Research ArticleDisplacement Calculation Method on Front Wall of CoveredSheet-Pile Wharf

Wen-xue Gong Li-yan Wang Jinsong Li and Bing-hui Wang

School of Civil and Architectural Engineering Jiangsu University of Science and Technology No 2 Mengxi Road ZhenjiangJiangsu Province China

Correspondence should be addressed to Li-yan Wang wly_yzu163com

Received 27 May 2018 Revised 1 November 2018 Accepted 18 November 2018 Published 24 December 2018

Academic Editor Hugo Rodrigues

Copyright copy 2018Wen-xueGong et alis is an open access article distributed under theCreative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Covered sheet-pile wharves are widely used in port engineering water conservancy and civil engineering is paper is based onthe theory of earth pressure and the soil arching effect According to the stress and deformation characteristics of the coveredsheet-pile wharf the formulas used to calculate the force and deformation of the front wall of a covered sheet-pile wharf understatic loads are deduced e accuracy of the theoretical derivation is verified by comparing actual measured stress and de-formation data of Jingtang Port 32 e comparison shows that when calculating the displacement of the section below the mudsurface boundary the results are in agreement with the in situ data However when calculating the displacement of the sectionabove the mud surface boundary if the anchorage point displacement is ignored because the anchorage point displacement islimited artificially the calculated tension of the tie rod is relatively largeis leads to a significant decrease in the calculation resultof the section above the mud surface boundary which is very different from actual in situ measurement results If anchorage pointdisplacement is considered the calculated tension of the tie rod is more accurate and the calculation results of the front walldisplacement are very close to in situ measurement results because the anchorage point displacement is assumed scientifically

1 Introduction

To develop sheet-pile wharves for deep water and large berthsChina Railway First Survey and Design Institute has designedand researched wharves for many years proposed a new typeof covered sheet-pile wharf in 2002 and successfully built a100 thousand ton deep-water berth wharf [1]

Sheet-pile wharf structures include front sheet-pile wallscovered piles anchorage walls tie rods and wharf equipmente structure of a sheet-pile wharf is shown in Figure 1 It ischaracterized by adding a row of reinforced concrete cast-in-place piles [2] which is the covered pile between the frontwalls and anchorage walls e distance between the frontsheet-pile walls is 3sim5m Usually covered piles are arrangedin intervals Front sheet-pile walls covered piles and an-chorage walls are connected as a whole structure by front andrear tie rodse existence of covered piles resists soil pressurebehind the wall and reduces the soil pressure acting directlyon the front sheet-pile walls Relevant studies have shown thatunder normal design conditions covered piles reduce the

positive and negative bending moment of front walls byapproximately 70 and 10 respectively and do not have agreat influence on anchorage wall forces [3] e applicationand development of the new type of covered sheet-pile wharfprovides technical feasibility for developing sheet-pilewharves for deep water [4] Researchers have made greatefforts to research seismic analysis of anchored sheet-pilewharf walls [6ndash8] Several theories and findings on the seismicanalysis of sheet-pile wharves have been developed over thelast several decades through experiments with shaking tabletests [6 8 9ndash11] A fundamental study on the simple eval-uation method of the seismic performance of sheet-pile quaywalls with vertical pile anchorage against level-one earthquakeground motion was proposed [12] e phenomenon of thelarge deformation of the sheet-pile quay wall and the failure ofpile foundation due to liquefaction-induced lateral spreadingin a port area were investigated [13ndash15] An optimizationmodel for predicting the lateral displacement caused byliquefaction was formed by Kalantary [16] Mitigation mea-sures can be taken for pile groups behind quay walls subjected

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 5037057 13 pageshttpsdoiorg10115520185037057

to lateral ow of liqueed soil [17] e transfer formula forthe horizontal thrust acting on the plane of covered sheet pileon land can be derived [17 18] Unfortunately at presentresearch on covered sheet-pile wharf structures is supercialTo date there are no systematic reasonable practical cal-culation method theories erefore research on coveredsheet-pile wharf structures has signicant practical value

In this paper front wall displacement calculation wasdeduced theoretically based on the Winkler hypothesis Soilpressure and displacement formulas of front sheet-pile wallsin the deep part of the soil are calculated using the ldquomrdquomethod under static loads Front sheet-pile walls in sheet-pile wharf forces were calculated according to the activeearth pressure theory e soil arching eect theory wascombined with the lateral pressure coecient values ofparallel wall soil by doctoral student Jiang [19] and the stresson the front walls of covered sheet-pile wharves was cal-culated Displacement formulas for the deformation of thefront walls of a sheet-pile wharf under static load werederived based on the deection curve equation and de-formation characteristics of the material mechanics

Finally using a relatively mature theory of static earthpressure and soil arching eect theory displacement formulasfor the front wall of a covered sheet-pile wharf under staticload are deduced and are compared with in situ observationdata of the Jingtang Port 10 berth wharf and the Jingtang Port32 wharf to verify the accuracy of the theoretical derivation

2 Winklerrsquos Assumption

In the elastic foundation reaction method based on Win-klerrsquos assumption pile calculation assumes the ground re-action force p is proportional to the n-th power of the piledisplacement y that is

p K(h)yn (1)

where y is the lateral deection of the pile calculation point(m) h is the depth of the pile calculation point (m) andK(h) is the ground coecient

Matlock and Rees [20] noted that the ground coecientK(h) should be as simple as possible and two kinds ofrelations are suggested namely

K(h) mhq (2)

K(h) m0 +m1h +m2h2 (3)

Currently according to some measured data and fromthe perspective of practicality and convenient analysis thefoundation coecient K(h) is considered to change with apower-law function with depth h consistent with the actualdepth that is

K(h) m h0 + h( )a (4)

wherem is the proportional coecient while the foundationcoecient varies with depth a is the pure values that changewith rock type [21ndash24] and h0 is a constant related to thecategory of rock soil e values of m a and h must bedetermined by experiments According to the dierentvalues of a the law of foundation coecient changing withdepth in equation (1) can be drawn as shown in Figure 2

3 Displacement Calculation of Front Wall

31 Simplied Calculation Model and Earth Pressure AreaDistribution of Covered Sheet-Pile Wharf Structure ecovered sheet-pile wharf calculation model is composed offront sheet-pile walls covered piles anchorage walls andfront and rear tie rods as shown in Figure 3 When cal-culating earth pressure the soils are assumed to be in limitequilibrium while the eect of wave force is not considered

e largest dierence between the covered sheet-pilewharf and the conventional sheet-pile wharf structure is thatcovered piles are set up between the front walls and an-chorage walls and covered piles resist the soil behind thepiles and decrease the earth pressure loaded directly on thefront walls To analyse the eects of covered piles in detailsoils are divided into ve regions to be discussed separatelyAreas 1 and 4 are the front sheet-pile wall and covered pilerespectively which are in soil Since the horizontal dis-placement of the structure under static loads is relativelysmall an elastic resistance method is adopted to calculate thehorizontal earth pressure and the horizontal resistancecoecient depends on the ldquomrdquo method e earth pressurein areas 2 and 3 is more complex Soils in these areas arebetween front sheet-pile walls and covered piles e relativedisplacement between front sheet-pile walls and coveredpiles has an important inuence on the amount of earthpressure In practical engineering design covered pilestiness is often designed to be larger to reduce the front wallearth pressure As a result front-wall displacement is greaterthan covered-pile displacement Soils between front wallsand covered piles tend to move towards the sea and earthpressure is partial to an active stateerefore earth pressurecoecients in areas 2 and 3 should be between the activeearth pressure and stationary earth pressure In this paperJiang Bo a doctoral student at Zhejiang University con-cluded that the lateral pressure coecients of parallel wall

SeaTie road

Wharf surface

Anchorage wallCovered pile

Front wall

Excavationmud surface

Figure 1 Diagram of blind sheet-pile wharf

2 Advances in Civil Engineering

soils should be used Recommended lateral pressure co-ecients are shown in Table 1

32 EarthPressureCalculationbetweenFront Sheet-PileWallsand Covered Piles e lateral earth pressure between frontsheet-pile walls and covered piles is usually calculated usingthe parallel wall theory When calculating a unit wall widthis taken along the front sheet-pile wall width in the hori-zontal direction e distance between tie rods can also beselected as a calculation unit In the vertical direction themicrocell dz is taken deep along the wall en force an-alyses of the microcell are carried out e vertical stress σzcan be obtained using the equilibrium equation integral elateral earth pressure at any depth of the front sheet-pile wallcan be obtained by multiplying the vertical stress σz by thelateral pressure coecient Kw [25]

According to the parallel wall theory along the length ofa parallel wall cross section at any depth z thickness B isused in microsoil as shown in Figure 4 e unit width iscalculated to analyse the microsoil forces

(1) Soil weight dW

dW cL times 1 times dz (5)

(2) Upper and lower surface pressure of microsoilVertical pressure of upper surface

p1 σz times L times 1 (6)

Vertical pressure of lower surface

p2 σz + dσz( ) times L times 1 (7)

(3) Friction near microsoil

τ dz times 1 σx times dz times 1 times tan δ (8)

σx σzKw (9)

where δ is the friction angle of soils near thefront sheet-pile walls e friction angle can beselected according to roughness and drainageconditions

(1) Smooth and poorly drained δ (0sim(13))ϕ(2) Rough and well drained δ ((13)sim(12))ϕ(3) Very rough and well drained δ ((12)sim

(23))ϕ

e above equilibrium equation can be obtainedaccording to a vertical force balance of microelements

cL dz + σzLminus σz + dσz( )L

minus 2σzKw dz tan δ 0(10)

σz c

A+ CeminusAz (11)

Boundary condition

σz0 q (12)

Taking equation (12) into account

σz 1A

cminus(cminusAq)eminusAz[ ] (13)

e above formulas do not take cohesive forces of clay soilsinto account erefore when the soil is clay internal forcesgenerated by cohesive force c should be considered e in-ternal force σc c cotφ produced by cohesive force c isregarded approximately as a uniform force on the boundarysurfaces of the soils substituting it into equation (13) thecalculation formula for σz in clay soils can be obtained

σz c

Aminus

c

Aminus(qminus c cotφ)[ ]eminusAz minus c cotφ (14)

33 Force Calculation of Front Walls Transmitted from Soilsbetween Covered Piles According to previous research re-sults the soil arch between piles can be divided into twoparts as shown in Figure 5

e earth pressure in the distance is assumed to betransferred to adjacent covered piles through the outer archarea and stable inner arch area and front sheet-pile walls canbe used as a pair of parallel walls When the pressure line ofthe arch coincides with the arch axis the bendingmoment ofeach section is zero and arches have no bending momentand thematerial cost is themost economical Since the three-

h0 h0h0

Hprime

h

(a = 0) (0 lt a lt 1) (a = 1) (a gt 1)

Figure 2 Law of foundation coecient changing with depth

Advances in Civil Engineering 3

Mud surface

Front sheet pile

Small tie rod Big tie rod

Covered pile Anchorage wall

1

2

3

4

Anchorage wall

Big tie rod

Covered pile

Small tie rodFront sheet pile

3

4

3

42

1

Figure 3 Structural calculation model of covered sheet-pile wharf

Table 1 Reference values of lateral pressure coefficient Kw

δφ

15deg 18deg 21deg 24deg 27deg 30deg 33deg 36deg 39deg 42deg 45deg

0deg 0589 0528 0472 0422 0376 0333 0295 0260 0228 0198 01723deg 0592 0530 0474 0423 0376 0334 0295 0260 0228 0198 01726deg 0601 0536 0478 0426 0378 0335 0296 0261 0228 0199 01729deg 0618 0547 0486 0431 0382 0338 0298 0262 0229 0200 017312deg 0652 0566 0498 0439 0388 0342 0301 0264 0231 0201 017315deg 0784 0601 0517 0452 0396 0348 0305 0267 0233 0202 017418deg 0733 0551 0471 0409 0356 0311 0271 0236 0204 017621deg 0682 0504 0427 0368 0319 0276 0239 0207 017824deg 0631 0459 0385 0330 0284 0244 0210 018027deg 0581 0415 0346 0294 0251 0214 018330deg 0531 0373 0308 0260 0220 018733deg 0482 0334 0273 0228 019236deg 0435 0296 0240 019939deg 0390 0261 021042deg 0347 022845deg 0306

Front sheet pile

q

Covered pile

σz + dσz

dWdz

ττ

L

σz

σx σx

Figure 4 Diagram of soil calculation

Inner arch area Outer arch area

Direct arch foot

Covered pile

Tie rod

Friction archfoot

b

1

q

Front sheet pile

Figure 5 Diagram of arch area division

4 Advances in Civil Engineering

hinged arch structure and loads are symmetrical half of thethree-hinged arch is considered as the research objecte coordinate system is set up as shown in Figure 6 eequation for a reasonable arch axis is

y 4f

l2(lminus x)x (15)

Reaction force of the arch foot

Rx ql2

8f

Ry ql

2

(16)

Combined with Rx Ry tan δ the equation for thereasonable arch axis is calculated by

f l

4 tan δ (17)

where l is the arch span f is the arch height and δ is thefriction angle

Along the vertical direction at any depth z microsoilwith a thickness of dz is taken as shown in Figure 7 Forcesacting on microsoils in the vertical direction are as follows

Gravity

W cs dz (18)

where s (L + f)lFriction between the soils and front sheet-pile walls

Tδ lτδ dz l dzσy tan δ (19)

Soil friction at soil arches

Tφ lτφ dz l dzσy tanφ (20)

Earth pressure difference between the upper and lowersurfaces

Δp σz + dσz minus σz( 1113857s (21)

Vertical force equilibrium equation of microsoils

Tδ + Tφ + σz + dσz minus σz( 1113857s W (22)

where σz and σy are the vertical stress and horizontal stressrespectively

e forces transmitted from the soils in the arches to thefront sheet-pile walls are assumed to be evenly distributed onthe horizontal plane Forces are distributed in the verticaldirection according to lateral pressure coefficient Kw

σyσz Combined with the above formulas the followingformula is obtained

c dz dσz +4Kw tan δ(tan δ + tanφ)

4L tan δ + lσz dz (23)

According to the analytic theory of differential equa-tions the following formula can be obtained

σz c

B+ CeminusAz

(24)

Boundary conditionσz0 q (25)

Substituting equation (25) into equation (24) the fol-lowing formula is obtained

C qminusc

B (26)

Therefore σz c

B1minus eminusAz

1113872 1113873 + qeminusAz

(27)

e above formulas do not take cohesive forces of claysoils into account erefore when the soil is clay the

x

y

q

N

Ry

Rx

Figure 6 Diagram of soil arch subjected to forces

dz

z

Front wall

q

Soils

Covered pile

σz + dσz

dW

σz

σyσy

τφτz

Figure 7 Soil force state considering arching effect

Advances in Civil Engineering 5

internal forces generated by cohesive force c should beconsidered e internal force σc c cotφ produced bycohesive force c is considered an approximately uniformforce on the boundary surfaces of the soils Substituting thisforce into equation (27) the calculation formula for σz inclay soils can be obtained

σz c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ (28)

e earth pressure on the front sheet-pile walls whichare close to land is calculated by

σy Kw

c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ1113882 1113883 (29)

34 Earth Pressure on Front Sheet-Pile Walls beneath MudSurface When calculating the earth pressure on the frontsheet-pile walls which are below the mud surface consid-ering the stiffness of the covered sheet-pile wharves understatic loads is large but the horizontal displacement gen-erated by the structure is relatively small and an elasticresistance method is adopted that is the soil horizontalresistance at any depth z is proportional to the soil hori-zontal displacement y that is

Pz K(h)y (30)

Currently the ldquomrdquo method is adopted in port engi-neering in China to determinate the horizontal resistancecoefficient KZ Assuming the earth resistance coefficientincreases linearly with depth

K(h) mh (31)

Substituting equation (31) into equation (30) Pz iscomputed by

Pz mhy m zminus h1( 1113857y (32)

35 Earth Pressure on Front Sheet-Pile Walls above MudSurface e displacement calculation for front sheet-pilewalls of covered sheet-pile wharves is the same as for tra-ditional sheet-pile wharves Since the stress characteristicsand deformation mechanism of front sheet-pile walls whichare in soils are completely different from those above themud surface the front sheet-pile wall is divided into upperand lower parts at the mud surface for separate calculationsBelow the mud surface the sheet-pile walls can be simplifiedas elastic structures buried in soil with the top layer beingflat with the mud surface e pile top has moment M0 andlateral force Q0 M0 and Q0 are the resultant moment andforce of the sheet-pile wall mud surface from the force abovethe sheet-pile wall mud surface e rotation angle anddisplacement of the pile top are φ0 and y0 respectivelyAccording to the previous description when a pile lateraldisplacement y occurs at depth z the soil resistance forceacting on the piles at depth z is

Pz K(h)yb0 m zminusH1( 1113857yb0 (33)

e overloaded soil pressure and residual water pressureabove the mud surface are assumed to be uniform externalloads e overloaded soil pressure is averagely distributedaccording to the soil width between covered piles and behindcovered piles and has a value qprime that is calculated by

qprime σxnb + σynl1

b + l1minus

cn

tanφn

1minusKw( 1113857 (34)

where b is the covered pile width (m) l1 is the covered pile netdistance (m) σyn is the horizontal earth pressure generated bysoils between covered piles and front sheet-pile walls at themud surface and cn and φn are the cohesive force (kPa) andthe internal friction angle (deg) at the mud surface respectively

Considering the conversion depth (h α(zminusH1))based on the deflection curve differential equation in ma-terial mechanics the following formulas are obtained

EId4y

dh4 minusPZ + qprime (35)

Substituting equation (33) into equation (35)

EId4y

dh4 minusmhyb0 + qprime (36)

Boundary conditionsy

h0( 1113857 y0

dy

dh zH1( )

φ0

EId2y

dh2

h0( 1113857

M0

EId3y

dh3

zH1( )

Q0

(37)

According to the analytical theory of differential equa-tions the solution of equation (36) can be expressed by thefollowing power series

y 1113944infin

i0αih

i (38)

e following formula can be obtained by derivation

y y0A1 +φ0α

B1 +M0

α2EIC1 +

Q0

α3EID1 +

qprimeα4EI

E1 (39)

M α2EIy0A3 + αEIφ0B3 + M0C3 +Q0

αD3 +

qprimeα2

E3 (40)

Q α3EIy0A4 + α2EIφ0B4 + αM0C4 + Q0D4 +qprimeα

E4

(41)

Combined with the bottom boundary conditionsM 0 Q 0 the initial displacement y0 and initial rotationangle φ0 at the mud surface are calculated separately as

6 Advances in Civil Engineering

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

(42)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

(43)

e shear force Q0 and bending moment M0 of frontsheet-pile walls at the mud surface should be calculatedaccumulatively

Q0 Ra minusb1113936

ni1 1113938

zi

zi1σx dz + l1113936

ni1 1113938

zi

zi1σy dz

b + l (44)

M0 Ra H1 minus h0( 1113857minusb1113936

ni1li 1113938

zi

zi1σx dz + l1113936

ni1li 1113938

zi

zi1σy dz

b + l

(45)

where zi is the distance from the bottom of the i-th layer to thewharf surface (m) li is the distance from the earth pressurepoint of the i-th layer to the front mud surface (m)

36 Displacement Calculation of FrontWallWhenAnchoragePoint Displacement Is Ignored e dynamic water load is avariable parameter and it is also helpful to reduce the dis-placement of the front wall sheet-pile wharf erefore inthe paper the calculation method of displacement on frontwall was deduced considering the most dangerous situationwithout dynamic water load

When the strength of the covered pile or anchoragestructure is sufficient the displacement of the upper part offront sheet-pile walls is smaller displacement in the middleand lower part is larger front sheet-pile walls tend to rotatearound the anchorage point and displacement at the an-chorage point is negligible compared to the bottom dis-placement Displacement at the anchorage point is assumedto be zero when tie rod tension and front wall displacementare solved and the solution process is as follows

e displacement of the front sheet-pile wall at the an-chorage point primarily consists of four parts displacement

y0 at the mud surface displacement caused by rotation φ0 atthe mud surface displacement Δ of front sheet-pile wall at theanchorage point caused by earth pressure behind the wall anddisplacement f of front sheet-pile wall at the anchorage pointcaused by tie rod tension Displacement of the front sheet-pilewall at the anchorage point is assumed to be zero e fol-lowing formula is obtained

y0 + φ0 H1 minus h0( 1113857 + Δ + f 0 (46)

(1) Calculate displacement f

According to material mechanics formula

Mh EId2y

dh2 Ra H1h0 minus h( 1113857 0le hleH1 minus h0 (47)

Boundary conditionsφ(h0) 0

y(h0) 0

⎧⎨

⎩ (48)

Combined with the boundary conditions the formulasolution is expressed by

y Rah2

6EI3 H1 minus h0( 1113857minus h1113858 1113859 0le hleH1 minus h0( 1113857

y Ra H1 minus h0( 1113857

2

6EI3hminus H1 minus h0( 11138571113858 1113859 H1 minus h0 le hleH1( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(49)

Converting equation (49) to a formula with depth z as avariable the formula is expressed by

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(50)

Displacement f is expressed by

f y zh0( ) Ra H1 minus h0( 1113857

3

3EI (51)

(2) Calculate displacement Δ

According to the material mechanics formula

EId2y

dz2 b 1113938

z

0 σx H1 minus z( 1113857 dz + l 1113938z

0 σy H1 minus z( 1113857 dzminus H1 minus z( 1113857 b 1113938z

0 σx dz + l 1113938z

0 σy dz1113872 1113873

b + l (52)

Boundary conditions

φ zH1( ) EIdy

dzzh1

0

y zH1( ) 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(53)

Advances in Civil Engineering 7

In summary displacement f and Δ are expressed by

y minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bz3

6+

bz3

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 1113877 ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1 +

lH1

A2 eminusAH11113888 1113889

+124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24+

bczKw cot φH31

6

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

(54)

Δ minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAh0 +

bh0H21

2minus

bh0H1

Aminus

bh0

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lh306

+lh2

0

2Aminus

l

A3eminusAh0 +

lH21h0

2minus

lh0H1

Aminus

lh0

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Ah40 minus

bKwh0cH31

6A+

bKwcH41

8A+

124

lKw

c

Bh40 minus

lKwh0cH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24

+bch0Kw cot φH3

16

minusbcKw cot φH4

18

minuslcKw cot φh4

024

+lczKw cot φH3

16

minuslcKw cot φH4

18

⎫⎬

⎭

(55)

e displacement at any point of the front sheet-pile wallabove the mud surface can be expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz (56)

Finally formulas to calculate the displacement of anypoint on the front sheet-pile wall above the mud surface canbe expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889 +

qprimeα4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889 +

qprimeα3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 1113877 1113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cotφz4

24

+bczKw cotφH3

16

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

8 Advances in Civil Engineering

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(57)

37ConsideringDisplacement ofAnchoragePoint toCalculateFront Wall Displacement When the strength of the coveredpile or anchorage structure is insufficient the displacement ofthe upper part of the front sheet-pile walls is larger dis-placement at the bottom part is smaller front sheet-pile wallstend to rotate around the front sheet-pile wall bottom anddisplacement at the anchorage point is not negligible edisplacement at the anchorage point is assumed to have aspecific value when the tie rod tension and front wall dis-placement are calculated and the solution process is as follows

e displacement at the anchorage point is yaSubstituting this into equation (57)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+qprime

α3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI

1120

ckz5

+124

ck H41 H1 minus z( 1113857minus

1120

ck H511113876 1113877

(58)

the following equation is obtained

y0 φ0 H1 minus h0( 1113857 + Δ + f ya (59)

e following formula is recommended to determine ya

ya H1 minus h0( 1113857y0

H2 (60)

Displacement at any point of the front sheet-pile wallsabove the mud surface can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz (61)

Finally the displacement at any point above the mudsurface of the front sheet-pile walls can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(62)

38 Flow Chart of Front Wall Displacement CalculationA flow chart of the displacement calculation process for thefront walls of covered sheet-pile wharves under static loads isshown in Figure 8

4 Example of Displacement Calculation forFront Wall of Covered Sheet-Pile Wharf

41 Project Overview e calculation model is based on theJingtang Port 32 wharf e front walls and anchorage wallstructure are continuous underground walls e distancebetween covered piles is 12m and the cross-sectional formis shown in Figure 9 e soil wall and tie rod parametersare shown in Table 2

e Nanjing Hydraulic Research Institute organizedrelevant personnel to complete the installation of the in-strumentation in February 2005 and the observation periodwas from June 2005 to February 2008 e observationresults are shown in Table 3

42 lteoretical Calculation Results According to the dis-placement calculation theory for the front wall of a coveredsheet-pile wharf under static loads the displacement of thefront wall when displacement at the anchorage point isneglected or considered is shown in Table 4

43 Comparison and Analysis of Calculation Results etheoretical calculation and in situ measurement results forthe front sheet-pile wall displacement of a covered sheet-pilewharf are shown in Figure 10

From the figure whether the displacement at the anchorpoint is considered or neglected has little effect on the dis-placement calculation of the front sheet-pile wall which is belowthe mud surface e results obtained using two calculationmethods are close to measured data e results of the twocalculation methods are very different when calculating thedisplacement of the front sheet-pile wall which is below themudsurface When displacement at the anchorage point is ignoredthe displacement at the anchorage point is limited artificiallytherefore the calculation result of tie rod tension is relativelylarge which leads to the displacement calculation of the frontwall above the mud surface being greatly reduced e de-formation mode of the front sheet-pile wall is a middle convexdrum and themaximumdisplacement is approximately 20mmwhich is very different from actual in situ measurement results

When considering displacement at the anchorage point thecalculated tie rod tension is more accurate and the front walldisplacement calculation is very close to the in situ measure-ment result because the anchorage point displacement is as-sumed scientifically e upper part of the front wall is partially

Advances in Civil Engineering 9

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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soils should be used Recommended lateral pressure co-ecients are shown in Table 1

32 EarthPressureCalculationbetweenFront Sheet-PileWallsand Covered Piles e lateral earth pressure between frontsheet-pile walls and covered piles is usually calculated usingthe parallel wall theory When calculating a unit wall widthis taken along the front sheet-pile wall width in the hori-zontal direction e distance between tie rods can also beselected as a calculation unit In the vertical direction themicrocell dz is taken deep along the wall en force an-alyses of the microcell are carried out e vertical stress σzcan be obtained using the equilibrium equation integral elateral earth pressure at any depth of the front sheet-pile wallcan be obtained by multiplying the vertical stress σz by thelateral pressure coecient Kw [25]

According to the parallel wall theory along the length ofa parallel wall cross section at any depth z thickness B isused in microsoil as shown in Figure 4 e unit width iscalculated to analyse the microsoil forces

(1) Soil weight dW

dW cL times 1 times dz (5)

(2) Upper and lower surface pressure of microsoilVertical pressure of upper surface

p1 σz times L times 1 (6)

Vertical pressure of lower surface

p2 σz + dσz( ) times L times 1 (7)

(3) Friction near microsoil

τ dz times 1 σx times dz times 1 times tan δ (8)

σx σzKw (9)

where δ is the friction angle of soils near thefront sheet-pile walls e friction angle can beselected according to roughness and drainageconditions

(1) Smooth and poorly drained δ (0sim(13))ϕ(2) Rough and well drained δ ((13)sim(12))ϕ(3) Very rough and well drained δ ((12)sim

(23))ϕ

e above equilibrium equation can be obtainedaccording to a vertical force balance of microelements

cL dz + σzLminus σz + dσz( )L

minus 2σzKw dz tan δ 0(10)

σz c

A+ CeminusAz (11)

Boundary condition

σz0 q (12)

Taking equation (12) into account

σz 1A

cminus(cminusAq)eminusAz[ ] (13)

e above formulas do not take cohesive forces of clay soilsinto account erefore when the soil is clay internal forcesgenerated by cohesive force c should be considered e in-ternal force σc c cotφ produced by cohesive force c isregarded approximately as a uniform force on the boundarysurfaces of the soils substituting it into equation (13) thecalculation formula for σz in clay soils can be obtained

σz c

Aminus

c

Aminus(qminus c cotφ)[ ]eminusAz minus c cotφ (14)

33 Force Calculation of Front Walls Transmitted from Soilsbetween Covered Piles According to previous research re-sults the soil arch between piles can be divided into twoparts as shown in Figure 5

e earth pressure in the distance is assumed to betransferred to adjacent covered piles through the outer archarea and stable inner arch area and front sheet-pile walls canbe used as a pair of parallel walls When the pressure line ofthe arch coincides with the arch axis the bendingmoment ofeach section is zero and arches have no bending momentand thematerial cost is themost economical Since the three-

h0 h0h0

Hprime

h

(a = 0) (0 lt a lt 1) (a = 1) (a gt 1)

Figure 2 Law of foundation coecient changing with depth

Advances in Civil Engineering 3

Mud surface

Front sheet pile

Small tie rod Big tie rod

Covered pile Anchorage wall

1

2

3

4

Anchorage wall

Big tie rod

Covered pile

Small tie rodFront sheet pile

3

4

3

42

1

Figure 3 Structural calculation model of covered sheet-pile wharf

Table 1 Reference values of lateral pressure coefficient Kw

δφ

15deg 18deg 21deg 24deg 27deg 30deg 33deg 36deg 39deg 42deg 45deg

0deg 0589 0528 0472 0422 0376 0333 0295 0260 0228 0198 01723deg 0592 0530 0474 0423 0376 0334 0295 0260 0228 0198 01726deg 0601 0536 0478 0426 0378 0335 0296 0261 0228 0199 01729deg 0618 0547 0486 0431 0382 0338 0298 0262 0229 0200 017312deg 0652 0566 0498 0439 0388 0342 0301 0264 0231 0201 017315deg 0784 0601 0517 0452 0396 0348 0305 0267 0233 0202 017418deg 0733 0551 0471 0409 0356 0311 0271 0236 0204 017621deg 0682 0504 0427 0368 0319 0276 0239 0207 017824deg 0631 0459 0385 0330 0284 0244 0210 018027deg 0581 0415 0346 0294 0251 0214 018330deg 0531 0373 0308 0260 0220 018733deg 0482 0334 0273 0228 019236deg 0435 0296 0240 019939deg 0390 0261 021042deg 0347 022845deg 0306

Front sheet pile

q

Covered pile

σz + dσz

dWdz

ττ

L

σz

σx σx

Figure 4 Diagram of soil calculation

Inner arch area Outer arch area

Direct arch foot

Covered pile

Tie rod

Friction archfoot

b

1

q

Front sheet pile

Figure 5 Diagram of arch area division

4 Advances in Civil Engineering

hinged arch structure and loads are symmetrical half of thethree-hinged arch is considered as the research objecte coordinate system is set up as shown in Figure 6 eequation for a reasonable arch axis is

y 4f

l2(lminus x)x (15)

Reaction force of the arch foot

Rx ql2

8f

Ry ql

2

(16)

Combined with Rx Ry tan δ the equation for thereasonable arch axis is calculated by

f l

4 tan δ (17)

where l is the arch span f is the arch height and δ is thefriction angle

Along the vertical direction at any depth z microsoilwith a thickness of dz is taken as shown in Figure 7 Forcesacting on microsoils in the vertical direction are as follows

Gravity

W cs dz (18)

where s (L + f)lFriction between the soils and front sheet-pile walls

Tδ lτδ dz l dzσy tan δ (19)

Soil friction at soil arches

Tφ lτφ dz l dzσy tanφ (20)

Earth pressure difference between the upper and lowersurfaces

Δp σz + dσz minus σz( 1113857s (21)

Vertical force equilibrium equation of microsoils

Tδ + Tφ + σz + dσz minus σz( 1113857s W (22)

where σz and σy are the vertical stress and horizontal stressrespectively

e forces transmitted from the soils in the arches to thefront sheet-pile walls are assumed to be evenly distributed onthe horizontal plane Forces are distributed in the verticaldirection according to lateral pressure coefficient Kw

σyσz Combined with the above formulas the followingformula is obtained

c dz dσz +4Kw tan δ(tan δ + tanφ)

4L tan δ + lσz dz (23)

According to the analytic theory of differential equa-tions the following formula can be obtained

σz c

B+ CeminusAz

(24)

Boundary conditionσz0 q (25)

Substituting equation (25) into equation (24) the fol-lowing formula is obtained

C qminusc

B (26)

Therefore σz c

B1minus eminusAz

1113872 1113873 + qeminusAz

(27)

e above formulas do not take cohesive forces of claysoils into account erefore when the soil is clay the

x

y

q

N

Ry

Rx

Figure 6 Diagram of soil arch subjected to forces

dz

z

Front wall

q

Soils

Covered pile

σz + dσz

dW

σz

σyσy

τφτz

Figure 7 Soil force state considering arching effect

Advances in Civil Engineering 5

internal forces generated by cohesive force c should beconsidered e internal force σc c cotφ produced bycohesive force c is considered an approximately uniformforce on the boundary surfaces of the soils Substituting thisforce into equation (27) the calculation formula for σz inclay soils can be obtained

σz c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ (28)

e earth pressure on the front sheet-pile walls whichare close to land is calculated by

σy Kw

c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ1113882 1113883 (29)

34 Earth Pressure on Front Sheet-Pile Walls beneath MudSurface When calculating the earth pressure on the frontsheet-pile walls which are below the mud surface consid-ering the stiffness of the covered sheet-pile wharves understatic loads is large but the horizontal displacement gen-erated by the structure is relatively small and an elasticresistance method is adopted that is the soil horizontalresistance at any depth z is proportional to the soil hori-zontal displacement y that is

Pz K(h)y (30)

Currently the ldquomrdquo method is adopted in port engi-neering in China to determinate the horizontal resistancecoefficient KZ Assuming the earth resistance coefficientincreases linearly with depth

K(h) mh (31)

Substituting equation (31) into equation (30) Pz iscomputed by

Pz mhy m zminus h1( 1113857y (32)

35 Earth Pressure on Front Sheet-Pile Walls above MudSurface e displacement calculation for front sheet-pilewalls of covered sheet-pile wharves is the same as for tra-ditional sheet-pile wharves Since the stress characteristicsand deformation mechanism of front sheet-pile walls whichare in soils are completely different from those above themud surface the front sheet-pile wall is divided into upperand lower parts at the mud surface for separate calculationsBelow the mud surface the sheet-pile walls can be simplifiedas elastic structures buried in soil with the top layer beingflat with the mud surface e pile top has moment M0 andlateral force Q0 M0 and Q0 are the resultant moment andforce of the sheet-pile wall mud surface from the force abovethe sheet-pile wall mud surface e rotation angle anddisplacement of the pile top are φ0 and y0 respectivelyAccording to the previous description when a pile lateraldisplacement y occurs at depth z the soil resistance forceacting on the piles at depth z is

Pz K(h)yb0 m zminusH1( 1113857yb0 (33)

e overloaded soil pressure and residual water pressureabove the mud surface are assumed to be uniform externalloads e overloaded soil pressure is averagely distributedaccording to the soil width between covered piles and behindcovered piles and has a value qprime that is calculated by

qprime σxnb + σynl1

b + l1minus

cn

tanφn

1minusKw( 1113857 (34)

where b is the covered pile width (m) l1 is the covered pile netdistance (m) σyn is the horizontal earth pressure generated bysoils between covered piles and front sheet-pile walls at themud surface and cn and φn are the cohesive force (kPa) andthe internal friction angle (deg) at the mud surface respectively

Considering the conversion depth (h α(zminusH1))based on the deflection curve differential equation in ma-terial mechanics the following formulas are obtained

EId4y

dh4 minusPZ + qprime (35)

Substituting equation (33) into equation (35)

EId4y

dh4 minusmhyb0 + qprime (36)

Boundary conditionsy

h0( 1113857 y0

dy

dh zH1( )

φ0

EId2y

dh2

h0( 1113857

M0

EId3y

dh3

zH1( )

Q0

(37)

According to the analytical theory of differential equa-tions the solution of equation (36) can be expressed by thefollowing power series

y 1113944infin

i0αih

i (38)

e following formula can be obtained by derivation

y y0A1 +φ0α

B1 +M0

α2EIC1 +

Q0

α3EID1 +

qprimeα4EI

E1 (39)

M α2EIy0A3 + αEIφ0B3 + M0C3 +Q0

αD3 +

qprimeα2

E3 (40)

Q α3EIy0A4 + α2EIφ0B4 + αM0C4 + Q0D4 +qprimeα

E4

(41)

Combined with the bottom boundary conditionsM 0 Q 0 the initial displacement y0 and initial rotationangle φ0 at the mud surface are calculated separately as

6 Advances in Civil Engineering

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

(42)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

(43)

e shear force Q0 and bending moment M0 of frontsheet-pile walls at the mud surface should be calculatedaccumulatively

Q0 Ra minusb1113936

ni1 1113938

zi

zi1σx dz + l1113936

ni1 1113938

zi

zi1σy dz

b + l (44)

M0 Ra H1 minus h0( 1113857minusb1113936

ni1li 1113938

zi

zi1σx dz + l1113936

ni1li 1113938

zi

zi1σy dz

b + l

(45)

where zi is the distance from the bottom of the i-th layer to thewharf surface (m) li is the distance from the earth pressurepoint of the i-th layer to the front mud surface (m)

36 Displacement Calculation of FrontWallWhenAnchoragePoint Displacement Is Ignored e dynamic water load is avariable parameter and it is also helpful to reduce the dis-placement of the front wall sheet-pile wharf erefore inthe paper the calculation method of displacement on frontwall was deduced considering the most dangerous situationwithout dynamic water load

When the strength of the covered pile or anchoragestructure is sufficient the displacement of the upper part offront sheet-pile walls is smaller displacement in the middleand lower part is larger front sheet-pile walls tend to rotatearound the anchorage point and displacement at the an-chorage point is negligible compared to the bottom dis-placement Displacement at the anchorage point is assumedto be zero when tie rod tension and front wall displacementare solved and the solution process is as follows

e displacement of the front sheet-pile wall at the an-chorage point primarily consists of four parts displacement

y0 at the mud surface displacement caused by rotation φ0 atthe mud surface displacement Δ of front sheet-pile wall at theanchorage point caused by earth pressure behind the wall anddisplacement f of front sheet-pile wall at the anchorage pointcaused by tie rod tension Displacement of the front sheet-pilewall at the anchorage point is assumed to be zero e fol-lowing formula is obtained

y0 + φ0 H1 minus h0( 1113857 + Δ + f 0 (46)

(1) Calculate displacement f

According to material mechanics formula

Mh EId2y

dh2 Ra H1h0 minus h( 1113857 0le hleH1 minus h0 (47)

Boundary conditionsφ(h0) 0

y(h0) 0

⎧⎨

⎩ (48)

Combined with the boundary conditions the formulasolution is expressed by

y Rah2

6EI3 H1 minus h0( 1113857minus h1113858 1113859 0le hleH1 minus h0( 1113857

y Ra H1 minus h0( 1113857

2

6EI3hminus H1 minus h0( 11138571113858 1113859 H1 minus h0 le hleH1( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(49)

Converting equation (49) to a formula with depth z as avariable the formula is expressed by

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(50)

Displacement f is expressed by

f y zh0( ) Ra H1 minus h0( 1113857

3

3EI (51)

(2) Calculate displacement Δ

According to the material mechanics formula

EId2y

dz2 b 1113938

z

0 σx H1 minus z( 1113857 dz + l 1113938z

0 σy H1 minus z( 1113857 dzminus H1 minus z( 1113857 b 1113938z

0 σx dz + l 1113938z

0 σy dz1113872 1113873

b + l (52)

Boundary conditions

φ zH1( ) EIdy

dzzh1

0

y zH1( ) 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(53)

Advances in Civil Engineering 7

In summary displacement f and Δ are expressed by

y minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bz3

6+

bz3

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 1113877 ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1 +

lH1

A2 eminusAH11113888 1113889

+124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24+

bczKw cot φH31

6

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

(54)

Δ minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAh0 +

bh0H21

2minus

bh0H1

Aminus

bh0

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lh306

+lh2

0

2Aminus

l

A3eminusAh0 +

lH21h0

2minus

lh0H1

Aminus

lh0

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Ah40 minus

bKwh0cH31

6A+

bKwcH41

8A+

124

lKw

c

Bh40 minus

lKwh0cH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24

+bch0Kw cot φH3

16

minusbcKw cot φH4

18

minuslcKw cot φh4

024

+lczKw cot φH3

16

minuslcKw cot φH4

18

⎫⎬

⎭

(55)

e displacement at any point of the front sheet-pile wallabove the mud surface can be expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz (56)

Finally formulas to calculate the displacement of anypoint on the front sheet-pile wall above the mud surface canbe expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889 +

qprimeα4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889 +

qprimeα3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 1113877 1113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cotφz4

24

+bczKw cotφH3

16

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

8 Advances in Civil Engineering

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(57)

37ConsideringDisplacement ofAnchoragePoint toCalculateFront Wall Displacement When the strength of the coveredpile or anchorage structure is insufficient the displacement ofthe upper part of the front sheet-pile walls is larger dis-placement at the bottom part is smaller front sheet-pile wallstend to rotate around the front sheet-pile wall bottom anddisplacement at the anchorage point is not negligible edisplacement at the anchorage point is assumed to have aspecific value when the tie rod tension and front wall dis-placement are calculated and the solution process is as follows

e displacement at the anchorage point is yaSubstituting this into equation (57)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+qprime

α3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI

1120

ckz5

+124

ck H41 H1 minus z( 1113857minus

1120

ck H511113876 1113877

(58)

the following equation is obtained

y0 φ0 H1 minus h0( 1113857 + Δ + f ya (59)

e following formula is recommended to determine ya

ya H1 minus h0( 1113857y0

H2 (60)

Displacement at any point of the front sheet-pile wallsabove the mud surface can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz (61)

Finally the displacement at any point above the mudsurface of the front sheet-pile walls can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(62)

38 Flow Chart of Front Wall Displacement CalculationA flow chart of the displacement calculation process for thefront walls of covered sheet-pile wharves under static loads isshown in Figure 8

4 Example of Displacement Calculation forFront Wall of Covered Sheet-Pile Wharf

41 Project Overview e calculation model is based on theJingtang Port 32 wharf e front walls and anchorage wallstructure are continuous underground walls e distancebetween covered piles is 12m and the cross-sectional formis shown in Figure 9 e soil wall and tie rod parametersare shown in Table 2

e Nanjing Hydraulic Research Institute organizedrelevant personnel to complete the installation of the in-strumentation in February 2005 and the observation periodwas from June 2005 to February 2008 e observationresults are shown in Table 3

42 lteoretical Calculation Results According to the dis-placement calculation theory for the front wall of a coveredsheet-pile wharf under static loads the displacement of thefront wall when displacement at the anchorage point isneglected or considered is shown in Table 4

43 Comparison and Analysis of Calculation Results etheoretical calculation and in situ measurement results forthe front sheet-pile wall displacement of a covered sheet-pilewharf are shown in Figure 10

From the figure whether the displacement at the anchorpoint is considered or neglected has little effect on the dis-placement calculation of the front sheet-pile wall which is belowthe mud surface e results obtained using two calculationmethods are close to measured data e results of the twocalculation methods are very different when calculating thedisplacement of the front sheet-pile wall which is below themudsurface When displacement at the anchorage point is ignoredthe displacement at the anchorage point is limited artificiallytherefore the calculation result of tie rod tension is relativelylarge which leads to the displacement calculation of the frontwall above the mud surface being greatly reduced e de-formation mode of the front sheet-pile wall is a middle convexdrum and themaximumdisplacement is approximately 20mmwhich is very different from actual in situ measurement results

When considering displacement at the anchorage point thecalculated tie rod tension is more accurate and the front walldisplacement calculation is very close to the in situ measure-ment result because the anchorage point displacement is as-sumed scientifically e upper part of the front wall is partially

Advances in Civil Engineering 9

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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Mud surface

Front sheet pile

Small tie rod Big tie rod

Covered pile Anchorage wall

1

2

3

4

Anchorage wall

Big tie rod

Covered pile

Small tie rodFront sheet pile

3

4

3

42

1

Figure 3 Structural calculation model of covered sheet-pile wharf

Table 1 Reference values of lateral pressure coefficient Kw

δφ

15deg 18deg 21deg 24deg 27deg 30deg 33deg 36deg 39deg 42deg 45deg

0deg 0589 0528 0472 0422 0376 0333 0295 0260 0228 0198 01723deg 0592 0530 0474 0423 0376 0334 0295 0260 0228 0198 01726deg 0601 0536 0478 0426 0378 0335 0296 0261 0228 0199 01729deg 0618 0547 0486 0431 0382 0338 0298 0262 0229 0200 017312deg 0652 0566 0498 0439 0388 0342 0301 0264 0231 0201 017315deg 0784 0601 0517 0452 0396 0348 0305 0267 0233 0202 017418deg 0733 0551 0471 0409 0356 0311 0271 0236 0204 017621deg 0682 0504 0427 0368 0319 0276 0239 0207 017824deg 0631 0459 0385 0330 0284 0244 0210 018027deg 0581 0415 0346 0294 0251 0214 018330deg 0531 0373 0308 0260 0220 018733deg 0482 0334 0273 0228 019236deg 0435 0296 0240 019939deg 0390 0261 021042deg 0347 022845deg 0306

Front sheet pile

q

Covered pile

σz + dσz

dWdz

ττ

L

σz

σx σx

Figure 4 Diagram of soil calculation

Inner arch area Outer arch area

Direct arch foot

Covered pile

Tie rod

Friction archfoot

b

1

q

Front sheet pile

Figure 5 Diagram of arch area division

4 Advances in Civil Engineering

hinged arch structure and loads are symmetrical half of thethree-hinged arch is considered as the research objecte coordinate system is set up as shown in Figure 6 eequation for a reasonable arch axis is

y 4f

l2(lminus x)x (15)

Reaction force of the arch foot

Rx ql2

8f

Ry ql

2

(16)

Combined with Rx Ry tan δ the equation for thereasonable arch axis is calculated by

f l

4 tan δ (17)

where l is the arch span f is the arch height and δ is thefriction angle

Along the vertical direction at any depth z microsoilwith a thickness of dz is taken as shown in Figure 7 Forcesacting on microsoils in the vertical direction are as follows

Gravity

W cs dz (18)

where s (L + f)lFriction between the soils and front sheet-pile walls

Tδ lτδ dz l dzσy tan δ (19)

Soil friction at soil arches

Tφ lτφ dz l dzσy tanφ (20)

Earth pressure difference between the upper and lowersurfaces

Δp σz + dσz minus σz( 1113857s (21)

Vertical force equilibrium equation of microsoils

Tδ + Tφ + σz + dσz minus σz( 1113857s W (22)

where σz and σy are the vertical stress and horizontal stressrespectively

e forces transmitted from the soils in the arches to thefront sheet-pile walls are assumed to be evenly distributed onthe horizontal plane Forces are distributed in the verticaldirection according to lateral pressure coefficient Kw

σyσz Combined with the above formulas the followingformula is obtained

c dz dσz +4Kw tan δ(tan δ + tanφ)

4L tan δ + lσz dz (23)

According to the analytic theory of differential equa-tions the following formula can be obtained

σz c

B+ CeminusAz

(24)

Boundary conditionσz0 q (25)

Substituting equation (25) into equation (24) the fol-lowing formula is obtained

C qminusc

B (26)

Therefore σz c

B1minus eminusAz

1113872 1113873 + qeminusAz

(27)

e above formulas do not take cohesive forces of claysoils into account erefore when the soil is clay the

x

y

q

N

Ry

Rx

Figure 6 Diagram of soil arch subjected to forces

dz

z

Front wall

q

Soils

Covered pile

σz + dσz

dW

σz

σyσy

τφτz

Figure 7 Soil force state considering arching effect

Advances in Civil Engineering 5

internal forces generated by cohesive force c should beconsidered e internal force σc c cotφ produced bycohesive force c is considered an approximately uniformforce on the boundary surfaces of the soils Substituting thisforce into equation (27) the calculation formula for σz inclay soils can be obtained

σz c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ (28)

e earth pressure on the front sheet-pile walls whichare close to land is calculated by

σy Kw

c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ1113882 1113883 (29)

34 Earth Pressure on Front Sheet-Pile Walls beneath MudSurface When calculating the earth pressure on the frontsheet-pile walls which are below the mud surface consid-ering the stiffness of the covered sheet-pile wharves understatic loads is large but the horizontal displacement gen-erated by the structure is relatively small and an elasticresistance method is adopted that is the soil horizontalresistance at any depth z is proportional to the soil hori-zontal displacement y that is

Pz K(h)y (30)

Currently the ldquomrdquo method is adopted in port engi-neering in China to determinate the horizontal resistancecoefficient KZ Assuming the earth resistance coefficientincreases linearly with depth

K(h) mh (31)

Substituting equation (31) into equation (30) Pz iscomputed by

Pz mhy m zminus h1( 1113857y (32)

35 Earth Pressure on Front Sheet-Pile Walls above MudSurface e displacement calculation for front sheet-pilewalls of covered sheet-pile wharves is the same as for tra-ditional sheet-pile wharves Since the stress characteristicsand deformation mechanism of front sheet-pile walls whichare in soils are completely different from those above themud surface the front sheet-pile wall is divided into upperand lower parts at the mud surface for separate calculationsBelow the mud surface the sheet-pile walls can be simplifiedas elastic structures buried in soil with the top layer beingflat with the mud surface e pile top has moment M0 andlateral force Q0 M0 and Q0 are the resultant moment andforce of the sheet-pile wall mud surface from the force abovethe sheet-pile wall mud surface e rotation angle anddisplacement of the pile top are φ0 and y0 respectivelyAccording to the previous description when a pile lateraldisplacement y occurs at depth z the soil resistance forceacting on the piles at depth z is

Pz K(h)yb0 m zminusH1( 1113857yb0 (33)

e overloaded soil pressure and residual water pressureabove the mud surface are assumed to be uniform externalloads e overloaded soil pressure is averagely distributedaccording to the soil width between covered piles and behindcovered piles and has a value qprime that is calculated by

qprime σxnb + σynl1

b + l1minus

cn

tanφn

1minusKw( 1113857 (34)

where b is the covered pile width (m) l1 is the covered pile netdistance (m) σyn is the horizontal earth pressure generated bysoils between covered piles and front sheet-pile walls at themud surface and cn and φn are the cohesive force (kPa) andthe internal friction angle (deg) at the mud surface respectively

Considering the conversion depth (h α(zminusH1))based on the deflection curve differential equation in ma-terial mechanics the following formulas are obtained

EId4y

dh4 minusPZ + qprime (35)

Substituting equation (33) into equation (35)

EId4y

dh4 minusmhyb0 + qprime (36)

Boundary conditionsy

h0( 1113857 y0

dy

dh zH1( )

φ0

EId2y

dh2

h0( 1113857

M0

EId3y

dh3

zH1( )

Q0

(37)

According to the analytical theory of differential equa-tions the solution of equation (36) can be expressed by thefollowing power series

y 1113944infin

i0αih

i (38)

e following formula can be obtained by derivation

y y0A1 +φ0α

B1 +M0

α2EIC1 +

Q0

α3EID1 +

qprimeα4EI

E1 (39)

M α2EIy0A3 + αEIφ0B3 + M0C3 +Q0

αD3 +

qprimeα2

E3 (40)

Q α3EIy0A4 + α2EIφ0B4 + αM0C4 + Q0D4 +qprimeα

E4

(41)

Combined with the bottom boundary conditionsM 0 Q 0 the initial displacement y0 and initial rotationangle φ0 at the mud surface are calculated separately as

6 Advances in Civil Engineering

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

(42)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

(43)

e shear force Q0 and bending moment M0 of frontsheet-pile walls at the mud surface should be calculatedaccumulatively

Q0 Ra minusb1113936

ni1 1113938

zi

zi1σx dz + l1113936

ni1 1113938

zi

zi1σy dz

b + l (44)

M0 Ra H1 minus h0( 1113857minusb1113936

ni1li 1113938

zi

zi1σx dz + l1113936

ni1li 1113938

zi

zi1σy dz

b + l

(45)

where zi is the distance from the bottom of the i-th layer to thewharf surface (m) li is the distance from the earth pressurepoint of the i-th layer to the front mud surface (m)

36 Displacement Calculation of FrontWallWhenAnchoragePoint Displacement Is Ignored e dynamic water load is avariable parameter and it is also helpful to reduce the dis-placement of the front wall sheet-pile wharf erefore inthe paper the calculation method of displacement on frontwall was deduced considering the most dangerous situationwithout dynamic water load

When the strength of the covered pile or anchoragestructure is sufficient the displacement of the upper part offront sheet-pile walls is smaller displacement in the middleand lower part is larger front sheet-pile walls tend to rotatearound the anchorage point and displacement at the an-chorage point is negligible compared to the bottom dis-placement Displacement at the anchorage point is assumedto be zero when tie rod tension and front wall displacementare solved and the solution process is as follows

e displacement of the front sheet-pile wall at the an-chorage point primarily consists of four parts displacement

y0 at the mud surface displacement caused by rotation φ0 atthe mud surface displacement Δ of front sheet-pile wall at theanchorage point caused by earth pressure behind the wall anddisplacement f of front sheet-pile wall at the anchorage pointcaused by tie rod tension Displacement of the front sheet-pilewall at the anchorage point is assumed to be zero e fol-lowing formula is obtained

y0 + φ0 H1 minus h0( 1113857 + Δ + f 0 (46)

(1) Calculate displacement f

According to material mechanics formula

Mh EId2y

dh2 Ra H1h0 minus h( 1113857 0le hleH1 minus h0 (47)

Boundary conditionsφ(h0) 0

y(h0) 0

⎧⎨

⎩ (48)

Combined with the boundary conditions the formulasolution is expressed by

y Rah2

6EI3 H1 minus h0( 1113857minus h1113858 1113859 0le hleH1 minus h0( 1113857

y Ra H1 minus h0( 1113857

2

6EI3hminus H1 minus h0( 11138571113858 1113859 H1 minus h0 le hleH1( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(49)

Converting equation (49) to a formula with depth z as avariable the formula is expressed by

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(50)

Displacement f is expressed by

f y zh0( ) Ra H1 minus h0( 1113857

3

3EI (51)

(2) Calculate displacement Δ

According to the material mechanics formula

EId2y

dz2 b 1113938

z

0 σx H1 minus z( 1113857 dz + l 1113938z

0 σy H1 minus z( 1113857 dzminus H1 minus z( 1113857 b 1113938z

0 σx dz + l 1113938z

0 σy dz1113872 1113873

b + l (52)

Boundary conditions

φ zH1( ) EIdy

dzzh1

0

y zH1( ) 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(53)

Advances in Civil Engineering 7

In summary displacement f and Δ are expressed by

y minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bz3

6+

bz3

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 1113877 ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1 +

lH1

A2 eminusAH11113888 1113889

+124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24+

bczKw cot φH31

6

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

(54)

Δ minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAh0 +

bh0H21

2minus

bh0H1

Aminus

bh0

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lh306

+lh2

0

2Aminus

l

A3eminusAh0 +

lH21h0

2minus

lh0H1

Aminus

lh0

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Ah40 minus

bKwh0cH31

6A+

bKwcH41

8A+

124

lKw

c

Bh40 minus

lKwh0cH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24

+bch0Kw cot φH3

16

minusbcKw cot φH4

18

minuslcKw cot φh4

024

+lczKw cot φH3

16

minuslcKw cot φH4

18

⎫⎬

⎭

(55)

e displacement at any point of the front sheet-pile wallabove the mud surface can be expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz (56)

Finally formulas to calculate the displacement of anypoint on the front sheet-pile wall above the mud surface canbe expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889 +

qprimeα4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889 +

qprimeα3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 1113877 1113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cotφz4

24

+bczKw cotφH3

16

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

8 Advances in Civil Engineering

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(57)

37ConsideringDisplacement ofAnchoragePoint toCalculateFront Wall Displacement When the strength of the coveredpile or anchorage structure is insufficient the displacement ofthe upper part of the front sheet-pile walls is larger dis-placement at the bottom part is smaller front sheet-pile wallstend to rotate around the front sheet-pile wall bottom anddisplacement at the anchorage point is not negligible edisplacement at the anchorage point is assumed to have aspecific value when the tie rod tension and front wall dis-placement are calculated and the solution process is as follows

e displacement at the anchorage point is yaSubstituting this into equation (57)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+qprime

α3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI

1120

ckz5

+124

ck H41 H1 minus z( 1113857minus

1120

ck H511113876 1113877

(58)

the following equation is obtained

y0 φ0 H1 minus h0( 1113857 + Δ + f ya (59)

e following formula is recommended to determine ya

ya H1 minus h0( 1113857y0

H2 (60)

Displacement at any point of the front sheet-pile wallsabove the mud surface can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz (61)

Finally the displacement at any point above the mudsurface of the front sheet-pile walls can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(62)

38 Flow Chart of Front Wall Displacement CalculationA flow chart of the displacement calculation process for thefront walls of covered sheet-pile wharves under static loads isshown in Figure 8

4 Example of Displacement Calculation forFront Wall of Covered Sheet-Pile Wharf

41 Project Overview e calculation model is based on theJingtang Port 32 wharf e front walls and anchorage wallstructure are continuous underground walls e distancebetween covered piles is 12m and the cross-sectional formis shown in Figure 9 e soil wall and tie rod parametersare shown in Table 2

e Nanjing Hydraulic Research Institute organizedrelevant personnel to complete the installation of the in-strumentation in February 2005 and the observation periodwas from June 2005 to February 2008 e observationresults are shown in Table 3

42 lteoretical Calculation Results According to the dis-placement calculation theory for the front wall of a coveredsheet-pile wharf under static loads the displacement of thefront wall when displacement at the anchorage point isneglected or considered is shown in Table 4

43 Comparison and Analysis of Calculation Results etheoretical calculation and in situ measurement results forthe front sheet-pile wall displacement of a covered sheet-pilewharf are shown in Figure 10

From the figure whether the displacement at the anchorpoint is considered or neglected has little effect on the dis-placement calculation of the front sheet-pile wall which is belowthe mud surface e results obtained using two calculationmethods are close to measured data e results of the twocalculation methods are very different when calculating thedisplacement of the front sheet-pile wall which is below themudsurface When displacement at the anchorage point is ignoredthe displacement at the anchorage point is limited artificiallytherefore the calculation result of tie rod tension is relativelylarge which leads to the displacement calculation of the frontwall above the mud surface being greatly reduced e de-formation mode of the front sheet-pile wall is a middle convexdrum and themaximumdisplacement is approximately 20mmwhich is very different from actual in situ measurement results

When considering displacement at the anchorage point thecalculated tie rod tension is more accurate and the front walldisplacement calculation is very close to the in situ measure-ment result because the anchorage point displacement is as-sumed scientifically e upper part of the front wall is partially

Advances in Civil Engineering 9

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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hinged arch structure and loads are symmetrical half of thethree-hinged arch is considered as the research objecte coordinate system is set up as shown in Figure 6 eequation for a reasonable arch axis is

y 4f

l2(lminus x)x (15)

Reaction force of the arch foot

Rx ql2

8f

Ry ql

2

(16)

Combined with Rx Ry tan δ the equation for thereasonable arch axis is calculated by

f l

4 tan δ (17)

where l is the arch span f is the arch height and δ is thefriction angle

Along the vertical direction at any depth z microsoilwith a thickness of dz is taken as shown in Figure 7 Forcesacting on microsoils in the vertical direction are as follows

Gravity

W cs dz (18)

where s (L + f)lFriction between the soils and front sheet-pile walls

Tδ lτδ dz l dzσy tan δ (19)

Soil friction at soil arches

Tφ lτφ dz l dzσy tanφ (20)

Earth pressure difference between the upper and lowersurfaces

Δp σz + dσz minus σz( 1113857s (21)

Vertical force equilibrium equation of microsoils

Tδ + Tφ + σz + dσz minus σz( 1113857s W (22)

where σz and σy are the vertical stress and horizontal stressrespectively

e forces transmitted from the soils in the arches to thefront sheet-pile walls are assumed to be evenly distributed onthe horizontal plane Forces are distributed in the verticaldirection according to lateral pressure coefficient Kw

σyσz Combined with the above formulas the followingformula is obtained

c dz dσz +4Kw tan δ(tan δ + tanφ)

4L tan δ + lσz dz (23)

According to the analytic theory of differential equa-tions the following formula can be obtained

σz c

B+ CeminusAz

(24)

Boundary conditionσz0 q (25)

Substituting equation (25) into equation (24) the fol-lowing formula is obtained

C qminusc

B (26)

Therefore σz c

B1minus eminusAz

1113872 1113873 + qeminusAz

(27)

e above formulas do not take cohesive forces of claysoils into account erefore when the soil is clay the

x

y

q

N

Ry

Rx

Figure 6 Diagram of soil arch subjected to forces

dz

z

Front wall

q

Soils

Covered pile

σz + dσz

dW

σz

σyσy

τφτz

Figure 7 Soil force state considering arching effect

Advances in Civil Engineering 5

internal forces generated by cohesive force c should beconsidered e internal force σc c cotφ produced bycohesive force c is considered an approximately uniformforce on the boundary surfaces of the soils Substituting thisforce into equation (27) the calculation formula for σz inclay soils can be obtained

σz c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ (28)

e earth pressure on the front sheet-pile walls whichare close to land is calculated by

σy Kw

c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ1113882 1113883 (29)

34 Earth Pressure on Front Sheet-Pile Walls beneath MudSurface When calculating the earth pressure on the frontsheet-pile walls which are below the mud surface consid-ering the stiffness of the covered sheet-pile wharves understatic loads is large but the horizontal displacement gen-erated by the structure is relatively small and an elasticresistance method is adopted that is the soil horizontalresistance at any depth z is proportional to the soil hori-zontal displacement y that is

Pz K(h)y (30)

Currently the ldquomrdquo method is adopted in port engi-neering in China to determinate the horizontal resistancecoefficient KZ Assuming the earth resistance coefficientincreases linearly with depth

K(h) mh (31)

Substituting equation (31) into equation (30) Pz iscomputed by

Pz mhy m zminus h1( 1113857y (32)

35 Earth Pressure on Front Sheet-Pile Walls above MudSurface e displacement calculation for front sheet-pilewalls of covered sheet-pile wharves is the same as for tra-ditional sheet-pile wharves Since the stress characteristicsand deformation mechanism of front sheet-pile walls whichare in soils are completely different from those above themud surface the front sheet-pile wall is divided into upperand lower parts at the mud surface for separate calculationsBelow the mud surface the sheet-pile walls can be simplifiedas elastic structures buried in soil with the top layer beingflat with the mud surface e pile top has moment M0 andlateral force Q0 M0 and Q0 are the resultant moment andforce of the sheet-pile wall mud surface from the force abovethe sheet-pile wall mud surface e rotation angle anddisplacement of the pile top are φ0 and y0 respectivelyAccording to the previous description when a pile lateraldisplacement y occurs at depth z the soil resistance forceacting on the piles at depth z is

Pz K(h)yb0 m zminusH1( 1113857yb0 (33)

e overloaded soil pressure and residual water pressureabove the mud surface are assumed to be uniform externalloads e overloaded soil pressure is averagely distributedaccording to the soil width between covered piles and behindcovered piles and has a value qprime that is calculated by

qprime σxnb + σynl1

b + l1minus

cn

tanφn

1minusKw( 1113857 (34)

where b is the covered pile width (m) l1 is the covered pile netdistance (m) σyn is the horizontal earth pressure generated bysoils between covered piles and front sheet-pile walls at themud surface and cn and φn are the cohesive force (kPa) andthe internal friction angle (deg) at the mud surface respectively

Considering the conversion depth (h α(zminusH1))based on the deflection curve differential equation in ma-terial mechanics the following formulas are obtained

EId4y

dh4 minusPZ + qprime (35)

Substituting equation (33) into equation (35)

EId4y

dh4 minusmhyb0 + qprime (36)

Boundary conditionsy

h0( 1113857 y0

dy

dh zH1( )

φ0

EId2y

dh2

h0( 1113857

M0

EId3y

dh3

zH1( )

Q0

(37)

According to the analytical theory of differential equa-tions the solution of equation (36) can be expressed by thefollowing power series

y 1113944infin

i0αih

i (38)

e following formula can be obtained by derivation

y y0A1 +φ0α

B1 +M0

α2EIC1 +

Q0

α3EID1 +

qprimeα4EI

E1 (39)

M α2EIy0A3 + αEIφ0B3 + M0C3 +Q0

αD3 +

qprimeα2

E3 (40)

Q α3EIy0A4 + α2EIφ0B4 + αM0C4 + Q0D4 +qprimeα

E4

(41)

Combined with the bottom boundary conditionsM 0 Q 0 the initial displacement y0 and initial rotationangle φ0 at the mud surface are calculated separately as

6 Advances in Civil Engineering

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

(42)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

(43)

e shear force Q0 and bending moment M0 of frontsheet-pile walls at the mud surface should be calculatedaccumulatively

Q0 Ra minusb1113936

ni1 1113938

zi

zi1σx dz + l1113936

ni1 1113938

zi

zi1σy dz

b + l (44)

M0 Ra H1 minus h0( 1113857minusb1113936

ni1li 1113938

zi

zi1σx dz + l1113936

ni1li 1113938

zi

zi1σy dz

b + l

(45)

where zi is the distance from the bottom of the i-th layer to thewharf surface (m) li is the distance from the earth pressurepoint of the i-th layer to the front mud surface (m)

36 Displacement Calculation of FrontWallWhenAnchoragePoint Displacement Is Ignored e dynamic water load is avariable parameter and it is also helpful to reduce the dis-placement of the front wall sheet-pile wharf erefore inthe paper the calculation method of displacement on frontwall was deduced considering the most dangerous situationwithout dynamic water load

When the strength of the covered pile or anchoragestructure is sufficient the displacement of the upper part offront sheet-pile walls is smaller displacement in the middleand lower part is larger front sheet-pile walls tend to rotatearound the anchorage point and displacement at the an-chorage point is negligible compared to the bottom dis-placement Displacement at the anchorage point is assumedto be zero when tie rod tension and front wall displacementare solved and the solution process is as follows

e displacement of the front sheet-pile wall at the an-chorage point primarily consists of four parts displacement

y0 at the mud surface displacement caused by rotation φ0 atthe mud surface displacement Δ of front sheet-pile wall at theanchorage point caused by earth pressure behind the wall anddisplacement f of front sheet-pile wall at the anchorage pointcaused by tie rod tension Displacement of the front sheet-pilewall at the anchorage point is assumed to be zero e fol-lowing formula is obtained

y0 + φ0 H1 minus h0( 1113857 + Δ + f 0 (46)

(1) Calculate displacement f

According to material mechanics formula

Mh EId2y

dh2 Ra H1h0 minus h( 1113857 0le hleH1 minus h0 (47)

Boundary conditionsφ(h0) 0

y(h0) 0

⎧⎨

⎩ (48)

Combined with the boundary conditions the formulasolution is expressed by

y Rah2

6EI3 H1 minus h0( 1113857minus h1113858 1113859 0le hleH1 minus h0( 1113857

y Ra H1 minus h0( 1113857

2

6EI3hminus H1 minus h0( 11138571113858 1113859 H1 minus h0 le hleH1( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(49)

Converting equation (49) to a formula with depth z as avariable the formula is expressed by

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(50)

Displacement f is expressed by

f y zh0( ) Ra H1 minus h0( 1113857

3

3EI (51)

(2) Calculate displacement Δ

According to the material mechanics formula

EId2y

dz2 b 1113938

z

0 σx H1 minus z( 1113857 dz + l 1113938z

0 σy H1 minus z( 1113857 dzminus H1 minus z( 1113857 b 1113938z

0 σx dz + l 1113938z

0 σy dz1113872 1113873

b + l (52)

Boundary conditions

φ zH1( ) EIdy

dzzh1

0

y zH1( ) 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(53)

Advances in Civil Engineering 7

In summary displacement f and Δ are expressed by

y minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bz3

6+

bz3

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 1113877 ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1 +

lH1

A2 eminusAH11113888 1113889

+124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24+

bczKw cot φH31

6

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

(54)

Δ minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAh0 +

bh0H21

2minus

bh0H1

Aminus

bh0

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lh306

+lh2

0

2Aminus

l

A3eminusAh0 +

lH21h0

2minus

lh0H1

Aminus

lh0

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Ah40 minus

bKwh0cH31

6A+

bKwcH41

8A+

124

lKw

c

Bh40 minus

lKwh0cH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24

+bch0Kw cot φH3

16

minusbcKw cot φH4

18

minuslcKw cot φh4

024

+lczKw cot φH3

16

minuslcKw cot φH4

18

⎫⎬

⎭

(55)

e displacement at any point of the front sheet-pile wallabove the mud surface can be expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz (56)

Finally formulas to calculate the displacement of anypoint on the front sheet-pile wall above the mud surface canbe expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889 +

qprimeα4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889 +

qprimeα3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 1113877 1113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cotφz4

24

+bczKw cotφH3

16

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

8 Advances in Civil Engineering

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(57)

37ConsideringDisplacement ofAnchoragePoint toCalculateFront Wall Displacement When the strength of the coveredpile or anchorage structure is insufficient the displacement ofthe upper part of the front sheet-pile walls is larger dis-placement at the bottom part is smaller front sheet-pile wallstend to rotate around the front sheet-pile wall bottom anddisplacement at the anchorage point is not negligible edisplacement at the anchorage point is assumed to have aspecific value when the tie rod tension and front wall dis-placement are calculated and the solution process is as follows

e displacement at the anchorage point is yaSubstituting this into equation (57)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+qprime

α3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI

1120

ckz5

+124

ck H41 H1 minus z( 1113857minus

1120

ck H511113876 1113877

(58)

the following equation is obtained

y0 φ0 H1 minus h0( 1113857 + Δ + f ya (59)

e following formula is recommended to determine ya

ya H1 minus h0( 1113857y0

H2 (60)

Displacement at any point of the front sheet-pile wallsabove the mud surface can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz (61)

Finally the displacement at any point above the mudsurface of the front sheet-pile walls can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(62)

38 Flow Chart of Front Wall Displacement CalculationA flow chart of the displacement calculation process for thefront walls of covered sheet-pile wharves under static loads isshown in Figure 8

4 Example of Displacement Calculation forFront Wall of Covered Sheet-Pile Wharf

41 Project Overview e calculation model is based on theJingtang Port 32 wharf e front walls and anchorage wallstructure are continuous underground walls e distancebetween covered piles is 12m and the cross-sectional formis shown in Figure 9 e soil wall and tie rod parametersare shown in Table 2

e Nanjing Hydraulic Research Institute organizedrelevant personnel to complete the installation of the in-strumentation in February 2005 and the observation periodwas from June 2005 to February 2008 e observationresults are shown in Table 3

42 lteoretical Calculation Results According to the dis-placement calculation theory for the front wall of a coveredsheet-pile wharf under static loads the displacement of thefront wall when displacement at the anchorage point isneglected or considered is shown in Table 4

43 Comparison and Analysis of Calculation Results etheoretical calculation and in situ measurement results forthe front sheet-pile wall displacement of a covered sheet-pilewharf are shown in Figure 10

From the figure whether the displacement at the anchorpoint is considered or neglected has little effect on the dis-placement calculation of the front sheet-pile wall which is belowthe mud surface e results obtained using two calculationmethods are close to measured data e results of the twocalculation methods are very different when calculating thedisplacement of the front sheet-pile wall which is below themudsurface When displacement at the anchorage point is ignoredthe displacement at the anchorage point is limited artificiallytherefore the calculation result of tie rod tension is relativelylarge which leads to the displacement calculation of the frontwall above the mud surface being greatly reduced e de-formation mode of the front sheet-pile wall is a middle convexdrum and themaximumdisplacement is approximately 20mmwhich is very different from actual in situ measurement results

When considering displacement at the anchorage point thecalculated tie rod tension is more accurate and the front walldisplacement calculation is very close to the in situ measure-ment result because the anchorage point displacement is as-sumed scientifically e upper part of the front wall is partially

Advances in Civil Engineering 9

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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internal forces generated by cohesive force c should beconsidered e internal force σc c cotφ produced bycohesive force c is considered an approximately uniformforce on the boundary surfaces of the soils Substituting thisforce into equation (27) the calculation formula for σz inclay soils can be obtained

σz c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ (28)

e earth pressure on the front sheet-pile walls whichare close to land is calculated by

σy Kw

c

Bminus

c

Bminus(qminus c cotφ)1113876 1113877e

minusAz minus c cotφ1113882 1113883 (29)

34 Earth Pressure on Front Sheet-Pile Walls beneath MudSurface When calculating the earth pressure on the frontsheet-pile walls which are below the mud surface consid-ering the stiffness of the covered sheet-pile wharves understatic loads is large but the horizontal displacement gen-erated by the structure is relatively small and an elasticresistance method is adopted that is the soil horizontalresistance at any depth z is proportional to the soil hori-zontal displacement y that is

Pz K(h)y (30)

Currently the ldquomrdquo method is adopted in port engi-neering in China to determinate the horizontal resistancecoefficient KZ Assuming the earth resistance coefficientincreases linearly with depth

K(h) mh (31)

Substituting equation (31) into equation (30) Pz iscomputed by

Pz mhy m zminus h1( 1113857y (32)

35 Earth Pressure on Front Sheet-Pile Walls above MudSurface e displacement calculation for front sheet-pilewalls of covered sheet-pile wharves is the same as for tra-ditional sheet-pile wharves Since the stress characteristicsand deformation mechanism of front sheet-pile walls whichare in soils are completely different from those above themud surface the front sheet-pile wall is divided into upperand lower parts at the mud surface for separate calculationsBelow the mud surface the sheet-pile walls can be simplifiedas elastic structures buried in soil with the top layer beingflat with the mud surface e pile top has moment M0 andlateral force Q0 M0 and Q0 are the resultant moment andforce of the sheet-pile wall mud surface from the force abovethe sheet-pile wall mud surface e rotation angle anddisplacement of the pile top are φ0 and y0 respectivelyAccording to the previous description when a pile lateraldisplacement y occurs at depth z the soil resistance forceacting on the piles at depth z is

Pz K(h)yb0 m zminusH1( 1113857yb0 (33)

e overloaded soil pressure and residual water pressureabove the mud surface are assumed to be uniform externalloads e overloaded soil pressure is averagely distributedaccording to the soil width between covered piles and behindcovered piles and has a value qprime that is calculated by

qprime σxnb + σynl1

b + l1minus

cn

tanφn

1minusKw( 1113857 (34)

where b is the covered pile width (m) l1 is the covered pile netdistance (m) σyn is the horizontal earth pressure generated bysoils between covered piles and front sheet-pile walls at themud surface and cn and φn are the cohesive force (kPa) andthe internal friction angle (deg) at the mud surface respectively

Considering the conversion depth (h α(zminusH1))based on the deflection curve differential equation in ma-terial mechanics the following formulas are obtained

EId4y

dh4 minusPZ + qprime (35)

Substituting equation (33) into equation (35)

EId4y

dh4 minusmhyb0 + qprime (36)

Boundary conditionsy

h0( 1113857 y0

dy

dh zH1( )

φ0

EId2y

dh2

h0( 1113857

M0

EId3y

dh3

zH1( )

Q0

(37)

According to the analytical theory of differential equa-tions the solution of equation (36) can be expressed by thefollowing power series

y 1113944infin

i0αih

i (38)

e following formula can be obtained by derivation

y y0A1 +φ0α

B1 +M0

α2EIC1 +

Q0

α3EID1 +

qprimeα4EI

E1 (39)

M α2EIy0A3 + αEIφ0B3 + M0C3 +Q0

αD3 +

qprimeα2

E3 (40)

Q α3EIy0A4 + α2EIφ0B4 + αM0C4 + Q0D4 +qprimeα

E4

(41)

Combined with the bottom boundary conditionsM 0 Q 0 the initial displacement y0 and initial rotationangle φ0 at the mud surface are calculated separately as

6 Advances in Civil Engineering

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

(42)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

(43)

e shear force Q0 and bending moment M0 of frontsheet-pile walls at the mud surface should be calculatedaccumulatively

Q0 Ra minusb1113936

ni1 1113938

zi

zi1σx dz + l1113936

ni1 1113938

zi

zi1σy dz

b + l (44)

M0 Ra H1 minus h0( 1113857minusb1113936

ni1li 1113938

zi

zi1σx dz + l1113936

ni1li 1113938

zi

zi1σy dz

b + l

(45)

where zi is the distance from the bottom of the i-th layer to thewharf surface (m) li is the distance from the earth pressurepoint of the i-th layer to the front mud surface (m)

36 Displacement Calculation of FrontWallWhenAnchoragePoint Displacement Is Ignored e dynamic water load is avariable parameter and it is also helpful to reduce the dis-placement of the front wall sheet-pile wharf erefore inthe paper the calculation method of displacement on frontwall was deduced considering the most dangerous situationwithout dynamic water load

When the strength of the covered pile or anchoragestructure is sufficient the displacement of the upper part offront sheet-pile walls is smaller displacement in the middleand lower part is larger front sheet-pile walls tend to rotatearound the anchorage point and displacement at the an-chorage point is negligible compared to the bottom dis-placement Displacement at the anchorage point is assumedto be zero when tie rod tension and front wall displacementare solved and the solution process is as follows

e displacement of the front sheet-pile wall at the an-chorage point primarily consists of four parts displacement

y0 at the mud surface displacement caused by rotation φ0 atthe mud surface displacement Δ of front sheet-pile wall at theanchorage point caused by earth pressure behind the wall anddisplacement f of front sheet-pile wall at the anchorage pointcaused by tie rod tension Displacement of the front sheet-pilewall at the anchorage point is assumed to be zero e fol-lowing formula is obtained

y0 + φ0 H1 minus h0( 1113857 + Δ + f 0 (46)

(1) Calculate displacement f

According to material mechanics formula

Mh EId2y

dh2 Ra H1h0 minus h( 1113857 0le hleH1 minus h0 (47)

Boundary conditionsφ(h0) 0

y(h0) 0

⎧⎨

⎩ (48)

Combined with the boundary conditions the formulasolution is expressed by

y Rah2

6EI3 H1 minus h0( 1113857minus h1113858 1113859 0le hleH1 minus h0( 1113857

y Ra H1 minus h0( 1113857

2

6EI3hminus H1 minus h0( 11138571113858 1113859 H1 minus h0 le hleH1( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(49)

Converting equation (49) to a formula with depth z as avariable the formula is expressed by

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(50)

Displacement f is expressed by

f y zh0( ) Ra H1 minus h0( 1113857

3

3EI (51)

(2) Calculate displacement Δ

According to the material mechanics formula

EId2y

dz2 b 1113938

z

0 σx H1 minus z( 1113857 dz + l 1113938z

0 σy H1 minus z( 1113857 dzminus H1 minus z( 1113857 b 1113938z

0 σx dz + l 1113938z

0 σy dz1113872 1113873

b + l (52)

Boundary conditions

φ zH1( ) EIdy

dzzh1

0

y zH1( ) 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(53)

Advances in Civil Engineering 7

In summary displacement f and Δ are expressed by

y minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bz3

6+

bz3

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 1113877 ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1 +

lH1

A2 eminusAH11113888 1113889

+124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24+

bczKw cot φH31

6

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

(54)

Δ minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAh0 +

bh0H21

2minus

bh0H1

Aminus

bh0

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lh306

+lh2

0

2Aminus

l

A3eminusAh0 +

lH21h0

2minus

lh0H1

Aminus

lh0

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Ah40 minus

bKwh0cH31

6A+

bKwcH41

8A+

124

lKw

c

Bh40 minus

lKwh0cH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24

+bch0Kw cot φH3

16

minusbcKw cot φH4

18

minuslcKw cot φh4

024

+lczKw cot φH3

16

minuslcKw cot φH4

18

⎫⎬

⎭

(55)

e displacement at any point of the front sheet-pile wallabove the mud surface can be expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz (56)

Finally formulas to calculate the displacement of anypoint on the front sheet-pile wall above the mud surface canbe expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889 +

qprimeα4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889 +

qprimeα3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 1113877 1113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cotφz4

24

+bczKw cotφH3

16

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

8 Advances in Civil Engineering

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(57)

37ConsideringDisplacement ofAnchoragePoint toCalculateFront Wall Displacement When the strength of the coveredpile or anchorage structure is insufficient the displacement ofthe upper part of the front sheet-pile walls is larger dis-placement at the bottom part is smaller front sheet-pile wallstend to rotate around the front sheet-pile wall bottom anddisplacement at the anchorage point is not negligible edisplacement at the anchorage point is assumed to have aspecific value when the tie rod tension and front wall dis-placement are calculated and the solution process is as follows

e displacement at the anchorage point is yaSubstituting this into equation (57)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+qprime

α3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI

1120

ckz5

+124

ck H41 H1 minus z( 1113857minus

1120

ck H511113876 1113877

(58)

the following equation is obtained

y0 φ0 H1 minus h0( 1113857 + Δ + f ya (59)

e following formula is recommended to determine ya

ya H1 minus h0( 1113857y0

H2 (60)

Displacement at any point of the front sheet-pile wallsabove the mud surface can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz (61)

Finally the displacement at any point above the mudsurface of the front sheet-pile walls can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(62)

38 Flow Chart of Front Wall Displacement CalculationA flow chart of the displacement calculation process for thefront walls of covered sheet-pile wharves under static loads isshown in Figure 8

4 Example of Displacement Calculation forFront Wall of Covered Sheet-Pile Wharf

41 Project Overview e calculation model is based on theJingtang Port 32 wharf e front walls and anchorage wallstructure are continuous underground walls e distancebetween covered piles is 12m and the cross-sectional formis shown in Figure 9 e soil wall and tie rod parametersare shown in Table 2

e Nanjing Hydraulic Research Institute organizedrelevant personnel to complete the installation of the in-strumentation in February 2005 and the observation periodwas from June 2005 to February 2008 e observationresults are shown in Table 3

42 lteoretical Calculation Results According to the dis-placement calculation theory for the front wall of a coveredsheet-pile wharf under static loads the displacement of thefront wall when displacement at the anchorage point isneglected or considered is shown in Table 4

43 Comparison and Analysis of Calculation Results etheoretical calculation and in situ measurement results forthe front sheet-pile wall displacement of a covered sheet-pilewharf are shown in Figure 10

From the figure whether the displacement at the anchorpoint is considered or neglected has little effect on the dis-placement calculation of the front sheet-pile wall which is belowthe mud surface e results obtained using two calculationmethods are close to measured data e results of the twocalculation methods are very different when calculating thedisplacement of the front sheet-pile wall which is below themudsurface When displacement at the anchorage point is ignoredthe displacement at the anchorage point is limited artificiallytherefore the calculation result of tie rod tension is relativelylarge which leads to the displacement calculation of the frontwall above the mud surface being greatly reduced e de-formation mode of the front sheet-pile wall is a middle convexdrum and themaximumdisplacement is approximately 20mmwhich is very different from actual in situ measurement results

When considering displacement at the anchorage point thecalculated tie rod tension is more accurate and the front walldisplacement calculation is very close to the in situ measure-ment result because the anchorage point displacement is as-sumed scientifically e upper part of the front wall is partially

Advances in Civil Engineering 9

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

(42)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

(43)

e shear force Q0 and bending moment M0 of frontsheet-pile walls at the mud surface should be calculatedaccumulatively

Q0 Ra minusb1113936

ni1 1113938

zi

zi1σx dz + l1113936

ni1 1113938

zi

zi1σy dz

b + l (44)

M0 Ra H1 minus h0( 1113857minusb1113936

ni1li 1113938

zi

zi1σx dz + l1113936

ni1li 1113938

zi

zi1σy dz

b + l

(45)

where zi is the distance from the bottom of the i-th layer to thewharf surface (m) li is the distance from the earth pressurepoint of the i-th layer to the front mud surface (m)

36 Displacement Calculation of FrontWallWhenAnchoragePoint Displacement Is Ignored e dynamic water load is avariable parameter and it is also helpful to reduce the dis-placement of the front wall sheet-pile wharf erefore inthe paper the calculation method of displacement on frontwall was deduced considering the most dangerous situationwithout dynamic water load

When the strength of the covered pile or anchoragestructure is sufficient the displacement of the upper part offront sheet-pile walls is smaller displacement in the middleand lower part is larger front sheet-pile walls tend to rotatearound the anchorage point and displacement at the an-chorage point is negligible compared to the bottom dis-placement Displacement at the anchorage point is assumedto be zero when tie rod tension and front wall displacementare solved and the solution process is as follows

e displacement of the front sheet-pile wall at the an-chorage point primarily consists of four parts displacement

y0 at the mud surface displacement caused by rotation φ0 atthe mud surface displacement Δ of front sheet-pile wall at theanchorage point caused by earth pressure behind the wall anddisplacement f of front sheet-pile wall at the anchorage pointcaused by tie rod tension Displacement of the front sheet-pilewall at the anchorage point is assumed to be zero e fol-lowing formula is obtained

y0 + φ0 H1 minus h0( 1113857 + Δ + f 0 (46)

(1) Calculate displacement f

According to material mechanics formula

Mh EId2y

dh2 Ra H1h0 minus h( 1113857 0le hleH1 minus h0 (47)

Boundary conditionsφ(h0) 0

y(h0) 0

⎧⎨

⎩ (48)

Combined with the boundary conditions the formulasolution is expressed by

y Rah2

6EI3 H1 minus h0( 1113857minus h1113858 1113859 0le hleH1 minus h0( 1113857

y Ra H1 minus h0( 1113857

2

6EI3hminus H1 minus h0( 11138571113858 1113859 H1 minus h0 le hleH1( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(49)

Converting equation (49) to a formula with depth z as avariable the formula is expressed by

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(50)

Displacement f is expressed by

f y zh0( ) Ra H1 minus h0( 1113857

3

3EI (51)

(2) Calculate displacement Δ

According to the material mechanics formula

EId2y

dz2 b 1113938

z

0 σx H1 minus z( 1113857 dz + l 1113938z

0 σy H1 minus z( 1113857 dzminus H1 minus z( 1113857 b 1113938z

0 σx dz + l 1113938z

0 σy dz1113872 1113873

b + l (52)

Boundary conditions

φ zH1( ) EIdy

dzzh1

0

y zH1( ) 0

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(53)

Advances in Civil Engineering 7

In summary displacement f and Δ are expressed by

y minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bz3

6+

bz3

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 1113877 ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1 +

lH1

A2 eminusAH11113888 1113889

+124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24+

bczKw cot φH31

6

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

(54)

Δ minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAh0 +

bh0H21

2minus

bh0H1

Aminus

bh0

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lh306

+lh2

0

2Aminus

l

A3eminusAh0 +

lH21h0

2minus

lh0H1

Aminus

lh0

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Ah40 minus

bKwh0cH31

6A+

bKwcH41

8A+

124

lKw

c

Bh40 minus

lKwh0cH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24

+bch0Kw cot φH3

16

minusbcKw cot φH4

18

minuslcKw cot φh4

024

+lczKw cot φH3

16

minuslcKw cot φH4

18

⎫⎬

⎭

(55)

e displacement at any point of the front sheet-pile wallabove the mud surface can be expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz (56)

Finally formulas to calculate the displacement of anypoint on the front sheet-pile wall above the mud surface canbe expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889 +

qprimeα4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889 +

qprimeα3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 1113877 1113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cotφz4

24

+bczKw cotφH3

16

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

8 Advances in Civil Engineering

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(57)

37ConsideringDisplacement ofAnchoragePoint toCalculateFront Wall Displacement When the strength of the coveredpile or anchorage structure is insufficient the displacement ofthe upper part of the front sheet-pile walls is larger dis-placement at the bottom part is smaller front sheet-pile wallstend to rotate around the front sheet-pile wall bottom anddisplacement at the anchorage point is not negligible edisplacement at the anchorage point is assumed to have aspecific value when the tie rod tension and front wall dis-placement are calculated and the solution process is as follows

e displacement at the anchorage point is yaSubstituting this into equation (57)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+qprime

α3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI

1120

ckz5

+124

ck H41 H1 minus z( 1113857minus

1120

ck H511113876 1113877

(58)

the following equation is obtained

y0 φ0 H1 minus h0( 1113857 + Δ + f ya (59)

e following formula is recommended to determine ya

ya H1 minus h0( 1113857y0

H2 (60)

Displacement at any point of the front sheet-pile wallsabove the mud surface can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz (61)

Finally the displacement at any point above the mudsurface of the front sheet-pile walls can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(62)

38 Flow Chart of Front Wall Displacement CalculationA flow chart of the displacement calculation process for thefront walls of covered sheet-pile wharves under static loads isshown in Figure 8

4 Example of Displacement Calculation forFront Wall of Covered Sheet-Pile Wharf

41 Project Overview e calculation model is based on theJingtang Port 32 wharf e front walls and anchorage wallstructure are continuous underground walls e distancebetween covered piles is 12m and the cross-sectional formis shown in Figure 9 e soil wall and tie rod parametersare shown in Table 2

e Nanjing Hydraulic Research Institute organizedrelevant personnel to complete the installation of the in-strumentation in February 2005 and the observation periodwas from June 2005 to February 2008 e observationresults are shown in Table 3

42 lteoretical Calculation Results According to the dis-placement calculation theory for the front wall of a coveredsheet-pile wharf under static loads the displacement of thefront wall when displacement at the anchorage point isneglected or considered is shown in Table 4

43 Comparison and Analysis of Calculation Results etheoretical calculation and in situ measurement results forthe front sheet-pile wall displacement of a covered sheet-pilewharf are shown in Figure 10

From the figure whether the displacement at the anchorpoint is considered or neglected has little effect on the dis-placement calculation of the front sheet-pile wall which is belowthe mud surface e results obtained using two calculationmethods are close to measured data e results of the twocalculation methods are very different when calculating thedisplacement of the front sheet-pile wall which is below themudsurface When displacement at the anchorage point is ignoredthe displacement at the anchorage point is limited artificiallytherefore the calculation result of tie rod tension is relativelylarge which leads to the displacement calculation of the frontwall above the mud surface being greatly reduced e de-formation mode of the front sheet-pile wall is a middle convexdrum and themaximumdisplacement is approximately 20mmwhich is very different from actual in situ measurement results

When considering displacement at the anchorage point thecalculated tie rod tension is more accurate and the front walldisplacement calculation is very close to the in situ measure-ment result because the anchorage point displacement is as-sumed scientifically e upper part of the front wall is partially

Advances in Civil Engineering 9

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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Submit your manuscripts atwwwhindawicom

In summary displacement f and Δ are expressed by

y minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bz3

6+

bz3

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 1113877 ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1 +

lH1

A2 eminusAH11113888 1113889

+124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24+

bczKw cot φH31

6

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

(54)

Δ minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 11138771113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAh0 +

bh0H21

2minus

bh0H1

Aminus

bh0

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lh306

+lh2

0

2Aminus

l

A3eminusAh0 +

lH21h0

2minus

lh0H1

Aminus

lh0

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Ah40 minus

bKwh0cH31

6A+

bKwcH41

8A+

124

lKw

c

Bh40 minus

lKwh0cH31

6B+

lKwcH41

8Bminus

bcKw cot φz4

24

+bch0Kw cot φH3

16

minusbcKw cot φH4

18

minuslcKw cot φh4

024

+lczKw cot φH3

16

minuslcKw cot φH4

18

⎫⎬

⎭

(55)

e displacement at any point of the front sheet-pile wallabove the mud surface can be expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz (56)

Finally formulas to calculate the displacement of anypoint on the front sheet-pile wall above the mud surface canbe expressed by

y y0 + φ0 H1 + z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889 +

qprimeα4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889 +

qprimeα3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI(b + l)

⎧⎨

⎩Kw

A

c

Aminus(qminus c cotφ)1113876 1113877 1113888minus

bh30

6+

bh20

2Aminus

b

A3 eminusAz

+bzH2

12minus

bzH1

Aminus

bz

A2 eminusAH1 minus

bH31

3+

bH21

2A+

b

A3 eminusAH1

+bH1

A2 eminusAH11113889 +

Kw

A

c

Bminus(qminus c cotφ)1113876 11138771113888ndash

lz3

6+

lz2

2Aminus

l

A3eminusAz

+lH2

1z

2minus

lzH1

Aminus

lz

A2eminusAH1 minus

lH31

3+

lH21

2A+

l

A3eminusAH1

+lH1

A2 eminusAH11113889 +

124

bKw

c

Az4 minus

bKwzcH31

6A+

bKwcH41

8A+

124

lKw

c

Bz4 minus

lKwzcH31

6B+

lKwcH41

8Bminus

bcKw cotφz4

24

+bczKw cotφH3

16

minusbcKw cotφH4

18minus

lcKw cotφz4

24+

lczKw cotφH31

6minus

lcKw cotφH41

8⎫⎬

⎭

8 Advances in Civil Engineering

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(57)

37ConsideringDisplacement ofAnchoragePoint toCalculateFront Wall Displacement When the strength of the coveredpile or anchorage structure is insufficient the displacement ofthe upper part of the front sheet-pile walls is larger dis-placement at the bottom part is smaller front sheet-pile wallstend to rotate around the front sheet-pile wall bottom anddisplacement at the anchorage point is not negligible edisplacement at the anchorage point is assumed to have aspecific value when the tie rod tension and front wall dis-placement are calculated and the solution process is as follows

e displacement at the anchorage point is yaSubstituting this into equation (57)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+qprime

α3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI

1120

ckz5

+124

ck H41 H1 minus z( 1113857minus

1120

ck H511113876 1113877

(58)

the following equation is obtained

y0 φ0 H1 minus h0( 1113857 + Δ + f ya (59)

e following formula is recommended to determine ya

ya H1 minus h0( 1113857y0

H2 (60)

Displacement at any point of the front sheet-pile wallsabove the mud surface can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz (61)

Finally the displacement at any point above the mudsurface of the front sheet-pile walls can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(62)

38 Flow Chart of Front Wall Displacement CalculationA flow chart of the displacement calculation process for thefront walls of covered sheet-pile wharves under static loads isshown in Figure 8

4 Example of Displacement Calculation forFront Wall of Covered Sheet-Pile Wharf

41 Project Overview e calculation model is based on theJingtang Port 32 wharf e front walls and anchorage wallstructure are continuous underground walls e distancebetween covered piles is 12m and the cross-sectional formis shown in Figure 9 e soil wall and tie rod parametersare shown in Table 2

e Nanjing Hydraulic Research Institute organizedrelevant personnel to complete the installation of the in-strumentation in February 2005 and the observation periodwas from June 2005 to February 2008 e observationresults are shown in Table 3

42 lteoretical Calculation Results According to the dis-placement calculation theory for the front wall of a coveredsheet-pile wharf under static loads the displacement of thefront wall when displacement at the anchorage point isneglected or considered is shown in Table 4

43 Comparison and Analysis of Calculation Results etheoretical calculation and in situ measurement results forthe front sheet-pile wall displacement of a covered sheet-pilewharf are shown in Figure 10

From the figure whether the displacement at the anchorpoint is considered or neglected has little effect on the dis-placement calculation of the front sheet-pile wall which is belowthe mud surface e results obtained using two calculationmethods are close to measured data e results of the twocalculation methods are very different when calculating thedisplacement of the front sheet-pile wall which is below themudsurface When displacement at the anchorage point is ignoredthe displacement at the anchorage point is limited artificiallytherefore the calculation result of tie rod tension is relativelylarge which leads to the displacement calculation of the frontwall above the mud surface being greatly reduced e de-formation mode of the front sheet-pile wall is a middle convexdrum and themaximumdisplacement is approximately 20mmwhich is very different from actual in situ measurement results

When considering displacement at the anchorage point thecalculated tie rod tension is more accurate and the front walldisplacement calculation is very close to the in situ measure-ment result because the anchorage point displacement is as-sumed scientifically e upper part of the front wall is partially

Advances in Civil Engineering 9

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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Submit your manuscripts atwwwhindawicom

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(57)

37ConsideringDisplacement ofAnchoragePoint toCalculateFront Wall Displacement When the strength of the coveredpile or anchorage structure is insufficient the displacement ofthe upper part of the front sheet-pile walls is larger dis-placement at the bottom part is smaller front sheet-pile wallstend to rotate around the front sheet-pile wall bottom anddisplacement at the anchorage point is not negligible edisplacement at the anchorage point is assumed to have aspecific value when the tie rod tension and front wall dis-placement are calculated and the solution process is as follows

e displacement at the anchorage point is yaSubstituting this into equation (57)

φ0 M0

αEI

A4C3 minusA3C4

A3B4 minusA4B31113888 1113889 +

Q0

α2EI

A4D3 minusA3D4

A3B4 minusA4B31113888 1113889

+qprime

α3EI

A4E3 minusA3E4

A3B4 minusA4B31113888 1113889

Δz minus1

EI

1120

ckz5

+124

ck H41 H1 minus z( 1113857minus

1120

ck H511113876 1113877

(58)

the following equation is obtained

y0 φ0 H1 minus h0( 1113857 + Δ + f ya (59)

e following formula is recommended to determine ya

ya H1 minus h0( 1113857y0

H2 (60)

Displacement at any point of the front sheet-pile wallsabove the mud surface can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz (61)

Finally the displacement at any point above the mudsurface of the front sheet-pile walls can be expressed by

y y0 + φ0 H1 minus z( 1113857 + Δz + fz

y0 M0

α2EI

B4C3 minusB3C4

A4B3 minusA3B41113888 1113889 +

Q0

α3EI

B4D3 minusB3D4

A4B3 minusA3B41113888 1113889

+qprime

α4EI

B4E3 minusB3E4

A4B3 minusA3B41113888 1113889

fz

y Ra H1 minusZ( 1113857

2

6EI3 H1 minus h0( 1113857minus H1 minus z( 11138571113858 1113859 h0 le zleH1( 1113857

y Ra H1 minus h0( 1113857

2

6EI3 H1 minus z( 1113857minus H1 minus h0( 11138571113858 1113859 0le zle h0( 1113857

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(62)

38 Flow Chart of Front Wall Displacement CalculationA flow chart of the displacement calculation process for thefront walls of covered sheet-pile wharves under static loads isshown in Figure 8

4 Example of Displacement Calculation forFront Wall of Covered Sheet-Pile Wharf

41 Project Overview e calculation model is based on theJingtang Port 32 wharf e front walls and anchorage wallstructure are continuous underground walls e distancebetween covered piles is 12m and the cross-sectional formis shown in Figure 9 e soil wall and tie rod parametersare shown in Table 2

e Nanjing Hydraulic Research Institute organizedrelevant personnel to complete the installation of the in-strumentation in February 2005 and the observation periodwas from June 2005 to February 2008 e observationresults are shown in Table 3

42 lteoretical Calculation Results According to the dis-placement calculation theory for the front wall of a coveredsheet-pile wharf under static loads the displacement of thefront wall when displacement at the anchorage point isneglected or considered is shown in Table 4

43 Comparison and Analysis of Calculation Results etheoretical calculation and in situ measurement results forthe front sheet-pile wall displacement of a covered sheet-pilewharf are shown in Figure 10

From the figure whether the displacement at the anchorpoint is considered or neglected has little effect on the dis-placement calculation of the front sheet-pile wall which is belowthe mud surface e results obtained using two calculationmethods are close to measured data e results of the twocalculation methods are very different when calculating thedisplacement of the front sheet-pile wall which is below themudsurface When displacement at the anchorage point is ignoredthe displacement at the anchorage point is limited artificiallytherefore the calculation result of tie rod tension is relativelylarge which leads to the displacement calculation of the frontwall above the mud surface being greatly reduced e de-formation mode of the front sheet-pile wall is a middle convexdrum and themaximumdisplacement is approximately 20mmwhich is very different from actual in situ measurement results

When considering displacement at the anchorage point thecalculated tie rod tension is more accurate and the front walldisplacement calculation is very close to the in situ measure-ment result because the anchorage point displacement is as-sumed scientifically e upper part of the front wall is partially

Advances in Civil Engineering 9

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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

restrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall is ap-proximately 55mm the measured maximum displacement isapproximately 60mm and the error is 833 which is ideal Inconclusion it is more scientic to use the hypothetical an-chorage point displacement proposed in this paper

5 Conclusion

is paper is based on the theory of soil pressure and the soilarching eect According to the stress and deformation

characteristics of a covered sheet-pile wharf the formulasused to calculate the force and deformation of the front wallof a covered sheet-pile wharf under static loads are deducedand a comparison of actual measured stress and deformationdata of Jingtang Port 32 is used to verify the accuracy of thetheoretical derivation e comparison shows that whencalculating the displacement of the front sheet-pile wallwhich is below the mud surface the results of the twomethods are not very dierent and are in good agreementwith eld measured data However when the displacementof the front sheet-pile wall is calculated which is above the

Outer soil parameters sheet pile wall parameterscovered pile parameters and wharf surface load

Find outqacute

Find out the displacement of frontsheet pile wall below the mud surface

Find out the displacement of front sheetpile wall above the mud surface

Find out the displacement of front sheet pile wall with

covered pile under static load

Find out y0 φ0(with unknown quantity Ra)

Find out M0 Q0 (with unknown quantity Ra)

Find out Δ f (withunknown quantity Ra)

Find out parameters A1 B1 C1 D1 E1Find out σx σy α

From y0 + φ0H +

Δ + f = solve Ra0y

Figure 8 Flow chart of displacement calculation process for the front walls of covered sheet-pile wharves under static loads

SUCI1450H-R0rubber fender

Backfall fine sand

1 Fine sand

1 Fine sand

2 1 Silty clay

2 2 Mucky clay

2 2 Silty clay

3 Fine sand

q = 20kNm3q = 80kNm3

Elevation unit m

Dimension unit mm

202 design high

027 design high

ndash153 extermely low

water level 170

00400ndash16

500ndash20

15030

12

Underground continuouswall with concrete anchorage

ndash155~ndash180

ndash050

δ = 103deg

10003000 2000

water level

water level

ndash160 front mud surfaceof wharf

ndash285

γ = 176Nm3 γprime = 76m3 c = 16kNm3 Φ = 171deg δ = 855deg

γ = 197Nm3 γprime = 97m3 c = 0 Φ = 31deg

ndash153 γ = 18kNm3 γprime = 9kNm3 Φ = 28deg δ = 93degc = 0

ndash54 δ = 93degγ = 18kNm3 γprime = 9kNm3 c = 0 Φ = 28deg

ndash66 δ = 135degγ = 191kNm3 γprime = 91kNm3 c = 20kNm3 Φ = 27deg

ndash76 δ = 14degγ = 193kNm3 γprime = 93Nm3 c = 16kNm3 Φ = 28deg

ndash142ndash153 γ = 191Nm3 γprime = 91m3 c = 18kNm3 Φ = 196deg δ = 98deg

ndash258

ndash286 γ = 197Nm3 γprime = 97m3 c = 31Nm3 Φ = 247deg δ = 1235deg

05 γ = 18kNm3 γprime = 95kNm3 Φ = 32deg δ = 107degc = 0

4 Silty clay

ndash320 γ = 197Nm3 γprime = 97m3 c = 0 Φ = 32deg δ = 107deg4 Fine sand

Figure 9 Schematic diagram of Jingtang Port 32 wharf

10 Advances in Civil Engineering

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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

mud surface and when displacement at the anchorage pointis ignored displacement at the anchorage point is limitedartificiallyerefore the result of tie rod tension is relativelylarge which leads to the calculated displacement of the front

Table 2 Soil wall and tie rod parameters

Material type Unit weight (kNm3) Angle of internal friction (deg) Cohesion (kPa) Elastic modulus (MPa) Poissonrsquos ratioSoil layer 1 180 320 5 2600 029Soil layer 2 180 280 5 2600 029Soil layer 3 191 270 20 897 030Soil layer 4 193 280 16 1260 030Soil layer 5 176 171 16 360 030Soil layer 6 191 196 18 897 030Soil layer 7 197 310 5 2600 029Soil layer 8 197 247 31 897 030Soil layer 9 197 320 5 2600 029Concrete 250 mdash mdash 280 times 104 020Steel tie rod 785 mdash mdash 206 times 105 020

Table 3 In situ measured data

Observation crosssection and calculationconditions

Bending moment offront wall (kNmiddotm)

Anchoragewall (kNmiddotm)

Bending momentPile (kNmiddotm) Tension

of tierod(kN)

Displacementof anchoragepoint (cm)

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Maximumnegativebendingmoment

Maximumpositivebendingmoment

Maximumnegativebendingmoment

Observationcross section

2 813 minus1119 minus762 1735 minus2001 601 623 682 minus936 minus847 1907 minus2054 5264 845 minus839 minus627 2180 minus1823 446 47

Result Condition 2 774 minus700 minus765 2739 minus1988 636 90Condition 4 548 minus568 minus766 1713 minus1713 433 65

Table 4 Data for displacement of front pile wall

Neglecting displacement ofanchorage point

Considering displacement ofanchorage point

Variable Value Variable Valueα 0255 α 0255qprime minus45025 qprime minus45025Q0 minus119445 Q0 minus154785M0 44788 M0 minus538322φ0 0001759 φ0 0003503y0 minus0016669 y0 minus0023716Ra 187218 Ra 151878yz222 minus0013 yz222 minus00172yz242 minus0010 yz242 minus00118yz262 minus0007 yz262 minus000782yz282 minus0005017 yz282 minus000491yz302 minus000204 yz302 minus000167yz322 0002316 yz322 000267yz327 0003769 yz327 000410Displacement formula of frontwall above mud surface

Displacement formula of frontwall below mud surface

y minus1002 times 10minus6z4 + 10106 times

10minus4z3 + 0222z minus 5630 times10minus3z2

+ 4587 times eminus0049z minus 4576

y minus1002 times 10minus6z4 + 9896 times

10minus5z3 + 0225z minus 5606 times10minus3z2

+ 4587 times eminus0049z minus 4643Note e unit of force is kN the unit of length is m the unit of torque iskNmiddotm

ndash006 ndash005 ndash004 ndash003 ndash002 ndash001 000 001ndash30

ndash25

ndash20

ndash15

ndash10

ndash5

0

5

ndash160m

Neglect the displacement of anchorage point Consider the displacement of anchorage point In situ measurement

Elev

atio

n (m

)

s (m)

Figure 10 Comparison of two methods and measured data

Advances in Civil Engineering 11

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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

sheet-pile wall which is above the mud surface being greatlyreduced e deformation mode of the front sheet-pile wallis a middle convex drum and the maximum displacement isapproximately 20mm which is very different from theactual in situ measurement results When displacement atthe anchorage point is considered the calculated tie rodtension is more accurate and the results of the front walldisplacement are very close to in situ measurement resultsbecause displacement at the anchorage point is assumedscientifically e upper part of the front wall is partiallyrestrained in an inclined deformation mode e maximumdisplacement at the anchorage point of the front wall isapproximately 55mm the measured maximum displace-ment is approximately 60mm and the error is 833 whichis ideal In conclusion it is more scientific to use the hy-pothetical anchorage point displacement proposed in thispaper

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

is research was financially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) Six Major Talents Peak in Jiangsu Province inChina (Grant no 2016-JZ-020) and Postgraduate Researchamp Practice Innovation Program of Jiangsu Province (Grantno SJCX17_0609)

References

[1] Y X Liu and Z D Wu ldquoWorking mechanism of sheet pilewharf with barrier pilesrdquo Hydro-Scienceand Engineeringvol 2 pp 8ndash12 2006

[2] W P Liu Y R Zheng Z Y Cai and Z B Jiao ldquoFiniteelement method for covered sheet pile wharvesrdquo ChineseJournal of Geotechnical Engineering vol 32 no 4 pp 573ndash577 2010

[3] W C Dong ldquoPractice in construction of deep water sheet-pile diaphragm-wall wharves in Jingtang port and experi-ential studyrdquo Port Engineering Technology vol 12 pp 20ndash242005

[4] Y Yu ldquoGeneration and study on proposal of covered type ofsheet pile wharfrdquo Port Engineering Technology no S1pp 30ndash32 2005

[5] L YWang H L Liu P M Jiang and X X Chen ldquoPredictionmethod of seismic residual deformation of caisson quay wallin liquefied foundationrdquo China Ocean Engineering vol 25no 1 pp 45ndash58 2011

[6] G Gazetas E Garini and A Zafeirakos ldquoSeismic analysis oftall anchored sheet-pile wallsrdquo Soil Dynamics and EarthquakeEngineering vol 91 pp 209ndash221 2016

[7] J Leal J C De La Llera and G Aldunate ldquoSeismic isolators inpile- supported wharvesrdquo Proceedings of Ports in Proceedingsof 13th Triennial International Seattle WA USA August2013

[8] A Zekri A Ghalandarzadeh P Ghasemi and M HossainAminfar ldquoExperimental study of remediation measures ofanchored sheet pile quay walls using soil compactionrdquo OceanEngineering vol 93 pp 45ndash63 2015

[9] CW Yu C J LeeW Y Hung and H-T Chen ldquoApplicationof Hilbert-Huang transform to characterize soil liquefactionand quay wall seismic responses modeled in centrifugeshaking-table testsrdquo Soil Dynamics and Earthquake Engi-neering vol 30 no 7 pp 614ndash629 2010

[10] L Y Wang S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[11] L Y Wang G X Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[12] K Miyashita and T Nagao ldquoA fundamental study on thesimple evaluation method of the seismic performance of sheetpile quay walls with vertical pile anchorage against Level-oneearthquake ground motionrdquo Journal of Applied Mechanicsvol 10 pp 601ndash611 2007

[13] M Sato and K Tabata ldquoShaking table test of a large-sizemodel on failure mechanism of sheet-pile quay wall and pilefoundation due to lateral spreadingrdquo Japanese GeotechnicalJournal vol 4 no 4 pp 259ndash271 2009

[14] P Ruggeri D Segato and G Scar-pelli ldquoSheet pile quay wallsafety investigation of posttensioned anchor failure- srdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 9 no 139 pp 1567ndash1574 2013

[15] B H Wang Z H Wang and X Zuo ldquoFrequency equationof flexural vibrating cantilever beam considering the rotaryinertial moment of an attached massrdquo MathematicalProblems in Engineering vol 2017 Article ID 15680195 pages 2017

[16] F Kalantary H MolaAbasi M Salahi and M VeiskaramildquoPrediction of liquefaction induced lateral displacementsusing robust optimization modelrdquo Scientia Iranica A vol 20no 2 pp 242ndash250 2013

[17] R Motamed and I Towhata ldquoMitigation measures for pilegroups behind quay walls subjected to lateral flow of liquefiedsoil shake table model testsrdquo Soil Dynamics and EarthquakeEngineering vol 10 no 30 pp 1043ndash1060 2010

[18] L Y Wang G X Chen P Gao and S K Chen ldquoPseudo-static calculation method of the seismic residual deforma-tion of a geogrid reinforced soil retaining wall with a liq-uefied backfillrdquo Journal of Vibroengineering vol 17 no 2pp 827ndash840 2015

[19] B Jiang ldquoStudies on soil arching effect and earth pressure forretaining structurerdquo Doctoral thesis Zhejiang UniversityHangzhou China 2005

[20] H Matlock and L C Reese ldquoGeneralized solutions for lat-erally loaded pilesrdquo Journal of Soil Mechanics and FoundationsDivision vol 86 no SM5 pp 63ndash91 1960

[21] A General Team Planning Group of theird Design Instituteof the Ministry of Railways ldquoCalculation of bridge pierfoundation considering soil elastic resistancerdquo RailwayStandard Design Newsletter no 7 pp 8ndash42 1972

[22] J E Bowles Analytical and Computer Methods in FoundationEngineering McGraw-Hill New York NY USA 1974

12 Advances in Civil Engineering

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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

[23] W T Fan ldquoDimensionless coefficient of ldquoKrdquo method in singlepile calculationrdquo Railway Standard Design Newsletter no 2pp 38ndash45 1975

[24] Ministry of Communications of Road Planning and DesignInstitute Highway Bridges and Culvert Design Specifica-tions (Trial) China Communications Press Beijing China1975

[25] Y H Chen ldquoDiscussion on calculation of earth pressure ofhigh parallel wallrdquo China Rural Water Conservancy andHydropower vol 11 pp 53-54 2002

Advances in Civil Engineering 13

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