Full-scale tests on bending behavior of segmental joints for large underwater shield tunnels

Tunnelling and Underground Space Technology 75 (2018) 100–116

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Full-scale tests on bending behavior of segmental joints for large underwater shield tunnels

T

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Kun Feng, Chuan He , Yue Qiu, Li Zhang, Wei Wang, Hongming Xie, Yanyang Zhang, Songyu Cao Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu 610031, Sichuan, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Underwater shield tunnels Segmental joints Bending behavior Full-scale tests Failure characteristics

This paper presents an experimental and numerical study on the bending behaviour of segmental joints for large underwater shield tunnels. A series of full-scale tests of segmental joint for underwater shield tunnel are carried out to investigate the bending performance under compression-bending loads. And comparative numerical simulations are conducted to compare with the test results and analyze the occurrence and development process of joint failure. The results indicate that the joint opens linearly and deforms nonlinearly after the visible concrete cracking occurred, the shape of joint interface is a curved surface during joint opening. The time when the bolt becomes stressed depended on axial force, and the bolt stress increased linearly with the growth of bending moment. Joint bending stiffness can be divided into three stages according to turning point of 'visible concrete cracking' and 'bolt yield', large axial force has a great influence on keeping it. The joint waterproof material could hardly promote the bending stiffness and capacity of segmental joint for its small rigidity. The failure process of segmental joint was different between under positive and negative bending moment, the compressive capacity of concrete in compression zone near the intrados played a vital role in the process of improving the bending capacity of segmental joint. The numerical results of joint opening and bending stiffness were in good agreement with tests during small deformation stage, while after visible cracking the results differ relatively. It is reasonable to simulate joint bending performance before visible concrete cracking, and estimated joint failure mode and its approximate range by using the proposed numerical model.

1. Introduction Shield tunnels, which are playing a crucial role in public transportation systems around the world, are usually constructed under unfavorable ground conditions (e.g. soft ground, riverbed, and seabed). Over the past decade, a considerably number of underwater shield tunnels have been constructed as river-cross channels in China. Compared with other tunnels (e.g. subway tunnels, road tunnels, water conveyance tunnels and power or gas tunnels, etc.), the underwater shield tunnel has larger cross-section (from Φ10 m to Φ15 m), deeper buried depth (from 48 m to 66 m depth), and bears higher water pressure (from 0.6 MPa to 1.4 MPa). Precast concrete segments and segmental joints are main components in the shield tunnel. The joints are used to connect adjacent segments to form segmental rings as shown in Fig. 1, which are the weakest and most complex components in tunnel lining structures. Due to the presence of the joints, a segmental lining structure is usually considered as a multi-hinged structure, which shows very complex structural behavior (Koyama, 2003). Past research (Murakami and

⁎

Koizumi, 1978; Teachavorasinskun et al., 2010; Ye et al., 2014) has shown that the bending stiffness of the segmental joint is a key factor in the structural design and analysis of segmental lining rings. It is also found that the bending performance and the opening value of each joint have significant influence on the mechanical behavior of the whole tunnel structure, especially in the complex underwater environment. The segmental joints of recent built and designed large-scale rivercross shield tunnel in China are presented in Table 1. With the aim of bearing high water and earth pressure, the joints shown in Table 1 are different with the joints used in normal shield tunnels, which have the following features: (1) the segments are thicker and wider to form a larger compression section; (2) oblique bolts are more preferable in the construction of segmental rings; (3) mortises are applied on the contact surfaces in the joints to enhance assembly precision; (4) rubber packers are rarely set to increase the friction between the concrete contact surface under high compression; (5) dual-channeled waterproof materials are applied in the joints to fulfill water proof requirements of the tunnels structures. Fig. 2 shows some typical segments and the arrangement of joints employed in Shiziyang underwater shield tunnel to

Corresponding author. E-mail address: [email protected] (C. He).

https://doi.org/10.1016/j.tust.2018.02.008 Received 7 March 2016; Received in revised form 18 December 2017; Accepted 23 February 2018 Available online 02 March 2018 0886-7798/ © 2018 Elsevier Ltd. All rights reserved.

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maintenance of tunnel lining structures. In this paper, a series of full-scale tests are carried out to investigate the bending performance and bending capacity of segmental joints in underwater shield tunnels. The opening behavior and bending stiffness of segmental joints, strain condition of concrete segments, and stress condition of joint bolts under different axial compression-bending loads are carefully examined. In particular, the influence of sealing gasket and rubber waterstop on the bending performance segmental joints are discussed. Then, the failure behavior and failure pattern of segmental joints under high compression-bending loads are investigated. A numerical study based on the finite element (FE) method is carried out to provide an experimental-numerical comparison and to provide a better understanding of the joint bending behavior from small deformation stage to failure stage. 2. Full-scale test program 2.1. Project overview

Fig. 1. Sketch of segmental joints and ring joints of a shield tunnel.

The full-scale tests are carried out based on the construction project of the Shiziyang tunnel, which is the first and longest underwater shield tunnel in China. The Shiziyang tunnel is a railway tunnel connecting the Dongchong Station and Humen Station, and crossing several rivers (e.g. Shiziyang River), with a total length of 10.8 km (the shield tunnel section is 9.34 km long). As shown in Fig. 3, the Shiziyang tunnel crosses through muddy silty clay (Q), strongly weathered sandstone (W3, W4), and weakly weathered sandstone (W2), with abundant and high underground water (the highest water pressure is about 0.67 MPa). The Shiziyang tunnel are constructed using reinforced concrete (RC) segments, and the concrete type is C50. Fig. 4 shows the layout of the segmental ring of Shiziyang tunnel. The outer diameter and inner diameter are 10,800 mm and 9800 mm respectively, with a 500 mm thickness. The segmental ring is assembled by eight universal wedgeshaped segments with an average width of 2000 mm, using 24 M36 circumferential bolts and 22 M30 longitudinal bolts in the segmental joints. The central angle of the key segment is 16°21′49.09″, while the angle of other segments is 49°5′27.27″. As shown in Fig. 5, each segmental joint consists of three M36 oblique bolts with the steel grade of 6.8. The tensile strength and the yield strength of the bolt is 600 MPa and 480 MPa, respectively, while the diameter and the length of the bolt is 42 mm and 639 mm, respectively. The bolt is inserted into the hand hole, passing through the bolt hole, and finally it is screwed into the embedded bolt nuts to connect the two adjacent segments. The bolt pretightening loads can be applied to the segmental joint by the pulling force from bolt nuts and steel cushion. Two sides dual-channeled waterproof is employed in the segmental joint, while tenon and mortise are applied in the middle section of the joints allowing the segments to be guided into the appropriate positions during construction.

provide a clear understanding of the above mentioned features. Due to the complex geometric and material features, the segmental joint in the underwater shield tunnel usually shows complicated structural behaviour under high compression-bending forces (caused by the high water and earth pressure), especially in transferring forces and constraints between adjacent segments, and allocating rigidity of the whole segmental lining structure. As a result, the contact behavior of the segmental joint in the underwater shield tunnel is usually controlled by the axial force, causing significant differences in load transfer effect, deformation and failure pattern compared with the joints in normal shied tunnels. Over the past few decades, a large number of research has been carried out to understand the bending behaviour of the segmental joint. Theoretical models (Murakami and Koizumi, 1980; Iftimie, 1992; Huang, 2003) were established to describe the bilinear/non-linear behavior of the bending stiffness of segmental joints with different types. Numerical investigations on the influences of joint size, bolt type or other factors were carried out (Zhang et al., 2002; Zeng et al., 2004; Zhong et al, 2006; Shi et al., 2015), where the bending stiffness and deformation properties were also provided. Laboratory and in-situ tests were carried out to investigate the bending performance of the segmental joint with different configuration and dimensions for different functions such as gas pipelines (Hayashi, 1997), metro tunnel (Wang and Li, 2005; Li et al., 2015), water conveyance tunnel (Zhang et al., 2002; Yan et al., 2011) and river-cross highway tunnel (Chen et al., 2010; Teng and Lu, 2010). In the above research, the general law of the joint bending stiffness under small joint deformation was obtained. However, most of the abovementioned theoretical models were established based on the plane section assumption under small deformation condition, which are not able to provide accurate description of the contact behavior of the segmental joints under high axial compression and large deformation condition. Besides, most of the theoretical models and numerical analyses have taken in to account the influence of sealing gasket and rubber waterstop, while the stiffness of the sealing gasket and rubber waterstop is too small compared with the joints. Therefore, the influence of the sealing gasket and waterstop on the bending capacity of segmental joints needs to be investigated. Moreover, most of the experimental research focused on the joint bending behavior in the linear-elastic stage, without investigating the bending performance, bending capacity and failure characteristics under large deformation condition and in the failure state. As concrete segments are required to bear very high water and earth pressure in existing underwater shield tunnels, concrete cracks may easily occur at the contact surfaces of adjacent segments under high axial compression. Thus, the structural performance of segmental joints under compression-bending loads after crack happening is essential to the structural design and

2.2. Test arrangement and procedure There were two types of specimens (named A and B) in the tests, and the size and mechanical properties of the specimens are listed in Table 2. In order to obtain the common regularity of the joint deformation and the complete process of the joint failure, four sets of test specimens have been casted before the experiment. Two sets are employed with a range of axial force from 3000 kN to 8000 kN respectively under normal load (positive bending and negative bending), while the other two sets are used for failure load under the effect of the axial force of 6000 kN (positive bending and negative bending). Due to the limit of loading system capacity, the width of specimens was selected as 1/3 segment width (667 mm) of the full-scale segment with one bolt in the middle connecting two specimens to meet the destructive test requirements. The configuration of specimen interface, the thickness and reinforcement ratio were manufactured exactly the same with the 101

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Table 1 Segmental joint configuration of recently constructed/designed large-scale river-cross shield tunnels in China. Tunnel project name

Outside diameter (m)

Maximum depth (m)

Maximum water pressure (MPa)

Segment width (m)

Segment thickness (m)

Connection type

Locating measures

Rubber packers

Joint waterproof type

Wuhan Yangtze River Tunnel

11

43

0.6

1.5

0.5

Curved bolt

Tenon and mortise

Yes

Two sides dualchanneled waterproof: the outer side is provided with sealing gasket, the inner side is provided with rubber waterstop

Shanghai Chongming Yangtze River Tunnel

15

27

0.6

2.0

0.65

Oblique bolt

No

No

Two sides dualchanneled waterproof: the outer side is provided with sealing gasket, the inner side is provided with rubber waterstop

Nanjing Yangtze River Tunnel

14.5

60

0.65

2.0

0.6

Oblique bolt

Shear pin

No

Two sides dualchanneled waterproof: the outer side is provided with sealing gasket, the inner side is provided with water swelling rubber

Nanjing Metro Line 10 River Crossing Tunnel

12

58

0.65

2.0

0.5

Oblique bolt

Shear pin

No

Two sides dualchanneled waterproof: both the outer and inner side are provided with sealing gasket

Guangzhou Shenzhen high-speed railway Shiziyang Tunnel

10.8

62

0.67

2.0

0.5

Oblique bolt

Tenon and mortise

No

Two sides dualchanneled waterproof: the outer side is provided with sealing gasket, the inner side is provided with water swelling rubber

Wuhan Sanyang Road River Crossing Tunnel

15.2

42

0.65

2.0

0.65

Oblique bolt

Tenon and mortise

No

One side dualchanneled waterproof: sealing gasket and rubber waterstop are

Detailed scheme

(continued on next page)

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Table 1 (continued) Tunnel project name

Outside diameter (m)

Maximum depth (m)

Maximum water pressure (MPa)

Segment width (m)

Segment thickness (m)

Connection type

Locating measures

Rubber packers

Joint waterproof type

Detailed scheme

provided at the outer side

Foshan Dongguan intercity railway Shiziyang Tunnel

13.1

63

0.78

2.0

0.55

Oblique bolt

Bump Slot

No

One side dualchanneled waterproof: sealing gasket and rubber waterstop are provided at the outer side

Fig. 2. Configuration of a segmental joint.

direction. Horizontal and vertical hydraulic jacks are applied on the specimens to provide axial forces and bending moments. The axial force is provided by two 1500 kN jacks, and the maximum axial force can reach 3000 kN. The bending moment is provided by two pairs of two 1500 kN jacks, and the maximum bending moment at the longitudinal seam can reach 933.75 kN m. As specimens are designed with 1/3 fullwidth in the tests, the maximum axial force and maximum bending moment for a full-width specimen can reach 9000 kN and 2801.5 kN m, respectively. Two kinds of load tests were applied for the experiment, namely as the positive flexural loading test and the negative bending loading test, shown in Fig. 8. In positive bending tests, jacks loaded at A′B′C′D′ and E′F′G′H′ surface in the extrados of specimens, while in negative bending tests, the specimens were reversed. The arrangements of the gauging

prototype segment, as shown in Fig. 6. And considering the small curvature of segments which could be simplified into straight segments, to obtain accurate loading and to easily control the loading status of the joint interface, the straight specimens were selected as alternative arcuate specimens. Thus, the test results of the specimens with 1/3 fullwidth should be consistent with the full-width specimens, which means that the applied load should be enlarged three times. The following tests results of 1/3 full-with specimens are all converted accordingly. The 'Multi-function Shield Tunnel Structure Test System', a full-scale test system which was previously developed at Southwest Jiaotong University is employed in the tests. Detailed description of the test setup is shown in Fig. 7. As shown in the figure, three pairs of counter-force beam are connected with six steel rods to provide constraints on the upper corners of the specimens and reaction forces along the axial

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Fig. 3. Longitudinal profile of Shiziyang Tunnel Project.

occurrence and propagation of concrete cracks. Based on these measurements, the opening angle and joint bending stiffness can be calculated.

3. Test results and discussion 3.1. Joint opening changes under compression-bending loads Fig. 11 shows the relationship between the joint opening amount and the bending moment under 5000 kN axial force. As shown in the figure, the joint opening amount grows complicatedly under compression-bending loads. The joint opening occurs near the intrados of segmental joint interface under positive bending. When the bending moment M is smaller than 500 kN m, the opening width and the opening height of segmental joint subjected to linear growth with bending moment, and the joint interface can be regarded as a linear opening. At this point, the maximum opening width is less than 3 mm, and the opening height was about 2/3 of the joint height. When M is increased over 500 kN m, the opening width increases significantly. However, the opening height increases slowly, and stops growing while the value reaches nearly 4/5 of the joint height. It can be seen that the shape of joint interface after deformation is not in plane as that assumed in the theoretical models, but a curved surface from the compression zone to disengagement region. Compared with positive bending, the general law of joint opening under negative bending is similar. However, the opening width and height are smaller than that of positive bending, and the linear section of curve is shorter. This shows that the time for bolt in tension is shorter than that of positive bending. When M deceases over

Fig. 4. Segment layout of Shiziyang Tunnel.

points of strain and displacement of the concrete specimens are shown in Fig. 9, while the gauging points of the bolt are in Fig. 10. The gauges are used to investigate the width and length of joint opening, strain condition around the seam and hand hole of the concrete segment, stress conditions of the bolt, vertical displacement of the joint, and the

Fig. 5. Sketch of segmental joint structures: (a) overall view and (b) detailed view of joint interface.

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Table 2 Details and mechanical material properties of specimens. Specimen

SZY

A B

Concrete

Bolt

Length (mm)

Height (mm)

Cubic compressive strength fc (MPa)

Young’s modulus Ec (MPa)

Diameter (mm)

1160 1155

500 500

32.0

3.45 × 104

42

(MPa)

Tensile strength fs (MPa)

Young’s modulus Es (MPa)

480

600

2.1 × 105

Yield strength f y

Fig. 6. Sketch of specimens selection for full-scale tests.

−700 kN m, the maximum opening width is close to 3 mm, and both the opening width and height of joint opening are subjected to nonlinear growth. As presented in Fig. 12, it is shown for the maximum opening width changing with bending moment under different axial forces. The maximum opening width grows with the increase of bending moment, and it can be divided into linear increase and nonlinear increase. Because of the constraint of axial force, the opening width can be divided into two clusters according to the magnitude of axial force: (1) when axial force N is less than 5000 kN, the constraint effect is not obvious, the joint surface opens when bending moment is applied; (2) when N is larger than 5000 kN, the contact interface opens while the bending moment is over a certain value due to restraints of axial force. In addition, the larger the axial force is, the smaller the growth rate will be. As shown in Fig. 13, the maximum opening height changes with bending moment under different axial forces, and the curves also present a 'stepped' change characteristic. At the initial stage of curves under positive bending (when M less than 300 kN m), the joint opening height increases rapidly. It is found that the bolts start to provide tensile forces and bear most of the bending moment until the opening height reaches 3/5–2/3 of the joint height. At the same time, the bolts start to strengthen the restriction of joint, and the opening height stops increasing. When the joint surface bears negative bending moment, a significant step of curve appears while maximum opening height reaches 150 mm with the decrease of the bending moment. It means that the joint interface starts to be restrained by the bolts.

increase of Kθ becomes very small, and the effect of axial force is mainly reflected in keeping Kθ. As axial force grows, the bending moment for joint capacity is also increased. The tested curves between Kθ and bending moment (Kθ-M curves) are shown in Fig. 15. It is observed that the negative bending stiffness is larger than that of positive bending, which is because that concrete nearby the intrados gasket is contacted to participate in compression, and thus it can improve negative bending stiffness. When the axial force is small (N = 3000–4000 kN), the curves increase firstly and then decrease slowly with the increase of absolute value of bending moment. When the axial force is large (N = 5000–8000 kN), the curves increase firstly, and then remain unchanged under positive bending. Hereafter, they grow rapidly, then decrease obviously, they show a slowly decline ultimately under negative bending after a slight increase.

3.3. Concrete strain changes under compression-bending loads The concrete surface strain of specimens has been investigated in tests, and the curves of side surface under positive and negative bending are presented in Figs. 16 and 17, respectively. It is noticed that the concrete strain nearby joint interface changed significantly nonlinearly in compression with the increase of bending moment. As shown in Fig. 16, under positive bending, when the bending moment is 100 kN m, the compressive strain is mainly distributed in the contact interface of the 100–200 mm and 300–400 mm of joint height, which is called “E” type distribution. Along with the moment increasing, the contact surface near the intrados starts opening, the compressive strain in the opening area decreases, resulting in significant increase for compressive strain of contact surface near the extrados. Finally, with the increase of joint opening height, the concrete in the disengagement region near the extrados of joint interface is contacted and involved in compression, while the compressive and tensile strain in the opening zone near the intrados are quite small. Besides, the magnitude of axial force also affects the distribution of concrete strain, and the high axial force level can effectively slow down and control the emergence and growth of tensile strain. Moreover, in case of high bending moment (M = 1300 kN m, M = 1900 kN m), tensile stress occurs at the central region of joint interface, which indicates that distortions of the joint interface occurs and does not remain flat. As presented in Fig. 17, changes of present concrete strain are observed under negative

3.2. Joint bending stiffness changes under compression-bending loads The curve relationship between joint opening angle and bending moment (M-θ curves) is shown in Fig. 14. The secant slope of M-θ curves is the joint bending stiffness (Kθ). The M-θ curves are linear in the initial section under small bending moment, and grow nonlinearly with the increase of bending moment. Besides, the larger the axial force is, the longer the linear section will be. The M-θ curves can be divided into two clusters, when axial force is small (N = 3000–4000 kN), the Kθ is affected by axial force. When axial force is larger than 4000 kN, there is no obvious difference in Kθ between curves. It has revealed that the effect of the increase for axial force on the improvement of Kθ has an upper limit. When the axial force increases to a certain value, the 105

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Fig. 7. Layout of experimental test of segmental joint: (a) front view; (b) lateral view; (c) plan view; and (d) test scene.

The concrete strain nearby the hand hole under positive and negative bending are presented in Figs. 18 and 19, respectively. The concrete strain nearby the hand hole is compressive strain showing a 'right convex' type distribution under positive bending. When the bending moment rises up to 500 kN m, the tensile strain occurs at the position

bending. Thus, it can be noticed that with the decrease of negative moment, along with the joint opening of extrados, the peak of compressive strain shifted downward. Besides, the change process also reflects the change of compression zone, and the strain distribution shows significantly nonlinear. 106

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Fig. 7. (continued)

to a 'left convex' type. When the bending moment reaches 1900 kN m, the bolt yields, the compressive strain near bolt hole decreases consequently. When under negative bending, the concrete strain near the hand hole maintains compressive since the intrados of specimen is under compression. The compressive strain decreases while the

corresponding to the bolt hole. When the bending moment reaches 800 kN m, the concrete strain nearby the hand hole shows a uniform tension. When the moment increases to 1000 kN m, the concrete strain at the position corresponding to the bolt hole turns compression due to the binding of bolt. Besides, the distribution of concrete strain is turning 107

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a) positive bending test

b) negative bending Fig. 8. The load mode of positive bending test and negative bending test.

Fig. 9. Layout of measuring points on segmental joint specimens: (a) positive bending and (b) negative bending.

3.4. Bolt stress changes under compression-bending loads

moment grows. The concrete strain nearby the bolt hole is relatively small owing to the effect of bolt force. In addition, the distribution of compressive strain shows a 'right convex' type. With the growth of bending moment, the curve curvature increases.

The change of oblique bolt stress was tested and shown in Fig. 20. It is exhibited that bolt stress is not linear growth with the increase of bending moment. The bolt is not stressed when the moment is small. 108

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Maximum opening height (mm)

400

0

-1000

-500

0

500

1000

1500

2000

Fig. 13. Relationship between maximum opening height and bending moment under different axial forces. M=100kN.m M=300kN.m M=500kN.m M=700kN.m M=900kN.m M=1100kN.m M=-100kN.m M=-300kN.m M=-500kN.m M=-700kN.m M=-900kN.m M=-1100kN.m

400

300

200

2000

Bending moment (kN.m)

Position in height (mm)

N=3000kN N=4000kN N=5000kN N=6000kN N=7000kN N=8000kN

100

Bending moment (kN.m)

Extrados

100

0 -15 -10 Intrados

200

-1500

Fig. 10. Layout of measuring points on bolt.

500

300

-5

0

5

10

15

20

1500 1000 500

-500 -1000 -1500

Joint opening (mm)

N=3000kN N=4000kN N=5000kN N=6000kN N=7000kN N=8000kN

0

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

Joint opening angle (rad)

Fig. 11. Joint opening amount changes with bending moment under axial force 5000 kN.

Fig. 14. Relationship between joint opening angle and bending moment under different axial forces (M-θ curves).

30

Bending stiffness (MN.m/rad)

Maximum opening (mm)

180

20

10 · ?

N=3000kN N=4000kN N=5000kN N=6000kN N=7000kN N=8000kN

0

-10

-20 -1500

-1000

-500

0

500

1000

1500

2000

160

120 100 80 60 40 20 0 -1500

Bending moment (kN.m)

N=3000kN N=4000kN N=5000kN N=6000kN N=7000kN N=8000kN

140

-1000

-500

0

500

1000

1500

2000

Bending moment (kN.m)

Fig. 12. Relationship between maximum opening amount and bending moment under different axial forces.

Fig. 15. Relationship between bending stiffness and bending moment under different axial forces (Kθ-M curves).

Until the bending moment increases to a certain degree, bolt stress begins to grow significantly, and then the growth slows down. Although the oblige bolt passes through the center of the joint interface, the stress time of the bolt is different when the joint sustained positive or negative bending loads because of the different configuration between the intrados and extrados side parts of joint interface. The greater the axial force is, the later the bolt is stressed, the smaller the magnitude of the value for bolt stress would be.

3.5. The effect of joint waterproof material A series of tests which had sealing gasket and rubber waterstop installed on the joint interface were carried out to ascertain the effect of joint waterproof materials on segmental joint bending performance. The changes of maximum joint opening width and height were

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Extrados

600

Position in Zidth (mm)

Position in height (mm)

500

400 N=5000kN, M=100kN.m N=5000kN, M=800kN.m N=5000kN, M=1100kN.m N=8000kN, M=100kN.m N=8000kN, M=800kN.m N=8000kN, M=1900kN.m

300

200

100

0

-600 Intrados

500 400 300 M=-100kN.m M=-500kN.m M=-700kN.m M=-1000kN.m M--1300kN.m

200 100 0

-400

-200

0

200

-400

-300

-200

-100

0

Surface strain (—İ)

Surface strain (—İ)

Fig. 19. Changes in surface strain around the hand hole under negative bending loads.

Fig. 16. Changes in surface strain near the joint interface under positive bending loads.

500

500

Extrados

400

300

Bolt stress (MPa)

Position in height (mm)

400 N=5000kN, M=-100kN.m N=5000kN, M=-700kN.m N=5000kN, M=-1200kN.m N=8000kN, M=-100kN.m N=8000kN, M=-700kN.m N=8000kN, M=-1300kN.m

200

300 200

N=3000kN N=4000kN N=5000kN N=6000kN N=7000kN N=8000kN

100 0

100 -1500 -1000

0

-800 Intrados

-600

-400

-200

0

500

1000

1500

2000

2500

Fig. 20. Relationship between bolt stress and bending moment under different axial forces.

Surface strain (—İ)

30

Maximum opening (mm)

600

Position in Zidth (mm)

0

Bending moment (kN.m)

Fig. 17. Changes in surface strain near the joint interface under negative bending loads.

500 M=100kN.m M=600kN.m M=800kN.m M=1000kN.m M=1300kN.m M=1900kN.m

400 300 200 100 0

-500

20

10

0

-20 -1500 -200

-100

0

100

200

300

N=5000kN N=5000kN, sealing waterproof installed N=8000kN N=8000kN, sealing waterproof installed

-10

-1000

-500

0

500

1000

1500

2000

Bending moment (kN.m)

400

Surface strain (—İ)

Fig. 21. The contrast of maximum opening under the conditions of with and without joint waterproof.

Fig. 18. Changes in surface strain around the hand hole under positive bending loads.

gasket and rubber waterstop is too soft compared with concrete, the joint waterproof material could hardly promote the bending capacity of joint. It indicates that the joint waterproof material has an ignorable effect on the segmental joint bending tests.

compared between results with and without joint waterproof materials, as shown in Figs. 21 and 22, respectively. By comparing the results of the trends and values of opening width and opening height respectively, the difference between with and without joint waterproof materials is very small. The result of joint bending stiffness exhibits the similar regularity, as shown in Fig. 23. Under different axial forces, the curves of the two cases have tiny differences. Since the material of sealing

3.6. Failure process and characteristics A series of failure tests of segmental joint was conducted under the 110

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Maximum opening height (mm)

400

joint was failed. It was observed for the segmental joint failure characteristics under negative compression-bending that the concrete fracture firstly occurred in the compression zone near the intrados of joint interface, then the cracks expansion and spreading was observed in this area, which eventually led to the failure of the segmental joint.

300

4. Comparative analysis

200 N=5000kN N=5000kN, sealing waterproof installed N=8000kN N=8000kN, sealing waterproof installed

100

0

-1000

0

1000

4.1. General A numerical study of the full-scale test specimens is presented here to offer a more thorough understanding of bending behavior of segmental joints and help explain the test results. More importantly, the proposed numerical model based on the FE modelling techniques and validated by the test results can be used to conduct further numerical studies in the future. The FE models discussed in this research were established using a general FE package, ANSYS (version 10.0, employing the so-called 'structure mechanics module'). In order to accurately model the test specimens in the comparative analysis, the measured geometrical dimensions and material properties of the specimens obtained in the full-scale test were used. Detailed descriptions of the FE modeling techniques are described as follows.

2000

Bending moment (kN.m) Fig. 22. Comparison of maximum open height under the condition of with and without joint waterproof.

Bending moment (kN.m)

2000 1500

4.2. Modelling strategy

1000

The segmental joint was modeled using eight-node hexahedron element (SOLID65), which was capable of cracking in tension and crushing in compression. The equivalent volume ratio of reinforcement along the circumferential direction was set as 0.015 to describe the dispersion distribution of reinforcement in concrete, while the element was treated as a continuous homogeneous material. The bolt was simulated using two-node quadratic beam element (BEAM188). The contact and slip interaction at joint interface was simulated using fournode surface-to-surface contact element (CONTACT173) and 3-D target segment element (TARGE170), a surface to surface contact group was formed with these two types of elements. Detailed description of the proposed numerical model is shown in Fig. 25. Moreover, the contact effect between the bolt and the bolt hole was not simulated owing to the large gap between them. The combined nodes were adopted at the both ends of the bolts to fix bolt and concrete element, and the middle section of bolt was not connected with the concrete element. In order to obtain the occurrence and development process of joint failure, the constitutive relation recommended by Hongnestad (Jiang et al., 2005) was adopted to represent the stress and strain relation of concrete, shown in Formula (1). Meanwhile, the concrete failure was described by the William-Warnke five-parameter failure criterion (Willam and Warnke, 1975) and the development of concrete cracks was described with the smeared cracking model. The bilinear isotropic hardening model was adopted to simulate the bolt material. The material properties of concrete and bolt mentioned above are shown in Table 3.

500 0

N=5000kN N=5000kN, sealing waterproof installed N=8000kN N=8000kN, sealing waterproof installed

-500 -1000 -1500

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

Joint opening angle (rad) Fig. 23. Comparison of M-θ curve under the condition of with and without joint waterproof.

axial force of 6000 kN. The load step size was reduced as much as possible in order to control the load precision. The failure process of segmental joint under compression-bending can be divided into three stages, that is small deformation stage, large deformation stage and joint failure stage, as shown in Fig. 24. And the failure characteristics of each stage under positive compression-bending was shown in Table 4 and can be summarized as: joint interface near the intrados opened, the concrete near the extrados compressed → micro concrete cracks occurred in compression zone near the extrados of joint interface → concrete cracks in compression zone developed and penetrating cracks occurred → concrete spalling occurred at compression zone → bolt was pulled off, then joint was destroyed, according to Table 4. It is observed for the segmental joint failure characteristics under positive bending that the concrete fracturing firstly occurred in the compression zone near the extrados of joint interface, and then the bolt would be pulled off before the whole joint failure. The failure characteristics of segmental joint under negative compression-bending was shown in Table 5 and can be summarized as: The joint failure process can be divided into three stages, namely small deformation, large deformation and failure stage. The failure characteristics of each stage are shown in Fig. 24. In particular, the failure process of the joint is: joint interface near the extrados opened, the concrete near the intrados compressed → micro concrete cracks generated in compression zone near the intrados of joint interface → concrete cracks in compression zone expanded along horizontal direction and penetrated → concrete spalling occurred at compression zone, then

ε 2 εc 0

( ) ( ) ⎤⎦, ( )⎤⎦,

⎧ σ = σ0 ⎡2 ε − ⎪ ⎣ εc 0 ⎨ 1−0. 15 ⎪ σ = σ0 ⎡ ⎣ ⎩

ε − εc 0 εcu − εc 0

ε ⩽ εc 0 εc 0 ⩽ ε ⩽ εcu

(1)

Besides, the width of FE model was selected as 1/3 segment width (667 mm), and other sizes were completely corresponding to the tests, shown in Table 2. Both ends of the model were constrained as 'simply supported beam' to ensure that the joint face is in a state of pure compression-bending. Moreover, the loading conditions of numerical simulation were consistent with the tests, the horizontal forces were applied to both ends of the model to input the axial forces as the beginning of load step, and then the symmetrical concentrated forces were applied at both sides of the joint surface with the distance of 300 mm 111

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Fig. 24. The failure process of segmental joints under positive bending and negative bending.

conditions of the bolt, and bending stiffness of the joint are carefully discussed as follows. Tables 4 and 5 show the test-numerical comparison of the failure characteristics of segmental joints under positive and negative bending loads, respectively. It is found that the crack and failure patterns predicted by the FE analysis are generally compared well with those from the test results. However, the loads of cracking, bolt yield and joint failure in tests are different from that of numerical simulations. Besides, the compressive capacity of compression zone for the adjacent concrete

from the joint interface. Six cases of axial forces was conducted range from 3000 kN to 8000 kN. For each axial force case, the bending moment starts at 0 kN m and increases progressively with the increment of 100 kN m till the joint failure.

4.3. Results and discussions The comparative analysis is performed based on the full-scale test results and the FE results, where the failure process of the joint, stress

Fig. 25. 3D numerical model of segmental joint.

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Table 3 The material properties of the specimens in finite element model. Concrete

Bolt

Cubic compressive strength fc (MPa)

Tensile strength ft (MPa)

Poisson ratio

32.0

2.6

0.19

Density (kg/m3)

2500

Shear transfer coefficients for an open crack

Shear transfer coefficients for a closed crack

0.5

1.0

Young’s Modulus Es (MPa)

Poisson ratio

Density (kg/m3)

(MPa)

Tensile strength fs (MPa)

Contact interface Friction coefficient

480

600

2.1 × 105

0.22

7800

0.65

Yield strength f y

Table 4 Test-numerical comparison of the failure characteristics of segmental joints under positive bending loads. Bending moment (kN m)

750

1300

1800

1900

Experimental tests Scenes

Features

Visible concrete cracks appeared in compression zone at the extrados

Bolt yield, and concrete spalling occurred at compression zone

Bolt was pulled off

Concrete in compression zone completely spalled, joint was destroyed

Bending moment (kN m)

600

1200

1400

1600

Bolt yield, a large number of micro concrete cracks occurred in the contact surface and penetrating cracks appeared near the extrados of joint

Bolt failure, a large number of concrete cracks and a small amount of concrete crush area occurred at the contact surface, many penetrating concrete cracks appeared at the end of bolt near the extrados

Joint was destroyed, large concrete crushing and crack occurred at contact surface. The horizontal cracks extended to the middle of joint

Numerical simulations Scenes

Features

Micro concrete cracks developed at compression zone and the end of bolt

Note: The blue and green areas is the crushing zones, the red area occurred tensile cracking.

Relative differences are found between the numerical results and test results after visible concrete cracking is mainly caused by the cracking occurrence and the stiffness degradation of cracked concrete in simulation, which leads to the bearing capacity of the bending loads drops significantly. Besides, the configuration of joint interface near the intrados is very complex and the occurrence of cracks on the adjacent segments seriously reduce the strength of the joint. Moreover, the cracking may cause a rapid decrease of the rigidity of the joint, resulting in greater discrepancy of joint opening between the numerical results and test results under negative bending loads compared with that under positive bending loads. And the discrepancy remains after the bolt yielding, and the bolt yielding load obtained in the FE analysis is smaller than that in the tests. After the yielding bolt is pulled up, the increment of the bolt stress slows down. Both of the test and numerical M-θ curves can be divided into three phases (namely I, II and III) according to the occurrence of 'visible concrete cracking' and 'bolt yielding'. Phase I is the small joint

segments near the intrados has significant influence on the negative bending capacity of the segmental joint. Because of the waterproof design requirement, the contact surfaces between the two adjacent segments in the joint are always cut down by grooves or mortises, which introduces unexpected complex configuration for the joint. Thus, it is necessary to set rubber packers at the joint interface to reduce the stress concentration, and it is more reasonable to use one side dualchanneled waterproof at the extrados of joint under high compressionbending loads. The test-numerical comparison of the maximum joint opening width, maximum joint opening height, bolt stress condition, and joint bending stiffness are shown in Figs. 26–29. It is found that the numerical results are in a good agreement with the test results under small joint deformation, while relative differences are observed after the occurrence of visible concrete cracking. In the small joint deformation stage, joint stars to open linearly, the bolt is still unstressed, the joint opening width is small, and the opening height is almost unchanged. 113

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Table 5 Test-numerical comparison the failure characteristics of segmental joints under negative bending loads. Bending moment (kN m)

−600

−1100

−1500

−2200

Experimental tests Scenes

Features

Visible concrete cracks occurred at the bottom force transfer area of the test piece is beginning to appear.

The concrete cracks expands along the approximate horizontal direction and though.

Bolt yield, and the specimens concrete near the intrados began to stripping off the block.

Concrete under compression zone is completely destroyed and the structure of the joint is destroyed

Bending moment (kN m)

−700

−800

−1100

−1800

The concrete cracks gradually expanded along horizontal direction

Bolt yield, a large number of micro cracks and a small amount of concrete crushing area occurred at the contact surface of the concrete. Cracks near the intrados spread rapidly along the horizontal direction

Joint was destroyed, large concrete crushing and cracking occurred at joint interface. The horizontal cracks extended to the middle of joint

Numerical simulations Scenes

Features

A small amount of micro concrete cracks arise at the end of bolt and contact surface nearby the intrados

Note: The blue and green areas is the crushing zones, the red area occurred tensile cracking.

Fig. 27. Test-numerical comparison of joint opening height.

Fig. 26. Test-numerical comparison of the maximum joint opening width.

stage, but shows relatively differences after entering the nonlinear stage. It is because that the joint in the FE analysis can still bear loads, but the joint in the tests shows sudden failure after the bolt yielding in phase III. As presented in Fig. 26, the M-θ curves of test and numerical results are in a good agreement in phase I and the early stage of phase II, while discrepancy of the test-numerical comparison occurs at the end of phase II and the difference grows gradually with the increment of the applied load. It is probably because the FE model of the joint is established using homogeneous and isotropic concrete material model,

deformation stage, where the joint bending stiffness remains substantially constant. In phase II, visible concrete cracks appear on the adjacent segments, and the cracks are developed gradually with the increment of the bending loads. Besides, the structural behavior of the joints shows clear nonlinearity and the joint bending stiffness decreases accordingly. In phase III, the bolt yielding and concrete spalling happens, the bolt is pulled off from the adjacent segments, and finally the joint failure is obtained. The joint bending stiffness obtained in the FE analysis is in a good agreement with the test results in the initial linear 114

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(3)

(4)

Fig. 28. Test-numerical comparison of bolt stress condition.

(5)

(6)

Fig. 29. Test-numerical comparison of joint bending stiffness.

while the concrete material used in the experiment does not satisfy this assumption, resulting in difference of the concrete cracking load and area of the two joints. Besides, the discrepancy may result from the simplification in the calculation of the descending constitutive curve for the constitutive model. The complex stress-strain relation of concrete yielding is simplified as the straight line with a negative slope of 15%, which is based on the concrete constitutive model proposed in Jiang et al. (2005)). The simplification is beneficial to the calculation convergence, however it will cause deviation in the stress-strain relationship of concrete failure and leads to the deviation between the experimental and numerical results after the visible concrete cracks are obtained.

(7)

5. Conclusions In this paper, the bending behavior of segmental joints in large-scale underwater shield tunnels is carefully investigated through a series of full-scale tests and a comprehensive numerical study. In particular, the joint deformation behavior, segment cracking, bolt yielding, and joint failure are discussed through the test-numerical comparison. Conclusions are summarized as follows:

significantly and shows great nonlinearity under compressionbending loads. The contact status of the joint interface opening leads to significant changes of surface strains. The bolt force accounts for tensile concrete strain at the joint interface nearby the bolt hole, which indicates that the joint interface distorts and does not remain flat. Axial force can effectively mitigate and control the emergence and growth of concrete tensile strain nearby the joint interface. The bolt is stressed until the bending moment increases to a certain degree under compression-bending loads, and the bolt stress increases linearly with the growth of bending moment. When the bolt is pulled up after yield, the increasing speed of the bolt stress starts to reduce. The M-θ curves of segmental joint bending stiffness under compression loads could be divided into three phases (namely phase I, II and III) according to inflection point of 'visible concrete cracking' and 'bolt yielding'. The growth of initial stage, phase I, under the small bending moment is approximately linear. In phase II and III, the structural behavior of the joint shows significant nonlinearity. The size of the linear section in the M-θ curve increases with the growth of the applied loads. The bending stiffness under negative bending moments is larger than that under positive bending moments, and the axial force shows a great effect on keeping bending stiffness. The joint waterproof material could hardly promote the bending stiffness and capacity of segmental joint because of its small rigidity, and thus it can be ignored in the design and analysis of segmental joint bending stiffness. The failure process of segmental joint under negative bending moments was different from the failure process under positive bending moments. The negative bending capacity is smaller than the positive bending capacity. The compressive strength of compression zone concrete near the intrados has significant influence on the negative bending capacity. Thus it is necessary to set rubber packers at this area to reduce the stress concentration, and it is more rational to use one side dual-channeled waterproof at the extrados of joint interface under high compression-bending loads. The numerical results are in a good agreement with the test results in small deformation stage (phase I), while in large deformation and failure stage (phases II and III) the results shows relatively larger difference. This difference is mainly because of the simplification of materials for the stress strain curve used in the FE analysis in large strain or even failure stage. In order to satisfy the convergence of the FE model, the complex stress-strain relation of concrete yielding is simplified as the straight line with a negative slope of 15%. This leads to the joint deformation obtained in the FE analysis is slightly larger than that obtained in the test under the same bending moment level. In other word, it shows that the numerical simulation results are relatively conservative. On the other hand, the failure process, cracking and failure pattern of the FE results are similar to the test results. Thus, it is reasonable to simulate joint bending performance before visible concrete cracking, and to estimate joint failure mode by using the proposed FE model.

Acknowledgements The authors appreciate the support of the National Natural Science Foundation of China (51578462, U1361210, 51208432, 51578459), and the Fundamental Research Funds for the Central Universities (2682015CX077).

(1) Based on the test results, it is found that the joint opens linearly at the beginning and deforms nonlinearly after the visible concrete cracking occurred under compression-bending loads, and the shape of joint interface is a curved surface during the joint opening. The joint opening height changes in a 'stepped shape', the axial force provides constraints to restrict the joint opening. (2) The concrete strain of side surface nearby joint interface changes

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