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
4 Advances in Civil Engineering
(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
Advances in Civil Engineering 5
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
6 Advances in Civil Engineering
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
Advances in Civil Engineering 7
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
8 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 Advances in Civil Engineering
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
4 Advances in Civil Engineering
(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
Advances in Civil Engineering 5
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
6 Advances in Civil Engineering
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
Advances in Civil Engineering 7
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
8 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 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
4 Advances in Civil Engineering
(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
Advances in Civil Engineering 5
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
6 Advances in Civil Engineering
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
Advances in Civil Engineering 7
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
8 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 Advances in Civil Engineering
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
4 Advances in Civil Engineering
(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
Advances in Civil Engineering 5
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
6 Advances in Civil Engineering
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
Advances in Civil Engineering 7
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
8 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 Advances in Civil Engineering
(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
Advances in Civil Engineering 5
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
6 Advances in Civil Engineering
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
Advances in Civil Engineering 7
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
8 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 Advances in Civil Engineering
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
6 Advances in Civil Engineering
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
Advances in Civil Engineering 7
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
8 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 Advances in Civil Engineering
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
Advances in Civil Engineering 7
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
8 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 Advances in Civil Engineering
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
8 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 Advances in Civil Engineering
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 + + + +
Advances in Civil Engineering 9
[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
10 Advances in Civil Engineering
[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
10 Advances in Civil Engineering