Hindawi Advances in Civil Engineering Volume 2019, Article ID 4145721, 12 pages https://doi.org/10.1155/2019/4145721

Research Article Numerical Study and Field Monitoring of the Ground Deformation Induced by Large Slurry Shield Tunnelling in Sandy Cobble Ground

Chengping Zhang ,1,2 Yi Cai,1,2 and Wenjun Zhu 1,2

1Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing 100044, China 2School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China

Correspondence should be addressed to Wenjun Zhu; [email protected]

Received 29 September 2018; Accepted 18 December 2018; Published 3 February 2019

Academic Editor: Daniele Baraldi

Copyright © 2019 Chengping Zhang et al. +is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. +is paper presents the ground deformation induced by the large slurry shield tunnelling with a diameter of about 12 m in urban areas, which may challenge the safety of the existing nearby constructions and infrastructures. In this study, the ground de- formation is analyzed by a three-dimensional finite difference model, involving the simulation of tunnelling advance, grouting, and grouting hardening. +e transverse settlement, longitudinal settlement, and horizontal displacement of the ground are analyzed by comparing the simulation results with the field measurements in the Rapid Transit Line Project from Beijing Railway station to West Beijing Railway station in China. +e numerical model proposed in this paper could well predict the ground deformation induced by large slurry shield tunnelling. +e results show that the main transverse settlement occurs within the zone about 1.5 times of the excavation diameter, and the settlement during the passage of the shield and the tail void plays a most important role in the excavation process.

1. Introduction roadway, the empirical method was first put forward by Martos [6], and the error function was suggested to present At present, lots of tunnels are constructed or being planned the surface settlement through profile approximately. A to relieve the traffic pressure in metropolis. +e application description of the green-field settlement was proposed by of the slurry shield method to urban tunnel construction in collecting field observations from many case histories over sandy cobble ground is more and more popular for its the years by Peck [7], and O’Reilly and New [8, 9] sum- comfortable work environment [1]. Ground deformation is marized plenty of empirical equations and pointed out that inevitably induced by the excavation of the slurry shield Peck’s empirical method is unable to provide a reasonable tunnel in urban areas, which is negative to the existing prediction for soils other than normally consolidated clays, structures and pipelines. As a result, a great deal of attention as the empirical model is based on limited scope of the has been attracted all over the world [2, 3]. Several ap- database. With the assumption that the ground loss is proaches, such as the empirical method, model test, nu- uniformly distributed along the longitudinal direction, the merical simulation, and field monitoring, have been used to settlement profile can be expressed by Gaussian distribution. estimate the ground deformation during the shield Attewell and Woodman [10] suggested that the longitudinal tunnelling. settlement at any longitudinal coordinate can be described +e empirical method is based on the regression analysis by cumulative Gaussian probability. of the recorded ground surface settlement and then used to Model test is also a common way to investigate the predict the ground surface settlement [4, 5]. Based on the evolution law of the ground deformation, including the ground surface settlement measured in the field of a mine centrifuge model test and physical model test [11]. Based on 2 Advances in Civil Engineering a series of plane-strain centrifuge model tests on the single 2. Project Description and Monitoring tunnels in moderately stiff clay, Grant and Taylor [12] found that the high-quality data can be used to improve the In order to alleviate traffic congestion and improve the predictions of both surface and subsurface movements in the ground surface environment of Beijing, the capital city in plane transverse to the tunnel. And a procedure for pre- China with a population of around 30,000,000, the RTLP was dicting horizontal movements as a function of the vertical started in 2005, which begins at Beijing West Railway Station settlement profile was also suggested. Kuwahara et al. [13] in the west and ends at Beijing Railway Station in the east as investigated the mechanism of ground settlement in the shown in Figure 1. +e total length of the RTLP is 9,151 m. process of tail void by the centrifuge model test and found +e tunnel takes up about 7,230 m in the whole project, with that the ground deformation mechanism in the field had a a buried depth varying from 16 to 22 m. 5,227 m of the close similarity with the results observed in the physical tunnel is constructed by the slurry shield, while other parts models. Atkinson and Potts [14] investigated the influence of are built by the open-cut method and mining method. It the depth of burial and crown settlement on the surface should be pointed out that there are several historical subsidence above shallow tunnels in soft ground. Compared buildings with traditional Chinese style above the tunnel with the observations of settlements above some existed including Jianlou and Zhengyangmen, which are particu- tunnels, the model’s behaviour matches with the field re- larly sensitive to the subsidence induced by excavation. cords well, and an empirical relationship is given between Considering the historical, cultural, and communal value of the buried depth, the trough width, the crown, and surface these buildings, the evaluation of the ground surface set- settlements for tunnels in sands and in clays. tlement is the key ingredient in the design stage and during With the development of the computer technique and the whole construction process. +us, a monitoring system numerical software, the numerical simulation method has was set along the tunnel to investigate the effects of exca- become more and more effective to solve the problem in vation on the ground deformation. +e monitoring portion tunnel construction [15, 16]. Finno and Clough [17] sim- considered in this study is the first 509 m of the shield tunnel ulated the entire EPB tunnelling process in five stages by the which begins at the north of Tianningsi Bridge. finite element program and obtained the lateral displace- In this project, results of extensive in situ and laboratory ment. Do et al. [18] proposed a finite element method to tests provided a description of the different geological for- study the failure mechanisms of deep excavations in soft mations. A typical geological profile of the shield tunnel is clay. Besides, Melis et al. [19] assessed the accuracy of each shown in Figure 2. +e profile reveals that the monitoring analytical or empirical predictive method with reference to portion of the shield tunnel is mainly located in gravel the soil movements using a numerical model of shield tunnel environment. Figure 3 shows the typical in situ soil of this excavation. project. Figure 4 shows the distribution of the grain size Field monitoring is also widely used in the tunnel obtained by the indoor screening test. +e results indicate construction [1]. Chen et al. [20] mainly focused on the field that the maximum grain diameter is about 300 mm. +e measurements of parallel tunnels using EPB shields in silty elliptical gravel with strong compression capacity accounts soils. +is research revealed the changes of pore pressure in for 12%. It can also be found that about 1/3 of the sands are the soils and ground deformation during EPB shield tun- in the size from 0.25 mm to 0.5 mm. According to the nelling. Generally, field measurement can be used in available documents about the water table in the excavation combination with other methods. Sugiyama et al. [21] area, the influence of the underground water level can be compared the field measurement of ground deformation due negligible. to slurry shield tunnelling with the model test and numerical +e slurry shield used in this project with a total length of simulation, and two kinds of practical design charts were about 11.52 m is characterized by an outer diameter of proposed to appropriately predict the transverse surface 11.97 m at the face and 11.95 m at the tail. However, in some settlement troughs in the clays or sands and gravels. Ocak special circumstances, the maximum excavation diameter at [22] proposed a new empirical formula for estimating the the face can reach up to 12.04 m. surface transverse settlement trough of twin tunnels. +e tunnel lining is fabricated by concrete with the Moreover, the comparison with field measurement validated maximum compressive strength of 50 MPa based on the the reasonability of an empirical formula. experimental tests on the cubic specimens with the di- However, it should be pointed out that the studies above mensions of 150 mm × 150 mm × 150 mm. +e tunnel lining mainly focused on the influences of small diameter shield is set in place inside the shield tail to support the sur- excavation on the ground deformation. +e research on the rounding rock as the machine moves forward. +e outer and large-diameter shield excavation in sands and gravels is still inner diameters of the lining ring are equal to 11.6 m and limited up to now. In this study, a three-dimensional nu- 10.5 m, respectively. +e thickness of the tunnel lining is merical model is carried out to investigate the ground de- 550 mm. +e width of each segment is 1.8 m. Stagger-jointed formation due to large-diameter slurry shield tunnelling in segmental linings are applied in this tunnel. As shown in sandy cobble stratum. +e reliability of the numerical model Figure 5, each lining ring is composed of 9 segments. is validated by comparing with the field measurement in the In order to validate the prediction results of numerical Rapid Transit Line Project from Beijing Railway Station to simulation, a monitoring system was set in the monitoring West Beijing Railway Station in Beijing, China (hereinafter section, as shown in Figure 6. +e monitoring system is referred to as RTLP). comprised of a total of 13 monitoring points on the ground Advances in Civil Engineering 3

Beijing Railway Station Zhengyangmen Tianningsi Xuanwumen Bridge Shield tunnel Jianlou Chongwenmen

West Beijing Railway Station

Figure 1: General layout of the RTLP.

Tianningsi West Beijing Zhengyangmen Bridge Beijing Railway Railway Station Monitored section Xuanwumen and Jianlou Chongwenmen Station

181241 633 5227 718 230

Backfill Silt Sand Silty sand Gravel Figure 2: Geological pro
le of the project (unit: m).

100

80

60

40 Cumulative percentage 20 Figure 3: Image of typical in situ soil.

0 surface, and the monitoring zone ranges to 41 m from the 0 0.25 0.50 1.002.00 5.00 15.010.0 30.0 80.060.0 tunnel center. 2 bore inclinometers are set about 2 m away Mesh size (mm) from the tunnel. e buried depth of the tunnel crown at the monitoring section is about 17 m. Sample 1 Sample 2 3. Numerical Model Figure 4: Grain size distribution of the soil samples.

e numerical test was carried out based on a three- stability simultaneously; (2) installing the tunnel lining, dimensional explicit
nite dierence program, FLAC3D.A applying the jacking force, and injecting the grout behind the three-dimensional model with small-strain formulation was segments to
ll the voids created at the shield tail; and (3) as applied to simulate the performance of the ground sur- the slurry shield machine continues to advance, the grout rounded by a mechanized tunnelling. e tunnel con- becomes stabilized gradually. struction process is modelled by a step-by-step approach. About the three main phases referred above, some key Each excavation step corresponds to an advancement of the points are required to be clari
ed. e face pressure is tunnel face of 1.8 m, which is equal to the width of a lining supposed to be in trapezoidal distribution on the excavation ring. In this numerical model, the tunnelling process consists face by taking into account the slurry density. In order to of three main phases: (1) excavating the ground at the tunnel simplify the simulation processes, the 9 segmental joints are face and applying a face pressure to ensure the tunnel face ignored and the lining is installed as a ring. e ring joint is 4 Advances in Civil Engineering

11.6m

10.5m

1.8m

Figure 5: Image of the segmental lining.

41 41 15 10 5 5 3 3 3 3 5 5 10 15

Bore 17 inclinometers

22Tunnel

Figure 6: Alignment of the monitoring system in the monitoring section (unit: m). simulated by using double connections. e jacking force is 0.18 MPa and 0.3 MPa at the monitoring section. e same assumed to be in linear distribution which is set on each values are applied to the numerical model. In the nu- segment with a total value of about 40,000 kN. A simpli
ed merical model, a trapezoid pressure is applied at the geometry is assumed, with the original cone-shaped shield cutterhead with a consideration of the slurry’s density of replaced by a cylindrical shape. Lambrughi et al. [23] about 1.05 g/cm3, and the pressure value at the center of simulated the grout hardening by the law, in which the the cutterhead is 0.18 MPa. Young’s modulus increases with time, as follows: e soil behaviour was described using an elastic-plastic constitutive model based on the Mohr–Coulomb criterion. E ,t0, initial According to the extensive in situ and laboratory tests, the Et 0.2 t/t0 ( ) project data and average geotechnical characteristics of Eg 1 e (),t t0, dierent layers are summarized in Table 2. ese parameters  − where E is the Young’s modulus of grout at time t, E is the1 are also adopted in the numerical analysis. t  − ≥ g Young’s modulus of grout  corresponding to complete In order to balance the boundary eect and the com- hardening, and t is the time interval from the grout injection. putational ežciency, the model was built with dimensions of An initial value (E , for t 0) must also be estimated for 99 m (length) 100 m (width) 60 m (depth). e bottom initial × × Young’s modulus. Lambrughi et al. [23] assumed that the boundary was
xed in the x, y, and z directions, and the four grout is completely hardened beyond 12 h. In this project, vertical boundaries were
xed in the x- and y-directions. e the excavation speed is about 1.8 m/d. Considering the actual typical cross section of the tunnel is illustrated in Figure 8. construction condition, the complete hardening of grout is e perspective view of the numerical model, which is 24 h. As a result, two dierent Young’s modules are adopted: composed of around 141,960 grid points and 134,200 zones, Ef and Eh represent the Young’s modules of fresh grout and is presented in Figure 9. e displacements are set to be zero hardened grout, respectively. e parameters for the in three directions before the excavation. modelling of grout mechanical behaviour are summarized in Table 1. e detailed layout of the proposed slurry shield 4. Definitions of Ground Movements model is shown in Figure 7. In this project, the actual values of the pressure applied 4.1. Transverse Settlement. Construction of a tunnel in- at the cutterhead and the grouting pressure are about evitably results in the ground movements with a ground Advances in Civil Engineering 5

Table 1: Parameters of the grout. Young’s modulus Poisson’s ratio μ ( ) Density c (kN m 3) Hardened grout E (MPa) Fresh grout E (MPa) g g · h f − 400 4 0.22 − 2 400

Fresh grout Tail void Overexcavation void Soil

Hardened Segmental Structure void grout Shield lining Shield tail brush

Grouting Slurry pressure pressure Tunnel direction

Figure 7: Layout of the slurry shield model.

Table 2: Physicomechanical parameters of surrounding rock and tunnel segment. Elastic modulus E Poisson’s ratio μ Unit weight c Cohesion c Internal friction angle φ ickness t Depth z (m) (MPa) ( ) (kN m 3) (kPa) (°) (m) · 0–6 10 0.4 18 − 10 20 — 6–20 30 0.35− 19 25 27 — 20–40 80 0.28 20 40 35 — 40–60 100 0.26 21 50 38 — Tunnel 33.5 103 0.2 25 — — 0.55 segment ×

Ground surface x Backfill 6 m

17 m z Silt

Sand 60m Segment inner diameter 11.5 m 20 m 14 m Segment outer diameter 11.6 m

Excavation diameter 11.97 m Gravel 20 m

50 m 50 m

Figure 8: Typical cross section of the tunnel. 6 Advances in Civil Engineering

(a) (b)

Figure 9: Numerical model introduced into FLAC3D: (a) perspective view; (b) zoom view. surface settlement trough above and ahead of the tunnel. 2.5i(0) Field observations [7–9] collected from a considerable i(0) number of case histories have demonstrated that the ground x surface transverse settlement trough can be described by a Smax(0) Point of inflection Gaussian distribution as follows: z x2 i(z) S � S �− �, (2) max 2i2 ��� 2 z0 Point of inflection VLR π S � , (3) Smax(z) max 4i 2 where S is the settlement, Smax is the maximum settlement on the tunnel centerline, x is the horizontal distance from the centerline, i is the horizontal distance from the tunnel z centerline to the point of inflection on the settlement trough, Figure 10: Definition of surface and subsurface settlement profiles. VL is the ground loss, and R is the radius of the tunnel. Based on a survey of the tunnelling monitoring data in London, O’Reilly and New [8] showed that the point of 0.50 − 0.325z/z � inflection i as shown in Figure 10 is an approximately linear K(z) � 0 . (6) function of the depth of the tunnel centerline, z0. A simple 1 −z/z0 � relationship was proposed as follows:

i � Kz0, (4) 4.2. Longitudinal Settlement. According to Sugiyama et al. where K is a parameter depending solely on the soil nature. [21], the ground displacement caused by shield tunnelling Field data during tunnelling collected all over the world can be divided into five types: indicate that K varies between 0.2 and 0.45 for sands and gravels, between 0.4 and 0.6 for stiff clays, and between 0.6 and 0.75 for soft clays [24], regardless of the tunnel size and Step 1. Preceding settlement occurs far ahead of the shield tunnelling method. tunnel’s arrival, which does not occur in all the shield Mair and Taylor [24] also pointed out that the transverse tunnellings. settlement trough below the ground surface can be described by Gaussian distribution, and the function of inflection i was Step 2. Ground deformation at the front of the tunnel face proposed as follows: that occurs immediately before the shield tunnel’s arrival is due to the imbalance of the support pressure at the tunnel i � K(z)z0 − z �, (5) face. where the parameter K(z) is a function of depth z. According to the field data, Mair and Taylor [24] found that i Step 3. Settlement during passage of the shield is sensitive to decreases with the depth and the parameter K(z) can be the thickness of the over-cutting edge and the steering deduced by problems in maintaining the alignment of the shield. Advances in Civil Engineering 7

Step 4. Settlement due to the tail void is induced by the From the overall perspective, the numerical ground interval time between excavation and grouting. surface settlement trough is symmetrical. However, influ- enced by the existed structures and the nonuniform exca- Step 5. Succeeding settlement is caused by the disturbance vation, the measured transverse settlement profile is not of the ground due to the shield driving. perfectly symmetrical. In general, the numerical model can predict the ground surface settlement very well. According to the Peck formula’s prediction, the numerical and field measurement results, the main settlement in the transverse 5. Numerical Results and Discussion section occurs within 18 m of the centerline. In this section, a detailed analysis on the evolution laws of It is possible to get the ground loss by integrating the ground settlement caused by shield tunnelling is made by ground surface settlement curve, and the ground loss of the comparing the field measurement with the numerical re- numerical simulation and the monitoring are 0.33% and sults. +e field measurement is conducted to verify and 0.27%, respectively. Compared with the experiential value evaluate the accuracy of numerical results. Transverse and VL � 0.5%, the ground loss of the simulation is closer to the longitudinal settlement troughs and horizontal displace- monitoring result, which means the numerical simulation is ments were obtained on the basis of measurements recorded more reasonable. during the excavation process, and the displacement results Moreover, the measured surface settlement data of two at the corresponding positions are extracted from the nu- typical sections in Beijing [26] and Changsha [27] metro merical model. construction are included in Figure 12. +e geological conditions of these two constructions are similar to the project investigated in this paper. +e diameters of these two 5.1. Transverse Settlement. +e eventual transverse ground shield tunnels are 6.0 m, and the depths of two tunnels are surface settlement trough is highlighted. Figure 11 shows the 15.0 m in the Beijing metro and 12.5 m in the Changsha transverse settlement trough of the ground surface at Step 5. metro, respectively. Obviously, both the settlement and the Both the numerical results and the monitoring results match main influenced range induced by the small shield tunnel well with the Gauss distribution. From the numerical results, with a diameter of 6 m are smaller than the large shield it can be found that the maximum surface settlement, Svvmax, tunnel with the diameter of 12 m. +e maximum settlement occurs at the tunnel axis x, and the final value of Sv,max is of the two metro tunnels is smaller than 6.7 mm. However, 17.25 mm. +e maximum settlement in the monitoring the main influence ranges of two small metro tunnels are section of the project is 14.44 mm, about 84% of the cor- about 9 m, about 1.5 times of the excavation diameter, which responding numerical result. is the same to that of the large shield tunnel investigated in In the area close to the tunnel axis (−18 < x < 18 m), this project. about 1.5 times of the excavation diameter, the numerical +e development of the transverse ground surface result is larger than the measured result with an average settlement trough obtained by the finite difference method value of about 4.00 mm, which means the numerical (FDM) during the face advancement is shown in Figure 13. prediction slightly overestimates the eventual surface +is figure shows that the settlement is close to Gaussian settlement. +e overestimation of numerical results could distribution. +e excavation causes an increase in the be treated as the safety margin in a reasonable way. In the surface settlement, which could be explained by the ac- area far away from the tunnel axis (x < −18 m and cumulated loss of the ground during tunnelling. Both the x > 18 m), the numerical result is smaller than the mea- settlement and the width of the transverse ground surface sured result, which means the numerical prediction settlement trough get increased during the excavation slightly underestimates the eventual surface settlement. As process. all the measured results are smaller than 2.30 mm, the +e transverse ground settlement troughs of different influence of the underestimation could be well accepted in subsurfaces are shown in Figure 14. According to Figure 14, the construction project. the maximum settlement magnitude increases as the depth. +e ground surface settlement predicted by the Peck With the distance decreasing from the tunnel, the ground is formula is also shown in Figure 11. Before using the Peck strongly influenced by the excavation. +us, the maximum formula, two experiential parameters K and VL are needed. settlement of the ground near the tunnel is much larger than Based on the parameter statics of the Peck formula in the that of the ground surface. It can also be observed that the Beijing area [25] and the actual condition of the project, the settlement area of the ground gets increased gradually with experiential parameters K � 0.4 and VL � 0.5% are adopted in the depth. Compared to the maximum settlement, the area this project. +e ground surface settlement predicted by the with the ground deformation induced by the excavation Peck formula is carried out by using formulas (2)–(4). In the expands with the distance between the tunnel and ground in area close to the tunnel axis (−18 < x < 18 m), Peck formula z-axis. Similar results are also found by Mair and Taylor [24], overestimates the ground surface settlement, which is at least as described in equation (4). 1.6 times of the settlement monitored in situ. It is obvious that the prediction results deduced by the Peck formula are much more conservative than that of the proposed model in 5.2. Longitudinal Settlement. +e longitudinal ground sur- this paper. face settlement troughs (x � 0) calculated by FLAC3D and 8 Advances in Civil Engineering

0 x = –18 x = 18 –2 –4 –6 –8 (mm)

v –10 –12 –14 –16 Settlement S –18 –20 –22 –24 –50 –40 –30 –20 –10 0 10 20 30 40 50 Distance from the tunnel axis x (m) FDM Peck formula (K = 0.4, VL = 0.5%) Monitoring Figure 11: Comparison of the predicted and measured transverse settlement pro
le (Step 5).

x = –18 x = –9 x =9 x = 18 0 –2 –4 –6 –8 (mm)

v –10 –12 –14 –16 Settlement S –18 –20 –22 –24 –50 –40 –30 –20 –10 0 10 20 30 40 50 Distance from the tunnel axis x (m) Monitoring (Rapid Transit Line Project) Monitoring (Beijing Metro Line 5) Monitoring (Changsha Metro Line 1) Figure 12: Monitoring transverse settlement pro
les by the slurry shield with dierent diameters (Step 5).

0 –2 –4 –6

(mm) –8 v –10 –12

Settlement S –14 –16 –18 –20 –50 –40 –30 –20 –10 0 10 20 30 40 50 Distance from the tunnel axis x (m) Step 1 Step 4 Step 2 Step 5 Step 3 Figure 13: Numerical results of settlements at the ground surface during tunnelling. Advances in Civil Engineering 9

0 –2 –4 –6 –8 –10

(mm) –12 v –14 –16 –18 –20 Settlement S –22 –24 –26 –28 –30 –50 –40 –30 –20 –10 0 10 20 30 40 50 Distance from the tunnel axis x (m) z =0 z = 10.6m z = 2.0m z = 12.8m z = 6.4m z = 14.4m Figure 14: Vertical displacements in the transverse section of dierent subsurfaces. measured in site are presented in Figure 15. It is obvious that method and monitoring method are more than 81.8% of the the performance of the longitudinal settlement troughs is total settlements before the succeeding settlement, and the similar. Before the tunnel face’s arrival, the ground settle- settlements in Steps 3 and 4 are about 66.2∼78.8% in the ments are almost zero. e main settlement occurs in Step 3 numerical method and 48.1∼63.9% in the monitoring and Step 4, which means that the tunnel passage and tail void method. Hence, the driving speed and lining construction disturb the ground seriously. From both the numerical and time are of great importance for controlling the settlement in monitoring results of this project, the settlement induced by slurry shield tunnelling. the excavation (in Step 3) is larger than that induced by the Table 4 compares the numerical results and the measured tail void (in Step 4), and similar conclusions were found by results at the tunnel centerline of dierent subsurfaces. e Melis et al. [19] and Lambrughi et al. [23]. In other words, settlements predicted by this model during the
rst three steps the passage of the shield is the most dangerous stage for the are much smaller than the measured settlements, especially in structures above the tunnel. Compared with the other curves Step 1 and Step 2. And the predicted settlements in the last in Figure 14, a similar conclusion can be obtained that the two steps are 15∼30% larger than the measured settlements. maximum settlement increases as the depth. However, 15∼30% overestimation of the
nal settlement in Table 3 represents the maximum settlements at dif- the numerical model can be regarded as a safety margin for ferent subsurfaces of each step during tunnelling both in the unpredictable factors during the construction progress. the numerical model and
eld measurement. Si is the us, this numerical model can predict the longitudinal cumulated settlement at the tunnel center (x 0) at the settlement in a more reasonable way. end of Step i i 1, 2, ..., 5 . S is the settlement at the ( ) i tunnel center that occurred in Step i and equals to 5.3. Settlement of the TunnelVault. In general, the maximum S S S 0 . i i 1( 0 ) Δ deformation at the tunnel vault may in§uence the normal In Step 1 of the numerical results, the settlement S 1 operation of the tunnel and threaten the tražc safety. As it is decreases− with the depth of the measured section, which is − impossible to construct the segmental lining immediately due to the slight in§uence of the excavation in this step on after the shield tail, there is a construction time lag which has the ground far away from the tunnel face. e monitoring great in§uence on the settlement of the tunnel vault, as results in§uenced by many unexpected factors in Step 1 do shown in Figure 16. e point A is the moment when the not have such features, and the values are much larger than shield tail has been passed, and the point B is the moment those of the numerical method. However, in Steps 2 to 4, the when the ring segmental lining has been formed. It is evident ground is strongly in§uenced by the excavation of the that the settlement of the tunnel vault between points A and tunnel, the ground near the tunnel has a signi
cant B is signi
cant, S , AB 9.00 mm which is 27.0% of the total movement, and the settlements both in numerical results V settlement. us, reduction of the construction time lag after and monitoring results increase with the distance from the the shield tail is of great importance. ground surface. is model magni
es the impact of tail void, the settlements in Steps 1 and 2 are underestimated, and the settlements in Steps 3 to 5 are overestimated by this nu- 5.4. Horizontal Displacement along the Depth. Figure 17 merical model, especially in Step 4. shows the computed and monitored horizontal displace- From Table 3, it also can be found that the cumulated ments of the ground along the depth, corresponding to the settlements of dierent subsurfaces both in the numerical tunnel face 5 m away from the measured section and 5 m 10 Advances in Civil Engineering

Step 1 Step 2 Step 3 Step 4 Step 5 0 –2 –4 –6 –8 –10

(mm) –12 v –14 –16 –18 –20 Settlement S –22 –24 –26 –28 –30 –20 –10 0 10 20 30 40 50 Distance from the tunnel face y (m) FDM Monitoring z =0 z = 10.6m z =0 z = 10.6m z = 2m z = 12.8m z = 2m z = 12.8m z = 6.4m z = 14.4m z = 6.4m z = 14.4m Figure 15: Vertical displacements in the longitudinal section of dierent subsurfaces.

Table 3: Settlements of dierent subsurfaces during excavation. z 0 z 2.0 m z 6.4 m z 10.6 m z 12.8 m z 14.4 m NMNMNMNMNMNM Step 1 S1 (mm) 1.18 2.09 0.62 4.01 0.42 3.36 0.26 3.18 0.15 2.94 0.06 3.76 S1/S5 (%) 6.84 14.47 3.34 26.33 1.96 19.73 1.09 17.34 0.58 14.26 0.22 15.47 S1 (mm) −1.18 −2.09 −0.62 −4.01 −0.42 −3.36 −0.26 −3.18 −0.15 −2.94 −0.06 −3.76 S1/S5 (%) 6.84 14.47 3.34 26.33 1.96 19.73 1.09 17.34 0.58 14.26 0.22 15.47 ΔStep 2 − − − − − − − − − − − − ΔS2 (mm) 2.82 5.80 2.90 5.59 3.03 4.84 3.21 5.81 3.42 6.80 3.68 7.55 S2/S5 (%) 16.35 40.17 15.60 36.70 14.13 28.42 13.43 31.68 13.23 32.99 13.21 31.07 S2 (mm) −1.64 −3.71 −2.28 −1.58 −2.61 −1.48 −2.95 −2.63 −3.27 −3.86 −3.62 −3.79 S2/S5 (%) 9.51 25.69 12.26 10.37 12.17 8.69 12.34 14.34 12.64 18.73 12.99 15.60 StepΔ 3 − − − − − − − − − − − − SΔ3 (mm) 8.73 10.93 9.49 10.82 11.24 12.27 12.97 16.30 14.40 17.67 15.80 18.99 S3/S5 (%) 50.61 75.69 51.05 71.04 52.43 72.05 54.27 88.88 55.68 85.74 56.71 78.15 S3 (mm) −5.91 − 5.13 −6.59 − 5.23 − 8.21 − 7.43 − 9.76 −10.49 −10.98 −10.87 −12.12 −11.44 S3/S5 (%) 34.26 35.53 35.45 34.34 38.29 43.63 40.84 57.20 42.46 52.74 43.50 47.08 StepΔ 4 − − − − − − − − − − − − SΔ4 (mm) 15.09 12.75 15.21 13.13 18.30 14.14 21.12 17.31 23.44 19.98 25.63 22.31 S4/S5 (%) 87.48 88.30 81.82 86.21 85.35 83.03 88.37 94.38 90.64 96.94 92.00 91.81 S4 (mm) − 6.36 − 1.82 − 5.72 − 2.31 − 7.06 − 1.87 − 8.15 − 1.01 − 9.04 − 2.31 − 9.83 − 3.32 S4/S5 (%) 36.87 12.60 30.77 15.17 32.93 10.98 34.10 5.51 34.96 11.21 35.28 13.66 StepΔ 5 − − − − − − − − − − − − SΔ5 (mm) 17.25 14.44 18.59 15.23 21.44 17.03 23.90 18.34 25.86 20.61 27.86 24.30 S5/S5 (%) 100 100 100 100 100 100 100 100 100 100 100 100 S5 (mm) − 2.16 − 1.69 − 3.38 − 2.1 − 3.14 − 2.89 − 2.78 − 1.03 − 2.42 − 0.63 − 2.23 − 1.99 S5/S5 (%) 12.52 11.70 18.18 13.79 14.65 16.97 11.63 5.62 9.36 3.06 8.00 8.19 NΔ is short for the− numerical− result; M is− short for the− monitoring− result. − − − − − − − Δ and 10 m past the measured section, which locates at the As the shield moves forward, the outward displacement distance from the tunnel side wall of 2 m, as shown in increases gradually. And the maximum outward dis- Figure 6. e three curves belong to the excavation pro- placements of the numerical model and monitoring result cedure Step 2 and Step 3, respectively. Before the arrival of are S 2.68 mm and 1.57 mm, respectively, both of x,max the shield, a tiny outward displacement with the value which appear at the tunnel centerline when the shield smaller than 1.00 mm is occurred at the measured section. passes. Advances in Civil Engineering 11

Table 4: Comparison of the numerical results with the monitoring simulates the step-by-step tunnel excavation. e nu- results. merical model is validated by the
eld measurements in the Rapid Transit Line Project from Beijing Railway Station to SN/SM West Beijing Railway Station in China (RTLP), which z z z z z z 0 2.0 m 6.4 m 10.6 m 12.8 m 14.4 m means the numerical model in this paper can predict the ground deformation induced by large slurry shield tun- Step 1 0.56 0.15 0.13 0.08 0.05 0.02 nelling very well. Some conclusions are summarized as Step 2 0.49 0.52 0.63 0.55 0.50 0.49 follows: Step 3 0.80 0.88 0.92 0.80 0.81 0.83 Step 4 1.18 1.16 1.29 1.22 1.17 1.15 (1) e transverse settlement reaches the peak at the Step 5 1.19 1.22 1.26 1.30 1.25 1.15 center and gets decreased with the distance from the center. e main settlement in the transverse section occurs within the zone about 1.5 times of the ex- Step 1 Step 2 Step 3 Step 4 Step 5 cavation diameter. In the main range of ground 0 surface settlement, the numerical prediction is larger –5 than the measured result with an average value of –10

(mm) about 4.00 mm. v –15 A (2) e main longitudinal settlement occurs when the –20 shield is passing and the tail has passed the measured –25 B section. e settlements during these two steps are Settlement S –30 more than 50% of the eventual settlement. Hence, –35 –20 –10 0 10 20 30 40 50 the driving speed and lining construction time are of Distance from the tunnel face y (m) great importance for controlling the settlement during the tunnelling process. Tunnel vault (3) e settlement of the tunnel vault accounts for 27% Figure 16: Settlement of the tunnel vault during the tunnelling of the total settlement. erefore, accomplishing the process (the numerical result).
rst ring segmental lining after the tunnel tail is also very important. 0 (4) e outward vertical deformation mainly happens to the ground layer where the tunnel exists. Besides, the –5 maximum vertical deformation is located at the tunnel centerline. –10

–15 Data Availability

Depth (m) –20 e data used to support the
ndings of this study are in- Tunnel cluded within the article. –25

–30 Conflicts of Interest –4 –3 –2 –1 0 1 2 3 4 Horizontal displacement (mm) e authors declare that there are no con§icts of interest Monitoring FDM regarding the publication of this paper. 5m away from 5m away from measured section measured section Acknowledgments 5m past 5m past measured section measured section e authors acknowledge the
nancial support provided by 10m past 10m past the Beijing Municipal Natural Science Foundation of China measured section measured section (Grant no. 8172037) and the National Natural Science Figure 17: Horizontal displacements along depth. Foundation of China (Grant no. 51378002). References

6. Conclusions [1] X. Yang and G. Liu, “Performance of a large-scale metro interchange station excavation in shanghai soft clay,” Journal A three-dimensional
nite dierence model for the large- of Geotechnical and Geoenvironmental Engineering, vol. 143, diameter slurry shield tunnelling is built to predict the no. 6, article 05017003, 2017. ground deformation. e
nite dierence model com- [2] A. Sainoki, S. Tabata, H. S. Mitri, D. Fukuda, and J.-I. Kodama, prehensively takes into account the entire shield tunnelling “Time-dependent tunnel deformations in homogeneous and components, such as face pressure, grouting pressure, heterogeneous weak rock formations,” Computers and Geo- structure void, and hardening of grout and realistically technics, vol. 92, pp. 186–200, 2017. 12 Advances in Civil Engineering

[3] K. Han, C. Zhang, W. Li, and C. Guo, “Face stability analysis [19] M. Melis, L. Medina, and J. M. Rodr´ıguez, “Prediction and of shield tunnels in homogeneous soil overlaid by multilay- analysis of subsidence induced by shield tunnelling in the ered cohesive-frictional soils,” Mathematical Problems in Madrid metro extension,” Canadian Geotechnical Journal, Engineering, vol. 79, pp. 1–9, 2016. vol. 39, no. 6, pp. 1273–1287, 2002. [4] A. Franza, A. M. Marshall, T. Haji, A. O. Abdelatif, [20] R. P. Chen, J. Zhu, W. Liu, and X. W. Tang, “Ground S. Carbonari, and M. Morici, “A simplified elastic analysis of movement induced by parallel EPB tunnels in silty soils,” tunnel-piled structure interaction,” Tunnelling and Un- Tunnelling and Underground Space Technology, vol. 26, no. 1, derground Space Technology, vol. 61, pp. 104–121, 2017. pp. 163–171, 2011. [5] B. Simpson and P. J. Vardanega, “Results of monitoring at the [21] T. Sugiyama, T. Hagiwara, T. Nomoto et al., “Observations of British Library excavation,” Proceedings of the Institution of ground movements during Tunnel construction by slurry Civil Engineers–Geotechnical Engineering, vol. 167, no. 2, shield method at the docklands light railway lewisham pp. 99–116, 2014. extention-East London,” Soils and Foundations, vol. 39, no. 3, [6] F. Martos, Concerning an Approximate Equation of the pp. 99–112, 1999. Subsidence Trough and its Time Factors, International Strata [22] I. Ocak, “A new approach for estimating the transverse surface Control Congress, Leipzig, Germany, 1958. settlement curve for twin tunnels in shallow and soft soils,” [7] R. B. Peck, “Deep excavations and tunnelling in soft ground, Environmental Earth Sciences, vol. 72, no. 7, pp. 1–11, 2014. state of the art report,” in Proceedings of 7th International [23] A. Lambrughi, L. Medina Rodr´ıguez, and R. Castellanza, “Development and validation of a 3D numerical model for Conference on Soil Mechanics and Foundation Engineering, TBM-EPB mechanised excavations,” Computers and Geo- pp. 225–290, Mexico City, Mexico, August 1969. technics, vol. 40, no. 1, pp. 97–113, 2012. [8] M. P. O’Reilly and B. M. New, “Settlements above tunnels in [24] R. J. Mair and R. N. Taylor, “+eme lecture: bored tunnelling the United Kingdom-their magnitude and prediction,” in in the urban environment,,” in Proceedings of 14th In- Tunneling’82, pp. 173–181, London Institute of. Mining and ternational Conference on Soil Mechanics and Foundation Metallury, Mexico City, Mexico, 1982. Engineering, pp. 2353–2385, Hamburg, Germany, September [9] B. M. New and M. P. O’Reilly, “Tunnelling-induced Ground 1997. Movements: predicting their magnitude and effects,” in [25] X. Han, N. Li, and R. S. Jamie, “An adaptability study of Proceedings of 4th International Conference on Ground Gaussian equation applied to predicting ground settlements Movements and Structures, pp. 691–697, Cardiff, UK, July induced by tunnelling in China,” Rock and Soil Mechanics, 1991. vol. 28, no. 1, pp. 23–28, 2007, in Chinese. [10] P. B. Attewell and J. P. Woodman, “Predicting the dynamics [26] X. M. Pan and C. H. Lei, Comprehensive Engineering Tech- of ground settlement and its derivatives caused by tunnelling nology Applied in Gravel Strata of Beijing, China Commun in soil,” Ground Engineering, vol. 15, no. 8, pp. 13–26, 1982. Press, Beijing, China, 2012, in Chinese. [11] A. Tyagi, M. F. B. Zulkefli, Y. Pan, S.-H. Goh, and F.-H. Lee, [27] D. H. Chen, “Numerical simulation of shield tunnel con- “Failure modes of tunnels with improved soil surrounds,” struction and the selection of shield in sandy pebble stratum,” Journal of Geotechnical and Geoenvironmental Engineering, Master thesis, Central South University, Hunan, China, 2013, vol. 143, no. 11, article 04017088, 2017. in Chinese. [12] R. J. Grant and R. N. Taylor, “Tunnelling-induced ground movements in clay,” Proceedings of the Institution of Civil Engineers–Geotechnical Engineering, vol. 143, no. 1, pp. 43–55, 2000. [13] H. Kuwahara, T. Yamazaki, and O. Kusakabe, “Ground de- formation mechanism of shield tunnelling due to tail void formation in soft clay,” in Proceedings of 14th International Conference on Soil Mechanics and Foundation Engineering, vol. 3, pp. 1457–1460, Rotterdam, Netherlands, September 1997. [14] J. H. Atkinson and D. M. Potts, “Subsidence above shallow tunnels in soft ground,” Journal of the Geotechnical Engi- neering Division ASCE, vol. 103, no. 4, pp. 307–325, 1977. [15] F. Zhang, Y. F. Gao, D. Leshchinsky, D. S. Zhu, and G. H. Lei, “+ree-dimensional stability of slurry-supported trenches: end effects,” Computers and Geotechnics, vol. 74, pp. 174–187, 2016. [16] C. Zhang, K. Han, and D. Zhang, “Face stability analysis of shallow circular tunnels in cohesive-frictional soils,” Tun- nelling and Underground Space Technology, vol. 50, pp. 345– 357, 2015. [17] R. J. Finno and G. W. Clough, “Evaluation of soil response to EPB shield tunneling,” Journal of Geotechnical Engineering, vol. 111, no. 2, pp. 155–173, 1985. [18] T.-N. Do, C.-Y. Ou, and R.-P. Chen, “A study of failure mechanisms of deep excavations in soft clay using the finite element method,” Computers and Geotechnics, vol. 73, pp. 153–163, 2016. International Journal of Rotating Advances in Machinery Multimedia

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