Research ArticleStudy on Calculation of Pile Sliding Interval of Large-DiameterSteel Pipe Piles on Offshore Platforms

Desen Kong 12 Meixu Deng 12 and Yu Xu1

1School of Civil Engineering and Architecture Shandong University of Science and Technology Qingdao 266590 China2Shandong Provincial Key Laboratory of Civil Engineering Disaster Prevention and MitigationShandong University of Science and Technology Qingdao 266590 China

Correspondence should be addressed to Desen Kong skd992012sdusteducn

Received 13 January 2019 Revised 9 April 2019 Accepted 15 April 2019 Published 23 April 2019

Academic Editor Jose Antonio Fonseca de Oliveira Correia

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

In ocean engineering pile sliding often occurs in the driving process of large-diameter pipe piles and will affect the engineeringquality so accurate pile sliding interval is necessary According to the stress situation of steel pipe pile out of actual engineering thecauses of pile sliding are analysed Using the static equilibrium equation themud depth at which the pipe pile may slip is calculatedThe influence of pile siding friction was considered when calculating the second pile sliding and the pile siding friction is dividedinto three influential areas Using integrating method the work done by pile resistance is calculated Combined with the workingprinciple and power principle the energy transformation equation of the pipe pile in the process of sliding is obtained and thesliding length and interval of the pile are calculated A comparison between the measured results and the real case calculation wasconducted using this new method The comparison indicated that the total relative errors in pile sliding interval are 8 to 16and the new method has high accuracyThe results of the new method are in accord with the measured data which can provide areference for predicting the interval of pile sliding in the project

1 Introduction

As a structure providing production and living facilitiesthe offshore platform integrates drilling transportation con-struction observation and navigation The pile foundationconstruction usually uses large-diameter and super-long steelpipe piles and the pipe piles are driven into the seabedsoil layer along the pipe by a hydraulic piling hammer Inthe process of piling when steel pipe piles encounter softsoil layers in marine soil layers pile sliding often occursdue to the decrease of pile end resistance and pile sidefriction resistance Slip pile not only affects the quality of pileformation and the bearing capacity of pile foundation butalso makes more errors in the actual penetration of pile andthe design elevation of pile foundation

In recent years scholars at home and abroad have carriedout a series of studies on pile sliding such as Guo andothers [1] analysing the causes of pile sliding in combinationwith the actual project and putting forward correspondingpreventive measures Sun and others [2ndash4] put forward

a calculation method for the length of the sliding piletaking into account the strength reduction of soil aroundthe pile and the excess pore pressure and other factorsLehane and others [5] used the static balance method toestimate the sliding pile interval Mijena [6] put forward aprediction method of pile slip and predicted the possibilityfor pile slip of 26 pipe piles Yin [7] analysed the pilesliding mechanism for large-diameter steel pipe piles andproposed the calculation method of pile sliding length Dover[8] analysed the influence of pile in situ stress interfacefriction angle and wall thickness on pile end resistancethrough experiments Yan [9] compared the pile side frictionresistance of friction piles based on theoretical and empiricalmathematical models Most of the above studies were carriedout for the reduction of pile side friction and calculation ofpile sliding length in the process of steel pipe pile slidingseldom considering the change of pile side friction at dif-ferent depths in the process of pile sliding and no differentcalculation methods were adopted for the actual engineeringsituation

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 3549296 8 pageshttpsdoiorg10115520193549296

2 Mathematical Problems in Engineering

surface soil layer

hard layer

so soil layer

hard soil layer

surface soil layer

hard soil layer

peening

pile running occurrence

end of pile runningpeening

pile running occurrence

end of pile running

Figure 1 Schematic diagram of pile-run phenomenon

Firstly the reasons for the sliding of large-diameter steelpipe piles of the offshore platform are analysed and thenthe relationship between the ultimate bearing capacity ofthe foundation and the pile ends resistance is calculated byconsidering the influence of sliding piles of the pile sidefriction resistance of different depths Then a new algorithmfor the sliding interval of large-diameter steeled pipe pilesis established by using the static balance and functionprinciple and the rationality and reliability of the algorithmare verified through the comparative analysis of engineeringexamples

2 Analysis of Slipping Pile

Engineering practice shows that [10] slip piles usually occurin the following two situations when the surface layer ofmarine soil is a soft soil layer with weak bearing capacitywhen the pile is driven into the soil layer with lower bearingcapacity from the soil layer with higher bearing capacity Dueto the nature of marine soil each steel pipe pile will slipbetween 0 to 3 times during piling

When the steel pipe pile has just entered the soil layer onthe ocean surface due to the weak bearing capacity of thesoil layer the pile will freely penetrate into the soil layer toa certain depth without hammering the pile hammer Whenthe pile enters the hard soil layer the pile end resistanceand side friction resistance become larger and the steel pipepile gradually penetrates into the soil under the action ofhammering When the pile enters the soft clay layer the pileend resistance decreases and the pile side friction resistance is

not enough to bear the quality of the pile and the pile hammerAt this time the pile will penetrate into the soil layer withouthammering ie the pile body will slip When the frictionresistance of the pile entering the hard soil layer or the pileside increases to a certain value the sliding of the pile stopsAs the pile continues to penetrate although the side frictionarea increases the side friction of the pile actually decreasesdue to the remolding of the soil Therefore when enteringthe soft soil layer again the phenomenon of secondary pilesliding will occur and Figure 1 is a schematic diagram of thephenomenon of pile sliding

When the total soil resistance of the pile body meets oneof the following conditions it is possible to slip the pile (1)the total soil resistance is less than the weight of the pile body(2) the total soil resistance is less than the gravity of pile andpile hammer (3) the total soil resistance is less than the inertiaforce of pile and pile hammer [11]

3 Calculation of Pile Driving Resistance

31 Calculation of Pile End Resistance Thepile end resistanceof large-diameter steel pipe pile in the process of pile slidingcan be obtained by calculating the soil resistance of theannular pile end Due to the different properties of soil layersnoncohesive soil and cohesive soil layers adopt differentformulas to calculate pile tip resistance For noncohesivesoil such as sand the resistance at the pile end is calculatedby formula of Berezantzev [12] and the ultimate bearingcapacity of annular end section of pile calculated is regardedas the end resistance of pile According to the calculation

Mathematical Problems in Engineering 3

Table 1 Ultimate bearing capacity coefficient of foundation

120593(∘) 0 5 10 15 20 25 30 35 40 45119873119903 0 051 120 180 40 110 218 454 125 326119873119902 10 164 269 445 742 127 225 413 813 1733

formula of Berezantzev the pile end resistance qu in sandysoil layer is

119902119906 = 119902119863119873119902 + 120574119861119873119903 (1)

where qu is the pile end resistance kPa Nq and Nr arethe ultimate bearing capacity coefficients of the foundationobtained from internal friction angle 120593 of foundation soilthe ultimate bearing capacity coefficient of the foundation islisted in Table 1[13] qD is effective overburden pressure at thebase level of the pile kPa B is the diameter of the steel pipepile m 120574 is the floating unit weight of the soil layer kNm3

For cohesive soil such as clay the annular section atthe bottom of the pile provides little bearing capacity forthe foundation According to API specifications it can becalculated by qu=Nrcu Som and Das [14] suggested that Nrof 9 is more suitable in viscous soil through experiment andanalysis so the pile end resistance in viscous soil is

119902119906 = 9119888119906 (2)

where cu is the undrained shear strength kNm2

32 Calculation of Pile Side Friction Through the analysisof pile sliding phenomenon it can be seen that the soil atthe bottom of the pile will undergo shear failure during theprocess of pile penetration into the soil the soil will form aremodelled area and the soil strengthwill change accordingly[15] This phenomenon will cause the plastic strength of thesoil to be lower than the strength of the original soil and theside friction coefficient to be reduced Therefore the staticfriction between piles and soil is not suitable for the sidefriction of piles and the dynamic friction between piles andsoil needs to be calculated

Dover and Davidson [8] found through experiments andanalysis that the dynamic side friction of steel pipe pilescan be reduced by 07 to 09 times in sandy soil Zhang [16]thinks that in the process of pile sinking a soil plug 10 timesthe pile diameter will be formed inside the steel pipe pile inthe large straight street and the friction resistance inside thepile wall is 50 of the friction resistance outside the pileTherefore on the basis of considering the internal frictionof the pile wall the static friction between pile and soil isreduced by a reduction factor and the dynamic friction 119891sformula of steel pipe pile in sandy soil layer is obtained asfollows

119891s = 1205721198961199010 tan 120575 (3)

where 120572 is the reduction factor of sand dynamic frictionside resistance and 075 is more reasonable in marine rockand soil k is the foundation pressure coefficient p0 is theoverburden pressure of the soil layer kNm2 120575 is the frictionangle outside the soil body

Friction per unit pile side (kPa)

zH

0 20 40 60

04

08

12

16

a

b

Figure 2 Change of unit friction resistance

The calculation of friction resistance of steel pipe pilein clay layer also needs to reduce the strength of soil Li[17] found through analysis and experiment that the pileside friction at different positions below the surface of theexcavated body is affected by sliding piles in different degreesdividing the depth of pile penetration into three affectedareas and Figure 2 shows the change of unit side friction indifferent affected areas

As shown in Figure 2 curve a represents the unit sidefrictional resistance at each depth at the end of pile slidingCurve b shows the unit side friction at each depth at the endof pile driving z is the depth of soil below the mud surfaceand H is the depth at the end of pile sliding According tothe ratio between the depth z of soil below the mud surfaceand the depth H at the end of pipe pile sliding the pipe pileentering the soil layer is divided into a complete influencearea an incomplete influence area and a non-influence area

Combined with the above considerations when the steelpipe pile slips for the first time the dynamic side friction ofthe pile can be calculated by the modified API method andthe calculation formula is

119891 = 03120573119888119906 (4)

where 120573 is the adhesion coefficient and cu is the undrainedshear strength kNm2 When cu ge72kpa 120573=05 and when24kPalecu lt72kPa 120573 increases linearly in the [051] range

For the case of secondary sliding of steel pipe piles whencalculating the dynamic side friction of piles in clay layer it is

4 Mathematical Problems in Engineering

necessary to consider the influence of the first sliding of pileson the side friction of piles and according to the differentdegree of influence the interval of pile penetration depth isdivided into three influence zones namely fully affected areasemi-fully affected area and no affected areas

(a) Fully Affected Area When zHlt05 the side frictionresistance at the end of pile sliding is basically the same asthe side friction resistance at the end of pile driving andthe value is very small This part of soil is the area mostseriously affected by pile sliding and is called the fully affectedarea Therefore the dynamic friction resistance of the pile isreduced to 0075 times of the static friction resistance and thecalculation formula is

119891119889 = 0075119891 (5)

where f d is the dynamic side friction in clay layer kN and fis the static side friction kN

(b) Semi-Fully Affected Areas When 05ltzHlt08 the soilmass in this area is characterized by a certain soil resistance atthe time of the second pile slip but with the subsequent pileslip the side friction decreases rapidly which is called partof the affected area The influence of the final depth of pilepenetration hence needs to be considered in the calculationA If zHend gt044 the designed depth of pile penetrationis small the design depth of pile driving distance after pilesliding is small and the influence of subsequent pile drivingon soil properties is small the modified API method can stillbe used for calculationB If zHend lt044 when the designeddepth of mud entry is large the subsequent piling will havea great impact on the soil properties and the formula forcalculating the dynamic side friction resistance at this timeis as follows

119891119889 = 0075119891 (6)

(c) No Affected Areas When zHgt08 the disturbance ofsliding pile to soil in this area is small the side friction of pilebody is ignored by sliding pile and the modified APImethodcan still be used to calculate the side friction of pile body sothe formula for calculating the side friction of this area is

119891 = 03120573119888119906 (7)

where when cu ge72kPa 120573=05 and when 24kPalecu lt72kPa120573 increases linearly in the [05 1] range4 Calculation of Pile Sliding Interval

Based on the analysis of pile sliding mechanism the calcu-lation process of the existing pile sliding interval algorithmis improved First the pile end resistance is obtained byusing Berezantzevrsquos formula and then the friction resistanceis calculated by using different reduction factors in differentinfluence areas In sandy soil the friction resistance of thepile side is calculated by conventional methods Based on thedynamic process of pile sliding a new algorithm of large-diameter steel pipe pile sliding interval is established by usingstatic balance and functional principles

When the steel pipe pile penetrates into the marinesoil layer the pile will be affected by the hammering forceof hydraulic hammer its own gravity buoyancy pile endresistance and pile side friction According to dynamicexperience when the hydraulic hammer blows the pipe pilethe power of the pipe pile and the hydraulic hammer isregarded as 12 times that of the gravity G1+G2 of the pile andthe hydraulic hammer [18] so when the stress condition ofthe pipe pile meets the following formula slip of the pipe pilewill occur and the mud depth L of the pipe pile when slip ofthe pipe pile occurs can be calculated through

12 (1198661 + 1198662) = 119891 + 119902119906 + 119865 (8)

where F is the buoyancy of the pipe pile kNWith the progress of sliding pile the speed of steel pipe

pile will gradually decrease to zero under the action ofsoil resistance and buoyancy the kinetic energy of pile willdissipate in overcoming soil resistance and buoyancy to dowork so the energy equation can be listed according to thefunctional principle and the length of sliding pile can becalculated The formula for calculating the work done by thefriction force on the pile side during pile sliding is

1198821 = 119909sum119894=1

(1198911198981198941205871198611198972) + 119910sum119895=1

(int1198970119891119898119895d119911) (9)

where1198821 is the work done by pile side friction resistance kJB is the diameter of steel pipe pile m x is the number of soillayers at the beginning of pile sliding f mj is the friction forceof layer i soil before the slip pile occurs kN 119910 is the quantityof soil layers included in the pile sliding interval f mj is thefriction force of the j-layer soil in the sliding pile interval kNz is the sliding distance of each layer of soil in the sliding pileinterval m

According to the integral calculus method f mj is apiecewise function in the sliding pile interval so the gen-eral formula for calculating the dynamic friction resistancebetween clay and sand layers in the sliding pile interval is asfollows

119891119898119889 = 120573119888119906120587119861 sdot 119911 (0 le 119911 le 119905)120573119888119906120587119861 sdot 119905 (t lt 119911 le 119897) (10)

119891119898119904 = 120572119896(119901119895minus1 + 1205871198612z1205741198954 ) tan 120575 (0 le 119911 le 119905)120572119896119901j tan 120575 (119905 lt 119911 lt 119897) (11)

where f md is the friction force of the j-layer clay in the slidingpile interval kN t is the thickness of the corresponding soillayer m f ms is the friction force of layer j sand in the slidingpile interval kN pj-1 is the overburden pressure of layer j-1soil kN 120574j is the severe degree of sand in layer j kNm3 pj isthe overburden pressure of layer j soil kN

In the process of pipe sliding the work done by thepile end resistance can be obtained by integrating the other

Mathematical Problems in Engineering 5

columns of Berezantzevrsquos formula and the calculation for-mula is as follows

1198822 = (119910minus1sum119895=1

119902119906 sdot 119905) + 119902119906 sdot 1199051015840 (12)

where1198822 is the work done by pile end resistance kJ and T1015840 is

the insertion length of steel pipe piles in the soil layer wherethey stay at the end of pile sliding m

The buoyancy Ff received by the steel pipe pile willgradually increase with the progress of the sliding pile so thecalculation method of the work1198823 done by buoyancy is

1198823 = int119897+119871119871(141205871198612120588g) 119911d119911 (13)

where 120588 is the water density kgm3 and g is the gravityacceleration ms2

When hydraulic hammer hammers a steel pipe pilethere will be energy dissipation usually corrected by usingthe coefficient so the energy of the pile and hammer atthe beginning of sliding pile is 120578E Based on the aboveconsiderations according to the conservation of energy it canbe concluded that the energy equation of the pile satisfies thefollowing

120578119864 = minus (1198661 + 1198662) 119897 + 1198821 +1198822 +1198823 (14)

According to (14) the length L of the slip pile can beobtained and the slip interval of the steel pipe pile can beobtained by combining the depth L of the pipe pile into themud when the slip pile occurs

5 Engineering Case Checking

According to the engineering data collected during theconstruction of Liwan pile foundation platform in the SouthChina Sea reasonable soil parameters are selected and thenew algorithm is used to calculate the pile sliding intervalof steel pipe piles The calculation results are comparedand analysed with the actual pile sliding interval and therationality of the new algorithm is verified through thecomparison results

The pile foundation platform has 16 steel pipe pileswhich are evenly distributed on the four corners of the pilefoundation platform Each steel pipe pile weighs 6439kg andhas a diameter of 274m and a pile length of 158mThemodelof hydraulic hammer is MHU1200s and the rated outputenergy is 1200kJ In order to ensure the same soil propertiesaround steel pipe piles four steel pipe piles on one cornerof the platform were selected for calculation and analysisThrough the analysis of soil parameters it can be seen thatthe soft and hard soil layers of the soil layer where the steelpipe pile is located alternate and the shallow soil layer has along clay layer so it is easy to slip the pile At the soil depths of588m and 108m the soft clay layer appears again at this timeit is likely that the secondary slip pile or even the tertiary slippile will occurThe soil parameters of the soil layer where thesteel pipe pile is located are listed in Table 2

Combined with the soil parameters selected in the actualproject the pile end resistance sand dynamic side frictionresistance and clay static friction resistance of each layer ofsoil in the pile driving process of steel pipe piles are calculatedusing (1)-(7) From the calculation results in Table 2 it canbe seen that the pile end resistance received by the pile bodyin the sand layer is larger the pile side friction resistance issmaller the pile end resistance in the clay layer is smaller andthe pile side friction resistance is larger When the pipe pilejust penetrates the soil layer the pile end resistance bears thegravity of the pile and the pile hammer which also verifies thereason for the slip pile

According to the calculated pile end resistance and pileside friction of each soil layer in Table 2 the mud entrydepth L of the pipe pile when slip pile occurs is calculatedby formula (8) and the mud entry depths L satisfyingformula (8) are 133m 380m and 649m m Then the workexpression of pile side friction including slip pile intervall is obtained through formulas (9)-(11) and three slip pileintervals are defined Through the formulas (12) and (13)the expressions of friction resistance and buoyancy work atthe pile end containing the slip pile interval l are obtainedBy substituting the above expressions into formula (14) theslip pile interval l is obtained as 137m 225m and 171mm Therefore under this actual working condition the slipinterval of pipe pile is 133 m sim 27 m 380 m sim 605 mand 649 m sim 840 m Through the comparison between thetheoretical pile sliding interval and the actual engineering pilesliding interval the comparison result shown in Figure 3 isobtained

From the comparison results it can be seen that thedepth of pile entry and the interval of the first two pile slipsare basically consistent with the actual engineering situationThere are some deviations in the calculation of the third pilesliding interval because the second pile sliding also affectsthe soil mass and changes the pile side friction but the thirdpile sliding interval is smaller than the theoretical calculationinterval length and within the safe range of pile foundationengineering so the theoretical pile sliding interval can stillprovide a reference for the design of pile foundation andalso verify the theory that the calculation of the pile slidinginterval needs to consider the influence of the pile slidingon the soil mass so the new algorithm and the traditionalmethod are more consistent with the actual pile slidinginterval and have higher accuracy The pile sliding intervalobtained by the new algorithm is basically consistent withthe actual pile sliding interval and the rationality of the newalgorithm is verified

6 Conclusions

Through the analysis and research on the process of pilesliding and its causes the conclusions are as follows

(1) When the steel pipe pile slips for the second timeconsidering the different influence degree of sliding pileon the pile side friction the side friction of the pile inthe clay layer is divided into three influence areas namelyfull influence area half influence area and no influencearea Using different reduction factors to calculate the

6 Mathematical Problems in Engineering

Table2Th

eparam

eterso

fsoillayersa

ndcalculationresults

ofsoilparameters

number

prop

erty

thickn

essm

cohesio

nkP

africtio

nangle(∘ )

unit

weightkNsdotmminus3

floor

elevationm

pileend

resistancekN

dynamicfrictio

nresistancekN

static

frictio

nresistancekN

1medium

dense

finetocoarse

sand

24

039

85

30

32917

39

2softto

hard

clay

7935

089

109

2599

10241

3denses

ilt23

037

89

132

5944

1123

4denses

andy

silt

andhard

clay

interbedded

7870

086

210

5198

1644

2

5hard

silty

clay

36

500

92246

3712

5

4119

6denses

iltyfin

esand

84

039

85

330

90846

2717

7denses

iltyfin

esand

203

900

83

533

6683

55016

8hard

silty

clay

61

800

90594

594

14479

9hard

silty

clay

54

036

86

648

155981

5827

10

hard

clay

114

100

088

762

7425

33891

11denses

andy

silt

34

036

83

796

139635

717

12

hard

silty

clay

293

120

085

1089

891

105875

13denses

andy

silt

29

036

85

1118

26554

13945

14

hard

clay

196

160

090

1314

1188

9443

Mathematical Problems in Engineering 7

No1 pile

No2 pile

No3 pile

No4 pile

10 20 30 40 50 60 70 80 90 100 110 Buried depth (m)

eoretical pile sliding intervalActual pile sliding interval

Figure 3 Comparison between theoretical and practical pile-run interval

side friction of the pile in different influence areas willmake the new calculation result closer to the engineeringpractice

(2) When calculating the sliding interval of steel pipepiles the static balance principle is used to calculate the depthof pipe pile entering the mud at the beginning of slidingthe expression of pile side friction resistance and pile endresistance in different influence areas is listed by integratingtheory and according to the functional principle the energyequation of pipe pile is listed thus obtaining the slidinginterval of steel pipe piles

(3)Through the verification of an engineering examplethe error range between the calculation result of the first andsecond sliding pile interval of the new algorithm and theactual situation is 8 sim 16 with high accuracy Althoughthe third result is somewhat deviated the actual slidingpile interval is smaller than the theoretical actual slidingpile interval and is within the safe range of pile foundationengineering which can still provide a reference for the designand construction of offshore platform pile foundation

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

This study was financially supported by the National NaturalScience Foundation of China (no 41372288) and the Projectof Science and Technology Innovation Fund for graduate stu-dents of the Shandong University of Science and Technology(no SDKDYC180212)

References

[1] S C Guo and S L Wu ldquoProblems of rapid sinking during piledriving and solutionsrdquoPortamp Waterway Engineering vol 12 pp163ndash166 2011

[2] L Sun T Jia S Yan and Z Jia ldquoResearch on prediction of pilerunning during large diameter pipe piles drivingrdquo Journal ofChina University of Petroleum vol 40 no 02 pp 115ndash122 2016

[3] L Sun Y Wang W Guo S Yan J Chu and X Liu ldquoCase studyon pile running during the driving process of large-diameterpipe pilesrdquo Marine Georesources amp Geotechnology vol 36 no6 pp 709ndash721 2018

[4] L Sun T Jia S Yan W Guo Y Ren and Z Lei ldquoPrediction ofpile running during the driving process of large diameter pipepilesrdquo Ocean Engineering vol 128 pp 48ndash57 2016

[5] B M Lehane and K G Gavin ldquoBase resistance of jacked pipepiles in sandrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 127 no 6 pp 473ndash480 2001

[6] E H Mijena A Comparison of Friction Piles Bearing Capac-ity Based on Theoretical and Empirical Mathematical ModelsGeotechnics and Geohazards Norwegian University of Scienceand Technology Norway 2012

[7] H J Yin Y X Liu XW Zhang et al ldquoThenewmethod for free-fall analysis of large diameter and super-long steel pilerdquo ChinaOffshore Oil and Cas vol 26 no S1 pp 35ndash38 2014

[8] A R Dover and J Davidson ldquoLarge Diameter Steel Pipe PilesRunning under SelfWeight in Soft Clay Predicted vs ObservedBehavior mdash Richmond San-Rafael Bridge Seismic Retrofitrdquo inProceedings of the 11th Triennial International Conference onPorts pp 1ndash10 San Diego Calif United States 2007

[9] S-W Yan Z-L Jia L-Q Sun and X-W Zhang ldquoMechanismsand calculation of pile-run for long and large diameter pilesrdquoEngineering Mechanics vol 32 no 09 pp 158ndash164 2015

[10] M F Randolph ldquoScience and empiricism in pile foundationdesignrdquo Geotechnique vol 53 no 10 pp 847ndash875 2003

[11] Z L Jia Study on the Dynamic Penetration Resistance andMechanism of Free-Running of Large Diameter and Super LongOcean Platform Piles Tianjin University 2016

[12] N S V K Rao Foundation Design Theory and Practice JohnWiley amp Sons Ltd Chichester UK 2010

8 Mathematical Problems in Engineering

[13] J-P Gao M-H Yu and S-P Li ldquoDouble-shear unified solutionof Terzaghi ultimate bearing capacity of foundationrdquo ChineseJournal of Rock Mechanics and Engineering vol 24 no 15 pp2736ndash2740 2005

[14] N Som and S CDasTheory and Practice of Foundation DesignPrentice-Hall of India New Delhi India 2003

[15] J DeKuiter andF L Beringen ldquoPile foundations for largeNorthSea structuresrdquoMarine Geotechnology vol 3 no 3 pp 267ndash3141979

[16] H S Zhang J Yang D Yan et al ldquoStudy on the slip piledepth prediction for offshore drilling conductor installationrdquoOil Drilling amp Production Technology vol 35 no 03 pp 22ndash242013

[17] S Li X Z Wu Y C Wang et al ldquoSoil resistance to drivingconsidering effect of pile running on pile installationrdquo ChineseJournal of Geotechnical Engineering vol 37 no 06 pp 1150ndash11572015

[18] L Zhang and J J Chen ldquoEffect of spatial correlation of standardpenetration test (SPT) data on bearing capacity of driven pilesin sandrdquo Canadian Geotechnical Journal vol 49 no 4 pp 394ndash402 2012

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Mathematical Problems in Engineering 3

Table 1 Ultimate bearing capacity coefficient of foundation

120593(∘) 0 5 10 15 20 25 30 35 40 45119873119903 0 051 120 180 40 110 218 454 125 326119873119902 10 164 269 445 742 127 225 413 813 1733

formula of Berezantzev the pile end resistance qu in sandysoil layer is

119902119906 = 119902119863119873119902 + 120574119861119873119903 (1)

where qu is the pile end resistance kPa Nq and Nr arethe ultimate bearing capacity coefficients of the foundationobtained from internal friction angle 120593 of foundation soilthe ultimate bearing capacity coefficient of the foundation islisted in Table 1[13] qD is effective overburden pressure at thebase level of the pile kPa B is the diameter of the steel pipepile m 120574 is the floating unit weight of the soil layer kNm3

For cohesive soil such as clay the annular section atthe bottom of the pile provides little bearing capacity forthe foundation According to API specifications it can becalculated by qu=Nrcu Som and Das [14] suggested that Nrof 9 is more suitable in viscous soil through experiment andanalysis so the pile end resistance in viscous soil is

119902119906 = 9119888119906 (2)

where cu is the undrained shear strength kNm2

32 Calculation of Pile Side Friction Through the analysisof pile sliding phenomenon it can be seen that the soil atthe bottom of the pile will undergo shear failure during theprocess of pile penetration into the soil the soil will form aremodelled area and the soil strengthwill change accordingly[15] This phenomenon will cause the plastic strength of thesoil to be lower than the strength of the original soil and theside friction coefficient to be reduced Therefore the staticfriction between piles and soil is not suitable for the sidefriction of piles and the dynamic friction between piles andsoil needs to be calculated

Dover and Davidson [8] found through experiments andanalysis that the dynamic side friction of steel pipe pilescan be reduced by 07 to 09 times in sandy soil Zhang [16]thinks that in the process of pile sinking a soil plug 10 timesthe pile diameter will be formed inside the steel pipe pile inthe large straight street and the friction resistance inside thepile wall is 50 of the friction resistance outside the pileTherefore on the basis of considering the internal frictionof the pile wall the static friction between pile and soil isreduced by a reduction factor and the dynamic friction 119891sformula of steel pipe pile in sandy soil layer is obtained asfollows

119891s = 1205721198961199010 tan 120575 (3)

where 120572 is the reduction factor of sand dynamic frictionside resistance and 075 is more reasonable in marine rockand soil k is the foundation pressure coefficient p0 is theoverburden pressure of the soil layer kNm2 120575 is the frictionangle outside the soil body

Friction per unit pile side (kPa)

zH

0 20 40 60

04

08

12

16

a

b

Figure 2 Change of unit friction resistance

The calculation of friction resistance of steel pipe pilein clay layer also needs to reduce the strength of soil Li[17] found through analysis and experiment that the pileside friction at different positions below the surface of theexcavated body is affected by sliding piles in different degreesdividing the depth of pile penetration into three affectedareas and Figure 2 shows the change of unit side friction indifferent affected areas

As shown in Figure 2 curve a represents the unit sidefrictional resistance at each depth at the end of pile slidingCurve b shows the unit side friction at each depth at the endof pile driving z is the depth of soil below the mud surfaceand H is the depth at the end of pile sliding According tothe ratio between the depth z of soil below the mud surfaceand the depth H at the end of pipe pile sliding the pipe pileentering the soil layer is divided into a complete influencearea an incomplete influence area and a non-influence area

Combined with the above considerations when the steelpipe pile slips for the first time the dynamic side friction ofthe pile can be calculated by the modified API method andthe calculation formula is

119891 = 03120573119888119906 (4)

where 120573 is the adhesion coefficient and cu is the undrainedshear strength kNm2 When cu ge72kpa 120573=05 and when24kPalecu lt72kPa 120573 increases linearly in the [051] range

For the case of secondary sliding of steel pipe piles whencalculating the dynamic side friction of piles in clay layer it is

4 Mathematical Problems in Engineering

necessary to consider the influence of the first sliding of pileson the side friction of piles and according to the differentdegree of influence the interval of pile penetration depth isdivided into three influence zones namely fully affected areasemi-fully affected area and no affected areas

(a) Fully Affected Area When zHlt05 the side frictionresistance at the end of pile sliding is basically the same asthe side friction resistance at the end of pile driving andthe value is very small This part of soil is the area mostseriously affected by pile sliding and is called the fully affectedarea Therefore the dynamic friction resistance of the pile isreduced to 0075 times of the static friction resistance and thecalculation formula is

119891119889 = 0075119891 (5)

where f d is the dynamic side friction in clay layer kN and fis the static side friction kN

(b) Semi-Fully Affected Areas When 05ltzHlt08 the soilmass in this area is characterized by a certain soil resistance atthe time of the second pile slip but with the subsequent pileslip the side friction decreases rapidly which is called partof the affected area The influence of the final depth of pilepenetration hence needs to be considered in the calculationA If zHend gt044 the designed depth of pile penetrationis small the design depth of pile driving distance after pilesliding is small and the influence of subsequent pile drivingon soil properties is small the modified API method can stillbe used for calculationB If zHend lt044 when the designeddepth of mud entry is large the subsequent piling will havea great impact on the soil properties and the formula forcalculating the dynamic side friction resistance at this timeis as follows

119891119889 = 0075119891 (6)

(c) No Affected Areas When zHgt08 the disturbance ofsliding pile to soil in this area is small the side friction of pilebody is ignored by sliding pile and the modified APImethodcan still be used to calculate the side friction of pile body sothe formula for calculating the side friction of this area is

119891 = 03120573119888119906 (7)

where when cu ge72kPa 120573=05 and when 24kPalecu lt72kPa120573 increases linearly in the [05 1] range4 Calculation of Pile Sliding Interval

Based on the analysis of pile sliding mechanism the calcu-lation process of the existing pile sliding interval algorithmis improved First the pile end resistance is obtained byusing Berezantzevrsquos formula and then the friction resistanceis calculated by using different reduction factors in differentinfluence areas In sandy soil the friction resistance of thepile side is calculated by conventional methods Based on thedynamic process of pile sliding a new algorithm of large-diameter steel pipe pile sliding interval is established by usingstatic balance and functional principles

When the steel pipe pile penetrates into the marinesoil layer the pile will be affected by the hammering forceof hydraulic hammer its own gravity buoyancy pile endresistance and pile side friction According to dynamicexperience when the hydraulic hammer blows the pipe pilethe power of the pipe pile and the hydraulic hammer isregarded as 12 times that of the gravity G1+G2 of the pile andthe hydraulic hammer [18] so when the stress condition ofthe pipe pile meets the following formula slip of the pipe pilewill occur and the mud depth L of the pipe pile when slip ofthe pipe pile occurs can be calculated through

12 (1198661 + 1198662) = 119891 + 119902119906 + 119865 (8)

where F is the buoyancy of the pipe pile kNWith the progress of sliding pile the speed of steel pipe

pile will gradually decrease to zero under the action ofsoil resistance and buoyancy the kinetic energy of pile willdissipate in overcoming soil resistance and buoyancy to dowork so the energy equation can be listed according to thefunctional principle and the length of sliding pile can becalculated The formula for calculating the work done by thefriction force on the pile side during pile sliding is

1198821 = 119909sum119894=1

(1198911198981198941205871198611198972) + 119910sum119895=1

(int1198970119891119898119895d119911) (9)

where1198821 is the work done by pile side friction resistance kJB is the diameter of steel pipe pile m x is the number of soillayers at the beginning of pile sliding f mj is the friction forceof layer i soil before the slip pile occurs kN 119910 is the quantityof soil layers included in the pile sliding interval f mj is thefriction force of the j-layer soil in the sliding pile interval kNz is the sliding distance of each layer of soil in the sliding pileinterval m

According to the integral calculus method f mj is apiecewise function in the sliding pile interval so the gen-eral formula for calculating the dynamic friction resistancebetween clay and sand layers in the sliding pile interval is asfollows

119891119898119889 = 120573119888119906120587119861 sdot 119911 (0 le 119911 le 119905)120573119888119906120587119861 sdot 119905 (t lt 119911 le 119897) (10)

119891119898119904 = 120572119896(119901119895minus1 + 1205871198612z1205741198954 ) tan 120575 (0 le 119911 le 119905)120572119896119901j tan 120575 (119905 lt 119911 lt 119897) (11)

where f md is the friction force of the j-layer clay in the slidingpile interval kN t is the thickness of the corresponding soillayer m f ms is the friction force of layer j sand in the slidingpile interval kN pj-1 is the overburden pressure of layer j-1soil kN 120574j is the severe degree of sand in layer j kNm3 pj isthe overburden pressure of layer j soil kN

In the process of pipe sliding the work done by thepile end resistance can be obtained by integrating the other

Mathematical Problems in Engineering 5

columns of Berezantzevrsquos formula and the calculation for-mula is as follows

1198822 = (119910minus1sum119895=1

119902119906 sdot 119905) + 119902119906 sdot 1199051015840 (12)

where1198822 is the work done by pile end resistance kJ and T1015840 is

the insertion length of steel pipe piles in the soil layer wherethey stay at the end of pile sliding m

The buoyancy Ff received by the steel pipe pile willgradually increase with the progress of the sliding pile so thecalculation method of the work1198823 done by buoyancy is

1198823 = int119897+119871119871(141205871198612120588g) 119911d119911 (13)

where 120588 is the water density kgm3 and g is the gravityacceleration ms2

When hydraulic hammer hammers a steel pipe pilethere will be energy dissipation usually corrected by usingthe coefficient so the energy of the pile and hammer atthe beginning of sliding pile is 120578E Based on the aboveconsiderations according to the conservation of energy it canbe concluded that the energy equation of the pile satisfies thefollowing

120578119864 = minus (1198661 + 1198662) 119897 + 1198821 +1198822 +1198823 (14)

According to (14) the length L of the slip pile can beobtained and the slip interval of the steel pipe pile can beobtained by combining the depth L of the pipe pile into themud when the slip pile occurs

5 Engineering Case Checking

According to the engineering data collected during theconstruction of Liwan pile foundation platform in the SouthChina Sea reasonable soil parameters are selected and thenew algorithm is used to calculate the pile sliding intervalof steel pipe piles The calculation results are comparedand analysed with the actual pile sliding interval and therationality of the new algorithm is verified through thecomparison results

The pile foundation platform has 16 steel pipe pileswhich are evenly distributed on the four corners of the pilefoundation platform Each steel pipe pile weighs 6439kg andhas a diameter of 274m and a pile length of 158mThemodelof hydraulic hammer is MHU1200s and the rated outputenergy is 1200kJ In order to ensure the same soil propertiesaround steel pipe piles four steel pipe piles on one cornerof the platform were selected for calculation and analysisThrough the analysis of soil parameters it can be seen thatthe soft and hard soil layers of the soil layer where the steelpipe pile is located alternate and the shallow soil layer has along clay layer so it is easy to slip the pile At the soil depths of588m and 108m the soft clay layer appears again at this timeit is likely that the secondary slip pile or even the tertiary slippile will occurThe soil parameters of the soil layer where thesteel pipe pile is located are listed in Table 2

Combined with the soil parameters selected in the actualproject the pile end resistance sand dynamic side frictionresistance and clay static friction resistance of each layer ofsoil in the pile driving process of steel pipe piles are calculatedusing (1)-(7) From the calculation results in Table 2 it canbe seen that the pile end resistance received by the pile bodyin the sand layer is larger the pile side friction resistance issmaller the pile end resistance in the clay layer is smaller andthe pile side friction resistance is larger When the pipe pilejust penetrates the soil layer the pile end resistance bears thegravity of the pile and the pile hammer which also verifies thereason for the slip pile

According to the calculated pile end resistance and pileside friction of each soil layer in Table 2 the mud entrydepth L of the pipe pile when slip pile occurs is calculatedby formula (8) and the mud entry depths L satisfyingformula (8) are 133m 380m and 649m m Then the workexpression of pile side friction including slip pile intervall is obtained through formulas (9)-(11) and three slip pileintervals are defined Through the formulas (12) and (13)the expressions of friction resistance and buoyancy work atthe pile end containing the slip pile interval l are obtainedBy substituting the above expressions into formula (14) theslip pile interval l is obtained as 137m 225m and 171mm Therefore under this actual working condition the slipinterval of pipe pile is 133 m sim 27 m 380 m sim 605 mand 649 m sim 840 m Through the comparison between thetheoretical pile sliding interval and the actual engineering pilesliding interval the comparison result shown in Figure 3 isobtained

From the comparison results it can be seen that thedepth of pile entry and the interval of the first two pile slipsare basically consistent with the actual engineering situationThere are some deviations in the calculation of the third pilesliding interval because the second pile sliding also affectsthe soil mass and changes the pile side friction but the thirdpile sliding interval is smaller than the theoretical calculationinterval length and within the safe range of pile foundationengineering so the theoretical pile sliding interval can stillprovide a reference for the design of pile foundation andalso verify the theory that the calculation of the pile slidinginterval needs to consider the influence of the pile slidingon the soil mass so the new algorithm and the traditionalmethod are more consistent with the actual pile slidinginterval and have higher accuracy The pile sliding intervalobtained by the new algorithm is basically consistent withthe actual pile sliding interval and the rationality of the newalgorithm is verified

6 Conclusions

Through the analysis and research on the process of pilesliding and its causes the conclusions are as follows

(1) When the steel pipe pile slips for the second timeconsidering the different influence degree of sliding pileon the pile side friction the side friction of the pile inthe clay layer is divided into three influence areas namelyfull influence area half influence area and no influencearea Using different reduction factors to calculate the

6 Mathematical Problems in Engineering

Table2Th

eparam

eterso

fsoillayersa

ndcalculationresults

ofsoilparameters

number

prop

erty

thickn

essm

cohesio

nkP

africtio

nangle(∘ )

unit

weightkNsdotmminus3

floor

elevationm

pileend

resistancekN

dynamicfrictio

nresistancekN

static

frictio

nresistancekN

1medium

dense

finetocoarse

sand

24

039

85

30

32917

39

2softto

hard

clay

7935

089

109

2599

10241

3denses

ilt23

037

89

132

5944

1123

4denses

andy

silt

andhard

clay

interbedded

7870

086

210

5198

1644

2

5hard

silty

clay

36

500

92246

3712

5

4119

6denses

iltyfin

esand

84

039

85

330

90846

2717

7denses

iltyfin

esand

203

900

83

533

6683

55016

8hard

silty

clay

61

800

90594

594

14479

9hard

silty

clay

54

036

86

648

155981

5827

10

hard

clay

114

100

088

762

7425

33891

11denses

andy

silt

34

036

83

796

139635

717

12

hard

silty

clay

293

120

085

1089

891

105875

13denses

andy

silt

29

036

85

1118

26554

13945

14

hard

clay

196

160

090

1314

1188

9443

Mathematical Problems in Engineering 7

No1 pile

No2 pile

No3 pile

No4 pile

10 20 30 40 50 60 70 80 90 100 110 Buried depth (m)

eoretical pile sliding intervalActual pile sliding interval

Figure 3 Comparison between theoretical and practical pile-run interval

side friction of the pile in different influence areas willmake the new calculation result closer to the engineeringpractice

(2) When calculating the sliding interval of steel pipepiles the static balance principle is used to calculate the depthof pipe pile entering the mud at the beginning of slidingthe expression of pile side friction resistance and pile endresistance in different influence areas is listed by integratingtheory and according to the functional principle the energyequation of pipe pile is listed thus obtaining the slidinginterval of steel pipe piles

(3)Through the verification of an engineering examplethe error range between the calculation result of the first andsecond sliding pile interval of the new algorithm and theactual situation is 8 sim 16 with high accuracy Althoughthe third result is somewhat deviated the actual slidingpile interval is smaller than the theoretical actual slidingpile interval and is within the safe range of pile foundationengineering which can still provide a reference for the designand construction of offshore platform pile foundation

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

This study was financially supported by the National NaturalScience Foundation of China (no 41372288) and the Projectof Science and Technology Innovation Fund for graduate stu-dents of the Shandong University of Science and Technology(no SDKDYC180212)

References

[1] S C Guo and S L Wu ldquoProblems of rapid sinking during piledriving and solutionsrdquoPortamp Waterway Engineering vol 12 pp163ndash166 2011

[2] L Sun T Jia S Yan and Z Jia ldquoResearch on prediction of pilerunning during large diameter pipe piles drivingrdquo Journal ofChina University of Petroleum vol 40 no 02 pp 115ndash122 2016

[3] L Sun Y Wang W Guo S Yan J Chu and X Liu ldquoCase studyon pile running during the driving process of large-diameterpipe pilesrdquo Marine Georesources amp Geotechnology vol 36 no6 pp 709ndash721 2018

[4] L Sun T Jia S Yan W Guo Y Ren and Z Lei ldquoPrediction ofpile running during the driving process of large diameter pipepilesrdquo Ocean Engineering vol 128 pp 48ndash57 2016

[5] B M Lehane and K G Gavin ldquoBase resistance of jacked pipepiles in sandrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 127 no 6 pp 473ndash480 2001

[6] E H Mijena A Comparison of Friction Piles Bearing Capac-ity Based on Theoretical and Empirical Mathematical ModelsGeotechnics and Geohazards Norwegian University of Scienceand Technology Norway 2012

[7] H J Yin Y X Liu XW Zhang et al ldquoThenewmethod for free-fall analysis of large diameter and super-long steel pilerdquo ChinaOffshore Oil and Cas vol 26 no S1 pp 35ndash38 2014

[8] A R Dover and J Davidson ldquoLarge Diameter Steel Pipe PilesRunning under SelfWeight in Soft Clay Predicted vs ObservedBehavior mdash Richmond San-Rafael Bridge Seismic Retrofitrdquo inProceedings of the 11th Triennial International Conference onPorts pp 1ndash10 San Diego Calif United States 2007

[9] S-W Yan Z-L Jia L-Q Sun and X-W Zhang ldquoMechanismsand calculation of pile-run for long and large diameter pilesrdquoEngineering Mechanics vol 32 no 09 pp 158ndash164 2015

[10] M F Randolph ldquoScience and empiricism in pile foundationdesignrdquo Geotechnique vol 53 no 10 pp 847ndash875 2003

[11] Z L Jia Study on the Dynamic Penetration Resistance andMechanism of Free-Running of Large Diameter and Super LongOcean Platform Piles Tianjin University 2016

[12] N S V K Rao Foundation Design Theory and Practice JohnWiley amp Sons Ltd Chichester UK 2010

8 Mathematical Problems in Engineering

[13] J-P Gao M-H Yu and S-P Li ldquoDouble-shear unified solutionof Terzaghi ultimate bearing capacity of foundationrdquo ChineseJournal of Rock Mechanics and Engineering vol 24 no 15 pp2736ndash2740 2005

[14] N Som and S CDasTheory and Practice of Foundation DesignPrentice-Hall of India New Delhi India 2003

[15] J DeKuiter andF L Beringen ldquoPile foundations for largeNorthSea structuresrdquoMarine Geotechnology vol 3 no 3 pp 267ndash3141979

[16] H S Zhang J Yang D Yan et al ldquoStudy on the slip piledepth prediction for offshore drilling conductor installationrdquoOil Drilling amp Production Technology vol 35 no 03 pp 22ndash242013

[17] S Li X Z Wu Y C Wang et al ldquoSoil resistance to drivingconsidering effect of pile running on pile installationrdquo ChineseJournal of Geotechnical Engineering vol 37 no 06 pp 1150ndash11572015

[18] L Zhang and J J Chen ldquoEffect of spatial correlation of standardpenetration test (SPT) data on bearing capacity of driven pilesin sandrdquo Canadian Geotechnical Journal vol 49 no 4 pp 394ndash402 2012

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4 Mathematical Problems in Engineering

necessary to consider the influence of the first sliding of pileson the side friction of piles and according to the differentdegree of influence the interval of pile penetration depth isdivided into three influence zones namely fully affected areasemi-fully affected area and no affected areas

(a) Fully Affected Area When zHlt05 the side frictionresistance at the end of pile sliding is basically the same asthe side friction resistance at the end of pile driving andthe value is very small This part of soil is the area mostseriously affected by pile sliding and is called the fully affectedarea Therefore the dynamic friction resistance of the pile isreduced to 0075 times of the static friction resistance and thecalculation formula is

119891119889 = 0075119891 (5)

where f d is the dynamic side friction in clay layer kN and fis the static side friction kN

(b) Semi-Fully Affected Areas When 05ltzHlt08 the soilmass in this area is characterized by a certain soil resistance atthe time of the second pile slip but with the subsequent pileslip the side friction decreases rapidly which is called partof the affected area The influence of the final depth of pilepenetration hence needs to be considered in the calculationA If zHend gt044 the designed depth of pile penetrationis small the design depth of pile driving distance after pilesliding is small and the influence of subsequent pile drivingon soil properties is small the modified API method can stillbe used for calculationB If zHend lt044 when the designeddepth of mud entry is large the subsequent piling will havea great impact on the soil properties and the formula forcalculating the dynamic side friction resistance at this timeis as follows

119891119889 = 0075119891 (6)

(c) No Affected Areas When zHgt08 the disturbance ofsliding pile to soil in this area is small the side friction of pilebody is ignored by sliding pile and the modified APImethodcan still be used to calculate the side friction of pile body sothe formula for calculating the side friction of this area is

119891 = 03120573119888119906 (7)

where when cu ge72kPa 120573=05 and when 24kPalecu lt72kPa120573 increases linearly in the [05 1] range4 Calculation of Pile Sliding Interval

Based on the analysis of pile sliding mechanism the calcu-lation process of the existing pile sliding interval algorithmis improved First the pile end resistance is obtained byusing Berezantzevrsquos formula and then the friction resistanceis calculated by using different reduction factors in differentinfluence areas In sandy soil the friction resistance of thepile side is calculated by conventional methods Based on thedynamic process of pile sliding a new algorithm of large-diameter steel pipe pile sliding interval is established by usingstatic balance and functional principles

When the steel pipe pile penetrates into the marinesoil layer the pile will be affected by the hammering forceof hydraulic hammer its own gravity buoyancy pile endresistance and pile side friction According to dynamicexperience when the hydraulic hammer blows the pipe pilethe power of the pipe pile and the hydraulic hammer isregarded as 12 times that of the gravity G1+G2 of the pile andthe hydraulic hammer [18] so when the stress condition ofthe pipe pile meets the following formula slip of the pipe pilewill occur and the mud depth L of the pipe pile when slip ofthe pipe pile occurs can be calculated through

12 (1198661 + 1198662) = 119891 + 119902119906 + 119865 (8)

where F is the buoyancy of the pipe pile kNWith the progress of sliding pile the speed of steel pipe

pile will gradually decrease to zero under the action ofsoil resistance and buoyancy the kinetic energy of pile willdissipate in overcoming soil resistance and buoyancy to dowork so the energy equation can be listed according to thefunctional principle and the length of sliding pile can becalculated The formula for calculating the work done by thefriction force on the pile side during pile sliding is

1198821 = 119909sum119894=1

(1198911198981198941205871198611198972) + 119910sum119895=1

(int1198970119891119898119895d119911) (9)

where1198821 is the work done by pile side friction resistance kJB is the diameter of steel pipe pile m x is the number of soillayers at the beginning of pile sliding f mj is the friction forceof layer i soil before the slip pile occurs kN 119910 is the quantityof soil layers included in the pile sliding interval f mj is thefriction force of the j-layer soil in the sliding pile interval kNz is the sliding distance of each layer of soil in the sliding pileinterval m

According to the integral calculus method f mj is apiecewise function in the sliding pile interval so the gen-eral formula for calculating the dynamic friction resistancebetween clay and sand layers in the sliding pile interval is asfollows

119891119898119889 = 120573119888119906120587119861 sdot 119911 (0 le 119911 le 119905)120573119888119906120587119861 sdot 119905 (t lt 119911 le 119897) (10)

119891119898119904 = 120572119896(119901119895minus1 + 1205871198612z1205741198954 ) tan 120575 (0 le 119911 le 119905)120572119896119901j tan 120575 (119905 lt 119911 lt 119897) (11)

where f md is the friction force of the j-layer clay in the slidingpile interval kN t is the thickness of the corresponding soillayer m f ms is the friction force of layer j sand in the slidingpile interval kN pj-1 is the overburden pressure of layer j-1soil kN 120574j is the severe degree of sand in layer j kNm3 pj isthe overburden pressure of layer j soil kN

In the process of pipe sliding the work done by thepile end resistance can be obtained by integrating the other

Mathematical Problems in Engineering 5

columns of Berezantzevrsquos formula and the calculation for-mula is as follows

1198822 = (119910minus1sum119895=1

119902119906 sdot 119905) + 119902119906 sdot 1199051015840 (12)

where1198822 is the work done by pile end resistance kJ and T1015840 is

the insertion length of steel pipe piles in the soil layer wherethey stay at the end of pile sliding m

The buoyancy Ff received by the steel pipe pile willgradually increase with the progress of the sliding pile so thecalculation method of the work1198823 done by buoyancy is

1198823 = int119897+119871119871(141205871198612120588g) 119911d119911 (13)

where 120588 is the water density kgm3 and g is the gravityacceleration ms2

When hydraulic hammer hammers a steel pipe pilethere will be energy dissipation usually corrected by usingthe coefficient so the energy of the pile and hammer atthe beginning of sliding pile is 120578E Based on the aboveconsiderations according to the conservation of energy it canbe concluded that the energy equation of the pile satisfies thefollowing

120578119864 = minus (1198661 + 1198662) 119897 + 1198821 +1198822 +1198823 (14)

According to (14) the length L of the slip pile can beobtained and the slip interval of the steel pipe pile can beobtained by combining the depth L of the pipe pile into themud when the slip pile occurs

5 Engineering Case Checking

According to the engineering data collected during theconstruction of Liwan pile foundation platform in the SouthChina Sea reasonable soil parameters are selected and thenew algorithm is used to calculate the pile sliding intervalof steel pipe piles The calculation results are comparedand analysed with the actual pile sliding interval and therationality of the new algorithm is verified through thecomparison results

The pile foundation platform has 16 steel pipe pileswhich are evenly distributed on the four corners of the pilefoundation platform Each steel pipe pile weighs 6439kg andhas a diameter of 274m and a pile length of 158mThemodelof hydraulic hammer is MHU1200s and the rated outputenergy is 1200kJ In order to ensure the same soil propertiesaround steel pipe piles four steel pipe piles on one cornerof the platform were selected for calculation and analysisThrough the analysis of soil parameters it can be seen thatthe soft and hard soil layers of the soil layer where the steelpipe pile is located alternate and the shallow soil layer has along clay layer so it is easy to slip the pile At the soil depths of588m and 108m the soft clay layer appears again at this timeit is likely that the secondary slip pile or even the tertiary slippile will occurThe soil parameters of the soil layer where thesteel pipe pile is located are listed in Table 2

Combined with the soil parameters selected in the actualproject the pile end resistance sand dynamic side frictionresistance and clay static friction resistance of each layer ofsoil in the pile driving process of steel pipe piles are calculatedusing (1)-(7) From the calculation results in Table 2 it canbe seen that the pile end resistance received by the pile bodyin the sand layer is larger the pile side friction resistance issmaller the pile end resistance in the clay layer is smaller andthe pile side friction resistance is larger When the pipe pilejust penetrates the soil layer the pile end resistance bears thegravity of the pile and the pile hammer which also verifies thereason for the slip pile

According to the calculated pile end resistance and pileside friction of each soil layer in Table 2 the mud entrydepth L of the pipe pile when slip pile occurs is calculatedby formula (8) and the mud entry depths L satisfyingformula (8) are 133m 380m and 649m m Then the workexpression of pile side friction including slip pile intervall is obtained through formulas (9)-(11) and three slip pileintervals are defined Through the formulas (12) and (13)the expressions of friction resistance and buoyancy work atthe pile end containing the slip pile interval l are obtainedBy substituting the above expressions into formula (14) theslip pile interval l is obtained as 137m 225m and 171mm Therefore under this actual working condition the slipinterval of pipe pile is 133 m sim 27 m 380 m sim 605 mand 649 m sim 840 m Through the comparison between thetheoretical pile sliding interval and the actual engineering pilesliding interval the comparison result shown in Figure 3 isobtained

From the comparison results it can be seen that thedepth of pile entry and the interval of the first two pile slipsare basically consistent with the actual engineering situationThere are some deviations in the calculation of the third pilesliding interval because the second pile sliding also affectsthe soil mass and changes the pile side friction but the thirdpile sliding interval is smaller than the theoretical calculationinterval length and within the safe range of pile foundationengineering so the theoretical pile sliding interval can stillprovide a reference for the design of pile foundation andalso verify the theory that the calculation of the pile slidinginterval needs to consider the influence of the pile slidingon the soil mass so the new algorithm and the traditionalmethod are more consistent with the actual pile slidinginterval and have higher accuracy The pile sliding intervalobtained by the new algorithm is basically consistent withthe actual pile sliding interval and the rationality of the newalgorithm is verified

6 Conclusions

Through the analysis and research on the process of pilesliding and its causes the conclusions are as follows

(1) When the steel pipe pile slips for the second timeconsidering the different influence degree of sliding pileon the pile side friction the side friction of the pile inthe clay layer is divided into three influence areas namelyfull influence area half influence area and no influencearea Using different reduction factors to calculate the

6 Mathematical Problems in Engineering

Table2Th

eparam

eterso

fsoillayersa

ndcalculationresults

ofsoilparameters

number

prop

erty

thickn

essm

cohesio

nkP

africtio

nangle(∘ )

unit

weightkNsdotmminus3

floor

elevationm

pileend

resistancekN

dynamicfrictio

nresistancekN

static

frictio

nresistancekN

1medium

dense

finetocoarse

sand

24

039

85

30

32917

39

2softto

hard

clay

7935

089

109

2599

10241

3denses

ilt23

037

89

132

5944

1123

4denses

andy

silt

andhard

clay

interbedded

7870

086

210

5198

1644

2

5hard

silty

clay

36

500

92246

3712

5

4119

6denses

iltyfin

esand

84

039

85

330

90846

2717

7denses

iltyfin

esand

203

900

83

533

6683

55016

8hard

silty

clay

61

800

90594

594

14479

9hard

silty

clay

54

036

86

648

155981

5827

10

hard

clay

114

100

088

762

7425

33891

11denses

andy

silt

34

036

83

796

139635

717

12

hard

silty

clay

293

120

085

1089

891

105875

13denses

andy

silt

29

036

85

1118

26554

13945

14

hard

clay

196

160

090

1314

1188

9443

Mathematical Problems in Engineering 7

No1 pile

No2 pile

No3 pile

No4 pile

10 20 30 40 50 60 70 80 90 100 110 Buried depth (m)

eoretical pile sliding intervalActual pile sliding interval

Figure 3 Comparison between theoretical and practical pile-run interval

side friction of the pile in different influence areas willmake the new calculation result closer to the engineeringpractice

(2) When calculating the sliding interval of steel pipepiles the static balance principle is used to calculate the depthof pipe pile entering the mud at the beginning of slidingthe expression of pile side friction resistance and pile endresistance in different influence areas is listed by integratingtheory and according to the functional principle the energyequation of pipe pile is listed thus obtaining the slidinginterval of steel pipe piles

(3)Through the verification of an engineering examplethe error range between the calculation result of the first andsecond sliding pile interval of the new algorithm and theactual situation is 8 sim 16 with high accuracy Althoughthe third result is somewhat deviated the actual slidingpile interval is smaller than the theoretical actual slidingpile interval and is within the safe range of pile foundationengineering which can still provide a reference for the designand construction of offshore platform pile foundation

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

This study was financially supported by the National NaturalScience Foundation of China (no 41372288) and the Projectof Science and Technology Innovation Fund for graduate stu-dents of the Shandong University of Science and Technology(no SDKDYC180212)

References

[1] S C Guo and S L Wu ldquoProblems of rapid sinking during piledriving and solutionsrdquoPortamp Waterway Engineering vol 12 pp163ndash166 2011

[2] L Sun T Jia S Yan and Z Jia ldquoResearch on prediction of pilerunning during large diameter pipe piles drivingrdquo Journal ofChina University of Petroleum vol 40 no 02 pp 115ndash122 2016

[3] L Sun Y Wang W Guo S Yan J Chu and X Liu ldquoCase studyon pile running during the driving process of large-diameterpipe pilesrdquo Marine Georesources amp Geotechnology vol 36 no6 pp 709ndash721 2018

[4] L Sun T Jia S Yan W Guo Y Ren and Z Lei ldquoPrediction ofpile running during the driving process of large diameter pipepilesrdquo Ocean Engineering vol 128 pp 48ndash57 2016

[5] B M Lehane and K G Gavin ldquoBase resistance of jacked pipepiles in sandrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 127 no 6 pp 473ndash480 2001

[6] E H Mijena A Comparison of Friction Piles Bearing Capac-ity Based on Theoretical and Empirical Mathematical ModelsGeotechnics and Geohazards Norwegian University of Scienceand Technology Norway 2012

[7] H J Yin Y X Liu XW Zhang et al ldquoThenewmethod for free-fall analysis of large diameter and super-long steel pilerdquo ChinaOffshore Oil and Cas vol 26 no S1 pp 35ndash38 2014

[8] A R Dover and J Davidson ldquoLarge Diameter Steel Pipe PilesRunning under SelfWeight in Soft Clay Predicted vs ObservedBehavior mdash Richmond San-Rafael Bridge Seismic Retrofitrdquo inProceedings of the 11th Triennial International Conference onPorts pp 1ndash10 San Diego Calif United States 2007

[9] S-W Yan Z-L Jia L-Q Sun and X-W Zhang ldquoMechanismsand calculation of pile-run for long and large diameter pilesrdquoEngineering Mechanics vol 32 no 09 pp 158ndash164 2015

[10] M F Randolph ldquoScience and empiricism in pile foundationdesignrdquo Geotechnique vol 53 no 10 pp 847ndash875 2003

[11] Z L Jia Study on the Dynamic Penetration Resistance andMechanism of Free-Running of Large Diameter and Super LongOcean Platform Piles Tianjin University 2016

[12] N S V K Rao Foundation Design Theory and Practice JohnWiley amp Sons Ltd Chichester UK 2010

8 Mathematical Problems in Engineering

[13] J-P Gao M-H Yu and S-P Li ldquoDouble-shear unified solutionof Terzaghi ultimate bearing capacity of foundationrdquo ChineseJournal of Rock Mechanics and Engineering vol 24 no 15 pp2736ndash2740 2005

[14] N Som and S CDasTheory and Practice of Foundation DesignPrentice-Hall of India New Delhi India 2003

[15] J DeKuiter andF L Beringen ldquoPile foundations for largeNorthSea structuresrdquoMarine Geotechnology vol 3 no 3 pp 267ndash3141979

[16] H S Zhang J Yang D Yan et al ldquoStudy on the slip piledepth prediction for offshore drilling conductor installationrdquoOil Drilling amp Production Technology vol 35 no 03 pp 22ndash242013

[17] S Li X Z Wu Y C Wang et al ldquoSoil resistance to drivingconsidering effect of pile running on pile installationrdquo ChineseJournal of Geotechnical Engineering vol 37 no 06 pp 1150ndash11572015

[18] L Zhang and J J Chen ldquoEffect of spatial correlation of standardpenetration test (SPT) data on bearing capacity of driven pilesin sandrdquo Canadian Geotechnical Journal vol 49 no 4 pp 394ndash402 2012

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 5

columns of Berezantzevrsquos formula and the calculation for-mula is as follows

1198822 = (119910minus1sum119895=1

119902119906 sdot 119905) + 119902119906 sdot 1199051015840 (12)

where1198822 is the work done by pile end resistance kJ and T1015840 is

the insertion length of steel pipe piles in the soil layer wherethey stay at the end of pile sliding m

The buoyancy Ff received by the steel pipe pile willgradually increase with the progress of the sliding pile so thecalculation method of the work1198823 done by buoyancy is

1198823 = int119897+119871119871(141205871198612120588g) 119911d119911 (13)

where 120588 is the water density kgm3 and g is the gravityacceleration ms2

When hydraulic hammer hammers a steel pipe pilethere will be energy dissipation usually corrected by usingthe coefficient so the energy of the pile and hammer atthe beginning of sliding pile is 120578E Based on the aboveconsiderations according to the conservation of energy it canbe concluded that the energy equation of the pile satisfies thefollowing

120578119864 = minus (1198661 + 1198662) 119897 + 1198821 +1198822 +1198823 (14)

According to (14) the length L of the slip pile can beobtained and the slip interval of the steel pipe pile can beobtained by combining the depth L of the pipe pile into themud when the slip pile occurs

5 Engineering Case Checking

According to the engineering data collected during theconstruction of Liwan pile foundation platform in the SouthChina Sea reasonable soil parameters are selected and thenew algorithm is used to calculate the pile sliding intervalof steel pipe piles The calculation results are comparedand analysed with the actual pile sliding interval and therationality of the new algorithm is verified through thecomparison results

The pile foundation platform has 16 steel pipe pileswhich are evenly distributed on the four corners of the pilefoundation platform Each steel pipe pile weighs 6439kg andhas a diameter of 274m and a pile length of 158mThemodelof hydraulic hammer is MHU1200s and the rated outputenergy is 1200kJ In order to ensure the same soil propertiesaround steel pipe piles four steel pipe piles on one cornerof the platform were selected for calculation and analysisThrough the analysis of soil parameters it can be seen thatthe soft and hard soil layers of the soil layer where the steelpipe pile is located alternate and the shallow soil layer has along clay layer so it is easy to slip the pile At the soil depths of588m and 108m the soft clay layer appears again at this timeit is likely that the secondary slip pile or even the tertiary slippile will occurThe soil parameters of the soil layer where thesteel pipe pile is located are listed in Table 2

Combined with the soil parameters selected in the actualproject the pile end resistance sand dynamic side frictionresistance and clay static friction resistance of each layer ofsoil in the pile driving process of steel pipe piles are calculatedusing (1)-(7) From the calculation results in Table 2 it canbe seen that the pile end resistance received by the pile bodyin the sand layer is larger the pile side friction resistance issmaller the pile end resistance in the clay layer is smaller andthe pile side friction resistance is larger When the pipe pilejust penetrates the soil layer the pile end resistance bears thegravity of the pile and the pile hammer which also verifies thereason for the slip pile

According to the calculated pile end resistance and pileside friction of each soil layer in Table 2 the mud entrydepth L of the pipe pile when slip pile occurs is calculatedby formula (8) and the mud entry depths L satisfyingformula (8) are 133m 380m and 649m m Then the workexpression of pile side friction including slip pile intervall is obtained through formulas (9)-(11) and three slip pileintervals are defined Through the formulas (12) and (13)the expressions of friction resistance and buoyancy work atthe pile end containing the slip pile interval l are obtainedBy substituting the above expressions into formula (14) theslip pile interval l is obtained as 137m 225m and 171mm Therefore under this actual working condition the slipinterval of pipe pile is 133 m sim 27 m 380 m sim 605 mand 649 m sim 840 m Through the comparison between thetheoretical pile sliding interval and the actual engineering pilesliding interval the comparison result shown in Figure 3 isobtained

From the comparison results it can be seen that thedepth of pile entry and the interval of the first two pile slipsare basically consistent with the actual engineering situationThere are some deviations in the calculation of the third pilesliding interval because the second pile sliding also affectsthe soil mass and changes the pile side friction but the thirdpile sliding interval is smaller than the theoretical calculationinterval length and within the safe range of pile foundationengineering so the theoretical pile sliding interval can stillprovide a reference for the design of pile foundation andalso verify the theory that the calculation of the pile slidinginterval needs to consider the influence of the pile slidingon the soil mass so the new algorithm and the traditionalmethod are more consistent with the actual pile slidinginterval and have higher accuracy The pile sliding intervalobtained by the new algorithm is basically consistent withthe actual pile sliding interval and the rationality of the newalgorithm is verified

6 Conclusions

Through the analysis and research on the process of pilesliding and its causes the conclusions are as follows

(1) When the steel pipe pile slips for the second timeconsidering the different influence degree of sliding pileon the pile side friction the side friction of the pile inthe clay layer is divided into three influence areas namelyfull influence area half influence area and no influencearea Using different reduction factors to calculate the

6 Mathematical Problems in Engineering

Table2Th

eparam

eterso

fsoillayersa

ndcalculationresults

ofsoilparameters

number

prop

erty

thickn

essm

cohesio

nkP

africtio

nangle(∘ )

unit

weightkNsdotmminus3

floor

elevationm

pileend

resistancekN

dynamicfrictio

nresistancekN

static

frictio

nresistancekN

1medium

dense

finetocoarse

sand

24

039

85

30

32917

39

2softto

hard

clay

7935

089

109

2599

10241

3denses

ilt23

037

89

132

5944

1123

4denses

andy

silt

andhard

clay

interbedded

7870

086

210

5198

1644

2

5hard

silty

clay

36

500

92246

3712

5

4119

6denses

iltyfin

esand

84

039

85

330

90846

2717

7denses

iltyfin

esand

203

900

83

533

6683

55016

8hard

silty

clay

61

800

90594

594

14479

9hard

silty

clay

54

036

86

648

155981

5827

10

hard

clay

114

100

088

762

7425

33891

11denses

andy

silt

34

036

83

796

139635

717

12

hard

silty

clay

293

120

085

1089

891

105875

13denses

andy

silt

29

036

85

1118

26554

13945

14

hard

clay

196

160

090

1314

1188

9443

Mathematical Problems in Engineering 7

No1 pile

No2 pile

No3 pile

No4 pile

10 20 30 40 50 60 70 80 90 100 110 Buried depth (m)

eoretical pile sliding intervalActual pile sliding interval

Figure 3 Comparison between theoretical and practical pile-run interval

side friction of the pile in different influence areas willmake the new calculation result closer to the engineeringpractice

(2) When calculating the sliding interval of steel pipepiles the static balance principle is used to calculate the depthof pipe pile entering the mud at the beginning of slidingthe expression of pile side friction resistance and pile endresistance in different influence areas is listed by integratingtheory and according to the functional principle the energyequation of pipe pile is listed thus obtaining the slidinginterval of steel pipe piles

(3)Through the verification of an engineering examplethe error range between the calculation result of the first andsecond sliding pile interval of the new algorithm and theactual situation is 8 sim 16 with high accuracy Althoughthe third result is somewhat deviated the actual slidingpile interval is smaller than the theoretical actual slidingpile interval and is within the safe range of pile foundationengineering which can still provide a reference for the designand construction of offshore platform pile foundation

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

This study was financially supported by the National NaturalScience Foundation of China (no 41372288) and the Projectof Science and Technology Innovation Fund for graduate stu-dents of the Shandong University of Science and Technology(no SDKDYC180212)

References

[1] S C Guo and S L Wu ldquoProblems of rapid sinking during piledriving and solutionsrdquoPortamp Waterway Engineering vol 12 pp163ndash166 2011

[2] L Sun T Jia S Yan and Z Jia ldquoResearch on prediction of pilerunning during large diameter pipe piles drivingrdquo Journal ofChina University of Petroleum vol 40 no 02 pp 115ndash122 2016

[3] L Sun Y Wang W Guo S Yan J Chu and X Liu ldquoCase studyon pile running during the driving process of large-diameterpipe pilesrdquo Marine Georesources amp Geotechnology vol 36 no6 pp 709ndash721 2018

[4] L Sun T Jia S Yan W Guo Y Ren and Z Lei ldquoPrediction ofpile running during the driving process of large diameter pipepilesrdquo Ocean Engineering vol 128 pp 48ndash57 2016

[5] B M Lehane and K G Gavin ldquoBase resistance of jacked pipepiles in sandrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 127 no 6 pp 473ndash480 2001

[6] E H Mijena A Comparison of Friction Piles Bearing Capac-ity Based on Theoretical and Empirical Mathematical ModelsGeotechnics and Geohazards Norwegian University of Scienceand Technology Norway 2012

[7] H J Yin Y X Liu XW Zhang et al ldquoThenewmethod for free-fall analysis of large diameter and super-long steel pilerdquo ChinaOffshore Oil and Cas vol 26 no S1 pp 35ndash38 2014

[8] A R Dover and J Davidson ldquoLarge Diameter Steel Pipe PilesRunning under SelfWeight in Soft Clay Predicted vs ObservedBehavior mdash Richmond San-Rafael Bridge Seismic Retrofitrdquo inProceedings of the 11th Triennial International Conference onPorts pp 1ndash10 San Diego Calif United States 2007

[9] S-W Yan Z-L Jia L-Q Sun and X-W Zhang ldquoMechanismsand calculation of pile-run for long and large diameter pilesrdquoEngineering Mechanics vol 32 no 09 pp 158ndash164 2015

[10] M F Randolph ldquoScience and empiricism in pile foundationdesignrdquo Geotechnique vol 53 no 10 pp 847ndash875 2003

[11] Z L Jia Study on the Dynamic Penetration Resistance andMechanism of Free-Running of Large Diameter and Super LongOcean Platform Piles Tianjin University 2016

[12] N S V K Rao Foundation Design Theory and Practice JohnWiley amp Sons Ltd Chichester UK 2010

8 Mathematical Problems in Engineering

[13] J-P Gao M-H Yu and S-P Li ldquoDouble-shear unified solutionof Terzaghi ultimate bearing capacity of foundationrdquo ChineseJournal of Rock Mechanics and Engineering vol 24 no 15 pp2736ndash2740 2005

[14] N Som and S CDasTheory and Practice of Foundation DesignPrentice-Hall of India New Delhi India 2003

[15] J DeKuiter andF L Beringen ldquoPile foundations for largeNorthSea structuresrdquoMarine Geotechnology vol 3 no 3 pp 267ndash3141979

[16] H S Zhang J Yang D Yan et al ldquoStudy on the slip piledepth prediction for offshore drilling conductor installationrdquoOil Drilling amp Production Technology vol 35 no 03 pp 22ndash242013

[17] S Li X Z Wu Y C Wang et al ldquoSoil resistance to drivingconsidering effect of pile running on pile installationrdquo ChineseJournal of Geotechnical Engineering vol 37 no 06 pp 1150ndash11572015

[18] L Zhang and J J Chen ldquoEffect of spatial correlation of standardpenetration test (SPT) data on bearing capacity of driven pilesin sandrdquo Canadian Geotechnical Journal vol 49 no 4 pp 394ndash402 2012

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

6 Mathematical Problems in Engineering

Table2Th

eparam

eterso

fsoillayersa

ndcalculationresults

ofsoilparameters

number

prop

erty

thickn

essm

cohesio

nkP

africtio

nangle(∘ )

unit

weightkNsdotmminus3

floor

elevationm

pileend

resistancekN

dynamicfrictio

nresistancekN

static

frictio

nresistancekN

1medium

dense

finetocoarse

sand

24

039

85

30

32917

39

2softto

hard

clay

7935

089

109

2599

10241

3denses

ilt23

037

89

132

5944

1123

4denses

andy

silt

andhard

clay

interbedded

7870

086

210

5198

1644

2

5hard

silty

clay

36

500

92246

3712

5

4119

6denses

iltyfin

esand

84

039

85

330

90846

2717

7denses

iltyfin

esand

203

900

83

533

6683

55016

8hard

silty

clay

61

800

90594

594

14479

9hard

silty

clay

54

036

86

648

155981

5827

10

hard

clay

114

100

088

762

7425

33891

11denses

andy

silt

34

036

83

796

139635

717

12

hard

silty

clay

293

120

085

1089

891

105875

13denses

andy

silt

29

036

85

1118

26554

13945

14

hard

clay

196

160

090

1314

1188

9443

Mathematical Problems in Engineering 7

No1 pile

No2 pile

No3 pile

No4 pile

10 20 30 40 50 60 70 80 90 100 110 Buried depth (m)

eoretical pile sliding intervalActual pile sliding interval

Figure 3 Comparison between theoretical and practical pile-run interval

side friction of the pile in different influence areas willmake the new calculation result closer to the engineeringpractice

(2) When calculating the sliding interval of steel pipepiles the static balance principle is used to calculate the depthof pipe pile entering the mud at the beginning of slidingthe expression of pile side friction resistance and pile endresistance in different influence areas is listed by integratingtheory and according to the functional principle the energyequation of pipe pile is listed thus obtaining the slidinginterval of steel pipe piles

(3)Through the verification of an engineering examplethe error range between the calculation result of the first andsecond sliding pile interval of the new algorithm and theactual situation is 8 sim 16 with high accuracy Althoughthe third result is somewhat deviated the actual slidingpile interval is smaller than the theoretical actual slidingpile interval and is within the safe range of pile foundationengineering which can still provide a reference for the designand construction of offshore platform pile foundation

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

This study was financially supported by the National NaturalScience Foundation of China (no 41372288) and the Projectof Science and Technology Innovation Fund for graduate stu-dents of the Shandong University of Science and Technology(no SDKDYC180212)

References

[1] S C Guo and S L Wu ldquoProblems of rapid sinking during piledriving and solutionsrdquoPortamp Waterway Engineering vol 12 pp163ndash166 2011

[2] L Sun T Jia S Yan and Z Jia ldquoResearch on prediction of pilerunning during large diameter pipe piles drivingrdquo Journal ofChina University of Petroleum vol 40 no 02 pp 115ndash122 2016

[3] L Sun Y Wang W Guo S Yan J Chu and X Liu ldquoCase studyon pile running during the driving process of large-diameterpipe pilesrdquo Marine Georesources amp Geotechnology vol 36 no6 pp 709ndash721 2018

[4] L Sun T Jia S Yan W Guo Y Ren and Z Lei ldquoPrediction ofpile running during the driving process of large diameter pipepilesrdquo Ocean Engineering vol 128 pp 48ndash57 2016

[5] B M Lehane and K G Gavin ldquoBase resistance of jacked pipepiles in sandrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 127 no 6 pp 473ndash480 2001

[6] E H Mijena A Comparison of Friction Piles Bearing Capac-ity Based on Theoretical and Empirical Mathematical ModelsGeotechnics and Geohazards Norwegian University of Scienceand Technology Norway 2012

[7] H J Yin Y X Liu XW Zhang et al ldquoThenewmethod for free-fall analysis of large diameter and super-long steel pilerdquo ChinaOffshore Oil and Cas vol 26 no S1 pp 35ndash38 2014

[8] A R Dover and J Davidson ldquoLarge Diameter Steel Pipe PilesRunning under SelfWeight in Soft Clay Predicted vs ObservedBehavior mdash Richmond San-Rafael Bridge Seismic Retrofitrdquo inProceedings of the 11th Triennial International Conference onPorts pp 1ndash10 San Diego Calif United States 2007

[9] S-W Yan Z-L Jia L-Q Sun and X-W Zhang ldquoMechanismsand calculation of pile-run for long and large diameter pilesrdquoEngineering Mechanics vol 32 no 09 pp 158ndash164 2015

[10] M F Randolph ldquoScience and empiricism in pile foundationdesignrdquo Geotechnique vol 53 no 10 pp 847ndash875 2003

[11] Z L Jia Study on the Dynamic Penetration Resistance andMechanism of Free-Running of Large Diameter and Super LongOcean Platform Piles Tianjin University 2016

[12] N S V K Rao Foundation Design Theory and Practice JohnWiley amp Sons Ltd Chichester UK 2010

8 Mathematical Problems in Engineering

[13] J-P Gao M-H Yu and S-P Li ldquoDouble-shear unified solutionof Terzaghi ultimate bearing capacity of foundationrdquo ChineseJournal of Rock Mechanics and Engineering vol 24 no 15 pp2736ndash2740 2005

[14] N Som and S CDasTheory and Practice of Foundation DesignPrentice-Hall of India New Delhi India 2003

[15] J DeKuiter andF L Beringen ldquoPile foundations for largeNorthSea structuresrdquoMarine Geotechnology vol 3 no 3 pp 267ndash3141979

[16] H S Zhang J Yang D Yan et al ldquoStudy on the slip piledepth prediction for offshore drilling conductor installationrdquoOil Drilling amp Production Technology vol 35 no 03 pp 22ndash242013

[17] S Li X Z Wu Y C Wang et al ldquoSoil resistance to drivingconsidering effect of pile running on pile installationrdquo ChineseJournal of Geotechnical Engineering vol 37 no 06 pp 1150ndash11572015

[18] L Zhang and J J Chen ldquoEffect of spatial correlation of standardpenetration test (SPT) data on bearing capacity of driven pilesin sandrdquo Canadian Geotechnical Journal vol 49 no 4 pp 394ndash402 2012

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

No1 pile

No2 pile

No3 pile

No4 pile

10 20 30 40 50 60 70 80 90 100 110 Buried depth (m)

eoretical pile sliding intervalActual pile sliding interval

Figure 3 Comparison between theoretical and practical pile-run interval

side friction of the pile in different influence areas willmake the new calculation result closer to the engineeringpractice

(2) When calculating the sliding interval of steel pipepiles the static balance principle is used to calculate the depthof pipe pile entering the mud at the beginning of slidingthe expression of pile side friction resistance and pile endresistance in different influence areas is listed by integratingtheory and according to the functional principle the energyequation of pipe pile is listed thus obtaining the slidinginterval of steel pipe piles

(3)Through the verification of an engineering examplethe error range between the calculation result of the first andsecond sliding pile interval of the new algorithm and theactual situation is 8 sim 16 with high accuracy Althoughthe third result is somewhat deviated the actual slidingpile interval is smaller than the theoretical actual slidingpile interval and is within the safe range of pile foundationengineering which can still provide a reference for the designand construction of offshore platform pile foundation

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

This study was financially supported by the National NaturalScience Foundation of China (no 41372288) and the Projectof Science and Technology Innovation Fund for graduate stu-dents of the Shandong University of Science and Technology(no SDKDYC180212)

References

[1] S C Guo and S L Wu ldquoProblems of rapid sinking during piledriving and solutionsrdquoPortamp Waterway Engineering vol 12 pp163ndash166 2011

[2] L Sun T Jia S Yan and Z Jia ldquoResearch on prediction of pilerunning during large diameter pipe piles drivingrdquo Journal ofChina University of Petroleum vol 40 no 02 pp 115ndash122 2016

[3] L Sun Y Wang W Guo S Yan J Chu and X Liu ldquoCase studyon pile running during the driving process of large-diameterpipe pilesrdquo Marine Georesources amp Geotechnology vol 36 no6 pp 709ndash721 2018

[4] L Sun T Jia S Yan W Guo Y Ren and Z Lei ldquoPrediction ofpile running during the driving process of large diameter pipepilesrdquo Ocean Engineering vol 128 pp 48ndash57 2016

[5] B M Lehane and K G Gavin ldquoBase resistance of jacked pipepiles in sandrdquo Journal of Geotechnical and GeoenvironmentalEngineering vol 127 no 6 pp 473ndash480 2001

[6] E H Mijena A Comparison of Friction Piles Bearing Capac-ity Based on Theoretical and Empirical Mathematical ModelsGeotechnics and Geohazards Norwegian University of Scienceand Technology Norway 2012

[7] H J Yin Y X Liu XW Zhang et al ldquoThenewmethod for free-fall analysis of large diameter and super-long steel pilerdquo ChinaOffshore Oil and Cas vol 26 no S1 pp 35ndash38 2014

[8] A R Dover and J Davidson ldquoLarge Diameter Steel Pipe PilesRunning under SelfWeight in Soft Clay Predicted vs ObservedBehavior mdash Richmond San-Rafael Bridge Seismic Retrofitrdquo inProceedings of the 11th Triennial International Conference onPorts pp 1ndash10 San Diego Calif United States 2007

[9] S-W Yan Z-L Jia L-Q Sun and X-W Zhang ldquoMechanismsand calculation of pile-run for long and large diameter pilesrdquoEngineering Mechanics vol 32 no 09 pp 158ndash164 2015

[10] M F Randolph ldquoScience and empiricism in pile foundationdesignrdquo Geotechnique vol 53 no 10 pp 847ndash875 2003

[11] Z L Jia Study on the Dynamic Penetration Resistance andMechanism of Free-Running of Large Diameter and Super LongOcean Platform Piles Tianjin University 2016

[12] N S V K Rao Foundation Design Theory and Practice JohnWiley amp Sons Ltd Chichester UK 2010

8 Mathematical Problems in Engineering

[13] J-P Gao M-H Yu and S-P Li ldquoDouble-shear unified solutionof Terzaghi ultimate bearing capacity of foundationrdquo ChineseJournal of Rock Mechanics and Engineering vol 24 no 15 pp2736ndash2740 2005

[14] N Som and S CDasTheory and Practice of Foundation DesignPrentice-Hall of India New Delhi India 2003

[15] J DeKuiter andF L Beringen ldquoPile foundations for largeNorthSea structuresrdquoMarine Geotechnology vol 3 no 3 pp 267ndash3141979

[16] H S Zhang J Yang D Yan et al ldquoStudy on the slip piledepth prediction for offshore drilling conductor installationrdquoOil Drilling amp Production Technology vol 35 no 03 pp 22ndash242013

[17] S Li X Z Wu Y C Wang et al ldquoSoil resistance to drivingconsidering effect of pile running on pile installationrdquo ChineseJournal of Geotechnical Engineering vol 37 no 06 pp 1150ndash11572015

[18] L Zhang and J J Chen ldquoEffect of spatial correlation of standardpenetration test (SPT) data on bearing capacity of driven pilesin sandrdquo Canadian Geotechnical Journal vol 49 no 4 pp 394ndash402 2012

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

8 Mathematical Problems in Engineering

[13] J-P Gao M-H Yu and S-P Li ldquoDouble-shear unified solutionof Terzaghi ultimate bearing capacity of foundationrdquo ChineseJournal of Rock Mechanics and Engineering vol 24 no 15 pp2736ndash2740 2005

[14] N Som and S CDasTheory and Practice of Foundation DesignPrentice-Hall of India New Delhi India 2003

[15] J DeKuiter andF L Beringen ldquoPile foundations for largeNorthSea structuresrdquoMarine Geotechnology vol 3 no 3 pp 267ndash3141979

[16] H S Zhang J Yang D Yan et al ldquoStudy on the slip piledepth prediction for offshore drilling conductor installationrdquoOil Drilling amp Production Technology vol 35 no 03 pp 22ndash242013

[17] S Li X Z Wu Y C Wang et al ldquoSoil resistance to drivingconsidering effect of pile running on pile installationrdquo ChineseJournal of Geotechnical Engineering vol 37 no 06 pp 1150ndash11572015

[18] L Zhang and J J Chen ldquoEffect of spatial correlation of standardpenetration test (SPT) data on bearing capacity of driven pilesin sandrdquo Canadian Geotechnical Journal vol 49 no 4 pp 394ndash402 2012

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom