Ground movement induced by triple stacked tunneling with different construction sequences

Yo Hu,Huyng Lei,Gng Zheng,Ling Shi,Tinqi Zhng,d,Zhiho Shen,Rui Ji,d

a School of Civil Engineering,Tianjin University,Tianjin,300350,China

b State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,Chengdu University of Technology,Chengdu,610059,China

c Department of Civil and Environmental Engineering,National University of Singapore,117576,Singapore

d Key Laboratory of Coast Civil Structure Safety of Ministry of Education,Tianjin University,Tianjin,300350,China

e Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration,Tianjin University,Tianjin,300350,China

f State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University,Tianjin,300350,China

Keywords:Triple stacked tunneling(TST)Ground movement Construction sequence Case study Surface settlement prediction Finite element analysis

A B S T R A C T This study tried to explore the ground movement induced by triple stacked tunneling(TST)with different construction sequences.A case study in Tianjin,China was used to investigate the ground movement during the TST(upper tunneling(UT)).For this,a modified Peck formula was proposed to predict the surface settlement induced by TST.Next,three sets of finite element analyses(FEA)were used to compare the effects of construction sequences(i.e.UT,middle tunneling(MT),and lower tunneling(LT))on vertical and lateral ground displacements.The results of Tianjin case and UT reveal that compared to a Gaussian distribution for a single tunnel,the surface settlement curve of triple stacked tunnels is a bimodal distribution.It seems that the proposed modified Peck formula can effectively predict the surface settlement induced by TST.The results of the three sets of FEA demonstrate that the construction sequence has a significant influence on the ground movement.Among the three construction sequences,the largest lateral displacement is observed in the MT and the smallest one in UT.The existing tunnel has an inhibitory effect on the vertical displacement.The maximum value of the lateral displacement occurs at the depth of the new tunnel in each construction sequence.

1.Introduction

As the metro line systems become denser,especially in denselybuilt city centers,the conventional single tunnel construction has gradually been replaced by multiple tunnels(Li and Yuan,2012;Li et al.,2014;Fang et al.,2015;Wang et al.,2018;Zheng et al.,2019;Hu et al.,2021).For instance,the London’s Jubilee Line Extension project in UK underpasses the existing Bakerloo and Northern tunnels to form a multi-tunnel network(Coutts et al.,1994;Standing and Selman,2001),the twin tunnels of the MRT North East Line in Singapore(Pang et al.,2006),the twin tunnels of Shanghai West Changjiang Road Tunnel project in China(Liu et al.,2014),the twin tunnels of Kuala Lumpur’s Sungai Buloh Kajang Line in Malaysia(Boon and Ooi,2018),and the twin tunnels of Shiraz’s subway line 2 in Iran(Nematollahi and Dias,2019).This type of multi-tunnel construction usually has very strict standards for ground settlement control.Therefore,it is important to effectively predict ground settlement for the multiple tunneling scenarios.

An empirical formula based on field measurement of surface settlement was proposed by Peck(1969)(known as the Peck formula)to describe the surface settlement induced by single tunneling.It is proven that the Peck formula can predict surface settlement(e.g.Attewell et al.,1978;O’Reilly and New,1982;Rankin,1988).The Peck formula has also been extended to predict subsurface settlement(Mair et al.,1993),three-dimensional(3D)subsurface movement(Han,2006),settlement related to twintunneling(Divall and Goodey,2015;Divall et al.,2017),and settlement by twin-tunneling under-crossing an existing tunnel(Lai et al.,2017).

The spatial location and construction sequence are important factors that can impact ground movement induced by multiple tunneling.Numerical analyses are widely used to study the influence of these two factors on the ground movement during tunneling.Models that determine the impact of spatial location of tunnels on ground movement often treat tunnels as horizontallyparallel(Kim,2004;Zhang et al.,2016;Soomro et al.,2018;Nematollahi et al.,2019),vertically-parallel(Chehade and Shahrour,2008;Ng et al.,2015;Hu et al.,2021)and intersecting(Shi et al.,2015;Liu et al.,2019).Models of twin tunnels that consider the construction sequence have focused on the effect of various construction sequences on existing piles(Ng and Lu,2014;Soomro et al.,2020a,b).However,the loading conditions of piles and tunnels are quite different,and the mutual influence between stacked tunnels considering the construction sequence is rarely reported.The researches on the spatial location of triple stacked tunneling(TST)are insufficient.Therefore,the responses of ground and exiting tunnels to TST with different construction sequences should be further studied.

In this study,we used finite element analysis(FEA)and field measurements to explore the ground movement of triple stacked tunnels in Tianjin,China.Based on this,a modified Peck formula was proposed to predict the surface settlement induced by TST.Then,three sets of FEA models(upper tunneling(UT),middle tunneling(MT),and lower tunneling(LT))were compared and analyzed to discuss the effect of construction sequence on the ground movement.This is the first time that FEA has been used to model triple stacked tunnels with different construction sequences.

2.Engineering background of the Tianjin case

2.1.Project overview

TST was undertaken in the Metro Line 6(M 6)in Tianjin,China from Wenhuazhongxin Station to Leyuandao Station(see Fig.1).The triple stacked segment adjacent to the Leyuandao Station is composed of M 6 in the uppermost position,Metro Line 5(M 5)in the middle position,and Metro Line Z1(M Z1)in the lowermost position.The vertical distance between M 6 and M 5 is 1.7 m,and the vertical distance between M 5 and M Z1 is 4.2 m(Fig.1).The shield machine is using earth pressure balanced(EPB),with a diameter of 6.4 m and a length of 10.5 m(equivalent to 7 linings,where each lining is 1.5 m).The outer diameter and thickness of the lining are 6.2 m and 0.35 m respectively.It should be noted M 5 and M Z1 are existing tunnels,and M 6 is new tunnel.

2.2.Geological conditions

Fig.2 displays the stratigraphic section and typical geotechnical property index with depth in triple stacked segment.The strata include silty clay,sandy silt,silty clay,and sandy silt from top to bottom.Also,the geotechnical properties investigated include the weight,water content,void ratio,plasticity index and liquidity index.

2.3.Field measurements

Nine measuring points(GS-1-9)were placed in the ground surface to investigate the surface settlement induced by the tunneling of the uppermost tunnel.The measuring points were monitored with an automatic DS05 level(Suzhou FOIF Co.,Ltd.,Suzhou,China).Fig.3a shows the plan view of the positions of field measurements(Fig.3a)and section A-A along transverse direction(Fig.3b).

3.Analyses of the TST process

3.1.Finite element model of the Tianjin case

A 3D FEA using ABAQUS was carried out to explore the ground movement induced by TST(Hasanpour et al.,2014;Zheng et al.,2015;and Zhang et al.,2016).Fig.4a presents a typical finite element(FE)model meshing of the Tianjin case.The FEA model was 50 m,60 m and 55 m inX-,Y-,andZ-direction,respectively.The stratigraphy is simplified into four layers composed of silty clay,sandy silt,silty clay and sandy silt.Other dimensions(e.g.tunnel diameter,the distance between the tunnels,lining thickness,grouting thickness and shield thickness)were consistent with the engineering design.

Fig.4b shows a quarter of the FE model cut alongX-andY-axis.The FE model consists of 5 parts:soil,shield,lining,grouting and existing tunnels(M5 and M Z1).All parts have a total of 48,100 elements.Based on the works of Dong et al.(2014)and Zhang et al.(2016),the element shape of the soil and other parts(i.e.shield,grouting,lining and existing tunnels)are“C3D8P”and“C3D8I”,respectively.Face and grouting pressures were applied and all constraints between two parts(e.g.soil and existing tunnel,soil and shield,etc.)were interacted by“Tie”.For the boundary conditions,the“U1”,“U2”,and“U3”were constrained on the bottom surface of theZ-axis direction,the“U1”and“U2”were constrained on both sides of the model’sX-andY-axis.

Fig.2.Stratigraphic section and typical geotechnical properties of the triple stack tunnel.

3.2.Finite element model of the different construction sequences

Based on the FE model of the Tianjin case(UT)(Fig.4),two FE models of MT and LT scenarios were established to discuss the effect of the construction sequence on the ground movement.The MT and LT scenarios are the same as UT scenario,except that the construction sequence differs.Three sets of FE simulation schemes are shown in Table 1.The construction sequence of UT corresponds to the Tianjin case,that is,M 5 and M Z1 are the existing tunnels,and M 6 is the new tunnel.For the MT,M 6 and M Z1 are the existing tunnels,and M 5 is the new tunnel.For the LT,M 6 and M 5 are the existing tunnels,while M Z1 is the new tunnel.

3.3.Constitutive model and parameters

The FE models involve three constitutive models:modified Cam-clay(MCC)model,porous elastic model,and linear elastic model.For the soil,a MCC model and porous elastic model were chosen(Huang et al.,2011;Liu et al.,2014),in consideration of its accuracy in simulating nonlinear properties under different stress paths.There are six parameters for the MCC model implemented in ABAQUS,and the specific constitutive parameters are shown in Table 2.All the parameters used in the MCC model were obtained from laboratory test and geotechnical investigations.For shield,lining,grouting and the existing tunnel,a linear elastic model(Zhang et al.,2016)was applied and the specific constitutive parameters are displayed in Table 3.Grouting includes soft and hard materials because the hardening process of the grouting was taken into account.Soft grouting reflects recently injected grout,while the hard grouting reflects grout that has hardened.Additionally,the lining was simulated as an entire structure in the light of the modified conventional design method(Lee and Ge,2001;Zheng et al.,2015).The stiffness reduction induced by the staggered lining assembly was considered by equivalent stiffness method(i.e.the Young’s modulus(E)of the lining was multiplied by a reduction factor of 0.85;Sun,2015).It is noteworthy that this article does not consider conicity of the shield machine(Lambrughi et al.,2012;Michael et al.,2017).

3.4.Modeling process

Since three FE models are all similar,except for the construction sequence,the UT is taken as an example to introduce the modeling process.The FE modeling process can be separated into five steps:initial earth stress balance,excavation 1,excavation 2,excavation 3,and repeat excavation 1-3(Fig.5).In this FE model,the shield tunneling process is“step-by-step”simulated and“element death”methods are used in ABAQUS(Mollon et al.,2013).To better introduce the modeling process,the physical model with steps III and IV is visualized in Fig.6.The Young’s modulus and Poisson’s ratio of the grouting are set as time-dependent to simulate the changing characteristics of the filling grout with two-phase elastic behaviors(Zheng et al.,2015;Zhao et al.,2021).As shown in Table 3,an initial Young’s modulus of 5 MPa and Poisson’s ratio of 0.4 are assigned to the grouting while it is soft grouting,whereas the hard grouting has a Young’s modulus of 18 MPa and Poisson’s ratio of 0.2 to change the initial elastic behavior,which is assigned after the shield advanced to the next slice.

Table 1Simulation scheme.

4.Results and discussion

4.1.Ground movement of the TST

4.1.1.Vertical displacement

(1)Monitoring point GS-5

The vertical displacement of the monitoring point GS-5(Figs.3 and 4b)at different tunneling positions is presented in Fig.7.The overall changes of the FEA and field measurement in vertical displacement with the distance from tunnel face are similar.The vertical displacement curve can be divided into three stages:slow decline,sharp rise,and rapid drop.When the shield machine is launched,the vertical displacement of the GS-5 decreases slowly as it approaches the face pre-arrival(-10.5 m).Then,the vertical displacement rises sharply from the face pre-arrival to tail passage(10.5 m).When the shield tail passes away,the vertical displacement decreases rapidly,and the field measurement drops faster than the FEA.This difference may be due to the conicity of the shield machine(Dias and Kastner,2013),and the uneven shrinkage of grouting(Zhang et al.,2016)is considered in field measurement,but not in FEA.

Fig.3.Field measurements:(a)Plan view and(b)Section A-A.

Three key positions of the shield crossing the GS-5 are identified,including the face pre-arrival,face arrival and tail passage.The change in vertical displacement starts from the position of the face pre-arrival,approaches the GS-5(position of the face arrival),and finally leaves the GS-5 to reach the position of the tail passage.It rises sharply,indicating that the GS-5 has uplifted in the process of crossing beneath the GS-5.

(2)At different tunneling positions

Fig.4.The FE model mesh of the Tianjin case:(a)Whole view and(b)A quarter along X and Y.

Fig.8 visualizes the transverse vertical displacement of the ground surface for the FEA and field measurement of different positions throughout tunneling.The trend in transverse vertical displacement manifests as large subsidence,small subsidence,and large uplift during the face pre-arrival,face arrival,and tail passage positions,respectively.It can be observed that the maximum settlement(Smax)in the face pre-arrival position is-0.95 mm(FEA)and-0.91 mm(field).During the face arrival position,Smaxis-0.28 mm(FEA)and-0.30 mm(field),respectively.Lastly,in the tail passage position,Smaxis 0.46 mm(FEA)and 1.63 mm(field),respectively.This indicates that vertical displacement significantly increases with the shield tunneling from face pre-arrival to tail passage.In addition,the width of the settlement trough(i)during the face pre-arrival position is different from that of the face arrival and tail passage positions.During the face pre-arrival position,theivalue is 6.42 m,while it is 15.14 m during the face arrival and tail passage positions.This indicates that different measurements should be carried out based on which tunneling stage is active to better control the vertical displacement of the ground surface.

(3)Comparison between the single tunnel and triple stacked tunnels

Fig.9 compares the surface settlement characteristics of the construction of the single tunnel(Cattoni et al.,2016;Zheng et al.,2020a)and triple stacked tunnels.The surface settlement induced by the triple stacked tunnels is near-inverse relationship with the single tunnel.For single tunnels,the curve of the surface settlement is of Gaussian shape,while that of the triple stacked tunnels surface settlement is bimodal in shape.Two reasons account for this difference.Firstly,the stiffness of the existing tunnel is greater than that of the soil,which can change the stiffness of the soil(Lai et al.,2017).Secondly,the depth of the new tunnel is shallow(1.47D,whereDis the diameter of the tunnel)and the stress is released and redistributed after the tunneling(Han,2006).This promotes tunnel uplift and leads to surface displacement(see Fig.10).

4.1.2.Prediction of surface settlement

(1)Prediction method-single tunneling

The surface settlement induced by single tunneling can be fitted by a Gaussian distribution(Peck,1969;O’Reilly and New,1982;Mair et al.,1993).The shape can be expressed as follows:

whereSSingleis the surface settlement at a given horizontal distance from the tunnel axis,Smaxis the maximum settlement above the tunnel axis,xis the horizontal distance from the tunnel axis,iis the horizontal distance from the tunnel axis to the point of inflection in the Gaussian distribution curve(also called width of the settlement trough),VLis the volume loss,expressed as a ratio of the volume of surface settlement trough to volume of excavated tunnel per unit length of tunnel(in practical,the volume loss is often selected through engineering experience,and some empirical values of the volume loss are listed in Table 4),andAis the volume of excavated tunnel per unit length of tunnel,for the circular tunnel,A=πD2／4.For a surface settlement trough of the single tunneling,theVLdetermines the magnitude of the settlement andidetermines the distribution of the settlement trough curve(Han,2006;Divall and Goodey,2015).Although theVLhas an important relationship with geological conditions,construction methods,and other conditions,it generally depends on factors such as the construction technology and engineering management experience(Han,2006).As per O’Reilly and New(1982),theican be expressed as

wherez0is the depth of tunnel axis,andKis a parameter describing the width of settlement trough,and the value is usually 0.5(Mairet al.,1993).For some areas in China,Han(2006)provided the suggested values ofKbased on measured data,as displayed in Table 5.

Table 2Constitutive parameters used in the soil layers.

Table 3Constitutive parameters used in the hard materials.

Table 4Some empirical values of the volume loss.

Fig.5.Flow chart used in the FEA.

By combining Eqs.(1)-(3),the final expression of the surface settlement induced by the single tunneling is as follows:

(2)Prediction method-TST

The surface settlement induced by TST is mainly affected by the stiffness of the existing tunnel and the uplift of the new tunnel.Therefore,the surface settlement trough curve is modified to better predict the surface settlement caused by TST.An expression is given as follows:

whereSTripleis the surface settlement induced by TST,S1is the surface settlement considering the stiffness of the existing tunnel,andS2is the surface uplift caused by the upward movement of the new tunnel.

For the surface settlement considering the stiffness of the existing tunnelS1,it is expressed as

Fig.6.FEA modeling procedure:(a)Step III and(b)Step IV.

Fig.7.Vertical displacement of the monitoring point GS-5 at the different tunneling positions.

Fig.8.Transverse vertical displacement of the ground surface at different tunneling positions.

Fig.9.Comparison between the single tunnel and triple stacked tunnels(x is the distance to tunnel axis).

whereSmax1is the maximum settlement above the tunnel axis considering the stiffness of the existing tunnel;andi1is the width of the settlement trough considering the stiffness of the existing tunnel,which can be obtained by the following equation(Lai et al.,2017):

Fig.10.Vertical displacement vector of triple stacked tunnels.

where λ1is the correction factor of the width of the settlement trough considering the stiffness of the existing tunnel,which can be calculated by Eqs.(8)and(9)(Wang et al.,2014);zis the depth of the bottom of the existing tunnel;K1is the modified width parameter of settlement trough,which can be calculated by Eq.(10)(Han,2006):

Fig.11.Comparison of the surface settlement of the triple stacked tunnels.

whereIis the second moment of area,dis the diameter of tunnel without lining,Dis the diameter of tunnel with lining,andBis the parameter considering the geological conditions(0.65 for clayey soils and 0.5 for sandy soils).

Combining Eqs.(7-10),the expression of the width of the settlement trough is written as,considering the stiffness of the existing tunnel:

For the surface uplift caused by the upward movement of the new tunnelS2,it is expressed as

whereSmax2is the maximum uplift caused by the upward movement of the new tunnel,andi2is the width of the uplift trough induced by the uplift of the new tunnel.It should be noted that thei2is calculated using the single tunneling method.

Finally,the surface settlement induced by TST can be expressed as follows:

Surface settlement for the Tainjin case was calculated using the prediction method of the TST.Fig.11 compares the surface settlement using different methods(FEA,field monitoring and prediction method).The predicted curve correlates well with the curves of FEA and the field measurement,which indicates that the prediction method can properly predict the surface settlement induced by TST.

4.1.3.Lateral displacement

Fig.12.Lateral displacement of the stratum at the different tunneling positions:(a)Left side and(b)Right side.Displacement to the left is positive,and displacement to the right is negative.

Fig.12 compares the lateral displacement of the stratum at the different tunneling positions for the FEA when the M 6 excavates to the middle position(i.e.when it reaches 31.5 m alongY-axis).It should be noted that the measuring points of the lateral displacement were not set up in field measurement,so only FEA data could be available.Fig.12a presents the lateral displacement on the left side of the M 6 at a position of 6 m from the tunnel center,whereas Fig.12b presents the right side of the M 6 at a position of 6 m from the tunnel center.

Fig.13.Comparison of the surface settlement of the triple stacked tunnels for the FEA,field and predicted.

It can be seen that the trend of the lateral displacement at the three tunneling positions is similar between the left and right sides,except for the direction of lateral displacement.For the lateral displacement value(center of M6,depth of 12.6 m),the lateral displacement values of the left side(face pre-arrival:0.21 mm;face arrival:-0.6 mm;tail passage:-2.1 mm)and right side(face prearrival:-0.19 mm;face arrival:0.58 mm;tail passage:2.09 mm)are similar.In the strata between M 5 and M Z1(depth of 26 m),the value of the right side(face pre-arrival:-0.07 mm;face arrival:-0.17 mm;tail passage:-0.28 mm)is slightly greater than the value of the left side(face pre-arrival:0.03 mm;face arrival:0.11 mm;tail passage:0.19 mm).The difference between left and right side may be due to the tunnel locations,where M Z1 on the right impacts the lateral displacement.

For different tunneling positions(face pre-arrival,face arrival,and tail passage)in terms of the lateral displacement,the left side(Fig.12a)is used as an example.The lateral displacement in the face pre-arrival position is positive,and then it becomes negative in the face arrival position and continues to increase negatively in the tail passage position.This indicates that the lateral direction of the M 6 at the face pre-arrival position is under compression;during the two positions after the face arrival,both are under extension.In addition,the position of maximum point of the lateral displacement is slightly higher than the center of M 6(depth of 12.6 m),indicating that the new tunnel of M 6 has been mobilized.

Fig.13 illustrates the lateral displacement of the stratum at different distances(6 m,9 m and 12 m)from the center of M 6 during the face arrival position.At the depth of the center of M6,the lateral displacement decreases as the distance from the center of M 6 increases.Specifically,the displacements are-0.60 mm,-0.26 mm and-0.15 mm at 6 m,9 m,12 m distance from the center,respectively.The change in displacement between from 6 m to 9 m is greater than that from 9 m to 12 m,which indicates that the main impact range of lateral displacement is within 9 m(1.41D).This differs from main impact range of the vertical displacement(8 m or 1.25D)as discussed in Section 4.1.Furthermore,the maximum points of lateral displacement on the left side of the M 6 are moving up gradually(recorded by 1.53 m,2.11 m,and 3.04 m)from 6 m to 12 m,which is similar to the results of Chai et al.(2009)and Zheng et al.(2020b).This implies that it is necessary to control the lateral displacement caused by excavation disturbance during construction.

4.2.Effect of construction sequence on the ground movement

4.2.1.Vertical displacement

(1)Along longitudinal direction

Fig.14 visualizes the vertical displacement of the stratum with different construction sequences(UT,MT,and LT scenarios),along longitudinal direction at different positions(surface,between M 6 and M 5;and between M 5 and M Z1).Fig.14a displays the position of surface after tunneling.In comparison of three construction sequences,the range in vertical displacement of the UT scenario(from 1.21 mm to-1.55 mm)is the largest,followed by the MT scenario(from-0.59 mm to-2.15 mm),and then the LT scenario(from-1.14 mm to-1.75 mm).This is mainly caused by the increasing depths of the new tunnel in three construction sequences.In all models,there is a sudden change of vertical displacement when crossing the existing tunnel.The distances between the point of the sudden change and the center of the existing tunnel are different during three construction sequences.This implies that the existing tunnel has a significant impact on the vertical displacement of surface ground,and the three construction sequences have different impact ranges(UT:(0.94-1.41)D;MT:(0.51-0.63)D;LT:(0.7-0.94)D).

Fig.14b illustrates the position between M 6 and M 5(depth of 16.65 m)after tunneling.The trends in the vertical displacement of the stratum between M 6 and M 5 during three construction sequences are different,but the displacement is affected by the position of the existing tunnel(i.e.an inhibitory effect).In the UT scenario,the vertical displacement is overall positive,and the stratum has moved upward.The displacement at the position crossing the existing tunnel is significantly smaller(from 8.21 mm to 3.6 mm).This indicates that the existing tunnel has a control effect on the displacement,in the main range of(1.64-1.88)D.In the MT scenario,the vertical subsidence of the stratum increases sporadically along the tunneling direction,except for a reduction in subsidence over the location of existing tunnel.The negative trend may be due to the model design,where the extracted data is very close to the new tunnel(0.85 m).This explains that the existing tunnel can also restrain the displacement,and the main impact range is(0.51-0.66)D.In the LT scenario,in contrary to the UT scenario,the vertical displacement is overall negative,and the stratum moves down.The existing tunnel also reduces the displacement(upward movement),mainly in the range of 1.41D.

Fig.14c illustrates the position between M 5 and M Z1(depth of 26 m)after tunneling.The trends in vertical displacement of the stratum between M 5 and M Z1 during three construction sequences are similar and all show a decrease trend in displacement at the position of the existing tunnel(UT:from 2.61 mm to 2.02 mm;MT:from 6.92 mm to 5.64 mm;LT:from-3.83 mm to-1.09 mm).The UT and MT scenarios display positive displacement and move upwards,whereas the LT scenario has negative displacement and moves downwards.Similarly,Fig.14 shows that the existing tunnel has a control effect on the vertical displacement of the stratum.The main range of UT is 1.64D,that of MT is(0.74-1.13)D,and that of LT is 1.17D.

The above analysis demonstrates the varied effects of construction sequence on the longitudinal vertical displacement of the stratum at different depths.However,the influence of existing tunnel is the same(control effect on the vertical displacement).The degree of influence is related to many factors,such as construction sequence,depth of new tunnel,and distance between extracted data location and new tunnel.

(2)Along transverse direction

Fig.15 illustrates the vertical displacement of the stratum during the construction sequences(UT,MT,and LT scenarios)in transverse direction.Fig.15a demonstrates the position of the surface when the new tunnel is half excavated.In comparison of three construction sequences,the largest change in settlement above new tunnel occurred in the UT scenario,followed by the LT scenario and MT scenario.The reason for the smallest displacement change occurring in the MT scenario may be related to the fact that the new tunnel(M 5)is sandwiched between two existing tunnels(M 6 and M Z1),which has limit impact on the ground settlement.In contrast,the largestioccurred in the MT scenario(19.75 m),followed by UT scenario(15.25 m),and LT scenario(13.87 m).

Fig.15b displays the position between M 6 and M 5(depth of 16.65 m)when the new tunnel is half excavated.Similar to the previous model,the vertical displacements in the UT and MT scenarios increase,with the exception of above the new tunnel in MT scenario.Displacement in the LT scenario decreases(i.e.subsidence occurs).TheSmaxin the UT scenario is the largest(3.75 mm),followed by MT scenario(-0.92mm),andLTscenario(-0.57mm).Thisislikely due to thepresenceofexistingtunnelsabovethenewtunnelthatsuppresses the ground movement in LT(all above)and MT(partly above).In the UT scenario,there is no suppression.For the value ofi,the difference between UT scenario and MT scenario is not obvious,but in the LT scenarioiis noticeably larger.In the LTscenario,this likely stems from the fact that the distance from the new tunnel to the extracted data location is significantly farther than the UT and MT scenarios.

Fig.15c presents the position between M 5 and M Z1(depth of 26 m)when the new tunnel is half excavated.The trends in vertical displacement of the stratum between M 5 and M Z1 for UT and MT scenarios are upward(positive),and the LT scenario is downward(negative).Of the three modeling scenarios,theSmaxof the MT scenario is largest(3.27 mm),followed by the UT and LT scenarios(1.53 mm and-1.77 mm).This is likely due to the presence of existing tunnels directly above the new tunnel in UT and LT scenarios,while only a portion is above the new tunnel(distance of 4.5 m between M 6 and M Z1 in the direction of M5 tunneling)in the MT scenario.For the value ofi,the UT scenario is noticeably larger than the MT and LT scenarios.Additionally,it is also because the distance of UT scenario from the extracted data location is significantly larger than MT and LT.

The above analysis demonstrates that,similar to the longitudinal direction,the effect of construction sequence on the vertical displacement of stratum in transverse direction has varied effects at different depths.If there is an existing tunnel above the new tunnel,theSmaxvalue is small;for no existing tunnel,theSmaxvalue is large.The value ofiis proportional to the distance from the new tunnel to the extracted data location,but the magnitude of the displacement is inversely proportional to distance.

4.2.2.Lateral displacement

Fig.16 illustrates the lateral displacement of the stratum on the left and right sides of the new tunnel under different construction sequences when tunneling to the half position,in which the MT scenario extracts data at positions of M 6 and M Z1,respectively.

The displacement on the sides of the tunnels in three scenarios is similar,irrespective of direction(left or right).The maximum lateral displacement occurs at the depth of the new tunnel,and the difference between left and right rides is direction(i.e.sign)of the displacement.The maximum value of the lateral displacement is largest in the MTscenario(left:-1.14 mm(M 6)and-0.88 mm(MZ1);right:1.3 mm(M 6)and 0.94 mm(M Z1)),moderate in the LTscenario(left:-0.85 mm;right:0.82 mm),and smallest in the UTscenario(left:-0.6 mm;right:0.58 mm).Lateral displacement of the ground surface inthe UTand LTscenarios isdifferenton the left and rightsides,which may be caused by the asymmetry of the left and right sides.Additionally,both sides of UT scenario at the maximum displacement are higher than the centerline location of the new tunnel(M 6),the MT scenario(new tunnel M 5)has only one side,and the LTscenario(new tunnel M 5)has none.This range of displacements may be caused by the difference in the depth of the new tunnel as well as the location of the existing tunnel in the different construction sequences.

5.Conclusions

This study reported a series of FEA and field measurement to explore the ground movement induced by TST with different construction sequences.In addition,a modified Peck formula was proposed to predict the surface settlement.

The vertical and lateral displacements of the ground due to TST were explored by computing FEA(UT scenario)and measuring ground displacement in Tainjin case.The vertical displacement was monitored by nine ground station points using a laser level throughout tunnel construction.The changes of monitoring point GS-5 over distance from tunnel face can be divided into three stages:slow decline,sharp rise and rapid drop.In different tunneling positions,this profile manifests as large subsidence,small subsidence,and large uplift.The surface settlement of the triple stacked tunnels shows a bimodal distribution compared to the Gaussian distribution curve of a single tunnel.For the lateral displacement,the value on the left side of the new tunnel in the face pre-arrival position is positive,then it becomes negative in the face arrival position,and continues to increase negatively in the tail passage position.The maximum of lateral displacement moves up gradually in each tunnel.

Fig.16.Lateral displacements of the stratum at different construction sequences:(a)Left side and(b)Right side.Displacement at the left is positive,and displacement at the right is negative.

Based on the difference in surface settlement between a single tunnel and triple stacked tunnels,a modified Peck formula that considers the stiffness of the existing tunnel,the uplift of the new tunnel,and other factors was proposed.The modified Peck formula was used to predict the surface settlement induced by TST.Three sets of FEA were performed to discuss the effect of construction sequence on the ground movement.Construction sequence has a significant influence on the ground movement at different depths.Vertical displacement is related to the depth of the new tunnel and the location of the existing tunnel.The presence of existing tunnels has a control effect on displacement.The lateral displacement reaches a maximum at the depth of the new tunnel.The largest amount of displacement occurred in the MT scenario,moderate displacement in the LT scenario,and the smallest displacement in the UT scenario.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The work described in this paper was financially supported by the Open Project of the State Key Laboratory of Disaster Reduction in Civil Engineering(Grant No.SLDRCE17-01),the National Key Research and Development Program of China(Grant No.2017YFC0805402),and the National Natural Science Foundation of China(Grant No.51808387).All of the support is greatly appreciated.