Investigation of the mechanical properties of double lining structure of shield tunnel with different joint surface

Tunnelling and Underground Space Technology 90 (2019) 404–419

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Investigation of the mechanical properties of double lining structure of shield tunnel with different joint surface Shimin Wang, Lei Ruan, Xingzhu Shen, Weijie Dong

T

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Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu, Sichuan 610031, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Shield tunnel Double-shell structure Composite structure Similar model method Joint surface

For the shield tunnel with double-layer lining, the type the joint surface between the segment and secondary lining has significant influence. Depending on the smoothness of the border and the transmit patterns of the forces between the segment and the secondary lining, the lining structure is divided into double-shell and composite structures. For the double-shell structure, only the axial force is transmitted through the border, while the axial and shear forces are transmitted through the border for the composite structure. In this paper, based on the similarity model test and the engineering background of the Shiziyang Tunnel, the influence of the joint surface type on the mechanical behaviors and failure characteristics of the lining structure is studied under the condition that the segment and secondary lining of the shield tunnel double-lining structure share the overload together. The result shows that (1) the differences in the bending moment values between the double-shell and composite structures are small, but the axial force values and the changing trends are obviously different; the load bore by the secondary lining and its ratio to the external load increases with the external load; further, the segment is still the main bearing structure; (2) after the macroscopic failure of the segmental lining structure, the double-shell lining loses stability rapidly, the bearing capacity loss is abrupt, and the damage of lining structure is more serious; when the composite structure loses stability, the failure process of the composite structure is longer, and the structural failure is ductile; (3) with the same load, the ratio of maximum displacement to the tunnel radius of the double-shell structure is larger, and the load level of the lining structure when failure occurs is lower. Generally speaking, the composite structure improves the overall stiffness of the double-lining structure, which is in favor of the joint load carrying of the segment and secondary lining to control the structural deformation; additionally, the bearing capacity of the composite structure is obviously better than that of the double-shell structure; therefore, it is recommended in the double-lining design of the shield tunnel.

1. Introduction Shield tunneling has been widely used in transportation in recent years (Koyama, 2003; Maidl et al., 2013). For the single-layer segment lining structure in shield tunnels, especially in water-bearing conditions, deterioration and damage during the construction and operation have attracted increasing attention and concern (Blom et al., 1999; Lee et al., 2001; Chang et al., 2001; Luttikholt, 2007; Chen and Mo, 2008; Lee and Ishihara, 2010; Lei et al., 2014; Huang and Zhang, 2016). The performance and durability of the tunnel lining structure are facing a severe test. Take the Blue Metro Line in Lisbon, for example: the inner steel of the segment was seriously corroded under the marine environment; the bearing capacity and durability of the lining structure declined significantly, and the risk of a tunnel cracking state was high. At the same time, excessive thrust or uneven thrust during shield

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propulsion caused cracks in the segments, and the durability of the lining structure was affected. Some scholars began to explore new segment lining structures. The P&PCSL (Prestressed and Precast Concrete Segmental Lining) has been implemented in three construction projects after undergoing various performance tests and workability verification tests (Nishikawa et al., 1997; Nishikawa, 2003). Steel segment has economic and welding disadvantages. The adopted ductile cast iron segment has economic disadvantage as well as steel segment (JSCE, 2007). Composite segment has been developed for obtaining high capacity in lining of shield tunnel subject to high hydraulic pressure and earth pressure in deep underground (Zhang and Koizumi, 2010). Therefore, the secondary lining of the tunnel is used as a remedy to maintain the performance and to improve the overall bearing capacity of the lining structure (van Empel et al., 2006). The double lining has advantages in load-bearing capacity, anti-erosion, disaster

Corresponding author. E-mail address: [email protected] (W. Dong).

https://doi.org/10.1016/j.tust.2019.04.011 Received 18 December 2017; Received in revised form 22 January 2019; Accepted 14 April 2019 Available online 27 May 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Plan of Shiziyang Tunnel Project.

Yellow River in the South-to-North Water Diversion Project, Zhang et al. (2001) suggested three joint interaction models corresponding to different forms of joints between the primary and secondary linings. It was recommended that the coupling between primary and secondary linings must be reinforced, thus forming an integrated structure to bear the external pressure in the engineering design. However, there is still a big difference between the hydraulic and traffic tunnels. Considering the influence of steel bars on the mechanical properties of lining structures and the nonlinear characteristics of concrete with a plastic defect, Wang et al. (2016a,b,c) established calculation models of a three-dimensional solid double-shell structure and composite structure of shield tunnel double lining for both double-shell and composite joint surfaces. Moreover, compared with similar model test segmental lining and secondary lining internal force and displacement results, it has good consistency. Based on the beam-spring model, Fujimori et al. (1983) suggested simulating the shear and compression effects in the joint surface with spring elements. Yan et al. (2015) proposed a numerical model, in which the beam, the joint spring, and the compression spring joint surface are combined; also, the mechanical behavior of the double lining of Qiantang River shield tunnel was investigated. The existing results mainly focused on the shield tunnel doublelayer lining interaction calculation model and the mechanical properties of the double-layer lining structure. However, there are few studies on the influence of different joint surface types on the mechanical properties of the double-layer lining structure. In this paper, the mechanical behaviors of a shield tunnel double-layer lining with different joint surfaces are compared and analyzed by adopting the similar model test method and using the engineering background of the Shiziyang Tunnel. The effect law of the joint surface type on the mechanical properties of the double-layer lining structure is studied, which can provide guidance for the selection and design of the double-layer lining structure of the shield tunnel.

prevention, etc., for the tunnel structure compared with the single-layer segmental lining. Therefore, applications of a double-lining structure are increasing in engineering practice. Some scholars proposed that “The secondary lining or reserving space for the secondary lining should be considered as a reinforcement of the tunnel structure in the design stage of the tunnel” (He and Feng, 2011). Japan is one of the pioneer countries in the world that applies a double-lining structure in urban subways, water tunnels, and other shield tunnels. Take the Tokyo Bay submarine road tunnel, which has been opened to the public for 20 years, for example: a thickness of 35 cm of cast-in-place reinforced concrete was used as the secondary lining (JTA, 1995). In China, the double lining is often used in hydraulic tunnels, but it’s relatively rarely used in traffic shield tunnels. In order to prevent the differential settlement of the lining structure, the Shiziyang Tunnel has a double-layer lining structure, in which the first lining is segment and the secondary lining is casted by cast-in-place concrete. Some scholars carried out research on the mechanical properties of the double lining of a shield tunnel by means of model and field tests. Murakami and Koizumi (1987) tested the shield tunnel double lining to study the enhancement effect of the secondary lining on the bearing capacity of the segment. Takamatsu et al. (1992) studied the longitudinal mechanical effects of a shield tunnel double lining via experimental and theoretical analysis. A more reasonable design method of a double-lining structure was proposed by evaluating the longitudinal mechanical behavior of a lining structure. Feng et al. (2013) analyzed the differences of the mechanical property between a single-layer lining and double-lining structure of an underwater shield tunnel via model and field tests; further, the reliability and rationality of a shield tunnel double-lining structure was also proposed. However, the model tests in the above studies did not consider the effect of the joint pattern on the double-lining structure. The Working Group International Tunnel Association (2000) divides the double-layer linings into a double-shell structure and composite structure according to the smoothness of the joint surface between the segment and the secondary lining. The interaction and mechanical properties of the double-lining structure are closely related to the type of the interlamination joint surface. Some scholars have established calculation models for double-layer lining interaction based on theoretical analysis; in addition, the mechanical behaviors of shield tunnel double-layer lining structures with different joint surfaces were investigated. On the basis of the tunnel crossing the

2. Design of model experiment 2.1. Engineering background The Shiziyang Tunnel, part of the Guangzhou-Shenzhen-Hong Kong passenger transport line, is the first large-section underwater highspeed railway tunnel in China. The tunnel passes through the Xiaohuli, Shazaili, and Shizi Ocean; the total length is 10.8 km. The tunnel is 405

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Fig. 2. Geologic Section of Shiziyang Tunnel Project.

the same time. Therefore, in order to simulate the physical–mechanical state of the shield double-layer lining structure under different soil depths, we can maintain a corresponding mapping relationship with the prototype structure to reveal the mechanical and deformation characteristics of the prototype structure. This experiment is based on the geometric similarity. To achieve the principle of gravity similarity, the geometric similarity ratio C1 = 20 and the gravity similarity ratio Cγ = 1 are used as the basic similarity ratio, and the main physical and mechanical parameters are guaranteed to satisfy the similarity relationship. According to the similarity principle, the similarity ratio of each physical mechanical parameter is shown in Table 1. Take the geometric similarity ratio of C1 = 20 and the bulk density similarity ratio of Cγ = 1 as the basic similarity ratios of the physical quantities of the model test and of the engineering prototype. The specific dimensions of the model tunnel are as follows: the external diameter of the segment is 54 cm and the internal diameter is 49 cm. The thickness and the average width of the segments are 2.5 and 10 cm, respectively. The thickness of the secondary lining is 1.5 cm.

mainly surrounded by weakly weathered bedrock, and the design hydraulic pressure is 0.67 MPa. The tunnel plan and geological section view are shown in Figs. 1 and 2, respectively. The portal section of the tunnel was designed as a double-lining structure, considering the long-term operational safety; at the same time, the joint surface type adopts a composite structure. The segments are reinforced concrete segments in a common wedge ring shape with a concrete grade of C50. The external diameter of the segment is 10.8 m, and the internal diameter is 9.8 m. The thickness and the average width of the segment are 0.5 and 2.0 m, respectively. One segment lining ring consists of “7 + 1” blocks. The standard blocks and adjacent blocks correspond to the central angle of 49° 5′27.27″, and the capping block’s center angle is 16°21′49.09″. The segments are connected by M36 inclined bolts, and there are 22 vertical bolts and 24 round bolts. The secondary lining is a pure concrete structure with strength grade of C30 and thickness of 0.3 m, as shown in Fig. 3.

2.2. Similarity relation of model experiment 2.3. Design of similar material In theory, the similarity ratio between the segment structure and the physical quantity of the soil should be consistent in the similar model test. In fact, it is difficult to ensure that each physical quantity of the model structure and the prototype structure meets similar conditions at

(1) Soil body of stratum

Fig. 3. Double-layer Lining Diagram of Shiziyang Tunnel. 406

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Table 1 Similar relations between physical quantities.

Table 3 Mechanical parameters of the ground. Similarity ratio

Name

γ /(kN·m−3)

E /MPa

c/MPa

φ /(°)

(°)

Cφ = 1

Pa – Pa Pa Pa N·m

Cc = 20 Cν = 1 CE = 20 CR = 20 Cσ = 20

Actual stratum Model stratum Prototype value

18.7–20.3 20.0 20.0

15.0–25.0 1.0 20.0

0 0 0

20.0–32.0 28.0 28.0

N

CN = 203 Cc = 20

Physical quantity

Symbol

Unit

Internal friction angle

Axial force

φ c ν E R σ M N

Displacement

d

mm

Cohesion Poisson’s ratio Elastic modulus Strength Stress Bending moment

failure mode is also closer to the failure mode of the prototype segment lining structure, as shown in Fig. 5. The groove depth is calculated and determined according to the equivalent principle of the bending resistance of the prototype and model joint (Chen and Mo (2008)). Table 6 shows the bending rigidity and groove depth and width corresponding to the positive and negative bending parts of the segment. The longitudinal joints of the shield tunnel segment generate small displacement. In this experiment, the radial shear stiffness and tangential shear stiffness of the joint are assumed to be infinite, which means no displacement happens in the longitudinal joints of the segment lining ring (Railway Comprehensive Technology Research Institute, 1997). According to the configuration of the longitudinal bolts of the Shiziyang Tunnel, a steel bar (diameter of 4 mm, length of 40 mm) was used to simulate the joint between segment rings (Fig. 6).

CM = 20 4

In this experiment, soil density, internal friction angle, cohesion, and elastic modulus are the main control parameters, and the sandy strata of the Shiziyang Tunnel are the prototype of the model test. The corresponding physical parameters of the model soil are calculated according to the similarity relationship; further, the river sand, coal ash, quartz sand, barite powder, and colophony are mixed evenly with a certain proportion. The mix proportion of the model soil material is adjusted through soil test to meet the requirements for the physical and mechanical parameters. The composition ratio (mass ratio) of the model soil material is shown in Table 2, and the physical and mechanical parameters are shown in Table 3.

2.4. Simulation of joint surface between the segment and secondary lining Depending on the smoothness of border and the transmit patterns of the forces between the segment and the secondary lining, the lining structure is divided into the double-shell and composite structures. For the double-shell structure, only the axial force is transmitted through the border, while the axial and shear forces are transmitted through the border for the composite structure. In the double-shell lining structure, a waterproof plate is designed between the segment and the secondary lining. The joint surface delivers only the normal pressure with very small tangential shear force (compared with the composite structure), as shown in Fig. 7(a); whereas in the composite lining structure, the segment and the secondary lining are connected by a device such as a steel bar or a connector. The joint surface delivers the normal pressure and the tangential shear force, as shown in Fig. 7(b). The secondary lining is directly constructed on the segment when the segmental lining structure is loaded with a design load. The additional load would be applied after the secondary lining is dry enough to fulfill the design strength. For the double-shell lining structure, a plastic film is placed between the segment and the secondary lining to simulate the waterproof layer in the engineering practice. For the composite lining, shallow grooves (not affecting the structural rigidity) arranged at equal intervals on the inner surface of the segment are preliminarily provided to achieve roughening of the inner surface of the segment. The secondary lining and the segmental lining are engaged with each other at this position and overlap, as shown in Fig. 7(b).

(2) Material of lining structure Because its brittleness is close to concrete, and the adjustment range of the elastic modulus and compressive strength is relatively large, special gypsum is the main material of the segment and secondary lining in the model test. Through the trial production of specimens with different gypsum model mixing ratios, the uniaxial compressive strength test of the specimens is performed, and the mixing ratio is adjusted according to the test results until a similar relationship is satisfied. Fig. 4 shows the test curves of the elastic modulus and uniaxial compressive strength of gypsum specimens with different mix ratios. In order to ensure that the physical and mechanical properties of similar model materials are closer to concrete, a small amount of diatomaceous earth is added to the gypsum (Wang et al., 2016a,b,c). Based on large numbers of gypsum model mixing ratio tests and uniaxial compressive strength tests, the final segmental lining material is mixed with water, gypsum, and diatomite with a ratio of 1:1.38:0.1, and the secondary lining material is water: gypsum: diatomite = 1:1.26:0.1. The mechanical parameters of the segment material are shown in Table 4. According to the similarity of the equivalent bending rigidity of the prototype and of the model, steel wire (diameter 1.3 mm) is used to simulate the main reinforcement of segment ring, and there are 10 wires in both sides of the model segment, respectively. The mechanical parameters are based on the experimental data (E = 1.64 × 104 MPa), as shown in Table 5.

2.5. Loading device of the experiment and experimental procedure (3) Simulation of segment joint In order to simulate the stress state of the lining structure under the combined action of water pressure and earth pressure, earth pressure and hydraulic load are applied to the outside of the segment, respectively. The method of application is as follows:

To simulate the segment ring joint, the bending rigidity of the joint was weakened by slotting. The grooves are created through inner and outer dividing groove; further, they are located on the tension side of the segment lining to simulate the open effect of the joint, and the joint

(1) Loading of earth pressure Table 2 Proportion of similar material. River sand

Coal ash

Rubble quartz sand

Fine quartz sand

Motor oil

Barite powder

Colophony

1

1

0.02

0.03

0.05

0.01

0.004

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(a) Elastic modulus

(b) Uniaxial compressive strength

Fig. 4. Mechanical parameter curves of gypsum test pieces under different gypsum model mixing ratio.

In this experiment, a device, called the “simulation test system of shield tunnel and stratum complex,” is adopted as a loading device to load the earth pressure of the model. This device can manage the stress field inside the stratum and adjust the lateral pressure coefficient of the soil. As shown in Fig. 8, four jacks are symmetrically arranged in directions I and II, respectively, where the vertical earth pressure in the Direction I simulated tunnel is determined according to theoretical calculations based on the conditions of the stratum and the depth of burial. The lateral earth pressure under the simulated tunnel in Direction II is the value of the vertical earth pressure multiplied by the lateral pressure coefficient of the stratum. In Direction III (vertical segment cross-section direction), the load applied by the vertical jacks acts on the lower soil through the cover plate to ensure that the segment structure maintains the plane strain state during the loading process.

force. With the combination of both nonuniform and uniform water pressure loading devices, the actual hydraulic pressure on the segment lining structure can be simulated accurately. The entire experiment is divided into the preparation and loading processes. In the experimental preparation process, the segmental lining with the hydraulic loading device installed is placed on the test bench at a predetermined position. Then, the layered soil around the segment is backfilled until the soil surface is slightly higher than the upper edge of the segment and the soil surface is flat, as shown in Fig. 10. Finally, the panel of the loading device is covered. During the loading process, the load in the third direction is first applied to ensure that the segment remains in the plane strain condition. After that, the water pressure (both uniform and nonuniform) is applied to simulate the hydraulic pressure of the segment in actual working condition. Soil pressure is added to directions I and II with a constant proportion (lateral pressure coefficient). When the design workload is reached and becomes stable, the secondary lining is built and maintained under the loading conditions. Considering the effect of structural behavior deterioration, the load increases continually according to the overloading equivalence method until the double-lining structure shows signs of damage and a cracking state.

(2) Loading of hydraulic pressure In the stratum with a large permeability coefficient, the external load of the segmental lining is usually calculated by estimating the water and earth pressures separately. In this experiment, considering the big hydraulic pressure difference between the tunnel vault and the bottom, the actual applied hydraulic pressure will be divided into uniform/nonuniform hydraulic pressure (Wang et al., 2016a,b,c), as shown in Fig. 9(a). And the uniform hydraulic pressure loading device and nonuniform hydraulic pressure loading device apply the two pressures separately, as shown in Fig. 9(b) and (c). As shown in Fig. 9(b), the uniform hydraulic pressure is generated by rotating the stressing beam. The steel stand hoop is pulled tight, and it increases the radial pressure on the segment’s outer surface at the same time. The uniform pressure load of different depths is simulated based on the conversion relationship between the tension from the steel strand and the uniform hydraulic pressure. Fig. 9(c) shows the generation of nonuniform hydraulic pressure. Multiple groups of semicircular arc-shaped steel strands are arranged on one side of the segment’s outer surface; further, the nonuniform water pressure applied to the segment is simulated by controlling the tension angle and tension

2.6. Experimental measuring system As shown in Fig. 7, the experimental segment model consists of one whole ring and two half rings. In order to discover the progressive failure pattern of the segment lining structure, the segment and second lining in the middle integral ring are taken as the main measuring objects with the following measurements: (1) The internal force of the segmental lining structure: A total number of 48 resistance strain gauges are installed every 15° inside and outside the segment ring, as shown in Fig. 11. The internal stress of the segmental lining structure can be calculated based upon the measured strain values of the segment. (2) The internal force of the secondary lining: As the secondary lining is

Table 4 Mechanical parameters of double-layer lining concrete. Lining type

Physical and mechanical parameters

Prototype value (MPa)

Model value (MPa)

Corresponding prototype value (MPa)

Segment

Standard values of uniaxial compressive strength Elastic modulus

32.4 34,500

1.6 1720

32.0 34,400

Secondary Lining

Standard values of uniaxial compressive strength Elastic modulus

16.7 28,000

0.84 1430

16.8 28,600

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Table 5 Mechanical parameters of the segment ring main reinforcement.

2

Reinforcement area (mm ) Reinforcement ratio

Prototype segment

Model segment

Corresponding prototype value

10,152 1.015%

26.6 1.064%

10,640 1.064%

Fig. 5. Joint of segment lining model.

Table 6 Bending rigidity and groove parameters of the segment joint. Bending rigidity (N·m/rad)

Groove depth of the model (mm)

Groove width of the model (mm)

Notes

Positive bending: 2.57 × 108 Negative bending: 1.60 × 108

14.0 15.5

6.0 6.0

Positive bending region A Negative bending region B

While for the secondary lining, the sensors are placed on the inner surface in the same layout of the sensors on the segmental lining. The displacements are measured by re-balancing the displacement meters. Thereafter, the displacement of the double lining structure is calculated according to the sum of the final displacement and the displacement reading of the sensor when the segment is individually loaded.

a cast-in-place structure, it is difficult to paste the stain gauges after its construction. Hence, gypsum blocks with the same thickness are prepared in advance and total 12 measuring points are evenly marked every 30° around the ring. The gypsum blocks are integrated with the secondary lining at these measuring points while pouring the secondary lining. (3) Radial displacements of the segment and secondary lining: There are six measuring points on one segment ring, as shown in Fig. 12. Five differential transformer displacement transducers with a precision of 0.001 mm are placed counterclockwise along the inner surface of the segmental lining ring from the vault to the arch bottom every 45°. Considering the symmetry of the structure, a measuring point is set up alone at the haunch of the other side.

(4) Acoustic emission measurement: The acoustic emission monitor is 16-channel full digital and is manufactured by American Physical Acoustics Corporation (PAC). The acoustic emission threshold is set to 35 dB. First, the probes of acoustic emission sensors are placed on the inner side the segment lining when the segment bears all the load alone; later, they are moved to the inner side of the secondary lining. In order to

Before application of the secondary lining, the sensor is removed.

Fig. 6. Assembly of longitudinal joint. 409

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(a) Double-shell structure

(b) Composite structure Fig. 7. Double-layer lining with different joint surface types.

data, and displacement value are determined by a computer-controlled data acquisition instrument. After collecting the data of the fifth loading step, the displacement meter and the acoustic emission probe of the inner wall of the segment structure are removed under the steady state, and the secondary lining model is applied; in addition, the test and measurement equipment is rearranged, and the loading is continued until the failure of the lining structure. The specific loading process adopts a multistage loading method, as shown in Table 8. The theoretical value of the overlying soil load is calculated according to the distribution of soil layer. Based on the theoretical value of the overlying soil load and the soil pressure from the earth pressure cells buried in the vault, the height of the vertical equivalent soil column can be obtained. In this experiment, soil pressures are calculated under different burial depths and imposed after they have been transformed into the equivalent jack pressures.

obtain more information and eliminate the interference between the sensor probes, four acoustic emission probes are arranged at a certain interval (90°) in the circumferential direction of the lining structure. (5) Soil pressure: The earth pressure cells are placed at the key measuring points in the vault, spandrels, haunch, and arch bottom; the location of these points is the same as that of the radial displacements. They were placed not only between the segment and soil but also between the segment and the secondary lining; therefore, the total number of earth pressure cells is 16. Fig. 13 shows a schematic diagram of the pressure cell arrangement between the segments and the secondary lining.

2.7. Grouping and loading pattern This experiment studies the mechanical behaviors of the doubleshell structure and composite structures, under the condition that the secondary lining is applied after the segments have carried all external loads. The secondary lining is constructed to the segment after the fifth loading stage, with a preset tunnel burial depth of 30 m and a water head of 50 m. The lateral pressure coefficient is always 0.4 in this experiment. The adjacent rings before or after the segment lining ring rotated 49.08° relative to the middle target ring segment and assembled staggered. Table 7 shows the grouping of the experiment. In order to find the difference of the bearing capabilities between different structural types, two different shield double-layer lining structures are loaded step by step using the same loading scheme. After the preparation work is completed before loading, the loading is performed step by step according to Table 8 in the article. After each loading, the corresponding strain, earth pressure, acoustic emission

3. Analysis of experiment result In this section, the results are processed and analyzed based on the obtained value of soil pressure, strain, displacement, acoustic emission information, and the failure course of the lining structure during the experiment. The stress state, failure characteristics, and failure process of the double-lining structure with different joint surface types are investigated. 3.1. Analysis of internal stress of segment structure The measured strains are processed to obtain the axial force and bending moment of the key points. The corresponding values of the prototype segment of the double-lining structure are obtained 410

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(a) Plane layout

(b) Side layout Fig. 8. Loading equipment of model test.

haunch, whereas the maximum axial force is 8484.72 kN at the vault for the composite structure. For the composite structure after the secondary lining, the axial force between the segment and secondary lining is transferred to each other under the action of the tangential force, causing the abrupt change of axial force in this step. According to the bending moment diagram, the increase of the bending moment for the composite structure is significantly larger than that of the double-shell structure. It is mainly due to the large overall stiffness of the composite structure, as the segment and secondary lining are connected tightly and have a significant effect on each other. This verifies that the joint surface type remarkably affects the stresses of the double lining. Table 9 shows the internal force between the segment and the secondary lining under the eighth loading step. The maximum positive bending moment for the double-shell lining structure is 1961.74 kN·m., and the maximum negative value is −2148.41 kN·m. Both values are smaller than those of the composite structure. The maximum eccentric distance calculated from the double-shell structure is 545.16 mm, which is twice the value of the composite structure. For the composite structure, it is observed that the interaction between the segment and the secondary lining is significant, and the overall stiffness is greater than that of the double-shell structure; therefore, the maximum positive and negative bending moments of the segment are generally larger than

according to the formula of material mechanics and the similarity relation. The relation between internal force change and the loading steps is shown in Figs. 14 and 15 for the double-shell structure and the composite structure, respectively. After the fifth loading stage, the load on the segment structure has reached the design load, and the secondary lining is constructed on the inner side of the segment. The segment and secondary lining bear the load together from then on. The vertical dashed lines in the figures mark the construction moment of the secondary lining. According to the internal force distribution, the values and trends of the double-shell structure and the composite structure are basically the same during the loading process before application of the secondary lining. After that, the bending moment on the haunch of the doubleshell structure increases rapidly while the bending moment and axial force increase relatively gradually to the rest positions. For the composite structure, the internal force of the segmental lining increases with acceleration and the value at the left haunch jumped and changed suddenly from the sixth to eighth loading step. Due to the different treatment methods of the joint surface, the values and distribution of the bending moment and the axial force for the two lining structures are obviously different. For example, in the sixth loading step, the maximum axial force of the double-shell structure is 6253.08 kN and in the 411

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(a) Hydraulic pressure simulation diagram

(b) Uniform hydraulic pressure loading device

(c) Nonuniform hydraulic pressure loading device Fig. 9. Loading of water pressure.

Fig. 16 shows the internal force distribution of the double-shell lining structure and the composite lining structure under the eighth loading step. According to this figure, the distribution patterns for the bending moment of the segment and second lining are basically the same. It presents tension at the inner side of the vault and arch bottom and compression on the inner side of the left and right haunches. For both types of lining, the axial force on the vault and bottom of the secondary lining is larger than that of other parts. The distribution of the axial force is fluctuating, which shows that the contact pressure between the joint surfaces is unevenly distributed due to the impact of the lining blocking form. The average axial forces for the double-shell structure segment and composite structure segment are 3836.23 and 8713.70 kN, respectively. The average axial forces of the secondary linings are 895.53 and 530.57 kN, respectively. The difference of the bending moment between the two lining types is small.

Fig. 10. Photo of the experimental preparation process.

3.2. Distribution of load

those of the double-shell structure segment. In this loading step, the maximum eccentric distance calculated of the composite lining is relatively smaller. Considering the joint action of the bending moment and the axial force on the structure, the composite lining structure is more favorable in terms of the stress state (see Table 10).

Shield tunnel double lining is a support system formed by the segment structure and the secondary lining. In order to study the mechanical characteristics of the double-lining structure, it is of great importance to determine the load transfer mechanism and the 412

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Fig. 11. Layout diagram of resistance strain gauges.

surrounding rock and the segment for the two types of lining structure. Fig. 18 shows the contact pressure distribution between the segment and the secondary lining. For the double-shell structure, the soil pressure gradually exerts on the segment after the second loading step (Fig. 17). The pressures on the vault, bottom, and right haunches of the segment increase and distribute in a diamond shape. The left haunch, where the key segment locates and the stiffness is quite low, shows smaller pressure growth. The maximum pressure at the vault is 860.91 kPa, which indicates that the vault is in an unfavorable position. After construction of the second lining at the sixth step, the pressure on the segment structure tends to be steady, and the growth rate is reduced obviously compared with the previous steps when the segment bears the load alone. During the whole loading process, the pressure on the arch bottom is larger than that of all the other parts. The pressure distribution around the segment ring of the composite structure is more uniform than that of the doubleshell structure. The vault is subjected to most of the vertical pressure, the maximum pressure at the vault reaches 910.03 kPa, which should be given enough attention at the design stage. Fig. 18 shows the development of contact pressure between the segments and the secondary lining. The load transfer mechanism and allocation proportion of the double-lining structure depend on the types of joint surfaces. For the double-shell structure, the deformation of the segment and secondary lining are not coordinated along the ring during the loading. This is due to the waterproof plate between the segment and the secondary lining of the double-shell structure. The growth of the contact pressure between the segment and the secondary lining on the haunch is not obvious. There are sudden changes of the load in the vault and bottom of the secondary lining. For the composite structure, segments are in close contact with the secondary lining, the shear force can be transferred between them. The entire lining system is kept coordinated and can be treated as a whole structure due to existence of the tangential force. The load of the secondary lining is more evenly distributed along the ring. With the increase of the external load, the load of the composite structure secondary lining grows more evenly compared with that of the doubleshell structure. After the secondary lining, as the external load increases, the load on the secondary lining generally tends to be growing, too. For the double-shell structure, the maximum percentage of the load on the secondary lining is 36.44% of the external load, while for the composite lining the value is 20.77%. The double-shell structure is in an unfavorable condition in terms of loading status. Under the same loading step, the external load ratio of the double-shell structure is obviously higher than that of the composite structure. However, the double-shell

Fig. 12. Layout diagram of displacement transducers.

Fig. 13. Layout of earth pressure cells.

allocation proportion between the segment and the secondary lining. Fig. 17 shows the contact pressure distribution between the 413

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Table 7 Grouping of the experimental scheme. Experimental group no.

Joint surface structure type

Assembling method

Lateral pressure coefficient

Position of middle target ring K block

1 2

Double-shell Composite

Staggered assembling

0.4

Vault, 90° to the left

structure, the maximum displacement is 25.28 cm at eleventh loading step and at the left haunch. In the ninth loading step, the double-shell structure starts to be unstable, while the composite structure is still stable, and the maximum displacement of the key points is 17.24 cm. This value is smaller than the corresponding value of the double-shell structure in this loading step. In the composite structure, the shear force can be transferred between the segment and the secondary lining; therefore, the overall mechanical property is better, and the bearing capacity is advantageous over that of the double-shell structure. Due to application of the secondary lining, the flexural rigidity of the structure improves compared with that of the single-layer lining. The displacement changes smoothly with the load without big fluctuation as the single-layer lining. Wang et al. (2016a,b,c) showed that the system loses stability and is damaged when the model displacement reaches 12.88 cm for the single-layer segmental lining under the same conditions. The critical cracking state displacement values of doublelayer linings are larger than that of single-layer segment lining, which rises by 40.53%. The load bearing capacity increases significantly.

lining structure is a better option if the secondary lining is expected to share more external load. For both structures, these values indicate that the main bearing structure is the segment, and the secondary lining shares less load in the double-lining shield tunnel.

3.3. Displacement of double-layer lining According to the similarity relationship, the data collected from the displacement transducers at the key points of the double-layer lining are converted to the corresponding displacements of the prototype structure. The displacement toward the inside of the tunnel is positive, otherwise negative. The key point displacements of the corresponding prototype double-lining structure are shown in Fig. 19. Fig. 19 shows that the displacements are changing linearly with the load when the segmental lining bears the load alone. During the initial loading stage, the lining structure is in the elastic range, and the deformation of the key points are small and changing consistently with the internal force. As the load rises, the displacements of the points increase linearly with a trend of slight acceleration. The deformation at the left and right haunch toward the outside of the tunnel is most obvious. When the segment and the secondary lining bear the load together, they are not fully fit in the initial construction stage of the secondary lining. The displacement fluctuates slightly. At the ninth loading step, the displacement of the arch bottom and left springing of the double-shell structure changes suddenly; further, the maximum displacement occurs at the vault when it reaches the critical cracking state. The composite structure loses stability at eleventh loading step; in addition, the displacement at left haunch is obviously more serious than the other key points. The corresponding displacement value when the double-layer lining structure reaches the critical cracking state is shown in Table 11. Concerning the structure of the double lining, there are slight differences between different joint surface types, and the carrying capacities are not the same. Table 11 shows the loading step when the cracking state happened and the corresponding maximum displacements are different for the two sets of experiments under different joint surface types. For the double-shell structure, it reaches the cracking state critical point at the ninth loading step, and the maximum displacement occurs at the vault, which is 18.10 cm. For the composite

3.4. Acoustic emission information The change of acoustic emission events and amplitude reflects the variation of energy in the structure during the loading process; further, it can reflect the mechanical properties and failure process of the structure. Two groups of experiments of acoustic emission events and the AE counts load curves are compared in this section. For the double-shell structure, as shown in Fig. 20(a), the AE activity was stable from the sixth to eighth loading steps after the secondary lining. The number of AE events increases by little, which is a quiet period. AE activity suddenly starts to be more frequent at the ninth loading step, and the AE event rate increased to 450 times/s. The secondary lining cracks and the lining structure lose stability, indicating that the failure of the double-shell structure after the secondary lining presents obvious brittle damage. In the loading process of the composite structure after the secondary lining, due to the great integrity of the interlayer structure, the number of AE events changes more evenly with the increase of the load. At the ninth loading step, the secondary lining is cracked on the surface, and the AE event rate raises to the peak at this point. The structure reaches the critical state of cracking state after two

Table 8 Loading conditions of experiments. Loading step

0 1 2 3 4 5 6 7 8 9 10 11 12

Direction III Jack Pressure/MPa

0 18 18 18 18 18 18 18 18 18 18 18 18

Load in Direction I

Water head (m)

Jack hydraulic pressure/MPa

Formation pressure of model vault/kPa

Formation pressure of prototype vault/kPa

Tunnel’s equivalent overlaying soil/m

0.0 0.6 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 4.2 4.6 5.0

0.00 1.44 5.52 8.67 11.86 14.46 18.70 21.79 24.95 29.29 33.96 41.88 47.31

0.00 28.80 110.40 173.40 237.20 289.20 374.00 435.80 499.00 585.80 679.20 837.60 946.20

0 3 11 17 25 30 37 43 50 60 70 85 95

414

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Fig. 14. Segment internal force–load curve of double-shell structure.

(a) Bending moment: loading step curve

(b) Axial force: loading step curve

Fig. 15. Segment internal force–load curve of the composite structure.

begun. During the loading process of the double-shell structure, macroscopic cracks first appeared at the vault; further, it developed vertically and passed throughout the structure. The main fractures happen in the vault and arch bottom in the end. For the secondary lining of the composite structure, the macroscopic cracks start in the arch bottom, and, as the load increases, the cracks expanded vertically and eventually throughout. It can be seen from Table 12 that the two structures are under the same loading step when they had macro damages. The double-shell structure became unstable and damaged after the macroscopic cracks of the secondary lining, while the composite structure can continue to bear a certain load even after the secondary lining macroscopic cracking. The composite structure has better carrying capacity than the double-shell structure and can avoid premature failure of the structure. This can be a reference for future maintenance and reinforcement of a tunnel shield.

more loading steps. The double-shell structure loses stability faster after macroscopic damage, and the AE energy increases less if continually loading on the composite structure. The load-carrying property of the composite structure is obviously better than that of the double-shell structure. Its failure process takes a longer time, which is beneficial for the system loading and the prevention and treatment of tunnel defects. 3.5. Structural failure pattern The occurrence and expansion of secondary lining cracks were recorded during the experiment. The fracture characteristics of the two group experiments are shown in Table 12. The main fracture of the double-lining structure locates on the position where penetrating cracks happen when continually loading after the macroscopic failure has Table 9 Characteristic statistics of lining structure in the eighth loading step. Type of lining

Lining type

Maximum positive bending moment (kN·m)

Axial force corresponding to the maximum positive bending moment

Maximum negative bending moment (kN·m)

Axial force corresponding to the maximum negative bending moment

Maximum eccentric distance (mm)

Average axial force (kN)

Double shell structure Composite structure

Segment Lining Segment Lining

1961.74 53.78 1998.96 132.21

3598.49 163.30 15690.19 640.31

−2148.41 −221.57 −2648.20 −108.66

8551.74 2494.26 12432.91 315.21

545.16 329.33 212.99 344.72

3836.23 895.53 8713.70 530.57

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in the segmental lining of the target ring. Besides, the double-shell structure has cracks at the segment joints. The distribution patterns and values of the internal force, displacement, acoustic emission information, and ultimate failure mode of the segment lining structure were analyzed synthetically in the experiments. In the condition that the secondary lining is applied after the segments have carried the design load (i.e., both the segments and the secondary lining share the overload), the stress state of the composite structure is better, and its deformation is smaller, which is conducive to the load bearing of the double-lining structure.

Table 10 Load and share ratio of secondary lining. Loading step

6 7 8 9 10 11 12

Percentage of the secondary lining’s load in the segment external load Double-shell structure

Composite structure

23.24 17.27 27.51 27.48 36.44 33.19 34.73

12.28 11.79 14.89 15.28 20.03 18.31 20.77

4. Conclusions In this paper, based on the similarity model test, the influence of the joint surface type on the mechanical behaviors and failure characteristics of the lining structure is studied in the condition that the segment and secondary lining of shield tunnel double-lining structure share the overload together. The main conclusions are as follows:

After the loading, the secondary linings were cleaned up to observe and record the main fractures and crushing areas of the segment structure. Fig. 21 shows the final damage sketches of the segments of double-shell and composite structures. Concerning the angles in the figures, it’s assumed to be 0° at the vault along with the clockwise direction. The ovals stand for collapsing areas. According to the distribution pattern of cracks and crushing zones shown in Fig. 21, the damages of the segment structure mainly centered upon the vault, arch bottom, and haunches, while, for the secondary lining, the macroscopic cracks mainly occurred near the vault and arch bottom. Both the segment and secondary lining have penetrating cracks in the longitudinal direction. The type of joint surface between the segment and secondary lining affects the failure mode and damage degree of the segmental lining structure. Compared with the composite structure, the double-shell structure has more cracks and crushing zones

(1) The differences in the bending moment values between the doubleshell structure and the composite structure are small, but the axial force values and the changing trends are obviously different. The axial force of composite structure is larger than that of the doubleshell structure. With the same load condition, considering the joint action of bending moment and axial force on the lining structure, the eccentric distance of the composite structure is relatively smaller, and its structural stress state is more favorable. (2) When the segments and secondary lining bear the load together, the maximum percentage of the load of the secondary lining is 36.44%

(a) Bending moment of segment

(b) Axial force of segment

(c) Bending moment of secondary lining

(d) Axial force of secondary lining

Fig. 16. Internal force of double-shell structure and composite structure in the eighth loading step. 416

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(a) Double-shell structure

(b) Composite structure

Fig. 17. Distribution of contacting pressure between surrounding rock and segment.

(a) Double shell structure

(b) Composite structure

Fig. 18. Distribution of contacting pressure between the segment and secondary lining.

(a) Displacement–load curve of double shell structure

(b) Displacement–load curve of the composite structure

Fig. 19. Displacement–load curve of the key points on the double-layer lining.

larger than that of the composite structure. (3) The displacement of the double-layer lining structure tends to change slowly with the load during the loading process. Compared with the single-layer segment lining in the same condition, the critical cracking state displacement values of double-layer linings

of the segment external load, which indicates that the segment is still the main bearing structure under this condition. As the external load increases, the ratio of the load on the secondary lining also increases. Under the same loading step, the ratio of the load on the secondary lining to the external load of the double-shell structure is 417

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Table 11 Statistics of the failure features of segment lining. Experiment group no.

1 2

Failure features Maximum displacement of the model /mm

Maximum displacement of the prototype/cm

Ratio of the maximum displacement to the external radius of the tunnel/%

Loading step at cracking state

Position of maximum displacement

9.05 12.64

18.10 25.28

3.93 5.49

9 11

Vault Left haunch

(a) AE counts–load curve of double shell structure

(b) AE counts–load curve of the composite structure

Fig. 20. Figure of AE counts–load curve.

Table 12 Statistics of the damage characteristic of secondary lining. Lining type

Loading step when macro-crack happens

Macroscopic crack position

Position of main fracture

Direction of main fracture

Double shell structure Composite structure

9th loading step 9th loading step

Vault Arch bottom

Vault, bottom Arch bottom

Longitudinal Longitudinal

(a) Double-shell structure

(b) Composite structure Fig. 21. Sketch of failure process of segment lining.

is abrupt. The failure process of the composite structure is longer and the structural failure is ductile. The bearing capacity of the composite structure is obviously better than that of the double-shell structure. (5) After failure of the double lining, damage of the segment is more serious than damage of the secondary lining. Damage of the segment is mainly concentrated in the vault, the arch bottom, and the haunch. However, the secondary lining cracks vertically on the vault and the bottom. The joint surface can change the failure mode of the segmental lining. Compared with composite structure, there

are raised by about 40%. With the same load, the ratio of maximum displacement to the tunnel radius of the double-shell structure is larger, and the load level of the lining structure when failure occurs is lower. The composite structure improves the overall stiffness of the double-lining structure, which is in favor of the joint load carrying of the segment and secondary lining to control the structural deformation and improves the ultimate bearing capacity of lining structure. (4) When macroscopic cracks occur in the double-shell lining structure, the structure will collapse rapidly, and the loss of bearing capacity

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are more cracks and crush zones on the target ring segment of the double-shell structure. Meanwhile, there are crevices at the segment joint position. Damage of the double-shell structure is more serious.

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