colli-sion point are applied to evaluate the injury of the human body

In Figure 14 the acceleration at point A reached1483ms2 Meanwhile the acceleration gradually decreasedat positions farther from the impact point where the localminimum acceleration at B (C) was 26ms2 e accelera-tion of segments A to B and A to C gradually decreased andthen increased slightly before decreasing to zero emaximum acceleration occurred at 068 s (Figure 15)

43 Analysis of Kinetic Results e impulse could beresponded by impact and time e impact force and

impulse are important parameters for evaluating an impactinjury e time-history curve of the impact force is shownin Figure 16 e curve of impact force against penetrationdepth is shown in Figure 17

As shown in Figure 16 the impact force rapidly reachedthe peak value of 723times106N at the moment of collision andthen decreased sharply e collision process from the start(055 s) to separation (068 s) lasted for 013 s According tothe time history of the impact force the impulse was618times106Nmiddots As shown by the arrow in Figure 17 theimpact force in the early stage (section ①sim②) was pro-portional to the penetration depth e impact force andpenetration depth of the impact at point②were 551times 106Nand 435mm respectively When the impact force reachedthe maximum value at point③ of 723times106N it decreasedgradually As the tunnel recovered its shape gradually thesubmarine moved in the opposite direction and the pene-tration depth fell back

Figure 18 shows a longitudinal stress nephogram of thetunnel at 059 s Figure 19 shows a distribution diagram ofthe stress peak at dierent longitudinal positions Figures 20and 21 indicate the stress and strain time-history curves ofpoint A

As shown in Figure 19 the stress at point A was thelargest and the stress at joint B (C) between the anchor cableand the tunnel was the second largest e maximum stressat point A was 0541GPa and the value exceeded the yieldstress (345MPa) of the Q345 steel and the area (red area ofFigure 17) of point A within 54m had already yielded ejoints and the ends of point B (C) (0284GPa) and D (E)suered a maximum stress value due to the stress con-centration e results from Figure 19 indicate that for thelarge stress the key parts (such as the joints between anchorcables and tunnels the connections between two tunnel pipesections and the connection between tunnel and coastal)should be taken special care except the impact pointStructural damage might happen when the tunnel en-counters an extreme load which endangers the safety of thetunnel

(72 22)

B

(11 30)

A (0 318)

Safety area

Safety area

Moderate injuryarea

Submarine

Tunnel

Anchorcables

B A C

Light injury area

C (25 045)

ndash50 m ndash25 m 0 m 25 m 50 m

00

05

10

15

25

25

30

35

Max

imum

spee

d in

the X

-dire

ctio

n (m

s)

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50

Lomgitudinal positions (m)

Maximum speed in the X-direction

Figure 10 Maximum X-direction speed at dierent longitudinalpositions

(056 318)

(071 189) (084 187)

(095 ndash023)

(092 ndash17)

(067 ndash264)

Speed in the X-direction

ndash3

ndash2

ndash1

0

1

2

3

Spee

d in

the X

-dire

ctio

n (m

s)

02 04 06 08 1000Time (s)

Figure 11 Time-history curve of X-direction speed at point A

Shock and Vibration 7

In Figure 20 the stress of point A reached the maximumstress of 0541GPa at 055 s With the development of theimpact process the stress decreased sharply e moment atwhich the tunnel and submarine were separated (066 s) theminimum stress value of point A was 0143GPa After theseparation the stress value was restored approximately to0427GPa and 13uctuated in the trend of declination In

Fig 21 055 s was the moment of impact and the initialstrain was 000326 As the submarine moved continually thestrain increased rapidly and maintained a large value of00218 during the impact process (055sim068 s) After sep-aration (068 s) the strain was increased slightly to 00231Figure 22 shows stress nephograms at 055 and 058 sFigure 23 shows strain nephograms at 055 and 066 s

2987e + 00

2630e + 00

2274e + 00

1917e + 00

1560e + 00

1203e + 00

8467e + 01

4900e + 01

1332e + 01

ndash2235e + 01

ndash5802e + 01

Fringe levels

(a)

6377e ndash 01

4349e ndash 01

2321e ndash 01

2929e ndash 01

ndash1735e ndash 01

ndash3763e ndash 01

ndash5791e ndash 01

ndash7819e ndash 01

ndash9847e ndash 01

ndash1187e + 00

ndash1390e + 00

Fringe levels

(b)

Figure 12 Speed nephograms of point A within 10m (a) 056 s nephogram (b) 062 s nephogram

428m 428m61m61m 22m

Safety area

Moderate injury areaLight injury area

1 2 3

3

2

2

1

1

Figure 13 Division of physical injury along the tunnel

B (ndash25 26) C (25 26)

Submarine

Tunnel

B A Cndash25m 0m 25m50mndash50m

Anchor cables

A (0 1483)

Maximum acceleration in the X-direction

0

20

40

60

80

100

120

140

160

Max

imum

acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50Longitudinal positions (m)

Figure 14 Maximum X-direction acceleration at dierent longi-tudinal positions

(068 1483)

Acceleration in the X-direction

02 04 06 08 1000Time (s)

ndash100

ndash50

0

50

100

150

Acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

Figure 15 Time-history curve of X-direction acceleration at pointA

8 Shock and Vibration

5 Conclusions

Based on the principles of the SPH and FEM methods amodel of the SFT impacted by the submarine was estab-lished e variation relationship of related physical quan-tities of the submarine and tunnel was analyzed based on theANSYSLS-DYNA software e conclusions could bedrawn as follows

e tunnel absorbed 40 of the total energy and mainlyin the form of internal energy generated by the tunnel walldeformation

e kinematic parameters such as the displacementspeed and acceleration of the impact point reached the peakvalue during the impact process e impacted parametersgenerally show an inverted ldquoVrdquo-shaped attenuation trendMoreover the anchor cables could inhibit the movement ofthe tunnel to prevent the expansion of a collision disaster

(068 125 times 106)

(058 723 times 106)

Impact force

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

02 04 06 08 1000Time (s)

Figure 16 Time-history curve of the impact force

1

Impact force

(ndash168 125 times 106)

(980 367 times 106)

5

2

4

3

(435 551 times 106)

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

0 20 40 60 80 100 120ndash20Penetration depth (mm)

Figure 17 Relationship between impact force and penetrationdepth

Anchor cable(point B)

Impact point(point A)

Anchor cable (point C)

5106e ndash 014596e ndash 014086e ndash 013575e ndash 013065e ndash 012555e ndash 012045e ndash 011534e ndash 011024e ndash 015138e ndash 023545e ndash 04

Fringe levels

Figure 18 Nephogram of stress along the tunnel at 059 s

Stress peak

The stress of this areagt345 MPa

D (50 0049)

C (25 0284)(27 0345)

B (ndash25 0284)

A (0 0541)

E (ndash50 0049)

00

01

02

03

04

05

06

Stre

ss p

eak

(GPa

)

ndash45ndash40ndash35ndash30ndash25ndash20ndash15ndash10 ndash5 0 5 10 15 20 25 30 35 40 45 50ndash50

Longitudinal positions (m)

Figure 19 Peak of stress at dierent longitudinal positions

(066 0143)

(068 0427)

(058 0537)(055 0541)

Stress

00

01

02

03

04

05

06St

ress

(GPa

)

02 04 06 08 1000Time (s)

Figure 20 Time-history curve of the stress at impact A

Shock and Vibration 9

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

32times106 J accounting for 30 of the initial kinetic energy ofthe submarine which showed that the resistance of the waterin the impact process cannot be ignored In same time thekinetic energy of the submarine was 44times106 J Most of thiskinetic energy was converted into internal energy(22times106 J) and kinetic energy (08times106 J) of the tunnel Inthe collision process the tunnel absorbed 40 of the total

energy as the main form of absorption which was theinternal energy generated by the deformation of the tunnelwall

42Analysis ofKinematicResults Safety Limits for the Eshyectsof Surface Ship Shock on Man [29] (GJB 2689-96) proposedsome regulations about safety In this standard the humanbody is in a standing posture

e time when the shiprsquos specic part got the maximumspeed was set to T after the ship was hit If T was less than15ms the injury of the passengers would be induced by theimpact speed and the degree about passengersrsquo injury wouldbe determined by the average impact accelerationAccording to the speed and acceleration the areas can bedivided into a safety zone light injury zone moderate injuryzone and severe injury zone the specic standards of whichare listed in Table 3

Figure 7 shows the maximum displacement of the im-pact direction (which in the following is simply referred asthe X-direction) at dierent positions along the longitudinaldirection of the tunnel and Figure 8 shows a time-historycurve for the displacement of the tunnel impact point in theX-direction

In Figure 7 the maximum displacement at impact pointA (longitudinal position of 0m) was 1188mm and themaximum displacement from the impact point along thelongitudinal direction of the tunnel to both ends of thetunnel (50m) generally attenuated in an inverted ldquoVrdquo-shaped trend with the two sides being symmetric eanchor cable was connected to the tunnel at point B (C) andthe displacement of the two points was 114mm in the X-direction Since the tunnel was pulled by the anchor cablefurther deformation of the tunnel was restrained andminimum value occurred at point B (C) Both ends of thetunnel were xed causing the displacement to be zero

In Figure 8 after a collision at 055 s the displacement ofpoint A increases obviously At 060 s the displacement inthe X-direction reached the maximum value e dis-placement then decreased signicantly After the submarineseparated from the tunnel at 068 s the displacement of thepoint A reciprocated with time and the amplitude graduallydecreased Figure 9 shows the displacement nephograms ofthe tunnel at 055 and 060 s

In Figure 10 the speed of point A was the largest with avalue of 318ms e maximum speed in the X-directionfrom point A to the tunnel ends gradually decreased sym-metrically Point B (C) got the local minimum of 045ms

Table 2 Material parameters and coecients in Gruneisenequation of state of water

ρ0 (kgm3) c (ms) c0 a S1 S2 S31000 1480 04934 13937 256 minus1986 02268

12

Kinetic energyInternal energy

Total energyHourglass energy

10

8

6

4

2

0

00 02 04 06Time (s)

Ener

gy (times

106 J)

08 10

Figure 5 Global energy

Kinetic energy of waterInternal energy of waterInternal energy ofsubmarine

Kinetic energy of tunnel

Kinetic energy ofsubmarine

Internal energy of tunnel

12

10

8

6

4

2

0

Ener

gy (times

106 J)

00 02 04 06Time (s)

08 10

Figure 6 Energy relationship between the tunnel and submarine

Table 3 Division of physical injury areas

Area determinantsImpact maxspeed (ms)(Tlt 15ms)

Impact averageacceleration (ms2)

(Tgt 15ms)Safety area lt22 lt140Light injury area 22sim30 140sim200Moderate injury area 30sim40 200sim250Severe injury area gt40 gt250

Shock and Vibration 5

25m120

ndash50 ndash40 ndash30 ndash20 ndash10 0 10

C (25 114)CB

CAB

Submarine

Longitudinal positions (m)

Maximum displacement in the X-direction

Anchorcables

Tunnel A (0 1188)

20 30 40 50

100

80

ndash25m 0m

50m

60

40

20

0Max

imum

disp

lace

men

t in

the X

-dire

ctio

n (m

m)

ndash50m

Figure 7 Maximum X-direction displacement at dierent longitudinal positions

Displacement in the X-direction

(068 ndash168)

(06 1188)120

100

80

60

40

20

ndash20

0

Disp

lace

men

t in

the X

-dire

ctio

n (m

m)

00 02 04 06Time (s)

08 10

Figure 8 Time-history curve of X-direction displacement at point A

1254e + 01

1115e + 01

9764e + 00

8374e + 00

6984e + 00

5593e + 00

4203e + 00

2813e + 00

1422e + 00

3193e ndash 02

ndash1358e + 00

Fringe levels

(a)

1242e + 02

1095e + 02

9487e + 01

8020e + 01

6554e + 01

5087e + 01

3621e + 01

2154e + 01

6873e + 00

ndash7793e + 00

ndash2246e + 01

Fringe levels

(b)

Figure 9 Displacement nephograms of point A within 10m (a) 055 s nephogram (b) 060 s nephogram

6 Shock and Vibration

As shown in Figure 11 after collision the speed of pointA increased signicantly At 056 s the X-direction speedreached a maximum value of 318ms (which was earlierthan the time that maximum displacement occurred) enthe speed of point A reciprocated with time and the am-plitude decreased gradually Figure 12 shows the speednephograms at 056 and 062 s

Referring to the evaluation criteria of the eects ofimpact on the human body in Table 3 the safety of thehuman body when the submarine impacted the tunnel wasanalyzed ere was T10ms between the start of theimpact process (055 s) and the time when speed reachingthe maximum (056 s) less than 15ms Accordingly theimpact speed played a decisive role in estimating thehumanrsquos injury e maximum speed of point A at thismoment (056 s) was 318ms A human body of 22m nearthe point acquired moderate injury According to themaximum speed at dierent areas along the longitudinaldirection of the tunnel the dierent degrees of the humanrsquosinjury were classied into three categories (Figure 13)

Please note that the displacement and velocity of thecollision point cannot represent the motion state of the pipe ofthe SFT Pedestrian walkways and maintenance passages onboth sides may be reserved during the design of the SFTPedestrians and maintenance workers will appear on bothsides of the side walls of the tunnel Based on the mostdangerous and worst conditions the parameters of the colli-sion point are applied to evaluate the injury of the human body

In Figure 14 the acceleration at point A reached1483ms2 Meanwhile the acceleration gradually decreasedat positions farther from the impact point where the localminimum acceleration at B (C) was 26ms2 e accelera-tion of segments A to B and A to C gradually decreased andthen increased slightly before decreasing to zero emaximum acceleration occurred at 068 s (Figure 15)

43 Analysis of Kinetic Results e impulse could beresponded by impact and time e impact force and

impulse are important parameters for evaluating an impactinjury e time-history curve of the impact force is shownin Figure 16 e curve of impact force against penetrationdepth is shown in Figure 17

As shown in Figure 16 the impact force rapidly reachedthe peak value of 723times106N at the moment of collision andthen decreased sharply e collision process from the start(055 s) to separation (068 s) lasted for 013 s According tothe time history of the impact force the impulse was618times106Nmiddots As shown by the arrow in Figure 17 theimpact force in the early stage (section ①sim②) was pro-portional to the penetration depth e impact force andpenetration depth of the impact at point②were 551times 106Nand 435mm respectively When the impact force reachedthe maximum value at point③ of 723times106N it decreasedgradually As the tunnel recovered its shape gradually thesubmarine moved in the opposite direction and the pene-tration depth fell back

Figure 18 shows a longitudinal stress nephogram of thetunnel at 059 s Figure 19 shows a distribution diagram ofthe stress peak at dierent longitudinal positions Figures 20and 21 indicate the stress and strain time-history curves ofpoint A

As shown in Figure 19 the stress at point A was thelargest and the stress at joint B (C) between the anchor cableand the tunnel was the second largest e maximum stressat point A was 0541GPa and the value exceeded the yieldstress (345MPa) of the Q345 steel and the area (red area ofFigure 17) of point A within 54m had already yielded ejoints and the ends of point B (C) (0284GPa) and D (E)suered a maximum stress value due to the stress con-centration e results from Figure 19 indicate that for thelarge stress the key parts (such as the joints between anchorcables and tunnels the connections between two tunnel pipesections and the connection between tunnel and coastal)should be taken special care except the impact pointStructural damage might happen when the tunnel en-counters an extreme load which endangers the safety of thetunnel

(72 22)

B

(11 30)

A (0 318)

Safety area

Safety area

Moderate injuryarea

Submarine

Tunnel

Anchorcables

B A C

Light injury area

C (25 045)

ndash50 m ndash25 m 0 m 25 m 50 m

00

05

10

15

25

25

30

35

Max

imum

spee

d in

the X

-dire

ctio

n (m

s)

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50

Lomgitudinal positions (m)

Maximum speed in the X-direction

Figure 10 Maximum X-direction speed at dierent longitudinalpositions

(056 318)

(071 189) (084 187)

(095 ndash023)

(092 ndash17)

(067 ndash264)

Speed in the X-direction

ndash3

ndash2

ndash1

0

1

2

3

Spee

d in

the X

-dire

ctio

n (m

s)

02 04 06 08 1000Time (s)

Figure 11 Time-history curve of X-direction speed at point A

Shock and Vibration 7

In Figure 20 the stress of point A reached the maximumstress of 0541GPa at 055 s With the development of theimpact process the stress decreased sharply e moment atwhich the tunnel and submarine were separated (066 s) theminimum stress value of point A was 0143GPa After theseparation the stress value was restored approximately to0427GPa and 13uctuated in the trend of declination In

Fig 21 055 s was the moment of impact and the initialstrain was 000326 As the submarine moved continually thestrain increased rapidly and maintained a large value of00218 during the impact process (055sim068 s) After sep-aration (068 s) the strain was increased slightly to 00231Figure 22 shows stress nephograms at 055 and 058 sFigure 23 shows strain nephograms at 055 and 066 s

2987e + 00

2630e + 00

2274e + 00

1917e + 00

1560e + 00

1203e + 00

8467e + 01

4900e + 01

1332e + 01

ndash2235e + 01

ndash5802e + 01

Fringe levels

(a)

6377e ndash 01

4349e ndash 01

2321e ndash 01

2929e ndash 01

ndash1735e ndash 01

ndash3763e ndash 01

ndash5791e ndash 01

ndash7819e ndash 01

ndash9847e ndash 01

ndash1187e + 00

ndash1390e + 00

Fringe levels

(b)

Figure 12 Speed nephograms of point A within 10m (a) 056 s nephogram (b) 062 s nephogram

428m 428m61m61m 22m

Safety area

Moderate injury areaLight injury area

1 2 3

3

2

2

1

1

Figure 13 Division of physical injury along the tunnel

B (ndash25 26) C (25 26)

Submarine

Tunnel

B A Cndash25m 0m 25m50mndash50m

Anchor cables

A (0 1483)

Maximum acceleration in the X-direction

0

20

40

60

80

100

120

140

160

Max

imum

acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50Longitudinal positions (m)

Figure 14 Maximum X-direction acceleration at dierent longi-tudinal positions

(068 1483)

Acceleration in the X-direction

02 04 06 08 1000Time (s)

ndash100

ndash50

0

50

100

150

Acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

Figure 15 Time-history curve of X-direction acceleration at pointA

8 Shock and Vibration

5 Conclusions

Based on the principles of the SPH and FEM methods amodel of the SFT impacted by the submarine was estab-lished e variation relationship of related physical quan-tities of the submarine and tunnel was analyzed based on theANSYSLS-DYNA software e conclusions could bedrawn as follows

e tunnel absorbed 40 of the total energy and mainlyin the form of internal energy generated by the tunnel walldeformation

e kinematic parameters such as the displacementspeed and acceleration of the impact point reached the peakvalue during the impact process e impacted parametersgenerally show an inverted ldquoVrdquo-shaped attenuation trendMoreover the anchor cables could inhibit the movement ofthe tunnel to prevent the expansion of a collision disaster

(068 125 times 106)

(058 723 times 106)

Impact force

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

02 04 06 08 1000Time (s)

Figure 16 Time-history curve of the impact force

1

Impact force

(ndash168 125 times 106)

(980 367 times 106)

5

2

4

3

(435 551 times 106)

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

0 20 40 60 80 100 120ndash20Penetration depth (mm)

Figure 17 Relationship between impact force and penetrationdepth

Anchor cable(point B)

Impact point(point A)

Anchor cable (point C)

5106e ndash 014596e ndash 014086e ndash 013575e ndash 013065e ndash 012555e ndash 012045e ndash 011534e ndash 011024e ndash 015138e ndash 023545e ndash 04

Fringe levels

Figure 18 Nephogram of stress along the tunnel at 059 s

Stress peak

The stress of this areagt345 MPa

D (50 0049)

C (25 0284)(27 0345)

B (ndash25 0284)

A (0 0541)

E (ndash50 0049)

00

01

02

03

04

05

06

Stre

ss p

eak

(GPa

)

ndash45ndash40ndash35ndash30ndash25ndash20ndash15ndash10 ndash5 0 5 10 15 20 25 30 35 40 45 50ndash50

Longitudinal positions (m)

Figure 19 Peak of stress at dierent longitudinal positions

(066 0143)

(068 0427)

(058 0537)(055 0541)

Stress

00

01

02

03

04

05

06St

ress

(GPa

)

02 04 06 08 1000Time (s)

Figure 20 Time-history curve of the stress at impact A

Shock and Vibration 9

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

25m120

ndash50 ndash40 ndash30 ndash20 ndash10 0 10

C (25 114)CB

CAB

Submarine

Longitudinal positions (m)

Maximum displacement in the X-direction

Anchorcables

Tunnel A (0 1188)

20 30 40 50

100

80

ndash25m 0m

50m

60

40

20

0Max

imum

disp

lace

men

t in

the X

-dire

ctio

n (m

m)

ndash50m

Figure 7 Maximum X-direction displacement at dierent longitudinal positions

Displacement in the X-direction

(068 ndash168)

(06 1188)120

100

80

60

40

20

ndash20

0

Disp

lace

men

t in

the X

-dire

ctio

n (m

m)

00 02 04 06Time (s)

08 10

Figure 8 Time-history curve of X-direction displacement at point A

1254e + 01

1115e + 01

9764e + 00

8374e + 00

6984e + 00

5593e + 00

4203e + 00

2813e + 00

1422e + 00

3193e ndash 02

ndash1358e + 00

Fringe levels

(a)

1242e + 02

1095e + 02

9487e + 01

8020e + 01

6554e + 01

5087e + 01

3621e + 01

2154e + 01

6873e + 00

ndash7793e + 00

ndash2246e + 01

Fringe levels

(b)

Figure 9 Displacement nephograms of point A within 10m (a) 055 s nephogram (b) 060 s nephogram

6 Shock and Vibration

As shown in Figure 11 after collision the speed of pointA increased signicantly At 056 s the X-direction speedreached a maximum value of 318ms (which was earlierthan the time that maximum displacement occurred) enthe speed of point A reciprocated with time and the am-plitude decreased gradually Figure 12 shows the speednephograms at 056 and 062 s

Referring to the evaluation criteria of the eects ofimpact on the human body in Table 3 the safety of thehuman body when the submarine impacted the tunnel wasanalyzed ere was T10ms between the start of theimpact process (055 s) and the time when speed reachingthe maximum (056 s) less than 15ms Accordingly theimpact speed played a decisive role in estimating thehumanrsquos injury e maximum speed of point A at thismoment (056 s) was 318ms A human body of 22m nearthe point acquired moderate injury According to themaximum speed at dierent areas along the longitudinaldirection of the tunnel the dierent degrees of the humanrsquosinjury were classied into three categories (Figure 13)

Please note that the displacement and velocity of thecollision point cannot represent the motion state of the pipe ofthe SFT Pedestrian walkways and maintenance passages onboth sides may be reserved during the design of the SFTPedestrians and maintenance workers will appear on bothsides of the side walls of the tunnel Based on the mostdangerous and worst conditions the parameters of the colli-sion point are applied to evaluate the injury of the human body

In Figure 14 the acceleration at point A reached1483ms2 Meanwhile the acceleration gradually decreasedat positions farther from the impact point where the localminimum acceleration at B (C) was 26ms2 e accelera-tion of segments A to B and A to C gradually decreased andthen increased slightly before decreasing to zero emaximum acceleration occurred at 068 s (Figure 15)

43 Analysis of Kinetic Results e impulse could beresponded by impact and time e impact force and

impulse are important parameters for evaluating an impactinjury e time-history curve of the impact force is shownin Figure 16 e curve of impact force against penetrationdepth is shown in Figure 17

As shown in Figure 16 the impact force rapidly reachedthe peak value of 723times106N at the moment of collision andthen decreased sharply e collision process from the start(055 s) to separation (068 s) lasted for 013 s According tothe time history of the impact force the impulse was618times106Nmiddots As shown by the arrow in Figure 17 theimpact force in the early stage (section ①sim②) was pro-portional to the penetration depth e impact force andpenetration depth of the impact at point②were 551times 106Nand 435mm respectively When the impact force reachedthe maximum value at point③ of 723times106N it decreasedgradually As the tunnel recovered its shape gradually thesubmarine moved in the opposite direction and the pene-tration depth fell back

Figure 18 shows a longitudinal stress nephogram of thetunnel at 059 s Figure 19 shows a distribution diagram ofthe stress peak at dierent longitudinal positions Figures 20and 21 indicate the stress and strain time-history curves ofpoint A

As shown in Figure 19 the stress at point A was thelargest and the stress at joint B (C) between the anchor cableand the tunnel was the second largest e maximum stressat point A was 0541GPa and the value exceeded the yieldstress (345MPa) of the Q345 steel and the area (red area ofFigure 17) of point A within 54m had already yielded ejoints and the ends of point B (C) (0284GPa) and D (E)suered a maximum stress value due to the stress con-centration e results from Figure 19 indicate that for thelarge stress the key parts (such as the joints between anchorcables and tunnels the connections between two tunnel pipesections and the connection between tunnel and coastal)should be taken special care except the impact pointStructural damage might happen when the tunnel en-counters an extreme load which endangers the safety of thetunnel

(72 22)

B

(11 30)

A (0 318)

Safety area

Safety area

Moderate injuryarea

Submarine

Tunnel

Anchorcables

B A C

Light injury area

C (25 045)

ndash50 m ndash25 m 0 m 25 m 50 m

00

05

10

15

25

25

30

35

Max

imum

spee

d in

the X

-dire

ctio

n (m

s)

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50

Lomgitudinal positions (m)

Maximum speed in the X-direction

Figure 10 Maximum X-direction speed at dierent longitudinalpositions

(056 318)

(071 189) (084 187)

(095 ndash023)

(092 ndash17)

(067 ndash264)

Speed in the X-direction

ndash3

ndash2

ndash1

0

1

2

3

Spee

d in

the X

-dire

ctio

n (m

s)

02 04 06 08 1000Time (s)

Figure 11 Time-history curve of X-direction speed at point A

Shock and Vibration 7

In Figure 20 the stress of point A reached the maximumstress of 0541GPa at 055 s With the development of theimpact process the stress decreased sharply e moment atwhich the tunnel and submarine were separated (066 s) theminimum stress value of point A was 0143GPa After theseparation the stress value was restored approximately to0427GPa and 13uctuated in the trend of declination In

Fig 21 055 s was the moment of impact and the initialstrain was 000326 As the submarine moved continually thestrain increased rapidly and maintained a large value of00218 during the impact process (055sim068 s) After sep-aration (068 s) the strain was increased slightly to 00231Figure 22 shows stress nephograms at 055 and 058 sFigure 23 shows strain nephograms at 055 and 066 s

2987e + 00

2630e + 00

2274e + 00

1917e + 00

1560e + 00

1203e + 00

8467e + 01

4900e + 01

1332e + 01

ndash2235e + 01

ndash5802e + 01

Fringe levels

(a)

6377e ndash 01

4349e ndash 01

2321e ndash 01

2929e ndash 01

ndash1735e ndash 01

ndash3763e ndash 01

ndash5791e ndash 01

ndash7819e ndash 01

ndash9847e ndash 01

ndash1187e + 00

ndash1390e + 00

Fringe levels

(b)

Figure 12 Speed nephograms of point A within 10m (a) 056 s nephogram (b) 062 s nephogram

428m 428m61m61m 22m

Safety area

Moderate injury areaLight injury area

1 2 3

3

2

2

1

1

Figure 13 Division of physical injury along the tunnel

B (ndash25 26) C (25 26)

Submarine

Tunnel

B A Cndash25m 0m 25m50mndash50m

Anchor cables

A (0 1483)

Maximum acceleration in the X-direction

0

20

40

60

80

100

120

140

160

Max

imum

acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50Longitudinal positions (m)

Figure 14 Maximum X-direction acceleration at dierent longi-tudinal positions

(068 1483)

Acceleration in the X-direction

02 04 06 08 1000Time (s)

ndash100

ndash50

0

50

100

150

Acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

Figure 15 Time-history curve of X-direction acceleration at pointA

8 Shock and Vibration

5 Conclusions

Based on the principles of the SPH and FEM methods amodel of the SFT impacted by the submarine was estab-lished e variation relationship of related physical quan-tities of the submarine and tunnel was analyzed based on theANSYSLS-DYNA software e conclusions could bedrawn as follows

e tunnel absorbed 40 of the total energy and mainlyin the form of internal energy generated by the tunnel walldeformation

e kinematic parameters such as the displacementspeed and acceleration of the impact point reached the peakvalue during the impact process e impacted parametersgenerally show an inverted ldquoVrdquo-shaped attenuation trendMoreover the anchor cables could inhibit the movement ofthe tunnel to prevent the expansion of a collision disaster

(068 125 times 106)

(058 723 times 106)

Impact force

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

02 04 06 08 1000Time (s)

Figure 16 Time-history curve of the impact force

1

Impact force

(ndash168 125 times 106)

(980 367 times 106)

5

2

4

3

(435 551 times 106)

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

0 20 40 60 80 100 120ndash20Penetration depth (mm)

Figure 17 Relationship between impact force and penetrationdepth

Anchor cable(point B)

Impact point(point A)

Anchor cable (point C)

5106e ndash 014596e ndash 014086e ndash 013575e ndash 013065e ndash 012555e ndash 012045e ndash 011534e ndash 011024e ndash 015138e ndash 023545e ndash 04

Fringe levels

Figure 18 Nephogram of stress along the tunnel at 059 s

Stress peak

The stress of this areagt345 MPa

D (50 0049)

C (25 0284)(27 0345)

B (ndash25 0284)

A (0 0541)

E (ndash50 0049)

00

01

02

03

04

05

06

Stre

ss p

eak

(GPa

)

ndash45ndash40ndash35ndash30ndash25ndash20ndash15ndash10 ndash5 0 5 10 15 20 25 30 35 40 45 50ndash50

Longitudinal positions (m)

Figure 19 Peak of stress at dierent longitudinal positions

(066 0143)

(068 0427)

(058 0537)(055 0541)

Stress

00

01

02

03

04

05

06St

ress

(GPa

)

02 04 06 08 1000Time (s)

Figure 20 Time-history curve of the stress at impact A

Shock and Vibration 9

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

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Submit your manuscripts atwwwhindawicom

As shown in Figure 11 after collision the speed of pointA increased signicantly At 056 s the X-direction speedreached a maximum value of 318ms (which was earlierthan the time that maximum displacement occurred) enthe speed of point A reciprocated with time and the am-plitude decreased gradually Figure 12 shows the speednephograms at 056 and 062 s

Referring to the evaluation criteria of the eects ofimpact on the human body in Table 3 the safety of thehuman body when the submarine impacted the tunnel wasanalyzed ere was T10ms between the start of theimpact process (055 s) and the time when speed reachingthe maximum (056 s) less than 15ms Accordingly theimpact speed played a decisive role in estimating thehumanrsquos injury e maximum speed of point A at thismoment (056 s) was 318ms A human body of 22m nearthe point acquired moderate injury According to themaximum speed at dierent areas along the longitudinaldirection of the tunnel the dierent degrees of the humanrsquosinjury were classied into three categories (Figure 13)

Please note that the displacement and velocity of thecollision point cannot represent the motion state of the pipe ofthe SFT Pedestrian walkways and maintenance passages onboth sides may be reserved during the design of the SFTPedestrians and maintenance workers will appear on bothsides of the side walls of the tunnel Based on the mostdangerous and worst conditions the parameters of the colli-sion point are applied to evaluate the injury of the human body

In Figure 14 the acceleration at point A reached1483ms2 Meanwhile the acceleration gradually decreasedat positions farther from the impact point where the localminimum acceleration at B (C) was 26ms2 e accelera-tion of segments A to B and A to C gradually decreased andthen increased slightly before decreasing to zero emaximum acceleration occurred at 068 s (Figure 15)

43 Analysis of Kinetic Results e impulse could beresponded by impact and time e impact force and

impulse are important parameters for evaluating an impactinjury e time-history curve of the impact force is shownin Figure 16 e curve of impact force against penetrationdepth is shown in Figure 17

As shown in Figure 16 the impact force rapidly reachedthe peak value of 723times106N at the moment of collision andthen decreased sharply e collision process from the start(055 s) to separation (068 s) lasted for 013 s According tothe time history of the impact force the impulse was618times106Nmiddots As shown by the arrow in Figure 17 theimpact force in the early stage (section ①sim②) was pro-portional to the penetration depth e impact force andpenetration depth of the impact at point②were 551times 106Nand 435mm respectively When the impact force reachedthe maximum value at point③ of 723times106N it decreasedgradually As the tunnel recovered its shape gradually thesubmarine moved in the opposite direction and the pene-tration depth fell back

Figure 18 shows a longitudinal stress nephogram of thetunnel at 059 s Figure 19 shows a distribution diagram ofthe stress peak at dierent longitudinal positions Figures 20and 21 indicate the stress and strain time-history curves ofpoint A

As shown in Figure 19 the stress at point A was thelargest and the stress at joint B (C) between the anchor cableand the tunnel was the second largest e maximum stressat point A was 0541GPa and the value exceeded the yieldstress (345MPa) of the Q345 steel and the area (red area ofFigure 17) of point A within 54m had already yielded ejoints and the ends of point B (C) (0284GPa) and D (E)suered a maximum stress value due to the stress con-centration e results from Figure 19 indicate that for thelarge stress the key parts (such as the joints between anchorcables and tunnels the connections between two tunnel pipesections and the connection between tunnel and coastal)should be taken special care except the impact pointStructural damage might happen when the tunnel en-counters an extreme load which endangers the safety of thetunnel

(72 22)

B

(11 30)

A (0 318)

Safety area

Safety area

Moderate injuryarea

Submarine

Tunnel

Anchorcables

B A C

Light injury area

C (25 045)

ndash50 m ndash25 m 0 m 25 m 50 m

00

05

10

15

25

25

30

35

Max

imum

spee

d in

the X

-dire

ctio

n (m

s)

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50

Lomgitudinal positions (m)

Maximum speed in the X-direction

Figure 10 Maximum X-direction speed at dierent longitudinalpositions

(056 318)

(071 189) (084 187)

(095 ndash023)

(092 ndash17)

(067 ndash264)

Speed in the X-direction

ndash3

ndash2

ndash1

0

1

2

3

Spee

d in

the X

-dire

ctio

n (m

s)

02 04 06 08 1000Time (s)

Figure 11 Time-history curve of X-direction speed at point A

Shock and Vibration 7

In Figure 20 the stress of point A reached the maximumstress of 0541GPa at 055 s With the development of theimpact process the stress decreased sharply e moment atwhich the tunnel and submarine were separated (066 s) theminimum stress value of point A was 0143GPa After theseparation the stress value was restored approximately to0427GPa and 13uctuated in the trend of declination In

Fig 21 055 s was the moment of impact and the initialstrain was 000326 As the submarine moved continually thestrain increased rapidly and maintained a large value of00218 during the impact process (055sim068 s) After sep-aration (068 s) the strain was increased slightly to 00231Figure 22 shows stress nephograms at 055 and 058 sFigure 23 shows strain nephograms at 055 and 066 s

2987e + 00

2630e + 00

2274e + 00

1917e + 00

1560e + 00

1203e + 00

8467e + 01

4900e + 01

1332e + 01

ndash2235e + 01

ndash5802e + 01

Fringe levels

(a)

6377e ndash 01

4349e ndash 01

2321e ndash 01

2929e ndash 01

ndash1735e ndash 01

ndash3763e ndash 01

ndash5791e ndash 01

ndash7819e ndash 01

ndash9847e ndash 01

ndash1187e + 00

ndash1390e + 00

Fringe levels

(b)

Figure 12 Speed nephograms of point A within 10m (a) 056 s nephogram (b) 062 s nephogram

428m 428m61m61m 22m

Safety area

Moderate injury areaLight injury area

1 2 3

3

2

2

1

1

Figure 13 Division of physical injury along the tunnel

B (ndash25 26) C (25 26)

Submarine

Tunnel

B A Cndash25m 0m 25m50mndash50m

Anchor cables

A (0 1483)

Maximum acceleration in the X-direction

0

20

40

60

80

100

120

140

160

Max

imum

acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50Longitudinal positions (m)

Figure 14 Maximum X-direction acceleration at dierent longi-tudinal positions

(068 1483)

Acceleration in the X-direction

02 04 06 08 1000Time (s)

ndash100

ndash50

0

50

100

150

Acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

Figure 15 Time-history curve of X-direction acceleration at pointA

8 Shock and Vibration

5 Conclusions

Based on the principles of the SPH and FEM methods amodel of the SFT impacted by the submarine was estab-lished e variation relationship of related physical quan-tities of the submarine and tunnel was analyzed based on theANSYSLS-DYNA software e conclusions could bedrawn as follows

e tunnel absorbed 40 of the total energy and mainlyin the form of internal energy generated by the tunnel walldeformation

e kinematic parameters such as the displacementspeed and acceleration of the impact point reached the peakvalue during the impact process e impacted parametersgenerally show an inverted ldquoVrdquo-shaped attenuation trendMoreover the anchor cables could inhibit the movement ofthe tunnel to prevent the expansion of a collision disaster

(068 125 times 106)

(058 723 times 106)

Impact force

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

02 04 06 08 1000Time (s)

Figure 16 Time-history curve of the impact force

1

Impact force

(ndash168 125 times 106)

(980 367 times 106)

5

2

4

3

(435 551 times 106)

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

0 20 40 60 80 100 120ndash20Penetration depth (mm)

Figure 17 Relationship between impact force and penetrationdepth

Anchor cable(point B)

Impact point(point A)

Anchor cable (point C)

5106e ndash 014596e ndash 014086e ndash 013575e ndash 013065e ndash 012555e ndash 012045e ndash 011534e ndash 011024e ndash 015138e ndash 023545e ndash 04

Fringe levels

Figure 18 Nephogram of stress along the tunnel at 059 s

Stress peak

The stress of this areagt345 MPa

D (50 0049)

C (25 0284)(27 0345)

B (ndash25 0284)

A (0 0541)

E (ndash50 0049)

00

01

02

03

04

05

06

Stre

ss p

eak

(GPa

)

ndash45ndash40ndash35ndash30ndash25ndash20ndash15ndash10 ndash5 0 5 10 15 20 25 30 35 40 45 50ndash50

Longitudinal positions (m)

Figure 19 Peak of stress at dierent longitudinal positions

(066 0143)

(068 0427)

(058 0537)(055 0541)

Stress

00

01

02

03

04

05

06St

ress

(GPa

)

02 04 06 08 1000Time (s)

Figure 20 Time-history curve of the stress at impact A

Shock and Vibration 9

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

In Figure 20 the stress of point A reached the maximumstress of 0541GPa at 055 s With the development of theimpact process the stress decreased sharply e moment atwhich the tunnel and submarine were separated (066 s) theminimum stress value of point A was 0143GPa After theseparation the stress value was restored approximately to0427GPa and 13uctuated in the trend of declination In

Fig 21 055 s was the moment of impact and the initialstrain was 000326 As the submarine moved continually thestrain increased rapidly and maintained a large value of00218 during the impact process (055sim068 s) After sep-aration (068 s) the strain was increased slightly to 00231Figure 22 shows stress nephograms at 055 and 058 sFigure 23 shows strain nephograms at 055 and 066 s

2987e + 00

2630e + 00

2274e + 00

1917e + 00

1560e + 00

1203e + 00

8467e + 01

4900e + 01

1332e + 01

ndash2235e + 01

ndash5802e + 01

Fringe levels

(a)

6377e ndash 01

4349e ndash 01

2321e ndash 01

2929e ndash 01

ndash1735e ndash 01

ndash3763e ndash 01

ndash5791e ndash 01

ndash7819e ndash 01

ndash9847e ndash 01

ndash1187e + 00

ndash1390e + 00

Fringe levels

(b)

Figure 12 Speed nephograms of point A within 10m (a) 056 s nephogram (b) 062 s nephogram

428m 428m61m61m 22m

Safety area

Moderate injury areaLight injury area

1 2 3

3

2

2

1

1

Figure 13 Division of physical injury along the tunnel

B (ndash25 26) C (25 26)

Submarine

Tunnel

B A Cndash25m 0m 25m50mndash50m

Anchor cables

A (0 1483)

Maximum acceleration in the X-direction

0

20

40

60

80

100

120

140

160

Max

imum

acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

ndash40 ndash30 ndash20 ndash10 0 10 20 30 40 50ndash50Longitudinal positions (m)

Figure 14 Maximum X-direction acceleration at dierent longi-tudinal positions

(068 1483)

Acceleration in the X-direction

02 04 06 08 1000Time (s)

ndash100

ndash50

0

50

100

150

Acce

lera

tion

in th

e X-d

irect

ion

(ms

2 )

Figure 15 Time-history curve of X-direction acceleration at pointA

8 Shock and Vibration

5 Conclusions

Based on the principles of the SPH and FEM methods amodel of the SFT impacted by the submarine was estab-lished e variation relationship of related physical quan-tities of the submarine and tunnel was analyzed based on theANSYSLS-DYNA software e conclusions could bedrawn as follows

e tunnel absorbed 40 of the total energy and mainlyin the form of internal energy generated by the tunnel walldeformation

e kinematic parameters such as the displacementspeed and acceleration of the impact point reached the peakvalue during the impact process e impacted parametersgenerally show an inverted ldquoVrdquo-shaped attenuation trendMoreover the anchor cables could inhibit the movement ofthe tunnel to prevent the expansion of a collision disaster

(068 125 times 106)

(058 723 times 106)

Impact force

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

02 04 06 08 1000Time (s)

Figure 16 Time-history curve of the impact force

1

Impact force

(ndash168 125 times 106)

(980 367 times 106)

5

2

4

3

(435 551 times 106)

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

0 20 40 60 80 100 120ndash20Penetration depth (mm)

Figure 17 Relationship between impact force and penetrationdepth

Anchor cable(point B)

Impact point(point A)

Anchor cable (point C)

5106e ndash 014596e ndash 014086e ndash 013575e ndash 013065e ndash 012555e ndash 012045e ndash 011534e ndash 011024e ndash 015138e ndash 023545e ndash 04

Fringe levels

Figure 18 Nephogram of stress along the tunnel at 059 s

Stress peak

The stress of this areagt345 MPa

D (50 0049)

C (25 0284)(27 0345)

B (ndash25 0284)

A (0 0541)

E (ndash50 0049)

00

01

02

03

04

05

06

Stre

ss p

eak

(GPa

)

ndash45ndash40ndash35ndash30ndash25ndash20ndash15ndash10 ndash5 0 5 10 15 20 25 30 35 40 45 50ndash50

Longitudinal positions (m)

Figure 19 Peak of stress at dierent longitudinal positions

(066 0143)

(068 0427)

(058 0537)(055 0541)

Stress

00

01

02

03

04

05

06St

ress

(GPa

)

02 04 06 08 1000Time (s)

Figure 20 Time-history curve of the stress at impact A

Shock and Vibration 9

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

5 Conclusions

Based on the principles of the SPH and FEM methods amodel of the SFT impacted by the submarine was estab-lished e variation relationship of related physical quan-tities of the submarine and tunnel was analyzed based on theANSYSLS-DYNA software e conclusions could bedrawn as follows

e tunnel absorbed 40 of the total energy and mainlyin the form of internal energy generated by the tunnel walldeformation

e kinematic parameters such as the displacementspeed and acceleration of the impact point reached the peakvalue during the impact process e impacted parametersgenerally show an inverted ldquoVrdquo-shaped attenuation trendMoreover the anchor cables could inhibit the movement ofthe tunnel to prevent the expansion of a collision disaster

(068 125 times 106)

(058 723 times 106)

Impact force

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

02 04 06 08 1000Time (s)

Figure 16 Time-history curve of the impact force

1

Impact force

(ndash168 125 times 106)

(980 367 times 106)

5

2

4

3

(435 551 times 106)

0

10

20

30

40

50

60

70

Impa

ct fo

rce (

106 times

N)

0 20 40 60 80 100 120ndash20Penetration depth (mm)

Figure 17 Relationship between impact force and penetrationdepth

Anchor cable(point B)

Impact point(point A)

Anchor cable (point C)

5106e ndash 014596e ndash 014086e ndash 013575e ndash 013065e ndash 012555e ndash 012045e ndash 011534e ndash 011024e ndash 015138e ndash 023545e ndash 04

Fringe levels

Figure 18 Nephogram of stress along the tunnel at 059 s

Stress peak

The stress of this areagt345 MPa

D (50 0049)

C (25 0284)(27 0345)

B (ndash25 0284)

A (0 0541)

E (ndash50 0049)

00

01

02

03

04

05

06

Stre

ss p

eak

(GPa

)

ndash45ndash40ndash35ndash30ndash25ndash20ndash15ndash10 ndash5 0 5 10 15 20 25 30 35 40 45 50ndash50

Longitudinal positions (m)

Figure 19 Peak of stress at dierent longitudinal positions

(066 0143)

(068 0427)

(058 0537)(055 0541)

Stress

00

01

02

03

04

05

06St

ress

(GPa

)

02 04 06 08 1000Time (s)

Figure 20 Time-history curve of the stress at impact A

Shock and Vibration 9

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Fringe levels5484e ndash 01

4936e ndash 01

4387e ndash 01

3839e ndash 01

3291e ndash 01

2743e ndash 01

2194e ndash 01

1646e ndash 01

1098e ndash 01

5498e ndash 02

1576e ndash 04

(a)

5531e ndash 01

4978e ndash 01

4425e ndash 01

3872e ndash 01

3320e ndash 01

2767e ndash 01

2214e ndash 01

1661e ndash 01

1108e ndash 01

5556e ndash 02

2793e ndash 04

Fringe levels

(b)

Figure 22 Stress nephograms of impact A within 10m (a) 055 s nephogram (b) 058 s nephogram

3704e ndash 03

3334e ndash 03

2963e ndash 03

2593e ndash 03

2223e ndash 03

1852e ndash 03

1482e ndash 03

1111e ndash 03

7408e ndash 04

3704e ndash 04

0000e ndash 00

Fringe levels

(a)

2404e ndash 02

2163e ndash 02

1923e ndash 02

1683e ndash 02

1442e ndash 02

1202e ndash 02

9614e ndash 03

7211e ndash 03

4807e ndash 03

2404e ndash 03

0000e + 00

Fringe levels

(b)

Figure 23 Strain nephograms of impact A within 10m (a) 055 s nephogram (b) 066 s nephogram

(06 00218)

(055 000326)

(069 00231)

Strain

02 04 06 08 1000Time (s)

0000

0005

0010

0015

0020

0025

Stra

in

Figure 21 Time-history curve of the strain at impact A

10 Shock and Vibration

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

According to the passengersrsquo safety evaluation indicatorsthe damage area can be divided into a moderate injury arealight injury area and safety area under the extreme condi-tions which are 22 122 and 856m respectively

$e stress and strain are the largest near the impactpoint at 0541GPa and 00231 respectively Other than theimpact point the stress of the key parts (such as the jointsbetween anchor cables and tunnels the connections betweentwo tunnel pipe sections and the connection between tunneland coastal) is complicated Considerable attention shouldbe paid to the actual build process $e seawater still had acertain effect on the tunnel after the collision and preventivemeasures should be taken

Data Availability

$e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

$e authors declare no potential conflicts of interest withrespect to the research authorship andor publication ofthis article

Acknowledgments

$is work was supported by the National Natural ScienceFoundation of China (Grant no 51708042) and NationalNatural Science Foundation of Shaanxi Province (Grant no2019JQ-008)

References

[1] S P Jiang and Q X Li ldquoDevelopment of conceptual designdynamic analysis theory and model experiment of submergedfloating tunnelsrdquo Tunnel Construction vol 38 no 7pp 352ndash359 2018

[2] Y Q Xiang and Y Yang ldquoChallenges and technical ideas forthe construction of Chinese coastal cross-strait channelsrdquoChina Municipal Engineering vol 5 pp 1ndash5 2016

[3] J T Mai and B S Guan ldquoSubmerged floating tunnelrdquo TunnelConstruction vol 27 no 5 pp 20ndash23 2007

[4] S Morita T Yamashita and Y Mizuno Earthquake ResponseAnalysis of Submerged Floating Tunnels Considering WaterCompressibility International Society of Offshore and PolarEngineers Osaka Japan 1994

[5] R Carpaneto ldquo$e dynamic seismic analysis of SFTrdquo inProceedings of the International Conference on SubmergedFloating Tunnels Sandnes Norway May 1996

[6] P Fogazzi and F Perotti ldquo$e dynamic response of seabedanchored floating tunnels under seismic excitationrdquo Earth-quake Engineering amp Structural Dynamics vol 29 no 3pp 273ndash295 2000

[7] W Chen and G Huang ldquoSeismic wave passage effect ondynamic response of submerged floating tunnelsrdquo ProcediaEngineering vol 4 pp 217ndash224 2010

[8] L Martinelli G Barbella and A Feriani ldquoA numericalprocedure for simulating the multi-support seismic responseof submerged floating tunnels anchored by cablesrdquo Engi-neering Structures vol 33 no 10 pp 2850ndash2860 2011

[9] M S Dong M Li Z Lin F Tang and S P Jiang ldquoDynamicresponse of the submerged floating tunnel under randomseismic excitationrdquo Applied Mathematics and Mechanicsvol 35 no 12 pp 1320ndash1329 2014

[10] J H Lee S I Seo and H S Mun ldquoSeismic behaviors of afloating submerged tunnel with a rectangular cross-sectionrdquoOcean Engineering vol 127 pp 32ndash47 2016

[11] S-I Seo M Sagong and S-W Son ldquoGlobal response of sub-merged floating tunnel against underwater explosionrdquo KSCEJournal of Civil Engineering vol 19 no 7 pp 2029ndash2034 2015

[12] S-I Seo H-S Mun J-H Lee and J-H Kim ldquoSimplifiedanalysis for estimation of the behavior of a submerged floatingtunnel in waves and experimental verificationrdquo MarineStructures vol 44 pp 142ndash158 2015

[13] G Luo S K Pan X J Zhou J X Chen and B Q DaildquoDynamic response of a submerged floating tunnel during non-contact underwater explosionsrdquo China Journal of Highway andTransport vol 31 no 6 pp 244ndash253 2018

[14] K-Y Hong and G-H Lee ldquoCollision analysis of submergedfloating tunnel by underwater navigating vesselrdquo Journal ofComputational Structural Engineering Institute of Koreavol 27 no 5 pp 369ndash377 2014

[15] Y Zhang M S Dong and F Tang ldquoDisplacement responsesof submerged floating tunnels under impact loadsrdquo AppliedMathematics and Mechanics vol 37 no 5 pp 483ndash491 2016

[16] Y Xiang and Y Yang ldquoSpatial dynamic response of sub-merged floating tunnel under impact loadrdquo Marine Struc-tures vol 53 pp 20ndash31 2017

[17] Y Q Xiang Z Y Chen and Y Yang ldquoResearch developmentof method and simulation for analyzing dynamic response ofsubmerged floating tunnelrdquo China Journal of Highway andTransport vol 30 no 1 pp 69ndash76 2017

[18] Z Wu and G Mei ldquoDynamic response analysis of cable ofsubmerged floating tunnel under hydrodynamic force andearthquakerdquo Shock and Vibration vol 2017 Article ID3670769 14 pages 2017

[19] Y M Mao W Y Wu G L Chen and Y C Gong ldquoNu-merical simulation of high velocity impact problems with SPHmethodrdquo Journal of PLA University of Science and Technology(Natural Science) vol 4 no 5 pp 84ndash87 2003

[20] Z X Xu W H Tang and Y Luo ldquoApplications of thesmoothed particle hydrodynamics method to hypervelocityimpact simulationsrdquo Explosion and Shock Waves vol 26no 5 pp 53ndash58 2006

[21] G Yang X Han and S Y Long ldquoSimulation of underwaterexplosion near air-water surface by SPH methodrdquo Engi-neering Mechanics vol 25 no 4 pp 204ndash208 2008

[22] L B Lucy ldquoA numerical approach to the testing of thefission hypothesisrdquo He Astronomical Journal vol 82pp 1013ndash1024 1977

[23] M B Liu and G R Liu ldquoSmoothed particle hydrodynamics(SPH) an overview and recent developmentsrdquo Archives ofComputational Methods in Engineering vol 17 no 1 pp 25ndash76 2010

[24] S Tariverdilo J Mirzapour M Shahmardani R Shabani andC Gheyretmand ldquoVibration of submerged floating tunnelsdue to moving loadsrdquo Applied Mathematical Modellingvol 35 no 11 pp 5413ndash5425 2011

[25] Y Q ZhangW J Cai J C Li and Z J Wang ldquoApplication ofa FEMSPH coupling method to Torpedo water entryrdquoTorpedo Technology vol 25 no 1 pp 1ndash6 2017

[26] L Tian and F Huang ldquoNumerical simulation method forship-bridge collision considering fluid effectrdquo EngineeringMechanics vol 32 no 8 pp 120ndash128 2015

Shock and Vibration 11

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[27] Y Cao P Wang X Jin J Wang and Y Yang ldquoTunnelstructure analysis using the multi-scale modeling methodrdquoTunnelling and Underground Space Technology vol 28pp 124ndash134 2012

[28] LSTC LS-DYNA_Manual_Volume_I_R90 Livermore Soft-ware Technology Corporation Troy MI USA 2016

[29] X H LE andW Q KE Safety Limits for the Effects of SurfaceShip Shock on Man GJB 2689-96 Military Standard Pub-lishing Department of Commission of Science Technologyand Industry for National Defense Beijing China 1996

12 Shock and Vibration

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom