a new method for predicting ground settlement induced by

Research ArticleANewMethod for Predicting Ground Settlement Induced by PipeJacking Construction

Zelin Niu123 Yun Cheng 12 Yuwei Zhang 12 Zhanping Song 12 Guiyang Yang1

and Hui Li1

1School of Civil Engineering Xirsquoan University of Architecture and Technology Xirsquoan 710055 China2Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering Xirsquoan 710055 China3Fifth Engineering Bureau Co Ltd China Railway Bridge Engineering Bureau Group Co Ltd Chengdu 610000 China

Correspondence should be addressed to Yuwei Zhang 1032659676qqcom and Zhanping Song songzhpytxauateducn

Received 4 September 2019 Revised 5 April 2020 Accepted 13 April 2020 Published 7 May 2020

Academic Editor Mijia Yang

Copyright copy 2020 Zelin Niu et al 0is 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

Pipe jacking technology has the advantages of fast construction speed high economic benefit and small impact on the urbanenvironment and mechanical vibration and mechanical soil interaction will lead to the settlement of upper part of pipe jackingand surrounding soil So the solution of soil settlement problem is of great significance for underground engineering con-struction 0e soil loss additional stress and friction during the construction of rectangular pipe jacking are the main factors thatcause the surface settlement Aiming at the problem of surface settlement caused by pipe jacking in no 6 subway in Kunming theformation deformation caused by additional stress and friction force on excavation surface during pipe jacking process wasanalyzed byMindlinrsquos displacement solution and the formation deformation caused by soil loss was analyzed by randommediumtheory Considering the independence of the three influencing factors the superposition of the three types of stratum deformationwas the superposition model of surface settlement and the model was compared with the empirical method and the measuredsettlement data to verify its practicability and reliability 0e results showed that the surface vertical settlement curve was roughlyin the shape of ldquoSrdquo which can be divided into uplift occurrence area sensitive settlement area stable settlement area and reboundsettlement area Friction force and additional stress caused the uplift of stratum in the front of construction area and soil losscaused the subsidence of stratum in the rear of construction area Rectangular pipe jacking in weak stratum caused the soil tomovetowards the excavation surface easily causing micro-overexcavation

1 Introduction

With the continuous development and utilization of urbanunderground space such as tunnel underground stationand underground commercial space [1ndash3] the constructionof many underground facilities has gradually failed to meetthe requirements of open-cut construction [4ndash7] Pipejacking is one of the typical trenchless underground con-struction methods [8 9] which has the advantages of highutilization rate of section area shallow burial depth nointerruption of surface traffic high efficiency and lowpollution By integrating factors such as equipment com-position construction technology construction speed andsocial and economic benefits pipe jacking has obvious

advantages in the construction of underground channels[10 11] However due to the vibration of soil (rock) bodyand interaction between mechanical and rock body causedby mechanical construction soil loss additional stress onend face and friction force in pipe jacking construction willinevitably produce surface settlement [12ndash15] which seri-ously threatens the safety of surrounding existing buildings(structures) With the development of pipe jacking tech-nology rectangular pipe jacking is gradually applied and thesurface settlement caused by rectangular pipe jacking isdifferent from that caused by circular pipe jacking 0ere-fore it is of great significance to clarify and solve the surfacesettlement caused by rectangular pipe jacking for the de-velopment of modern underground space engineering

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 1681347 11 pageshttpsdoiorg10115520201681347

At present many scholars have studied the surfacesettlement caused by pipe jacking and the research methodsmainly include theoretical analysis field measurement andnumerical analysis Because the theoretical research andengineering application of circular pipe jacking have beengradually mature the rectangular pipe jacking mainly usesthe calculation method of circular pipe jacking for referenceAs for the research status of the surface settlement in thecurrent subway construction the results obtained from thethree aspects of theoretical analysis field measurement andnumerical simulation are analyzed as follows

11 -eoretical Analysis 0e peak empirical formulamethod was the most widely used and first proposed thequasi-normal distribution of lateral surface settlementestimation method in 1969 Attewell and Farmer [16 17]analyzed the longitudinal surface settlement of shield ex-cavation and proposed the method of cumulative proba-bility curve to estimate the longitudinal surface settlementRen et al [18] put forward a calculation method of surfacesettlement caused by circular pipe jacking construction andcarried out case analysis Cheng et al [19] conducted asystematic analysis of the variation law of jacking forcewhen the earth-pressure-balanced pipe jacking machinetraverses different strata according to the pipe jackingconstruction project in Taiwan Sagaseta [20] provided thesurface strain solution in the case of surface loss caused byelastic isotropic homogeneous mass Verruijt and Booker[21] considered the elliptical deformation under the initialstress field and modified Sagasetarsquos method Wei et al [22]used Mindlinrsquos elastic theory solution and deduced theformula for calculating the ground deformation caused bythe additional thrust on the front of circular pipe jackingand the lateral friction resistance of pipe jacking machineand subsequent pipe joints Based on the random mediumtheory Han [23] deduced the calculation formulas ofvarious section shapes in the nonuniform convergencemode

12 Field Measurement To meet the safety and efficientconstruction requirements in the process of urban subwaytunnel construction Sun et al [24] used field monitoringmethod to analyze key parameters such as pore waterpressure jacking force and earth pressure in pipe jackingconstruction of double-line underground pedestrian chan-nel Zhang et al [25] summarized four jacking force cal-culation methods and carried out the field test about thejacking force during the pipe jacking construction process ofGongbei tunnel and the comparative analysis was carriedout with the theoretical calculation method Relying on apipe jacking project in Chongqing Li et al [26] tested thedamage of large-section concrete pipe segments on-site andconducted systematic analysis in parallel

13 Numerical Simulation Lin [27] used MARC programto study the influence of rectangular pipe jacking con-struction of Shanghai metro line 6 on surface settlement at

different burial depths Bing et al [28] simulated the actualworking conditions and found that the influence ranges oftransverse and longitudinal surface deformation caused bycircular pipe jacking were minus36sim36D and minus214sim214Drespectively (D was the external diameter of pipe joints)Tang et al [29] took the construction of the first rectangularsubway shield in China as the background and adoptedABAQUS three-dimensional finite element simulationsoftware to simulate the actual project It can be seen thatcompared with the more mature circular pipe jacking thedevelopment of rectangular pipe jacking is not yet maturewhich is still a new technology of underground spaceconstruction

From the above research results it can be seen that manyexperts have paid attention to the ground surface settlementof soil mass and rock mass in the process of tunnel con-struction and have obtained abundant research resultsPrevious studies on the soil deformation caused by rect-angular pipe jacking mainly refer to shield construction andcircular section pipe jacking Moreover the surface settle-ment law and prediction of rectangular pipe jacking con-struction caused by soil loss additional stress and frictionforce are rarely reported Because of the great difference ofcross-sectional shape between circular and rectangular pipejacking construction the soil stress variation form andrandom movement mode are quite different In the face ofthe gradual popularization of rectangular pipe jackingtechnology its theoretical research is inevitably greatlydifferent from that of circular pipe jacking and shieldconstruction which puts forward higher requirements forthe study of stratum subsidence caused by rectangular pipejacking

0e rectangular top pipe project of the undergroundconnection passage between Tuodong stadium station online 6 of Kunming metro and Tuodong Dacheng centralbusiness district is located at the intersection of Tuodongroad and east Huancheng road with busy surface trafficand numerous underground pipelines not meeting theconstruction conditions of open excavation Consideringthe complex construction environment comprehensivelythe project plans to adopt the rectangular pipe jackingmachine with multiblade-earth pressure balance for tun-neling construction In this study the influence of soil lossadditional stress on end face and friction force on surfacesettlement during construction was comprehensivelyconsidered 0e surface settlement caused by rectangularpipe jacking was divided into three parts namely thesettlement caused by soil loss the settlement caused byadditional stress on end face and the settlement caused byfriction force 0en based on the basic hypothesis of thesuperposition model Mindlinrsquos elastic theory and randommedium theory were used to solve the surface settlementequation caused by various factors and the superpositionmodel was obtained after the three kinds of settlement wereadded Finally according to the established settlementmodel the empirical method and the measured settlementamount the surface settlement deformation characteristicscaused by the rectangular pipe jacking construction dis-turbance were studied

2 Mathematical Problems in Engineering

2 Soil Stress Characteristics andBasic Assumptions

21 Analysis of Soil Force Characteristics A number offactors in pipe jacking construction can affect the finalsurface subsidence the transverse pressure (the additionalstress is provided to make the excavation face stable in pipejacking construction process) of end face and wall friction(the larger friction between the subsequent pipe section anddigger propulsion process) and ground subsidence causedby soil loss (soil loss caused by overexcavation of the earthbody around the pipeline) are most obvious 0erefore thispaper mainly analyzes the surface settlement caused by theabove three factors in the construction of rectangular pipejacking and assumes that the final surface settlement is thesuperposition of the three settlement amounts

Son and Peck [16] analyzed a large number of engi-neering data and believed that under the condition of un-drained soil mass the volume of surface settlement troughcaused by soil mass loss was the same as that of soil layer lossand the surface settlement trough was normally distributedin a curve 0e lateral surface settlement is

S(x) Smax exp minusx2

2i21113888 1113889

Smax Vloss2π

radiciasymp

Vloss

25i

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(1)

where S (x) is the lateral surface settlement (m) caused by soilloss x is the horizontal distance (m) from the calculated pointto the pipe jacking axis Smax is the maximum surface settle-ment value (appearing above the pipe jacking axis) (m) andVloss refers to the formation loss per unit length in the tunnelingprocess For clay it is usually 05sim25 of the excavation area(A) K is the percentage of soil loss and soil loss VlossAk (m3m) i is settlement trough coefficient (m) Verruijt and Booker[21] believed that when 3mlthlt 34m the empirical formulaof i was i 043h+110 (clay) i 028hminus 010 (granular soil)

However among the many factors that cause surfacesubsidence during the construction of the top pipe Peckrsquosempirical formula only considers the surface settlementcaused by the vertical movement of soil caused by formationloss but does not consider the surface settlement caused bythe three-dimensional displacement and stress change of soilwithin a certain range 0erefore based on Mindlinrsquos so-lution [22 30 31] and random medium theory [16] thispaper proposes a superposition model of surface subsidenceunder the combined action of three factors

ω ω1 + ω2 + ωloss (2)

where ω is the total surface settlement value (m) ω1 issurface settlement (m) caused by end pressure ω2 is thesurface subsidence caused by friction (m) and ωloss isground subsidence (m) caused by soil loss

22 Basic Assumptions of the Model Force analysis of pipejacking construction is shown in Figure 1 which is mainly

caused by the sectional reaction force of the jacking face andfriction force of the pipe wall Based on the stress regionintegral based on Mindlinrsquos solution the ground settlementcaused by stress can be obtained and the ground settlementcaused by soil loss can be considered to obtain the groundsettlement during pipe jacking

During the construction of pipe jacking the superpo-sition model of surface settlement includes five basic as-sumptions (1) During construction the digger digs in astraight line in the normal solidification soft soil regardlessof the influence of factors such as correction and slurrypressure (2) 0e soil mass is a uniform linear elastic semi-infinite body which is consolidated under the condition ofno drainage (3) 0e tunneling of tunneling machine in theconstruction process is only the change of space positionwhich has nothing to do with time (4) 0e front end of theroadheader is the load action surface and the end pressure isapproximately rectangular uniform load (5) According toits position the friction force of tunneling machine andsubsequent pipe joints is divided into upper surface frictionlower surface friction left-side friction and right-sidefriction 0e friction resistance of upper and lower surface isthe product of normal stress and friction coefficient of soiland the friction resistance of left and right side is the productof active soil pressure and friction coefficient

Based on the above five basic assumptions in the process ofrectangular pipe jacking the derivation of surface subsidenceω1 ω2 and ωloss is caused by the three factors respectivelyshown in Section 31 Since the rectangular top pipe has foursurfaces namely upper lower left and right the corre-sponding surface subsidence caused by the four kinds offriction are respectively expressed as ω21 ω22 ω23 and ω24

3 Superposition Model of Surface Subsidence

31 Surface Settlement Caused by End Pressure As can beseen from Figure 1 it can be known that the area where theadditional stress on the end surface acts on the soil is the

continuous plane ofminusaleyle a

hle zle h + 2b

x 0

⎧⎪⎨

⎪⎩ To distinguish the

calculated point coordinate and the integral variable theintegral variable (x y z) was replaced by (l m n) and themicroelement dmdn was taken from the action plane of theadditional stress on the end surface and then the groundsettlement caused by the stress in the differential area wassolved by Mindlinrsquos solution Since the surface settlement is

S L

h

o x

zy

Friction force Heading machine

Subsequent pipeline End pressure

2b2a

Figure 1 Schematic diagram of soil force characteristics

Mathematical Problems in Engineering 3

discussed in this paper the calculated depth is zero (iez 0) 0e surface settlement caused by end stress is

ω1 P1x

4πG1113946

a

minusa11139462b

0

1M1

1 minus 2μM1 + h + n

minush + n

M21

1113888 1113889dmdn (3)

whereω1 is surface settlement (m) caused by end face stress x isthe horizontal distance (m) from the calculated point to theexcavation face and the jacking direction is positive y is thehorizontal distance (m) from the calculated point to the axisboth of which are positive h is the distance from the top surfaceof the pipe jacking to the ground (m) 2a is end face width (m)of roadheader 2b is the face height of the roadheader (m) P1 isthe additional stress on the face of roadheader (kPa) and G issoil shear elastic modulus (MPa) G (1minus2μ) Eso[2 (1+μ)]where Eso is soil compression modulus μ is soil Poissonrsquos ratioand K0 is static earth-pressure coefficient [22] K0 μ(1-μ)M1 [x2 + (yminusm)2 + (h+n)2]05

32 Surface Settlement Caused by Friction 0e frictiongenerated during pipe jacking mainly includes two parts one isthe friction between the side wall of the roadheader and soilmass and the other is the friction between the subsequent pipejoints and soil mass In the construction process the tunnelingmachine is in close contact with soil mass and there is a layer ofthixostatic mud sleeve between subsequent pipe joints andsurrounding soil mass so the lubrication effect of groutingsleeve should be considered when calculating the friction forcebetween subsequent pipe joints and soil mass At the sametime considering the small difference between the outsidedimension of roadheader and the outside dimension of pipesection it can be assumed that the size of pipe section is equal tothe section size of roadheader 0e calculation method ofsurface settlement caused by friction force is similar to thatcaused by end pressure However when integrating Mindlinrsquossolution in this case it should be noted that the four faces ofroadheader and subsequent pipe joints are discontinuous andsmooth so the four faces of upper lower left and right need tobe integrated respectively

321 Surface Settlement Caused by Upper Surface FrictionAs can be seen from Figure 1 the area of friction acting onthe upper surface of the pipe section is a continuous plane of

minusSlexle 0minusaleyle a

z h

⎧⎪⎨

⎪⎩ Considering that the friction effect produced by

the roadheader and the subsequent pipe section is different fromthat produced by the soil mass it needs to be solved in sectionsTake the microelement dldm on the upper surface and thesurface settlement caused by friction on the upper surface is

ω21 P2f1

4πG1113946

a

minusa11139460

minusL

x minus l

M2

1 minus 2μM2 + h

minush

M22

1113888 1113889dldm

+αP2f2

4πG1113946

a

minusa1113946

minusL

minusS

x minus l

M2

1 minus 2μM2 + h

minush

M22

1113888 1113889dldm

(4)

where ω21 is the surface settlement caused by friction on theupper surface (m) L is length of roadheader (m) S is the

distance from the end face of the tunneling machine to thetunneling starting point (m) P2 is the upper pressure of tubejacking (kPa) P2 ch a is the friction reduction coefficientbetween soil and pipe joints under thixotropic mud f1 is thefriction coefficient between roadheader and soil mass f2 isthe friction coefficient between pipe joint and soil mass andM2 [(xminus 1)2 + (yminusm)2 + h2]05

322 Surface Settlement Caused by Lower Surface FrictionSince the lower surface of the pipe joint and the uppersurface are parallel and the depth difference is 2b thepressure of the lower soil after excavation is the sum of thepressure of the upper Earth and the pressure of the road-header (pipe joint) on the soil0erefore when deducing thesurface displacement and settlement caused by the lowersurface friction it is only necessary to replace the upperEarth pressure P2 in equation (4) with the lower earthpressure P3 (P4) after tunneling and the upper depth h withthe lower depth h+ 2b 0e surface settlement caused by thelower surface friction is

ω22 P3f1

4πG1113946

a

minusa11139460

minusL

x minus l

M3

1 minus 2μM3 + h + 2b

minush + 2b

M23

1113888 1113889dldm

+αP4f2

4πG1113946

a

minusa1113946

minusL

minusS

x minus l

M3


minush + 2b

M23

1113888 1113889dldm

(5)

where ω22 is the surface settlement (m) caused by the lowersurface friction P3 is the earth pressure (kPa) on the bottomsurface of the roadheader P4 is the earth pressure (kPa) on thelower surface of the concrete pipe section and M3 [(xminus l)2 + (yminusm)2 + (h+2b)2]05 P3 and P4 are expressed as follows

P3 ch +Tj

2aL

P4 ch +Tg

2as

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)

where Tj is the weight of roadheader (kN) Tg is concrete pipejoint weight (kN) and s is the length of single concrete (m)

323 Surface Settlement Caused by Left Surface FrictionAs the left and right surfaces of the tube jacking are verticallyparallel the distribution of friction force on the left and rightsurfaces can be considered to be identical when other minorinfluencing factors are ignored It is assumed that the lateralpressure of soil on the left and right sides is P5 (kPa) and thatthe lateral pressure of soil increases with the increase ofdepth 0erefore P5 is a function of soil depth 0e ex-pression of P5 is

P5 K1(h + n)c (7)

According to Figure 2 the area affected by the frictionforce on the left surface of the tube jacking is a continuous

plane ofminusSle xle 0hle zle h + 2b

y a

⎧⎪⎨

⎪⎩ If dldn is taken from the left


surface the surface settlement caused by friction on the leftsurface is

ω23 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

(8)

where ω23 is the surface settlement (m) caused by left surfacefriction M4 [(xminus l)2 + (yminus a)2 + (h+ n)2]05

0e right-side frictional force and the left-side frictionalforce are only 2a apart in position and symmetric about thexoz plane 0erefore when deducing the formula of surfacedisplacement and settlement caused by friction on the rightside it is only necessary to replace a in the above equationwith ₋a and the amount of surface settlement caused by theright side during jacking is

ω24 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

(9)

where ω24 is the surface settlement caused by left surfacefriction (m) M5 [(xminus l)2 + (y+ a)2 + (h+ n)2]05

0erefore based on equations (4)sim(9) it can be knownthat the surface settlement caused by tube jacking friction isthe sum of the surface settlement caused by upper lowerleft and right surface friction

33 Surface Settlement Caused by Soil Loss Soil mass lossduring pipe jacking refers to actual excavation of the soilbody more than the design of the earth body 0e mainreason for soil mass loss is that there is a gap of about 5 cm inthe construction building during construction (the differ-ence between the size of the tunneling head and the size ofthe pipe joints) With the gradual optimization of con-struction technology and grouting effect soil loss has beenwell controlled but still inevitable resulting in surfacesettlement

A large number of measured results show that the soilmass around the pipe jacking has an obvious movementtrend during the tunneling process 0e soil mass cannotbe regarded as a simple elastomer or elastoplastic bodyunder general conditions and the traditional mechanicalmodel analysis method is no longer applicable to the soilmass movement state Due to the complicated controlfactors of soil mass movement soil mass can be used asrandommedium according to randommedium theory Asshown in Figure 2 the unitrsquos infinitesimal length widthand height are defined as the excavation units and thesurface settlement caused by excavation is expressed asωloss Under the condition of no drainage the final set-tlement tank volume and soil loss volume are the same0erefore when the excavation unit completely collapsesthe settlement tank volume is dξdζdη and the spatialrectangular coordinate system is established with theexcavation unit center then the settlement amount of theupper soil mass is

ωloss 1

r2(z)exp minus

πr2(z)

x2

+ y2

1113872 11138731113890 1113891dξdζdη (10)

where ωloss is the surface settlement (m) caused by soilloss r (z) is the influence radius of excavation unit in thez-direction r (z) ztanβ and β is the soil influence angleon the top of pipe jacking tanβ h(250i) [19]According to the random medium theory when theexcavation face completely collapses the soil loss area istaken as the integral domain and the settlement value atany point on the surface can be obtained by integratingequation (10) 0e schematic diagram of soil loss is shownin Figure 3

In fact the volume of soil collapse during pipe jackingis equal to the volume of soil loss It is assumed that theloss area of engineering soil is a rectangular ring of equalthickness set outside the excavation face (due to the in-fluence of gravity and grouting and other factors the gapon the lower side of the pipe section is transferred to theupper side as shown in Figure 3(b)) To simplify thecalculation the square area at the four corners of therectangle ring is ignored and then the relational ex-pression is

4aΔt + 4bΔt Aκ (11)

So

Δt Aκ

4(a + b) (12)

By integrating the soil loss area shown in Figure 3 theexpression of surface settlement caused by soil loss can beobtained as follows

ωloss BΩ

dζdη1113946minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dξ

(13)

After substituting equation (12) into equation (13) wecan obtain

o

z

y

x

dξdζdη w

Figure 2 Schematic diagram of unit excavation


ωloss 1113946hminusΔt

h+2b+Δt1113946

a+Δt

minusaminusΔt1113946

minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

211139601113896

+(y minus ζ)21113961⎫⎬

⎭dζdηdξ minus 1113946h+Δt

h+2b+Δt1113946

a

minusa1113946

minusL

minusS

tan2 βη2

exp

middot minusπ tan2 β

η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dζdηdξ

(14)

34 SurfaceSettlementOverlayModelduringRectangularPipeJacking By substituting equations (3)ndash(5) (8) (9) and (14)into equation (2) the surface settlement during the con-struction period of rectangular pipe jacking can be expressedas follows

ω ω1 + ω21 + ω22 + ω23 + ω24 + ωloss (15)

4 Analysis and Discussion of Models

41 Physical and Mechanical Indexes of Foundation and SoilLayer 0e connection channel between Tuodong stadiumstation of Kunming metro line 6 and Dacheng businessdistrict is located under the intersection of Huancheng southroad and Tuodong road in Kunming Yunnan province 0eexcavation face is mainly composed of clay clayey silty soiland silty clay layer with high groundwater level andcomplicated geological conditions Soil distribution con-crete pipe joints and pipe jacking machine cutterhead of thestratum where the pipe jacking channel is located are shownin Figure 4 Physical parameters of each soil layer [32] areshown in Table 1 0e cohesive force and internal frictionangle are obtained under the condition of undrainage whichis consistent with the test conditions of the natural capacityTo facilitate calculation physical parameters of soil layer arecalculated according to the average value 0e total length ofpipe jacking in this project is about 9808m the depth ofoverlaying is about 550m and the pipe jacking joints aremade of concrete pipes with outer dimensions of490mtimes 690m pipe thickness of 045m and mass of 39 tand the design slope is 1 A rectangular pipe jackingmachine with an external size of 5mtimes 7m and a mass of165 t is adopted for construction In order to ensure thestability of the excavation face the additional stress on theend face is 20 kPa In addition friction coefficient betweenconcrete roof wall and soil mass is shown in Table 2

42 Analysis of Surface Lateral Settlement According to thecalculation of jacking force on-site the friction between soilmass and pipe joints after grouting is about 30sim40 of theoriginal friction force so the reduction factor α 035 istaken in this paper With the MATLAB software Peckrsquosempirical formula and the calculation model in this paperwere compared to obtain the land surface settlement valuecaused by various factors and the final overall land surfacesettlement value In this paper 45m jacking of roadheader is

selected for calculation and data comparison analysisPositive values indicate subsidence and negative values in-dicate uplift

Figures 5ndash7 show the lateral surface deformation curvesunder the separate and combined action of formation lossend stress and friction when x 3m x 0m and x minus3mrespectively It can be seen from Figures 5ndash7 that themaximum value of surface settlement or uplift caused byvarious factors appears directly above the pipe jacking axisand the change curve is symmetric with respect to the pipeaxis When soil loss is the main control factor the lateralsurface settlement caused by it has a strong response todistance and the influence range is mainly within 10m onthe left and right sides of the vertical axis When endpressure and friction are the main control factors the lateralsurface settlement caused by it has a relatively mild responseto the distance and the influence scope is mainly concen-trated in the range of 15m on the left and right sides of thevertical axis of the pipeline It can also be seen that theamount of surface settlement caused by end pressure andfriction is small

43 Analysis of Surface Longitudinal Settlement Figure 8shows the longitudinal surface settlement curve under theseparate and combined action of soil loss end pressure andfriction when y 0m According to the analysis in Figure 8when soil loss is the main control factor a large surfacesettlement is generated behind the roadheader

According to the settlement calculation model in thispaper significant settlement still occurs within 150m fromthe nose of the roadheader to the front and the change rate isfast When the end face additional stress and friction for themain control factors the surface subsidence change causedby it is small face additional stress in the excavation frontend causes surface uplift and in the back end causes thesurface subsidence 0e ground settlement change is angledantisymmetric of excavation 0e friction force mainly af-fects the surface change within 9m of the front of the ex-cavation and makes the surface swell up

Longitudinal changes of the surface under the com-bined action of the three factors (based on the calculationmodel of surface settlement derived in this paper) thesurface about 150m in front of excavation is shown asuplift with the maximum uplift of 515mm occurring at6m in front of excavation 0e main control factors areadditional pressure and friction on the end face Settle-ment occurs after the roadheader with the maximumsettlement of 3263mm occurring at 9m behind theroadheader and the settlement decreases to some extentafter that 0e main control factor is soil loss On thewhole the surface longitudinal settlement change curve isroughly in the shape of ldquoSrdquo and can be divided into fourareas according to its change trend uplift occurrence areasensitive settlement area settlement stability area andsettlement rebound area

44ComparativeAnalysis of-eoreticalCalculationandFieldMeasured Data To verify the reliability of the calculation


model of surface settlement Peckrsquos empirical formula andthe calculation formula deduced in this paper are comparedand analyzed and field measured data are introduced 0edata results are shown in Figures 9ndash12

From the surface longitudinal settlement curve shown inFigures 9 and 10 it can be seen that the calculated values ofsurface changes in the uplift occurrence area settlementstability area and settlement rebound area by the empirical

h

2Δt

LPipeline

Soil loss

dξdη

x

z

o

2b

(a)

h2b

2Δt

Soil loss

dξdη

y

z

o

ΔtΔt

2a

Pipeline

(b)

Figure 3 Schematic diagram of soil loss (a) Longitudinal soil loss map (b) Transverse soil loss map

(1) Subgrade

(2) Mucky clay

(3) Clay stratum

(4) Clayey silt (interlayer)

(5) Silty clay

(6) Silty soil

Pipe jacking channel

080m

210m

620m

090m

800m

(a)

490

m

690m

045m

(b)

500

m

700m

(c)

Figure 4 Soil distribution (location of pipe jacking channel) concrete pipe joints and cutterhead of pipe jacking machine (a) Soildistribution (b) Concrete pipe joint (c) Cutterhead of pipe jacking machine


method and the method in this paper are basically consistentwith the measured values However in the sensitive area ofsubsidence because the Peck empirical formula does notconsider the change of vertical strata the surface subsidencecurve obtained shows a cliff-type change within the range ofminus3sim0m 0ere is no surface deformation on the surfaceabove the excavation end which is quite different from themeasured value However the surface settlement curvecalculated by this model is in good agreement with themeasured variation trend

Figures 11 and 12 show the lateral surface settlementcurves at x 3m and x 0m Compared with the empiricalmethod the calculated results of this model are in good

consistency with the field measured results It can be seenfrom Figure 11 that the development trend of lateral surfacesettlement curve under the three conditions of empiricalmethod measured value and joint action is basically similarbut the corresponding maximum settlement scale has sig-nificant differences which are 2992mm 1943mm and

Table 1 Basic physical and mechanical indexes of foundation soil layer

Soil layer 0ickness(m)

Natural capacity(kgmiddotmminus3)

Cohesive force(kPa)

Internal frictionangle (deg)

Modulus of compression(MPa)

Poissonrsquosratio

Subgrade 080 1850 1500 2150 1182 035Mucky clay 210 1710 1400 1200 456 030Claystratum 620 1790 1650 1850 589 035

Clay silt 090 1830 800 3100 729 037Silty clay 800 1940 3900 2100 893 035Silty soil mdash 1970 200 3250 1182 038

Table 2 Friction coefficients [32]

Soil typesReinforced concrete pipe Steel tube

Dry Moist Typicalvalue Dry Moist Typical

valueSoft soil mdash 020 020 mdash 020 020Claystratum 040 020 030 040 020 030

Silt 045 030 038 045 030 037Mucky clay 035 020 028 035 020 027Silty clay 040 030 035 040 030 035Gravel soil 050 040 045 050 050 050

Stratum lossFriction force

End forceInteraction (in this paper)

2

1

0

ndash1

ndash2

ndash3

ndash4

Surfa

ce se

ttlem

ent (

mm

)

ndash18 ndash12 ndash6 0 6 12 18 24ndash24Lateral y (m)

Figure 5 Lateral surface settlement (x 3m)



6

4

2

0

ndash2

ndash4

Surfa

ce se

ttlem

ent (

mm

)



18

15

12

9

6

3

0

ndash3



Surfa

ce se

ttlem

ent (

mm

)


Figure 7 Lateral surface settlement (x minus3m)


1513mm respectively Compared with the surface settle-ment value obtained by the empirical method the surfacesettlement value calculated by this model is closer to themeasured surface settlement value 0e surface settlementcurve at x 0m shows that the surface settlement valueobtained by the empirical method is significantly lower thanthe measured value which is not conducive to engineeringsafety analysis 0e settlement value calculated by this modelis close to the measured value

It can also be seen from Figure 12 that the actual set-tlement value is 3sim4mm larger than the calculated value ofthis model within 5m or so of the longitudinal axis of thepipeline 0e main reason is that the stratum traversed bythis project is mainly clay and the soil layer is relatively softIn the construction process the soil around the excavationface collapses to the excavation face resulting in the micro-overexcavation phenomenon resulting in a slight gap

between the measured value and the calculated value of thispaper

It can be seen from the above analysis that the surfacesettlement amount calculated by this model has goodpracticability and reliability and has significant advantagesover the empirical algorithm 0e three-dimensional set-tlement trough on the surface during the construction ofrectangular pipe jacking is drawn by using the calculationresults of the model as shown in Figure 13

Figure 13 further illustrates the distribution law ofsurface changes caused by rectangular pipe jacking (1) Largesettlement is mainly concentrated in the range of 150 timesof pipe joint width on both sides of pipe axis after excavationface and the maximum settlement is in the range of 050times of pipe joint width (directly above the pipe joint) on



36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)

ndash25 ndash20 ndash15 ndash10 ndash5 0 5 10 15 20ndash30Lateral x (m)

Figure 8 Longitudinal surface settlement (y 0m)

Empirical method

Measured valueInteraction (in this paper)

30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)

ndash24 ndash18 ndash12 ndash6 0 6 12 18ndash30Lateral x (m)

Figure 9 Longitudinal surface settlement (y minus35m)Empirical method


36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)

ndash25 ndash20 ndash15 ndash10 ndash5 50 10 15 20ndash30Lateral x (m)



both sides of the axis (2) 0e longitudinal direction of theuplift area is mainly concentrated within the range of 150mto 15m in front of the excavation and the transverse range iswithin the width of 150 times of the pipe joints on both sidesof the pipeline axis

5 Conclusion

Based on the engineering background of Kunming metroline 6 this paper studied the influence of soil loss additionalstress on end face and friction force on surface settlementduring the construction and arrived at the followingconclusions

(1) Based on Mindlinrsquos solution and random mediumtheory the superposition model of surface settle-ment caused by friction force additional stress onend surface and soil loss is proposed 0eoreticalanalysis shows that the vertical settlement curve of

the surface is roughly in the shape of ldquoSrdquo which canbe divided into uplift occurrence area sensitivesettlement area stable settlement area and reboundsettlement area 0e measured data verify the ra-tionality of the model Because the three-dimen-sional displacement of soil is not considered by theempirical method cliff-type changes appear in thesensitive areas of settlement which is not consistentwith the actual settlement

(2) 0e front part of the rectangular pipe jacking area isshown as stratum uplift while the rear part is shownas stratum settlement and the dividing line isroughly located on the excavation face Among thethree main factors that cause the formation defor-mation in rectangular pipe jacking constructionfriction force and additional stress on excavationsurface mainly cause the stratum uplift in the front ofthe construction area 0e soil loss mainly causes thestratum settlement at the rear of the constructionarea

(3) Rectangular pipe jacking in weak strata causes thesurrounding soil to move towards the excavationsurface making the actual overbreak value greaterthan the theoretical overbreak value which is easyto cause micro-overexcavation 0e large surfacesettlement is mainly concentrated within 150times of the width of the pipe section on both sidesof the pipe axis after the excavation face 0elongitudinal settlement in the uplift area is mainlyconcentrated in the range of 150m to 15m infront of excavation while the transverse settlementis mainly concentrated in the range of 150 timesthe width of pipe joints on both sides of thepipeline axis

Data Availability

0e data used to support the findings of this studyare available from the corresponding author uponrequest

Conflicts of Interest

0e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

0e authors thank the National Natural Science Foundation ofChina (Grant no 51578447) Fund of Housing Urban andRural Construction Technology Research and DevelopmentProject Foundation of Shaanxi Province (Grant no 2019-K39)Project Funded by China Postdoctoral Science Foundation(Grant no 2018M643809XB) Natural Science Basic ResearchProgram of Shaanxi (Grant no 2019JQ-762) and the NaturalScience Basic Research Program of Science and TechnologyDepartment of Shaanxi Province of China (Grant no2018JM5153)

Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)

Figure 13 Surface three-dimensional settlement trough


References

[1] Z Song J Mao X Tian Y Zhang and J Wang ldquoOptimi-zation analysis of controlled blasting for passing throughhouses at close range in super-large section tunnelsrdquo Shockand Vibration vol 2019 Article ID 1941436 16 pages 2019

[2] Z Song G Shi J Wang H Wei T Wang and G ZhouldquoResearch on management and application of tunnel engi-neering based on BIM technologyrdquo Journal of Civil Engi-neering and Management vol 25 no 8 pp 785ndash797 2019

[3] X X Tian Z P Song and J B Wang ldquoStudy on thepropagation law of tunnel blasting vibration in stratum andblasting vibration reduction technologyrdquo Soil Dynamics andEarthquake Engineering vol 126 Article ID 105813 2019

[4] Z Song G Shi B Zhao K Zhao and J Wang ldquoStudy of thestability of tunnel construction based on double-headingadvance construction methodrdquo Advances in MechanicalEngineering vol 12 no 1 p 17 2020

[5] Z P Song S H Li J B Wang Z Y Sun J Liu andY Z Chang ldquoDetermination of equivalent blasting loadconsidering millisecond delay effectrdquo Geomechanics andEngineering vol 15 no 2 pp 745ndash754 2018

[6] P Jia B Jiang W Zhao Y Guan J Han and C ChengldquoCalculating jacking forces for circular pipes with weldingflange slabs from a combined theory and case studyrdquo KSCEJournal of Civil Engineering vol 23 no 4 pp 1586ndash15992019

[7] Z P Song Y Cheng X X Tian J B Wang and T T YangldquoMechanical properties of limestone fromMaixi tunnel underhydro-mechanical couplingrdquo Arabian Journal of Geosciences2020 in press

[8] X Ji W Zhao P Ni et al ldquoA method to estimate the jackingforce for pipe jacking in sandy soilsrdquo Tunnelling and Un-derground Space Technology vol 90 pp 119ndash130 2019

[9] P Ni S Mangalathu and Y Yi ldquoFragility analysis of con-tinuous pipelines subjected to transverse permanent grounddeformationrdquo Soils and Foundations vol 58 no 6pp 1400ndash1413 2018

[10] J Wang Q Zhang Z Song and Y Zhang ldquoCreep propertiesand damage constitutive model of salt rock under uniaxialcompressionrdquo International Journal of Damage Mechanics2019 in press

[11] YW Zhang X LWeng Z P Song and Y F Sun ldquoModelingof loess soaking induced impacts on metro tunnel using watersoaking system in centrifugerdquo Geofluids vol 2019 17 pages2019

[12] C Yin ldquoHazard assessment and regionalization of highwayflood disasters in Chinardquo Natural Hazards vol 100 no 2pp 535ndash550 2020

[13] Y Cheng Z Song J Jin and T Yang ldquoAttenuation char-acteristics of stress wave peak in sandstone subjected todifferent axial stressesrdquo Advances in Materials Science andEngineering vol 2019 Article ID 6320601 11 pages 2019

[14] Y Chen W Zhao J Han and P Jia ldquoA CEL study of bearingcapacity and failure mechanism of strip footing resting on c-φsoilsrdquo Computers and Geotechnics vol 111 pp 126ndash136 2019

[15] H Wu CK Yao CH Li et al ldquoReview of application andinnovation of geotextiles in geotechnical engineeringrdquo Ma-terials vol 13 no 7 p 1174 2020

[16] J L Qiu Y Q Lu J X Lai Y W Zhang T Yang andK Wang ldquoExperimental study on the effect of water gushingon loess metro tunnelrdquo Environmental Earth Sciences vol 79no 9 pp 1ndash12 2020

[17] Y W Zhang Z P Song and X L Weng ldquoA constitutivemodel for loess considering the characteristics of structuralityand anisotropyrdquo Soil Mechanics and Foundation Engineeringin press 2020

[18] 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

[19] W-C Cheng J C Ni J S-L Shen and H-W HuangldquoInvestigation into factors affecting jacking force a casestudyrdquo Proceedings of the Institution of Civil Engineer-smdashGeotechnical Engineering vol 170 no 4 pp 322ndash3342017

[20] C Sagaseta ldquoAnalysis of undraind soil deformation due toground lossrdquo Geotechnique vol 37 no 3 pp 301ndash320 1987

[21] A Verruijt and J R Booker ldquoSurface settlements due todeformation of a tunnel in an elastic half planerdquoGeotechnique vol 46 no 4 pp 753ndash756 1996

[22] G Wei Z Y Huang and R P Xu ldquoStudy on calculationmethods of ground deformationrdquo Chinese Journal of RockMechanics and Engineering vol 24 no supp2 pp 5808ndash5815 2005

[23] X Han -e Analysis and Prediction of Tunneling InducedBuilding Deformations Xirsquoan University of Technology XirsquoanChina 2006

[24] Y Sun F Wu W J Sun H M Li and G J Shao ldquoTwounderground pedestrian passages using pipe jacking casestudyrdquo Journal of Geotechnical and Geoenvironmental Engi-neering vol 145 no 2 Article ID 05018004 2019

[25] P Zhang S S Behbahani B Ma T Iseley and L Tan ldquoAjacking force study of curved steel pipe roof in Gongbeitunnel calculation review and monitoring data analysisrdquoTunnelling and Underground Space Technology vol 72pp 305ndash322 2018

[26] C Li Z Zhong C Bie and X Liu ldquoField performance of largesection concrete pipes cracking during jacking in Chongqing -a case studyrdquo Tunnelling and Underground Space Technologyvol 82 pp 568ndash583 2018

[27] Q Q Lin Analysis and Control of the Surface DeformationCaused by Rectangular Pipe Jacking Construction TongjiUniversity Shanghai China 2008

[28] F J Bing X Wang N Xi and L Fang ldquo3D numericalsimulation of pipe jacking and its soil applicability studyrdquoChinese Journal of Underground Space and Engineering vol 6no 7 pp 1209ndash1215 2011

[29] J X Tang L S Wang J I Chang and X Y Kou ldquo0ree-dimensional numerical analysis of ground deformation in-duced by quasi rectangle EPB shield tunnelingrdquo Journal ofEast China Jiaotong University vol 1 no 33 pp 9ndash15 2016

[30] C W W Ng and H Lu ldquoEffects of the construction sequenceof twin tunnels at different depths on an existing pilerdquo Ca-nadian Geotechnical Journal vol 51 no 2 pp 173ndash183 2014

[31] R D Mindlin ldquoForce at a point in the interior of a semi-infinite solidrdquo Physics vol 7 no 5 pp 195ndash202 1936

[32] N X Gao and X Z Zhang Pipe Jacking Technique ChinaArchitecture and Building Press Beijing China 1984


At present many scholars have studied the surfacesettlement caused by pipe jacking and the research methodsmainly include theoretical analysis field measurement andnumerical analysis Because the theoretical research andengineering application of circular pipe jacking have beengradually mature the rectangular pipe jacking mainly usesthe calculation method of circular pipe jacking for referenceAs for the research status of the surface settlement in thecurrent subway construction the results obtained from thethree aspects of theoretical analysis field measurement andnumerical simulation are analyzed as follows

11 -eoretical Analysis 0e peak empirical formulamethod was the most widely used and first proposed thequasi-normal distribution of lateral surface settlementestimation method in 1969 Attewell and Farmer [16 17]analyzed the longitudinal surface settlement of shield ex-cavation and proposed the method of cumulative proba-bility curve to estimate the longitudinal surface settlementRen et al [18] put forward a calculation method of surfacesettlement caused by circular pipe jacking construction andcarried out case analysis Cheng et al [19] conducted asystematic analysis of the variation law of jacking forcewhen the earth-pressure-balanced pipe jacking machinetraverses different strata according to the pipe jackingconstruction project in Taiwan Sagaseta [20] provided thesurface strain solution in the case of surface loss caused byelastic isotropic homogeneous mass Verruijt and Booker[21] considered the elliptical deformation under the initialstress field and modified Sagasetarsquos method Wei et al [22]used Mindlinrsquos elastic theory solution and deduced theformula for calculating the ground deformation caused bythe additional thrust on the front of circular pipe jackingand the lateral friction resistance of pipe jacking machineand subsequent pipe joints Based on the random mediumtheory Han [23] deduced the calculation formulas ofvarious section shapes in the nonuniform convergencemode

12 Field Measurement To meet the safety and efficientconstruction requirements in the process of urban subwaytunnel construction Sun et al [24] used field monitoringmethod to analyze key parameters such as pore waterpressure jacking force and earth pressure in pipe jackingconstruction of double-line underground pedestrian chan-nel Zhang et al [25] summarized four jacking force cal-culation methods and carried out the field test about thejacking force during the pipe jacking construction process ofGongbei tunnel and the comparative analysis was carriedout with the theoretical calculation method Relying on apipe jacking project in Chongqing Li et al [26] tested thedamage of large-section concrete pipe segments on-site andconducted systematic analysis in parallel

13 Numerical Simulation Lin [27] used MARC programto study the influence of rectangular pipe jacking con-struction of Shanghai metro line 6 on surface settlement at

different burial depths Bing et al [28] simulated the actualworking conditions and found that the influence ranges oftransverse and longitudinal surface deformation caused bycircular pipe jacking were minus36sim36D and minus214sim214Drespectively (D was the external diameter of pipe joints)Tang et al [29] took the construction of the first rectangularsubway shield in China as the background and adoptedABAQUS three-dimensional finite element simulationsoftware to simulate the actual project It can be seen thatcompared with the more mature circular pipe jacking thedevelopment of rectangular pipe jacking is not yet maturewhich is still a new technology of underground spaceconstruction

From the above research results it can be seen that manyexperts have paid attention to the ground surface settlementof soil mass and rock mass in the process of tunnel con-struction and have obtained abundant research resultsPrevious studies on the soil deformation caused by rect-angular pipe jacking mainly refer to shield construction andcircular section pipe jacking Moreover the surface settle-ment law and prediction of rectangular pipe jacking con-struction caused by soil loss additional stress and frictionforce are rarely reported Because of the great difference ofcross-sectional shape between circular and rectangular pipejacking construction the soil stress variation form andrandom movement mode are quite different In the face ofthe gradual popularization of rectangular pipe jackingtechnology its theoretical research is inevitably greatlydifferent from that of circular pipe jacking and shieldconstruction which puts forward higher requirements forthe study of stratum subsidence caused by rectangular pipejacking

0e rectangular top pipe project of the undergroundconnection passage between Tuodong stadium station online 6 of Kunming metro and Tuodong Dacheng centralbusiness district is located at the intersection of Tuodongroad and east Huancheng road with busy surface trafficand numerous underground pipelines not meeting theconstruction conditions of open excavation Consideringthe complex construction environment comprehensivelythe project plans to adopt the rectangular pipe jackingmachine with multiblade-earth pressure balance for tun-neling construction In this study the influence of soil lossadditional stress on end face and friction force on surfacesettlement during construction was comprehensivelyconsidered 0e surface settlement caused by rectangularpipe jacking was divided into three parts namely thesettlement caused by soil loss the settlement caused byadditional stress on end face and the settlement caused byfriction force 0en based on the basic hypothesis of thesuperposition model Mindlinrsquos elastic theory and randommedium theory were used to solve the surface settlementequation caused by various factors and the superpositionmodel was obtained after the three kinds of settlement wereadded Finally according to the established settlementmodel the empirical method and the measured settlementamount the surface settlement deformation characteristicscaused by the rectangular pipe jacking construction dis-turbance were studied






2i21113888 1113889

Smax Vloss2π

radiciasymp

Vloss

25i

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(1)



ω ω1 + ω2 + ωloss (2)









hle zle h + 2b

x 0

⎧⎪⎨



S L

h

o x

zy



2b2a




ω1 P1x

4πG1113946

a

minusa11139462b

0

1M1


minush + n

M21

1113888 1113889dmdn (3)





z h

⎧⎪⎨



ω21 P2f1

4πG1113946

a

minusa11139460

minusL

x minus l

M2

1 minus 2μM2 + h

minush

M22

1113888 1113889dldm

+αP2f2

4πG1113946

a

minusa1113946

minusL

minusS

x minus l

M2

1 minus 2μM2 + h

minush

M22

1113888 1113889dldm

(4)




ω22 P3f1

4πG1113946

a

minusa11139460

minusL

x minus l

M3


minush + 2b

M23

1113888 1113889dldm

+αP4f2

4πG1113946

a

minusa1113946

minusL

minusS

x minus l

M3


minush + 2b

M23

1113888 1113889dldm

(5)


P3 ch +Tj

2aL

P4 ch +Tg

2as

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)



P5 K1(h + n)c (7)



y a

⎧⎪⎨




ω23 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

(8)



ω24 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

(9)





ωloss 1

r2(z)exp minus

πr2(z)

x2

+ y2

1113872 11138731113890 1113891dξdζdη (10)




So

Δt Aκ

4(a + b) (12)


ωloss BΩ

dζdη1113946minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dξ

(13)


o

z

y

x

dξdζdη w




h+2b+Δt1113946

a+Δt


minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

211139601113896

+(y minus ζ)21113961⎫⎬


h+2b+Δt1113946

a

minusa1113946

minusL

minusS

tan2 βη2

exp


η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dζdηdξ

(14)


ω ω1 + ω21 + ω22 + ω23 + ω24 + ωloss (15)













h

2Δt

LPipeline

Soil loss

dξdη

x

z

o

2b

(a)

h2b

2Δt

Soil loss

dξdη

y

z

o

ΔtΔt

2a

Pipeline

(b)


(1) Subgrade

(2) Mucky clay

(3) Clay stratum


(5) Silty clay

(6) Silty soil


080m

210m

620m

090m

800m

(a)

490

m

690m

045m

(b)

500

m

700m

(c)









Cohesive force(kPa)



Poissonrsquosratio










2

1

0

ndash1

ndash2

ndash3

ndash4

Surfa

ce se

ttlem

ent (

mm

)





6

4

2

0

ndash2

ndash4

Surfa

ce se

ttlem

ent (

mm

)



18

15

12

9

6

3

0

ndash3



Surfa

ce se

ttlem

ent (

mm

)











36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)



Empirical method


30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)




36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)





5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References






































2i21113888 1113889

Smax Vloss2π

radiciasymp

Vloss

25i

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(1)



ω ω1 + ω2 + ωloss (2)









hle zle h + 2b

x 0

⎧⎪⎨



S L

h

o x

zy



2b2a




ω1 P1x

4πG1113946

a

minusa11139462b

0

1M1


minush + n

M21

1113888 1113889dmdn (3)





z h

⎧⎪⎨



ω21 P2f1

4πG1113946

a

minusa11139460

minusL

x minus l

M2

1 minus 2μM2 + h

minush

M22

1113888 1113889dldm

+αP2f2

4πG1113946

a

minusa1113946

minusL

minusS

x minus l

M2

1 minus 2μM2 + h

minush

M22

1113888 1113889dldm

(4)




ω22 P3f1

4πG1113946

a

minusa11139460

minusL

x minus l

M3


minush + 2b

M23

1113888 1113889dldm

+αP4f2

4πG1113946

a

minusa1113946

minusL

minusS

x minus l

M3


minush + 2b

M23

1113888 1113889dldm

(5)


P3 ch +Tj

2aL

P4 ch +Tg

2as

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)



P5 K1(h + n)c (7)



y a

⎧⎪⎨




ω23 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

(8)



ω24 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

(9)





ωloss 1

r2(z)exp minus

πr2(z)

x2

+ y2

1113872 11138731113890 1113891dξdζdη (10)




So

Δt Aκ

4(a + b) (12)


ωloss BΩ

dζdη1113946minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dξ

(13)


o

z

y

x

dξdζdη w




h+2b+Δt1113946

a+Δt


minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

211139601113896

+(y minus ζ)21113961⎫⎬


h+2b+Δt1113946

a

minusa1113946

minusL

minusS

tan2 βη2

exp


η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dζdηdξ

(14)


ω ω1 + ω21 + ω22 + ω23 + ω24 + ωloss (15)













h

2Δt

LPipeline

Soil loss

dξdη

x

z

o

2b

(a)

h2b

2Δt

Soil loss

dξdη

y

z

o

ΔtΔt

2a

Pipeline

(b)


(1) Subgrade

(2) Mucky clay

(3) Clay stratum


(5) Silty clay

(6) Silty soil


080m

210m

620m

090m

800m

(a)

490

m

690m

045m

(b)

500

m

700m

(c)









Cohesive force(kPa)



Poissonrsquosratio










2

1

0

ndash1

ndash2

ndash3

ndash4

Surfa

ce se

ttlem

ent (

mm

)





6

4

2

0

ndash2

ndash4

Surfa

ce se

ttlem

ent (

mm

)



18

15

12

9

6

3

0

ndash3



Surfa

ce se

ttlem

ent (

mm

)











36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)



Empirical method


30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)




36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)





5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References



































ω1 P1x

4πG1113946

a

minusa11139462b

0

1M1


minush + n

M21

1113888 1113889dmdn (3)





z h

⎧⎪⎨



ω21 P2f1

4πG1113946

a

minusa11139460

minusL

x minus l

M2

1 minus 2μM2 + h

minush

M22

1113888 1113889dldm

+αP2f2

4πG1113946

a

minusa1113946

minusL

minusS

x minus l

M2

1 minus 2μM2 + h

minush

M22

1113888 1113889dldm

(4)




ω22 P3f1

4πG1113946

a

minusa11139460

minusL

x minus l

M3


minush + 2b

M23

1113888 1113889dldm

+αP4f2

4πG1113946

a

minusa1113946

minusL

minusS

x minus l

M3


minush + 2b

M23

1113888 1113889dldm

(5)


P3 ch +Tj

2aL

P4 ch +Tg

2as

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(6)



P5 K1(h + n)c (7)



y a

⎧⎪⎨




ω23 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

(8)



ω24 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

(9)





ωloss 1

r2(z)exp minus

πr2(z)

x2

+ y2

1113872 11138731113890 1113891dξdζdη (10)




So

Δt Aκ

4(a + b) (12)


ωloss BΩ

dζdη1113946minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dξ

(13)


o

z

y

x

dξdζdη w




h+2b+Δt1113946

a+Δt


minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

211139601113896

+(y minus ζ)21113961⎫⎬


h+2b+Δt1113946

a

minusa1113946

minusL

minusS

tan2 βη2

exp


η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dζdηdξ

(14)


ω ω1 + ω21 + ω22 + ω23 + ω24 + ωloss (15)













h

2Δt

LPipeline

Soil loss

dξdη

x

z

o

2b

(a)

h2b

2Δt

Soil loss

dξdη

y

z

o

ΔtΔt

2a

Pipeline

(b)


(1) Subgrade

(2) Mucky clay

(3) Clay stratum


(5) Silty clay

(6) Silty soil


080m

210m

620m

090m

800m

(a)

490

m

690m

045m

(b)

500

m

700m

(c)









Cohesive force(kPa)



Poissonrsquosratio










2

1

0

ndash1

ndash2

ndash3

ndash4

Surfa

ce se

ttlem

ent (

mm

)





6

4

2

0

ndash2

ndash4

Surfa

ce se

ttlem

ent (

mm

)



18

15

12

9

6

3

0

ndash3



Surfa

ce se

ttlem

ent (

mm

)











36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)



Empirical method


30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)




36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)





5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References



































ω23 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M4


minush + n

M24

1113888 1113889dldn

(8)



ω24 f1

4πG11139462b

011139460

minusL

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

+αf2

4πG11139462b

01113946

minusL

minusS

P5(x minus l)

M5


minush + n

M25

1113888 1113889dldn

(9)





ωloss 1

r2(z)exp minus

πr2(z)

x2

+ y2

1113872 11138731113890 1113891dξdζdη (10)




So

Δt Aκ

4(a + b) (12)


ωloss BΩ

dζdη1113946minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dξ

(13)


o

z

y

x

dξdζdη w




h+2b+Δt1113946

a+Δt


minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

211139601113896

+(y minus ζ)21113961⎫⎬


h+2b+Δt1113946

a

minusa1113946

minusL

minusS

tan2 βη2

exp


η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dζdηdξ

(14)


ω ω1 + ω21 + ω22 + ω23 + ω24 + ωloss (15)













h

2Δt

LPipeline

Soil loss

dξdη

x

z

o

2b

(a)

h2b

2Δt

Soil loss

dξdη

y

z

o

ΔtΔt

2a

Pipeline

(b)


(1) Subgrade

(2) Mucky clay

(3) Clay stratum


(5) Silty clay

(6) Silty soil


080m

210m

620m

090m

800m

(a)

490

m

690m

045m

(b)

500

m

700m

(c)









Cohesive force(kPa)



Poissonrsquosratio










2

1

0

ndash1

ndash2

ndash3

ndash4

Surfa

ce se

ttlem

ent (

mm

)





6

4

2

0

ndash2

ndash4

Surfa

ce se

ttlem

ent (

mm

)



18

15

12

9

6

3

0

ndash3



Surfa

ce se

ttlem

ent (

mm

)











36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)



Empirical method


30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)




36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)





5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References



































h+2b+Δt1113946

a+Δt


minusL

minusS

tan2 βη2

exp minusπ tan2 β

η2(x minus ξ)

211139601113896

+(y minus ζ)21113961⎫⎬


h+2b+Δt1113946

a

minusa1113946

minusL

minusS

tan2 βη2

exp


η2(x minus ξ)

2+(y minus ζ)

21113960 11139611113896 1113897dζdηdξ

(14)


ω ω1 + ω21 + ω22 + ω23 + ω24 + ωloss (15)













h

2Δt

LPipeline

Soil loss

dξdη

x

z

o

2b

(a)

h2b

2Δt

Soil loss

dξdη

y

z

o

ΔtΔt

2a

Pipeline

(b)


(1) Subgrade

(2) Mucky clay

(3) Clay stratum


(5) Silty clay

(6) Silty soil


080m

210m

620m

090m

800m

(a)

490

m

690m

045m

(b)

500

m

700m

(c)









Cohesive force(kPa)



Poissonrsquosratio










2

1

0

ndash1

ndash2

ndash3

ndash4

Surfa

ce se

ttlem

ent (

mm

)





6

4

2

0

ndash2

ndash4

Surfa

ce se

ttlem

ent (

mm

)



18

15

12

9

6

3

0

ndash3



Surfa

ce se

ttlem

ent (

mm

)











36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)



Empirical method


30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)




36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)





5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References




































h

2Δt

LPipeline

Soil loss

dξdη

x

z

o

2b

(a)

h2b

2Δt

Soil loss

dξdη

y

z

o

ΔtΔt

2a

Pipeline

(b)


(1) Subgrade

(2) Mucky clay

(3) Clay stratum


(5) Silty clay

(6) Silty soil


080m

210m

620m

090m

800m

(a)

490

m

690m

045m

(b)

500

m

700m

(c)









Cohesive force(kPa)



Poissonrsquosratio










2

1

0

ndash1

ndash2

ndash3

ndash4

Surfa

ce se

ttlem

ent (

mm

)





6

4

2

0

ndash2

ndash4

Surfa

ce se

ttlem

ent (

mm

)



18

15

12

9

6

3

0

ndash3



Surfa

ce se

ttlem

ent (

mm

)











36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)



Empirical method


30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)




36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)





5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References








































Cohesive force(kPa)



Poissonrsquosratio










2

1

0

ndash1

ndash2

ndash3

ndash4

Surfa

ce se

ttlem

ent (

mm

)





6

4

2

0

ndash2

ndash4

Surfa

ce se

ttlem

ent (

mm

)



18

15

12

9

6

3

0

ndash3



Surfa

ce se

ttlem

ent (

mm

)











36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)



Empirical method


30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)




36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)





5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References









































36

30

24

18

12

6

0

ndash6Su

rface

settl

emen

t (m

m)



Empirical method


30

25

20

15

10

5

0

ndash5

ndash10

Surfa

ce se

ttlem

ent (

mm

)




36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)



Empirical method


42

36

30

24

18

12

6

0

ndash6

Surfa

ce se

ttlem

ent (

mm

)





5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References



































5 Conclusion






Data Availability




Acknowledgments


Empirical method


6

5

4

3

2

1

0

ndash1

ndash2

ndash3Su

rface

settl

emen

t (m

m)



30

ndash5

0

5

10

15

20

20

20

15

15

10

10

5

5

0

0

ndash5

ndash5

ndash10

ndash10

ndash15

ndash15ndash20

ndash20ndash25

25

Surfa

ce se

ttlem

ent (

mm

)

ndash5200

ndash1410

2380

6170

9960

1375

1754

2133

2512

2891

3270

Longitudinal x (m)

Literal y (m)



References


































References


































a new method for predicting ground settlement induced by

Documents