effect of subway excavation with different support

Research ArticleEffect of Subway Excavation with Different Support Pressures onExisting Utility Tunnel in Xirsquoan Loess

Min Yang Hongru Li Ning Li and Shun Yang

Institute of Geotechnical Engineering Xirsquoan University of Technology Xirsquoan China

Correspondence should be addressed to Hongru Li lhrbjxauteducn

Received 2 June 2020 Revised 27 July 2020 Accepted 8 September 2020 Published 21 September 2020

Academic Editor Tayfun Dede

Copyright copy 2020 Min Yang 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

e interaction between two shield tunnels and the integrated pipe corridor is complicated and still lacks understanding ispaper investigated the influence of the double-track subway construction on the deformation characteristics of the existingcomprehensive pipe corridor based on numerical simulation on a case history in Xirsquoan China First loess is a special kind of clayedsoil In the theoretical calculation of overburden earth pressure of shield tunnel the loose earth pressure theory under theincomplete soil arching effect can be used for calculation when considering the soil arching effect en in the loess area of Xirsquoanthe existing comprehensive pipe corridor is affected by the construction disturbancee vertical displacement of the existing pipecorridor utility tunnel affected by different support pressures which considers the soil arch effect or not was extracted from theFEM e results indicated that in the case where the left and right lines are constructed at different times the vertical dis-placement of the pipe gallery is affected by different support pressures If the support pressure is small the settlement will be largeand the uplift will be diminutive According to the construction methods and supporting pressures of this article shield tunnelconstruction will not damage the safety of the comprehensive pipe corridor

1 Introduction

In urban areas a utility tunnel is a kind of undergroundstructure to transport water sewage oil natural gas andother materials Utility tunnels have been widely con-structed throughout the world after the first one wasconstructed in Paris in 1851 Nowadays the domestic andforeign countries are in the period of high-speed devel-opment of underground space e increasingly densesubway lines pipelines underground lane lines and so onwill restrict each other [1ndash3] How to reduce the influencebetween the lines will be a big problem to be solved ur-gently in the construction of underground buildings in thefuture

erefore it is encountered under the existing com-prehensive pipe corridor in the process of using the shieldmethod in the construction of subway tunnels In additionshield tunneling is often carried out in soft soil Once the soilis disturbed it is particularly easy to cause surface settlementand deformation of surrounding soil layers and upper

pipelines [4ndash6] is will greatly affect the stability of theexisting comprehensive pipe gallery

At present amount of work has been carried out at homeand abroad on the simulation research of the three-di-mensional dynamic construction process of shield tunnelsA large number of studies have been conducted to inves-tigate the impact of undercrossing shield tunneling on theexisting tunnels [7ndash11] And shield construction affects theinternal force and deformation of adjacent buildings [12 13]

However the numerical simulation of the influence ofshield tunnel three-dimensional dynamic constructionprocess on the comprehensive pipe gallery is relatively rareAn increasing number of studies have been conducted ontunnel-pipe interaction most of which chose to simplifytunnel-pipe interaction as a two-dimensional problemese include several analytical solutions [14ndash18] Wanget al [19] developed a Winkler-based pipe-soil-tunnelinginteraction model which is focused on different pipe-soilinteractions in relative uplift and downward pipe move-ments In Lin et alrsquos study [20] analytical solutions

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8818949 14 pageshttpsdoiorg10115520208818949

incorporating the tensionless Pasternak model which takesfull account of the gap formation and the pipeline orien-tation have been formulated to estimate the response of thepipeline and the overlying ground Since all these previousstudies reduced the interaction of the tunnel and the pipelineto a two-dimensional problem these three problems cannotbe determined

erefore it is particularly important to use numericalmethods to simulate the impact of shield tunnel construc-tion on the comprehensive pipe corridor and the con-struction of the comprehensive pipe corridor has a long-term development plan in China Based on the Xirsquoan subwayshield tunnel passing through the existing comprehensivepipe corridor this article will establish a numerical model tosimulate the construction process of the subway shieldtunnel passing through the existing comprehensive pipecorridor e construction method of ldquoline re-excavationrdquoanalyzes the influence of the shield tunneling on the de-formation of the existing comprehensive pipe corridorunder the conditions of considering the soil arch effect andthe supporting pressure without considering the soil archeffect

2 Related Theory of Shield Support Pressure

21 eory of Terzaghi Loose Soil Pressure Based on theassumption that the sliding surface is vertical Terzaghideduced that the loose earth pressure formula is widely used[21]

σv cB minus c

K tanφ1 minus e

((minusKH tanφ)B)1113872 1113873 + qe

((minusKH tanφ)B)

B R cotπ8

+φ4

1113874 1113875

(1)

whereK is the pressure coefficient of the soil side the value isbetween 10 and 15 it is recommended to take 10 H is theheight of the overlying soil q is the upper load R is thetunnel radius B is the span of the cavern φ is internalfriction angle of soil c is cohesion of soil and c is unitweight

22 Loose Earth Pressure eory under the Incomplete SoilArching Effect In the Terzaghi loose earth pressure theorythe selection of the lateral pressure coefficient of the soil isrecommended to be 10 e selection of this value being thebest one is arguable Handy [22] analyzed the insufficiency ofthe pressure arch model and derived the coefficient ofconfinement pressure of the soil based on Mohrrsquos circle ofstress

Since the shield driving method can better control theformation damage it can be considered that the soil archingeffect is not as assumed in the Terzaghi loose earth pressureat is the soil arch is an incomplete soil arch and thearching effect is not fully exerted Based on Handyrsquos theoryLi [23] puts out the side compression of soil considering theincomplete arch effect Sketch of partially developed soilarching effect is shown in Figure 1

Calculation formula for loose earth pressure under in-complete soil arching effect is as follows

σv B1c

A11 minus e

minus A1hB1( )1113874 1113875 + qeminus A1hB1( ) (2)

A1 K 1 minus Ka( 1113857tan θ1 + Katan

2 θ (3)

K 1 + Katan

2 θtan2 θ + Ka

(4)

For clayed soil the active earth pressure coefficientshould take cohesion into account in the soil lateral pressurecoefficient formula According to Rankine earth pressuretheory the active earth pressure coefficient Ka of clayed soilis

Ka tan2 45∘ minusφ2

1113874 1113875 minus2c

chtan 45∘ minus

φ2

1113874 1113875 (5)

erefore when calculating the loosening earth pressureunder the incomplete soil arch effect of cohesive soil for-mula (6) can be substituted into formula (4) and formula (5)for calculation It obtains the calculation formula of looseearth pressure under the incomplete soil arch effect con-sidering cohesion as follows

σv B1c minus c

A11 minus e

minusA1hB1( )1113874 1113875 + qeminusA1hB1( ) (6)

In a certain case of Ka A1 and K are determined by θthe greater the rate of ground loss the larger the deflectionangle of the maximum principal stress resulting in thesmaller the θ erefore θ depends on the formation lossrate and B1 is the width of loose bandat is displacementof the vault is

tan θ B1

2sminus

s

2B1 (7)

where s is the formation loss parameter that is the dis-placement of the arch surface of the excavation face

23 Comparative Analysis of Earth Pressure at Tunnel TopIn the theory of loose earth pressure under the incompletesoil arching effect considering cohesion the formation lossparameter is required is parameter can be calculated bythe equivalent formation loss formula proposed by Loga-nathan and Poulos [24]

ε0 4sR + s

2

4R2 times 100 (8)

where ε0 is the formation loss rate R is the tunnel radius ands is the gap parameter which is also the vault sedimentation

According to formula (8) transformation

s 2R1 + ε0

1113968minus 1( 1113857 (9)

erefore combined with the corresponding parame-ters different loose soil pressure values can be calculated

2 Advances in Civil Engineering

under the incomplete soil arching effect consideringcohesion

e stratum parameters of a section of Xirsquoan Metro areshown in Table 1e overlying soil thickness of the tunnel is180 and the tunnel radius is 307

According to the empirical data the literature [25]concluded that the formation loss rate of the clay formationis about 05sim25 By formula (6) the corresponding loosesoil pressure value can be obtained under the incomplete soilarching effect considering the cohesion Here for the sake ofconvenience the pressure ratio concept is applied in thispaper e pressure ratio is the ratio of the loose earthpressure σi to the full earth pressure σv at the soil

η σi

σv

(10)

e pressure ratio of the earth pressure considering thecohesion of the section tunnel condition (ηp) is comparedwith the pressure ratio of the Terzaghi loose earth pressure(ηT) as shown in Figure 2

Figure 2 shows that the law of different earth pressurescan be obtained

(1) Because the theory of loose earth pressure under theincomplete soil arching effect considering cohesiontakes into account the rate of ground loss there is acorresponding earth pressure value for differentground loss ratios However the ground loss ratio isnot considered in the calculation of full overburdenpressure and Terzaghi loose earth pressure and thecalculated earth pressure value is constant at a fixeddepth and the hole diameter

(2) Due to the soil arch effect the theory of loose earthpressure under the incomplete soil arching effectconsidering cohesion and Terzaghi earth pressure aresmaller than the full earth pressure When theground loss ratio is less the earth pressure is not lessdifferent in value

(3) When the ground loss ratio is less than 065 thetheory of loose earth pressure under the incompletesoil arching effect considering cohesion is larger thanthe Terzaghi earth pressure due to the less principalstress deflection angle In the case where the groundloss ratio is greater than 065 the soil arch effect ismore obvious as the formation loss rate is larger andthe value of the theory of loose earth pressure underthe incomplete soil arching effect considering co-hesion is gradually reduced Terzaghi earth pressurehas not considered the formation loss so the soilarching effect has always been a fixed value atshows the rationality of the earth pressure methodproposed by the authorat is the greater the loss ofthe formation the more obvious the soil archingeffect

3 Project Overview

e project studied herein is located in Metro Line 2 (ML2in operation) in Xirsquoan City China ML2 consisted of twinsingle tube tunnels constructed by using the shield-drivenmethod e support method is prefabricated C50 rein-forced concrete segments which are connected by usingbent bolts e outer diameter of segments is 60m the ring

σhα

σv

τ

σ3

σ3

σh

τ

σ1

σ

σh

σ1

σv

θ

σ3

φ0

τ

σ1

σv

Figure 1 Sketch of partially developed soil arching effect

Table 1 Soil basic physical property index

Soil layer c (kNm3) c (kPa) φ (deg) Layer (m)Soil 1 17 25 17 3Soil 2 183 35 20 4Soil 3 189 50 18 3Soil 4 201 45 20 20

0626

0628

063

0632

0634

0636

0638

064

0642

0 05 1 15 2 25 3

Pres

sure

ratio

Rate of ground loss ()

The earth pressure considering the cohesionof the section tunnel conditionThe Terzaghi loose earth pressure

Figure 2 e pressure ratio in different strata loss rate

Advances in Civil Engineering 3

width is 15m and the thickness is generally 300mm eburied depth of the tunnel is generally between 80m and250m and the tunnel spacing is generally between 9m and20m except for the key protection of ancient buildingsaround the construction section

In this paper combined with a comprehensive pipegallery project in Xirsquoan City the subway tunnel is planned tobe built under the comprehensive pipe gallery e subwayaxis is parallel to the pipe gallery axise relative position ofa cross section tunnel and the pipe gallery is shown inFigure 3

e cross section of the comprehensive pipe gallery projectis in the form of three tanks including natural gas tankcomprehensive tank and power tank e buried depth of thepipe gallery is 3m e pipe gallery structure is made of C35concrete and its specific dimensions are shown in Figure 4

Considering the economy the construction method ofthe utility tunnel adopts the cut-and-cover method ereinforcement form adopts sloping and soil nailing wall eslope is 1 075 e excavation method adopts layered ex-cavatione excavation depth of each layer does not exceed15m and 20m After the excavation shotcrete with mesh ofC20 concrete is applied in time and then soil nails are ap-plied e soil nails are made of HRB400 steel bars with adiameter of 14mm a vertical spacing of 15m and a verticalspacing of 10me thickness of sprayed concrete is 60mmWhen the excavation is 30 cm from the bottom of the pitmanual excavation shall be adopted e bedding con-struction shall be completed within 24 hours of bottoming tominimize the exposure time of the soil at the bottom of thepit e cushion thickness of 10m shall be poured with C15concrete Since the left and right support and treatment ofthe utility tunnel are the same only the right half of theutility tunnel is shown in Figure 5

4 Three-Dimensional Numerical Model

41 Numerical Scheme Since the theory of loose earthpressure under the incomplete soil arching effect consid-ering cohesion is improved on the basis of Terzaghirsquos theoryon loosening earth pressure it is used as the calculation basisfor considering the soil arch effect

e supporting pressure is calculated by using thestandard method [26] e overburden pressure (σv) iscalculated by the all-covering theory (without soil arch) andthe theory of loose earth pressure under the incomplete soilarching effect considering cohesion (with soil arch) edistribution of support pressure is trapezoidal in Figure 6

e supporting pressure on the edge of the tunnel is

σT kσv + p0 (11)

e supporting pressure at the lower edge of the tunnel is

σT k σv + Dc( 1113857 + p0 (12)

where k is the experienced coefficient and in this article 072is taken as the value of k the average from 065 to 085 [27]p0 is the preloading generally 20sim30kPa and in this paper20 kPa is taken as the value of p0 D is the diameter c is the

soil volume weight behind heading face σv is the overburdensoil pressure of the tunnel

e overburden pressure is carried out according todifferent calculation theories e soil pressure of the theoryof loose earth pressure under the incomplete soil archingeffect considering cohesion is calculated according to therate of ground loss of 05e calculation results are shownin Table 2

In this paper synchronous injection of inert groutingpressure simplifies the form of a uniform distribution of theentire ring e tunnel radial outward uniform load is ap-plied to the contact surface of the surrounding rock and thegrouting layer and the radial surface is applied to the outersurface of the segment as shown in Figure 7

is paper selects the optimal grouting pressure methodAt the same time the safety factor only considers the activeearth pressure and the passive earth pressures [28] ecalculated optimal grouting pressure is 332069 kPa

42 FEM A three-dimensional finite element model usingthe commercial software Abaqus and Hyperworks wasestablished to investigate the utility tunnels deformation dueto the construction of twin shield tunnels underneathFigure 8 shows the finite element mesh used in this studywhich was 120m in length 90m in width and 50m in depthFigure 9 gives details on the simulation of utility tunnels overnew tunnels Tunnel depth is 18m Tunnel clear distance is18m e shield tunneling diameter is 614m Tunnel seg-ment thickness is 03m e outer diameter of tunnelsegment is 60m

According to the actual geological conditions of Xirsquoan inChina the soil layer is divided into 5 layers the backfillingsoil layer of pipe gallery is① and the stratum is②sim⑤ fromtop to bottom

e soil layer backfill and cushion are made of C3D8solid element e tube piece adopts S4 shell unit e shieldmachine casing adopts S4R shell unit e grouting layersoil nail wall surface layer and pipe trunk main structureadopt C3D8I solid element e soil nail is made of T3D2rod unit and embedded in the soil and by the ldquoembededrdquocommand ere are 112280 physical units in the wholemodel with a total of 8640 shell units and 3560 rod unitstotaling 124520 units and 137358 nodes Besides soil nailsthe rest of the structure is treated with ldquoTierdquo e dis-placement boundary conditions permitted were no hori-zontal displacement down the all vertical mesh boundariesno vertical and horizontal displacement along the bottomboundary of the mesh and freedom to displace along the topboundary

43 Material Model and Parameters In the analysis of soilsimulation the compression modulus is selected for the one-dimensional consolidation problem for the deformationproblem the deformation modulus can be selected [29] Sofor this model the deformation modulus is selected as one ofthe soil parameters and the calculation parameters of themodel for selecting a section are shown in Table 3 Amongthem① represents 1-1 artificial fill② represents 1-2 plain


fill ③ represents 3-1-3 new loess ④ represents 3-2-2paleosol and ⑤ represents 4-4 silty clay e soil consti-tutive model is selected as follows① and② are linear D-P③ ④ and ⑤ are adopted MCC

e segment of the shield-driven tunnel is C50 rein-forced concrete material Considering the stiffness reduc-tionrsquos effect of the spliced segments the modulus of elasticityof the segment is reduced by 20e elastic modulus of thegrouting slurry is corresponding according to the earlystrength and the late strength taking the value [29ndash31]

Considering the weight of the entire shield machine theweight of the shield shell is correspondingly increased in themodel and the structure is simplified to the elastic modele specific parameters are shown according to the ldquoCodefor Design of Concrete Structuresrdquo [32] and the ldquoCode forDesign of Railway Tunnelsrdquo [33] in Table 4

e soil nail wall modulus of the utility tunnel uses theweighting method and the corresponding structures ofwhich are simplified to the elastic model e parameters areselected in accordance with the ldquoConcrete Structure Design

3510

7

Existingutilitytunnel

Shield tunneling

3

18

Existing ground

Shield tunneling

Soil nail

1

Artificial fill

18

Soil nail

3

Cushion

66

35

Figure 3 Sketch of relative position of the utility tunnel and metro tunnel (unit m)

Earth

Natural gas tank Comprehensive tank Power tank

23003300

9000 100

300 300350 3502100

3000

3300

2600

350

350

100

Figure 4 Standard cross-sectional profile of utility tunnel (unit mm)


500

Surface thick

107

5

1500

1000

Existing ground

1500

Soil nail

Land drainFriction pin

1000

1500

1500

7300

Powertank

Drainage ditch

Figure 5 Schematic diagram of the right half of the foundation pit of the pipe gallery (unit mm)

H

D σT

Existing ground

Figure 6 Sketch of support pressure

Table 2 Calculation table of support pressure

Condition Calculation method Overburden pressureσv (kPa)

Top edge supportforce σtop (kPa)

Lower edge supportforce σbot (kPa)

1 All-covering theory 341700 266024 354882

2 e theory of loose earth pressure under theincomplete soil arching effect considering cohesion 218724 177481 266339

Tunnel segment

Grouting pressure

(a)

Surrounding rock

Groutingpressure

(b)

Figure 7 Sketch of synchronous grouting (a) Segment grouting pressure diagram (b) Schematic diagram of grouting pressure around thecave


Coderdquo [32] and the ldquoBuilding Foundation Design Coderdquo[34] e parameters are shown in Table 5

44 Numerical Simulation Process e simulation processwas divided into two stages (i) excavation of the existingutility tunnel and (ii) the shield tunneling under the utilitytunnel is paper focuses on the selection of the secondstage After completion of the first stage the displacement ofthe soils and structures was reset to zero erefore thecalculated uplift values were actually the incremental de-formation because of new tunnel excavation

441 Construction Course Simulation of the Utility TunnelFor the excavation of the utility tunnel according to theprinciple of no more than 15m and 20m for each exca-vation and 300mm from the bottom of the pit the exca-vation depth of the foundation pit is arranged as follows

It is divided into 5 excavations the first and secondexcavation depths are 20m the third and fourth excavationdepths are 15m and the fifth excavation depth is 03m

In addition after the excavation shotcrete with mesh isapplied in time and then soil nails are applied e soil nailsare made of HRB400 steel bars with a diameter of 14mm avertical spacing of 15m and a vertical spacing of 10mebedding construction shall be completed immediately afterbottoming to minimize the exposure time of the soil at thebottom of the pit erefore the fifth excavation is alsobedding construction Because it is a simulation of the fillingduring the construction period the filling process is dividedinto two simulations here e specific construction processis as follows

Step 1 the gravity field is applied to perform the in situground stress balance and the displacement incrementis controlled to be on the order of eminus 4 degree eprinciple of this step is nonlinear iteration Iterationmay be used to ensure that equilibrium is achieved ateach step of the analysis to within a specified con-vergence tolerance rough repeated iterations tocorrect the solution results until convergence it has abetter convergence effect e iterative method inAbaqus uses the tangent stiffness iteration method e

Tunneling direction

Subway le

yz

x

Subway right

Utility tunnel

120m90m

50m

2345

1

Figure 8 Numerical model of engineering

Surface layer

Soil nailCushion

yz

x

Utility tunnel

Figure 9 Structures of the foundation pit of the utility tunnel


Soil layer c (kNm3) E0 (MPa) ] β d λ κ e0 M

① 1-1 artificial fill 181 43 028 2024 3099 mdash mdash mdash mdash② 1-2 plain fill 17 4 033 3294 6757 mdash mdash mdash mdash③ 3-1-3 new loess 183 6 033 mdash mdash 010206 000912 0866 077④ 3-2-2 paleosol 189 8 031 mdash mdash 007687 000782 0756 069⑤ 4-4 silty clay 201 13 03 mdash mdash 006514 000782 064 077


tangent stiffness iterative method is a variable stiffnessiterative method which uses changing tangent stiffnessto continuously modify the iterative resultis methodis also called the NewtonndashRaphson method which hashigh iteration accuracyStep 2 for the first excavation it uses the ldquoModelChangerdquo command that comes with ABAQUS to in-validate excavation soil (within 20m depth) and ac-tivates soil nails and surface units within 20m depthStep 3 the second third and fourth excavations areconsistent with what was done in Step 2Step 4 in the fifth excavation it uses the ldquoModelChangerdquo command that comes with ABAQUS to in-validate the fifth layer (03m thick) of soil and activatesthe surface layer and cushion unitStep 5 it constructs the pipe gallery and then activatesthe pipe gallery unitStep 6 for the first backfill filling at the same elevationat the top of the pipe gallery will activate the backfill soilunit in the corresponding rangeStep 7 for the second backfill it fills back to the designheight (the surface) and activates the backfill soil withinthe corresponding range

442 Construction Course Simulation of the Shield-DrivenTunnel e length of the TBM shield machine is set to be9m which is equal to the width of 6 rings In the first stageelaborate simulation of the shield tunneling process wasconducted and the simulation steps are as follows (thedrifting footage is 15m which is equal to width of 1 ring)

Step 1 the gravity field is applied to perform the in situground stress balance and the displacement incrementis controlled to be on the order of eminus 4 degreeStep 2 using the ldquoModel Changerdquo command that comeswith ABAQUS to invalidate excavation soil of the lefttunnel (LT) the construction advances the first ring Atthe same time the pressure acting is applied on the

tunnel face top to activate the first ring of the shieldshellStep 3 the second step is to be recycled until the 7thring is excavated At the same time as the failuretreatment of the excavated soil the tail unit of the shieldmachine casing is also failed At this time it keeps thelength of the shield machine unchanged (6 rings) andactivates segment unit of the LT and the jet groutingunit at which time the strength of the jet grouting is theearly strength and the grouting pressure is appliedStep 4 the second and third steps are to be recycleduntil the 13th ring is excavated At this time on thebasis of the first two steps the grouting pressure at thetail of the segment is invalidated and the strength of thejet grouting is adjusted to the late strengthStep 5 the third and fourth steps are to be recycled Itkeeps the length of the shield shell of the shieldmachineto 6 rings (the length of the shield machine) e jetgrouting range is within the 6-ring piece until thetunneling of the shield machine is completedStep 6 the construction process of the right tunnel (RT)can be repeated in the above Steps 2 and 5

45 Arrangement ofMonitoring Points and Time of the UtilityTunnel e monitoring lines are arranged inside the threecabins of the utility tunnel Here for the convenience ofdescription the natural gas tank is briefly described as theleft cabin (LC) the comprehensive tank is briefly describedas the middle cabin (MC) and the power tank is brieflydescribed as the right cabin (RC) Along the pipe gallery axismonitoring lines are arranged on the roof and floor of thethree cabins namely the LC floor survey line LBC-1 the LCroof survey line LCT-4 the MC floor survey line MCB-2 theMC roof survey line MCT-5 the RC floor line RCB-3 andthe RC roof line RCT-6

Since the model is symmetrical in the longitudinal di-rection the middle section of the pipe gallery is selected asthe monitoring section at is the position correspondingto the 30th ring (at 45m) of the tunnel segment emonitoring lines are set on the top and bottom sections ofthe section as R30-7 and R30-8 e specific layout diagramis shown in Figure 10

In addition monitoring points are laid at themidpoint ofeach cabin of the monitoring section of the pipe gallery asshown in Figure 11 e midpoint of the midcabin hererefers to the point where the midpoint between the twotunnels is projected to the pipe gallery

It selects the typical monitoring time as the left lineadvances to 15th 30th and 45th rings and the right lineadvances to 15th 30th and 45th rings at is the headingface of the shield machine reaches 15 rings in front of themonitoring sections directly below the monitoring sectionand 15 rings away from the monitoring section e relativepositional relationship between the shield machine and thepipe gallery at the time of monitoring is shown in Figure 12

Table 5 Parameters of structures of the utility tunnel

Subject c (kNm3) E (MPa) ]Soil-nailed wall 22 218E+ 04 02Soil nailing 785 200E+ 05 03Cushion 23 260E+ 04 02Corridor 25 315E+ 04 02

Table 4 Parameters of structures of metro tunnel

Subject c (kNm3) E (MPa) ] Layer (m)Shield 46384 210E+ 05 030 004Segment 25 284E+ 04 020 03Grouting (early) 23 09 030 mdashGrouting (late) 23 400 02 mdashldquomdashrdquo means that the grouting layer completely fills the gap at the shield tailwithout a fixed thickness


5 Deformation Behaviors of the ExistingUtility Tunnel

e urban underground common trench is a shelter formultiple underground pipelines and its deformation controlstandards should be stricter than the general pipelineHowever at this stage the relevant regulations for the utilitytunnel in China are not yet complete e relevant defor-mation standard of the underground pipeline of degree 1level of magnitude of pipelines is the benchmark that is themaximum settlement value is minus10mm In addition for theuplifting this article is selected according to the subwaycontrol standards that is the maximum value of theuplifting is 5mm

51 Analysis of Vertical Displacement of Pipe GalleryCross-Sectional Monitoring Point During the whole shieldtunnel construction process the vertical displacement of themonitoring points arranged on the monitoring section isshown in Figure 13

It can be observed in Figure 13 that the displacement lawof the top and bottom plate measuring points is the same andthe displacement law of the monitoring points on both sidesof the pipe gallery partition wall is similar From the set-tlement value of each measuring point the final settlementof R30-LL-4 is the largest at minus318mm and the settlement ofR30-RR-10 is the smallest at minus174mm At the same time itcan be found that the closer the monitoring point to the

construction side the earlier the settlement occurs After thecompletion of the construction the vertical displacement ofeach measurement point is shown as a settlement

According to the curve in the figure it can be found thatwith the midcabin monitoring point (R30-MT-5 and R30-MB-7) as the center of symmetry the displacement laws ofthe monitoring points on the left and right sides are dif-ferent To simplify the difficulty of analysis only two typicalpoints were selected for analysis which were R30-LL-4 nearthe left line and R30-RR-10 near the right line

During the construction on the left line during the firstfew rounds of construction the uplift phenomenon wouldappear at both measuring pointse uplift value of R30-LL-4 was relatively small while that of R30-RR-10 was relativelylarge With the advancement of the shield machine it can befound that the vertical displacement curves of the twomeasuring points are differente performance is that R30-LL-4 begins to sink and the uplift value of R30-RR-10gradually increases e peak of the uplift was 038mmduring the excavation of the 19th ring (the first uplift) Afterthe 19th ring R30-RR-10 began to appear to settle At thistime R30-LL-4 still maintained the trend of settlement untilthe construction of the 41st ring e settlement of R30-RR-10 reached a peak of 022mm After the 41st ring R30-LL-4still maintained the trend of subsidence and R30-RR-10bulged again (the second bulge) After the completion of theconstruction of ring 60 the uplift stopped e settlement ofR30-LL-4 reached the peak value of minus383mm and the peakvalue of the second uplift of R30-RR-10 was 06mm In the

MCT-5R30-7

LCT-4

LCB-1 R30-8RCT-6

RCB-3MCB-2xy

z

Figure 10 Monitoring line arrangement in the utility tunnel

R30-LT-1

R30-LL-4

R30-LB-3

R30-LR-2

R30-MT-5

R30-ML-8

R30-MB-7

R30-MR-6

R30-RT-9

R30-RL-12

R30-RR-10

R30-RB-11

Figure 11 Monitoring points arrangement on cross section of the utility tunnel


subsequent construction progress the two monitoringpoints remained relatively stable until the construction ofthe left line was completed

During the excavation of the right line the two mea-suring points will be uplifted during the first few loops ofconstruction For now the measuring point R30-RR-10becomes the point near the construction side and themeasuring point R30-LL-4 becomes a point far away fromthe construction side e measurement point R30-RR-10will maintain settlement while the measurement point R30-LL-4 is the phenomenon of R30-RR-10 during the con-struction of the left line Due to the secondary constructiondisturbance and when completed the final settlement value

of R30-LL-4 (minus318mm) will be less than the maximumsettlement value (minus383mm) e measuring point R30-RR-10 will eventually settle instead of uplifting and its finalsettlement will be minus174mm

52 Comparison of Vertical Displacement of Pipeline AxialSurvey Line Because the vertical displacement of the topand bottom of the pipe gallery is consistent with the verticaldisplacement law the axial survey line at the bottom of thepipe gallery under two conditions is selected for analysis

e more typical monitoring time is the left line ad-vancing 30 circles and the right line advancing 30 rings e

Monitoring sectionShield machine

Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )

Figure 12 Relative position of the shield machine and utility tunnel at the selected moment of monitoring (a) Left lane to 15th ring (b) Leftlane to 30th ring (c) Left lane to 45th ring (d) Right lane to 15th ring (e) Right lane to 30th ring (f ) Right lane to 45th ring


vertical displacement of each longitudinal survey line isshown in Figure 14

Because the support pressure is reduced by consideringthe soil arch effect in condition 2 a large settlement in frontof the palm face is expected which is consistent with thephenomenon shown in the data in Figure 14

For line LCB-1 during the construction of left line(Figure 14(a)) the starting point of working condition 1 infront of the palm face is earlier than that of working con-dition 2 and the horizontal distance between them is about2D In addition due to the small support pressure inworking condition 2 the settlement in front of the palm faceis slightly larger than that in working condition 1 and thedifference between the two settlements is smaller In thesubsequent settlement after the shield machine passes thesettlement value of the working condition 2 is smaller thanthat of the working condition 1 and the difference is alsosmall At the same time it can be found that the settlement ofthe two working conditions is basically the same within thelength of the shield machine behind the palm face Duringthe construction of the right line (Figure 14(b)) the locationrule of the settlement point in front of the palm face isconsistent with that of the left line but the difference be-tween the two in vertical displacement value is obvious esettlement is significantly larger than that of working con-dition 1 Within the length of the shield machine behind thepalm face the vertical displacement curve of workingcondition 2 is smoother than that of working condition 1Similarly the settlement value of working condition 2 isgreater than the working condition 1 after the shield ma-chine is slightly smaller and the difference between the twois not large

For line MCB-2 during the construction of left line(Figure 14(c)) the starting point of working condition 1 infront of the same palm face is closer than that of workingcondition 2 e horizontal distance between the twostarting points is about 05 d and the settlement difference isnot large e settlement rule of the two working conditions

within the length of the shield machine is basically the sameBeyond the shield machine the settlement of workingcondition 2 is smaller than that of working condition 1 andthe settlement difference between the two working condi-tions is not large During the construction on the right line(Figure 14(d)) the settlements in the front of the palm faceare significantly different e settlement in working con-dition 2 is larger than that in working condition 1 Withinthe range of the length of the shield machine the settlementis relatively gentle in working condition 2

For line RCB-3 during the construction of the left line(Figure 14(e)) the vertical displacement in front of the palmface in both cases shows a bulging phenomenon e upliftdifference in working condition 2 is smaller than that inworking condition 1 and the rest of the rules are basicallythe same as the above two lines

In conclusion during the left line construction there isno significant difference in the effect of controlling thevertical displacement of the pipe gallery in the workingcondition 1 and condition 2 with less support pressureDuring the right line construction the control effect in theworking condition 2 is not as obvious as that in the workingcondition 1 e main difference is that the settlement infront of the palm surface in the working condition 2 is largerthan that in the working condition 1

53 Comparison of Vertical Displacement of MonitoringPoints in the Cross Section of the Pipe Gallery is sectionselects the representative monitoring points R30-LL-4 that isclosest to the left line and R30-RR-10 that is closest to theright line in the monitoring section for comparison andanalysis as shown in Figure 15

During the entire construction process in Figure 15 thevariation of vertical displacement of the two workingconditions of monitoring points is consistente settlementvalue of working condition 2 is larger than that of workingcondition 1 It is minus40mm at the measuring point R30-LL-4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)

Excavation step (step)

Excavation direction

ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

The left line is completed the right line is excavatedR30-LT-1R30-MT-5R30-RT-9

R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

The left line is completed the right line is excavatedR30-LL-4R30-ML-8R30-RL-12

R30-LR-2R30-MR-6R30-RR-10

(b)

Figure 13 e vertical displacement curves of each monitoring point during construction (a) pipe gallery top and bottom (b) pipe gallerywall


e uplift value of the working condition 1 is larger than theworking condition 2 It is 06mm at the measuring pointR30-RR-10 In addition the vertical displacement differencebetween the two conditions during the left line constructionis not large and the vertical displacement difference willincrease during the right line construction

In summary under the condition that the remainingconditions remain unchanged due to the consideration ofthe soil arch effect in case 2 the settlement value is large andthe uplift value is small at is to say the trend of lateral upwarping decreases with the decrease of support pressure Forthe construction method of ldquocompletion of the left line

ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005

ndash10 0 10 20 30 40 50 60 70 80 90 100Excavation length (m)

Excavation directionV

ertic

al d

ispla

cem

ent (

mm

)

Working condition 1Working condition 2Location of the palm face of the left tunnel

(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Excavation length (m)


ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)

Working condition 1Working condition 2Location of the palm face of the right tunnel

(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )

Figure 14 e vertical displacement curves of each monitoring longitudinal line in two cases at the selected moment (a) Verticaldisplacement of LCB-1 when the left line is advanced to 30 rings (b) Vertical displacement of LCB-1 when the left line is advanced to 30rings (c) Vertical displacement of MCB-2 when the left line is advanced to 30 rings (d) Vertical displacement of MCB-2 when the left line isadvanced to 30 rings (e) Vertical displacement of RCB-3 when the left line is advanced to 30 rings (f ) Vertical displacement of RCB-3 whenthe left line is advanced to 30 rings


reexcavation of the right linerdquo under the reasonable supportpressure value theory this paper considers that the influenceof vertical displacement of the pipe gallery caused by dif-ferent support pressures is mainly reflected in the process ofexcavation of the back line

For the working condition 2 in which the soil arch effectis considered the maximum settlement is minus40mm and themaximum uplift is 048mm Both the settlement and theuplift do not exceed the displacement control standardserefore under the condition of spatial layout of under-ground buildings in this paper considering the soil archeffect the construction of the metro shield tunnel will nothave a destructive impact on the existing comprehensivepipe gallery which is safe

6 Conclusions

is paper investigates the stability influence of twin tunnelsexcavation under the existing pipe gallery tunnel Based onthe calculated results the following conclusions can bedrawn

(1) Loess is a special kind of clayed soil In the theoreticalcalculation of overburden earth pressure of shieldtunnel in Xirsquoan loess the loose earth pressure theoryunder the incomplete soil arching effect can be usedfor calculation when considering the soil archingeffect

(2) In the case where the left and right lines are con-structed at different times the vertical displacementof the pipe gallery is affected by different supportpressures If the support pressure is small the set-tlement will be large and the uplift will be smallatis to say the overall deformation of the pipe corridoris mainly subsidence and the lateral upturning doesnot increase with the increase in settlement on theside of the pipe gallery settlement

(3) In this paper under the combined conditions ofunderground comprehensive pipe corridor andsubway line it is applicable to the supporting

pressure calculated by different overlying earthpressure theories According to the constructionmethod and supporting pressure of this articleshield tunnel construction will not affect the safety ofthe comprehensive pipe corridor

Data Availability

All data used in this study are available from the corre-sponding author upon request is paper uses ABAQUSfinite element software to build a three-dimensional modeland for calculation

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is research was financially supported by the XirsquoanUniversity of Technology Foundation (107256211404)Loess Soil Mechanics and Engineering Key Laboratory ofShaanxi Province Foundation (13JS073) Natural ScienceFoundation of Shaanxi Province (2017JM5059) and Na-tional Natural Science Foundation of China (Grant Nos11572246 and 51779207)

References

[1] R P Chen J Zhu W Liu and X W Tang ldquoGroundmovement induced by parallel EPB tunnels in silty soilsrdquoTunnelling and Underground Space Technology vol 1 no 26pp 163ndash171 2011

[2] R P Chen L J Tang D S Ling Y M Chen and Y M ChenldquoFace stability analysis of shallow shield tunnels in dry sandyground using the discrete element methodrdquo Computers andGeotechnics vol 38 no 2 pp 187ndash195 2011

[3] S Ma Y Shao Y Liu J Jiang and X Fan ldquoResponses ofpipeline to side-by-side twin tunnelling at different depths 3Dcentrifuge tests and numerical modellingrdquo Tunnelling andUnderground Space Technology vol 66 pp 157ndash173 2017

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Excavation directionVer

tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

Working condition 1Working condition 2

The left line is completed the right line is excavated

(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)

Figure 15 e vertical displacement curves of monitoring points (a) R30-LL-4 and (b) R30-RR-10 during construction


[4] R-p Chen J Li L-g Kong and L-j Tang ldquoExperimentalstudy on face instability of shield tunnel in sandrdquo Tunnellingand Underground Space Technology vol 33 pp 12ndash21 2013

[5] R Chen X Yin L Tang and Y Chen ldquoCentrifugal modeltests on face failure of earth pressure balance shield inducedby steady state seepage in saturated sandy silt groundrdquoTunnelling and Underground Space Technology vol 81 no 81pp 315ndash325 2018

[6] K Soga R G Laver and Z Li ldquoLong-term tunnel behaviourand ground movements after tunnelling in clayey soilsrdquoUnderground Space vol 2 no 3 pp 149ndash167 2017

[7] R E Ranken and J Ghaboussi ldquoAnalysis of interaction be-tween two parallel tunnelsrdquo Finite Element Method vol 34no 2 pp 45ndash52 1976

[8] V Avgerinos D M Potts and J R Standing ldquoNumericalinvestigation of the effects of tunnelling on existing tunnelsrdquoGeotechnique vol 67 no 9 2017

[9] CWW Ng K Y Fong and H L Liu ldquoe effects of existinghorseshoe-shaped tunnel sizes on circular crossing tunnelinteractions three-dimensional numerical analysesrdquo Tun-nelling and Underground Space Technology vol 77 pp 68ndash792018

[10] M Yin H Jiang Y Jiang Z Sun and Q Wu ldquoEffect of theexcavation clearance of an under-crossing shield tunnel onexisting shield tunnelsrdquo Tunnelling and Underground SpaceTechnology vol 78 pp 245ndash258 2018

[11] Z Zhang and M Huang ldquoGeotechnical influence on existingsubway tunnels induced by multiline tunneling in Shanghaisoft soilrdquo Computers and Geotechnics vol 56 pp 121ndash1322014

[12] M Maleki H Sereshteh M Mousivand and M Bayat ldquoAnequivalent beam model for the analysis of tunnel-buildinginteractionrdquo Tunneling and Underground Space Technologyvol 26 no 9 pp 524ndash533 2011

[13] J Liu T Qi and ZWu ldquoAnalysis of groundmovement due tometro station driven with enlarging shield tunnels underbuilding and its parameters sensitivity analysisrdquo Tunnelingand Underground Space Technology vol 28 no 8 pp 287ndash296 2012

[14] P B Attewell J Yeates and A R Selby Soil MovementsInduced by Tunnelling and eir Effects on Pipelines andStructures Blackie amp Son London UK 1986

[15] A Klar T E B Vorster K Soga and R J Mair ldquoSoil-pipeinteraction due to tunnelling comparison between Winklerand elastic continuum solutionsrdquo Geotechnique vol 55 no 6pp 461ndash466 2005

[16] A Klar T E Vorster K Soga and R J Mair ldquoElastoplasticsolution for soil-pipe-tunnel interactionrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 133 no 7pp 782ndash792 2007

[17] A Klar and A M Marshall ldquoLinear elastic tunnel pipelineinteraction the existence and consequence of volume lossequalityrdquo Geotechnique vol 65 no 9 pp 788ndash792 2015

[18] T E Vorster A Klar K Soga and R J Mair ldquoEstimating theeffects of tunneling on existing pipelinesrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 131 no 11pp 1399ndash1410 2005

[19] Y Wang QWang and K Y Zhang ldquoAn analytical model forpipe-soil-tunneling interactionrdquo Procedia Engineering vol 14pp 3127ndash3135 2011

[20] C Lin M Huang F Nadim and Z Liu ldquoTunnelling-inducedresponse of buried pipelines and their effects on groundsettlementsrdquo Tunnelling and Underground Space Technologyvol 96 pp 103ndash193 2020

[21] K Terzaghi ldquoStress distribution in dry and in saturated sandabove a yielding trap-doorrdquo in Proceedings of First Interna-tional Conference on Soil Mechanics and Foundation Engi-neering pp 307ndash311 Cambridge MA USA June 1936

[22] R L Handy ldquoe arch in soil archingrdquo Journal of Geotech-nical Engineering vol 111 no 3 pp 302ndash318 1985

[23] C Li ldquoMethod for calculating loosening earth pressure duringconstruction of shield tunnelsrdquo Chinese Journal of Geotech-nical Engineering vol 36 no 9 pp 1714ndash1720 2014

[24] N Loganathan and H G Poulos ldquoAnalytical prediction fortunneling-induced ground movements in claysrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 124no 9 pp 846ndash856 1998

[25] C Zhu Research on Ground Settlements Induced by SubwayShield Tunnel Construction in Xirsquoan Loess Strata XirsquoanUniversity of Technology Xirsquoan China 2009

[26] C Ou Deep Excavation eory and practice Taylor andFrancis Group London UK 2006

[27] Z Zhang and W Hu ldquoInvestigation on excavation facesupport pressure calculation methods of shield tunnelling inclayey soilrdquo Chinese Journal of Rock Mechanics and Engi-neering vol 33 no 3 pp 606ndash614 2014

[28] F Ye C Gou J Mao P Yang Z Chen and T Jia ldquoCal-culation of critical grouting pressure during shield tunnelingin clay stratum and analysis of the influencing factorsrdquo Rockand Soil Mechanics vol 36 no 4 pp 937ndash945 2015

[29] L Wang Study on Interaction Mechanism and DeformationControl Standard of Collapsible Loess Layer and MetroStructure Changrsquoan University Xirsquoan China 2016

[30] C Zhu Li Ning H Liu and Z Zhang ldquoAnalysis of groundsettlement induced by workmanship of shield tunnellingrdquoRock and Soil Mechanics vol 32 no 1 pp 158ndash164 2011

[31] C Zhu Li Ning and Z Zhang ldquoAnalysis and prediction ofground settlement induced by shield construction in Xirsquoanloess stratardquo Chinese Journal of Geotechnical Engineeringvol 32 no 7 pp 1087ndash1095 2010

[32] GB50010-2010 Ministry of Housing and Urban-Rural De-velopment of the Peoplersquos Republic of China GB50010-2010Code for Design of Concrete structures China Architecture andBuilding Press Beijing China 2015 in Chinese

[33] TB10003-2016 National Railway Administration of the Peo-plersquos Republic of China TB10003-2016 Code for Design ofRailway tunnel China Railway Press Beijing China 2016 inChinese

[34] GB50007-2011 Ministry of Housing and Urban-Rural De-velopment of the Peoplersquos Republic of China GB50007-2011Code for Design of Building Foundation China Architectureand Building Press Beijing China 2011 in Chinese


incorporating the tensionless Pasternak model which takesfull account of the gap formation and the pipeline orien-tation have been formulated to estimate the response of thepipeline and the overlying ground Since all these previousstudies reduced the interaction of the tunnel and the pipelineto a two-dimensional problem these three problems cannotbe determined

erefore it is particularly important to use numericalmethods to simulate the impact of shield tunnel construc-tion on the comprehensive pipe corridor and the con-struction of the comprehensive pipe corridor has a long-term development plan in China Based on the Xirsquoan subwayshield tunnel passing through the existing comprehensivepipe corridor this article will establish a numerical model tosimulate the construction process of the subway shieldtunnel passing through the existing comprehensive pipecorridor e construction method of ldquoline re-excavationrdquoanalyzes the influence of the shield tunneling on the de-formation of the existing comprehensive pipe corridorunder the conditions of considering the soil arch effect andthe supporting pressure without considering the soil archeffect

2 Related Theory of Shield Support Pressure

21 eory of Terzaghi Loose Soil Pressure Based on theassumption that the sliding surface is vertical Terzaghideduced that the loose earth pressure formula is widely used[21]

σv cB minus c

K tanφ1 minus e

((minusKH tanφ)B)1113872 1113873 + qe

((minusKH tanφ)B)

B R cotπ8

+φ4

1113874 1113875

(1)

whereK is the pressure coefficient of the soil side the value isbetween 10 and 15 it is recommended to take 10 H is theheight of the overlying soil q is the upper load R is thetunnel radius B is the span of the cavern φ is internalfriction angle of soil c is cohesion of soil and c is unitweight

22 Loose Earth Pressure eory under the Incomplete SoilArching Effect In the Terzaghi loose earth pressure theorythe selection of the lateral pressure coefficient of the soil isrecommended to be 10 e selection of this value being thebest one is arguable Handy [22] analyzed the insufficiency ofthe pressure arch model and derived the coefficient ofconfinement pressure of the soil based on Mohrrsquos circle ofstress

Since the shield driving method can better control theformation damage it can be considered that the soil archingeffect is not as assumed in the Terzaghi loose earth pressureat is the soil arch is an incomplete soil arch and thearching effect is not fully exerted Based on Handyrsquos theoryLi [23] puts out the side compression of soil considering theincomplete arch effect Sketch of partially developed soilarching effect is shown in Figure 1

Calculation formula for loose earth pressure under in-complete soil arching effect is as follows

σv B1c

A11 minus e

minus A1hB1( )1113874 1113875 + qeminus A1hB1( ) (2)

A1 K 1 minus Ka( 1113857tan θ1 + Katan

2 θ (3)

K 1 + Katan

2 θtan2 θ + Ka

(4)

For clayed soil the active earth pressure coefficientshould take cohesion into account in the soil lateral pressurecoefficient formula According to Rankine earth pressuretheory the active earth pressure coefficient Ka of clayed soilis

Ka tan2 45∘ minusφ2

1113874 1113875 minus2c

chtan 45∘ minus

φ2

1113874 1113875 (5)

erefore when calculating the loosening earth pressureunder the incomplete soil arch effect of cohesive soil for-mula (6) can be substituted into formula (4) and formula (5)for calculation It obtains the calculation formula of looseearth pressure under the incomplete soil arch effect con-sidering cohesion as follows

σv B1c minus c

A11 minus e

minusA1hB1( )1113874 1113875 + qeminusA1hB1( ) (6)

In a certain case of Ka A1 and K are determined by θthe greater the rate of ground loss the larger the deflectionangle of the maximum principal stress resulting in thesmaller the θ erefore θ depends on the formation lossrate and B1 is the width of loose bandat is displacementof the vault is

tan θ B1

2sminus

s

2B1 (7)

where s is the formation loss parameter that is the dis-placement of the arch surface of the excavation face

23 Comparative Analysis of Earth Pressure at Tunnel TopIn the theory of loose earth pressure under the incompletesoil arching effect considering cohesion the formation lossparameter is required is parameter can be calculated bythe equivalent formation loss formula proposed by Loga-nathan and Poulos [24]

ε0 4sR + s

2

4R2 times 100 (8)

where ε0 is the formation loss rate R is the tunnel radius ands is the gap parameter which is also the vault sedimentation

According to formula (8) transformation

s 2R1 + ε0

1113968minus 1( 1113857 (9)

erefore combined with the corresponding parame-ters different loose soil pressure values can be calculated





η σi

σv

(10)






3 Project Overview


σhα

σv

τ

σ3

σ3

σh

τ

σ1

σ

σh

σ1

σv

θ

σ3

φ0

τ

σ1

σv




0626

0628

063

0632

0634

0636

0638

064

0642

0 05 1 15 2 25 3

Pres

sure

ratio













σT kσv + p0 (11)


σT k σv + Dc( 1113857 + p0 (12)















3510

7


Shield tunneling

3

18

Existing ground

Shield tunneling

Soil nail

1

Artificial fill

18

Soil nail

3

Cushion

66

35


Earth


23003300

9000 100

300 300350 3502100

3000

3300

2600

350

350

100



500

Surface thick

107

5

1500

1000

Existing ground

1500

Soil nail


1000

1500

1500

7300

Powertank

Drainage ditch


H

D σT

Existing ground








Tunnel segment

Grouting pressure

(a)

Surrounding rock

Groutingpressure

(b)









Tunneling direction

Subway le

yz

x

Subway right

Utility tunnel

120m90m

50m

2345

1


Surface layer

Soil nailCushion

yz

x

Utility tunnel


























MCT-5R30-7

LCT-4

LCB-1 R30-8RCT-6

RCB-3MCB-2xy

z


R30-LT-1

R30-LL-4

R30-LB-3

R30-LR-2

R30-MT-5

R30-ML-8

R30-MB-7

R30-MR-6

R30-RT-9

R30-RL-12

R30-RR-10

R30-RB-11









Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )












ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)






































η σi

σv

(10)






3 Project Overview


σhα

σv

τ

σ3

σ3

σh

τ

σ1

σ

σh

σ1

σv

θ

σ3

φ0

τ

σ1

σv




0626

0628

063

0632

0634

0636

0638

064

0642

0 05 1 15 2 25 3

Pres

sure

ratio













σT kσv + p0 (11)


σT k σv + Dc( 1113857 + p0 (12)















3510

7


Shield tunneling

3

18

Existing ground

Shield tunneling

Soil nail

1

Artificial fill

18

Soil nail

3

Cushion

66

35


Earth


23003300

9000 100

300 300350 3502100

3000

3300

2600

350

350

100



500

Surface thick

107

5

1500

1000

Existing ground

1500

Soil nail


1000

1500

1500

7300

Powertank

Drainage ditch


H

D σT

Existing ground








Tunnel segment

Grouting pressure

(a)

Surrounding rock

Groutingpressure

(b)









Tunneling direction

Subway le

yz

x

Subway right

Utility tunnel

120m90m

50m

2345

1


Surface layer

Soil nailCushion

yz

x

Utility tunnel


























MCT-5R30-7

LCT-4

LCB-1 R30-8RCT-6

RCB-3MCB-2xy

z


R30-LT-1

R30-LL-4

R30-LB-3

R30-LR-2

R30-MT-5

R30-ML-8

R30-MB-7

R30-MR-6

R30-RT-9

R30-RL-12

R30-RR-10

R30-RB-11









Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )












ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)











































σT kσv + p0 (11)


σT k σv + Dc( 1113857 + p0 (12)















3510

7


Shield tunneling

3

18

Existing ground

Shield tunneling

Soil nail

1

Artificial fill

18

Soil nail

3

Cushion

66

35


Earth


23003300

9000 100

300 300350 3502100

3000

3300

2600

350

350

100



500

Surface thick

107

5

1500

1000

Existing ground

1500

Soil nail


1000

1500

1500

7300

Powertank

Drainage ditch


H

D σT

Existing ground








Tunnel segment

Grouting pressure

(a)

Surrounding rock

Groutingpressure

(b)









Tunneling direction

Subway le

yz

x

Subway right

Utility tunnel

120m90m

50m

2345

1


Surface layer

Soil nailCushion

yz

x

Utility tunnel


























MCT-5R30-7

LCT-4

LCB-1 R30-8RCT-6

RCB-3MCB-2xy

z


R30-LT-1

R30-LL-4

R30-LB-3

R30-LR-2

R30-MT-5

R30-ML-8

R30-MB-7

R30-MR-6

R30-RT-9

R30-RL-12

R30-RR-10

R30-RB-11









Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )












ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)







































3510

7


Shield tunneling

3

18

Existing ground

Shield tunneling

Soil nail

1

Artificial fill

18

Soil nail

3

Cushion

66

35


Earth


23003300

9000 100

300 300350 3502100

3000

3300

2600

350

350

100



500

Surface thick

107

5

1500

1000

Existing ground

1500

Soil nail


1000

1500

1500

7300

Powertank

Drainage ditch


H

D σT

Existing ground








Tunnel segment

Grouting pressure

(a)

Surrounding rock

Groutingpressure

(b)









Tunneling direction

Subway le

yz

x

Subway right

Utility tunnel

120m90m

50m

2345

1


Surface layer

Soil nailCushion

yz

x

Utility tunnel


























MCT-5R30-7

LCT-4

LCB-1 R30-8RCT-6

RCB-3MCB-2xy

z


R30-LT-1

R30-LL-4

R30-LB-3

R30-LR-2

R30-MT-5

R30-ML-8

R30-MB-7

R30-MR-6

R30-RT-9

R30-RL-12

R30-RR-10

R30-RB-11









Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )












ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)



































500

Surface thick

107

5

1500

1000

Existing ground

1500

Soil nail


1000

1500

1500

7300

Powertank

Drainage ditch


H

D σT

Existing ground








Tunnel segment

Grouting pressure

(a)

Surrounding rock

Groutingpressure

(b)









Tunneling direction

Subway le

yz

x

Subway right

Utility tunnel

120m90m

50m

2345

1


Surface layer

Soil nailCushion

yz

x

Utility tunnel


























MCT-5R30-7

LCT-4

LCB-1 R30-8RCT-6

RCB-3MCB-2xy

z


R30-LT-1

R30-LL-4

R30-LB-3

R30-LR-2

R30-MT-5

R30-ML-8

R30-MB-7

R30-MR-6

R30-RT-9

R30-RL-12

R30-RR-10

R30-RB-11









Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )












ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)









































Tunneling direction

Subway le

yz

x

Subway right

Utility tunnel

120m90m

50m

2345

1


Surface layer

Soil nailCushion

yz

x

Utility tunnel


























MCT-5R30-7

LCT-4

LCB-1 R30-8RCT-6

RCB-3MCB-2xy

z


R30-LT-1

R30-LL-4

R30-LB-3

R30-LR-2

R30-MT-5

R30-ML-8

R30-MB-7

R30-MR-6

R30-RT-9

R30-RL-12

R30-RR-10

R30-RB-11









Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )












ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)























































MCT-5R30-7

LCT-4

LCB-1 R30-8RCT-6

RCB-3MCB-2xy

z


R30-LT-1

R30-LL-4

R30-LB-3

R30-LR-2

R30-MT-5

R30-ML-8

R30-MB-7

R30-MR-6

R30-RT-9

R30-RL-12

R30-RR-10

R30-RB-11









Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )












ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)









































Tunnel segment

yx

z

(a)


Tunnel segment

yx

z

(b)

Monitoring section

Shield machine

Tunnel segment

yx

z

(c)

Monitoring section

Shield machine

Tunnel segment

Tunnel segmenty

xz

(d)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(e)

yx

z

Monitoring section

Shield machine

Tunnel segment

Tunnel segment

(f )












ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)












































ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LB-3R30-MB-7R30-RB-11

(a)

Ver

tical

disp

lace

men

t (m

m)

ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

051



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150


R30-LR-2R30-MR-6R30-RR-10

(b)





ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)





































ndash4ndash35

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



ertic

al d

ispla

cem

ent (

mm

)


(a)

ndash4ndash45

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(b)

ndash25

ndash2

ndash15

ndash1

ndash05

0

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(c)

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(d)

ndash1

ndash05

0

05

1



ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(e)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005



1ndash10 0 10 20 30 40 50 60 70 80 90 100

Ver

tical

disp

lace

men

t (m

m)


(f )





6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)





































6 Conclusions






Data Availability




Acknowledgments


References




ndash45ndash4

ndash35ndash3

ndash25ndash2

ndash15ndash1

ndash050

05


tical

disp

lace

men

t (m

m)


ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(a)

ndash25ndash2

ndash15ndash1

ndash050

051

Ver

tical

disp

lace

men

t (m

m)



ndash10

0 10 20 30 40 50 60 70 80 90 100

110

120

130

140

150



(b)



































effect of subway excavation with different support

Documents