CalculationofFrictionForceforSlurryPipeJackingconsidering...

Research ArticleCalculation of Friction Force for Slurry Pipe Jacking consideringSoil-Slurry-Pipe Interaction

Yichao Ye Limin Peng Weichao Yang Yang Zou and Chengyong Cao

School of Civil Engineering Central South University Changsha 410075 China

Correspondence should be addressed to Weichao Yang weic_yang163com

Received 4 October 2019 Revised 23 March 2020 Accepted 12 May 2020 Published 9 June 2020

Academic Editor Claudia Vitone

Copyright copy 2020 Yichao Ye et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+is paper aims to provide a new approach to predict the friction resistance of slurry pipe jacking Friction force usuallyconstitutes themain component of jacking force It can be calculated bymultiplying an effective friction coefficient and the normalforce acting on the external surface of the pipe+is effective friction coefficient is introduced to reflect the effect of contact state ofpipe soil slurry highly affected by the effect of lubrication and the interaction of pipe soil slurry Firstly by making somereasonable assumptions the analytical formula of the effective friction coefficient is obtained in which the critical quantity ofcontact (contact angle or width) is calculated by using the Persson contact model +en the analytical formula of normal force ofcircular pipeline is derived which needs to determine the vertical soil pressure To allow for a better prediction three typical silomodels are introduced and compared Finally a method for calculating the friction resistance of slurry pipe jacking is established+e main difference from the existing method is that this method takes into full consideration the influence of lubrication soilproperties (such as internal friction angle cohesion and void ratio) and design parameters (such as buried depth overcut andpipe diameter) By using reasonable silo models the predicted results are in good agreement with the measured values collectedfrom 10 in situ cases which proves that the new approach can provide accuracy prediction of friction resistance for slurry pipejacking with various soil conditions and it may help for better future design and less construction costs

1 Introduction

Pipe jacking is defined as a trenchless excavation techniquewhich employs hydraulic jacks to push specially made pipesthrough the ground behind a jacking machine from a driveshaft to a reception shaft Due to its short time limit highsecurity low environmental effect and little traffic distur-bance it has been widely used in the construction of in-frastructures of the traffic and transportation system in thecity [1 2] In pipe jacking the jacking force is a critical factorthat determines the thickness of pipe and reaction wall typeof jacking machine and lubricant requirements which isdirectly related to the structural safety and construction costFriction resistance is the main component of jacking forceApplication of lubricant such as bentonite slurry in pipejacking (that is the so-called ldquoslurry pipe jackingrdquo) is es-sential to reduce the friction resistance and therefore thejacking force [3 4] However it does make it more complex

for the calculation or prediction of friction resistance due tothe change in contact conditions between the pipe and soil

At present the main calculation methods of pipe jackingfriction resistance can be divided into the following threecategories First evaluating from construction experiencesfor example China standard GB50268 suggests the averagefriction resistance to be 3ndash5 kPa for slurry pipe jackingSecond to calculate by multiplying a friction coefficient bythe earth pressure [5 6] +is method for the calculation ofEarth pressure assumes that the excavated bore is unstableand the surrounding soil is in full contact with the wholearea of the jacking pipes +ird the same form with thesecond one but using the weight of the pipe or the value ofthe weight of pipe divided by the contact width instead of theEarth pressure And the Hertzian contact model is usuallyused to calculate the contact width [7 8] +is kind ofmethod in turn assumes that the excavated bore is stable andthe pipeline simply slides along the bottom of the bore due to

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 6594306 10 pageshttpsdoiorg10115520206594306

its own weight For the later two methods the frictioncoefficient is also evaluated by experience for example Steinsuggested it to be 01ndash03 [9] Some other authors argued thatit can be determined by the tangent of the interfriction angleof soil φ or φ2 or φ3 or an angle between them [5 7 10 11]

However the field monitoring results of 12 relatedprojects (see in Table 1) show that the measured frictionresistance is 05ndash5 kPa (conversion of Ff(πDp) is re-quired) most of which are less than 3 kPa or even morethan half of which are less than 2 kPa +ere seems that thesuggested value in Chinese standard GB50268 (3ndash5 kPa) isconservative Relevant authors used one or more of theabove calculation models to predict the friction resistanceand most of the results showed that the measured frictionresistances were less than the predicted values of thesecond type model [5 6] but larger than that of the thirdtype model [5 7 11] +e reason may be attributed to thetotal contact hypothesis of the second type model whichoverestimates the contact area between the pipe and soilwhile the third type model is just the opposite for thelimiting contact angle of the Hertzian model which is only30deg [12] In addition the value of friction coefficient of pipesoil not only fluctuates greatly and experience dominatesbut also depends entirely on soil property (internal frictionangle) and ignoring the importance of slurry (as discussedlater)

In fact the factors affecting the friction resistance ofslurry pipe jacking are far more complex Chapman andIchioka [13] counted 47 in situ cases and found that thefrictional resistance along the pipe run (Ff(πDp)) (kPa) ispositively correlated with pipe diameter In addition Pellet-Beaucour and Kastner [5] analyzed 6 cases and found thatfriction resistance is also related to the overcut (or radialclearance) stoppages and the size of soil particles (or voidratio) According to Terzaghirsquos silo model (5) [5] the soilpressure has no correlation with the pipe diameter overcutor soil void ratio If the calculation result of soil pressure isreliable it can be argued that the effective friction coefficientis also affected by these factors

+erefore based on the basic principle of tribology andtogether with the existing silo models and Persson contactmodel a new method suitable for calculating the frictionresistance of slurry pipe jacking is established in this paper Itcan not only reflect the lubrication effect of slurry but alsocomprehensively reflect the influence of redial clearance (orovercut) pipe diameter soil void ratio etc on frictionresistance

2 Calculation Method of Friction Force forSlurry Pipe Jacking

In tribology friction force can be uniformly expressed bymultiplying a friction coefficient by the vertical force actingon the surface of an object [5 7]

Ff μ middot N (1)

For slurry pipe jacking μ is the effective friction coef-ficient due to the interaction of soil lubricant and the pipe

and N is the total normal force acting on the pipe of unitlength under the assumption of plane strain kNm It is noteasy to calculate μ and N Authors and engineers often sufferfrom two basic problems that which one of the silo models touse and how to determine the value of μ Particularly for thesecond one as far as the author can know there seem nogood enough calculation formulas or methods to use forslurry pipe jacking

21 Calculation of N If σn represents the normal stressacting on any point of pipes (see in Figure 1) together withthe symmetry of the geometry of the problem the totalnormal force N acting on the external surface of the pipeper unit length can be uniformly expressed as an integralform

N 21113946π2

minus π2σn

Dp

2dθ (2)

whereDp is the external diameter of pipes and θ is defined asthe angle between the corresponding radius line and thehorizontal line at each point of the pipe positive forcounterclockwise and negative for clockwise (see inFigure 1)

In general the surrounding earth pressure can be de-scribed by the vertical earth pressure σv and lateral earthpressure σa It is therefore that the normal stress σn can beexpressed as (see in Figure 1)

σn σv sin θ + σa cos θ (3)

Substitute (3) in (2) giving that

N 2σvDp (4)

As known from (4) the normal force N should only berelated to the magnitude of vertical soil stress σv acting onthe pipe crown It has to be noted that at the present time byfar the most commonly used model for soil pressure cal-culation is Terzaghirsquos silo model [5 7] Terzaghirsquos theoryassumes that the ground above the excavated tunnel issettling along two vertical planes +ese displacements aresignificant enough to produce sliding planes see Figure 2+e formula of the vertical soil stress on the pipe crown isgiven by [5]

σv bc minus 2c

2K tan(δ)1 minus e

(minus 2K tan(δ)middoth)b1113872 1113873 (5)

where h is the height of cover at pipe crown c is the unitweight of soil c is the soil cohesion φ is the internal frictionangle of soil δ is the friction angle between the pipe andsoil K is the coefficient of soil pressure above the pipe andb is the influencing width of soil above the pipe ideal silowidth

It is noted that when the height of cover above the pipe issmall (hlt b) the ldquovaultrdquo effect of the ground considered byTerzaghi is neglected and the whole Earth weight is takeninto account By introducing a coefficient kwhich representsthe ldquovaultrdquo effect of the ground the vertical stress at the pipecrown σv can also be rewritten as

2 Advances in Civil Engineering

Tabl

e1

Com

parisonbetweenthecalculated

frictio

nsandthemeasuredfrictio

ns

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly1

Neuilly2

Bordeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

aiMeasuredfrictio

n(kNm

)679

513

669

955

1037

079sim3

93

104

164

679

151

246sim5

01059sim

1773

Calculatio

nresults

Terzaghi

(Japan)

2ε(deg )

4sim13

7sim21

128

1sim8

125sim

130

2sim130

40sim8

740sim8

734sim5

715sim4

622sim7

316sim1

9μ

0014sim

0019

0017sim

0024

0071sim

0072

0011sim

0015

0151sim

0099

0011sim

0122

0037sim

0065

0037sim

0065

0046sim

0049

0016sim

0027

0029sim

0077

0023sim

0025

F f064sim2

33

059sim1

73

268sim3

42

015sim0

58

225sim3

95

019sim1

78

257sim9

86

257sim9

86

233sim3

94

092sim2

27

2064sim

5809

784sim1

973

Ratio

9sim3

412sim3

440sim5

12

sim6

22sim3

824sim4

525sim9

316sim5

934sim5

861sim1

50

84sim1

16

74sim1

11

934

34

12

51

40

2

622

38

45

24

93

25

16

59

34

58

61

150

8411

674

111

PJA

(UK)

2ε(deg )

15sim2

221sim3

3128

3sim14

125sim

130

4sim130

47sim9

947sim9

956sim6

615sim4

637sim8

917sim2

7μ

0019sim

0033

0024sim

0045

0071sim

0104

0012sim

0026

0094sim

0158

0013sim

0122

004sim0

078

004sim0

078

0048sim

008

0017sim

0026

009sim0

091

0023sim

0031

F f283sim7

40

277sim5

42

315sim5

16

069sim1

77

568sim1

129

049sim5

10

327sim1

763

327sim1

763

469sim8

28

092sim2

22

4377sim

10962

784sim3

864

Ratio

42sim1

09

54sim1

06

47sim7

77

sim19

55sim1

09

62sim1

30

31sim1

70

20sim1

08

69sim1

22

61sim1

47

178

sim219

83sim2

03

109

42

106

54

77

47

19

710

955

13

062

17

031

10

820

12

269

14

761

17

821

983

203

ATV

A(G

ermany)

2ε(deg )

14sim2

626sim3

4128

4sim14

125sim

130

5sim130

50sim1

0550sim1

0559sim6

616sim4

934sim9

018sim2

9μ

0024sim

0029

0027sim

0045

0071sim

0104

0012sim

0026

0094sim

0158

0014sim

0122

0041sim

0082

0041sim

0082

005sim0

08

0017sim

0027

004sim0

092

0024sim

0033

F f353sim7

72

372sim5

65

369sim6

17

089sim1

70

705sim1

099

07sim

876

363sim2

291

363sim2

291

528sim8

41

1sim252

4683sim

11523

978sim4

057

Ratio

52sim1

14

72sim1

10

55sim9

29

sim18

68sim1

06

88sim2

23

35sim2

20

22sim1

40

78sim1

24

66sim1

67

190

sim230

92sim2

29

5211

472

11

055

92

9

18

6810

688

223

3522

022

140

7812

466

167

190

230

229

92

Advances in Civil Engineering 3

σv kch

k 1 hlt b

k 1 minus e(minus 2K tan(δ)middoth)b

2K tan(δ)

b

hminus2c

ch1113888 1113889 hgt b

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)

+e k coefficient is a constant below one +e larger k isthe larger the ldquovaultrdquo effect of the ground will be

Even though the Terzaghi silo model is widely acceptedby the authors from all over the world but for the deter-mination of empirical parameters (such as bδ and K)authors are divided +e most representative modifiedmodel is that proposed by UK PJA (Pipe Jacking Associa-tion) which assumes another boundary planes of thesewedge failures based on TerzaghiHouska formula see inFigure 2 And this modified model is also accepted byGermany Standard ATVA 161 but assumes a constant valuefor the angle of internal friction of 30deg It is obvious that themodified model has a smaller b leading to a larger value of k(or in other wards it weakens the ldquovaultrdquo effect of soil) So theEarth pressure calculated by the modified model is generally

larger than that calculated by Terzaghirsquos initial silo model+e rules to calculate the three parameters for the threemodels were summarized by Pellet-Beaucour and Kastner[5] as given in Table 2

Specifically comparison of vertical stresses calculatedaccording to the three different models had been done byPellet-Beaucour and Kastner He figured out that the verticalstresses calculated by ATVA 161 model is the largest whilethat calculated by Terzaghi initial model is the smallestHowever it is still not convincing to pick out a model to usewithout checking out with the field data +is work will becarried out in Section 3

22 Calculation of μ At the present time by far the frictioncoefficient is usually considered to be a constant which canbe expressed as [5 6 10 12 14]

μ tan(δ) (7)

It is generally accepted that δ φ for the calculation ofstatic friction and δ φ2 for the calculation of kinematicfriction [6 14] But for slurry pipe jacking the determinationof δ varies from person to person for example Barla et al[12] suggest δ to be between φ2 and φ and Pellet-Beaucourand Kastner Stein et al [5 10] suggest δ to be between φ3and φ2 depending on the roughness of the pipe-soil in-terface and the amplitude of motion As we have discussedabove the range of values seems too large to determine andmore importantly the effect of lubrication is absolutelyneglected

In slurry pipe jacking the use of slurry changes thecontact conditions between soil and the pipe In designphilosophy the overcut should be completely filled withslurry to reduce the friction resistance for maximum effi-ciency with no interpenetration or interpenetration ter-minates in a short time creating a ldquofilter cakerdquo layer aroundthe cavity and then pressurized to the support pressurerequired for the soil (see in Figure 3(a)) [15] In this case thefriction force is only related to the friction coefficient be-tween slurry and the pipe However the more general case isthat the excavated bore is stable and part of the pipe in-evitably comes into contact with soil (see in Figure 3(b)) [3]+e reasons for the occurrence of pipe-soil contact arecomplex such as the design and control of grouting amountof slurry jacking speed pipeline deviating from the intendedline and level irregular deformation of the surrounding soiland interpenetration between the soil and slurry In such acase the accurate calculation of friction force should takeinto account contact position value of contact angle (orwidth) and contact force However for various reasonslisted above it seems impossible and unnecessary to cal-culate these quantities in a target section of the pipeline Ifwe focus on the final contact state of pipe soil slurry byignoring the various factors that lead to it and taking thewhole pipeline into consideration this problem can begreatly simplified by introducing some basic hypotheses

(i) Contact can occur at any position of a section of thepipeline with the same probability

σa σa

σa

σn

σs

σvDp

σv

σn

θ

θ

dθ

Figure 1 Earth pressure and the normal stress acting on the pipe

b2 = De2 + De tan(α) b2 = Dp2 tan(β)

Terzaghi TerzaghiHouska

α = π4 ndash φ2β = π4 + α2

h

Dp

α

α

α

β

Figure 2 Boundary planes of wedge failure Terzaghi and TerzaghiHouska silo model


(ii) +e occurrence of contact does not significantlychange the soil pressure in the contact area

(iii) +e interpenetration between slurry and soil isquasistatic and that does not change the geometricstructure of soil

(iv) After the slurry injected and filled up the overcutthe slurry pressure can be redistributed and bal-anced with the soil pressure

Hypotheses (i) and (ii) exactly eliminate the influence ofcontact position and contact force on the effective frictioncoefficient Hypothesis (iii) is for careful consideration infact it will not have a significant impact on the final cal-culation result

Generally the friction force of slurry pipe jacking Ff canbe divided into the pipe-soil friction force fs and the pipe-slurry friction force fm

Ff μN fs + fm (8)

fs μsNs (9)

fm μmNm (10)

where μs( tan(φ2)) is the coefficient of kinematic frictionbetween soil and the pipe [6] μm is the coefficient of ki-nematic friction between slurry and the pipe its value can betaken as 001 [16] and Ns and Nm are the total normal forceacting on the pipe in the pipe-soil and pipe-slurry contactarea respectively

According to hypothesis (i) we have the followingequations

Ns Bs

CN

επ

N (11)

Nm Bm

CN (12)

where C is the external circumference of pipe Bs and Bm arethe width of contact area between soil and the pipe and thatbetween lubricant slurry and the pipe respectively and ε isthe semiangle of contact (as see in Figure 4) It is noted thatthe value of ε is roughly supposed to be π3 for any for-mation [6] however there is no evidence to support thisconclusion

By substituting (9)ndash(12) into (8) after some algebra theexpression of the effective friction coefficient μ can bewritten as

μ μsλs + μmλm

λs Bs

Cεπ

λm Bm

C

(13)

According to hypothesis (iii) the relation between Bmand Bs can be expressed as

Bm C minusBs

1 + e (14)

where e is the void ratio of soil

Table 2 Summary table of assumed model parameters

Terzaghi (Japan) ATVA 161 (Germany) PJA (UK)B Dp(1 + 2 tan((π4) minus (ϕ2)))

3

radicDp Dp tan((3π8) minus (ϕ4))

Δ φ φ2 φK 1 05 (1 minus sin ϕ)(1 + sin ϕ)

Pm

(a)

P

Pipe-soil contact

(b)

Figure 3 +e contact state of pipe soil slurry (a) the ideal state (b) the general state


By substituting (9) and (10) into (8) after some algebra(12) can be further rewritten as

μ μs

επ

+ μm 1 minusε

π(1 + e)1113888 1113889 (15)

From (15) the key to calculate the effective friction co-efficient μ is to calculate the width (or angle) of contact It hasto be noted that at the present time by far themost usedmodelis the Hertz contact model [7 8]+e contact width is given by

Bs 16 PkdCe( 111385712

(16)

kd DcDp

Dc minus Dp

Ce 1 minus v2p

Ep

+1 minus v2s

Es

(17)

where Dc and Dp are the internal diameter of cavity andexternal diameter of pipe respectively vp and vs are Poissonrsquosratio of the pipe and soil material respectively Ep and Es arethe elastic modulus for pipe and soil material respectivelyand P is the external force acting on the center of the pipe Ifthe excavation cavity is stable the pipe is in contact with thecavity at the bottom due to its own weight and P is equal tothe weight of pipe per unit length [5 7] For slurry pipejacking according to hypothesis (ii) P is approximately equalto the total Earth pressure at contact area it then gives

P επ

N (18)

Hertzian model provides a simple way for the calculationof the width of contact however the Hertzian contactproblem is approached only when the applied force is smallor the large radial clearance is large and the limited angle ofcontact is smaller than about 30deg [12] Due to the technical

limitations most of the pipe jacking projects encounter clayor sandy soils with small radial clearance it is therefore thatthe applicability of Hertz contact model is extremely limitedhere Actually the Hertz contact model is just a special caseof the Persson contact model with a small contact width (orangle) [12] If a large possible contact angle (larger than 30deg)happens the more general contact model proposed byPersson should be taken as the first consideration Forsimple the approximate form for the contact angle relationput forward by Michele and Paolo [17] from Persson modelis used in this paper +e expression is given by

π(α + 1)EpΔR1 minus v2p1113872 1113873P

(α minus 1) ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961 + 2

ξ2 + 11113872 1113873ξ2minus 4β

(19)

ΔR Dc minus Dp

2

ξ tanε2

1113874 1113875

η Ep

Es

1 minus v2s1 minus v2p

λ 1 minus 2vp

1 minus vp

minus η1 minus 2vs

1 minus vs

α 1 minus η1 + η

β λ

2(1 + η)

(20)

As comparison with (16) (19) is a more complex non-linear equation It can be further simplified with respect tothe actual situation that the elastic modulus of soil Es is muchsmaller than that of pipe Ep (the difference between the two

Bs

P

Op

Rp

5 43

2 1

1 Soil

Mixture of soil and slurry

ldquoFilter cakerdquo layer

Slurry

Jacking pipe

2

3

4

5

Oc

Rc

2ε ∆R

Figure 4 Contact model and symbols used


is usually three orders of magnitude) +us from (20) thevalue of auxiliary variable η should be very large and theapproximate relations can be obtained as

π(α + 1)Ep

1 minus v2p1113872 1113873asymp

2πEs

1 minus v2s( 1113857

α asymp minus 1

β asymp1 minus 2vs

2 1 minus vs( 1113857

(21)

Using (21) (19) is simplified as

πEsΔR1 minus v2s( 1113857P

+1 minus 2vs

1 minus vs

1 minus ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961

ξ2 + 11113872 1113873ξ2 (22)

Together with (5) (15) (18) and (22) the contact angle2ε the effective friction coefficient μ and the friction force Ffnow can be uniquely identified Apparently the effectivefriction coefficient here is not just related to the interfrictionangle of soil φ but the other soil parameters (Es vs and e) anddesign parameters (h Dp and ΔR) +at is to say for aspecific pipe jacking project the effective friction coefficientis probably not a constant for the complex geologicalconditions

3 Comparison between the Predicted Frictionand the Measured Friction

Ten slurry pipe jacking projects with 12 measured data werecollected from literature [5ndash7 18 19] to check with thepredicted result of the model +ese projects encounteredsome representative soils such as sandy clay silt sand andgravels Also they have different overburden depth of5ndash12m radial clearance of 0ndash30mm and pipe diameters of05ndash414m (see in Table 3) In particular Cases 11ndash12 werein the condition of water rich for passing through a river+ese characteristics of the projects provide good founda-tion for evaluating the capability of the model

Some parameters that needed to calculate the predictedequations were not given in the literature So the values ofgeological parameters involved in the new model (takenfrom the Geological Engineering Handbook [20]) aresummarized in Table 4 In principle during the calculationthe parameters given in the in situ case should be used andthe missing parameters can be selected from Table 4+erefore the parameters in each case were finally deter-mined and summarized in Table 3

Frequently some parameter given is a value range ratherthan a specific number +ereby it faces a problem of pa-rameter combination to calculate the maximum and min-imum friction force Accordingly the relationships betweenvarious parameters and the calculated friction force werestudied first by single-factor analysis the results have beenshown in Table 5

In Table 5 the symbol ldquo+rdquo indicates that the relationshipbetween the two is positively correlated and the symbol ldquominus rdquoindicates that they are negatively correlated When the

maximum friction force is to be calculated the quantities ofnegative correlation should be the minimums while thequantities of positive correlation should be the maximumsAnd for the calculation of minimum friction force theopposite is true

In Table 1 for each of the drives measured frictionalforce values are presented and compared to values cal-culated by the three approaches of Terzaghirsquos initialmodel and the two modified models One can see thatmost of the in situ results are included in the predictedrange of values calculated by PJA (UK) and AVTA(Germany) model respectively suggesting that both ofthem are capable of accurately calculating the frictionresistance of slurry pipe jacking And the frictions cal-culated by AVTA (Germany) model are slightly largerthan that calculated by PJA (UK) model which isexplained by the different parameters b K and δ used(see in Table 2)

Despite overall poor performance (much smaller pre-dictions) for Terzaghirsquos initial model it makes even betterpredictions in Cases 11ndash12 (especially in Case 11) whichdrive under a river It may indicate that in the condition ofwater rich the boundary planes of wedge failures (a bigger b)assumed by Terzaghi are more consistent with the actualsituation

+e calculation results of the contact angle and thecorresponding effective friction coefficient in each case arealso given in Table 1 According to the calculation resultsthe friction coefficient of slurry pipe jacking may be001ndash016 which is almost the same as the result 003ndash013acquired by backcalculation with Terzaghi initial silo model[5] Special Case 5 is with radial clearance ΔR 0 whichmakes the calculated contact angle as high as 130deg indi-rectly leading to a large friction coefficient of 016 Apartfrom this case most of effective friction coefficients varybetween 002 and 01

It is noted that Case 4 and Case 5 have almost the samegeological conditions and design parameters except forthe radial clearance (Case 4 is 20mm and Case 5 is 0mm)And the calculated friction in Case 5 is consistent with themeasured value while that in Case 4 is much smaller (seein Table 1) However if we reset ΔR in Case 4 as 0 usingATVA model the recalculated friction is 748ndash1048 kNm which is then consistent with the measured value(955 kNm) One explanation is that the amount ofgrouting in Case 4 may be insufficient causing the soilrelaxation and fill the whole annular space Another moreplausible explanation here is that in sand and gravels withlarge voids the injected slurry soon penetrates into thesoil accompany with pressure dissipation and the soilthen comes into full contact with the pipe In addition thecalculation of Case 10 with similar strata (drive in sandand gravels under a river) does not encounter the sameproblem as that in Case 4 It suggests that under thecondition of water rich volts in soil are completely filledwith water so the interpenetration between the injectedslurry and soil does not occur notably thereby thepressure of the injected slurry is sufficient to keep theannular space open and stable


Tabl

e3

+eparameterswhich

areneeded

tocalculatethepredictio

nequatio

nsin

each

case

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly

1Neuilly

2Bo

rdeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

ai

Geotechnical

description

Silty

sand

with

clay

Clean

fine

sand

Sand

yclay

Sand

andgravels

Clean

sand

Sand

yclay

Silty

fine

sand

Organic

silt

Roun

dgravel

gravel

sand

Silty

clay

sand

ysilt

Parameters

h(m

)7

65

57

6sim12

272

815

97sim

105

Dp(m

)108

096

076

064

066

065

149

12

096

414

406

ΔR(m

m)

3015

020

010

55

530

20c(kNm

3 )18sim2

018sim2

017sim2

020

18sim2

018sim2

119sim2

05

175sim1

919sim2

05

176sim1

94

c(kPa

)0

05sim

300

010sim1

50

100

5sim33

φ(deg )

28sim4

228sim4

220sim3

035

30sim3

526sim2

828sim4

215sim1

8366sim3

719sim3

2E s

(MPa

)10sim1

410sim1

49sim

4510sim4

610sim4

68sim

1310sim1

214sim2

810sim4

630sim4

5v s

025sim0

30

025sim0

30

025sim0

35

015sim0

30

025sim0

30

025sim0

35

025sim0

30

03sim

042

015sim0

25

025sim0

35

e031sim1

27

050sim0

80

080sim2

24

028sim1

27

031sim1

27

080sim2

24

090sim1

27

1sim25

028sim1

27

080sim2

24


4 Conclusions

+is paper presents a new method for the calculation offriction resistance for slurry pipe jacking Good predictionswere made in 12 in situ cases with various soils and designparameters +e following conclusions in the calculation canbe drawn

(1) In most cases assuming a big influencing width ofsoil above the pipe of Terzaghi initial silo model leadsto an underestimation of the soil pressure and themodified models proposed by PJA (UK) and ATVA(Germany) seem more realistic And under thecondition of water rich Terzaghi initial silo modelperforms even better which may need more cases tocheck out

(2) +e effective friction coefficient for slurry pipejacking taking the approach of ATVA model forexample is mostly ranging from 002 to 01depending on the contact state of pipe soil slurrywhich is not only affected by geological parametersbut also closely related to design parameters such asburied depth pipe diameter and radial clearance(overcut)

(3) +e overcut of design determines the volume ofinjected lubricant slurry its value has a significantinfluence on the effective friction coefficient andtherefore the friction resistance In some strata suchas sand and gravels the injected slurry may notcreate a screen to keep the excavated bore stable Inthis case the effect of overcut can be underestimatedor even ignored to get a better prediction result

Abbreviations

Ff Friction force per meter length driveμ Effective friction coefficient for slurry pipe jackingμs Soil-pipe friction coefficient

μm Slurry-pipe friction coefficientN Normal force due to ground pressure acting on pipeσn Normal soil stress acting on any point of pipesσv Vertical soil stressσh Horizontal soil stressDc Internal diameter of cavityDp External diameter of pipeb Influencing width of soil above the pipe ideal silo widthc Soil cohesionφ Inner friction angle of soilδ Soil-pipe friction anglec Unit weight of soile Void ratio of soilK Coefficient of soil pressure above the pipek Terzaghi coefficient which represents the ldquovaultrdquo effect

of the groundh Height of cover at pipe crownε Semiangle of contact areaBs Width of contact area between the pipe and soilRc Internal radius of cavityRp External radius of pipeΔR Radial clearance (or overcut)Ep Elasticity modulus of pipeEs Elasticity modulus of soilvp Poissonrsquos ratio of pipevs Poissonrsquos ratio of soilP External load applied at the center of the pipes

Data Availability

All the measured data and calculation results data used tosupport the findings of this study are available and includedwithin the article

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+e authors acknowledge the financial support of the Na-tional Natural Science Foundation of China (no 51878670)

References

[1] D-J Ren Y-S Xu J Shen A Zhou and A ArulrajahldquoPrediction of ground deformation during pipe-jackingconsidering multiple factorsrdquo Applied Sciences vol 8 no 7p 1051 2018

[2] Y Zhang Z G Yan and H H Zhu ldquoA Full-Scale Experi-mental study on the performance of jacking prestressedconcrete cylinder pipe with misalignment anglerdquo Proceedingsof GeoShanghai 2018 International Conference Multi-physicsProcesses in Soil Mechanics and Advances in GeotechnicalTesting Springer Singapore pp 345ndash354 2018

[3] S Khazaei H Shimada T Kawai J Yotsumoto andK Matsui ldquoMonitoring of over cutting area and lubricationdistribution in a large slurry pipe jacking operationrdquo Geo-technical and Geological Engineering vol 24 no 3 pp 735ndash755 2006

Table 4 +e general geotechnical parameters

Soilgroup

c

(kNm3) φ (deg) c(kPa)

Es(MPa) vs e

Gravel 187sim228 33sim45 0 14sim42 015sim025 028sim062Sand 19sim205 28sim42 0 10sim46 025sim035 031sim127Clayeysand 195sim21 13sim30 2sim7 11sim23 030sim040 041sim196

Sandyclay 18sim21 17sim24 5sim40 9sim45 025sim035 080sim224

Clay 175sim19 15sim18 25sim65 14sim28 025sim042 100sim250

Table 5 +e relationship between the parameters and the calcu-lated friction

Models c φ c Es vs e De h

FfTerzaghi + mdash mdash mdash + + + +

PJA and ATVA + + mdash mdash + + + +


[4] X Yang Y Liu and C Yang ldquoResearch on the slurry for long-distance large-diameter pipe jacking in expansive soilrdquo Ad-vances in Civil Engineering vol 2018 Article ID 90404719 pages 2018

[5] A-L Pellet-Beaucour and R Kastner ldquoExperimental andanalytical study of friction forces during microtunnelingoperationsrdquo Tunnelling and Underground Space Technologyvol 17 no 1 pp 83ndash97 2002

[6] S Hideki K Saeid and M Kikuo ldquoSmall diameter tunnelexcavation method using slurry pipe-jackingrdquo Geotechnicaland Geological Engineering vol 22 no 2 pp 161ndash186 2004

[7] A I Sofianos P Loukas and C Chantzakos ldquoPipe jacking asewer under Athensrdquo Tunnelling and Underground SpaceTechnology vol 19 no 2 pp 193ndash203 2004

[8] G W E Milligan and P Norris ldquoSite-based research in pipejacking-objectives procedures and a case historyrdquo Tunnellingand Underground Space Technology vol 11 pp 3ndash24 1996

[9] C Michele and D Paolo ldquo+e state of stress induced by theplane frictionless cylindrical contact I +e case of elasticsimilarityrdquo International Journal of Solids and Structuresvol 38 no 26-27 pp 4507ndash4523 2001

[10] D Stein K Mollers and R Bielecki Microtunnelling p 352W Ernst und Sohn Berlin Germany 1989

[11] K J Shou and M J Jiang ldquoA study of jacking force for acurved pipejackingrdquo Journal of Rock Mechanics and Geo-technical Engineering vol 2 no 4 pp 298ndash304 2010

[12] M Barla M Camusso and S Aiassa ldquoAnalysis of jackingforces during microtunnelling in limestonerdquo Tunnelling andUnderground Space Technology vol 21 no 6 pp 668ndash6832006

[13] D N Chapman and Y Ichioka ldquoPrediction of jacking forcesfor microtunnelling operationsrdquo Tunnelling and UndergroundSpace Technology vol 14 no 1 pp 31ndash41 1999

[14] K Shou J Yen and M Liu ldquoOn the frictional property oflubricants and its impact on jacking force and soil-pipe in-teraction of pipe-jackingrdquo Tunnelling and Underground SpaceTechnology vol 25 no 4 pp 469ndash477 2010

[15] G W E Milligan and P Norris ldquoPipe-soil interaction duringpipe jackingrdquo Proceedings of the Institution of Civil Engi-neersmdashGeotechnical Engineering vol 137 no 1 pp 27ndash441999

[16] W Guo H Xie R Wu and B Zhou ldquoExperimental study onbentonite lubrication during pipe jacking constructionrdquoJournal of Henan Science and Technology vol 555 no 1pp 115ndash118 2015 in Chinese

[17] C Michele and D Paolo ldquo+e state of stress induced by theplane frictionless cylindrical contact II +e general case(elastic dissimilarity)rdquo International Journal of Solids andStructures vol 38 no 26-27 pp 4523ndash4533 2001

[18] J Wang K Wang T Zhang and S Wang ldquoKey aspects of aDN4000 steel pipe jacking project in China a case study of awater pipeline in the Shanghai Huangpu riverrdquo Tunnellingand Underground Space Technology vol 72 pp 323ndash3322018

[19] X-B Ji W Zhao P Jia et al ldquoPipe jacking in sandy soil undera river in Shenyang Chinardquo Indian Geotechnical Journalvol 47 no 3 pp 246ndash260 2017

[20] Z H Shi M Wang D Q Xian and Y Yang GeologicalEngineering Handbook pp 174ndash179 China Building IndustryPress Beijing China 2018


its own weight For the later two methods the frictioncoefficient is also evaluated by experience for example Steinsuggested it to be 01ndash03 [9] Some other authors argued thatit can be determined by the tangent of the interfriction angleof soil φ or φ2 or φ3 or an angle between them [5 7 10 11]

However the field monitoring results of 12 relatedprojects (see in Table 1) show that the measured frictionresistance is 05ndash5 kPa (conversion of Ff(πDp) is re-quired) most of which are less than 3 kPa or even morethan half of which are less than 2 kPa +ere seems that thesuggested value in Chinese standard GB50268 (3ndash5 kPa) isconservative Relevant authors used one or more of theabove calculation models to predict the friction resistanceand most of the results showed that the measured frictionresistances were less than the predicted values of thesecond type model [5 6] but larger than that of the thirdtype model [5 7 11] +e reason may be attributed to thetotal contact hypothesis of the second type model whichoverestimates the contact area between the pipe and soilwhile the third type model is just the opposite for thelimiting contact angle of the Hertzian model which is only30deg [12] In addition the value of friction coefficient of pipesoil not only fluctuates greatly and experience dominatesbut also depends entirely on soil property (internal frictionangle) and ignoring the importance of slurry (as discussedlater)

In fact the factors affecting the friction resistance ofslurry pipe jacking are far more complex Chapman andIchioka [13] counted 47 in situ cases and found that thefrictional resistance along the pipe run (Ff(πDp)) (kPa) ispositively correlated with pipe diameter In addition Pellet-Beaucour and Kastner [5] analyzed 6 cases and found thatfriction resistance is also related to the overcut (or radialclearance) stoppages and the size of soil particles (or voidratio) According to Terzaghirsquos silo model (5) [5] the soilpressure has no correlation with the pipe diameter overcutor soil void ratio If the calculation result of soil pressure isreliable it can be argued that the effective friction coefficientis also affected by these factors

+erefore based on the basic principle of tribology andtogether with the existing silo models and Persson contactmodel a new method suitable for calculating the frictionresistance of slurry pipe jacking is established in this paper Itcan not only reflect the lubrication effect of slurry but alsocomprehensively reflect the influence of redial clearance (orovercut) pipe diameter soil void ratio etc on frictionresistance

2 Calculation Method of Friction Force forSlurry Pipe Jacking

In tribology friction force can be uniformly expressed bymultiplying a friction coefficient by the vertical force actingon the surface of an object [5 7]

Ff μ middot N (1)

For slurry pipe jacking μ is the effective friction coef-ficient due to the interaction of soil lubricant and the pipe

and N is the total normal force acting on the pipe of unitlength under the assumption of plane strain kNm It is noteasy to calculate μ and N Authors and engineers often sufferfrom two basic problems that which one of the silo models touse and how to determine the value of μ Particularly for thesecond one as far as the author can know there seem nogood enough calculation formulas or methods to use forslurry pipe jacking

21 Calculation of N If σn represents the normal stressacting on any point of pipes (see in Figure 1) together withthe symmetry of the geometry of the problem the totalnormal force N acting on the external surface of the pipeper unit length can be uniformly expressed as an integralform

N 21113946π2

minus π2σn

Dp

2dθ (2)

whereDp is the external diameter of pipes and θ is defined asthe angle between the corresponding radius line and thehorizontal line at each point of the pipe positive forcounterclockwise and negative for clockwise (see inFigure 1)

In general the surrounding earth pressure can be de-scribed by the vertical earth pressure σv and lateral earthpressure σa It is therefore that the normal stress σn can beexpressed as (see in Figure 1)

σn σv sin θ + σa cos θ (3)

Substitute (3) in (2) giving that

N 2σvDp (4)

As known from (4) the normal force N should only berelated to the magnitude of vertical soil stress σv acting onthe pipe crown It has to be noted that at the present time byfar the most commonly used model for soil pressure cal-culation is Terzaghirsquos silo model [5 7] Terzaghirsquos theoryassumes that the ground above the excavated tunnel issettling along two vertical planes +ese displacements aresignificant enough to produce sliding planes see Figure 2+e formula of the vertical soil stress on the pipe crown isgiven by [5]

σv bc minus 2c

2K tan(δ)1 minus e

(minus 2K tan(δ)middoth)b1113872 1113873 (5)

where h is the height of cover at pipe crown c is the unitweight of soil c is the soil cohesion φ is the internal frictionangle of soil δ is the friction angle between the pipe andsoil K is the coefficient of soil pressure above the pipe andb is the influencing width of soil above the pipe ideal silowidth

It is noted that when the height of cover above the pipe issmall (hlt b) the ldquovaultrdquo effect of the ground considered byTerzaghi is neglected and the whole Earth weight is takeninto account By introducing a coefficient kwhich representsthe ldquovaultrdquo effect of the ground the vertical stress at the pipecrown σv can also be rewritten as


Tabl

e1

Com


frictio


ns

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly1

Neuilly2

Bordeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

aiMeasuredfrictio

n(kNm

)679

513

669

955

1037

079sim3

93

104

164

679

151

246sim5

01059sim

1773

Calculatio

nresults

Terzaghi

(Japan)

2ε(deg )

4sim13

7sim21

128

1sim8

125sim

130

2sim130

40sim8

740sim8

734sim5

715sim4

622sim7

316sim1

9μ

0014sim

0019

0017sim

0024

0071sim

0072

0011sim

0015

0151sim

0099

0011sim

0122

0037sim

0065

0037sim

0065

0046sim

0049

0016sim

0027

0029sim

0077

0023sim

0025

F f064sim2

33

059sim1

73

268sim3

42

015sim0

58

225sim3

95

019sim1

78

257sim9

86

257sim9

86

233sim3

94

092sim2

27

2064sim

5809

784sim1

973

Ratio

9sim3

412sim3

440sim5

12

sim6

22sim3

824sim4

525sim9

316sim5

934sim5

861sim1

50

84sim1

16

74sim1

11

934

34

12

51

40

2

622

38

45

24

93

25

16

59

34

58

61

150

8411

674

111

PJA

(UK)

2ε(deg )

15sim2

221sim3

3128

3sim14

125sim

130

4sim130

47sim9

947sim9

956sim6

615sim4

637sim8

917sim2

7μ

0019sim

0033

0024sim

0045

0071sim

0104

0012sim

0026

0094sim

0158

0013sim

0122

004sim0

078

004sim0

078

0048sim

008

0017sim

0026

009sim0

091

0023sim

0031

F f283sim7

40

277sim5

42

315sim5

16

069sim1

77

568sim1

129

049sim5

10

327sim1

763

327sim1

763

469sim8

28

092sim2

22

4377sim

10962

784sim3

864

Ratio

42sim1

09

54sim1

06

47sim7

77

sim19

55sim1

09

62sim1

30

31sim1

70

20sim1

08

69sim1

22

61sim1

47

178

sim219

83sim2

03

109

42

106

54

77

47

19

710

955

13

062

17

031

10

820

12

269

14

761

17

821

983

203

ATV

A(G

ermany)

2ε(deg )

14sim2

626sim3

4128

4sim14

125sim

130

5sim130

50sim1

0550sim1

0559sim6

616sim4

934sim9

018sim2

9μ

0024sim

0029

0027sim

0045

0071sim

0104

0012sim

0026

0094sim

0158

0014sim

0122

0041sim

0082

0041sim

0082

005sim0

08

0017sim

0027

004sim0

092

0024sim

0033

F f353sim7

72

372sim5

65

369sim6

17

089sim1

70

705sim1

099

07sim

876

363sim2

291

363sim2

291

528sim8

41

1sim252

4683sim

11523

978sim4

057

Ratio

52sim1

14

72sim1

10

55sim9

29

sim18

68sim1

06

88sim2

23

35sim2

20

22sim1

40

78sim1

24

66sim1

67

190

sim230

92sim2

29

5211

472

11

055

92

9

18

6810

688

223

3522

022

140

7812

466

167

190

230

229

92


σv kch

k 1 hlt b


2K tan(δ)

b

hminus2c

ch1113888 1113889 hgt b

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)






μ tan(δ) (7)




σa σa

σa

σn

σs

σvDp

σv

σn

θ

θ

dθ





h

Dp

α

α

α

β








Ff μN fs + fm (8)

fs μsNs (9)

fm μmNm (10)



Ns Bs

CN

επ

N (11)

Nm Bm

CN (12)



μ μsλs + μmλm

λs Bs

Cεπ

λm Bm

C

(13)


Bm C minusBs

1 + e (14)




3



Pm

(a)

P

Pipe-soil contact

(b)




μ μs

επ

+ μm 1 minusε

π(1 + e)1113888 1113889 (15)


Bs 16 PkdCe( 111385712

(16)

kd DcDp

Dc minus Dp

Ce 1 minus v2p

Ep

+1 minus v2s

Es

(17)


P επ

N (18)



π(α + 1)EpΔR1 minus v2p1113872 1113873P

(α minus 1) ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961 + 2

ξ2 + 11113872 1113873ξ2minus 4β

(19)

ΔR Dc minus Dp

2

ξ tanε2

1113874 1113875

η Ep

Es


λ 1 minus 2vp

1 minus vp

minus η1 minus 2vs

1 minus vs

α 1 minus η1 + η

β λ

2(1 + η)

(20)


Bs

P

Op

Rp

5 43

2 1

1 Soil



Slurry

Jacking pipe

2

3

4

5

Oc

Rc

2ε ∆R




π(α + 1)Ep

1 minus v2p1113872 1113873asymp

2πEs

1 minus v2s( 1113857

α asymp minus 1

β asymp1 minus 2vs

2 1 minus vs( 1113857

(21)



+1 minus 2vs

1 minus vs

1 minus ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961

ξ2 + 11113872 1113873ξ2 (22)













Tabl

e3

+eparameterswhich

areneeded


nequatio

nsin

each

case

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly

1Neuilly

2Bo

rdeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

ai

Geotechnical

description

Silty

sand

with

clay

Clean

fine

sand

Sand

yclay

Sand

andgravels

Clean

sand

Sand

yclay

Silty

fine

sand

Organic

silt

Roun

dgravel

gravel

sand

Silty

clay

sand

ysilt

Parameters

h(m

)7

65

57

6sim12

272

815

97sim

105

Dp(m

)108

096

076

064

066

065

149

12

096

414

406

ΔR(m

m)

3015

020

010

55

530

20c(kNm

3 )18sim2

018sim2

017sim2

020

18sim2

018sim2

119sim2

05

175sim1

919sim2

05

176sim1

94

c(kPa

)0

05sim

300

010sim1

50

100

5sim33

φ(deg )

28sim4

228sim4

220sim3

035

30sim3

526sim2

828sim4

215sim1

8366sim3

719sim3

2E s

(MPa

)10sim1

410sim1

49sim

4510sim4

610sim4

68sim

1310sim1

214sim2

810sim4

630sim4

5v s

025sim0

30

025sim0

30

025sim0

35

015sim0

30

025sim0

30

025sim0

35

025sim0

30

03sim

042

015sim0

25

025sim0

35

e031sim1

27

050sim0

80

080sim2

24

028sim1

27

031sim1

27

080sim2

24

090sim1

27

1sim25

028sim1

27

080sim2

24


4 Conclusions





Abbreviations




Data Availability




Acknowledgments


References





Soilgroup

c


Es(MPa) vs e



























Tabl

e1

Com


frictio


ns

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly1

Neuilly2

Bordeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

aiMeasuredfrictio

n(kNm

)679

513

669

955

1037

079sim3

93

104

164

679

151

246sim5

01059sim

1773

Calculatio

nresults

Terzaghi

(Japan)

2ε(deg )

4sim13

7sim21

128

1sim8

125sim

130

2sim130

40sim8

740sim8

734sim5

715sim4

622sim7

316sim1

9μ

0014sim

0019

0017sim

0024

0071sim

0072

0011sim

0015

0151sim

0099

0011sim

0122

0037sim

0065

0037sim

0065

0046sim

0049

0016sim

0027

0029sim

0077

0023sim

0025

F f064sim2

33

059sim1

73

268sim3

42

015sim0

58

225sim3

95

019sim1

78

257sim9

86

257sim9

86

233sim3

94

092sim2

27

2064sim

5809

784sim1

973

Ratio

9sim3

412sim3

440sim5

12

sim6

22sim3

824sim4

525sim9

316sim5

934sim5

861sim1

50

84sim1

16

74sim1

11

934

34

12

51

40

2

622

38

45

24

93

25

16

59

34

58

61

150

8411

674

111

PJA

(UK)

2ε(deg )

15sim2

221sim3

3128

3sim14

125sim

130

4sim130

47sim9

947sim9

956sim6

615sim4

637sim8

917sim2

7μ

0019sim

0033

0024sim

0045

0071sim

0104

0012sim

0026

0094sim

0158

0013sim

0122

004sim0

078

004sim0

078

0048sim

008

0017sim

0026

009sim0

091

0023sim

0031

F f283sim7

40

277sim5

42

315sim5

16

069sim1

77

568sim1

129

049sim5

10

327sim1

763

327sim1

763

469sim8

28

092sim2

22

4377sim

10962

784sim3

864

Ratio

42sim1

09

54sim1

06

47sim7

77

sim19

55sim1

09

62sim1

30

31sim1

70

20sim1

08

69sim1

22

61sim1

47

178

sim219

83sim2

03

109

42

106

54

77

47

19

710

955

13

062

17

031

10

820

12

269

14

761

17

821

983

203

ATV

A(G

ermany)

2ε(deg )

14sim2

626sim3

4128

4sim14

125sim

130

5sim130

50sim1

0550sim1

0559sim6

616sim4

934sim9

018sim2

9μ

0024sim

0029

0027sim

0045

0071sim

0104

0012sim

0026

0094sim

0158

0014sim

0122

0041sim

0082

0041sim

0082

005sim0

08

0017sim

0027

004sim0

092

0024sim

0033

F f353sim7

72

372sim5

65

369sim6

17

089sim1

70

705sim1

099

07sim

876

363sim2

291

363sim2

291

528sim8

41

1sim252

4683sim

11523

978sim4

057

Ratio

52sim1

14

72sim1

10

55sim9

29

sim18

68sim1

06

88sim2

23

35sim2

20

22sim1

40

78sim1

24

66sim1

67

190

sim230

92sim2

29

5211

472

11

055

92

9

18

6810

688

223

3522

022

140

7812

466

167

190

230

229

92


σv kch

k 1 hlt b


2K tan(δ)

b

hminus2c

ch1113888 1113889 hgt b

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)






μ tan(δ) (7)




σa σa

σa

σn

σs

σvDp

σv

σn

θ

θ

dθ





h

Dp

α

α

α

β








Ff μN fs + fm (8)

fs μsNs (9)

fm μmNm (10)



Ns Bs

CN

επ

N (11)

Nm Bm

CN (12)



μ μsλs + μmλm

λs Bs

Cεπ

λm Bm

C

(13)


Bm C minusBs

1 + e (14)




3



Pm

(a)

P

Pipe-soil contact

(b)




μ μs

επ

+ μm 1 minusε

π(1 + e)1113888 1113889 (15)


Bs 16 PkdCe( 111385712

(16)

kd DcDp

Dc minus Dp

Ce 1 minus v2p

Ep

+1 minus v2s

Es

(17)


P επ

N (18)



π(α + 1)EpΔR1 minus v2p1113872 1113873P

(α minus 1) ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961 + 2

ξ2 + 11113872 1113873ξ2minus 4β

(19)

ΔR Dc minus Dp

2

ξ tanε2

1113874 1113875

η Ep

Es


λ 1 minus 2vp

1 minus vp

minus η1 minus 2vs

1 minus vs

α 1 minus η1 + η

β λ

2(1 + η)

(20)


Bs

P

Op

Rp

5 43

2 1

1 Soil



Slurry

Jacking pipe

2

3

4

5

Oc

Rc

2ε ∆R




π(α + 1)Ep

1 minus v2p1113872 1113873asymp

2πEs

1 minus v2s( 1113857

α asymp minus 1

β asymp1 minus 2vs

2 1 minus vs( 1113857

(21)



+1 minus 2vs

1 minus vs

1 minus ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961

ξ2 + 11113872 1113873ξ2 (22)













Tabl

e3

+eparameterswhich

areneeded


nequatio

nsin

each

case

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly

1Neuilly

2Bo

rdeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

ai

Geotechnical

description

Silty

sand

with

clay

Clean

fine

sand

Sand

yclay

Sand

andgravels

Clean

sand

Sand

yclay

Silty

fine

sand

Organic

silt

Roun

dgravel

gravel

sand

Silty

clay

sand

ysilt

Parameters

h(m

)7

65

57

6sim12

272

815

97sim

105

Dp(m

)108

096

076

064

066

065

149

12

096

414

406

ΔR(m

m)

3015

020

010

55

530

20c(kNm

3 )18sim2

018sim2

017sim2

020

18sim2

018sim2

119sim2

05

175sim1

919sim2

05

176sim1

94

c(kPa

)0

05sim

300

010sim1

50

100

5sim33

φ(deg )

28sim4

228sim4

220sim3

035

30sim3

526sim2

828sim4

215sim1

8366sim3

719sim3

2E s

(MPa

)10sim1

410sim1

49sim

4510sim4

610sim4

68sim

1310sim1

214sim2

810sim4

630sim4

5v s

025sim0

30

025sim0

30

025sim0

35

015sim0

30

025sim0

30

025sim0

35

025sim0

30

03sim

042

015sim0

25

025sim0

35

e031sim1

27

050sim0

80

080sim2

24

028sim1

27

031sim1

27

080sim2

24

090sim1

27

1sim25

028sim1

27

080sim2

24


4 Conclusions





Abbreviations




Data Availability




Acknowledgments


References





Soilgroup

c


Es(MPa) vs e



























σv kch

k 1 hlt b


2K tan(δ)

b

hminus2c

ch1113888 1113889 hgt b

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(6)






μ tan(δ) (7)




σa σa

σa

σn

σs

σvDp

σv

σn

θ

θ

dθ





h

Dp

α

α

α

β








Ff μN fs + fm (8)

fs μsNs (9)

fm μmNm (10)



Ns Bs

CN

επ

N (11)

Nm Bm

CN (12)



μ μsλs + μmλm

λs Bs

Cεπ

λm Bm

C

(13)


Bm C minusBs

1 + e (14)




3



Pm

(a)

P

Pipe-soil contact

(b)




μ μs

επ

+ μm 1 minusε

π(1 + e)1113888 1113889 (15)


Bs 16 PkdCe( 111385712

(16)

kd DcDp

Dc minus Dp

Ce 1 minus v2p

Ep

+1 minus v2s

Es

(17)


P επ

N (18)



π(α + 1)EpΔR1 minus v2p1113872 1113873P

(α minus 1) ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961 + 2

ξ2 + 11113872 1113873ξ2minus 4β

(19)

ΔR Dc minus Dp

2

ξ tanε2

1113874 1113875

η Ep

Es


λ 1 minus 2vp

1 minus vp

minus η1 minus 2vs

1 minus vs

α 1 minus η1 + η

β λ

2(1 + η)

(20)


Bs

P

Op

Rp

5 43

2 1

1 Soil



Slurry

Jacking pipe

2

3

4

5

Oc

Rc

2ε ∆R




π(α + 1)Ep

1 minus v2p1113872 1113873asymp

2πEs

1 minus v2s( 1113857

α asymp minus 1

β asymp1 minus 2vs

2 1 minus vs( 1113857

(21)



+1 minus 2vs

1 minus vs

1 minus ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961

ξ2 + 11113872 1113873ξ2 (22)













Tabl

e3

+eparameterswhich

areneeded


nequatio

nsin

each

case

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly

1Neuilly

2Bo

rdeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

ai

Geotechnical

description

Silty

sand

with

clay

Clean

fine

sand

Sand

yclay

Sand

andgravels

Clean

sand

Sand

yclay

Silty

fine

sand

Organic

silt

Roun

dgravel

gravel

sand

Silty

clay

sand

ysilt

Parameters

h(m

)7

65

57

6sim12

272

815

97sim

105

Dp(m

)108

096

076

064

066

065

149

12

096

414

406

ΔR(m

m)

3015

020

010

55

530

20c(kNm

3 )18sim2

018sim2

017sim2

020

18sim2

018sim2

119sim2

05

175sim1

919sim2

05

176sim1

94

c(kPa

)0

05sim

300

010sim1

50

100

5sim33

φ(deg )

28sim4

228sim4

220sim3

035

30sim3

526sim2

828sim4

215sim1

8366sim3

719sim3

2E s

(MPa

)10sim1

410sim1

49sim

4510sim4

610sim4

68sim

1310sim1

214sim2

810sim4

630sim4

5v s

025sim0

30

025sim0

30

025sim0

35

015sim0

30

025sim0

30

025sim0

35

025sim0

30

03sim

042

015sim0

25

025sim0

35

e031sim1

27

050sim0

80

080sim2

24

028sim1

27

031sim1

27

080sim2

24

090sim1

27

1sim25

028sim1

27

080sim2

24


4 Conclusions





Abbreviations




Data Availability




Acknowledgments


References





Soilgroup

c


Es(MPa) vs e
































Ff μN fs + fm (8)

fs μsNs (9)

fm μmNm (10)



Ns Bs

CN

επ

N (11)

Nm Bm

CN (12)



μ μsλs + μmλm

λs Bs

Cεπ

λm Bm

C

(13)


Bm C minusBs

1 + e (14)




3



Pm

(a)

P

Pipe-soil contact

(b)




μ μs

επ

+ μm 1 minusε

π(1 + e)1113888 1113889 (15)


Bs 16 PkdCe( 111385712

(16)

kd DcDp

Dc minus Dp

Ce 1 minus v2p

Ep

+1 minus v2s

Es

(17)


P επ

N (18)



π(α + 1)EpΔR1 minus v2p1113872 1113873P

(α minus 1) ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961 + 2

ξ2 + 11113872 1113873ξ2minus 4β

(19)

ΔR Dc minus Dp

2

ξ tanε2

1113874 1113875

η Ep

Es


λ 1 minus 2vp

1 minus vp

minus η1 minus 2vs

1 minus vs

α 1 minus η1 + η

β λ

2(1 + η)

(20)


Bs

P

Op

Rp

5 43

2 1

1 Soil



Slurry

Jacking pipe

2

3

4

5

Oc

Rc

2ε ∆R




π(α + 1)Ep

1 minus v2p1113872 1113873asymp

2πEs

1 minus v2s( 1113857

α asymp minus 1

β asymp1 minus 2vs

2 1 minus vs( 1113857

(21)



+1 minus 2vs

1 minus vs

1 minus ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961

ξ2 + 11113872 1113873ξ2 (22)













Tabl

e3

+eparameterswhich

areneeded


nequatio

nsin

each

case

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly

1Neuilly

2Bo

rdeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

ai

Geotechnical

description

Silty

sand

with

clay

Clean

fine

sand

Sand

yclay

Sand

andgravels

Clean

sand

Sand

yclay

Silty

fine

sand

Organic

silt

Roun

dgravel

gravel

sand

Silty

clay

sand

ysilt

Parameters

h(m

)7

65

57

6sim12

272

815

97sim

105

Dp(m

)108

096

076

064

066

065

149

12

096

414

406

ΔR(m

m)

3015

020

010

55

530

20c(kNm

3 )18sim2

018sim2

017sim2

020

18sim2

018sim2

119sim2

05

175sim1

919sim2

05

176sim1

94

c(kPa

)0

05sim

300

010sim1

50

100

5sim33

φ(deg )

28sim4

228sim4

220sim3

035

30sim3

526sim2

828sim4

215sim1

8366sim3

719sim3

2E s

(MPa

)10sim1

410sim1

49sim

4510sim4

610sim4

68sim

1310sim1

214sim2

810sim4

630sim4

5v s

025sim0

30

025sim0

30

025sim0

35

015sim0

30

025sim0

30

025sim0

35

025sim0

30

03sim

042

015sim0

25

025sim0

35

e031sim1

27

050sim0

80

080sim2

24

028sim1

27

031sim1

27

080sim2

24

090sim1

27

1sim25

028sim1

27

080sim2

24


4 Conclusions





Abbreviations




Data Availability




Acknowledgments


References





Soilgroup

c


Es(MPa) vs e




























μ μs

επ

+ μm 1 minusε

π(1 + e)1113888 1113889 (15)


Bs 16 PkdCe( 111385712

(16)

kd DcDp

Dc minus Dp

Ce 1 minus v2p

Ep

+1 minus v2s

Es

(17)


P επ

N (18)



π(α + 1)EpΔR1 minus v2p1113872 1113873P

(α minus 1) ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961 + 2

ξ2 + 11113872 1113873ξ2minus 4β

(19)

ΔR Dc minus Dp

2

ξ tanε2

1113874 1113875

η Ep

Es


λ 1 minus 2vp

1 minus vp

minus η1 minus 2vs

1 minus vs

α 1 minus η1 + η

β λ

2(1 + η)

(20)


Bs

P

Op

Rp

5 43

2 1

1 Soil



Slurry

Jacking pipe

2

3

4

5

Oc

Rc

2ε ∆R




π(α + 1)Ep

1 minus v2p1113872 1113873asymp

2πEs

1 minus v2s( 1113857

α asymp minus 1

β asymp1 minus 2vs

2 1 minus vs( 1113857

(21)



+1 minus 2vs

1 minus vs

1 minus ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961

ξ2 + 11113872 1113873ξ2 (22)













Tabl

e3

+eparameterswhich

areneeded


nequatio

nsin

each

case

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly

1Neuilly

2Bo

rdeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

ai

Geotechnical

description

Silty

sand

with

clay

Clean

fine

sand

Sand

yclay

Sand

andgravels

Clean

sand

Sand

yclay

Silty

fine

sand

Organic

silt

Roun

dgravel

gravel

sand

Silty

clay

sand

ysilt

Parameters

h(m

)7

65

57

6sim12

272

815

97sim

105

Dp(m

)108

096

076

064

066

065

149

12

096

414

406

ΔR(m

m)

3015

020

010

55

530

20c(kNm

3 )18sim2

018sim2

017sim2

020

18sim2

018sim2

119sim2

05

175sim1

919sim2

05

176sim1

94

c(kPa

)0

05sim

300

010sim1

50

100

5sim33

φ(deg )

28sim4

228sim4

220sim3

035

30sim3

526sim2

828sim4

215sim1

8366sim3

719sim3

2E s

(MPa

)10sim1

410sim1

49sim

4510sim4

610sim4

68sim

1310sim1

214sim2

810sim4

630sim4

5v s

025sim0

30

025sim0

30

025sim0

35

015sim0

30

025sim0

30

025sim0

35

025sim0

30

03sim

042

015sim0

25

025sim0

35

e031sim1

27

050sim0

80

080sim2

24

028sim1

27

031sim1

27

080sim2

24

090sim1

27

1sim25

028sim1

27

080sim2

24


4 Conclusions





Abbreviations




Data Availability




Acknowledgments


References





Soilgroup

c


Es(MPa) vs e




























π(α + 1)Ep

1 minus v2p1113872 1113873asymp

2πEs

1 minus v2s( 1113857

α asymp minus 1

β asymp1 minus 2vs

2 1 minus vs( 1113857

(21)



+1 minus 2vs

1 minus vs

1 minus ln ξ2 + 11113872 1113873 + 2ξ41113960 1113961

ξ2 + 11113872 1113873ξ2 (22)













Tabl

e3

+eparameterswhich

areneeded


nequatio

nsin

each

case

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly

1Neuilly

2Bo

rdeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

ai

Geotechnical

description

Silty

sand

with

clay

Clean

fine

sand

Sand

yclay

Sand

andgravels

Clean

sand

Sand

yclay

Silty

fine

sand

Organic

silt

Roun

dgravel

gravel

sand

Silty

clay

sand

ysilt

Parameters

h(m

)7

65

57

6sim12

272

815

97sim

105

Dp(m

)108

096

076

064

066

065

149

12

096

414

406

ΔR(m

m)

3015

020

010

55

530

20c(kNm

3 )18sim2

018sim2

017sim2

020

18sim2

018sim2

119sim2

05

175sim1

919sim2

05

176sim1

94

c(kPa

)0

05sim

300

010sim1

50

100

5sim33

φ(deg )

28sim4

228sim4

220sim3

035

30sim3

526sim2

828sim4

215sim1

8366sim3

719sim3

2E s

(MPa

)10sim1

410sim1

49sim

4510sim4

610sim4

68sim

1310sim1

214sim2

810sim4

630sim4

5v s

025sim0

30

025sim0

30

025sim0

35

015sim0

30

025sim0

30

025sim0

35

025sim0

30

03sim

042

015sim0

25

025sim0

35

e031sim1

27

050sim0

80

080sim2

24

028sim1

27

031sim1

27

080sim2

24

090sim1

27

1sim25

028sim1

27

080sim2

24


4 Conclusions





Abbreviations




Data Availability




Acknowledgments


References





Soilgroup

c


Es(MPa) vs e



























Tabl

e3

+eparameterswhich

areneeded


nequatio

nsin

each

case

Cases

12

34

56

78

910

1112

Mon

tmor

Chatenay

Champigy

Neuilly

1Neuilly

2Bo

rdeaux

Anthens

1Anthens

2Fcity

Hcity

Shenyang

Shangh

ai

Geotechnical

description

Silty

sand

with

clay

Clean

fine

sand

Sand

yclay

Sand

andgravels

Clean

sand

Sand

yclay

Silty

fine

sand

Organic

silt

Roun

dgravel

gravel

sand

Silty

clay

sand

ysilt

Parameters

h(m

)7

65

57

6sim12

272

815

97sim

105

Dp(m

)108

096

076

064

066

065

149

12

096

414

406

ΔR(m

m)

3015

020

010

55

530

20c(kNm

3 )18sim2

018sim2

017sim2

020

18sim2

018sim2

119sim2

05

175sim1

919sim2

05

176sim1

94

c(kPa

)0

05sim

300

010sim1

50

100

5sim33

φ(deg )

28sim4

228sim4

220sim3

035

30sim3

526sim2

828sim4

215sim1

8366sim3

719sim3

2E s

(MPa

)10sim1

410sim1

49sim

4510sim4

610sim4

68sim

1310sim1

214sim2

810sim4

630sim4

5v s

025sim0

30

025sim0

30

025sim0

35

015sim0

30

025sim0

30

025sim0

35

025sim0

30

03sim

042

015sim0

25

025sim0

35

e031sim1

27

050sim0

80

080sim2

24

028sim1

27

031sim1

27

080sim2

24

090sim1

27

1sim25

028sim1

27

080sim2

24


4 Conclusions





Abbreviations




Data Availability




Acknowledgments


References





Soilgroup

c


Es(MPa) vs e



























4 Conclusions





Abbreviations




Data Availability




Acknowledgments


References





Soilgroup

c


Es(MPa) vs e



























CalculationofFrictionForceforSlurryPipeJackingconsidering...

Documents

Transcript of CalculationofFrictionForceforSlurryPipeJackingconsidering...