Mechanical behavior of quasi-rectangular segmental tunnel linings: Further insights from full-scale ring tests

Tunnelling and Underground Space Technology 79 (2018) 304–318

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Mechanical behavior of quasi-rectangular segmental tunnel linings: Further insights from full-scale ring tests

T

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Xian Liua,b, Zhen Liua, , Yuhang Yea, Yun Baia, Yaohong Zhuc a

College of Civil Engineering, Tongji University, Shanghai, China Key Laboratory of Performance Evolution and Control for Engineering Structures, Ministry of Education, Tongji University, Shanghai, China c Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Quasi-rectangular shield tunnel Full-scale ring test Segmental reinforcement Shear bearing capacity Longitudinal joint bolt position Robustness

Compared with traditional circular shield tunnels and rectangular shield tunnels, quasi-rectangular shield tunnels have advantages in space efficiency, bearing capacity and applicability in urban areas. This new type of cross-section was first utilized in Ningbo Metro Line 3 in China, a full-scale ring test of corresponding lining structure was conducted to investigate the bearing mechanism of the structure preliminarily. In order to investigate the influence of segmental reinforcement, longitudinal joint position and shear bearing capacity of a T block on the mechanical behavior of a structure, two more full-scale ring tests are conducted. The failure process, structural convergence deformation, joint deformation and bolt strain of the lining structure are obtained. The bearing mechanism and robustness of the structure under unexpected circumstances are analyzed as well. The experimental results show that: (1) Optimization of segmental reinforcement and bolt position has little effect on the mechanical performance at elastic stage. (2) With the same joint configuration, an increase in the segmental reinforcement has a minor effect on the performance of the longitudinal joint. The robustness of the structure is not improved significantly either. (3) When the shear bearing capacity of the T block is guaranteed, the optimization of longitudinal joint bolt position can improve the mechanical performance of the structure significantly. When the overall rigidity of the structure is raised, the ultimate bearing capacity increases by 30% and the failure mode is ductile. As a conclusion, in order to increase the robustness and overall safety of a quasirectangular segmental tunnel lining, shear bearing capacity of T blocks should be strengthened to ensure that the segment would reach its bending moment bearing capacity first. The bolt hole of the positive moment joint should be moved inward while that of the negative moment joint should be moved outward as well.

1. Introduction Urban railways have become the first choice for relieving traffic congestion, especially in old urban areas. However, population and buildings are highly concentrated in these areas where buildings leave small space for roads and underground pipelines are intensive. Therefore, how to cross these congested areas has become a major problem in current urban railway construction. For conventional two circular shield tunnels, the total width of the tunnels is about 18–20 m. Under narrow roads, shield machine is unable to dig through and surrounding buildings will be disturbed by construction. Underground space is limited with the construction process and secondary excavation will cause secondary disturbance to the surrounding soil and buildings. Thus, a change in the form of cross-section has become necessary. The use of a two-way tunnel can reduce the distance between train lines,

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and increase the distance between shield tunnels and nearby buildings, while avoiding secondary excavation impact on existing buildings. There are three types of two-way tunnels: one large circular shield tunnel, DOT (Double-O-Tube) shield tunnel and rectangular/ quasirectangular shield tunnel. It has to be emphasized that a quasi-rectangular tunnel has the following advantages: (1) high utilization of underground space, (2) shallow buried depth and great ability to be excavated through narrow blocks, (3) easier control in relation to soil stick and earth settlement compared to DOT tunnel (Chow, 2006, Ye et al., 2015). As a result, it is of great significance and economic value to explore and study the tunneling technology of quasi-rectangular shield tunnels. Non-circular shield tunneling was applied and developed rapidly in Japan in the 1990s and it still leads the world. So far, Japan has built about 20 rectangular shield tunnels. For example, in a flood-control

Corresponding author. E-mail addresses: [email protected] (X. Liu), [email protected] (Z. Liu), [email protected] (Y. Ye), [email protected] (Y. Bai), [email protected] (Y. Zhu). https://doi.org/10.1016/j.tust.2018.05.016 Received 30 November 2017; Received in revised form 4 April 2018; Accepted 14 May 2018 0886-7798/ © 2018 Elsevier Ltd. All rights reserved.

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Fig. 1. Schematic diagram of test tunnel ring.

the durability of shield tunnel structures. Little has been done on the effect of segmental reinforcement to the structural bearing mechanism of tunnel structures. As for mechanical performance of longitudinal joints, there have been many studies on the composition form and structural optimization of longitudinal joints. In order to investigate mechanical behavior of longitudinal joints with and without transmission cushion, different methods were adopted to analyze the relation between stress, strain, internal force and bending angle of joints, using two different joints (Zhong et al., 2006). Based on experimental monitoring, a progressive model was proposed to investigate the development of longitudinal joint opening with bending moment under different axial stress levels, and longitudinal joint opening in Ultimate Limit State (Li et al., 2015). Full-scale joint tests were also conducted to investigate the bearing capacity of the longitudinal joint in a quasi-rectangular shield tunnel. Failure mechanism, mechanical behavior and ultimate bearing capacity of longitudinal joints were analyzed as well (Lin et al., 2016). When it comes to the fact that longitudinal joints are the weak parts of a shield tunnel, more attention is paid to its bearing mechanism. At present, research of longitudinal joints mainly focuses on joint stiffness, joint strength, failure process, influence on the distribution of internal force and mechanical properties of the whole structure. However, there is no research on the influence of bolt position on the mechanical performance. The quasi-rectangular shield tunnel is a new type of structure in shield tunneling. It combines the advantages of circular and rectangular tunnel, and will surely be widely used in the future. Based on existing research, positive and negative bending moment of different joints under operation condition is known. By moving the position of the bolts, the connecting bolt of a joint can be fully utilized and the mechanical performance of the joint can be optimized. Therefore, it is necessary to investigate the influence of the bolt position on the bearing mechanism of a quasi-rectangular segmental tunnel lining. Based on the first full-scale ring test of Ningbo quasi-rectangular segmental tunnel lining, the ultimate bearing capacity of the tunnel was reached. The bearing mechanism and weakness of the lining were revealed. In this research, two more full-scale ring tests are carried out by improving the reinforcement of the segment and optimizing the position of the longitudinal joint bolt. Based on the fact that shear failure phenomenon appeared at the haunch of T2 block in the first full-scale ring test, shear stirrup at two T blocks is strengthened in the third test to increase the shear bearing capacity. In this paper, the failure mechanism of the quasi-rectangular tunnel

sewerage tunnel in Narashino City in the suburbs of Tokyo, an 11.0 m × 7.08 m rectangular tunnel was constructed. In the project, a single DPLEX shield was used to excavate a couple of tunnels with a 4.2 m wide and 3.8 m high rounded rectangular cross-section (Kashima et al., 1996). From Rokujizo Station to Ishida Station in the East West Line of Kyoto subway, a 9.9 m × 6.5 m rectangular tunnel was built (Nakamura et al., 2003). In Metropolitan Tokyu Toyoko Line ShibuyaDaikanyan extension line project, a rectangular section with a dimension of 10.3 m × 7.1 m was applied. However, insufficient published literature on mechanical properties and design models of corresponding tunnel structures can be found. In 2016, a quasi-rectangular shield tunnel was the first to be successfully applied in Ningbo Rail Transit Line 3 in China. As the mechanical performance and design method of quasi-rectangular shield tunnel lining structures is not clear, a full-scale ring test is conducted (Liu et al., 2018). The design model and ultimate bearing capacity of the structure under overburden condition are obtained, which lays the foundation for further development of this new type of tunnel. It is also found that longitudinal joints and haunches of T blocks are the weak parts of the lining structure (As shown in Fig. 1, there are four haunches on the structure where critical cross-section 1, 5, 6 and 10 are located). In order to ensure a successful application of the new structure, failure mechanism and overall safety of the structure are key issues to be resolved. In a shield tunnel lining, a ring is composed of a number of segments and neighboring segments are connected by longitudinal joints. Therefore, the bearing mechanism of a structure is determined by both the segments and longitudinal joints, which are the main focus of this research. Conducting a full-scale ring test is an efficient way to determine the bearing mechanism of a tunnel lining. Experimental studies on tunnel lining structures of Elbe Tunnel in Germany were conducted in laboratories (Schreyer and Winselmann, 2000). For Shanghai Yangzi River Tunnel, the largest segmental tunnel lining at the time, a fullscale ring experiment was performed. The experimental results verified the safety of the structure under several operation conditions (Lu et al., 2011). With growing attention to serviceability of segmental tunnel linings, several full-scale ring tests were conducted by Xian Liu to determine the ultimate bearing capacity of continuously jointed segmental tunnel linings under different surrounding environment (Liu et al., 2016). According to the above-mentioned studies, existing research mainly focuses on the design model of shield tunnels, optimization design of segments, mechanical performance of the whole structure, failure mechanism and ultimate bearing capacity, as well as 305

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optimized one is shown in Fig. 2. In this test, No.1, No.3, No.5 and No.8 joints are negative moment joints, while the others are all positive.

structure is revealed by analyzing the experimental results of the three tests. The comparative analysis of the segment reinforcement and the longitudinal joint bolt position is performed to investigate their influence on the bearing mechanism under elastic phase and at the ultimate stage. The ultimate bearing capacity, structural ductility together with energy absorbing capacity are taken into consideration to evaluate the overall structural safety. This research lays the foundation for further optimization of the structure, the reinforcement of the segment and a better design of longitudinal joints for Quasi-rectangular segmental tunnel lining.

2.2. Loading system The horizontal loading system is composed of hydraulic jacks, loaddistribution beams and a counterforce steel frame. Oil cylinders of hydraulic jacks are installed on the steel frame to provide loading. Each load-distribution beam transforms point loads provided by two hydraulic jacks to distributed load exerted on the test ring. The counterforce steel frame provides holding resistance for the hydraulic jacks and the load is designed to be self-balancing. Ample steel balls with diameter of 50 mm are deployed under the test ring. Therefore rolling bearing condition with neglectable friction is provided. In order to simulate soil and water pressure exerted on the structure, thirty load points are deployed around the test ring. Each load point is composed of two hydraulic jacks and a load-distribution beam. The maximum horizontal load of a single point is 2000 kN and the maximum displacement of that is 300 mm. During the loading process, thirty load points are divided into several groups and hydraulic jacks in the same group provide equivalent load simultaneously.

2. The experiment design 2.1. Experimental rings In this research, three full-scale ring tests are carried out. A typical illustration of the test ring is shown in Fig. 1. Its outside dimension is 11,500 mm × 6937 mm and the width of the segment is 1200 mm. A single ring is composed of two T-shaped blocks (T1 and T2), three C blocks (C1, C2 and C3), three standard blocks (B1, B2 and B3), a contiguous block (L), a key block (F) and an interior column (LZ). The thickness of the segment (blocks) is 450 mm while that of the interior column is 350 mm. The concrete grade of the segments is C50 and the compressive strength of the concrete is 55.2 MPa, which is determined by the in-situ material experiment. The yield limit and ultimate strength of the steel HRB400 are 400 MPa and 550 MPa, respectively. To prevent the steel from corrosion, concrete cover is used on each side, measuring 66 mm. The longitudinal joint is formed by an embedded steel box, and four 6.8 M33 bolts are utilized to connect neighboring blocks at each longitudinal joint. The reinforcement ratio of each block, average flexural rigidity of the segment, stirrup of the T block, bolt position of the positive and negative moment joints are listed in Table 1. As shown in Fig. 1, there are ten joints on the segment. They can be divided into two types under overburden condition. If the inner side of a joint is in tension after the test, the joint is defined as a positive moment joint, like No.2, No.4, No.6, No.7, No.9 and No.10 joints. If the outer side of a joint is in tension, the joint is defined as a negative moment joint, like No.1, No.3, No.5 and No.8 joints. The average flexural rigidity of the segment is determined using formula (1). 10

Average(EI/L) = 1/ ∑ 1

Li EIi

2.3. Loading process In order to investigate the influence of the segmental reinforcement and the bolt position on the mechanical performance and overall safety of the quasi-rectangular shield tunnel lining structure, whole process limit condition tests are conducted for the three test linings. In a whole process limit condition, soil overburden acts on the top of the tunnel. During the simulation process, load exerted on the lining reaches the normal operation condition first. (Normal operation condition is the design condition, where offset load, buried earth load, shoulder ground load, resistance of elastic foundation, lateral load are all taken into consideration.) It increases progressively to the ultimate limit condition. (In the ultimate limit condition, partial safety factors are multiplied based on the normal operation condition). Thereafter, the load increases simultaneously until the lateral load is equal to the calculated passive earth pressure. The final condition is called overburden condition. When the loading enters the overburden condition, the lateral load is kept constant, with the top and corner load increasing until the structure reaches its ultimate bearing capacity. A key point in load design is to simulate the load exerted on the real tunnel lining. Here the applied principle is the equivalence of both load distribution and internal force of the lining between real and experimental results. As shown in Fig. 3, all together ten critical cross-sections are distributed on the lining and these critical cross-sections are all governed by the bending moment except for No 11 critical cross-section, which is deployed on the interior column. When preparing for the simulation, several numerical calculations of the test ring are conducted to ensure that the internal force and deformation are approximately equivalent to those of an actual structure under operation. Therefore, thirty load points are divided into three groups including P1 (eight load points), P2 (ten load points), and P3 (twelve load points), which is shown in Fig. 3. According to the survey of previous studies, a similar principle was used in the structural experiment of Botleck railway

(1)

where Li refers to the arc length of each block and EIi refers to the flexural rigidity of each block. According to Table 1, the reinforcement of the second ring increases compared to that of the first ring, as the reinforcement ratio of the second ring is 1.56 times that of the first. Compared to the second ring, the longitudinal joint design and shear bearing capacity of the third ring are both optimized, where the stirrup of T2 block becomes two times that of the former design. Thus, the ductility of the tunnel structure is guaranteed. The bolt hole at the positive moment joint is moved inward by 50 mm while that of the negative moment joint is moved outward by 50 mm. An illustration of the original joint and the Table 1 Reinforcement and the average stiffness of segment. Test ring

First Second Third

Segmental reinforcement (mm2)

81,301 127,322 127,322

Reinforcement ratio (%)

1.51 2.36 2.36

Average flexural rigidity of segment (kN·m2)

3.565 × 105 3.799 × 105 3.799 × 105

Stirrup of T block

4Ф10@109 2 16@200 4 16@100

306

Bolt position (Distance to internal surface) Positive moment joint (mm)

Negative moment joint (mm)

200 200 150

200 200 250

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Optimized positive moment joint

Original joint

Optimized negative moment joint

(a) Illustration of original joints and optimized joints

Optimized positive moment joint

Original joint

Optimized negative moment joint

b) Photos of original joints and optimized joints Fig. 2. Bolt position of original joint and optimized joints of the third test ring.

2.4. Measurement

tunnel (Blom, 2002). Because soil-structure interaction is more sophisticated, the load exerted on the test ring cannot be accurately simulated during our test. However, with a deeper investigation of the structural behavior of the Quasi-rectangular tunnel, experimental methods with further improvement will be carried out in future. As shown in Fig. 4, the loading process of the whole process limit condition can be divided into four stages: In stage 1, P1, P2 and P3 increase simultaneously until the load reaches the normal operation condition. At the end of the first stage, P1 is equal to 300 kN, P2 is equal to 170 kN and P3 is equal to 212 kN. In stage 2, P1, P2 and P3 increase simultaneously until the load reaches the ultimate limit condition. At the end of the second stage, P1 is equal to 480 kN, P2 is equal to 240 kN and P3 is equal to 297 kN. In stage 3, P1, P2 and P3 increase simultaneously with a constant ratio until the lateral load reaches the calculated passive earth pressure. At the end of the third stage, P1 is equal to 871 kN, P2 is equal to 394 kN and P3 is equal to 633 kN. In stage 4, the test enters the overburden condition. P1 and P3 increase continuously and P2 is kept constant until the structure reaches the ultimate bearing capacity.

Data measured in this test includes the convergence deformation of the structure, displacement of the structure, side displacement of the interior column, strain of rebar and concrete, strain of bolts, and opening and dislocation of joints. Segment cracks and damage of joints are observed during the entire experiment. Deployment of corresponding sensors are as follows: (1) The convergence deformation of the structure. Measuring points are arranged at the long axis and the two short axes of the test ring. Each measuring point contains two displacement meters. (2) The displacement of the structure. Based on the principle of symmetry, twenty measuring points are arranged at the test ring. Each measuring point contains two sensors, one for radial displacement and one for circumferential displacement. (3) The side displacement of the interior column. Three measuring points are arranged at the interior column. Each measuring point contains two displacement meters. (4) The internal force of the structure. Resistance strain gauges are arranged at 25 cross-sections of the entire structure. Thereafter,

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Fig. 3. Division of load points.

1500

Stage 1

Stage 2

Stage 3

Table 2 Summary of measuring points.

Stage 4

P(kN)

1200 900

P1 P2

600

P3

300 0 0

10

20

30

40

50

Loading step

60

70

80

Fig. 4. Loading process of the overburden condition.

strain of concrete and rebar is measured. (5) The internal force of bolts. Each bolt is grooved at both sides. Resistance strain gauges are arranged symmetrically to measure the bolt strain. (6) The opening of joints. Measuring points are arranged at both the outer and inner side of each joint. At each point, three sensors are arranged on the side where the joint opens while two sensors are arranged on the opposite side. (7) The dislocation of joints. Two sensors are arranged at the inner side of each joint.

Measured items

Measurement scope

Accuracy

Quantity

Convergence deformation of the structure Displacement of the structure Side displacement of the interior column Strain of rebar Strain of concrete Bolts strain Opening of joints Dislocation of joints Segment cracks

500 mm

0.01 mm

6

100 mm 500 mm

0.01 mm 0.01 mm

40 6

20,000 με 20,000 με 20,000 με 100 mm 50 mm # Total

1 με 1 με 1 με 0.01 mm 0.01 mm 0.01 mm

424 224 80 50 20 # 850

LA1 and point LA2 is 10,600 mm before the test, which is the initial length of the long axis. Under overburden condition, if the distance between the two points becomes larger, it means that the convergence deformation of the long axis grows as load increses. At the beginning of the experiments, the test linings are at elastic stage. According to the monitoring measurement, opening of joint, bolt strain and convergence deformation all develop linearly. When the load of the first ring reaches 53.1% of the corresponding ultimate bearing load, a turning point (point ① of the curve a) in Fig. 5) occurs on the load-convergence deformation curve. For the second ring, it occurs when the load reaches 47.5% of the ultimate bearing load (point ① of the curve b) in Fig. 5). When it comes to the third ring, the overall structural rigidity decreases when the load reaches 37.0% of the ultimate bearing load (point ① of the curve c) in Fig. 5). However, the load value P1 of the turning points of all three test rings are almost the same, at about 520 kN. When the curve of the first test ring enters the plastic stage, the following phenomena occurs in sequence. ②Concrete cracks at the compression side of No.2 joint (② refers to point ② of the corresponding curve in Fig. 5). ③Concrete cracks at the compression side of No.5 joint and the bolt of No.8 joint is yielded. ④Concrete cracks at the compression side of No.2, No.3 and No.8 joints. ⑤Concrete cracks at the compression side of No.9 joint. ⑥Concrete cracks at the compression side of No.4 and No.6 joints. ⑦A bolt of No.6 joint is yielded. ⑧Bolts of No.3 and No.10 joints are yielded while cracks at the compression side

The measurement scope, accuracy and number of sensors for each full-scale ring test are listed in Table 2.

3. Structural failure process 3.1. Failure process The failure process of the three test linings under whole process limit condition is shown in Fig. 5. Throughout the entire loading process, the load-convergence deformation curves have two typical stages: elastic and plastic (working with cracks) stages. Here the convergence deformation refers to the deformation of the deformed structure relative to the initial state. As shown in Fig. 1, the distance between point 308

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1200

1200

1200

900

900

900

600

600

300

300

P1(kN)

1500

P1(kN)

1500

P 1(kN)

1500

300

0

0 0

10

20

30

40

50

60

70

80

90 100

Convergence deformation of long axis(mm)

a) First test ring

600

0

10

20

30

40

50

60

70

80

90 100

Convergence deformation of long axis(mm)

0 0

20

40

60

80

100 120 140 160 180

Convergence deformation of long axis(mm)

b) Second test ring

c) Third test ring

Fig. 5. Load-convergence deformation of long axis curves of three test rings.

of No.1 joint develop rapidly. ⑨A bolt of No.9 joint is yielded and concrete at the compression side of No.5 joint is crushed. ⑩A bolt of No.5 joint is yielded and concrete at the compression side of No.8 joint is crushed. ⑪The segment is broken at the haunch of T2 block near No.6 joint and a stirrup is found broken there. Thereafter, concrete at the compression side of No.6 joint is crushed and a bolt is broken. At the end of the test, the ultimate bearing capacity is reached and the corresponding load value P1 is equal to 1081.90kN. As shown in Fig. 5 a), the load-convergence deformation curve does not experience a platform phase before the ultimate bearing capacity is reached, which means the failure of the first test ring has the characteristic of brittle damage. The load-convergence deformation curve of the second ring is very similar to that of the first. But the structural failure characteristic points are more dispersed than those of the first. After entering the plastic stage, the following phenomena occurs in sequence. ②Cracks at the compression side of No.8 joint develop. ③Concrete cracks at the compression side of No.3 joint. ④Concrete cracks at the compression side of No.6 joint. ⑤Cracks at the compression side of No.5 joint develop rapidly and a bolt of No.8 joint is yielded. ⑥Concrete cracks at the compression side of No.9 joint and a bolt of No.6 joint is yielded. ⑦A bolt of No.9 joint is yielded. ⑧Concrete cracks at the compression side of No.4 joint. ⑨A bolt of No.10 joint is yielded. ⑩Concrete is crushed at the compression side of No.3 and No.4 joints. ⑪A bolt of No.3 joint is yielded and concrete at the compression side of No.5 and No.8 joints is crushed. A stirrup is found broken at the segment of T2 block near No.5 joint, which finally causes the structural failure. The ultimate bearing capacity of the second ring is 1093.56kN. Similar to the first ring, the curve of the second ring does not experience any platform phase before failure, which suggests brittle damage. Comparing the two test rings, the structural characteristic points are different. However, the failure sequence and ultimate bearing capacity are almost the same. After entering the plastic stage, the mechanical behavior of the third ring is totally different from the first and second rings. As shown in Fig. 5(c), the structural rigidity of the third ring is obviously higher than that of the first and second. In addition, a platform phase occurs at the end of the loading process, which means the failure has the characteristic of ductile damage. The following phenomena occur in sequence with the test of the third ring. ②Cracks at the compression side of No.3 joint develop. ③Concrete cracks at the compression side of No.6 joint and bolts of No.6 and No.8 joints are yielded. ④Concrete cracks at the compression side of No.3 joint and a bolt of No.9 joint is yielded. ⑤Cracks at the compression side of No.8 joint develop. ⑥A bolt of No.3 joint is yielded. ⑦Concrete cracks at the compression side of No.4 joint and a bolt of No.10 joint is yielded. ⑧A bolt of No.5 joint is yielded. ⑨Concrete cracks at the compression side of No.9 joint and bolts of No.1 and No.4 joints are yielded. ⑩Concrete cracks at the compression side of No.2 joint and a main reinforcement located at the outer side of the critical cross-section 10 is yielded. ⑪ A bolt of No.2 joint is yielded. ⑫Concrete crushes at the compression side of No.8 and No.10 joints.

Bolts of No.8 and No.10 joints are broken and a main reinforcement located at the inner side of the critical cross-section 10 is yielded. The segment is broken at the haunch of T1 block near No.10 joint and the structure finally loses its bearing capacity. The ultimate bearing capacity of the third ring is 1412.43 kN. 3.2. Analysis of failure mechanism The failure process of the three test rings shows that the load-convergence deformation curve of a typical test ring will experience elastic and plastic stages. At the elastic stage, the convergence deformation, opening of joints and strain of joints all grow linearly. As the load increases, cracks gradually occur at the segment and the compression side of the joints, which lead to the decrease of overall rigidity. However, the curve does not experience an obvious turning point. That is because the stiffness of the segment is larger than that of the joints. Therefore, the segment shares more internal force and additional load. According to the results observed, the failure of each test ring begins with joint damage, and the structure finally loses its bearing capacity because of segment failure. For all three full-scale ring tests, a longitudinal joint is assumed to be a plastic hinge if a bolt is yielded while a cross-section is assumed to be a plastic hinge if the main reinforcement is yielded and concrete at the compression side is cracked. According to the failure sequence and the final state of the first ring, there are four plastic hinges on the left half of the test ring and two plastic hinges on the right, which is shown in Fig. 6(a). With load increasing, plastic hinges emerge at No.8, No.6, No.3, No.5 joints and No.6 critical cross-section in sequence and these plastic hinges lead to redistribution of the internal force. At the end of the test, the haunch of T2 block near No.6 joint is broken by bending moment and shear force together. The left half of the structure becomes geometrically unstable and the structure finally loses its bearing capacity. As shown in Fig. 7, a large number of diagonal cracks appear while a shear bearing stirrup is found broken. It suggests that the failure of the critical cross-section of T2 block has the obvious characteristic of shear bearing failure. Compared to the first ring, the failure of the second ring is similar but not identical. As mentioned before, the reinforcement ratio of the second ring is larger than that of the first and the overall rigidity of the segment also increases 1.07 times. Under the same circumstance, the deformation of the lining structure is small. The segment shares more load, while the internal force of the joints, development of joint bending angle and bolt strain are relatively small. The comparison of the experimental results are shown in Figs. 8 and 9. It indicates that the structural characteristic points of the second ring also occur relatively late, compared with the first. According to the results of the joint damage, the failure situation of concrete and bolt of the second ring is not as severe, i.e., the joints still have bearing capacity left. It means that a higher ultimate bearing capacity is not reached under the same failure 309

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a)First test ring

b)Second test ring

c) Third test ring Fig. 6. Failure order and final state of three test rings.

Fig. 7. Shear bearing failure photo of segment at huanch of T2 block.

mode. However, the ultimate bearing capacity of the first and the second ring are almost the same. From the final state of the second ring (as shown in Fig. 6b), the number of plastic hinges is not enough to keep the structure geometrically stable. The failure of the second ring is because a critical cross-section has reached its shear bearing capacity and the corresponding stirrup is broken, resulting in local damage and loss of bearing capacity of the whole structure. According to the monitored test load and knowledge of structural mechanics, the shear internal force at the haunch of T2 block of the first and second rings are obtained. The ultimate shear capacity of T2 block can also be calculated by referencing the Code for the Design of Concrete Structures in China. The comparison of these two values are listed in Table 3. The calculation results of the shear force under ultimate load

Fig. 8. Comparison of joint bending angle of the first and second test rings.

suggests that the internal shear force of the first and second rings are beyond their ultimate shear capacity. As shown in Fig. 10, stirrups are all found broken at the critical cross-section of T2 block, which proves the accuracy of the above analysis. It means that the bearing capacity of the longitudinal joints and the segment of the second ring have not been fully utilized. The failure of the test ring is because of the shear bearing failure of T2 block, resulting in local and structural failure. 310

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a)First test ring

Fig. 9. Comparison of joint bending angle of the first and second test rings.

b)second test ring

Fig. 10. Photos of shear bearing failure of T2 block of two test rings.

When it comes to the failure process of the third ring, the failure mode is significantly different from the first and second. As mentioned before, the bolt holes of the positive moment joints are moved inward while those of the negative moment joints are moved outward. As shown in Fig. 12, at elastic stage, the development of the three loadconvergence deformation curves are almost the same and the overall structural rigidity of the three rings are close. After entering the elastic stage, the long axis convergence deformation of the third ring grows noticeably slower than that of the first and second. The overall structural rigidity is obviously larger and the structural characteristic points appear later as well. This is because after the optimization of the longitudinal joints, the movement of bolt position leads to a higher compression area of the joint, an increase in bending stiffness and a decrease in joint deformation. The stronger bearing capacity of joints also makes the internal force distribution more uniform. As the load increases, the bolts of the longitudinal joint are fully utilized and the ultimate bearing capacity of the joints are obviously increased. Therefore, the failure of joints is later than the first and second rings. Another important optimization is the increase of shear bearing capacity of T blocks. As listed in Table 3, the shear bearing capacity of the T blocks has been increased to 3253.88kN, which is 56.3% higher than that of the second ring. According to the final state of the third ring, the shear failure does not appear at the T blocks and only a large number of bending cracks appear, which is shown in Fig. 11. Different from the first and second rings, the local failure does not appear on the third ring. In the final state of the third ring (as shown in Fig. 6c), there are 5 plastic hinges on both the right and left, where plastic hinges of No.10 and No.2 joints and T1 block appear almost simultaneously. Concrete at the compression side of No.2 and No.4 joints are all cracked but not crushed. The failure mechanism of the third ring is that the plastic hinges emerge at No.8, No.6, No.3, No.5, No.9, No.1, and No.10 joints in sequence. At the end of the test, a main reinforcement located at the critical cross-section 10 is yielded and the last plastic hinge finally appears here. Finally, the structure becomes geometrically unstable and loses its bearing capacity.

Fig. 11. Bending moment bearing failure photo at huanch of T1 block near No.10 joint.

4. Discussion of results 4.1. Structural performance at elastic stage From the turning points of the load-convergence deformation curve of the three test rings, load value P1 at the end of the elastic stage of the three rings are almost the same, measuring about 520 kN. In order to analyze the structural behavior of the test rings at elastic stage, a comparison of the convergence deformation and internal force of the test rings is performed. The convergence deformation is monitored by the displacement meter. The internal force is calculated by the basic principle of reinforced concrete and monitored strain of concrete and

Table 3 Shear force of segment at T2 block under ultimate load. Test ring

Stirrup of segment at T2 block

Ultimate tensile strength of the rebar (MPa)

Ultimate tensile strength of the concrete (MPa)

P1 (kN)

Shear force of segment at T2 block (kN)

Ultimate shear bearing capacity (kN)

First Second Third

4Ф10@109 2 16@200 4 16@100

300 400 400

55.2 53.8 53.8

1081.90 1093.56 1412.43

2325.44 2336.54 3062.13

2169.25 2095.77 3253.88

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structural ductility, consumed energy. The definition of corresponding robustness indexes are listed below (Liu et al., 2017). Robustness index based on bearing capacity: Generalized overload index K.

Table 4 Comparison of convergence deformation of three test rings under elastic stage. Convergence deformation

Long axis Right short axis Left short axis

First ring (mm)

Second ring (mm)

Third ring (mm)

Reduction percentage (Second/First) (%)

Reduction percentage (Third/ Second) (%)

5.49 7.34 8.49

4.98 7.18 7.9

4.57 6.26 6.74

9.3 2.2 6.9

8.2 12.8 14.7

(2)

K = F / F0

where F refers to the ultimate bearing capacity, F0 refers to the load under normal operation condition. Robustness index based on structural deformation: Deformation index D. (3)

D = d/d 0

rebar, as in Liu et al. (2018). The calculation results are shown in Tables 4 and 5. When comparing the convergence deformation and internal force of the first and second rings under elastic stage, the convergence deformation of the long and short axes of the second ring is reduced by 2.2–9.3%. The axial force of the second ring is the same as that of the first, while the bending moment of the second is larger. Among the ten critical cross-sections, No 1, No.3, No.5 and No.9 have the largest change of bending moment, with an increase ratio of about 8–11%. It suggests that the increased segment reinforcement leads to an increase in segment stiffness while the structural deformation is reduced at the same time. Because the segment shares more internal force, the bending moment of the critical cross-sections also becomes larger. When comparing the second and third rings, the convergence deformation of the long and short axes of the third ring is reduced by 8.2–14.7%. The axial force of the third ring is the same as that of the second, while the bending moment of the third ring is smaller. No 1, No.3, No.5 and No.10 critical cross-sections have the largest change of bending moment, with a decrease ratio of about 8–12%. It suggests that the movement of the joint bolt position increases stiffness of the longitudinal joints, resulting in a decrease in structural deformation. In addition, the internal force of the segment reduces and the structural bending moment distribution becomes more uniform. In general, an adjustment of the segment reinforcement and bolt position does little to the convergence deformation and internal force of the test structure at elastic stage.

where d refers to the convergence deformation of the long axis in the final state, d 0 refers to corresponding deformation under normal operation condition. Robustness index based on structural ductility: Ductility index μ .

μ = d/μ y

(4)

where μ y refers to the convergence deformation of the long axis when the structure first develops local yielded phenomenon. Robustness index based on consumed energy: Energy dissipation index I. (5)

I = Eu/ E0

where Eu and E0 refers to the energy consumed by the lining structure under the final state and normal operation condition, respectively. The load-long axis convergence deformation curves of the three test rings are illustrated in Fig. 12. The performance points (normal operation condition, first yielded condition, final state) are shown in the same Figure. As shown in Fig. 12, the three test rings have similar mechanical behavior at elastic stage. After entering the plastic stage, the curves of the first and second rings are similar to each other. However, the curve of the third ring is significantly different from the other two. In comparison, the performance point (first yielded condition) of the first ring appears the earliest while that of the third appears last. When the convergence deformation of the three test rings reaches about 30 mm, the structure first develops local yielded phenomenon. Based on the above-defined principle and monitored measurement, the robustness indexes of the three rings are calculated and listed in Tables 6 and 7. According to the calculated robustness indexes in Table 7, the robustness of the first and second rings are close. Compared to the first, the robustness of the second ring is slightly increased but the ductility index is reduced. The comparison of the first and second rings suggests that an increase in segment reinforcement does not obviously improve the robustness of the structure. This is mainly because the damage of the structure is caused by joint failure. Therefore, the robustness of the structure cannot be improved significantly when the joints are not

4.2. Robustness of test rings In order to evaluate the overall safety of a quasi-rectangular segmental tunnel lining, security of the structure is evaluated in relation to its robustness. In the event of accidents and sudden damage, structural robustness requires that the structural stability is ensured without dislocations such as continuous collapse. Considering that the test structure is mainly broken by “generalized load”, a robustness evaluation method is utilized. Several generalized indexes are taken into evaluation, including the ultimate bearing capacity, structural deformation, Table 5 Comparison of internal force of three test rings under elastic stage. Number of critical cross-section

1 2 3 4 5 6 7 8 9 10 11

First ring

Second ring

Third ring

Second/First

Third/Second

Axial force (kN)

Bending moment (kN·m)

Axial force (kN)

Bending moment (kN·m)

Axial force (kN)

Bending moment (kN·m)

Axial force

Bending moment

Axial force

Bending moment

−1162 −1071 −1226 −1090 −1087 −1110 −1045 −1214 −1023 −1137 −1915

−350 360 −193 417 −318 −327 411 −217 352 −378 −1

−1166 −1065 −1244 −1071 −1076 −1119 −1039 −1228 −999 −1100 −1908

−377 373 −215 434 −347 −335 436 −223 383 −373 −20

−1165 −1050 −1229 −1066 −1070 −1082 −1003 −1246 −1036 −1053 −1881

−331 371 −198 428 −310 −316 420 −213 371 −332 9

1.00 0.99 1.01 0.98 0.99 1.01 0.99 1.01 0.98 0.97 1.00

1.08 1.04 1.11 1.04 1.09 1.02 1.06 1.03 1.09 0.99 #

1.00 0.99 0.99 1.00 0.99 0.97 0.97 1.01 1.04 0.96 0.99

0.88 0.99 0.92 0.99 0.89 0.94 0.96 0.96 0.97 0.89 #

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Table 7 Comparison of robustness indexes of three test rings. Robustness index

Generalized overload indexK

Deformation index-D

Ductility index-μ

Energy dissipation index-I

First ring Second ring Third ring

2.07 2.10 2.70

15.71 17.51 37.55

3.05 2.67 5.53

51.29 55.20 192.39

are both governed by local failure rather than overall failure. The ultimate bearing capacity and corresponding convergence deformation of the three test rings are listed in Table 8. Compared to the second ring, the ultimate bearing capacity of the third ring increases by about 30% and the ultimate deformation increases by about 97%, which suggests that the structural failure is ductile. The above results show that the ultimate bearing capacity of a quasi-rectangular segmental tunnel lining can be enhanced by optimizing the joint bolt positions and shear bearing capacity of T blocks. When the bolt hole of a positive moment joint is moved inward or that of a negative moment joint is moved outward, the height of the compression zone is increased, resulting in an increased stiffness and bearing capacity of the longitudinal joint. With the optimization of joints, joint failure is postponed, which benefits the mechanical behavior of the structure at plastic stage. At the same time, the bearing capacity of the segment is fully utilized. Furthermore, increase of stirrups at T blocks also improves the safety reserve of the shear bearing capacity. This optimization ensures that the shear bearing failure of T blocks is later than the bending moment bearing failure of the segment, which can prevent structural failure from local failure. According to the structural robustness analysis in chapter 4.2, robustness indexes of the third ring are obviously higher than those of the first and second rings. The optimization of joints and improvement of shear bearing capacity ensure the ductile characteristic of the structural failure. It significantly improves the robustness of a quasi-rectangular segmental tunnel lining and ensures the overall safety of the structure.

Fig. 12. Comparison of load-convergence deformation curves of three test rings.

optimized. In addition, the failure of the second ring is caused by the shear bearing failure of the T2 block, which has the characteristic of local damage. The bearing capacity of the structure is not fully utilized either. Compared to the first and second rings, the robustness of the third ring is significantly higher. Among the four robustness indexes, the improvement of the energy dissipation index is the most obvious. The improvement of robustness indexes suggests that the bolt position optimization has an obvious effect on the robustness of a quasi-rectangular segmental tunnel lining. In addition, the shear bearing capacity of the third ring is enhanced, and no shear bearing failure appears during the whole loading process either. The curve of the third test ring indicates that the structural failure has the characteristic of ductile damage, resulting in a big improvement to the ductility index. This goes to show that ensuring the shear bearing capacity of the segment is another key point in improving the robustness of a quasi-rectangular segmental tunnel lining.

4.3.2. Structural reinforcement As mentioned before, the reinforcement ratio of the second test ring is 1.56 times of the first. In this chapter, the influence of the structural reinforcement is investigated based on the comparison between the first and second rings. According to chapter 4.1, the convergence deformation of the long and short axes of the second ring at elastic stage is reduced by 2.2–9.3% compared with the first ring. The internal force of the second ring is increased by up to 11.4% compared with the first. At elastic stage, an increase in segment reinforcement has little impact on the mechanical behavior of the structure. When it comes to plastic stage, the ultimate bearing capacity and ultimate convergence deformation of the first and second rings are basically the same. The robustness indexes of these two rings are also similar. During the whole loading process, the load-rebar strain curves of critical cross-section 1 are shown in Fig. 13 while those of critical crosssection 6 are shown in Fig. 14. As for critical cross-section 1, the development of rebar strain of two rings shows the same tendency and the curve of the second ring grows a little faster. When the ultimate bearing

4.3. Considerations on design aspects 4.3.1. Structural weakness Based on the analysis of the failure process and failure mechanism of the structure in chapters 3.1 and 3.2, the shear bearing capacity of T blocks and bending moment bearing capacity of longitudinal joints are the weak parts of a quasi-rectangular segmental tunnel lining. The failure of the three test rings all begins with joint failure and finally loses its bearing capacity due to the failure of T blocks under bending moment and shear force. According to the final state of the first and second rings, the critical cross-section of a T block is broken by the shear force and the failure of the structure has the characteristic of brittle damage. Since the ultimate bearing capacity and convergence deformation of the first and second rings are almost the same, it suggests that the failure of these two rings Table 6 Generalized indexes of three test rings. Generalized indexes

First ring Second ring Third ring

Load under normal operation condition-F0 (kN)

524 520 522

Convergence deformation of long axis under first yielded condition- μ y

ultimate bearing capacity-F (kN)

Convergence deformation of long axis under normal operation condition-d0 (mm)

(mm)

1082 1094 1412

5.49 4.98 4.57

28.29 32.71 31.00

313

Ultimate convergence deformation of long axis- μm (mm)

Energy consumed under normal operation condition-E0 (kJ)

Energy consumed under final stateEu (kJ)

86.25 87.19 171.50

1451 1377 1089

74,409 76,008 209,584

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Table 8 Ultimate bearing capacity and ultimate convergence deformation comparison. Test ring

First

Second

Third

Increase percentage (Second/First) (%)

Increase percentage (Third/Second) (%)

Ultimate bearing capacity-P1 Ultimate convergence deformation of long axis

1082 kN 86.25 mm

1094 kN 87.19 mm

1412 kN 171.50 mm

1.1 1.2

29.1 96.7

rebars are yielded at the end of the whole process limit condition. The above results show that an increase in reinforcement causes the internal force on the segment to be slightly increased. As mentioned in chapter 3.2, the failure of the second ring is due to the local damage at T block and the bearing capacity of the joints is not fully utilized. However, considering the quasi-rectangular tunnel lining is governed by joint failure and shear bearing failure of T blocks, an increase in reinforcement has little influence on the ultimate bearing capacity of the structure when the longitudinal joint design remains unchanged. According to the robustness analysis in chapter 4.2, the robustness of the structure cannot significantly improve either by simply adjusting the main reinforcement. In conclusion, an increase in reinforcement does little to the mechanical behavior of a quasi-rectangular segmental tunnel lining. Therefore, segmental reinforcement should be optimized during the design process to ensure that the failure of critical cross-sections and longitudinal joints appear simultaneously. However, the design of critical cross-sections in tunneling is usually governed by crack width. Thus, it is suggested that the main reinforcement is optimized with the most effective crack width, paying attention to the performance requirement.

Fig. 13. Load-rebar strain of inner and outer side of critical cross-section 1 of two rings.

capacity is reached, the final strain of the rebar located at the inner side of the first and second rings are −725 με and −795 με respectively, while the final strain of the rebar located at the outer side of the first and second rings are 1207 με and 1358 με respectively. The development rule of the rebar located at critical cross-section 6 is similar to that located at cross-section 1. Before the structural failure, a turning point appears on the load-strain of the rebar curve of the first ring and then the curve grows at higher speed compared with the second ring. When the ultimate bearing capacity is reached, the final strain of the rebar located at the inner side of the first and second rings are −1286 με and −857 με respectively, with the final strain of the rebar located at the outer side of the first and second rings being 1884 με and 1225 με respectively. Such phenomenon is because the critical cross-section 6 of the first ring is broken. According to the monitoring results, none of the

4.3.3. Position of connection bolts As mentioned before, the longitudinal joint bolt position of the third test ring is optimized compared to the second ring. In this chapter, the influence of the bolt position is investigated based on the comparison between the second and third rings. According to chapter 4.1, the optimization of the longitudinal joint bolt does reduce structural deformation and bending moment of the test ring at elastic stage. The structural deformation reduction rate is 8.2–14.7% while the maximum reduction rate of the bending moment is about 12.3%. It suggests that the movement of joint bolts also has little effect on the mechanical behavior of the quasi-rectangular segmental tunnel lining at elastic stage. The opening and compression of joints are measured during the test.

Fig. 14. Load-rebar strain of inner and outer side of critical cross-section 6 of two rings. 314

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Fig. 15. Comparison of load-bending angle curve of positive moment joint.

of the joint bolt position, the bolts of the third ring get to bear the load earlier, which results in a slightly faster development of the bolt strain at elastic stage. When the test rings enter plastic stage, the movement of the joint bolt position increases the height of the compression zone of the longitudinal joints. As a result, the bending stiffness of the joints increases. The development of the joint bending angle is slowed down and the internal force distribution of the structure is more uniform. As a result, the bolt strain grows slower than when it is not optimized and the bearing capacity of the longitudinal joints is fully utilized. Furthermore, the rigidity and ultimate bearing capacity of the longitudinal joints are significantly increased and the mechanical behavior of the structure is noticeably improved at plastic stage. According to the discussion and analysis in chapter 4.1 and 4.2, the overall rigidity, ultimate bearing capacity and robustness indexes of the third ring are significantly optimized compared to the second ring. In summary, the optimization of the longitudinal joints does little to the mechanical behavior of the structure at elastic stage. However, it makes an obvious improvement on the overall rigidity and bearing capacity of the structure at plastic stage. With optimization, the failure of the structure is ductile, the robustness and overall safety of the structure are obviously improved. This optimization measure can be widely utilized in quasi-rectangular segmental tunnel lining.

Here the bending angle of the joint is defined by the following formula (6) (Positive value of the bending angle means the outer side of the joint compresses and the inner side opens).

Φ = (uin−uout )/ h

(6)

where Φ refers to the bending angle of the joint, uin refers to the opening/compression deformation on the inner side of the joint, uout refers to the opening/compression deformation on the outer side of the joint, h refers to the thickness of the segment (The value of h is 450 mm). The load-bending angle curves of the positive and negative moment joints are shown in Fig. 15 and Fig. 16, respectively. At elastic stage, the bending angle of the second ring grows slightly faster than that of the third ring. After the turning points appear, the development of the bending angle of the second ring is larger. In addition, the curves of the third ring all experience a significant platform phase at the end of the test. It suggests that the joint bearing capacity of the third ring is fully utilized but that of the second ring is not. The load-strain of the joint bolt curves of the positive and negative moment joints are shown in Fig. 17 and Fig. 18, respectively. In these figures, the curves all show similar tendency to the bending angle curves. For the two test rings, there is little difference at elastic stage and the bolt strain of the second ring grows faster at plastic stage. A significant platform also appears in the curves of the third ring. As a result, more bolts are yielded in the third ring test, which suggests that the bearing capacity of the connection bolts is fully utilized. The above comparison results show that the two test rings have similar mechanical behavior at elastic stage. Because of the movement

5. Conclusions Based on the results of the first full-scale ring test, two more fullscale ring tests are conducted in this study. The main reinforcement of the second ring is increased compared to the first ring, while the 315

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Fig. 16. Comparison of load-bending angle curve of negative moment joint.

the critical cross-section of a T block is reached earlier than the shear bearing capacity of the T block, which is a key to keep the failure of a quasi-rectangular segmental tunnel lining ductile. (3) An increase in reinforcement and movement of the longitudinal joint bolt position makes little difference to the mechanical behavior of a quasi-rectangular segmental tunnel lining at elastic stage. However, the optimization of bolt position can enhance the overall rigidity and bearing capacity of the structure at plastic stage. Increase of stirrups at T blocks and optimization of bolt position can significantly improve the ultimate bearing capacity of a quasi-rectangular segmental tunnel lining. (4) Segmental reinforcement ratio has little effect on the structural robustness. An increase in the shear bearing reserve and optimization of the longitudinal joint bolt position can significantly improve the robustness of the structure, which is beneficial to the overall safety of a quasi-rectangular shield tunnel structure. (5) In the design of a quasi- rectangular segmental tunnel lining, segmental reinforcement and bolt position of longitudinal joints can be optimized to fully exert the structural bearing capacity. However, when optimizing segmental reinforcement, special attention should be paid to the control of the crack width based on its performance requirement.

longitudinal joint bolt position and shear bearing capacity of the third ring are optimized compared to the second ring. Several analyses of the experimental results are carried out to investigate the influence of the segmental reinforcement, shearing bearing capacity and longitudinal joint bolt position on the failure mechanism, ultimate bearing capacity and overall safety. The results show that: (1) The weak parts of a quasi-rectangular shield tunnel lining are the longitudinal joints and T blocks. According to the results, failure of the three test rings all begin with the failure of the longitudinal joint. In the first full-scale ring test, the failure of the structure is due to the fact that the haunch of T2 block near No.6 joint is broken by the bending moment and shear force. As for the second ring test, the bearing capacity of the longitudinal joints is not fully exerted when the structure is damaged. The failure of the structure is also due to the shear bearing failure of a T block. When it comes to the third full-scale ring test, optimization measures to the longitudinal joints are given a full play. At the end of the test, a plastic hinge appears when the rebar located at the critical cross-section of a T block is yielded. The structure finally loses its bearing capacity. (2) Based on the results of the first and second rings, the critical crosssection of the T block is broken by shear force. Therefore, the structural failure has the characteristic of brittle damage. As for the third ring, when the critical cross-section of the T block is broken by bending moment, the structural failure becomes ductile. It is therefore necessary to ensure that the bending bearing capacity of

Based on the three full-scale ring tests, the influence of segmental reinforcement, shear bearing capacity of T blocks, and longitudinal joint bolt position on the mechanical behavior of a quasi-rectangular 316

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Fig. 17. Comparison of load-bolt strain curve of positive moment joint.

Fig. 18. Comparison of load-bolt strain curve of negative moment joint.

segmental tunnel lining is fully investigated. However, corresponding parameter analysis has not been carried out to obtain an optimal decision. In future, numerical simulation and nonlinear analysis will be carried out to further investigate the bearing mechanism and optimization measures of a quasi-rectangular segmental tunnel lining.

j.tust.2005.11.003. Kashima, Y., Kondo, N., Inoue, M., 1996. Development and application of the DPLEX shield method: results of experiments using shield and segment models and application of the method in tunnel construction. Tunn. Undergr. Space Technol. 11 (1), 45–50. http://dx.doi.org/10.1016/0886-7798(96)00053-3. Li, Xiaojun, Yan, Zhiguo, Wang, Zhen, Zhu, Hehua, 2015. Experimental and analytical study on longitudinal joint opening of concrete segmental lining. Tunn. Undergr. Space Technol. Incorporating Trenchless Technol. Res. 46 (46), 52–63. http://dx.doi. org/10.1016/j.tust.2014.11.002. Lin, Ping, Weixi, Zhang, Chen, Zhang, Xian, Liu, 2016. Experimental study on bearing capacity of longitudinal joints in quasi-rectangular shield tunnels. Mod. Tunn. Technol. (S1), 98–107. http://dx.doi.org/10.13807/j.cnki.mtt.2016.S1.015. Liu, Xian, Bai, Yun, Yuan, Yong, Mang, Herbert A., 2016. Experimental investigation of the ultimate bearing capacity of continuously jointed segmental tunnel linings. Struct. Infrastruct. Eng. 12 (10), 1364–1379. http://dx.doi.org/10.1080/15732479. 2015.1117115. Liu, Xian, Ye, Yuhang, Liu, Zhen, Yang, Zhihao, Zhu, Yaohong, 2017. Full-scale test study on overall safety of quasi-rectangular shield tunnel lining. China J. Highway Transport 30 (08), 164–173. Liu, Xian, Ye, Yuhang, Liu, Zhen, Huang, Dezhong, 2018. Mechanical behavior of Quasirectangular segmental tunnel linings: First results from full-scale ring tests. Tunn. Undergr. Space Technol. 71, 440–454. http://dx.doi.org/10.1016/j.tust.2017.09. 019. Lu, Liang, Lu, Xilin, Fan, Peifang, 2011. Full-ring experimental study of the lining structure of Shanghai Changjiang tunnel. J. Civil Eng. Archit. 5 (8).

Acknowledgements Financial support by National Key Research and Development Program of China (Grant No. 2017YFC0805004), the National Natural Science Foundation of China (Grant No. 51578409), the National Basic Research Program of China (2015CB070563), Shanghai Engineering Research Center of Industrialized and Prefabricated Municipal Civil Engineering (17DZ2251900) are gratefully acknowledged. References Blom, C.B.M., 2002. Design philosophy of concrete linings for tunnels in soft soils. Chow, B., 2006. Double-O-tube shield tunneling technology in the Shanghai Rail Transit Project. Tunn. Undergr. Space Technol. 21 (6), 594–601. http://dx.doi.org/10.1016/

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X. Liu et al.

Ye, G., Hashimoto, T., Shen, S., et al., 2015. Lessons learnt from unusual ground settlement during Double-O-Tube tunnelling in soft ground. Tunn. Undergr. Space Technol. 49, 79–91. http://dx.doi.org/10.1016/j.tust.2015.04.008. Zhong, Xiaochun, Zhu, Wei, Huang, Zhengrong, Han, Yuewang, 2006. Effect of joint structure on joint stiffness for shield tunnel lining. Tunn. Undergr. Space Technol. 21 (3–4), 406–407.

Nakamura, H., Kubota, T., Furukawa, M., et al., 2003. Unified construction of running track tunnel and crossover tunnel for subway by rectangular shape double track cross-section shield machine. Tunn. Undergr. Space Technol. 18 (2), 253–262. http:// dx.doi.org/10.1016/S0886-7798(03)00034-8. Schreyer, J., Winselmann, D., 2000. Suitability tests for the lining for the 4th Elbe tunnel tube–Results of large-scale tests. Tunnel 1, 34–44.

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