surfacesettlementanalysisinducedbyshieldtunneling ...lateral stress at rest (and is equal to 1.0...

Research ArticleSurface Settlement Analysis Induced by Shield TunnelingConstruction in the Loess Region

Caihui Zhu 123

1State Key Laboratory of Eco-hydraulics in Northwest Arid Region Xirsquoan University of Technology Xirsquoan Shaanxi 710048 China2Institute of Geotechnical Engineering Xirsquoan University of Technology 5 South Jinhua Road Xirsquoan Shaanxi 710048 China3Shaanxi Provincial Key Laboratory of Loess Mechanics Xirsquoan University of Technology Xirsquoan Shaanxi 710048 China

Correspondence should be addressed to Caihui Zhu zhucaihui123163com

Received 19 January 2021 Revised 8 February 2021 Accepted 27 February 2021 Published 12 March 2021

Academic Editor Xiangtian Xu

Copyright copy 2021 Caihui Zhuis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e influence and prediction of shield tunneling construction on surface settlement (SS) and adjacent buildings is a hot topic inunderground space engineering In this work several analytical methods are utilized to estimate the maximum surface settlement(MSS) and conduct a parametric sensitivity analysis based on Xirsquoan Metro line 2 e results show that there are mainly ninefactors influencing the SS induced by shield tunneling construction in loess strata e disturbance degree of the surrounding soilduring the shield advancing stage has the largest influence on the SS followed by the seepage of the shield lining segments orfalling water levels which lead to the overlying soil consolidation After this is the grouting filling effect at the shield tail followedby the reinforcement effect of the tunnel foundation and the track e smallest influencing factors on the SS are the shieldoverexcavation and improper shield attitudes during the construction period e sensitivity analysis results of the aboveinfluencing factors may offer a scientific guidance for the control of shield tunneling construction

1 Introduction

In the Xirsquoan loess strata more than 20 subway lines are underconstruction or being designede subways are constructedwith the shield tunneling method and these subways crossbeneath ancient sites architectural structures ground fis-sures underground pipelines (eg water and natural gas)and other buildingsrough long-term investigations of theexisting subway lines constructed in loess strata seriousissues with the tunnels and subway stations have been re-ported such as the uneven deformation of lining segmentssoil strata and pavements lining seepage undergroundpipeline ruptures and tilting of buildings and foundationsese issues greatly influence the surface settlement (SS) andthe structural integrity of adjacent structures e SS in-duced by shield construction can be classified into twocategories In the first category the SS is caused by theimproper control of the shield excavation during the con-struction period In the second category the SS occursduring the postconstruction period because of changes in the

mechanical properties of the soil around the tunnel Con-trolling and forecasting the SS during shield tunneling arethe most important geotechnical engineering problem to besolved A number of analytic methods have been proposedand widely used to predict the SS in the engineering practice[1ndash11]

In previous research results there are many analyticalestimation methods to predict the SS induced by tunnelingconstruction e displacement-controlled boundaryaround the tunnel opening has usually been expressed asdifferent convergence modes in the reported methods suchas the point source theory [1ndash3 12] the complex variabletheory [4 5 13ndash16] the stress function elastic theory[6 7 17 18] and the stochastic medium method [8 9]Huang and Zeng [10] proposed the uniform convergencemodel and the analytical solution of the stratum displace-ment for the double-circle shield tunnel Based on the elasticsolutions of Lame and Kiersch Liu and Zhang [19] alsoproposed an analytical solution of the SS caused by tunnelexcavation under the condition of plane strain and

HindawiAdvances in Materials Science and EngineeringVolume 2021 Article ID 5573372 13 pageshttpsdoiorg10115520215573372

nonuniform stress field Lu et al [20] proposed a unifieddisplacement function of the cross section of a circularshallow tunnel under complex geological and constructionconditionsis function is expressed by a Fourier series andcan reflect the horizontal and vertical asymmetrical defor-mation behaviors of the tunnel cross section Shen and Zhu[21] proposed an analytical method using the virtual imagetechnique and Fourier transform solutions to estimate theground SS caused by the tail void grouting pressure in shieldtunnel construction Fang et al [22] reported that a normalprobability function can be extended to estimate the SS dueto shield tunneling which can consider various types ofshield machines depths and diameters Zhang et al [11]presented an analytical solution by the complex variablemethod to predict the soil deformation due to tunneling inclay this approach considers the linear stiffness influenceand the nonuniform convergence boundary condition

e analytical methods that are described above sys-tematically consider the stratum conditions and the shieldconstruction technologies However when predicting the SSin the postconstruction period it is difficult to consider thevariable features of unsaturated-saturated loess strata suchas the underground water level decline the dissipation ofpore water pressure the creep deformation of the sur-rounding soil and the train vibration loading e waterseepage issues and the causes of the uneven settlement of thetunnel in Shanghai Metro lines 1 and 2 have been widelyinvestigated and reported In addition the SS that has beeninduced by the additional load the underground con-struction and fall of the ground water level has also beenstudied by Shen et al [23ndash27] Ng et al [28] summarized thesettlement measurements of Shanghai Metro line 1 from1994 to 2007 and the relationship between groundpumping foundation soil compression and the tunnelsettlement has been reported Soga et al [29] studied thetunnel deformation caused by the dissipation of excess porewater pressure of the soil and the aging of grouting materialsafter lining segments in the London subway A theory forcalculating the SS has been proposed which considers theinteractions between the soil and the lining Based on dy-namic load testing the critical dynamic stress ratio and thedynamic stress amplitude of saturated loess were proposedby Cui [30] and the SS caused by the subway vibrationloading has been calculated

In addition the surface settlement induced by freezingconstruction is becoming a trending issue in the freeze-thawzone Zhou et al [31] and Shen et al [23] studied the path-dependent mechanical behaviours of frozen loess based onthe experimental investigation Zheng et al [32] proposed apractical method to simulate and predict the ground surfacedeformation during the entire artificial ground freezingconstruction process A model test system and numericalmethod were used by Cai et al [33] to simulate horizontalground freezing on the heaving displacement of twin tun-nels Zhou et al [34] published a segregation potential modelto predict the frost heaves during freezing construction

From the above valuable results have been reported onanalytical methods for the SS induced by undergroundconstruction however there is still no systematic research to

explore the influence degrees of different factors on the SSwhich is essential for determining the prioritization of SScontrol measures On the basis of summarizing previouslyreported analytical methods and taking the shield con-struction of the Xirsquoan Metro in the loess stratum as theresearch background the calculation methods of surfacesettlement induced by nine factors were proposed and aparametric sensitivity analysis of the maximum surfacesettlement (MSS) induced by each individual influencefactor was conducted e resulting sensitivity indexes aresorted in order to provide technical guidance for SS controlsduring the shield tunneling construction

2 Estimation of the MaximumSurface Settlement

21 Maximum Settlement Estimation of the Tunnel Vaultduring theConstructionPeriod Due to the improper controlof the shield excavation the factors inducing the settlementof the tunnel vault mainly include (1) inadequate shieldsupport pressure (2) insufficient grout filling in the shieldtail (3) insufficient grouting pressure (4) overexcavation bythe shield yawing and (5) improper shield attitude emethods to calculate the volume loss of the stratum and theSS generated when the tunnel vault deformation is inducedby these factors are summarized in the following

211 Tunnel Vault Settlement Induced by Inadequate ShieldSupport Pressure During the tunneling of the earth pres-sure-balanced shield machine the shield support pressure(Pi) plays a dynamic balancing role on the lateral soilpressure (K0P0 or K0primePv

prime+Pw) at the excavation surfaceWhen the lateral soil pressure between the shield head andthe excavation surface is unbalanced it inevitably leads tothe ground uplift and settlement When Pi K0P0 (seeFigure 1(a)) the lateral soil pressure is in an equilibriumstate and little additional stress occurs on the excavationsurface When the shield support pressure is lower than thelateral earth pressure (PiltK0P0 see Figure 1(b)) the tunnelvault settlement occurs When the shield support pressure ishigher than the lateral earth pressure (PigtK0P0 seeFigure 1(c)) the tunnel vault and surface uplift isprinciple is illustrated in Figure 1

In order to determine the tunnel vault settlement in-duced by an inadequate shield support pressure underundrained conditions Lee and Rowe [35] proposed a two-dimensional analytical solution by considering the three-dimensional elastic-plastic deformation at the excavationsurface e shield support pressure ratio β Pi(K0primePv

prime+Pw)is introduced into the above solution and the tunnel vaultsettlement (uc1) formula can be written as follows

uc1 ΩR K0primePV

prime + Pw minus Pi( 1113857

2Eu

ΩR(1 minus β) K0primePV

prime + Pw( 1113857

2Eu

(1)

where uc1 is the tunnel vault settlement and Ω is the hor-izontal displacement coefficient at the shield excavationsurface which is determined by a 3D numerical simulation

2 Advances in Materials Science and Engineering

of the shield tunnel excavation In addition K0 is the co-efficient of the lateral soil pressure in the tunnel P0 is thevertical soil pressure at the tunnel axis (kPa) K0prime is thehorizontal lateral pressure coefficient under the undrainedcondition Pv

prime is the vertical effective stress (kPa) at the tunnelaxis Pw is the pore water pressure (kPa) at the tunnel axis Piis the support pressure of the shield chamber (kPa) RD2is the tunnel excavation radius (m) D is the shield exca-vation diameter (m) and Eμ represents the undrained elasticmodulus of the overlying soil stratum of the tunnel (MPa)

Liu [36] reported that in reality drained elastic modulusE0 is 20sim50 times larger than the compression modulus EsHe suggested that the relationship between E0 and Es couldbe a function of the initial void ratio (e0) in the loess stratum

E0 2718Es

e0 (2)

According to elastic theory the relationship between theundrained elastic modulus Eu and the partially drainedelastic modulus E0 can be expressed as

Eu

E01 + ]u

1 + ]0 (3)

erefore by combining (2) and (3) the undrainedelastic modulus can be written as

Eu 2718Es 1 + ]u( 1113857

1 + ]0( 1113857e0 (4)

where ]u 05 is the undrained Poissonrsquos ratio and ]0 is thedrained Poissonrsquos ratio In the loess stratum ]0 can be es-timated using ]0 K0(1 +K0) where K0 is the coefficient oflateral stress at rest (and is equal to 10 under undrainedconditions)

Based on the above theory in shield tunneling con-struction the undrained condition means that the soilaround the tunnel will not be consolidated and drainedduring the rapid shield advancing e soil element is in theuniform compression state and the coefficient of lateralstress at rest is K0 10 therefore the undrained Poissonrsquosratio ]u K0(1 +K0) 12 05

212 Tunnel Vault Settlement Induced by InsufficientGrouting at the Shield Tail During shield tunneling forcontrolling the volume loss of the stratum the grouting atthe shield tail can be rapidly filled in the physical gap be-tween the shield shell and the lining Gp 2Δ+ δ [35] asillustrated in Figure 2 However due to the lengthy oper-ation time span grouting losses can occur during transportand the grouting volume can shrink and harden As a resultthe grouting cannot fully fill the gap e soil behind thelining segments collapses and the tunnel crown settlementoccurs

e settlement of the tunnel crown caused by insufficientgrouting at the shield tail is

uc2 (1 minus ω)Gp (5)

K0P0

Balance

Shield machine

Pi+ = 0

(a)

K0P0 Pi

Settlement

Shield machineAddi

tiona

l stre

ss

+ =

(b)

K0P0

Uplift

Shield machine

PiAd

ditio

nal s

tress

+

(c)

Figure 1 Surface movement behavior during the shield machine advancing (a) Pi K0P0 (b) PiltK0P0 (c) PigtK0P0

Advances in Materials Science and Engineering 3

where the parameter Gp is the shield physical gap (mm) d isthe outer diameter of the shield segment lining Δ is thethickness of the shield tail appendages δ is the lining as-sembling clearance and ω is the grouting filling rate evalue of ω is controlled between 08 and 10 the averagevalue of ω is between 090 and 095 when the shield controltechnology is rigorously applied

213 Tunnel Vault Settlement Induced by InsufficientGrouting Pressure As the shield tunnel advances thesynchronous grouting at the shield tail is mainly distributedin the range of 90sim180deg around the lining arch ring For asimple analysis the grouting pressure (Pil) at the shield tail isdistributed in the ldquocrescent shaperdquo as illustrated in Figure 3In this way when the grouting equipment fails or thegrouting pressure is not balanced with the initial soil

pressure the soil around the tunnel is inevitably filled intothe shield gap and the volume loss of the stratum occursWhen PilltPv (see Figure 3(a)) the overlying soil stratumsubsides in contrast when PilgtPv (see Figure 3(b)) thesurface uplifts (ie heaves) is principle is illustrated inFigure 3

Rowe et al [37] proposed the tunnel vault settlementis caused by an insufficient supporting force is can beextended to the condition in which the grouting pressureis less than the tunnel vault settlement (uc3) Because thegrouting pressure (Pil) and the initial soil pressure (P0)are a pair of unbalanced forces the grouting pressureratio λ PilP0 can be introduced to Rowersquos formula tocalculate the tunnel vault settlement under differentgrouting pressure ratios

uc3 13sim14

1113874 1113875 times R 1 minus

1

1 + 2 1 + vu( 1113857cuEu( 1113857 exp (1 minus λ)P0 minus cu2cu( 11138571113858 11138592

1113971

⎡⎢⎣ ⎤⎥⎦ (6)

where Eu cu and ]u are the undrained elastic modulus(MPa) cohesive strength (kPa) and Poissonrsquos ratio of theoverlying strata of the tunnel respectively P0 is the verticalsoil pressure of the tunnel axis Pil is the average groutingpressure (kPa) on the tunnel vault and Pv is the overburdenpressure at the tunnel vault According to the theory of Roweet al [37] the values of the coefficients 13 and 14 inequation (4) are set as follows when the soil mass at thetunnel crown undergoes elastic deformation the value is setto 13 when the elastic-plastic deformation of the soil massat the tunnel crown occurs the value is set to 14 edeformation pattern at the tunnel crown is determined bythe stability coefficient of the excavation surface N whichhas been introduced in Section 211

214 Tunnel Vault Settlement Induced by OverexcavationAs the shield tunnel advances the heterogeneity of the soilstratum leads to the shield snaking or yawing causing anoverexcavation of the shield Suppose the radial maximum

eccentricity is δ0 which can be calculated from the measuredvalues of the horizontal eccentricity SH and vertical eccen-tricity SV and its eccentricity angle is α en the shadedarea (Se) on the tunnel section is the overexcavation areaWhen the shield tunneling machine is corrected to thedesign axis overexcavation inevitably occurs as illustrated inFigure 4 In order to calculate the volume loss of theoverburden soil caused by overexcavation the over-excavation area (Se) is equivalent to the ldquocrescentrdquo area of thearch According to the gap parameter principle in Figure 2the tunnel vault settlement (uc4) caused by the over-excavation can be obtained

uc4 2

2R2 1 minus

1πarccos

κL

2R1113874 1113875 +

κL

2π

4R2

minus κ2L21113969

1113971

minus R⎛⎝ ⎞⎠

(7)

where δ0 κL is the yawing distance of the shield head (mm)κ is the overexcavation rate κ 00ndashplusmn20 and L is thelength of the shield tunneling machine (m)

d d

∆ = thickness of the tailpiece

δ = clearance for erection of lining

Gap

Simulated tunnel opening

Tail void

Lining

2D plane strain representation of tunnel heading

Tunnel heading

Initial position of points on what will become the crown after excavation

D =

d +

2∆

+ δ

Figure 2 Gap of the shield tail (after Lee and Rowe [35])


215 Tunnel Vault Settlement Induced by Improper ShieldAttitude As the shield tunneling advances compressiondeformation occurs at the top or the bottom of the tunneldue to the failure of the tunneling system e tunnel vaultsettlement (uc5) caused by the head knocking and lifting ofthe shield tunneling machine is described as follows

uc5 Lξ (8)

where ξ is the head knocking and lifting slope of the shieldtunneling machine deviating from the central axis generallythe term ξ minus30sim+30 and L is the length of the shieldtunneling machine (m)

22 Estimation of the Surface Settlement during the Post-construction Period e SS caused by the shield tunneladvancing during the construction period can be strictlycontrolled within the allowed values according to con-struction experience However during the postconstructionperiod the geological conditions change over time whichimpacts the SS ese dynamic conditions include (1) therecompression of the soil in the loosened circle around the

tunnel (2) the dissipation of excess pore water pressureinduced by the shield tunneling advancing (3) the sur-rounding soil consolidation due to the failure of the wa-terproofing behind the lining and the underground waterlevel decline (4) the foundation settlement caused by thetrain vibration loading etc

221 Recompression Settlement of the Soil in the LoosenedCircle As the shield advances and cuts the surrounding soilis disturbed and loosened due to the friction effect betweenthis soil and the shield machine is can lead to the plasticdeformation and instability of the surrounding soil eradius of the loosened circle is R0 and the ratio of theloosened circle radius to the shield tunnel excavation radiusis defined as ηR0R Because of the recompression of theloosened soil around the tunnel the uniform convergencedeformation of the tunnel boundary is calculated as follows

up1 mvprime c H minus R0( 1113857 minus Pil1113858 1113859 R0 minus R( 1113857

mvprime(η minus 1)R c(H minus ηR) minus Pil1113858 1113859

(9)

Natural ground

GroutingGrouting pressurePil

Pv

Ph

Initial vertical stress

Horizontal stress

Surrounding soil

Ph

Pil lt Pv

R

Surface settlement

Lining

Excavationboundary

(a)

Pil gt Pv

GroutingGrouting pressure

Pil

Pv

Ph


Horizontal stress

Surrounding soil

Ph

R

Lining

Excavationboundary

Surface heave

Natural ground

(b)

Figure 3 e surface movement during the shield tail grouting (a) PilltPv and (b) PilgtPv

Se

Monitoring point

uc4

R

Crown settlement

Overexcavationarea Se

Yawing angle

αShield axis

Shield length (L)

δ0-yawingdistance

Yawingdistance

SV δ 0

δ 0

SHθ0

θ0

Equivalent

Figure 4 Tunnel vault deformation caused by shield overexcavation


where up1 is the uniform convergence deformation of theloosened soil circle H is the buried depth of the tunnel axis(m) mv

prime is the soil volume compression coefficient of theloosened circle (MPaminus1) which is 3sim5 times that of un-disturbed soil if considering the secondary grouting or

strata pre-reinforcement effect the volume compressioncoefficient of the soil mv

prime is 02sim10 times that of undisturbedsoil and R0 is the plastic zone radius of the loosened soilcircle (m) which is calculated as follows

R0 R(1 minus sin φ) 05 1 + K0( 1113857P0 minus 1 minus K0( 1113857P0 + ctanφ1113858 1113859

Pil + ctanφ1113896 1113897

((1minussinφ)2 sinφ)

(10)

where c and φ are the cohesive force (kPa) and theinternal friction angle (deg) of the soil mass respectively K0is the lateral pressure coefficient of the soil mass and Pil isthe grouting pressure (kPa) If no measured data areavailable Pil can be taken as the recommendation by Liu[36]

Pil (025 minus 050)cR[1 + tan(π4 minus φ2)]

tan φ (11)

Suppose the stratum volume loss (V) due to therecompression of the soil in the loosened circle can beexpressed as follows

V π R20 minus R0 minus up11113872 1113873

21113876 1113877 (12)

en according to equation (7) the relationship amongthe total convergence deformations of the tunnel (2up1) theMSS (Sp1) and the volume loss (V) is

2up1 V

2π

radiciz1

Sp1 V2π

radici1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)

e settlement trough width (iz1) caused by soilrecompression in the loosened circle during the post-construction period is inconsistent with the surface settle-ment trough width (i1) during the construction periodAccording to experience [38] the relationship between iz1and i1 can be expressed as iz1 (1minus 065z1H)i1 wherez1 HminusR0 us Sp1 induced by the recompression of theloosened circle can be written as

Sp1 2up1 1 minus 065z

H1113874 1113875 2up1 035 + 065

R0

H1113876 1113877 (14)

222 Consolidation Deformation Caused by the Dissipationof Excess Pore Pressure As the tunnel advances below theunderground water level when the thrust and friction of theshield tunneling machine and the grouting pressure are notbalanced in the initial stress field the additional load gen-erates en the soil within a certain range around thetunnel exhibits an excess pore pressure It is assumed that theexcess pore pressure at the tunnel crown is P1 and the excesspore pressure at the ground surface is P2 e underground

water level is dw below the surface and the vertical distancebetween the initial underground water level and the tunnelaxis is hw According to the measurement the distributioncharacteristics of the excess pore pressure around the tunnelare illustrated in the shaded part in Figure 5

When the shield tunnel passes through the researchregion the excess pore pressure gradually dissipates and theconsolidation deformation of the ground surface occurs Itcan be calculated as follows [39]

Sp2 hw minus R( 1113857kyt

2π

radici2

(15)

where Sp2 is the SS value caused by the excess pore pressuredissipation ky is the weighted average of the vertical per-meability coefficient (md) of the overlying soil layers i2 isthe settlement trough width hw is the depth of the un-derground water level from the tunnel axis (m) and t is thedissipation time of the excess pore pressure (d) e dissi-pation time is related to the average excess pore pressure Pand the average compression modulus Es of the soil skeletonas follows

t

2π

radickHP

Esky

(16)

When considering situations in which foundation re-inforcement measures are taken the term Es can be replacedwith the composite foundation formula Esp [1 +m(nminus 1)]αEs where m is the replacement rate n is the pile-soilmodulus ratio and α is the compression modulus ratiobetween the piles and the soil According to engineeringexperience Espasymp 15ndash60Es for saturated loess strata theaverage value is Esp 40Es

When there are nomeasured data the average additionalpressure (P) at the excavation surface is Pplusmn20 kPa eaverage excess pore pressure (P (P1 +P2)2) in the satu-rated soil around the tunnel during shield tunnel advancingcan also be approximately calculated by Xu [40]

(1) When N (K0primePvprime+Pw minus Pi)cugt 0

P 05cu (N + 1 + a6

radic) + a

6

radic R

H1113874 1113875

2exp(N minus 1)1113890 1113891

(17)

(2) When N (K0primePvprime+Pw minus Pi)cult 0


P 05cu (a6

radicminus N minus 1) + a

6

radic R

H1113874 1113875

2exp(minusN minus 1)1113890 1113891

(18)

where cu is the undrained shear strength a is theHenkel coefficient for saturated loess a 012 andthe other parameters have the same physicalmeaning as for (1) Now assuming the excess porepressure ratio ψ PP0 the SS caused by the excesspore pressure dissipation is written as

Sp2 hw minus R( 1113857P

Es

hw minus R( 1113857ψP0

Es

(19)

223 Consolidation Deformation Caused by the Decline ofthe Underground Water Level e underground water leveldeclines when the drainage facilities of the undergroundstructure of the shield tunnel fail which leads to the long-term consolidation settlement of the ground surface Sup-pose that the initial underground water level below thesurface is dw andH0 is the reference depth below the surfacee initial water level the final water level and the decline ofthe water level are h1 h2 and Δh h1 minus h2 respectively Es1 isthe soil compression modulus after consolidation (MPa)and Es2 is the compression modulus of the saturated soil(MPa) e water level decline and the effective stress of soilchanges are illustrated in Figure 6

According to Figure 6 based on one-dimensional con-solidation theory the consolidation deformation (S1) caused bythe water level decline within the scope of Δh and the com-pression deformation (S2) caused by the increase of the ef-fective stress within the scope of h2 can be calculated as follows

S1 05cwΔh

2

Es1

S2 cwΔh H0 minus Δh minus dw( 1113857

Es2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(20)

Assume that the average densities of loess strata and porewater are cl 19 kNm3 and cw 98 kNm3 respectivelyandH0 is the calculation depth of the additional stress due tothe water level decline According to the theory of soilmechanics suppose that cwΔh 02clH0 and the term H0 isapproximately equal to 3Δh then the total consolidationsettlement (up3) at the initial water level caused by the waterlevel decline is

up3 ζcwΔhΔh2Es1

+2Δh minus dw

Es21113890 1113891 (21)

When 2Δhminus dw le 0 take 2Δhminus dw 0 when Δhgthw +Rtake Δh hw +R If there are no measured values the termEs1 is equal to 12Es2 ζ is the settlement adjustment coef-ficient which considers the loess structural and hardeningeffect after the water loss in the loess the term ζ 03 is usedin the saturated loess area e decline in the ratio of thewater level can be defined as θΔhhw while equation (21)can be expressed as a function of θ as follows

up3 ζcwΔhθhw

2Es1+

(2θ + 1)hw minus H

Es21113890 1113891 (22)

Assume that the stratum volume loss (V) due to theconsolidation settlement is equal to 2Rup3 while the rela-tionship among the maximum SS (Sp3) up3 and V can beexpressed as follows

up3 V

2π

radiciz3

Sp3 V2π

radici3

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(23)

According to the theory proposed by Han [38] therelationship between the deep layer settlement trough width(iz3) and the surface settlement trough width (i3) can bewritten as iz3 (1minus 065z3H) i3 and the term z3 dw Basedon the above principles the MSS value of Sp3 caused byconsolidation can be obtained as follows

dwR

X

Y

HP2

P1

hw

Natrual ground

Undergroundwater level

Increase zoneof excess pore

pressure

Decrease zoneof excess pore

pressure

Figure 5 Distribution of excess pore water pressure

dw∆h

h 1

h 2

R

H0

ES1

ES2

Natrual ground

Initial water level

Final water levelγw∆h

γw∆h

Figure 6 Additional stress caused by the decline of the under-ground water level


Sp3 iz3i3

up3 up3 1 minus 065dw

H1113888 1113889 (24)

224 Seismic Surface Settlement Caused by the Train Vi-bration Loading During the operational period of thesubway the large and medium pores of saturated loess in thetunnel foundation collapse under the train vibration cyclicloading is causes a certain fatigue damage and com-paction phenomenon of the tunnel foundation and thesettlement of the overlying soil and tunnel occurs Based onextensive dynamic triaxial cyclic testing of saturated loessstrata of the Xirsquoan subway Zhang [41] reported that thedynamic stress ratio Rd 0026sim0192 when the vibrationfrequency f 20Hz In addition the author reported thefollowing empirical equation that relates the loess residualstrain (εc

s) and Rd

εcs 2cR

md

arctan 20244Rmd( 1113857

π (25)

where c 0333 m 1259 and Rd 05σdσ3 σd is theamplitude of the dynamic stress (kPa) and σ3 is the initialconfining pressure of the soil (kPa)

According to the existing empirical analyses the influ-ence depth of the dynamic stress load (hd) is reported to asbeing between 30 and 50m beneath the tunnel foundationIn this way the seismic SS of the saturated loess under thetunnel foundation can be obtained It should be noted thatwhen the tunnel foundation is unsaturated loess the seismicdeformation does not exist Based on the theory of stratumvolume loss the volume loss due to seismic deformation (V)is equal to 2Rhdεc

s and the seismic settlement at the tunnelcrown can be obtained as follows

up4 V

2π

radiciz4

2Rhdε

cs

2πradic

iz4051cRR

md arctan 20244R

md( 1113857hd

iz4

(26)

where iz4 is the width of the settlement trough at depthz4 H-R i4 is the width of the surface settlement troughcaused by the seismic settlement According to the theoryproposed by Han [38] iz4 [1minus 065(H-R)H)]i4eMSS ofSp4 caused by the train vibration loading can be written asfollows

Sp4 iz4

i4up4 up4 1 minus 065

H minus R

H1113874 1113875 up4 035 + 065

R

H1113874 1113875

(27)

23 Modified Peck Curve of the Surface Settlement Trough

231 Surface Settlement Prediction during the ConstructionPeriod It is assumed that the convergence form of tunnelsections is ldquocrescentrdquo shaped as shown in Figure 2 and thevolume loss caused by the convergence of tunnel sectionsbeneath undrained conditions during the shield tunnel

construction is equal to that caused by the SS According tothe concept of volume loss [12] and the Peck formula [42]the MSS during the shield construction period under dif-ferent influencing factors can be estimated e relationshipamong Sc volume loss (Vl) surface settlement trough width(i) shield tunnel excavation radius (R) and tunnel vaultsettlement (uc) during the construction period is written asfollows

Sc VlπR

22π

radici

πR

2 4ucR + u2c1113872 1113873

4R2

2πradic

i0313 4ucR + u

2c1113872 1113873

i (28)

By taking the aforementioned five influencing factorsinto consideration the estimated expressions of the cu-mulative MSS (Sc) and the cumulative tunnel vault settle-ment (uc) during the construction period can be obtained asfollows

Sc 11139445

j1Scj

uc 11139445

j1ucj

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(29)

where Scj and ucj are the MSS value and the tunnel vault set-tlement during the construction period respectively j 1sim5 isthe number of influencing factors and i is the SS trough width(m) Based on reported experiences the SS trough width i kHwhere k is the coefficient of the SS trough width

e formula for estimating the SS trough curve (Sxc)during the construction period can be obtained byintegrating the aforementioned five factors (the fivefactors are shown in Section 21 which are the settlementinduced by inadequate shield support pressure thesettlement induced by insufficient grouting at the shieldtail the settlement induced by insufficient groutingpressure the settlement induced by overexcavation of theshield and the settlement induced by improper shieldattitude respectively) as follows

Sxc Sc

minusx2

2i21113890 1113891 (30)

where x is the horizontal distance between the surface pointand the tunnel axis (m)

232 Surface Settlement Trough Prediction during thePostconstruction Period Based on Peckrsquos formula [42] the SSduring the postconstruction period by considering the abovefour influencing factors (the four factors are shown in Section22 which are the recompression settlement of the soil in theloosened circle the consolidation deformation caused by thedissipation of excess pore pressure the consolidation defor-mation caused by the decline of the underground water leveland the seismic SS caused by the train vibration loading re-spectively) can be obtained as follows


Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)

where i1 i2 i3 and i4 are the width of the SS trough underdifferent influencing factors during the postconstructionperiod

233 Total Surface Settlement Trough PredictionAccording to the SS characteristics during the constructionperiod and the postconstruction period the estimatingformula for the SS curve with consideration of the abovenine influencing factors based on Peckrsquos formula is obtainedas follows

Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)

3 Sensitivity Analysis of the MSS Inducement

31 Determination of the Influencing Factors In order tofurther explore the nine factors (shield support pressureratio β grouting filling rate ω grouting pressure ratio λoverexcavation rate κ slope of the shield tunneling machinedeviating from the central axis ξ the ratio of the loosenedcircle radius η excess pore pressure ratio ψ decline in theratio of the water level θ and dynamic stress ratio Rd) withrespect to their influence degree of the MSS it is necessary tocarry out a single-factor sensitivity analysis For this studyXirsquoan Metro line 2 is taken as the engineering backgroundand the soil stratum of the tunnel is described as follows (1)miscellaneous fill (05sim120m) (2) plain fill (00sim120m) (3)new loess (00sim90m) (4) saturated loess (00sim50m) (5)ancient soil (20sim50m) (6) old loess (30sim60m) and (7)silty clay (more than 20m) e underground water level is9sim12m below the ground surface and the tunnel vault isapproximately 1sim8m below the underground water levele shield tunnel crosses the silty clay layer and above the

tunnel crown is the saturated loess e physical indexes andmechanical parameters of the soil stratum are presented inTable 1 [43]

e tunnel axis of Xirsquoan Metro line 2 is buried 14sim22mbelow the ground surface with an average of H 19m thetunnel excavation diameter is D 62m the length of theshield tunneling machine L 868m the physical gap of theshield tunneling machine is Gp 160mm the controlstandards for the overexcavation rate are κ minus20sim+20and the slope of the shield tunneling machine deviating fromthe central axis is ξ minus30sim+30 According to the en-gineering experiences of the XirsquoanMetro the variation rangeof the aforementioned influencing factors and other cal-culation parameters can be determined these are presentedin Table 2

32 Determination and Analysis of the Sensitivity IndexIn order to accurately describe the influence degree ofvarious factors on the MSS the sensitivity coefficient (M) isintroducede sensitivity index of a certain factor (F) to theMSS is MF

MF (ΔSS)

ΔFF (33)

where ΔS is the difference between the MSS of a certaininfluencing factor and its reference value F S is the MSSunder the reference influencing factor ΔSS is the variationratio of the MSS F is the reference value of the influencingfactor ΔF is the variation of the influencing factor F and ΔFF is the variation rate of the influencing factor WhenMFgt 0it means that the MSS is positively correlated with theinfluencing factor F when MFlt 0 it means that the MSS isinversely related to the influencing factor F

According to formula (33) the sensitivity coefficients ofthe nine factors mentioned above are defined as followsMβMωMλMκMξMηMψMθ andMRd these factors can becalculated according to formulas (34) to (42) in Table 3

Based on equation (32) and Table 2 the calculated MSSand the average sensitivity indexes with different influencingfactors are presented in Figure 7e curves of ΔSS and ΔFF are illustrated in Figure 8

From Figures 7 and 8 it can be seen that

Table 1 Physical and mechanics parameters of the tunnelrsquos surrounding soils

Soil types w () cd(kNm3) e0

crsquo(kPa) φrsquo (deg) cu

(kPa) K0primeK20 times10minus5

(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)

Miscellaneousfill 225 148 084 mdash mdash mdash mdash mdash mdash 56 054

Plain fill 238ndash258 139ndash148 086ndash096 mdash mdash 15 070 mdash mdash 53ndash60 05ndash07New loess 246ndash254 149ndash155 076ndash083 35ndash36 241ndash260 20ndash24 065ndash063 12ndash35 109ndash216 68ndash76 039ndash044Saturated loess 255 157 078 35 222 26 mdash mdash mdash 60 050Ancient soil 228ndash249 158ndash164 066ndash073 40 250ndash267 25ndash26 062ndash064 292 096 58ndash72 042ndash052Old loess 228ndash239 160ndash164 066ndash070 32ndash46 201ndash264 22ndash30 060ndash069 042ndash61 012ndash219 69ndash71 040ndash042Silty clay 220ndash225 164ndash166 064ndash066 42ndash50 273ndash293 23ndash35 059ndash061 001ndash14 106ndash192 72ndash78 038ndash042Note the physical meaning of the parameters is namely w water content cd dry bulk density Es compression modulus e0 pore ratio cprime and φprime index ofeffective shear strength mv

prime compression coefficient of remorphic loess in the disturbed area K0prime side pressure coefficient K20 permeability coefficient andCv consolidation coefficient under nondrainage conditions


(1) e MSS tends to decrease with the increase of β ωand λ indicating that the rate of change of thesethree influencing factors is inversely correlated withthe change rate of the SS Six influence factors (ie κη ξ ψ θ and Rd) have positive relationships with theMSS

(2) From the slope of the relationship curve between theincremental change rate of (ΔSS) and the incre-mental change rate of influencing factors (ΔFF) itshows that during the construction period thechange of the grouting filling rate (ω) is the mostsensitive influence factor to the MSS followed by thegrouting pressure ratio (λ)

(3) During the postconstruction period the ratio of theloosened circle radius (η) has the most sensitiveinfluence on the MSS followed by the declineamount ratio of the water level (θ) It can be seen thatthe grouting effect of the shield tail and the

disturbance degree to the surrounding soil duringthe construction period of shield tunneling havesignificant influence on the MSS

(4) Table 3 shows that the average sensitivity index of thenine influencing factors can be ordered from highestto lowest ie Mη 9897 Mθ 1120 Mω 400MRd 214 Mλ 130 Mβ 115 Mψ 100Mκ 099 and Mξ 099 is order shows that thedisturbance degree to the surrounding soil duringthe shield tunnel advancing has the most significantinfluence on the MSS When the declining ratio forthe water level is high due to seepage of liningsegments the long-term SS during the post-construction period is also significant During theconstruction period of shield tunneling the groutingfilling effect and the control of grouting pressurehave great influence on the SS When the tunnelfoundation and track are not reinforced the SS

Table 2 Numerical analysis schemes for a single factor

Influencingfactors Parameterrsquos range Calculate required parameters

β 03 04 05 08 09 H 19m RD2 31m Gp 160mm i 817mEs1 66MPa Es2 55MPa Eu 256MPa e0 076 ]u 050 ]0 039 c 19 kN

m3 K0prime 064cu 209 kPa cprime 355 kPa φprime 244degP0 cHminus Pw 281 kPa Pw 800 kPa

Pv c(Hminus hw) + cprime(hw minusR) 2531 kPa K0primePvprime+Pw 242 kPa

ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028

hw 80m when Δhle 05(Hminus hw)Δh 05(Hminus hw) 55m and ΔhleR+ hw 111mθ 069 094 119 131 138Rd 003 008 0a13 016 02 hd 3m

Table 3 Sensitivity indexes of different influencing factors of the MSS

Mβ (ΔSc1Sc1)(Δββ) (34) Mη (ΔSp1Sp1)(Δηη) (39)Mω (ΔSc2Sc2)(Δωω) (35) Mψ (ΔSp2Sp2)(Δψψ) (40)Mλ (ΔSc3Sc3)(Δλλ) (36) Mθ (ΔSp3Sp3)(Δθθ) (41)Mκ (ΔSc4Sc4)(Δκκ) (37) MRd (ΔSp3Sp3)(ΔRdRd) (42)Mξ (ΔSc5Sc5)(Δξξ) (38)

ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd

Figure 7 MSS values under different influencing factors


ΔSc1Sc1 = ndash01183 (Δββ) ndash07416

ndash10ndash10ndash09ndash09ndash08ndash08ndash07

00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)

ΔSc3Sc3 = ndash00989 (Δλλ) ndash08832

ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)

ΔSp3Sp3 = 14641 (Δθθ) ndash22209

ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)

ΔSp4Sp4 = 24725 (ΔRdRd) ndash10246

ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)

Figure 8 Relationship between theMSS ratio and the influencing factor ratios (a)ΔSc1Sc1minusΔββ (b)ΔSc2Sc2minusΔωω (c)ΔSc3Sc3minusΔλλ (d)ΔSc4Sc4 minus Δκκ (e) ΔSc5Sc5 minus Δξξ (f) ΔSp1Sp1 minus Δηη (g) ΔSp2Sp2 minusΔψψ ΔSp3Sp3minusΔθθ and (i) Sp4Sp4 minus ΔRdRd


caused by the train vibration loading cannot be ig-nored e dissipation of the excess pore waterpressure and the adjustment of the shield attitude areall related to the control technology during theconstruction period of shield tunneling

4 Conclusion

(1) e SS during the construction period and thepostconstruction period induced by the shield tun-neling construction mainly includes nine influencingfactors ① inadequate shield support pressure ②insufficient grouting filling in the shield tail ③ in-sufficient grouting pressure ④ overexcavation byshield yawing ⑤ improper shield attitude ⑥ therecompression of the soil in the loosing circle aroundthe tunnel ⑦ the dissipation of excess pore waterpressure induced by the shield tunneling advancing⑧ the surrounding soil consolidation due to thefailure of waterproofing techniques used behind thelining and the decline in the underground waterlevel and⑨ the foundation settlement caused by thetrain vibration loading

(2) e average sensitivity index of the above nineinfluencing factors can be ordered from highest tolowest Mη 9897 (the ratio of the loosened circleradius η)Mθ 1120 (decline in the ratio of the waterlevel θ) Mω 400 (grouting filling rate ω)MRd 214 (dynamic stress ratio Rd) Mλ 130(grouting pressure ratio λ)Mβ 115 (shield supportpressure ratio β) Mψ 100 (excess pore pressureratio ψ) Mκ 099 (overexcavation rate κ) andMξ 099 (slope of the shield machine deviatingfrom the central axis ξ) It indicates that the largestinfluencing factor on surface settlement is the ratio ofthe loosened circle radius and the smallest one is theslope of the shield tunneling machine deviating fromthe central axis

(3) In summary the disturbance degree of the sur-rounding soil during the shield tunnel advancing hasthe most significant influence on the MSS e de-cline of the underground water level has the secondlargest influence on the SSe grouting fill effect hasthe third greatest influence on the SS e groutingpressure at the shield tail and the shield supportpressure at the shield head have the fifth and sixthlargest influences on the SS When the tunnelfoundation and the track are not reinforced the SScaused by the train vibration loading cannot be ig-nored e dissipation of the excess pore waterpressure overexcavation rate and shield machinedeviating from the central axis have the seventheighth and ninth influence on the SS

(4) When the shield tunnels pass through the saturatedloess stratum the disturbance degree on the sur-rounding soil during shield advancing should be wellcontrolled e pre-reinforcement measures for thesaturated soil within 3sim5m around the tunnel should

be taken and the appropriate antiseepage and vi-bration reduction measures should be taken for thelining segments and the track respectively

Data Availability

No data models or code were generated or used during thestudy

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

e author would like to extend their gratitude to theNational Natural Science Foundation of China (no51678484) and the Research Fund of the State Key Labo-ratory of Eco-hydraulics in Northwest Arid Region XirsquoanUniversity of Technology (2019KJCXTD-12) who fundedthis research

References

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

[2] 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

[3] 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

[4] L-ZWang L-L Li and X-J Lv ldquoComplex variable solutionsfor tunneling-induced ground movementrdquo InternationalJournal of Geomechanics vol 9 no 2 pp 63ndash72 2009

[5] J Fu J Yang L Yan and S M Abbas ldquoAn analytical solutionfor deforming twin-parallel tunnels in an elastic half planerdquoInternational Journal for Numerical and Analytical Methods inGeomechanics vol 39 no 5 pp 524ndash538 2015

[6] A Abbas ldquoDrained and undrained response of deep tunnelssubjected to far-field shear loadingrdquo Tunnelling and Under-ground Space Technology vol 25 no 1 pp 21ndash31 2010

[7] K H Park ldquoElastic solution for tunneling-induced groundmovements in claysrdquo International Journal of Geomechanicsvol 4 no 4 pp 310ndash318 2004

[8] L Ding L Ma H Luo M Yu and X Wu ldquoWavelet analysisfor tunneling-induced ground settlement based on a sto-chastic modelrdquo Tunnelling and Underground Space Technol-ogy vol 26 no 5 pp 619ndash628 2011

[9] X L Yu and J M Wang ldquoGround movement prediction fortunnels using simplified procedurerdquo Tunnelling and Under-ground Space Technology vol 26 no 3 pp 462ndash471 2011

[10] D Huang and B Zeng ldquoInfluence of double-o-tube shieldrolling on soil deformation during tunnelingrdquo InternationalJournal of Geomechanics vol 17 no 11 Article ID 040171052017

[11] Z Zhang M Huang X Xi et al ldquoComplex variable solutionsfor soil and liner deformation due to tunneling in claysrdquoInternational Journal of Geomechanics vol 18 no 7 ArticleID 04018074 2018

[12] C Gonzalez and C Sagaseta ldquoPatterns of soil deformationsaround tunnels Application to the extension of Madrid


Metrordquo Computers and Geotechnics vol 28 no 6-7pp 445ndash468 2001

[13] A Verruijt ldquoDeformations of an elastic half plane with acircular cavityrdquo International Journal of Solids and Structuresvol 35 no 21 pp 2795ndash2804 1998

[14] A Verruijt and J R Booker ldquoComplex variable analysis ofMindlinrsquos tunnel problemrdquo in Proceedings of the BookerMemorial Symposium Developments in Teoretical Geo-mechanics pp 3ndash22 Balkema Rotterdam Netherlands 2000

[15] A Verruijt and O E Strack ldquoBuoyancy of tunnels in softsoilsrdquo Geotechnique vol 58 no 6 pp 513ndash515 2008

[16] J Fu J Yang H Klapperich et al ldquoAnalytical prediction ofground movements due to a nonuniform deforming tunnelrdquoInternational Journal of Geomechanics vol 16 no 4 ArticleID 04015089 2016

[17] W-I Chou and A Bobet ldquoPredictions of ground deforma-tions in shallow tunnels in clayrdquo Tunnelling and UndergroundSpace Technology vol 17 no 1 pp 3ndash19 2002

[18] K-H Park ldquoAnalytical solution for tunnelling-inducedground movement in claysrdquo Tunnelling and UndergroundSpace Technology vol 20 no 3 pp 249ndash261 2005

[19] J F Liu and H Z Zhang ldquoSemianalytical solution and pa-rameters sensitivity analysis of shallow shield tunneling-in-duced ground settlementrdquo Advances in Materials Science andEngineering vol 2017 Article ID 3748658 8 pages 2017

[20] D Lu F Kong X Du C Shen Q Gong and P Li ldquoA unifieddisplacement function to analytically predict ground defor-mation of shallow tunnelrdquo Tunnelling and Underground SpaceTechnology vol 88 pp 129ndash143 2019

[21] C Shen and Z Zhu ldquoAnalytical method for evaluating theground surface settlement caused by tail void groutingpressure in shield tunnel constructionrdquo Advances in CivilEngineering vol 2018 Article ID 3729143 10 pages 2018

[22] Y-S Fang C-T Wu S-F Chen and C Liu ldquoAn estimationof subsurface settlement due to shield tunnelingrdquo Tunnellingand Underground Space Technology vol 44 pp 121ndash129 2014

[23] M D Shen Z W Zhou and S J Zhang ldquoEffect of stress pathon mechanical behaviours of frozen subgrade soilrdquo RoadMaterials and Pavement Design vol 2021 no 8 pp 1ndash302020

[24] S-L Shen H-N Wu Y-J Cui and Z-Y Yin ldquoLong-termsettlement behaviour of metro tunnels in the soft deposits ofShanghairdquo Tunnelling and Underground Space Technologyvol 40 no 1 pp 309ndash323 2014

[25] Y-S Yin L Ma Y-J Du and S-L Shen ldquoAnalysis of ur-banisation-induced land subsidence in Shanghairdquo NaturalHazards vol 63 no 2 pp 1255ndash1267 2012

[26] H-N Shen R-Q Huang W-J Sun et al ldquoLeaking behaviorof shield tunnels under the Huangpu River of Shanghai withinduced hazardsrdquo Natural Hazards vol 70 no 2pp 1115ndash1132 2014

[27] C-Y Shen S-L Shen J Han G-L Ye and S HorpibulsukldquoHydrogeochemical environment of aquifer groundwater inShanghai and potential hazards to underground infrastruc-turesrdquo Natural Hazards vol 78 no 1 pp 753ndash774 2015

[28] C W W Ng G B Liu and Q Li ldquoInvestigation of the long-term tunnel settlement mechanisms of the first metro line inShanghairdquo Canadian Geotechnical Journal vol 50 no 6pp 674ndash684 2013

[29] 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

[30] G Q Cui Dynamic Constitutive Model for Saturated Loessand Deformation Analysis for Soil Around Subway

TunnelXirsquoan University of Architecture amp Technology XirsquoanChina 2014

[31] Z W Zhou W Ma S J Zhang Y H Mu and G Y LildquoExperimental investigation of the path-dependent strengthand deformation behaviours of frozen loessrdquo EngineeringGeology vol 265 Article ID 105449 2020

[32] L Zheng Y Gao Y Zhou T Liu and S Tian ldquoA practicalmethod for predicting ground surface deformation inducedby the artificial ground freezing methodrdquo Computers andGeotechnics vol 130 Article ID 103925 2021

[33] H Cai S Li Y Liang Z Yao and H Cheng ldquoModel test andnumerical simulation of frost heave during twin-tunnelconstruction using artificial ground-freezing techniquerdquoComputers and Geotechnics vol 115 Article ID 103155 2019

[34] J Zhou W Zhao Y Tang et al ldquoPractical prediction methodon frost heave of soft clay in artificial ground freezing withfield experimentrdquo Tunnelling and Underground Space Tech-nology vol 107 Article ID 103647 2021

[35] K M Lee and R K Rowe ldquoSettlement due to tunneling PartII -Evaluation of a prediction techniquerdquo Canadian Geo-technical Journal vol 29 no 5 pp 941ndash954 1992

[36] Z D LiuMechanics and Engineering of Loess Shanxi Scienceand Technique Publishing House Xirsquoan China 1997

[37] R K Rowe K Y Lo and G J Kack ldquoA method of estimatingSS above tunnels constructed in soft groundrdquo CanadianGeotechnical Journal vol 20 no 8 pp 11ndash22 1983

[38] X Han Te Analysis and Prediction of Tunnelling-InducedBuilding Deformation Xirsquoan University of Technology XirsquoanChina 2006

[39] J Liu and X Hou Shield Tunneling China Railway PressBeijing China 1991

[40] F Xu ldquoe analysis of pore water pressure and groundsettlement caused by shield tunneling and deep excavation insoft clayrdquo Doctorial thesis Tongji University ShanghaiChina 1991

[41] K Zhang Vibration and Settlement of Loess Due to SubwayMoving Loads Xirsquoan University of Architecture amp Technol-ogy Xirsquoan China 2011

[42] R B Peck ldquoDeep excavations and tunneling in soft groundrdquoin Proceedings of the 7th International Conference on SoilMechanics and Foundation Engineering pp 225ndash290 Bal-kema Rotterdam Netherlands 1969

[43] C Zhu and N Li ldquoPrediction and analysis of surface set-tlement due to shield tunneling for Xirsquoan Metrordquo CanadianGeotechnical Journal vol 54 no 4 pp 529ndash546 2017

[44] Zhang Study on the Laws of Surface Settlement Induced byShield Construction and Control Technology of Xian SubwayTunnelXian University of Science and Technology XirsquoanChina 2011


nonuniform stress field Lu et al [20] proposed a unifieddisplacement function of the cross section of a circularshallow tunnel under complex geological and constructionconditionsis function is expressed by a Fourier series andcan reflect the horizontal and vertical asymmetrical defor-mation behaviors of the tunnel cross section Shen and Zhu[21] proposed an analytical method using the virtual imagetechnique and Fourier transform solutions to estimate theground SS caused by the tail void grouting pressure in shieldtunnel construction Fang et al [22] reported that a normalprobability function can be extended to estimate the SS dueto shield tunneling which can consider various types ofshield machines depths and diameters Zhang et al [11]presented an analytical solution by the complex variablemethod to predict the soil deformation due to tunneling inclay this approach considers the linear stiffness influenceand the nonuniform convergence boundary condition

e analytical methods that are described above sys-tematically consider the stratum conditions and the shieldconstruction technologies However when predicting the SSin the postconstruction period it is difficult to consider thevariable features of unsaturated-saturated loess strata suchas the underground water level decline the dissipation ofpore water pressure the creep deformation of the sur-rounding soil and the train vibration loading e waterseepage issues and the causes of the uneven settlement of thetunnel in Shanghai Metro lines 1 and 2 have been widelyinvestigated and reported In addition the SS that has beeninduced by the additional load the underground con-struction and fall of the ground water level has also beenstudied by Shen et al [23ndash27] Ng et al [28] summarized thesettlement measurements of Shanghai Metro line 1 from1994 to 2007 and the relationship between groundpumping foundation soil compression and the tunnelsettlement has been reported Soga et al [29] studied thetunnel deformation caused by the dissipation of excess porewater pressure of the soil and the aging of grouting materialsafter lining segments in the London subway A theory forcalculating the SS has been proposed which considers theinteractions between the soil and the lining Based on dy-namic load testing the critical dynamic stress ratio and thedynamic stress amplitude of saturated loess were proposedby Cui [30] and the SS caused by the subway vibrationloading has been calculated

In addition the surface settlement induced by freezingconstruction is becoming a trending issue in the freeze-thawzone Zhou et al [31] and Shen et al [23] studied the path-dependent mechanical behaviours of frozen loess based onthe experimental investigation Zheng et al [32] proposed apractical method to simulate and predict the ground surfacedeformation during the entire artificial ground freezingconstruction process A model test system and numericalmethod were used by Cai et al [33] to simulate horizontalground freezing on the heaving displacement of twin tun-nels Zhou et al [34] published a segregation potential modelto predict the frost heaves during freezing construction

From the above valuable results have been reported onanalytical methods for the SS induced by undergroundconstruction however there is still no systematic research to

explore the influence degrees of different factors on the SSwhich is essential for determining the prioritization of SScontrol measures On the basis of summarizing previouslyreported analytical methods and taking the shield con-struction of the Xirsquoan Metro in the loess stratum as theresearch background the calculation methods of surfacesettlement induced by nine factors were proposed and aparametric sensitivity analysis of the maximum surfacesettlement (MSS) induced by each individual influencefactor was conducted e resulting sensitivity indexes aresorted in order to provide technical guidance for SS controlsduring the shield tunneling construction

2 Estimation of the MaximumSurface Settlement

21 Maximum Settlement Estimation of the Tunnel Vaultduring theConstructionPeriod Due to the improper controlof the shield excavation the factors inducing the settlementof the tunnel vault mainly include (1) inadequate shieldsupport pressure (2) insufficient grout filling in the shieldtail (3) insufficient grouting pressure (4) overexcavation bythe shield yawing and (5) improper shield attitude emethods to calculate the volume loss of the stratum and theSS generated when the tunnel vault deformation is inducedby these factors are summarized in the following

211 Tunnel Vault Settlement Induced by Inadequate ShieldSupport Pressure During the tunneling of the earth pres-sure-balanced shield machine the shield support pressure(Pi) plays a dynamic balancing role on the lateral soilpressure (K0P0 or K0primePv

prime+Pw) at the excavation surfaceWhen the lateral soil pressure between the shield head andthe excavation surface is unbalanced it inevitably leads tothe ground uplift and settlement When Pi K0P0 (seeFigure 1(a)) the lateral soil pressure is in an equilibriumstate and little additional stress occurs on the excavationsurface When the shield support pressure is lower than thelateral earth pressure (PiltK0P0 see Figure 1(b)) the tunnelvault settlement occurs When the shield support pressure ishigher than the lateral earth pressure (PigtK0P0 seeFigure 1(c)) the tunnel vault and surface uplift isprinciple is illustrated in Figure 1

In order to determine the tunnel vault settlement in-duced by an inadequate shield support pressure underundrained conditions Lee and Rowe [35] proposed a two-dimensional analytical solution by considering the three-dimensional elastic-plastic deformation at the excavationsurface e shield support pressure ratio β Pi(K0primePv

prime+Pw)is introduced into the above solution and the tunnel vaultsettlement (uc1) formula can be written as follows

uc1 ΩR K0primePV

prime + Pw minus Pi( 1113857

2Eu

ΩR(1 minus β) K0primePV

prime + Pw( 1113857

2Eu

(1)

where uc1 is the tunnel vault settlement and Ω is the hor-izontal displacement coefficient at the shield excavationsurface which is determined by a 3D numerical simulation





E0 2718Es

e0 (2)


Eu

E01 + ]u

1 + ]0 (3)


Eu 2718Es 1 + ]u( 1113857

1 + ]0( 1113857e0 (4)






K0P0

Balance

Shield machine

Pi+ = 0

(a)

K0P0 Pi

Settlement

Shield machineAddi

tiona

l stre

ss

+ =

(b)

K0P0

Uplift

Shield machine

PiAd

ditio

nal s

tress

+

(c)







uc3 13sim14

1113874 1113875 times R 1 minus

1


1113971

⎡⎢⎣ ⎤⎥⎦ (6)




uc4 2

2R2 1 minus

1πarccos

κL

2R1113874 1113875 +

κL

2π

4R2

minus κ2L21113969

1113971


(7)


d d



Gap


Tail void

Lining


Tunnel heading


D =

d +

2∆

+ δ




uc5 Lξ (8)







(9)

Natural ground


Pv

Ph


Horizontal stress

Surrounding soil

Ph

Pil lt Pv

R

Surface settlement

Lining

Excavationboundary

(a)

Pil gt Pv


Pil

Pv

Ph


Horizontal stress

Surrounding soil

Ph

R

Lining

Excavationboundary

Surface heave

Natural ground

(b)


Se

Monitoring point

uc4

R

Crown settlement


Yawing angle

αShield axis

Shield length (L)

δ0-yawingdistance

Yawingdistance

SV δ 0

δ 0

SHθ0

θ0

Equivalent








Pil + ctanφ1113896 1113897


(10)



tan φ (11)



21113876 1113877 (12)


2up1 V

2π

radiciz1

Sp1 V2π

radici1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)



H1113874 1113875 2up1 035 + 065

R0

H1113876 1113877 (14)





2π

radici2

(15)


t

2π

radickHP

Esky

(16)




P 05cu (N + 1 + a6

radic) + a

6

radic R

H1113874 1113875

2exp(N minus 1)1113890 1113891

(17)



P 05cu (a6


6

radic R

H1113874 1113875


(18)



Es


Es

(19)



S1 05cwΔh

2

Es1


Es2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(20)


up3 ζcwΔhΔh2Es1

+2Δh minus dw

Es21113890 1113891 (21)


up3 ζcwΔhθhw

2Es1+

(2θ + 1)hw minus H

Es21113890 1113891 (22)


up3 V

2π

radiciz3

Sp3 V2π

radici3

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(23)


dwR

X

Y

HP2

P1

hw

Natrual ground



pressure


pressure


dw∆h

h 1

h 2

R

H0

ES1

ES2

Natrual ground

Initial water level


γw∆h



Sp3 iz3i3


H1113888 1113889 (24)


s) and Rd

εcs 2cR

md

arctan 20244Rmd( 1113857

π (25)




up4 V

2π

radiciz4

2Rhdε

cs

2πradic

iz4051cRR

md arctan 20244R

md( 1113857hd

iz4

(26)


Sp4 iz4


H minus R

H1113874 1113875 up4 035 + 065

R

H1113874 1113875

(27)




Sc VlπR

22π

radici

πR

2 4ucR + u2c1113872 1113873

4R2

2πradic

i0313 4ucR + u

2c1113872 1113873

i (28)


Sc 11139445

j1Scj

uc 11139445

j1ucj

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(29)



Sxc Sc

minusx2

2i21113890 1113891 (30)




Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)



Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)






MF (ΔSS)

ΔFF (33)









(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)















ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References




















































E0 2718Es

e0 (2)


Eu

E01 + ]u

1 + ]0 (3)


Eu 2718Es 1 + ]u( 1113857

1 + ]0( 1113857e0 (4)






K0P0

Balance

Shield machine

Pi+ = 0

(a)

K0P0 Pi

Settlement

Shield machineAddi

tiona

l stre

ss

+ =

(b)

K0P0

Uplift

Shield machine

PiAd

ditio

nal s

tress

+

(c)







uc3 13sim14

1113874 1113875 times R 1 minus

1


1113971

⎡⎢⎣ ⎤⎥⎦ (6)




uc4 2

2R2 1 minus

1πarccos

κL

2R1113874 1113875 +

κL

2π

4R2

minus κ2L21113969

1113971


(7)


d d



Gap


Tail void

Lining


Tunnel heading


D =

d +

2∆

+ δ




uc5 Lξ (8)







(9)

Natural ground


Pv

Ph


Horizontal stress

Surrounding soil

Ph

Pil lt Pv

R

Surface settlement

Lining

Excavationboundary

(a)

Pil gt Pv


Pil

Pv

Ph


Horizontal stress

Surrounding soil

Ph

R

Lining

Excavationboundary

Surface heave

Natural ground

(b)


Se

Monitoring point

uc4

R

Crown settlement


Yawing angle

αShield axis

Shield length (L)

δ0-yawingdistance

Yawingdistance

SV δ 0

δ 0

SHθ0

θ0

Equivalent








Pil + ctanφ1113896 1113897


(10)



tan φ (11)



21113876 1113877 (12)


2up1 V

2π

radiciz1

Sp1 V2π

radici1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)



H1113874 1113875 2up1 035 + 065

R0

H1113876 1113877 (14)





2π

radici2

(15)


t

2π

radickHP

Esky

(16)




P 05cu (N + 1 + a6

radic) + a

6

radic R

H1113874 1113875

2exp(N minus 1)1113890 1113891

(17)



P 05cu (a6


6

radic R

H1113874 1113875


(18)



Es


Es

(19)



S1 05cwΔh

2

Es1


Es2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(20)


up3 ζcwΔhΔh2Es1

+2Δh minus dw

Es21113890 1113891 (21)


up3 ζcwΔhθhw

2Es1+

(2θ + 1)hw minus H

Es21113890 1113891 (22)


up3 V

2π

radiciz3

Sp3 V2π

radici3

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(23)


dwR

X

Y

HP2

P1

hw

Natrual ground



pressure


pressure


dw∆h

h 1

h 2

R

H0

ES1

ES2

Natrual ground

Initial water level


γw∆h



Sp3 iz3i3


H1113888 1113889 (24)


s) and Rd

εcs 2cR

md

arctan 20244Rmd( 1113857

π (25)




up4 V

2π

radiciz4

2Rhdε

cs

2πradic

iz4051cRR

md arctan 20244R

md( 1113857hd

iz4

(26)


Sp4 iz4


H minus R

H1113874 1113875 up4 035 + 065

R

H1113874 1113875

(27)




Sc VlπR

22π

radici

πR

2 4ucR + u2c1113872 1113873

4R2

2πradic

i0313 4ucR + u

2c1113872 1113873

i (28)


Sc 11139445

j1Scj

uc 11139445

j1ucj

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(29)



Sxc Sc

minusx2

2i21113890 1113891 (30)




Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)



Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)






MF (ΔSS)

ΔFF (33)









(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)















ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References





















































uc3 13sim14

1113874 1113875 times R 1 minus

1


1113971

⎡⎢⎣ ⎤⎥⎦ (6)




uc4 2

2R2 1 minus

1πarccos

κL

2R1113874 1113875 +

κL

2π

4R2

minus κ2L21113969

1113971


(7)


d d



Gap


Tail void

Lining


Tunnel heading


D =

d +

2∆

+ δ




uc5 Lξ (8)







(9)

Natural ground


Pv

Ph


Horizontal stress

Surrounding soil

Ph

Pil lt Pv

R

Surface settlement

Lining

Excavationboundary

(a)

Pil gt Pv


Pil

Pv

Ph


Horizontal stress

Surrounding soil

Ph

R

Lining

Excavationboundary

Surface heave

Natural ground

(b)


Se

Monitoring point

uc4

R

Crown settlement


Yawing angle

αShield axis

Shield length (L)

δ0-yawingdistance

Yawingdistance

SV δ 0

δ 0

SHθ0

θ0

Equivalent








Pil + ctanφ1113896 1113897


(10)



tan φ (11)



21113876 1113877 (12)


2up1 V

2π

radiciz1

Sp1 V2π

radici1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)



H1113874 1113875 2up1 035 + 065

R0

H1113876 1113877 (14)





2π

radici2

(15)


t

2π

radickHP

Esky

(16)




P 05cu (N + 1 + a6

radic) + a

6

radic R

H1113874 1113875

2exp(N minus 1)1113890 1113891

(17)



P 05cu (a6


6

radic R

H1113874 1113875


(18)



Es


Es

(19)



S1 05cwΔh

2

Es1


Es2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(20)


up3 ζcwΔhΔh2Es1

+2Δh minus dw

Es21113890 1113891 (21)


up3 ζcwΔhθhw

2Es1+

(2θ + 1)hw minus H

Es21113890 1113891 (22)


up3 V

2π

radiciz3

Sp3 V2π

radici3

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(23)


dwR

X

Y

HP2

P1

hw

Natrual ground



pressure


pressure


dw∆h

h 1

h 2

R

H0

ES1

ES2

Natrual ground

Initial water level


γw∆h



Sp3 iz3i3


H1113888 1113889 (24)


s) and Rd

εcs 2cR

md

arctan 20244Rmd( 1113857

π (25)




up4 V

2π

radiciz4

2Rhdε

cs

2πradic

iz4051cRR

md arctan 20244R

md( 1113857hd

iz4

(26)


Sp4 iz4


H minus R

H1113874 1113875 up4 035 + 065

R

H1113874 1113875

(27)




Sc VlπR

22π

radici

πR

2 4ucR + u2c1113872 1113873

4R2

2πradic

i0313 4ucR + u

2c1113872 1113873

i (28)


Sc 11139445

j1Scj

uc 11139445

j1ucj

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(29)



Sxc Sc

minusx2

2i21113890 1113891 (30)




Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)



Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)






MF (ΔSS)

ΔFF (33)









(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)















ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References


















































uc5 Lξ (8)







(9)

Natural ground


Pv

Ph


Horizontal stress

Surrounding soil

Ph

Pil lt Pv

R

Surface settlement

Lining

Excavationboundary

(a)

Pil gt Pv


Pil

Pv

Ph


Horizontal stress

Surrounding soil

Ph

R

Lining

Excavationboundary

Surface heave

Natural ground

(b)


Se

Monitoring point

uc4

R

Crown settlement


Yawing angle

αShield axis

Shield length (L)

δ0-yawingdistance

Yawingdistance

SV δ 0

δ 0

SHθ0

θ0

Equivalent








Pil + ctanφ1113896 1113897


(10)



tan φ (11)



21113876 1113877 (12)


2up1 V

2π

radiciz1

Sp1 V2π

radici1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)



H1113874 1113875 2up1 035 + 065

R0

H1113876 1113877 (14)





2π

radici2

(15)


t

2π

radickHP

Esky

(16)




P 05cu (N + 1 + a6

radic) + a

6

radic R

H1113874 1113875

2exp(N minus 1)1113890 1113891

(17)



P 05cu (a6


6

radic R

H1113874 1113875


(18)



Es


Es

(19)



S1 05cwΔh

2

Es1


Es2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(20)


up3 ζcwΔhΔh2Es1

+2Δh minus dw

Es21113890 1113891 (21)


up3 ζcwΔhθhw

2Es1+

(2θ + 1)hw minus H

Es21113890 1113891 (22)


up3 V

2π

radiciz3

Sp3 V2π

radici3

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(23)


dwR

X

Y

HP2

P1

hw

Natrual ground



pressure


pressure


dw∆h

h 1

h 2

R

H0

ES1

ES2

Natrual ground

Initial water level


γw∆h



Sp3 iz3i3


H1113888 1113889 (24)


s) and Rd

εcs 2cR

md

arctan 20244Rmd( 1113857

π (25)




up4 V

2π

radiciz4

2Rhdε

cs

2πradic

iz4051cRR

md arctan 20244R

md( 1113857hd

iz4

(26)


Sp4 iz4


H minus R

H1113874 1113875 up4 035 + 065

R

H1113874 1113875

(27)




Sc VlπR

22π

radici

πR

2 4ucR + u2c1113872 1113873

4R2

2πradic

i0313 4ucR + u

2c1113872 1113873

i (28)


Sc 11139445

j1Scj

uc 11139445

j1ucj

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(29)



Sxc Sc

minusx2

2i21113890 1113891 (30)




Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)



Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)






MF (ΔSS)

ΔFF (33)









(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)















ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References






















































Pil + ctanφ1113896 1113897


(10)



tan φ (11)



21113876 1113877 (12)


2up1 V

2π

radiciz1

Sp1 V2π

radici1

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(13)



H1113874 1113875 2up1 035 + 065

R0

H1113876 1113877 (14)





2π

radici2

(15)


t

2π

radickHP

Esky

(16)




P 05cu (N + 1 + a6

radic) + a

6

radic R

H1113874 1113875

2exp(N minus 1)1113890 1113891

(17)



P 05cu (a6


6

radic R

H1113874 1113875


(18)



Es


Es

(19)



S1 05cwΔh

2

Es1


Es2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(20)


up3 ζcwΔhΔh2Es1

+2Δh minus dw

Es21113890 1113891 (21)


up3 ζcwΔhθhw

2Es1+

(2θ + 1)hw minus H

Es21113890 1113891 (22)


up3 V

2π

radiciz3

Sp3 V2π

radici3

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(23)


dwR

X

Y

HP2

P1

hw

Natrual ground



pressure


pressure


dw∆h

h 1

h 2

R

H0

ES1

ES2

Natrual ground

Initial water level


γw∆h



Sp3 iz3i3


H1113888 1113889 (24)


s) and Rd

εcs 2cR

md

arctan 20244Rmd( 1113857

π (25)




up4 V

2π

radiciz4

2Rhdε

cs

2πradic

iz4051cRR

md arctan 20244R

md( 1113857hd

iz4

(26)


Sp4 iz4


H minus R

H1113874 1113875 up4 035 + 065

R

H1113874 1113875

(27)




Sc VlπR

22π

radici

πR

2 4ucR + u2c1113872 1113873

4R2

2πradic

i0313 4ucR + u

2c1113872 1113873

i (28)


Sc 11139445

j1Scj

uc 11139445

j1ucj

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(29)



Sxc Sc

minusx2

2i21113890 1113891 (30)




Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)



Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)






MF (ΔSS)

ΔFF (33)









(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)















ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References

















































P 05cu (a6


6

radic R

H1113874 1113875


(18)



Es


Es

(19)



S1 05cwΔh

2

Es1


Es2

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(20)


up3 ζcwΔhΔh2Es1

+2Δh minus dw

Es21113890 1113891 (21)


up3 ζcwΔhθhw

2Es1+

(2θ + 1)hw minus H

Es21113890 1113891 (22)


up3 V

2π

radiciz3

Sp3 V2π

radici3

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(23)


dwR

X

Y

HP2

P1

hw

Natrual ground



pressure


pressure


dw∆h

h 1

h 2

R

H0

ES1

ES2

Natrual ground

Initial water level


γw∆h



Sp3 iz3i3


H1113888 1113889 (24)


s) and Rd

εcs 2cR

md

arctan 20244Rmd( 1113857

π (25)




up4 V

2π

radiciz4

2Rhdε

cs

2πradic

iz4051cRR

md arctan 20244R

md( 1113857hd

iz4

(26)


Sp4 iz4


H minus R

H1113874 1113875 up4 035 + 065

R

H1113874 1113875

(27)




Sc VlπR

22π

radici

πR

2 4ucR + u2c1113872 1113873

4R2

2πradic

i0313 4ucR + u

2c1113872 1113873

i (28)


Sc 11139445

j1Scj

uc 11139445

j1ucj

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(29)



Sxc Sc

minusx2

2i21113890 1113891 (30)




Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)



Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)






MF (ΔSS)

ΔFF (33)









(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)















ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References

















































Sp3 iz3i3


H1113888 1113889 (24)


s) and Rd

εcs 2cR

md

arctan 20244Rmd( 1113857

π (25)




up4 V

2π

radiciz4

2Rhdε

cs

2πradic

iz4051cRR

md arctan 20244R

md( 1113857hd

iz4

(26)


Sp4 iz4


H minus R

H1113874 1113875 up4 035 + 065

R

H1113874 1113875

(27)




Sc VlπR

22π

radici

πR

2 4ucR + u2c1113872 1113873

4R2

2πradic

i0313 4ucR + u

2c1113872 1113873

i (28)


Sc 11139445

j1Scj

uc 11139445

j1ucj

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(29)



Sxc Sc

minusx2

2i21113890 1113891 (30)




Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)



Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)






MF (ΔSS)

ΔFF (33)









(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)















ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References

















































Sxp Sp1minusx

2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891 + Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(31)



Sx Sxc + Sxp Sc

minusx2

2i21113890 1113891 + Sp1

minusx2

2i21

1113890 1113891 + Sp2minusx

2

2i22

1113890 1113891

+ Sp3minusx

2

2i23

1113890 1113891 + Sp4minusx

2

2i24

1113890 1113891

(32)






MF (ΔSS)

ΔFF (33)









(cms)Cv

(10minus3 cm2s)Es

(MPa)mvprime

(MPaminus1)















ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References



























































ω 08 085 09 095 099λ 05 07 09 10 12κ 01 05 10 15 20ξ 01 08 15 25 30η 101 105 11 12 15ψ 002 007 014 021 028




ndash140

ndash120

ndash100

ndash80

ndash60

ndash40

ndash20

0

2000 02 04 06 08 10 12 14 16

MSS

(mm

)

Influencing factors

βκψ

ωξθ

ληRd





00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References



















































00 05 10 15 20 25ΔS

c1S

c1

Δββ

(a)

ΔSc2Sc2 = ndash4002 (Δωω) + 00007

ΔSc2

Sc2

ndash10

ndash08

ndash06

ndash04

ndash02

00005 010 015 020 025

Δωω

(b)


ΔSc3

Sc3

ndash11

ndash10

ndash09

ndash0803 06 08 11 13 16

Δλλ

(c)

ΔSc4Sc4 = ndash09791 (Δκκ) + 00874

ΔSc4

Sc4

00

50

100

150

200

00 50 100 150 200Δκκ

(d)

ΔSc5Sc5 = 09741 (Δξξ) + 01757

ΔSc5

Sc5

Δξξ

0050

100150200250300

50 100 150 200 250 300

(e)

ΔSp1Sp1 = 94999 (Δηη) + 04607

ΔSp1

Sp1

Δηη

00

100

200

300

400

500

00 01 02 03 04 05

(f)

ΔSp2Sp2 = Δψψ

ΔSp2

Sp2

Δψψ

0020406080

100120140160

00 30 60 90 120 150

(g)


ΔSp3

Sp3

Δθθ

00

40

80

120

160

03 05 07 09 11

(h)


ΔSp4

Sp4

ΔRdRd

00

40

80

120

160

10 20 30 40 6050

(i)




4 Conclusion






Data Availability




Acknowledgments


References


















































4 Conclusion






Data Availability




Acknowledgments


References

















































surfacesettlementanalysisinducedbyshieldtunneling ...lateral stress at rest (and is equal to 1.0...

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