improvement on structural forms of pile group foundations...

Research ArticleImprovement on Structural Forms of Pile GroupFoundations of Deepwater Bridges

Enbo Yu Sen Ren Haojun Tang Yongle Li and Chen Fang

Department of Bridge Engineering Southwest Jiaotong University Chengdu 610031 China

Correspondence should be addressed to Haojun Tang thjswjtueducn

Received 8 March 2019 Revised 30 June 2019 Accepted 22 July 2019 Published 14 August 2019

Academic Editor Zhixiong Li

Copyright copy 2019 EnboYu et al-is is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

As long-span cross-sea bridges extend to deeper sea areas the bridge pile tends to increase in its slenderness ratio and becomesmore susceptible to waves To improve the structural stability at the construction stage this study analyses wave-induced responseof foundations -e wave theory and the method used for computing wave forces on foundations are first introduced -en a pilegroup foundation is taken as the research object and different pile lengths ranging from 16m to 46m are considered -e wave-induced response of the piles and the cap is calculated After understanding the effect of the pile length three optimizedfoundations are proposed with the aim of reducing the free length of the pile and the corresponding finite element models areestablished to compare their wave-induced response-e results show that the displacement at the top of the foundation increaseswith the increase in the pile length until the cap partly emerges from water and so does the internal force at the bottom Setting aconstraint in the middle of the piles can reduce their free lengths and is favourable to the wave-induced response of the foundationexcept for the shearing force A stronger constraint shows better effects on improvement of the stability of the foundation -econclusions provide reference for optimization on pile foundations of deepwater bridges

1 Introduction

With the rapid development of construction technology anincreasing number of long cross-sea bridges have beenconstructed greatly promoting the transportation and theeconomy in coastal areas For instance the Chesapeake BayBridge completed in 1964 connects the banks of theChesapeake Bay -e Great Belt Bridge completed in 1998crosses the Great Belt Strait -e Oresund Bridge completedin 2000 associates Denmark with Sweden -e Pingtan StraitBridge and the Hong KongndashZhuhaindashMacao Bridge werecompleted in 2010 and 2018 respectively As the weathercondition and hydrological environment are more com-plicated cross-sea bridges may be subject to strong windswith huge waves and prone to vibrate affecting the structuralstability and the running safety of vehicles [1 2] Apparentlythe foundation is the key structure supporting the pier andthe superstructure so its dynamic response closely associateswith the vibration of the whole structure and so does thevehicle -e deeper the water is the longer the foundation

could be and thereby its dynamic response becomes moreobvious In the construction stage when its top is not yetconstrained by the pier the freestanding foundation can beregarded as a cantilever Although the vehicle is not involvedat this situation possible vibration of the foundation haspotential effects on the construction of the pier In generalthe wave is accompanied with the wind but the foundationis almost or even totally submerged in water so it is moresensitive to effects of waves while less affected by winds Inthe service stage a rigid foundation which can better resiststrong waves is also favourable to its own safety as well as thestability of bridges and does the vehicle travelling through

Apparently the accurate simulation of the wave load isthe basis of evaluation of structural response under wavesAs for the expression of the wave motion a linear wavetheory which uses the potential function was proposed in1845 [3]-e Stokes wave which assumes the wavemotion aspotential motion and belongs to finite amplitude theory wasthen proposed [4] After that the second-order third-orderand fifth-order Stokes wave were successively derived [5 6]

HindawiShock and VibrationVolume 2019 Article ID 7381852 15 pageshttpsdoiorg10115520197381852

-e motion of waves was also described using the ellipticalcosine wave theory [7] On the basis of this the theory wasfurther studied by other scholars and engineers so that it canbe better applied in practice [8ndash10]With the development ofcomputer technology the numerical simulation becomes aneffective way to achieve the target [6 11 12] As for thecomputation of fluid-structure interaction the methodproposed by Morison et al [13] is used for calculating thewave force on the small-scale structure while the theory ofdiffraction put forward by MacCamy and Fuchs [14] is usedfor the large-scale structure

-e dynamic response of offshore structures hasattracted great attention of designers and scholars especiallyfor offshore wind turbines [15 16] Wave loads acting on thelower part below the water surface and wind loads acting onthe upper part above the water surface play important rolesAdhikari and Bhattacharya [17] showed that the naturalfrequency of the turbine tower decreases with the decrease instiffness of the foundation and the increase in axial loadZhang et al [18] investigated the dynamic response of afloating foundation of a turbine in 60m deepwater andpointed out that the semisubmersible floating foundationcan work with significant wave height less than 4m Weiet al [19] computed the capacity of monopile- and jacket-supported wind turbines and found that structural responsecan be dominated by either the wind or the wave dependingon structural characteristics and site conditions Wang et al[20] studied the dynamic response of a monopile-supportedwind turbine subjected to wind wave and earthquake ac-tions and indicated that it is necessary to consider thecombination of the three actions in the design of such aturbine Bachynski et al [21] further studied the response ofa monopile-supported wind turbine subjected to irregularwave loads and the experimental results highlighted theresonant response of the monopile when subjected to severewave loads Sarmiento et al [22] validated a multiusefloating platform which combines wave energy convertersand wind harvesting Wu et al [23] discussed geotechnicaland structural issues affecting the foundation of the offshorewind turbine It is concluded that the foundation presentsone of the main challenges in the design

-e bridge foundation has a variety of forms such as thecaisson foundation the tube caisson foundation and theopen caisson foundation When the water is deep the pilefoundation which consists of a group of bored pilesextending to soil at the bottom and connected to a large capat the top has widely been used owing to its convenientconstruction and good adaptability [24ndash26] However it isdifficult to model the precise dynamic response of the pilefoundation under various dynamic loads due to large di-mensions structural complexity and three-dimensionalcharacteristics [27] On the basis of the bridge foundationdesigned for the East Sea Bridge Liu et al [28] investigatedthe wave current forces on the pile foundation and examinedthe group effectiveness and the reduction coefficient forengineering design Yao et al [29] numerically simulated asuper-long pile foundation in stratified soils under bothvertical and lateral loads and concluded that the sleeved pilegroup can significantly reduce the horizontal displacement

Deng et al [30] experimentally studied the effect of fluid-structure interaction on the modal dynamic response of abridge pier supported by the pile foundation and found thatthe effect increases with the rise in water level especiallywhen the pier body is submerged in water Deng et al [31]further experimentally studied the modal dynamic responseof a hollow bridge pier with the pile foundation submergedin water and provided better understanding of the effect offluid-structure interaction Deng et al [32] investigated thecap effect on wave loads on piles and the force-increasingeffect on piles was observed when the relative cap dimensionis small In addition Ya et al [33] found that the dynamicresponse of a pile-cap structure under random sea waveaction is the largest Tomisawa and Kimura [34] proposednew techniques to improve seismic performance of the pilefoundation for long life bridges -e seismic excitation onthe pile foundation was also considered in some studies[35 36]

-e aforementioned studies have improved our un-derstanding of the dynamic response of the pile foundationbut optimization on the form has not yet been fully exploredWith long-span bridges extending to deeper sea areas thelength of the pile has to be increased leading to more slenderand flexible foundations To reduce the structural dynamicresponse optimization on the pile foundation with longerpiles becomes important Taking a long-span deepwaterbridge into account this paper studies the wave-inducedresponse of a pile group foundation using ANSYS softwareand further optimizes the structural form -e main contentis organized as follows -e wave loads on the piles and capof the foundation are computed in Section 2 Five finiteelement models with different pile lengths are establishedand their wave-induced vibration is compared and discussedin Section 3 After determining the relationship between thedynamic response and the pile length the foundation isoptimized with different structural forms in Section 4 andthe effectiveness is evaluated by comparing the changes inthe dynamic characteristics including the caprsquos displace-ment and the pilesrsquo internal forces Finally some mainconclusions are drawn in Section 5 providing reference foroptimization on pile foundations of deepwater bridges

2 Wave Force on the Foundation

21 Case Description -e engineering background of thepaper is a deepwater long-span cable-stayed bridge with atotal length of 1188m and its main span length is 532m-eoverall layout is shown in Figure 1-e measured data of thebridge location show that in a-hundred-year return periodthe wave on the transverse bridge direction has the maxi-mum heightH of 969m-e wave period T is 108 s and thewave circle frequency ω 0581 rads According to thedispersion relation the wavelength is about 169m -edensity of seawater ρ takes 1000 kgm3 and the water depthd is considered as 45m after flushing

-e bridge is supported by six pile group foundationsmarked with N01simN06 among which N03 and N04 are themain ones Each of the six pile foundations consists of agroup of piles and a cap on the top (Figure 1) In particular

2 Shock and Vibration

N03 has the longest free length in water so it is easier to beaffected by the wave force Because of this reason thesubsequent analysis of this paper will be carried out aroundthe N03 pile foundation -e cap dimension of N03 is812mtimes 332m and the thickness is 75m -e immense capis submerged in water and supported by as much as 38 boredpiles each of which has a diameter of 3m -e basic cross-sectional design and the pile numbers are shown inFigure 2(a) For the deepwater pile foundation the pilelength is a key parameter in its design because long piles andshort piles have their own advantages and disadvantages Tostudy the effect of the pile length on wave-induced responseof the foundation the length of N03 is decreased and in-creased respectively Five lengths ranging from 16m to 46muntil the cap completely emerges from water are selected asshown in Figure 2(b) It should be noted that the studymainly focuses the foundation itself and the difference inconstruction is not considered for a fair comparison

22 Wave Forces on the Pile As discussed previously theaccurate simulation of the wave load is the basis of evalu-ation of structural response Here two indicators HgT2 anddgT2 where the parameters were defined and the corre-sponding values at the bridge site were given in Section 22are computed According to Le Mehautersquos map and theory[37] the results show that the linear wave theory is appli-cable as the water is deep enough (Figure 3(a)) With the aimof comparing the wave-induced response for different formsof foundations the linear wave theory is adopted in thispaper-erefore velocity ux and acceleration ax of the wavecan be expressed by the following equations in considerationof the dispersion relationship

ux zΦzx

πH

T

cosh k(z + d)

sinh kdcos(kx minus ωt) (1)

ax zux

zt2π2H

T2cosh k(z + d)

sinh kdsin(kx minus ωt) (2)

where Φ is the velocity potential function z is the depth ofthe water particle when the origin of coordinates is set on thehydrostatic surface k is the number of fluctuations in thelength of 2π x is the horizontal coordinate and theremaining parameters are unchanged

For a cylinder the structure with DLle 02 is usuallydefined as a small-scale structure and the structure with

DLgt 02 is defined as a large-scale structure where D is thehorizontal dimension of the structure and L is the wave-length Specially the piles of N03 have a DL of 0018 so thewave force can be calculated according to the theory pro-posed by Morison as shown in Figure 3(b) When the originof coordinates is set on the seabed the wave force of thesingle pile at the height z is expressed as follows

fH fD + fI 12

CDρAux ux

11138681113868111386811138681113868111386811138681113868 + CMρV0

dux

dt (3)

where fD and fI are the drag and the inertia forces and CDand CM are the corresponding coefficients respectivelywhich are set as 12 and 20 according to Chinese code [38]Taking a pile of N03 as an example and dividing it intodifferent parts each of which has a unit length (Figure 4(b))the time series of fD and fI on the top are shown inFigure 4(a) with dashed lines -ere is a certain phasedifference between the two series As the maximum valueand change speed of fI are larger than those of fD the waveforce fH is dominated by fI and they almost reach themaxima simultaneously

Figure 4(a) also shows the time series of fH at the heightsof 5m 10m and 16m and it can be seen that the waveforces have similar phases and periods -e longer thedistance from the calculated position to the seabed is thelarger the amplitude of fH becomes Figure 4(c) furthershows the change in the amplitude of fH along the heightdirection and it can be seen that the growth rate graduallyaccelerates as the height increases and so does the waterspeed For the single pile the total maximum wave force fHis 15418 kN

When the pile length increases the time series of fH on asingle pile is computed in the same way and the results areshown in Figure 5(a) For the five cases the piles of thefoundation are immersed in water so they are completelysubject to wave loads With the increase in pile length from16m to 46m the period of the wave force on the pile re-mains the same but the amplitude increases gradually ie154 kN 274 kN 432 kN 510 kN and 669 kN respectively asshown in Figure 5(b) Moreover it can be seen that theincreasing range of the wave force is obviously larger thanthe increasing range of the pile length For instance the pileheight increases by 188 times from the minimum to themaximum but the wave force increases by 334 times -isphenomenon occurs because the water velocity increaseswith the increase in the distance from the calculated position

532 1961188

132196132

N01 N02 N03 N04 N05 N06

Calculated water level

Figure 1 Layout of the target bridge (unit m)

Shock and Vibration 3

to the seabed As a result the wave effect on the foundationwith longer piles becomes more obvious which is unfav-ourable to the structural stability

-e previous calculations of the wave loads focus on asingle pile However there are 38 piles for N03 foundationand the pile group effect has to be taken into account in thefollowing analysis To do this the phase differences of thewave forces on the 38 piles are modified according to theirspatial position relationships -en the group pile co-efficient K which is related to the ratio of the center distancel between two adjacent piles to their diameter D is in-troduced to consider the interference among piles For thepiles in parallel arrangement that is the vertical direction tothe flow direction of water the ratio Dl is equal to about 2so K 15 is adopted according to the code [38] For thepiles in tandem arrangement that is the parallel direction tothe flow direction of water the shadowing effect of theupstream pile on the downstream pile is not consideredconservatively and K 10 is adopted

23 Wave Forces on the Cap For the cap of the foundationthe dumbbell-type cross section is converted into a circular

cross section based on area equivalent -e original cross-sectional area of the cap is 202852m2 so the diameter D ofthe equivalent circular cross section is equal to 508m AsDL 03gt 02 the cap belongs to a large-scale structure onwhich the wave force could be calculated according to themethod proposed by MacCamy and Fuchs As shown inFigure 3(c) when the origin of the coordinate axis is set onthe seabed its forward wave force at a height of z is expressedas follows

FH(z) minus2ρgH

k

cosh kz

cosh kdA(ka)sin(ωt minus α) (4)

A(ka) 1

J1prime(ka)1113858 11138592

+ Y1prime(ka)1113858 11138592

1113969 (5)

tan α J1prime(ka)

Y1prime(ka) (6)

where J1prime and Y1prime are the derivatives of the first-order first-class and the first-order second-class Bessel functions re-spectively a is the radius of the cap and α is the phase lagangle

166

62

62

42

332

46 58 62 58 120 100 30662

812

180 x

y

Wave direction

1

2 3 4

6 7 85

9 19 1011

16 17 1815

12 13 14

21

222324

26272825

29203031

36373835

323334

(a)

h=

16m

h=

26m

h=

36m

h=

40m

h=

46m

d =

45m

(b)

Figure 2 Computed pile foundations with different pile lengths (a) Cross section (b) Elevation


-e time series of the wave force on the cap at differentpositions are shown in Figure 6(a) For the five cases themaximum of FH is observed at 88 s as compared inFigure 6(b) When the cap is totally submerged in water FHincreases as the distance from the calculated position to theseabed increases and so does the water velocity It can beseen that FH on the cap is larger than fH on a single pileobviously and is also larger than the total value of fH on allthe piles When the cap emerges from water the wave forceon the part exceeding sea level is no longer considered andthereby FH decreases rapidly until the cap completely floats

out of water and the wave force on the cap disappears At thistime the wave force on the foundation is gradually domi-nated by fH on the piles

3 Wave-Induced Response of the Foundation

31 Structural Dynamic Characteristics Five finite elementmodels of the foundation with different pile lengths areestablished using ANSYS software Beam4 and Mass21 el-ements are adopted and Figure 7 shows the first four modesincluding their modal shapes and frequencies For each of

dz

x

z

z

Wave direction

fH

a adz

x

z

z

Wave direction

x

z

d Wave direction

Mean sea levelη = 05Hcos (kx-ωt)

(a)

For a small-scaleobject calculation

For a large-scaleobject calculation

(b)

(c)

Figure 3 Computations of wave forces (a) Schematic diagram of the linear wave theory (b) For a small-scale object (c) For a large-scaleobject

0

2

4

6

8

10

12

14

16

8 9 10 11 12FH (kNm)

t = 81sDist

ance

to th

e sea

bed

(zm

)

Wave force on each part

Wave forcetime series

(a) (b) (c)

0 5 10 15 20

ndash10

0

10

fD (z = 16m)

fI (z = 16m)

Hor

izon

tal w

ave f

orce

f H (k

Nm

)

Time t (s)

z = 16mz = 10m z = 5m

81s

Figure 4 Horizontal wave forces on a pile (a) Time series at different heights (b) Schematic diagram of the division (c) Maximum waveforces along the pile


the five foundations the first-order and the second-ordermodes correspond to the translations of the cap along y axisand x axis (Figure 2(a)) respectively -e frequencies of thetwo modes are close to each other especially for larger pilelengths When the pile length is larger than 36m the dif-ference between the two frequencies is only about 01Hz sothe wave-induced vibration could occur in both directions-e third-order and fourth-order modes correspond to therotations of the cap around x axis and z axis but they ex-change with each other when the pile height is equal or largerthan 26m indicating that the torsional stiffness around zaxis decreases more rapidly As can be seen from Figure 7with the increase in pile height from 16m to 46m thefundamental frequency of the foundation significantly de-creases from 282Hz to 054Hz Although the fundamentalfrequency is still larger than the wave frequency that is009Hz the foundation with longer piles obviously becomesflexible and is easier to be affected by the wave

32 Structural Response with Different Pile LengthsUnder the action of the wave force the response of thefoundation with different pile lengths is analyzed usingANSYS software in the time domain As is discussed in theintroduction the foundation can be regarded as a cantileverstructure in the construction stage so the response of the capis the most obvious

-e results are shown in Figure 8 including the timeseries of the acceleration the velocity and the displacementat the top of the foundation As can be seen from the figurethe time series include two components the higher fre-quency response in the initial stage and the lower frequencyresponse in the stable stage which is particularly obvious inthe acceleration series -e further spectrum analysis on thetime series shows that the higher frequency is close to thefundamental frequency of the foundation while the lowerfrequency is consistent with the wave frequency -isphenomenon can be verified by the damped structure model

0 6 12 18

ndash06

ndash03

00

03

06

Wav

e for

ce o

n pi

le F

H (M

N)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

10 20 30 40 50

02

04

06

Max

imum

pile

forc

e fH

(MN

)

Pile height h (m)

(b)

Figure 5 Total wave force on a pile with different lengths (a) Time series (b) Maximum values

0 6 12 18ndash45

ndash30

ndash15

0

15

30

45

h = 16mh = 26mh = 36m

h = 40mh = 46m

Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)

88s

(a)

10 20 30 40 50

0

15

30

Max

imum

wav

e for

ce F

H (M

N)

Pile height h (m)

(b)

Figure 6 Total wave force on a cap with different pile lengths (a) Time series (b) Maximum values


analysis in structural dynamics Although the accelerationand velocity of the foundation vary greatly in the initialstage the vibration is largely attenuated in the stable stagebecause there is no external energy input -e followingstudy will focus the structural response in the stable stage

-e results show that the foundation with the pile lengthof 40m when the cap partly emerges from water is the mostsensitive to wave effects though the wave force on the capdecreases to some extent One reason is that the wave forceson the piles continue to increase and another reason is thefoundation further becomes flexible As a result the max-imum response of the foundation occurs in this situationMoreover the wave force on the cap is no longer consideredwhen it emerges from water completely and the time seriesof the acceleration and the velocity have multiple dominantfrequencies

Among the three parameters the displacement responseis the most intuitive parameter to evaluate the structuralstability under the wave It can be seen from Figure 8(c) thatthe amplitude of the displacement response of the cap in-creases from 146mm when the pile length is 16m to

395mm when the pile length is 40m but then decreases to271mm when the pile length is 46m For the piles themaximum displacements are observed at their tops and areapproximate to that of the cap due to the fixed connectionIn the following study therefore the displacement responseof the piles is omitted for brevity while the internal forceresponse at the bottom is further studied

-e research begins with the comparison of the internalforces at the bottom for different piles Taking the pile lengthof 16m as an example the peaks of the bending momentsand the shearing forces of piles 1ndash5 (Figure 2(a)) on theupstream side and piles 31ndash35 on the downstream side areshown in Figure 9 For different piles as there are phasedifferences in the wave forces the corresponding times whenthe internal forces reach their peaks are different -e waveforces on the piles located in the middle have smaller phasedifferences from that of the cap so these piles show higherinternal forces Among the ten piles it can be seen that pile35 has the maximum bending moment of 469MNmiddotm andthe maximum shearing force of 064MN Pile 1 has theminimum bending moment of 443MNmiddotm and the

h = 16m

Mode 1 (282Hz) Mode 2 (291Hz) Mode 3 (611Hz) Mode 4 (928Hz)





h = 26m

h = 36m

h = 40m

h = 46m

Figure 7 Dynamic characteristics of the foundations with different pile heights


minimum shearing force of 057MN Although Figure 9shows only one peak of the time series the results are typicalbecause the internal force changes periodically

Subsequently the internal forces at the bottom fordifferent pile lengths are compared Taking pile 1 as anexample the time series of the bending moments and theshearing forces for the five foundations with differentheights are shown in Figure 10 When the cap is totallysubmerged in water the amplitude of the internal forceincreases with the increase in pile length When the capemerges from water partly the amplitude of the internalforce decreases especially for the shearing force When thecap completely floats out of water surface and the pile lengthis 46m the shearing force is even less than the value with thepile length of 16m It can be seen that the maximum internal

force at the bottom is observed with the pile length of 36mwhile the maximum displacement at the top is observed withthe pile length of 40m In other words with the increase inpile length from 36m to 40m the displacement response isfurther enhanced though the internal force has decreasedwhich verifies the adverse effect of the decreasing stiffness ofthe foundation as discussed above

In summary the lower foundation with shorter pilesshows better mechanical performance and the wave-in-duced vibration is relatively small However the construc-tion of this type of foundations is more complex Forinstance the lower foundation may require a bigger cof-ferdam Such cofferdam also suffers from the wave andproduces extra loads on the foundation and an anchoringsystem may be necessary to keep the cofferdam stable With

0 20 40 60 80 100

ndash003

000

003

ndash008000

008

ndash021000021

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26mAcc

eler

atio

n a x

(ms

2 )

h = 36m

h = 40m

h = 46m

(a)

0 20 40 60 80 100

ndash006

000

006

ndash008000008

ndash018000018

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26m

Vel

ocity

ux (

ms

)

h = 36m

h = 40m

h = 46m

(b)

0 20 40 60 80 100 120

ndash40

ndash20

0

20

40

Cap

disp

lace

men

t Disp

x (m

m)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(c)

Figure 8 Response time series under the wave (a) Acceleration (b) Velocity (c) Displacement


404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

Pile 1Pile 2Pile 3Pile 4Pile 5


(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)

Figure 9 Internal forces of piles (a) Bending moment (b) Shearing force

0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)

Figure 10 Internal forces of the five foundations (a) Bending moment (b) Shearing force


the increase in pile length when the cap is close to or exceedssea level the difficulty in constructing the foundationmay bereduced to some extent However the higher foundationwith longer piles becomes more flexible and sensitive to thewave

4 Optimization of the Foundation

41 Structural Forms and Dynamic Characteristics To re-duce deepwater operations and effects on navigation thehigher foundation with longer piles seems to be moresuitable in deepwater areas with stronger waves However itcan be seen from the previous analysis that the increase inpile length makes the structural stiffness decrease and so dothe structural natural frequencies Under the action of thewave the dynamic response of the foundation is moreobvious Based on the understanding reducing the freelength of the pile may be favourable to improvement of thestructural stability and thereby three optimized forms arecompared Taking the foundation with the pile length of36m as an example the first scheme is to set another cap atthe center of the piles and is called the double caps foun-dation -e lower cap has a thickness of 80m and the samecross-sectional size with the upper cap -e finite elementmodel of the foundation adopts a double caps rigid framestructure However the wave force on the double capsfoundation increases as the lower cap also suffers from thewave In order to reduce the block area of the lower cap butnot seriously weakening the overall rigidity of the founda-tion the lower cap is divided into two separated caps withthe diameter of 332m As there are three separated capsincluding one upper cap and two lower caps this foundationis called the three caps foundation In the third scheme theseparated lower cap is replaced by the steel lattice structurewhich is installed among the piles and makes them into anintegrated whole to further reduce the block area and thisfoundation is called the joint piles foundation -e steellattice structure consists of many circular steel pipes with thediameter of 1m and a thickness of 18mm -e schemes ofthe three optimized foundations and the correspondingfinite element models are shown in Figure 11

-e dynamic characteristics of the first four modes arelisted in Table 1 -e results show that the added structurecould enhance the constraint on the foundation and improveits natural frequencies -e constraint effect of the doublecaps scheme is the most obvious for the increases in the firstfour frequencies are the largest with an average percentageincrease of 1117 -e three caps scheme with the averagepercentage increase of 944 takes the second place -ejoint piles scheme with the average percentage increase of206 has the weakest constraint effect For the first modecorresponding to the translation of the upper cap towards yaxis the frequency is gradually increased with the increase inconstraint effect -e improvement by the double capsscheme is the highest but it is slightly higher than that of thethree caps scheme -e trends of the second and the thirdmodes which correspond to the translation towards x axisand the rotation around z axis of the upper cap are similarwith that of the first mode In particular the lower cap in the

double caps scheme connects the left pile group and the rightpile group so it has strong constraint on the rotation aroundz axis and makes this modal to occur at a higher order Forthe fourth mode corresponding to the rotation of the uppercap around x axis the frequency is still increased by the threeoptimized schemes However the effect of the double capsscheme becomes limited and is even less than that of thejoint piles scheme -e probable reason is that the lower capin the double caps scheme has the constraint effect but thelarger mass placed at the middle position with the maximummodal displacement makes the modal frequency to decreaseat the same time

42 Wave Forces on Optimized Forms Since the three op-timized foundations are obtained by installing the extrastructures on the original foundation the wave forces on theextra structures should be determined before analyzing theirwave-induced response For the joint piles scheme the steellattice members have a smaller diameter and shorter lengthswhen compared with the piles or the cap so the wave forceson them are also smaller -e results show that the maxi-mum wave forces on the members whose axes are vertical tothe flow direction of water vary from 11 kN to 15 kN whilethe members whose axes are parallel to the flow directionreceive even less wave forces -erefore the wave force onthe steel lattice structure is ignored For the double caps andthe three caps scheme the wave forces on their lower capsare computed as shown in Figure 12 Specifically the upperand the lower caps in the double caps scheme have the samegeometric dimension so the wave forces on them have thesame phase but different amplitudes -e maximum waveforce on the lower cap is 1850MN and the maximum waveforce on the upper cap is 3229MN -e lower cap in thethree caps scheme consists of two separated caps named asthe upstream lower cap and the downstream lower capaccording to the flow direction As their values of DL areequal to 0196 and less than 02 the separated caps belong tosmall-scale structures and the Morison equation is suitableto calculate the wave forces on them -e maximum waveforce on each of the two separated caps is 1094MN but thetotal wave force has the maximum value of 138MN due tothe phase difference between the two caps In summaryalthough the structural fundamental frequency increases theoptimized foundation is subject to a larger wave force and itis necessary to understand which factor has more effects onthe structural stability

43 Structural Response with Different Forms -e wave-induced vibration of the optimized foundations is com-puted and the time series of their displacements bendingmoments and shearing forces are shown in Figure 13 Ascan be seen from the figure the higher frequency response isalso observed in the initial stage and it is close to thestructural fundamental frequency When the constrainteffect of the extra structure increases and so does thestructural fundamental frequency the higher frequencyresponse disappears gradually Figure 13(a) compares thedisplacement response of the foundations with different


forms at the tops As the stiffness is improved after addingthe lower cap or the steel lattice structure the displacementresponse of the optimized foundations significantly

decreases -e double caps foundation and the three capsfoundation have almost the same performance for dis-placement optimization and their percentage decreases ofthe maximum displacement are 862 and 859 re-spectively -e joint piles foundation has weak effects on thedisplacement suppression and its percentage decrease of themaximum displacement is 399 Figure 13(b) compares thebending moment response of pile 1 at the bottom withdifferent constraints -e optimized foundations effectivelysuppress their bending moments especially for the threecaps foundation with which the maximum bending momentdecrease from the original value of 206MNmiddotm to104MNmiddotm Although the double caps foundation has betterconstraint effects the larger wave force on the lower capincreases the maximum bending moment slightlyFigure 13(c) compares the shearing force response of pile 1at the bottom with different constraints However the threeoptimized foundations all show adverse effects on theirshearing forces-emaximum shearing force increases from118MN for the original scheme to 134MN for the jointpiles scheme 149MN for the three caps scheme and163MN for the double caps scheme Unlike the displace-ment and the bending moment response the stronger theconstraint effect on the foundation is the larger the shearingforce at the bottom becomes

180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)

Figure 11 Optimized foundations (unit m) (a) -e double caps foundation (b) -e three caps foundation (c) -e joint piles foundation

Table 1 Dynamic characteristics of the foundations with different forms

ModeFrequency (Hz) (modal shape)

Double caps foundation -ree caps foundation Joint piles foundation Original foundation1 187 (T-y axis) 186 (T-y axis) 099 (T-y axis) 080 (T-y axis)2 211 (T-x axis) 208 (T-x axis) 104 (T-x axis) 081 (T-x axis)3 408 (R-x axis) 338 (R-z axis) 241 (R-z axis) 193 (R-z axis)4 555 (R-y axis) 445 (R-x axis) 414 (R-x axis) 393 (R-x axis)T represents the translation of the upper cap towards x or y axis and R represents the rotation of the upper cap around x y or z axis

0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60

ree caps schemeUpstream lower capDownstream lower cap

Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)

Double caps schemeUpper capLower cap

Figure 12 Wave forces on different caps


Subsequently the changes in bending moment andshearing force along pile 1 are studied and the results for thethree optimized foundations are shown in Figure 14 For thedouble caps scheme and the three caps scheme due to theexistence of the lower cap the pile can be regarded as twoparts the upper one between the upper cap and the lowercap and the lower one between the lower cap and the groundEach part can be regarded a member consolidated at its two

sides where the internal forces are the maximum and theminimum respectively -e bending moments at the twosides are opposite and change the sign in the middle po-sition while the shearing forces have the same sign -ebending moment of the lower part is larger than that of theupper part -e shearing force of the lower part is also largerdue to the existence of the lower cap which increases thewave force on the foundation For the joint piles scheme

0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)

Single capDouble caps

ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)

Figure 13 Response of different foundations (a) Displacement (b) Bending moment (c) Shearing force


however the distributions of the bending moment and theshearing force along the pile are different It seems that thesteel lattice structure provides an articulated constraint on thepiles as the bending moment in this region is close to zero

5 Conclusions

-is paper investigates the wave-induced response of a pilegroup foundation in deepwater area to improve the

structural stability at the construction stage -e effects ofthe pile length and the structural form on the displacementand internal force of the foundation are studied and thefollowing main conclusions are made

(1) For a determined water depth the wave force on apile increases with the increase in its length and theincreasing range of the former is obviously largerthan that of the latter Meanwhile the wave force on

0

10

20

30

40

Lower cap Lower cap

Pile Pile

ndash10 ndash5 0 5 10Bending moment Mz (MNmiddotm) Sharing force FxMN

Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile

0Bending moment Mz (MNmiddotm)

Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40

ndash10 ndash5 5 100

10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile

Steel lattice Steel lattice

Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx

Bending moment Mz (MNmiddotm)

0

10

20

30

40

ndash12 ndash6 0 6 120

10

20

30

40


(c)

Figure 14 Comparison of internal forces on different foundations (a) Double caps foundation (b) -ree caps foundation (c) Joint pilesfoundation


the cap also increases before it emerges from waterand is larger than the total wave force on the 38 pilesOn the contrary the foundation with longer pilesobviously becomes flexible and its natural frequenciessignificantly decrease though the fundamental fre-quency is still larger than the wave frequency

(2) -e lower foundation with shorter piles shows bettermechanical performance -e wave-induced re-sponse of the foundation including the displacementand the internal force is relatively small but itsconstruction may be more complex -e higherfoundation with longer piles is convenient to theconstruction As the wave force increases and thenatural frequencies decrease the foundation be-comes more sensitive to the wave especially when itscap partly emerges from water

(3) All piles of the foundation have the same maximumdisplacement at the top where they are constrainedby the rigid cap but the time series of the internalforces have different amplitudes and phases -einternal force of a pile is larger when the wave forceon the pile has a smaller phase difference from that ofthe cap Setting a whole lower cap two separatedlower caps or a steel lattice in the middle height ofthe foundation can reduce the free length of the pileand improve the structural frequencies to varyingdegrees -e lower cap and the steel lattice providethe consolidated constraint and the articulatedconstraint on the piles respectively Apparently thelower cap has stronger constraint effects and de-creases the displacement and the bending momentresponse of the foundation effectively However thewave force on the lower cap increases which en-hances the shearing force response

(4) -e study mainly focuses the wave-induced responseof the foundation itself while the practical con-struction conditions need to be considered as wellwhen determining structural forms of pile groupfoundations of deepwater bridges

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 that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-e authors are grateful for the financial supports from theNational Natural Science Foundation of China (51525804)

References

[1] C Fang Y Li K Wei J Zhang and C Liang ldquoVehicle-bridgecoupling dynamic response of sea-crossing railway bridge

under correlated wind and wave conditionsrdquo Advances inStructural Engineering vol 22 no 4 pp 893ndash906 2019

[2] H Tang K M Shum and Y Li ldquoInvestigation of flutterperformance of a twin-box bridge girder at large angles ofattackrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 186 pp 192ndash203 2019

[3] G B Airy Tides and Waves Vol 5 Encyclopedia Metro-politan London UK 1845

[4] G Stokes ldquoOn the theory of oscillatory wavesrdquo in Trans-actions of the Cambridge Philosophical Society vol 8 no 310pp 441ndash473 1880

[5] T Sarpkaya M Isaacson and J V Wehausen Mechanics ofWave Forces on Offshore Structures Van Nostrand ReinholdCo New York NY USA 1981

[6] M M Larmaei and T-F Mahdi ldquoSimulation of shallow waterwaves using VOF methodrdquo Journal of Hydro-EnvironmentResearch vol 3 no 4 pp 208ndash214 2010

[7] R G Dean and R A Dalrymple Water Wave Mechanics forEngineers and Scientists Prentice-Hall Upper Saddle RiverNJ USA 1984

[8] G H Keulegan ldquoSpatially variable discharge over a slopingplanerdquo Transactions American Geophysical Union vol 25no 6 pp 956ndash959 1944

[9] J B Keller A D D Craik J T Stuart P L Christiansen andR K Bullough ldquoSoliton generation and nonlinear wavepropagationrdquo Philosophical Transactions of the Royal SocietyA Mathematical Physical and Engineering Sciences vol 315no 1533 pp 367ndash377 1985

[10] Y Xu X Xia and JWang ldquoCalculation and approximation ofthe cnoidal function in cnoidal wave theoryrdquo Computers ampFluids vol 68 pp 244ndash247 2012

[11] P De Palma M D de Tullio G Pascazio and M NapolitanoldquoAn immersed-boundary method for compressible viscousflowsrdquo Computers amp Fluids vol 35 no 7 pp 693ndash702 2006

[12] A Sawicki and R Staroszczyk ldquoWave-induced stresses andpore pressures near a mudlinerdquo Oceanologia vol 50 no 4pp 539ndash555 2008

[13] J R Morison J W Johnson and S A Schaaf ldquo-e forceexerted by surface waves on pilesrdquo Journal of PetroleumTechnology vol 2 no 5 pp 149ndash154 1950

[14] R C MacCamy and R A Fuchs ldquoWave forces on piles adiffraction theoryrdquo Report No 69 US Army Corps of En-gineers Beach Erosion Board Washington DC USA 1954

[15] F Liu S Gao H Han Z Tian and P Liu ldquoInterferencereduction of high-energy noise for modal parameter identi-fication of offshore wind turbines based on iterative signalextractionrdquo Ocean Engineering vol 183 pp 372ndash383 2019

[16] B Y Dagli Y Tuskan and U Gokkus ldquoEvaluation of offshorewind turbine tower dynamics with numerical analysisrdquo Ad-vances in Civil Engineering vol 2018 Article ID 305485111 pages 2018

[17] S Adhikari and S Bhattacharya ldquoDynamic analysis of windturbine towers on flexible foundationsrdquo Shock and Vibrationvol 19 no 1 pp 37ndash56 2012

[18] R Zhang Y Tang J Hu S Ruan and C Chen ldquoDynamicresponse in frequency and time domains of a floatingfoundation for offshore wind turbinesrdquo Ocean Engineeringvol 60 pp 115ndash123 2013

[19] K Wei S R Arwade and A T Myers ldquoIncremental wind-wave analysis of the structural capacity of offshore windturbine support structures under extreme loadingrdquo Engi-neering Structures vol 79 pp 58ndash69 2014

[20] P Wang M Zhao X Du J Liu and C Xu ldquoWind wave andearthquake responses of offshore wind turbine on monopile


foundation in clayrdquo Soil Dynamics and Earthquake Engi-neering vol 113 pp 47ndash57 2018

[21] E Bachynski M-ys and V Delhaye ldquoDynamic response ofa monopile wind turbine in waves experimental uncertaintyanalysis for validation of numerical toolsrdquo Applied OceanResearch vol 89 pp 96ndash114 2019

[22] J Sarmiento A Iturrioz V Ayllon R Guanche andI J Losada ldquoExperimental modelling of a multi-use floatingplatform for wave and wind energy harvestingrdquo Ocean En-gineering vol 173 pp 761ndash773 2019

[23] X Wu Y Hu Y Li et al ldquoFoundations of offshore windturbines a reviewrdquo Renewable and Sustainable Energy Re-views vol 104 pp 379ndash393 2019

[24] K Wei W Yuan and N Bouaanani ldquoExperimental andnumerical assessment of the three-dimensional modal dy-namic response of bridge pile foundations submerged inwaterrdquo Journal of Bridge Engineering vol 18 no 10pp 1032ndash1041 2013

[25] T J Ingham S Rodriguez R Donikian and J Chan ldquoSeismicanalysis of bridges with pile foundationsrdquo Computers ampStructures vol 72 no 1-3 pp 49ndash62 1999

[26] S S AbdelSalam S Sritharan and M T Suleiman ldquoCurrentdesign and construction practices of bridge pile foundationswith emphasis on implementation of LRFDrdquo Journal of BridgeEngineering vol 15 no 6 pp 749ndash758 2010

[27] C Liu S Zhang and E Hao ldquoJoint earthquake wave andcurrent action on the pile group cable-stayed bridge towerfoundation an experimental studyrdquo Applied Ocean Researchvol 63 pp 157ndash169 2017

[28] S-x Liu Y-c Li and G-w Li ldquoWave current forces on thepile group of base foundation for the east sea bridge ChinardquoJournal of Hydrodynamics vol 19 no 6 pp 661ndash670 2007

[29] W-J Yao W-X Yin J Chen and Y-Z Qiu ldquoNumericalsimulation of a super-long pile group under both vertical andlateral loadsrdquo Advances in Structural Engineering vol 13no 6 pp 1139ndash1151 2010

[30] Y Deng Q Guo and L Xu ldquoExperimental and numericalstudy on modal dynamic response of water-surroundedslender bridge pier with pile foundationrdquo Shock and Vibra-tion vol 2017 Article ID 4769637 20 pages 2017

[31] Y Deng Q Guo Y I Shah and L Xu ldquoStudy on modaldynamic response and hydrodynamic added mass of water-surrounded hollow bridge pier with pile foundationrdquo Ad-vances in Civil Engineering vol 2019 Article ID 156275323 pages 2019

[32] L Deng W Yang Q Li and A Li ldquoCFD investigation of thecap effects on wave loads on piles for the pile-cap foundationrdquoOcean Engineering vol 183 pp 249ndash261 2019

[33] L Ya C Zekun and N Qinqin ldquoDynamic response of pile-cap structure under random sea wave actionrdquo Procedia En-gineering vol 116 pp 1027ndash1035 2015

[34] K Tomisawa and M Kimura ldquoNew technology on seismicreinforcement of pile foundation for long life bridgesrdquo Pro-cedia Engineering vol 171 pp 1035ndash1042 2017

[35] Z H Wang R Q Xi and G X Chen ldquoState of arts onresponse of bridge of pile foundation under earthquake ex-citationrdquo Journal of Nanjing University of Technology (NaturalScience Edition) vol 31 no 1 pp 106ndash112 2009 in Chinese

[36] A G Sextos G E Mylonakis and E-K V Mylona ldquoRota-tional excitation of bridges supported on pile groups in soft orliquefiable soil depositsrdquo Computers amp Structures vol 155pp 54ndash66 2015

[37] B Le Mehaute An Introduction to Hydrodynamics and WaterWaves Springer New York NY USA 1976

[38] CCCC First Harbor Consultants Co Ltd JTS 145-2015 Codeof Hydrology for Harbor and Waterway China Communi-cations Press Co Ltd Beijing China 2015 in Chinese


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



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



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

-e motion of waves was also described using the ellipticalcosine wave theory [7] On the basis of this the theory wasfurther studied by other scholars and engineers so that it canbe better applied in practice [8ndash10]With the development ofcomputer technology the numerical simulation becomes aneffective way to achieve the target [6 11 12] As for thecomputation of fluid-structure interaction the methodproposed by Morison et al [13] is used for calculating thewave force on the small-scale structure while the theory ofdiffraction put forward by MacCamy and Fuchs [14] is usedfor the large-scale structure

-e dynamic response of offshore structures hasattracted great attention of designers and scholars especiallyfor offshore wind turbines [15 16] Wave loads acting on thelower part below the water surface and wind loads acting onthe upper part above the water surface play important rolesAdhikari and Bhattacharya [17] showed that the naturalfrequency of the turbine tower decreases with the decrease instiffness of the foundation and the increase in axial loadZhang et al [18] investigated the dynamic response of afloating foundation of a turbine in 60m deepwater andpointed out that the semisubmersible floating foundationcan work with significant wave height less than 4m Weiet al [19] computed the capacity of monopile- and jacket-supported wind turbines and found that structural responsecan be dominated by either the wind or the wave dependingon structural characteristics and site conditions Wang et al[20] studied the dynamic response of a monopile-supportedwind turbine subjected to wind wave and earthquake ac-tions and indicated that it is necessary to consider thecombination of the three actions in the design of such aturbine Bachynski et al [21] further studied the response ofa monopile-supported wind turbine subjected to irregularwave loads and the experimental results highlighted theresonant response of the monopile when subjected to severewave loads Sarmiento et al [22] validated a multiusefloating platform which combines wave energy convertersand wind harvesting Wu et al [23] discussed geotechnicaland structural issues affecting the foundation of the offshorewind turbine It is concluded that the foundation presentsone of the main challenges in the design

-e bridge foundation has a variety of forms such as thecaisson foundation the tube caisson foundation and theopen caisson foundation When the water is deep the pilefoundation which consists of a group of bored pilesextending to soil at the bottom and connected to a large capat the top has widely been used owing to its convenientconstruction and good adaptability [24ndash26] However it isdifficult to model the precise dynamic response of the pilefoundation under various dynamic loads due to large di-mensions structural complexity and three-dimensionalcharacteristics [27] On the basis of the bridge foundationdesigned for the East Sea Bridge Liu et al [28] investigatedthe wave current forces on the pile foundation and examinedthe group effectiveness and the reduction coefficient forengineering design Yao et al [29] numerically simulated asuper-long pile foundation in stratified soils under bothvertical and lateral loads and concluded that the sleeved pilegroup can significantly reduce the horizontal displacement

Deng et al [30] experimentally studied the effect of fluid-structure interaction on the modal dynamic response of abridge pier supported by the pile foundation and found thatthe effect increases with the rise in water level especiallywhen the pier body is submerged in water Deng et al [31]further experimentally studied the modal dynamic responseof a hollow bridge pier with the pile foundation submergedin water and provided better understanding of the effect offluid-structure interaction Deng et al [32] investigated thecap effect on wave loads on piles and the force-increasingeffect on piles was observed when the relative cap dimensionis small In addition Ya et al [33] found that the dynamicresponse of a pile-cap structure under random sea waveaction is the largest Tomisawa and Kimura [34] proposednew techniques to improve seismic performance of the pilefoundation for long life bridges -e seismic excitation onthe pile foundation was also considered in some studies[35 36]

-e aforementioned studies have improved our un-derstanding of the dynamic response of the pile foundationbut optimization on the form has not yet been fully exploredWith long-span bridges extending to deeper sea areas thelength of the pile has to be increased leading to more slenderand flexible foundations To reduce the structural dynamicresponse optimization on the pile foundation with longerpiles becomes important Taking a long-span deepwaterbridge into account this paper studies the wave-inducedresponse of a pile group foundation using ANSYS softwareand further optimizes the structural form -e main contentis organized as follows -e wave loads on the piles and capof the foundation are computed in Section 2 Five finiteelement models with different pile lengths are establishedand their wave-induced vibration is compared and discussedin Section 3 After determining the relationship between thedynamic response and the pile length the foundation isoptimized with different structural forms in Section 4 andthe effectiveness is evaluated by comparing the changes inthe dynamic characteristics including the caprsquos displace-ment and the pilesrsquo internal forces Finally some mainconclusions are drawn in Section 5 providing reference foroptimization on pile foundations of deepwater bridges

2 Wave Force on the Foundation

21 Case Description -e engineering background of thepaper is a deepwater long-span cable-stayed bridge with atotal length of 1188m and its main span length is 532m-eoverall layout is shown in Figure 1-e measured data of thebridge location show that in a-hundred-year return periodthe wave on the transverse bridge direction has the maxi-mum heightH of 969m-e wave period T is 108 s and thewave circle frequency ω 0581 rads According to thedispersion relation the wavelength is about 169m -edensity of seawater ρ takes 1000 kgm3 and the water depthd is considered as 45m after flushing

-e bridge is supported by six pile group foundationsmarked with N01simN06 among which N03 and N04 are themain ones Each of the six pile foundations consists of agroup of piles and a cap on the top (Figure 1) In particular




ux zΦzx

πH

T

cosh k(z + d)


ax zux

zt2π2H

T2cosh k(z + d)





fH fD + fI 12

CDρAux ux

11138681113868111386811138681113868111386811138681113868 + CMρV0

dux

dt (3)




532 1961188

132196132

N01 N02 N03 N04 N05 N06








FH(z) minus2ρgH

k

cosh kz


A(ka) 1

J1prime(ka)1113858 11138592

+ Y1prime(ka)1113858 11138592

1113969 (5)

tan α J1prime(ka)

Y1prime(ka) (6)


166

62

62

42

332

46 58 62 58 120 100 30662

812

180 x

y

Wave direction

1

2 3 4

6 7 85

9 19 1011

16 17 1815

12 13 14

21

222324

26272825

29203031

36373835

323334

(a)

h=

16m

h=

26m

h=

36m

h=

40m

h=

46m

d =

45m

(b)







dz

x

z

z

Wave direction

fH

a adz

x

z

z

Wave direction

x

z

d Wave direction


(a)



(b)

(c)


0

2

4

6

8

10

12

14

16

8 9 10 11 12FH (kNm)

t = 81sDist

ance

to th

e sea

bed

(zm

)



(a) (b) (c)

0 5 10 15 20

ndash10

0

10

fD (z = 16m)

fI (z = 16m)

Hor

izon

tal w

ave f

orce

f H (k

Nm

)

Time t (s)

z = 16mz = 10m z = 5m

81s






0 6 12 18

ndash06

ndash03

00

03

06

Wav

e for

ce o

n pi

le F

H (M

N)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

10 20 30 40 50

02

04

06

Max

imum

pile

forc

e fH

(MN

)

Pile height h (m)

(b)


0 6 12 18ndash45

ndash30

ndash15

0

15

30

45

h = 16mh = 26mh = 36m

h = 40mh = 46m

Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)

88s

(a)

10 20 30 40 50

0

15

30

Max

imum

wav

e for

ce F

H (M

N)

Pile height h (m)

(b)








h = 16m






h = 26m

h = 36m

h = 40m

h = 46m







0 20 40 60 80 100

ndash003

000

003

ndash008000

008

ndash021000021

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26mAcc

eler

atio

n a x

(ms

2 )

h = 36m

h = 40m

h = 46m

(a)

0 20 40 60 80 100

ndash006

000

006

ndash008000008

ndash018000018

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26m

Vel

ocity

ux (

ms

)

h = 36m

h = 40m

h = 46m

(b)

0 20 40 60 80 100 120

ndash40

ndash20

0

20

40

Cap

disp

lace

men

t Disp

x (m

m)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(c)



404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)



(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)


0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)













180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




ux zΦzx

πH

T

cosh k(z + d)


ax zux

zt2π2H

T2cosh k(z + d)





fH fD + fI 12

CDρAux ux

11138681113868111386811138681113868111386811138681113868 + CMρV0

dux

dt (3)




532 1961188

132196132

N01 N02 N03 N04 N05 N06








FH(z) minus2ρgH

k

cosh kz


A(ka) 1

J1prime(ka)1113858 11138592

+ Y1prime(ka)1113858 11138592

1113969 (5)

tan α J1prime(ka)

Y1prime(ka) (6)


166

62

62

42

332

46 58 62 58 120 100 30662

812

180 x

y

Wave direction

1

2 3 4

6 7 85

9 19 1011

16 17 1815

12 13 14

21

222324

26272825

29203031

36373835

323334

(a)

h=

16m

h=

26m

h=

36m

h=

40m

h=

46m

d =

45m

(b)







dz

x

z

z

Wave direction

fH

a adz

x

z

z

Wave direction

x

z

d Wave direction


(a)



(b)

(c)


0

2

4

6

8

10

12

14

16

8 9 10 11 12FH (kNm)

t = 81sDist

ance

to th

e sea

bed

(zm

)



(a) (b) (c)

0 5 10 15 20

ndash10

0

10

fD (z = 16m)

fI (z = 16m)

Hor

izon

tal w

ave f

orce

f H (k

Nm

)

Time t (s)

z = 16mz = 10m z = 5m

81s






0 6 12 18

ndash06

ndash03

00

03

06

Wav

e for

ce o

n pi

le F

H (M

N)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

10 20 30 40 50

02

04

06

Max

imum

pile

forc

e fH

(MN

)

Pile height h (m)

(b)


0 6 12 18ndash45

ndash30

ndash15

0

15

30

45

h = 16mh = 26mh = 36m

h = 40mh = 46m

Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)

88s

(a)

10 20 30 40 50

0

15

30

Max

imum

wav

e for

ce F

H (M

N)

Pile height h (m)

(b)








h = 16m






h = 26m

h = 36m

h = 40m

h = 46m







0 20 40 60 80 100

ndash003

000

003

ndash008000

008

ndash021000021

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26mAcc

eler

atio

n a x

(ms

2 )

h = 36m

h = 40m

h = 46m

(a)

0 20 40 60 80 100

ndash006

000

006

ndash008000008

ndash018000018

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26m

Vel

ocity

ux (

ms

)

h = 36m

h = 40m

h = 46m

(b)

0 20 40 60 80 100 120

ndash40

ndash20

0

20

40

Cap

disp

lace

men

t Disp

x (m

m)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(c)



404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)



(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)


0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)













180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






FH(z) minus2ρgH

k

cosh kz


A(ka) 1

J1prime(ka)1113858 11138592

+ Y1prime(ka)1113858 11138592

1113969 (5)

tan α J1prime(ka)

Y1prime(ka) (6)


166

62

62

42

332

46 58 62 58 120 100 30662

812

180 x

y

Wave direction

1

2 3 4

6 7 85

9 19 1011

16 17 1815

12 13 14

21

222324

26272825

29203031

36373835

323334

(a)

h=

16m

h=

26m

h=

36m

h=

40m

h=

46m

d =

45m

(b)







dz

x

z

z

Wave direction

fH

a adz

x

z

z

Wave direction

x

z

d Wave direction


(a)



(b)

(c)


0

2

4

6

8

10

12

14

16

8 9 10 11 12FH (kNm)

t = 81sDist

ance

to th

e sea

bed

(zm

)



(a) (b) (c)

0 5 10 15 20

ndash10

0

10

fD (z = 16m)

fI (z = 16m)

Hor

izon

tal w

ave f

orce

f H (k

Nm

)

Time t (s)

z = 16mz = 10m z = 5m

81s






0 6 12 18

ndash06

ndash03

00

03

06

Wav

e for

ce o

n pi

le F

H (M

N)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

10 20 30 40 50

02

04

06

Max

imum

pile

forc

e fH

(MN

)

Pile height h (m)

(b)


0 6 12 18ndash45

ndash30

ndash15

0

15

30

45

h = 16mh = 26mh = 36m

h = 40mh = 46m

Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)

88s

(a)

10 20 30 40 50

0

15

30

Max

imum

wav

e for

ce F

H (M

N)

Pile height h (m)

(b)








h = 16m






h = 26m

h = 36m

h = 40m

h = 46m







0 20 40 60 80 100

ndash003

000

003

ndash008000

008

ndash021000021

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26mAcc

eler

atio

n a x

(ms

2 )

h = 36m

h = 40m

h = 46m

(a)

0 20 40 60 80 100

ndash006

000

006

ndash008000008

ndash018000018

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26m

Vel

ocity

ux (

ms

)

h = 36m

h = 40m

h = 46m

(b)

0 20 40 60 80 100 120

ndash40

ndash20

0

20

40

Cap

disp

lace

men

t Disp

x (m

m)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(c)



404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)



(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)


0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)













180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






dz

x

z

z

Wave direction

fH

a adz

x

z

z

Wave direction

x

z

d Wave direction


(a)



(b)

(c)


0

2

4

6

8

10

12

14

16

8 9 10 11 12FH (kNm)

t = 81sDist

ance

to th

e sea

bed

(zm

)



(a) (b) (c)

0 5 10 15 20

ndash10

0

10

fD (z = 16m)

fI (z = 16m)

Hor

izon

tal w

ave f

orce

f H (k

Nm

)

Time t (s)

z = 16mz = 10m z = 5m

81s






0 6 12 18

ndash06

ndash03

00

03

06

Wav

e for

ce o

n pi

le F

H (M

N)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

10 20 30 40 50

02

04

06

Max

imum

pile

forc

e fH

(MN

)

Pile height h (m)

(b)


0 6 12 18ndash45

ndash30

ndash15

0

15

30

45

h = 16mh = 26mh = 36m

h = 40mh = 46m

Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)

88s

(a)

10 20 30 40 50

0

15

30

Max

imum

wav

e for

ce F

H (M

N)

Pile height h (m)

(b)








h = 16m






h = 26m

h = 36m

h = 40m

h = 46m







0 20 40 60 80 100

ndash003

000

003

ndash008000

008

ndash021000021

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26mAcc

eler

atio

n a x

(ms

2 )

h = 36m

h = 40m

h = 46m

(a)

0 20 40 60 80 100

ndash006

000

006

ndash008000008

ndash018000018

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26m

Vel

ocity

ux (

ms

)

h = 36m

h = 40m

h = 46m

(b)

0 20 40 60 80 100 120

ndash40

ndash20

0

20

40

Cap

disp

lace

men

t Disp

x (m

m)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(c)



404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)



(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)


0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)













180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





0 6 12 18

ndash06

ndash03

00

03

06

Wav

e for

ce o

n pi

le F

H (M

N)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

10 20 30 40 50

02

04

06

Max

imum

pile

forc

e fH

(MN

)

Pile height h (m)

(b)


0 6 12 18ndash45

ndash30

ndash15

0

15

30

45

h = 16mh = 26mh = 36m

h = 40mh = 46m

Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)

88s

(a)

10 20 30 40 50

0

15

30

Max

imum

wav

e for

ce F

H (M

N)

Pile height h (m)

(b)








h = 16m






h = 26m

h = 36m

h = 40m

h = 46m







0 20 40 60 80 100

ndash003

000

003

ndash008000

008

ndash021000021

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26mAcc

eler

atio

n a x

(ms

2 )

h = 36m

h = 40m

h = 46m

(a)

0 20 40 60 80 100

ndash006

000

006

ndash008000008

ndash018000018

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26m

Vel

ocity

ux (

ms

)

h = 36m

h = 40m

h = 46m

(b)

0 20 40 60 80 100 120

ndash40

ndash20

0

20

40

Cap

disp

lace

men

t Disp

x (m

m)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(c)



404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)



(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)


0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)













180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







h = 16m






h = 26m

h = 36m

h = 40m

h = 46m







0 20 40 60 80 100

ndash003

000

003

ndash008000

008

ndash021000021

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26mAcc

eler

atio

n a x

(ms

2 )

h = 36m

h = 40m

h = 46m

(a)

0 20 40 60 80 100

ndash006

000

006

ndash008000008

ndash018000018

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26m

Vel

ocity

ux (

ms

)

h = 36m

h = 40m

h = 46m

(b)

0 20 40 60 80 100 120

ndash40

ndash20

0

20

40

Cap

disp

lace

men

t Disp

x (m

m)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(c)



404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)



(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)


0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)













180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0 20 40 60 80 100

ndash003

000

003

ndash008000

008

ndash021000021

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26mAcc

eler

atio

n a x

(ms

2 )

h = 36m

h = 40m

h = 46m

(a)

0 20 40 60 80 100

ndash006

000

006

ndash008000008

ndash018000018

ndash018000018

ndash008

000

008

Time t (s)

h = 16m

h = 26m

Vel

ocity

ux (

ms

)

h = 36m

h = 40m

h = 46m

(b)

0 20 40 60 80 100 120

ndash40

ndash20

0

20

40

Cap

disp

lace

men

t Disp

x (m

m)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(c)



404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)



(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)


0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)













180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


404 408 412 416 420 424

44

45

46

47

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)



(a)

240 248 256 264 272050

055

060

065

Shea

ring

forc

e Fx

(MN

)

Time t (s)



(b)


0 20 40 60 80 100 120ndash30

ndash20

ndash10

0

10

20

Bend

ing

mom

ent M

z (M

Nmiddotm

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(a)

0 20 40 60 80 100 120ndash15

ndash10

ndash05

00

05

10

15

Shea

ring

forc

e Fx (

MN

)

Time t (s)

h = 16mh = 26mh = 36m

h = 40mh = 46m

(b)













180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












180

80

360

75

812

FEM

X

Y

Z

(a)

75

180

80

360

330 8122

FEM

X

Y

Z

(b)

180

360

812

80

75

FEM

X

Y

Z

(c)





0 3 6 9 12 15 18 21ndash60

ndash40

ndash20

0

20

40

60


Wav

e for

ce o

n ca

p F H

(MN

)

Time t (s)






0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0 20 40 60 80 100ndash40

ndash20

0

20

40

Disp

lace

men

t Disp

x (m

m)

Time t (s)


ree capsJoint piles

(a)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash30

ndash20

ndash10

0

10

20

30

Bend

ing

mom

ent M

z (M

Nmiddotm

)

(b)

Time t (s)


ree capsJoint piles

0 20 40 60 80 100ndash2

ndash1

0

1

2

Shea

ring

forc

e Fx

(MN

)

(c)




5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



5 Conclusions




0

10

20

30

40

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz Fx

0

10

20

30

40

ndash2 ndash1 0 1 2

(a)

Lower cap Lower cap

Pile Pile


Hei

ght z

(m)

Hei

ght z

(m)

Mz

Sharing force FxMN

Fx

0

10

20

30

40


10

20

30

40

ndash2 ndash1 0 1 2

(b)

Pile


Pile

Hei

ght z

(m)

Hei

ght z

(m)

Sharing force FxMN

Mz Fx


0

10

20

30

40


10

20

30

40


(c)







Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Data Availability




Acknowledgments


References













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


improvement on structural forms of pile group foundations...

Documents