Geotechnical influence on existing subway tunnels induced by multiline tunneling in Shanghai soft soil

Computers and Geotechnics 56 (2014) 121–132

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Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo

Geotechnical influence on existing subway tunnels induced by multiline tunneling in Shanghai soft soil Zhiguo Zhang a,b,c,⇑, Maosong Huang b,d a

School of Environment and Architecture, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai 200093, China Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China c State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China d Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China b

a r t i c l e

i n f o

Article history: Received 19 August 2013 Received in revised form 14 November 2013 Accepted 28 November 2013 Available online 15 December 2013 Keywords: EPB shield Multiline tunneling Geotechnical deformation Simplified analysis Numerical simulation Case history

a b s t r a c t Multiline tunneling construction in soft soil significantly impedes risk control and environmental protection. Current research has investigated on the effect of single-line shield excavation on surrounding environments and tunneling for parallel-crossing or perpendicular down-crossing underground structures. However, minimal attention has been given to soil disturbances induced by multiline tunneling and complex overlapped interaction mechanics for adjacent structures, such as existing above-crossing and down-crossing subway tunnels. Few studies focus on oblique crossing construction and setting rules for the operation parameters of shield machines. Based on the Shanghai Railway transportation project and in situ monitoring data, the deformation analyses of existing subway tunnels induced by an earth pressure balance (EPB) shield during the process of above-overlapped and down-overlapped crossing tunnels with oblique angles are presented. The deformation analyses employ the three-dimensional finite element (3D FE) numerical simulation method, and the simplified analytical method. The analysis results from the theoretical methods are consistent with the monitoring data. The setting rules of multiline propulsion main parameters, including the earth pressure for cutting open, and the synchronized grouting, are also established. This study may provide a theoretical basis for the development of properly overlapped crossing schemes and geotechnical protective measures during multiline tunneling construction in soft soil. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Rapid economic development and urbanization in China has substantially accelerated land utilization; as a result, city planners are becoming more interested in the use of underground space to construct transportation infrastructures and facilities. Recently, complicated urban railway transportation systems, which serve as a 3D framework for underground space utilization, have been planned in cities such as Beijing, Shanghai, Nanjing, and Shenzhen. This ambitious plan is currently being implemented in high-speed construction [1–5]. In Shanghai, 11 metro lines with a total length of 420 km have been completed. By the end of 2020, 22 metro lines comprising a total length of 880 km will be operational; the majority of the lines are being constructed using the shield tunneling method. Shield tunneling technology has been extensively applied to urban underground spaces due to advantages such as high speeds, ⇑ Corresponding author at: School of Environment and Architecture, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai 200093, China. E-mail address: [email protected] (Z. Zhang). 0266-352X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compgeo.2013.11.008

a strong safety record, and minor disturbances to surface traffic. However, the underground structures of piles, municipal pipelines, and subway tunnels have hindered the use of potential construction space for new tunnels. Shield tunneling frequently overlaps and bypasses existing structures. Significant construction risks and potential safety hazards are encountered during complex overlapped construction. Because Shanghai is located in the Yangtze River Basin, a thick layer of soft clay is distributed throughout the underground space. Overlapped tunneling in soft ground will inevitably perturb the surrounding soil, which may induce adverse effects on adjacent structures (e.g., cracks in buildings and reductions in pipeline and service tunnel capacities). Therefore, a comprehensive understanding of the deformation behavior of adjacent metro tunnels induced by overlapped tunneling is critical. Theoretically, the response of existing tunnels to adjacent construction is problematic due to the interaction between soil disturbance induced by tunneling and the bearing capacity of existing tunnels. This problem has been examined in recent years using a variety of approaches: field observation, physical model testing and finite element numerical simulation.

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Based on field investigation data, significant progress in the calculation of ground surface settlements or lining stresses induced by tunneling has been made over the past few decades [6–13]. Field observations of the interactions between closely spaced crossing tunnels on the Jubilee Line Extension in London were conducted by Kimmance et al. [14]. Asano et al. [15] proposed an observational excavation control method for a mountain tunnel that was excavated adjacent to an existing tunnel. Li and Yuan [16] presented displacements of an existing tunnel caused by undercrossing tunnels in different undercrossing stages using an automatic high-performance total station measuring system. Field observations remain the most prevalent and recognized approach for understanding the interaction behavior between adjacent and crossing tunnels. Numerous attempts have been made to develop physical model tests, including scale model tests and centrifuge model tests, to investigate the influence of tunneling on adjacent tunnels, such as twin parallel tunnel engineering. Adachi et al. [17] used scale model tests to analyze the interaction behavior between doubleline tunnels. Kim [18,19] performed scale model tests to investigate the influence of tunnel proximity and alignment and liner stiffness on the interactions between closely spaced tunnels in clay. Vorster et al. [20] discussed the underlying mechanisms governing pipeline response to tunneling based on centrifuge model tests. Lee et al. [21] performed a series of centrifuge model tests to investigate tunnel stability and arching effects during single-line and double-line tunneling in soft clay soil. Byun et al. [22] conducted several large-scale model tests to estimate the ground behavior around tunnel-crossing zones and tunnel behavior for tunnels located above newly excavated tunnels. In addition, finite element numerical simulation is an effective method to analyze the deformation behavior of adjacent tunnels induced by tunneling. It considers the nonlinear interaction between existing tunnels and surrounding soils, soil elasto-plastic behavior, the freedom for the tunnel to heave, and the complexity of construction operations. Addenbrooke and Potts [23,24] used a 2D finite element method to analyze ground movements and lining behavior induced by twin tunnel construction. Chapman et al. [25] conducted a series of 2D finite element analyses to study the settlements above the closely spaced multiple tunnel construction of the London Clay. Ng et al. [26] reported multiple interactions between large parallel twin tunnels that were constructed with stiff clay using the 3D finite element method. Chehade and Shahrour [27] presented a 2D finite element numerical model for the optimization of the relative position of twin-tunnels and the construction procedure. Previous studies have primarily focused on the tunneling case of parallel-crossing or perpendicular down-crossing underground structures. However, minimal attention is given to multiline overlapped tunneling engineering, such as existing above-crossing and down-crossing subway tunnels. Case histories of oblique crossings are rarely reported in the literature. Numerical simulation is a common analysis technique. No research on special overlapped interactions using a simplified theoretical method has been reported. The problem of tunnel construction using multiline crossing with an oblique angle is becoming increasingly important in urban areas where available underground space is limited. Because the total cost of the construction of deep transport tunnels in urban areas is generally greater than the construction of shallow tunnels, a tunnel route that is located closer to existing underground structures is generally financially preferable. Thus, there has been considerable interest in recent years for the development of analysis theories and field measurement techniques for the investigation of the tunnel interaction problem. This research presents a tunneling case of the second-stage north route of Shanghai Railway transportation line 11 to study

the deformation behavior of the subway tunnel in service, which is induced by an EPB shield in soft clay during above-traversing and down-traversing processes. Various research approaches, including the simplified theoretical method, and 3D FE numerical simulation method, are performed to investigate the influence of multiline overlapped tunneling on existing tunnels. The simplified theoretical method is derived from the Winkler foundation. The longitudinal settlement equation for above-overlapped and down-overlapped construction of existing tunnels is obtained. The 3D numerical simulation method enables the optimization of the construction scheme and shield excavation parameters. The study cases of above-overlapped and down-overlapped crossings with large oblique angles are analyzed. The setting rules of shield tunneling parameters, including earth pressure for cutting open, and synchronized grouting are established based on the monitoring data. The proposed methods provide a theoretical basis for the development of proper protective measures for subway tunnels in service during tunneling excavation and the overlap traversing process. The research results provide shield propulsion references for the future construction of similar projects, such as multiline passing through existing structures.

2. Engineering background Shanghai Railway transportation line 11, which is one of the main components of the municipal transportation network, is located in the downtown area of Shanghai. Metro line 11 runs in a north–south direction and transports an extremely large number of passengers daily. The second-stage of the north route of line 11 passes through four districts: Changning, Xujiahui, Pudong New Area and Nanhui. It comprises a total length of 20.89 km and thirteen stations and extends from Huashan Road to Luoshan Road. As shown in Fig. 1, the transit tunnel from Xujiahui station to Shanghai Gymnasium station (Section No. 11.G.8) is a critical part of the second-stage of the north route of line 11. Existing line 1 and line 4 are encountered in the excavation site. The case of multiline overlapped tunneling discussed in this study is located between the Oriental Golden Horse building and the park under Lingling Road, in which the sport cultural center is located, as shown in Fig. 2. This transit tunnel is outfitted with two earth pressure balance shield machines. The shield tunneling machine is a mudding earth pressure balance-type machine with an outside diameter of 6.43 m. The up-line and down-line shields begin from the south shaft of Xujiahui station in a successive manner and subsequently propel to Shanghai gymnasium station from north to south. The up-line shield, which takes the lead out of the hole, covers a distance of approximately 100 rings with the down-line shield. When the up-line and down-line shields pass through Lingling Road, the shield of line 11 will obliquely cross the service tunnel of line 4 at a 75° angle. The sectional view of the position relationship between the shield of line 11 and the existing tunnel of line 4 is shown in Fig. 3. It should be noted that this material for the bottom layer extends indefinitely. The up-line shield crosses below line 4 and the minimum clear distance between the up-line shield and line 4 is 1.82 m; the down-line shield crosses above line 4 and the minimum clear distance between the down-line shield and line 4 is 1.69 m. The figure also shows that the covering soil depth of the down-line tunnel is approximately 6 m. The tunnel lining, which is a universal ring wedge segment, is composed of concrete. The outside diameter of the segment is 6.2 m and the inner diameter of the segment is 5.5 m. The ring width is 1.2 m and the segment thickness is 0.35 m. The segment concrete strength is classified as grade C55 and the concrete impermeability is classified as grade S12. The full circumference straight-joint assembly process is

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Lingling road

Caoxi north road

Line 4

Shanghai gymnasium station

Line 1 Line 11 Xujiahui station

Fig. 1. Plan view for transit tunnel of line 11 s-stage north route.

Fig. 2. Plan view for multiline overlapped tunneling in this study.

strength, and low modulus of deformation. Water leakage is detected in the tunnel segments according to the field survey and leak-blocking measures are implemented for part of the longitudinal joints between the lining rings, as shown in Fig. 4. In order to reduce disturbance impacts on adjacent line 4, and to reduce the ground loss caused by the physical gap between the outer diameter of the shield machine and the segment lining, six grouting holes are drilled in the shield waist and the shield tail, which are evenly distributed along the circumference and sealed with a high-quality ball valve. The side-view of the shield machine and a portion of the grouting hole locations are shown in Fig. 5. To effectively control the synchronized grouting volume and to achieve uniform pressure injection, the multiple-points rotation grouting method is applied in the overlapped crossing stage. By considering that the propulsion distance of each shield ring is 1200 mm, two diagonal and adjacent grouting holes are established as a group and one rotation is conducted every 300 mm. 3. 3D FE numerical simulation analysis 3.1. Numerical model and simulation parameters

Fig. 3. Sectional view for multiline overlapped tunneling in this study.

applied, and the segment rings are connected with high-strength bolts. The construction site is characterized by coastal plain topography, which primarily consists of saturated cohesive soil and silty soil. According to the genetic type, strata composition and characteristics, the soil in situ can be divided into eight layers. The geotechnical properties are shown in Table 1. The soils surrounding the shield tunnels predominantly consist of muddy clay and silty clay and exhibit the following characteristics: large void ratio, high plasticity, poor permeability, high water content, low shear

The deformation of the existing tunnels in soft clay induced by multiline overlapped tunneling is examined using the 3D finite element numerical simulation method. A commercial 3D finite element program (ABAQUS) is employed as a numerical tool to specify drained behavior in an effective stress analysis. The Drucker–Prager model is used to simulate soil mechanical behavior and the third-invariant dependence is introduced to account for the lower strength along extension paths. Based on the previous researches [28–31], the soil stress history and stress–strain response of consolidated soil have been conducted by the triaxial tests. In this finite element study, the initial stresses of the entire stratum, assumed to be normally consolidated, are generated by using gravity loading. Accompanied by the initial stress calculation, steady-state pore water pressures can be generated by means of a steady-state groundwater flow calculation in the water condition mode. This requires the input of boundary conditions on the groundwater head. The mechanical parameters of drained type applied to this soil model are summarized in Table 1. The tunnel lining is modeled as linear elastic. The hexahedral eight-node element C3D8R simulates the soil and the tunnel lining. The strength of the lining concrete is classified as grade C55 and the elastic modulus and Poisson’s ratio are 3.55  104 MPa and 0.2, respectively, according to the specification. To reflect the comprehensive influences caused by the shield tail void closure, the effects of grouting filling, and the surrounding soil disturbance by the shield propulsion, an equivalent layer is

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Table 1 Geotechnical parameter for in situ soil. Layer no.

Soil name

H (m)

w (%)

e

csat (kN/m3)

Es (MPa)

l

C (kPa)

u (°)

kv (cm/s)

kh (cm/s)

r1 s t u v1 v1a v1 v3

Backfill Silty clay Muddy silty clay Muddy clay Clay Sandy silt Clay Silty clay

2.0 1.3 3.3 8.4 1.0 4.5 4.3 15.0

28.9 37.9 30.1 55.7 42.1 24.6 42.1 32.7

0.82 1.04 0.87 1.55 1.16 0.74 1.16 0.95

18.0 18.5 17.4 16.7 17.8 18.2 17.8 18.1

8.86 4.48 2.54 2.09 3.36 8.21 3.36 4.66

0.33 0.32 0.32 0.33 0.26 0.24 0.26 0.29

0 26.0 10.0 11.0 14.0 5.0 14.0 16.0

22.0 17.0 16.5 12.5 14.5 33.0 14.5 22.5

N/A 7.11  107 1.57  106 4.65  107 4.78  107 1.21  104 4.78  107 2.20  106

N/A 2.09  106 6.72  106 1.05  106 1.22  106 2.11  104 1.22  106 3.60  106

Notes: N/A = not available. H is the thickness of every layer; w is the water content; e is the void ratio; csat is the saturated unit weight; Es and l are the oedometric compression modulus and Poisson’s ratio, respectively; C and u are the effective cohesion force and friction angle of drained type, respectively; kv and kh are the vertical and horizontal coefficients of permeability, respectively.

Gp = (6.34–6.2)/2 = 0.07 m; g is the soil property coefficient, for hard clay, 0.7–0.9; for dense sand, 0.9–1.3; for loose sand, 1.3–1.8; for soft clay, 1.6–2.0. It can be selected as 1.5 for this project. Then the thickness of equivalent layer is: d = 1.5  0.07 = 0.105 m. Considering the soil disturbance sphere influenced by the excavation, the size of the three-dimensional model size is 95 m  144 m  120 m. Fig. 7 shows the 3D finite element numerical analysis for the multiline tunneling in existing tunnels. The model contains 147,656 nodes and 130,112 elements. In this numerical study, the sensitivity analyses are carried out to evaluate the influence of mesh resolution on model results. It is found that the mesh adopted in this study can simulate the overlapped tunneling problem with satisfactory precision. Actually, the sensitivity analyses show that the grid discretization degree in the region of shield excavation is more influenced on the calculation precision than that in the region of existing tunnel of line 4. Then the special grid local refinements have been conducted in the region of the up-line and down-line shield excavation. As shown in Fig. 2, the angle between the direction of the shield propulsion and line 4 is approximately 75°. This oblique crossing not only creates enormous risks and challenges for construction but also produces significant challenges for the numerical model. According to the discrete element and disregarding that the discrete types for the regions of line 4, up-line 11 and down-line 11 are consistent, the element nodes are unnaturally coupled in the contact surfaces in the three regions due to the 75° oblique crossing condition. To produce natural node coupling from different regions, the thin-layer elements are separately established in the region between line 4 and up-line line 11, and the region between line 4 and down-line line 11, as shown in Fig. 8. It should be noted that the material properties for thin-layer elements are same with the soil in its region.

(a) Water leakage

(b) Leak-blocking measurement Fig. 4. Present situation for line 4 at the overlapped construction stage.

established for simulation (shown as Fig. 6). Discrete elements use the hexahedral eight-node element C3D8R. To obtain the geotechnical parameter for in situ disturbed soils and provide a reference for the overlapped crossing stage, the total distance of 30 rings from the 951th ring to the 980th ring of the up-line and down-line, respectively, are selected for the shield propelling trial prior to crossing construction. During the shield trial propulsion stage, the sampling soils are drilled surrounding the grouting region. The six sections are selected for drilling along the propulsion direction. The distance for the every two sections is 6000 mm. The soil properties have been measured by geotechnical tests and the soil conditions along with the average soil properties are presented. The equivalent layer density is 1900 kg/m3, the elastic modulus is 15.5 MPa, and Poisson’s ratio is 0.2. Its thickness can be calculated by [32]:

d ¼ gGp

ð1Þ

in which Gp is the physical gap between the outer skin of shield machine and segment lining and it can be calculated:

3.2. Construction process and calculation steps To optimize the shield operation parameters for adaptation to the geologic condition and to provide a reference for the overlapped crossing stage, the total distance of 30 rings from the 951th ring to the 980th ring of the up-line and down-line, respectively, are selected for the shield propelling trial prior to crossing construction. Fig. 9 shows the soil lateral pressure coefficients in the trial propulsion stages of the up-line and down-line shields. Fig. 10 shows the initial soil displacement by cutting open in the trial propulsion stage. For the trial results of the up-line shield propulsion, when the soil lateral pressure coefficient is 0.85, the corresponding initial soil displacement by cutting open is in the range of 0.09 to 0.03 mm for these five rings, which indicates that the soil disturbance is comparatively small with a small amount of soil upheaval. The soil lateral pressure coefficient of the up-line shield is 0.85, and the initial soil pressure by cutting open is 0.37 MPa in the crossing stage. For the trial results of the down-line shield

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Cutter head Screw machine

Fig. 5. Grouting hole location of EPB shield (Unit: mm).

Equivalent layer

Metro train Lining segment layer

Fig. 6. Equivalent layer for simulation of disturbed soils.

propulsion, the corresponding initial soil displacement by cutting open is in the range of 0.07 to 0.04 mm when the soil lateral pressure coefficient is 0.75. The soil lateral pressure coefficient of the down-line shield is 0.75, and the initial soil pressure by cutting open is 0.13 MPa in the crossing stage. Because the buried depths of the up-line and down-line tunnels differ, the corresponding synchronized grouting amounts also differ. Fig. 11 shows the synchronized grouting amounts for the upline and down-line shield trial propulsion stages, and Fig. 12 shows the shield tail settlement curves for the up-line and down-line shields. Regarding the trial results of the up-line shield propulsion, when the synchronized grouting amount is 3.5 m3 per ring, the shield tail settlement is in the range of 0.23 to 0.31 mm, which indicates a small disturbance on the soil body. Thus, the synchronized grouting amount for the up-line shield in the overlapped crossing stage is 3.5 m3 per ring, and at this moment the grouting injection pressure is 0.85 MPa. Similarly, based on the trial results of the down-line shield propulsion, when the synchronized grouting amount is 2.5 m3 per ring, the shield tail settlement is in the range of 0.06 to 0.25 mm with a small disturbance of the soil body. Thus, the synchronized grouting amount or down-line shield in the overlapped crossing stage is 2.2 m3 per ring, and at this moment the grouting injection pressure is 0.53 MPa.

(a) Whole meshed model

Outer-ring 4 Down-line 11

Up-line 11

Inner-ring 4

(b) Local meshed model Fig. 7. 3D finite element numerical model for multiline overlapped tunneling.

The propelling forward in the simulation of the shield construction process can be assumed a discontinuous process, which can be calculated by changing the element material type in the finite element software, namely, the stiffness migration method. Based on the geotechnical tests, the change in modulus of the slurry during the process of grouting hardening involves three stages: an initial period of 0.1 MPa, an interim period of 1 MPa and a stable period of 10 MPa. Based on the shield propelling trial, the grouting injection pressure and the support pressure applied at the

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Fig. 8. Thin-layer elements for obliquely crossing construction.

4

0.9 0.8 0.7 0.6

Down-line shield Up-line shield

Grouting volume (m3 )

Lateral pressure coefficient

1

3

2

1

Down-line shield Up-line shield

0.5

950

960

970

0 950

980

Ring number

Fig. 9. Soil lateral pressure coefficient in trial propulsion stage.

Ring number

980

970

Fig. 11. Synchronized grouting amounts in trial propulsion stage.

-0.4

-2

-0.3 -0.2

Settlement value (mm)

S oil dis p a lce me nt (mm)

960

-0.1 0 0.1 0.2 0.3

Down-line shield Up-line shield

0.4

-1

0

1

Down-line shield Up-line shield

0.5

950

960

970 Ring number

980

Fig. 10. Soil displacements ahead by cutting open in trial propulsion stage.

2 950

960

Ring number

970

980

Fig. 12. Shield tail settlements in trial propulsion stage.

excavation front for the up-line shield are set as 0.85 MPa and 0.37 MPa, respectively. According to the down-line shield, the grouting injection pressure and the support pressure applied at the excavation front are set as 0.53 MPa and 0.13 MPa, respectively. The numerical simulation for the tunneling construction process can be divided into six calculation steps and it is shown in Fig. 13. 3.3. Numerical simulation results According to the finite element numerical model, a total of 120 ring segments are installed in the up-line and down-line of line 11;

each ring is 1.2 m in length. To facilitate the description, the shield initial propulsion ring in this model is set to the first ring (corresponds to the 951th ring in situ from Fig. 2), and the end of the shield tunneling ring in this model is set to the 120th ring (corresponds to the 1070th ring in situ from Fig. 2). To conduct the deformation analyses of existing line 4 induced by multiline overlapped tunneling, the construction conditions are such that the up-line shield propels to the 40th ring, the 80th ring, and the 120th ring. In addition, the construction conditions in which the down-line shield propels to the 40th ring, the 80th ring, and the 120th ring,

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Step 1

Step 2

Step 3

Step 4

Step 5

Destruction of first-ring soil, setting support pressure

Destruction of second-ring soil, setting support pressure

Destruction of third-ring soil, setting support pressure

Destruction of fourth-ring soil, setting support pressure

Initial geo-stress balance

Activation of equivalent layer and lining layer of first-ring, setting equivalent layer to bracing state

Activation of equivalent layer and lining layer of second-ring, setting grouting injection pressure

Activation of equivalent layer and lining layer of third-ring, setting grouting injection pressure

Activation of equivalent layer and lining layer of fourth-ring, setting grouting injection pressure

Step 6

Equivalent layer of first ring is set to grouting state and a modulus of 0.1 MPa

Equivalent layer of second ring is set to grouting state and a modulus of 0.1 MPa

Equivalent layer of third ring is set to grouting state and a modulus of 0.1 MPa

Equivalent layer of first ring is set to hardening state and a modulus of 1 MP

Equivalent layer of first and second ring is set to hardening state and a modulus of 10 MP, 1 MP, respectively

Soil excavation and lining bracing of other rings and complete shield grouting and hardening process

Fig. 13. Numerical simulation steps for tunneling excavation.

which occurs after the completion of the shield propulsion of the up-line, are also selected. Fig. 14 shows the longitudinal deformation of the inner and outer ring of line 4, which is caused by the up-line shield propulsion to the 40th ring, 80th ring, and 120th ring. Fig. 15 displays the longitudinal deformation of the inner and outer ring of line 4, which is caused by the down-line shield propulsion to the 40th ring, 80th ring, and 120th ring after the completion of the shield propulsion of the up-line. The numerical simulation results indicate that when the up-line shield of line 11 crosses below line 4, different deformation degrees are produced between the inner-ring and outerring of line 4. Because the inner-ring line is closer to the initial shield excavation position, it is affected by more construction impacts than the outer-ring line. For instance, when the up-line shield propels to the 40th ring, the largest deformation of the inner-ring line is 2.15 mm, whereas the largest deformation of the outer-ring line is 1.5 mm. Due to the propulsion of the shield, the deformation of the inner-ring and outer-ring line gradually increases. For example, when the up-line shield propels to the 80th ring, the largest deformation of the inner-ring line increases to 2.65 mm, which is 0.5 mm greater than the deformation of the previous construction condition. The largest deformation of the outerring line is 2.15 mm, which is 0.65 mm greater than the previous construction condition. After the completion of the up-line shield propulsion, the deformations of the inner and outer ring of line 4 gradually decrease with the propulsion of the down-line shield machine. For instance, when the down-line shield propels to the 40th ring, the largest deformation of the inner-ring and the outer-ring line of line 4 reduces from the previous condition (when the up-line shield

propels to the 120th ring) of 2.95 mm and 2.72 mm to 2.8 mm and 2.56 mm, respectively. When the down-line shield propels to the 80th and 120th ring, the largest deformation of the inner-ring reduces to 2.3 mm and 1.5 mm, respectively, and the largest deformation of the outer-ring reduces to 2.1 mm and 1.41 mm, respectively. Due to a horizontal distance of 4 m between the down-line and up-line shield propulsion directions (shown in Fig. 3), the maximum positions in the longitudinal deformation curve of line 4 also change. For example, when the up-line shield propels to the 120th ring, the position of the largest displacements of the inner and outer ring lines is x = 50 m; however, when the down-line shield propels to the 40th ring after the up-line excavation is completed, the position of the largest displacements of the inner- and outer-ring lines shift to x = 48 m. When the down-line shield excavation propels to the 80th ring, the position of the largest displacements of the inner- and outer-ring lines shift to x = 45 m. The numerical simulation analysis of the up-line and down-line shields of line 11 crossing line 4 shows that the deformations of the existing tunnels experienced a complex evolution. The tunnel displacement value and the deformation impact trend, as well as the maximum positions, all significantly change. Therefore, the theoretical prediction of overlapped crossing impacts is required. Constant adjustment of the propulsion parameters of the earth pressure balance shield machine based on the on-site monitoring program is required to ensure the structural safety of the existing tunnels and effortless progress of shield propulsion. In this study for Shanghai soft soils, compared with the undrained condition, the drained condition is the more severe on the performance of the existing tunnels of line 4. Although a preliminary study using 3D FE numerical simulation method is

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0

1

2

3

Inner-ring tunnel Outer-ring tunnel

Up-line

Vertical displacement (mm)

Vertical displacement (mm)

0

20

40

60

80

2

3

0

100

20

40

60

80

100

Tunnel longitudinal position (m)

Tunnel longitudinal position (m)

(a) Shield propulsion to 40th ring

(a) Shield propulsion to 40th ring

1

2

3

Inner-ring tunnel Outer-ring tunnel

Up-line

Vertical displacement (mm)

0

0

Vertical displacement (mm)

Inner-ring tunnel Outer-ring tunnel

Up-line 4

4 0

Down-line 1

20

40

60

80

2

3

Inner-ring tunnel Outer-ring tunnel

Up-line 4

4 0

Down-line 1

0

100

20

40

60

80

100

Tunnel longitudinal position (m)

Tunnel longitudinal position (m)

(b) Shield propulsion to 80th ring

(b) Shield propulsion to 80th ring

Vertical displacement (mm)

1

2

3

Inner-ring tunnel Outer-ring tunnel

Up-line 4

Vertical displacement (mm)

0 0

Down-line 1

2

3

4 0

0

20

40

60

80

Inner-ring tunnel Outer-ring tunnel

Up-line

100

20

40

60

80

100

Tunnel longitudinal position (m)

Tunnel longitudinal position (m)

(c) Shield propulsion to 120th ring

(c) Shield propulsion to 120th ring

Fig. 15. Longitudinal deformation of line 4 caused by down-line shield propulsion. Fig. 14. Longitudinal deformation of line 4 caused by up-line shield propulsion.

conducted, a comprehensive study is still required to estimate the drained settlements for the multiline tunneling construction. This comprehensive study could benefit the future design and construction of tunnels in similar ground.

of the shield and the tunnel lining, the elasto-plastic deformation U3D at the tunnel excavation face, and the over-excavation value x, which considers the quality of workmanship. The gap parameter g can be estimated as

g ¼ Gp þ U 3D þ x 4. Simplified analytical analysis 4.1. Basic theory and calculation method In simplified analytical research on the impacts of multiline overlapped crossing on existing tunnels, the green-field displacements caused by shield construction, which would occur if the existing tunnels did not exist, can be analyzed. An analysis of the application of soil displacements to the existing tunnels was subsequently conducted. The previous results [33,34] indicate that the soil deformation and surface settlements are primarily caused by ground loss induced by tunneling. Lee et al. [34] used the gap parameter to measure ground loss and considered that the gap parameter g primarily consists of the physical gap Gp between the outer skin

ð2Þ

where Gp is the physical gap, U3D is the elasto-plastic deformation, and x is the over-excavation value. Due to the continuous development of shield mechanical properties and improvements in the operation skills of engineers, the ground loss due to the elasto-plastic deformation U3D and the over-excavation x in Eq. (2) decreases. Thus, the difference Gp between the outer diameter of the shield machine and the outer diameter of the tunnel lining has become a major component of the gap parameter g. In this study, the green-field displacement induced by tunneling can be obtained by the multiple integral of gap unit deformation, which is based on the gap parameter in Eq. (2). Based on the theory proposed by Sagaseta [35], for a spherical gap with a unit radius of 1 in an infinite medium to sink, the radial displacement ur(r) of an arbitrary point located at a distance r from the gap unit is expressed as follows:

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ur ðrÞ ¼ 

 2 1 1 3 r

ð3Þ

As shown in Fig. 16, in the Cartesian coordinate system according to a gap with a unit radius of 1 at a point F(x0, y0, z0), the z axis displacement expression at an arbitrary point P(x, y, z) is [35]:

 z1 ¼  u

1 z  z0 3 c31

ð4Þ

where c1 = [(x  x0)2 + (y  y0)2 + (z  z0)2]1/2 . Note that Eqs. (3) and (4) are the displacement expressions based on the infinite medium, whereas the tunnel construction site is a semi-infinite soil body. Therefore, the infinite medium issue should be transformed to a semi-infinite medium issue. Thus, the known point F(x0, y0, z0) is mirrored to another point F0 (x0, y0, z0) (Fig. 16), and an equivalent volume expansion will occur at this image point. Thus, the z axis displacement expression at point P(x, y, z) is [35]:

h

Z

y0 þa

Z

x0 þb



1

p z0 ða  x0 Þðx  aÞ y0 a

x0 b

ða  x0 Þ2 þ ðb  y0 Þ2 þ z20 Z y0 þa Z x0 þb 1 þ lim lim  a!1b!1

h

y0 a

x0 b

 i5=2

p

z0 ðb  y0 Þðy  bÞ ða  x0 Þ2 þ ðb  y0 Þ2 þ z20

c

 i5=2

þ

 ð1  2lÞ da db c3 ðc3 þ zÞ

þ 3

 ð1  2lÞ da db c3 ðc3 þ zÞ

z 3 3

z

c3

ð6Þ

where c3 = [(x  a)2 + (y  b)2 + z2]1/2 and l is Poisson’s ratio. The z-axis displacement at point P(x, y, z) caused by the unit gap with a unit volume of 1 located at point F(x0, y0, z0) in a semiinfinite body can be expressed as follows:

 z ðx; y; zÞ ¼ u

Z

l

0



Z

Z

l

3  z1 þ u  z2 þ u z3  ½u 4p

 f0 Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

Z

h2 þR

h2 Rg

ð5Þ

where c2 = [(x  x0)2 + (y  y0)2 + (z + z0)2]1/2 . In the derivation processes of Eqs. (4) and (5), the ground surface generates additional shear stress. To correspond with the realistic boundary condition, the additional shear stress should be given an opposite sign and applied to the surface; thus the z-axis displacement expression at point P(x, y, z) is [35]:

a!1b!1

uz ¼

Z

0

1 z þ z0  z2 ¼ u 3 c32

 z3 ¼ lim lim u

Based on the soil displacement caused by any unit gap deformation in a semi-infinite body, the soil deformation induced by multiline tunneling can be obtained by the integral in Eq. (7) in the soil loss domain. Assuming that the shield forward propulsion begins at the initial position y = 0 and the propelling length along the y axis is l, the sectional schematic view of the model is shown in Fig. 3. The physical gap caused by the shield construction is g, the lining radius of the up-line and the down-line tunnel is R, the depth of the down-line tunnel is h1, the depth of the up-line tunnel is h2, and the horizontal distance between the double-line tunnels is c0. To simplify the calculation, it is assumed that the central location of the down-line tunnel is (0, 0, h1). Thus, the z-axis soil displacement induced by the shield construction is ðRþg=2Þ ðh2 g=2zÞ c0



h2 þR

l

Z

0

 ð1  f0 Þ

ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

R ðh2 zÞ c0



pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 2

h1 Rg l

0

Z

z ðx þ c0 ; y; zÞ dx dz dy þ ð1 u

R ðh2 zÞ c0

Z

h1 þR

Z

 z ðx þ c0 ; y; zÞ dx dz dy u

ðRþg=2Þ ðh2 g=2zÞ c0

Z

h2 R

Z

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2



ðRþg=2Þ ðh1 g=2zÞ

z ðx; y; zÞ dx dz dy u pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

h1 þR

h1 R

ðRþg=2Þ ðh1 g=2zÞ

Z

ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2



R ðh1 zÞ

 z ðx; y; zÞ dx dz dy pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiu 2 2

ð8Þ

R ðh1 zÞ

where, for f0 = 1, it represents the situation of up-line shield single construction and, when f0 = 0, it represents the situation of downline shield construction after the up-line shield crossing propulsion is completed. For actual double-line tunnels, it is generally accepted that a single-line shield initially crosses the adjacent structures and the remaining line shield was successively conducted for crossing to significantly decrease the soil disturbance. Regarding this project, the up-line shield leads the crossing and has a distance of approximately 100 rings (120 m) with the down-line shield. After formulation of the expression of green-field displacements caused by the shield construction, research on interaction mechanics between the disturbed soils and adjacent structures is conducted. In this study, the elastic interaction between the existing tunnel and the surrounding soil is assumed and the deformation compatibility condition is satisfied. The tunnel is assumed continuous and the Euler–Bernoulli beam is used to simulate the deformation behavior. The governing differential equation for the longitudinal displacement of the existing tunnel due to adjacent excavation is given by

ð7Þ

4

EI

d U z ðxÞ 4

dx

þ K½U z ðxÞ  uz  ¼ 0

ð9Þ

where Uz(x) is the vertical displacement of the existing tunnel; uz is the green-field vertical displacement due to multiline overlapped tunneling, which can be calculated by Eq. (8); EI is the bending stiffness of the tunnel; and K is the subgrade coefficient per unit length of the tunnel, where K = kD, k is the subgrade modulus coefficient, and D is the outer diameter of tunnel. The proper subgrade modulus coefficient k is required in Eq. (9). The coefficient value is influenced by complex factors, such as the soil compressibility, the foundation area and its shape, as well as the foundation stress related to loading and stiffness. Based on the performance experiment for a beam on an elastic foundation, Biot [36], Vesic [37], and Christian and Vanmarcke [38] provided a formula that reflects the soil properties (Poisson’s ratio and compression modulus) and reflects the properties of the beam (section width and bending stiffness) as

Fig. 16. Mirrored model for gap deformation.

0:65Es k¼ 1  l2

sffiffiffiffiffiffiffiffiffiffi Es B 4 EI

12

ð10Þ

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Z. Zhang, M. Huang / Computers and Geotechnics 56 (2014) 121–132

where B is the beam width (in this study, for the tunnel outer diameter D), EI is the bending stiffness of the beam, and Es and l are the soil compression modulus and Poisson’s ratio, respectively. According to a non-homogeneous case, the soil elastic parameters for an equivalent homogeneous foundation are calculated using the weighted average proposed by Poulos and Davis [39] and the weighted average values of the layered soil profile are estimated:

i¼1 Hi

X n Esi Hi

ð11Þ

i¼1

ð12Þ

where Esav and lav are the weighted average value of soil modulus and Poisson’s ratio, respectively; Esi and li are is the soil modulus and Poisson’s ratio of layer i; Hi is the thickness of layer i; and n is the number of soil layer. Note that Eq. (9) is a fourth-order non-homogeneous differential equation in which the solution can be obtained using the finite element approach, where the tunnel is represented by Euler– Bernoulli Hermite elements based on the pre-assumption. The displacement variable Uz(x) is approximated in terms of discrete nodal values as

U z ðxÞ ¼ fNgfUge

ð13Þ

where {N} is the interpolation function matrix fNg ¼ f N1 N2 N 3 N 4 gT ; fUge is the displacement vector of the beam T element e; fUge ¼ ½ xi hi xj hj  ; xi and hi are the vertical and rotational displacement, respectively, at node i; and xj and hj are the vertical and rotational displacement, respectively, at node j. The shape functions Ni(i = 1, 2, 3, 4) are defined as 3

2

2

2

N2 ¼ ðl x  2lx þ x3 Þ=l 2

N3 ¼ ð3lx  2x3 Þ=l 2

N4 ¼ ðx3  lx Þ=l

3

ð14Þ

2

ð15Þ

3

ð16Þ

2

ð17Þ

where l is the unit length of the beam element. By applying the Galerkin method to the governing differential equation in Eq. (9), the following form of the elements matrix is obtained

½K s e fUge þ ½K t e fUge 

Z

l

KfNguz dx ¼ f0g

ð18Þ

0

where [Ks]e and [Kt]e are the soil element matrix and tunnel element matrix, respectively, for the unit e. The form of the element matrices for the soil and tunnel are as follows:

½K s e ¼

Z

l

KfNgfNgT dx

ð19Þ

0

½K t e ¼

Z

l

EI

o

( 2 )( 2 )T d N d N 2

dx

2

dx

dx

ð20Þ

Eq. (18) can be expressed as

ð½K s e þ ½K t e ÞfUge ¼ fFge

ð21Þ

where {F}e is the element force vector acting on the tunnel structure induced by multiline overlapped excavation, that is,

fFge ¼

Z 0

ð23Þ

where [Kt] and [Ks] are the global stiffness matrix of the tunnel and surrounding soils, respectively and {F} is the global matrix of the force vector acting on the tunnel due to adjacent excavation. 4.2. Simplified analytical results and comparison with other methods

 X n 1 lav ¼ Pn li Hi i¼1 H i i¼1

N1 ¼ ðl  3lx þ 2x3 Þ=l

ð½K s  þ ½K t ÞfUg ¼ fFg

To verify the validity of the simplified analytical method, a comparative analysis is conducted with the in situ monitoring data. The 3D FE numerical simulation results are also compared. The construction conditions are selected when the up-line shield is propelled to the 120th ring and when the down-line shield is propelled to the 120th ring after the up-line propulsion is completed. Figs. 17 and 18 show the longitudinal deformations of inner-ring line 4 calculated by the simplified analytical method and the 3D FE numerical software; the in situ monitoring data are also provided for the comparative study. To prevent disruption of the normal operations of line 4, this project primarily employed automated monitoring to supplement the manual monitoring. The manual monitoring points are periodically retested to validate the accuracy of the automated monitoring. The manual monitoring points are distributed at the bottom of the up-line and down-line track beds. Measurement nails with smooth convex spherical tops are buried after drilling by an electric impact drill or nail gun, which produces distinct marks at the measurement points. The electronic level bar is employed in automated monitoring. The electronic level bars are installed to the track bed to measure the changes in angle; the angle can be converted into the displacement of the beam. Based on the measured displacement value, the cumulative deformation value can be immediately transferred to the designated location by the data collection terminal. To control deformation of the existing metro tunnels, the following construction requirements are determined according to the Shanghai provisional regulation of protection technique for metro tunnels with adjacent subway construction: (1) both horizontal and vertical maximum displacements, including final settlement after building loading in the metro tunnels within 20 mm; (2) maximum displacement rebound in the metro tunnel within 15 mm; (3) curvature of the longitudinal displacement in the metro tunnel within 1/ 15,000; (4) lateral displacements of the cross-section diameters, which are caused by longitudinal displacements of the tunnel lining structure within 10 mm. In this study, the previously mentioned criteria should be satisfied. The following additional requirements have been proposed: (1) the maximum displacement

-1

Vertical displacement (mm)

 1 Esav ¼ Pn

Based on the assembly of element matrices, the displacement vector {U} for adjacent tunnels due to excavation-induced soil disturbance is expressed as

0 1 2 3 Observation Numerical software results Simplified analytical results

4 5 0

20

40

60

80

100

Tunnel longitudinal position (m)

l

KfNguz dx

ð22Þ

Fig. 17. Comparisons for longitudinal deformation of inner-ring line 4 due to up-line shield propulsion to 120th ring.

Z. Zhang, M. Huang / Computers and Geotechnics 56 (2014) 121–132

Vertical displacement (mm)

-1

0

1

Observation Numerical software results Simplified analytical results

2

3 0

20

40

60

80

100

Tunnel longitudinal position (m) Fig. 18. Comparisons for longitudinal deformation of inner-ring line 4 due to downline and up-line shield propulsion to 120th ring.

after multiline overlapped crossing in the service metro tunnels within 5 mm; (2) the value of the settlements for the ground surface after multiline overlapped crossing from +5 mm to 20 mm; and (3) the absolute displacement of the overlapped tunnel axis controlled within 70 mm. As illustrated in the figures, the longitudinal deformation curves calculated by the simplified analytical method are consistent with the deformation curves calculated by the 3D FE numerical method; however, there are slight differences between the two results. For the vertical displacements of inner-ring line 4, which is caused by up-line shield propulsion, the largest deformation is 3.277 mm using the simplified analytical method and the largest deformation is 2.95 using the finite element numerical simulation method, as shown in Fig. 17. The difference between these values is 0.327 mm. For the longitudinal deformation values of inner-ring line 4 induced by the up-line and down-line shield propulsions, the largest deformation is 1.668 mm using the simplified analytical method and the largest deformation using the finite element numerical simulation method is 1.5 mm, as shown in Fig. 18. The difference between these values is 0.168 mm. The vertical displacements calculated by these two methods are consistent with the monitoring data, which demonstrates that the existing tunnel deformation caused by the multiline shield propulsion can be effectively analyzed using the simplified analytical method and 3D FE numerical simulation technology. Note that the calculation speed of the simplified analytical method in this study is significantly higher than the calculation speed of large commercial finite element software. Thus, the simplified method is recommended for assisting civil engineers with efficient calculation of the deformation properties of adjacent tunnels and timely adjustments to the construction program.

5. Conclusions Previous research primarily focused on the impacts of singleline shield excavation on surrounding environments and the tunneling of parallel crossing or perpendicular down-crossing existing structures. However, few studies refer to obliquely overlapped tunneling and complex above-crossing and down-crossing existing subway tunnels due to its rare global application. This paper presents the tunneling construction history of the second-stage of the Shanghai Railway transportation line 11 project. The longitudinal deformation of existing tunnel line 4, which is caused by shield line 11 during the process of above-overlapped and downoverlapped crossing tunnels, is conducted using a 3D FE numerical simulation method, and simplified analytical method. The analysis results from the theoretical methods are consistent with the monitoring data. In addition, the tunneling case about the above-overlapped and down-overlapped crossing tunnels with

131

lager oblique angles is the first time to be encountered in China, which is a valuable chance to introduce and analyze on this interaction mechanics. The 3D FE numerical simulation method fully considers shield propulsion, shield tail grouting, lining construction and oblique excavation conditions. By setting thin-layer elements, this numerical method is capable of considering the condition of any oblique angle crossing construction. The simplified analytical method is derived from the Winkler foundation. The complex interaction analyses are divided into two simple steps: first, the green-field displacements caused by shield overlapped construction; second, the analysis of the application of soil displacements on the existing tunnels. The simplified method can assist civil engineers with rapid assessment of the impacts of multiline tunneling on adjacent tunnels and timely adjustments to the excavation scheme. The results of theoretical analyses show that the tunnel settlement value, the deformation impact trend, and the maximum position significantly change with the difference in overlapped crossing positions. The shield operation main parameters, such as earth pressure for cutting open, and synchronized grouting, also change. This study proposes the setting law of the above-mentioned parameters as an important reference for future overlapped tunneling construction. The proposed simplified method can be extended to the analysis of other related crossing problems, such as double-line abovecrossing and double-line down-crossing of existing structures. Although the good agreement between the simplified results and the FE analysis results do not address the lack of non-linearity, the linearity and elasticity is still a major limitation of the simplified method. Advanced mechanisms such as relative uplift failure and gapping between existing tunnels and the surrounding soil, which also contribute to nonlinear soil behavior, should be included in the analysis. It should be noted that the subgrade modulus coefficient can be used for the case of soil character not only for the incompressible case, but for arbitrary drained values of Poisson’s ratio. However, the simplified solution for green-field displacements caused by shield construction is based on the assumption of incompressive medium. Therefore, additional research requires complicated excavation-soil-structure interaction to comprehensively assess the deformation behavior of existing structures induced by multiline overlapped tunneling. Acknowledgments The authors would like to thank the editor and reviewers for their great comments, which have enhanced the presentation of this paper. The authors acknowledge the financial support provided by National Natural Science Foundation of China for Young Scholars (No. 51008188), and by Key Laboratory Fund of Geotechnical and Underground Engineering (Tongji University, Supported by Ministry of Education, No. KLE-TJGE-B1302), and by Open Project Program of State Key Laboratory for Geomechanics and Deep Underground Engineering (No. SKLGDUEK1205). References [1] Liao SM, Peng FL, Shen SL. Analysis of shearing effect on tunnel induced by load transfer along longitudinal direction. Tunnel Undergr Space Technol 2008;23(4):421–30. [2] Shen SL, Xu YS. Numerical evaluation of land subsidence induced by groundwater pumping in Shanghai. Can Geotech J 2011;48(9):1378–92. [3] Fang Q, Zhang DL, Wong LNY. Shallow tunnelling method (STM) for subway station construction in soft ground. Tunnel Undergr Space Technol 2012;29(5):10–30. [4] Tan Y, Li MW. Measured performance of a 26 m deep top-down excavation in downtown Shanghai. Can Geotech J 2011;48(5):704–19. [5] Peng FL, Wang HL, Tan Y, Xu ZL, Li YL. Field measurements and finite-element method simulation of a tunnel shaft constructed by pneumatic caisson method in Shanghai soft ground. J Geotech Geoenviron Eng 2011;137(5):516–24.

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