Experimental investigation of mechanical behavior of horseshoe-shaped segmental tunnel linings

Abstract

The fully mechanized tunnelling method using an earth pressure balance tunnel boring machine (EPB-TBM) with a horseshoe-shaped cross section was first developed and applied to a loess mountain tunnel, along with the application of a horseshoe-shaped segmental tunnel lining. The mechanical behavior of this novel type of segmental tunnel lining still contained uncertainties, and full-scale ring tests were conducted for further investigation. During the loading process, the ring deformation, joint opening, and concrete strain were measured, and the occurrence and progression of structural damage were observed and documented. The experimental results demonstrate that the structural failure of the horseshoe-shaped segmental ring mainly occurred in the arch area, while the invert did not prove to be a weak area. The deformation and failure mechanisms of the horseshoe-shaped segmental ring were found to be similar to those of circular ones. Significantly, the specific characteristics of the ring convergence deformation and bending moment distribution were significantly affected by the distribution positions of segment joints. In addition, during the initial stages of TBM advancement, frequent segment damage was observed at inferior joints, and the elaboration on the causes and corresponding measures was provided. This study provides significant evidence for the design and optimization of horseshoe-shaped segmental tunnel linings.

Introduction

As a mechanized and automated tunnelling technology, the TBM method has been widely used in various kinds of tunnelling projects owing to its inherent advantages of safety, speed, high efficiency, stable quality, and little impact on the environment^1,2. The development and application of the tunnelling technology using circular TBMs has reached a considerable level of maturity. And it is important to note that the circular tunnel typically cannot achieve a high utilization of its space and a good match with its service function, especially for traffic tunnels^3,4. Consequently, in cases where the tunnelling method does not impose restrictions on the design of the tunnel cross section, the optimal design usually adopts a noncircular cross section for a better balance of safety, efficiency, cost, etc. The relatively irregular shapes of noncircular cross sections, however, pose much greater difficulties in the design and manufacture of the TBMs, the design and assembly of the segmental tunnel linings, and the control of the construction accuracy. The tunnelling technology using noncircular TBMs is far from being fully developed and is still in its preliminary stage^3,5. By contrast, the use of the noncircular TBM method allows a smaller excavation volume, less consumption of construction materials and energy, and a higher cost efficiency, especially for large section tunnels³. Besides, noncircular TBMs obviously have greater advantages when tunneling through narrow underground space or shallow overburden conditions. These benefits have been driving the development and application of the noncircular TBM method.

The noncircular TBMs that have been applied in practice mainly include rectangular, quasi-rectangular, elliptic, multi-circular, and horseshoe-shaped ones. Among them, there are few application cases of the horseshoe-shaped TBM. In the construction of Japan’s Hokriku Shinkansen, an open face TBM with a horseshoe-shaped cross section was employed to construct a 3580 m long tunnel, and an extruded concrete lining was applied (1982)². In China, the mechanized method using a horseshoe-shaped EPB-TBM was developed and applied to a 3345 m long mountain railway tunnel (Baicheng Tunnel) located in a loess area, and a horseshoe-shaped segmental tunnel lining was used accordingly (2018)⁵. The application of the horseshoe-shaped tunnel in tunnelling projects is widespread; however, its more irregular cross section compared to other noncircular cross sections poses greater technical challenges for developing the horseshoe-shaped TBM method. For civil engineers and researchers, the structural design of horseshoe-shaped segmental tunnel linings is one of the key technical problems to be solved, as it directly affects the safety, quality, and cost of the tunnel, and even the application and promotion of this method. Therefore, it is essential to investigate the mechanical behavior of horseshoe-shaped segmental tunnel linings for the structural design and optimization.

The mechanical behaviors of segmental tunnel linings are characterized by their complexity due to the presence of joints. A direct way to investigate the mechanical behaviors is to perform full-scale experiments, which allows for real structural responses. The existing research mostly focuses on circular segmental tunnel linings, mainly based on metro, underwater, and municipal tunnels. Different kinds of tunnels need to cope with different working conditions. The urban metro tunnel typically has a shallow burial depth, making it susceptible to surrounding disturbances. The underwater tunnel is usually subjected to significant external water pressure, and the fluctuation of internal water pressure must be taken into account in the drainage tunnel. The researchers conducted investigations into the mechanical behaviors of circular segmental tunnel linings under typical load conditions, revealing the deformation and failure processes, ultimate bearing capacity, failure mechanism, etc., as well as the difference in structural behavior between the straight-jointed and staggered-jointed assembly structures^6–25. However, the research on noncircular segmental tunnel linings remains relatively limited and mainly involves rectangle and quasi-rectangular ones. The aim is to verify the rationality and safety of the design and reveal the strained condition, bearing mechanism, and weakness of the linings^25–31. These research findings are highly significant in clarifying the mechanical behaviors of segmental tunnel linings. It is noteworthy that while segmental tunnel linings share some commonalities in mechanical behavior, they can also show significant differences due to the differences in the cross-sectional shape, joint configuration, reinforcement design, load condition, etc. The existing results are insufficient to provide comprehensive insights into the mechanical behavior of the horseshoe-shaped segmental tunnel lining and cannot reveal the potential problems arising from its unique cross-sectional design. Therefore, a direct investigation of the horseshoe-shaped segmental tunnel lining is indispensable.

This paper presents the experimental investigations of horseshoe-shaped segmental tunnel linings and the occurrence of segment damage during the advancement of the Baicheng Tunnel. The full-scale loading tests reveal the failure processes, deformation characteristics, and redistribution processes of internal forces in single horseshoe-shaped segmental rings under different loading conditions. Furthermore, the results and the key issues in structural design are analyzed and discussed, providing significant evidence for the design and optimization of horseshoe-shaped segmental tunnel linings.

Experimental program

Experimental specimen

The Baicheng Tunnel is a mountain railway tunnel with a length of 3345 m and maximum overburden of 81 m, and the strata that the tunnel passes through are mainly fine sand (Q₄^eol), sandy loess (Q₃^eol), and silty sand (Q₄^eol). In view of the limitations of the available construction technology, a mechanized method using a horseshoe-shaped EPB-TBM was developed and applied. Accordingly, the horseshoe-shaped segmental tunnel lining was adopted with a stagger-jointed assembly, and two types of segmental rings were designed, called odd and even rings. As illustrated in Fig. 1, the horseshoe-shaped segmental ring had an outer height of 10.589 m and an outer width of 11.540 m. The segment thickness was 0.5 m, and the ring width was 1.6 m. The ring was composed of eight segments, including one key block (OK/EK), two adjacent blocks (OB1/EB2 and OB2/EB1) and five “standard” blocks (OA1/EA5, OA2/EA4, OA3/EA3, OA4/EA2 and OA5/EA1). The segments in the same ring were connected using 16 grade-8.8 RD36 bolts, and a tongue-and-groove structure was used for the segment joints. Adjacent segmental rings were connected using 44 grade-8.8 RD30 bolts, and a plain joint was adopted for the ring joints⁵. All the bolts were straight bolts with an oblique arrangement, as shown in Fig. 2.

Fig. 1.

Schematic diagram of the horseshoe-shaped segmental rings (unit: mm): (a) odd ring, (b) even ring.

Fig. 2.

Joint design of the horseshoe-shaped segmental tunnel lining: (a) segment joint (longitudinal joint), (b) ring joint (circumferential joint).

According to the three types of effective overburden depths (H ≤ 1.5B, 1.5B < H ≤ 2.5B, and 2.5B < H, where H is the effective overburden depth, and B is the span of the lining, i.e., 11.540 m), the tunnel was correspondingly classified as having a shallow-buried section, medium-buried section, and deep-buried section, respectively. Therefore, there were three types of reinforcement designs for the lining. In contrast to the circular segmental tunnel lining, each segment in the horseshoe-shaped segmental ring was unique and had a relatively fixed position, which allowed a nonuniform reinforcement design according to their respective stress states, as shown in Table 1. Take Block OA1 as an example, the segment reinforcement diagram is shown in Fig. 3. The segment materials were mainly C50 concrete and HRB400 steel bars. The compressive strength of the C50 concrete was 32.4 MPa, and the HRB400 hot-rolled ribbed steel bars had a yield strength of 400 MPa⁵.

Table 1.

Reinforcement design of the horseshoe-shaped segmental tunnel lining (area of main reinforcement, unit: mm²).

Blocks	Shallow-buried section		Medium-buried section		Deep-buried section
	Outside	Inside	Outside	Inside	Outside	Inside
OK/EK	3308.5	4084.6	3308.5	4084.6	3308.5	4084.6
OB1/EB2	3308.5	4941.3	3308.5	8005.4	3308.5	4941.3
OB2/EB1	6381.7	3308.5	8005.4	3308.5	6381.7	3308.5
OA1/EA5	5716.9	4084.6	7380.9	4084.6	4941.3	4084.6
OA2/EA4	6631.5	3308.5	7380.9	3308.5	4941.3	3308.5
OA3/EA3	3308.5	4084.6	3308.5	4480.0	3308.5	4084.6
OA4/EA2	3308.5	4941.3	4084.6	6381.7	3308.5	4941.3
OA5/EA1	3308.5	4084.6	3308.5	4084.6	3308.5	4084.6

Fig. 3.

Segment reinforcement diagram: (a) longitudinal cross-section, (b) circumferential cross-section.

Two even rings were employed as the experimental specimens. The two rings were taken from the shallow-buried and medium-buried sections, named Ring A and Ring B, respectively.

Loading system

The horizontal loading system with an inner reaction structure was adopted, as shown in Fig. 4, considering the flexibility, operability, and economical efficiency of the full-scale loading system. The loading system was mainly comprised of hydraulic jacks, loading beams, a reinforced concrete reaction structure, steel strands and supporting seats. Oil cylinders of hydraulic jacks were installed outside the beams to provide loading. Rubber bearings were set between the loading beams and tested ring to improve the contact status. The tested ring was assembled horizontally on the supporting seats, with two-layer galvanized iron sheets placed between the segments and seats. A sufficient amount of lubricating grease was applied between the two-layer sheets to ensure neglectable friction conditions. The reaction structure is designed to provide resistance for the hydraulic jacks by steel strands, while also being reinforced with additional steel strands to improve its stiffness and strength.

Fig. 4.

Layout of loading system: (a) top view, (b) profile.

Twenty-three loading points were deployed around the tested ring, as shown in Fig. 5, to simulate soil pressure exerting on the lining. Each loading point comprised one loading beam and two hydraulic jacks, providing a maximum load of 4000 kN. Notably, the test load was designed to be self-balancing.

Fig. 5.

Layout and serial number of loading points.

Loading scheme

Two loading conditions were designed to simulate the design loads (Fig. 6) of the linings under the shallow-buried and medium-buried conditions, respectively. The radial forces (Table 2), approximately equivalent to the design load, are applied synchronously to the tested ring through all the loading points. The principle of the loading scheme is based on the equivalence of both load distribution and the internal force of the lining between design and the experimental conditions. Due to the complexity of soil-structure interaction, it is difficult to exactly replicate actual load-bearing conditions using current laboratory loading techniques. During the test loading design, several numerical calculations of the tested ring were conducted to ensure that the deformation and internal forces of critical cross sections in the ring are approximately equivalent to those of an actual structure under operation¹⁰. In fact, the same principle was also used in previous structure-level tests for segmental tunnel linings^6,10,27,32. During the loading process, the test loads increased linearly until the structure entered the plastic phase, and then the loading was repeated after unloading.

Fig. 6.

Distribution diagram of design loads.

Table 2.

Radial forces equivalent to design loads (unit: kN).

Loading point	Shallow-buried section	Medium-buried section
No. 1	574	824
No. 3	582	831
No. 5	604	839
No. 7	559	763
No. 9	544	763
No. 11	582	914
No. 13	680	952
No. 15	536	982
No. 17	861	1133
No. 19	725	1005
No. 21	476	627
No. 23	332	529

Measurement plan

During the experiment, four items were measured: surface strains of segments, radial displacements of rings, openings of segment joints, and strains of bolts. Concrete cracks on the structure’s surface were observed and documented by crack observers after each loading and stabilization phase to monitor their occurrence and growth.

1. The internal forces of the tested ring were determined by selecting 23 typical sections along the ring’s circumferential direction for monitoring surface strains. Vibrating wire strain gauges, with a maximum measuring range of 20,000 µε and measurement accuracy of 0.01 µε, were used to measure the surface strains, enabling the subsequent calculation of the internal forces within these sections.

2. The radial displacement of the tested ring was measured using 16 radial monitoring points positioned at 22.5° intervals along the circumferential direction. Differential transformer displacement sensors (LVDTs) were employed to measure the radial deformation, with a maximum measuring range of 200 mm and measurement accuracy of 0.01 mm.

3. The openings of segment joints were measured using vernier calipers with a measurement accuracy of 0.01 mm, as concrete spalling was prone to occur at joints during the loading process. To minimize personal error, multiple measurers performed repeated measurements of the opening at each measuring point.

4. The strains of bolts were measured using electric resistance strain gauges arranged symmetrically on both sides of each bolt, with a maximum measuring range of 20,000 µε and measurement accuracy of 1 µε.

Experimental results

Loading test of Ring A

Failure process of Ring A

Figure 7 illustrates the load-displacement curve of Ring A in the first loading test. Here, P_A represents the radial force at loading point No. 1, indicating the applied load level. The vertical convergence deformation refers to the relative displacement between the vault and bottom along the vertical symmetry axis. The characteristic points (marked with①, ②, ③, etc.) indicate the progressive failure process.

Fig. 7.

Load-displacement curve of Ring A in the first test.

As P_A increased from 0 to 720 kN, Ring A went through an elastic phase. When P_A reached 720 kN, initial structural damage occurred at joint No. 3 (marked with ①). More specifically, block EB2 cracked at the outside of the joint under compressive stress, while block EA5 cracked inside the joint due to shearing force. The slight concrete cracking had little impact on the overall stiffness of Ring A. However, the structure was unable to completely recover after cracking. Therefore, Ring A entered the elastoplastic phase.

The first turning point of the load-displacement curve occurred when P_A reached 960 kN (②). After that, the overall stiffness gradually decreased with the progressive failure of joints. The following phenomena occurred in sequence. When P_A reached 960 kN (②), cracks at joint No. 3 developed, and block EA5 cracked at the inside of joint No. 4 under compressive stress. When P_A reached 1080 kN (③), concrete at the outside of joint No. 3 further cracked, and block EA3 cracked at the inside of joint No. 5 under compressive stress. When P_A reached 1200 kN (④), concrete spalling occurred at the outside of joint No. 3, cracks at joint No. 4 further developed, and concrete cracking occurred at the outside of joint No. 6 under compressive stress. When P_A reached 1560 kN (⑤), concrete at the inside of joint No. 1 spalled under compressive stress, concrete at the outside of joint No. 3 further spalled, cracks at joint No. 4 ran through the intrados of block EA5, and cracks at joint No. 6 further developed. When P_A reached 1680 kN (⑥), concrete at joint No. 1 further spalled. When P_A reached 1800 kN (⑦), concrete at joints No. 1 and No. 3 was crushed, block EA4 cracked at the inside of joint No. 4 under compressive stress, and cracks at joint No. 6 further developed. When P_A reached 1920 kN (⑧), block EA1 cracked at the inside of joint No. 8 under compression-shear stress, and cracks at joint No. 4 extended through the intrados of block EA4. Meanwhile, the oil pressures of the hydraulic jacks located in the vault area rapidly dropped, indicating a rapid increase in the vertical convergence deformation rate. As the pressures exerted by the jacks on the ring can be thought of as deformation pressure, there was no a sharp increase in the vertical convergence deformation. It became evident at this point that Ring A had entered the plastic phase.

After the first test, the loading test was repeated twice, and no further structural damage was observed. The final failure characteristics of Ring A are shown in Fig. 8 (here, J-1 refers to joint No. 1).

Fig. 8.

Failure characteristics of Ring A: (a) final state of Ring A, (b) outside of joint No. 3, (c) inside of joint No. 3.

Structural deformation of Ring A

The overall deformation of Ring A in the first test is illustrated in Fig. 9, and the rotation angles of the joints are listed in Table 3. It should be noted that when concrete cracking or spalling occurs at a joint, the measurement of the joint opening becomes impracticable, as in the case of joint No. 3. The maximum values of segment dislocation at each joint were listed in Table 4.

Fig. 9.

Deformation of Ring A in the first test.

Table 3.

Rotation angles of the joints of Ring A in the first test.

Joint number	Open side	Maximum rotation angle (rad)	PA (kN)
No. 1	Extrados	-6.87 × 10− 3	1320
No. 2	Intrados	1.23 × 10− 3	1080
No. 3	Intrados	6.29 × 10− 3	720
No. 4	Extrados	-11.85 × 10− 3	1320
No. 5	Extrados	-1.80 × 10− 3	600
No. 6	Intrados	5.01 × 10− 3	1320
No. 7	Intrados	1.91 × 10− 3	1200
No. 8	Extrados	-2.51 × 10− 3	960

Table 4.

Segment dislocation of Ring A (unit: mm).

Joint number	Dislocation
J-1	2.6
-2	0.0
J-3	10.5
J-4	3.3
J-5	0.0
-6	0.0
J-7	2.8
J-8	3.7

Ring A deformed inward in the vertical direction and outward in the horizontal direction under the loading, showing significant asymmetric deformation about the vertical symmetry axis. Based on the measured data, the largest convergence deformation occurred at the vault (D-1, denoting No. 1 displacement measuring point), with a maximum radial displacement of 105.16 mm, and the maximum vertical convergence deformation was 114.71 mm. The radial displacements of D-2 were 1.56–2.20 times those of D-16 during the entire loading process, and reached a maximum displacement of 102.03 mm compared to 46.44 mm for D-16. Additionally, D-3 deformed inward while D-15 deformed outward. The asymmetric deformations were mainly attributed to the significant rotations and asymmetrical arrangement of joints Nos. 1, 3, and 4. The deformations on both sides were at comparable levels, and the maximum displacements of D-5 and D-13 were − 35.61 mm and − 32.85 mm, respectively. As to the bottom, the displacements of D-9 were within 12.95 mm. The relatively small deformations in these areas were directly correlated with the relatively small rotations of joints Nos. 5–8.

In conclusion, the deformation of Ring A was mainly attributed to the relative rotations at segment joints, as no concrete cracking occurred in the segment bodies. Furthermore, the local characteristics of ring deformation were significantly influenced by joint position. The horseshoe-shaped segmental ring exhibits a similar deformation mechanism to circular ones.

Structural internal force of Ring A

The distributions of the bending moment and axial force over the cross section of Ring A in the first test are shown in Fig. 10. The values of bending moment or axial force for adjacent measuring sections were fitted using straight lines. Surface strain measurement would be aborted if there was any cracking or spalling of the concrete cover at the measuring sections, such as C-11, C-12, C-13, and C-20 (denoting the surface strain measuring sections).

Fig. 10.

Internal force distributions of Ring A: (a) bending moment, (b) axial force.

During the loading process, positive bending moments appeared in the crown and invert areas, while negative bending moments were present on both sides. As P_A increased from 0 to 1080 kN, the largest values of positive bending moments occurred at the vault (C-1). However, when P_A exceeded 1080 kN, they shifted to the bottom (C-13). The largest values of the negative bending moments on the left side appeared at C-19, while on the right side, they occurred at C-5. The bending moments on the lower right side were significantly greater than those on the lower left side. It is also evident that there was a certain degree of reduction in the bending moments near joints Nos. 3, 6, and 7. These findings indicate that segment joints have an impact on the distribution of bending moments; specifically, there is a decrease in the bending moments near segment joints due to their lower flexural stiffness compared to segment bodies, resulting in an asymmetric distribution. Therefore, joint position significantly affects the specific characteristics of bending moment distribution, along with the stress states within segment bodies.

The effect of the joint on the axial force was mainly observed near the key block, where the fluctuations of axial forces were obvious. Joints Nos. 1 and 2 were designed with insertion angles, resulting in extra tangential forces on the joint interfaces. Furthermore, the contact conditions of these joint interfaces became more complicated, especially after opening or damage happening to the joints. These factors affected the transfer and distribution of axial force. Overall, segment joint had limited effects on the axial force.

From another perspective, the redistribution of bending moments occurs continually with the progressive failure of joints, as shown in Fig. 11. The process of bending moment redistribution is complex, yet there are some regularities. By and large, as P_A increases from 0 to 1080 kN, the load-bending moment curves generally show monotonically increasing trends. When P_A exceeds 1080 kN, the positive bending moments (C-1, C-2, C-3, C-22, and C-23) in the crown area no longer increase significantly due to the reduction in the stiffness of this area, and the areas involving C-4, C-5, C-6, and C-21 share more bending moments. The bending moments at the bottom (C-13) increase obviously, and those near the maximum span (C-7, C-17, and C-18) decrease.

Fig. 11.

Bending moment redistributions of Ring A: (a) upper part, (b) lower part.

On the other hand, the process of axial force redistribution is also complicated during the progressive failure of joints and does not present clear regularities as observed in the bending moment redistribution, as shown in Fig. 12. As segment joints have comparable compressional stiffnesses to segment bodies, the contact conditions in joints affect the redistributions of axial forces within local areas. It can be seen that although some load-axial force curves show significant fluctuations (e.g., C-5, C-6, C-9, C-10, C-19), most curves present a monotonic increase in general. Therefore, the effect of the progressive failure of joints on the axial force is relatively limited.

Fig. 12.

Axial force redistributions of Ring A: (a) C-1 to C-8, (b) C-9 to C-16, (c) C-17 to C-23.

In brief, the progressive failure of joints mainly causes the redistribution of bending moments and has a limited impact on axial forces.

Repeated loading tests of Ring A

The load-displacement curves of three loading tests are plotted in Fig. 13. In the first test, Ring A went through both elastic and elastoplastic phases before entering the plastic phase, and the overall stiffness showed a decreasing trend. However, the overall stiffness was approximate to a constant in the subsequent two tests and even greater than that in the final phase of the first test. The reason might be that the rotational stiffness of the joint did not change significantly anymore in the last two tests or that the rotational stiffness hardly affected the overall stiffness anymore.

Fig. 13.

Load-displacement curves of Ring A in three loading tests.

Combined with the internal force for further analysis, take the internal forces under the same load level (P_A = 1200 kN) in three tests as an example (Fig. 14), it can be observed that the bending moments significantly decreased in the second test on the whole, and further decreased in the third test. While the axial forces were at nearly the same levels in the first two tests and had some decreases in the third test. It indicated that the rotational stiffnesses of joints did decrease after each loading test since the stiffnesses of the segments hardly changed. Therefore, it suggested that the effect of the rotational stiffnesses of joints on the overall stiffness of the ring became very little in the last two tests.

Fig. 14.

Comparison of internal force distributions of Ring A in three loading tests: (a) bending moment, (b) axial force.

Since the deformation of Ring A was mainly attributed to the concentrated rotations at joints, the overall stiffness of the ring was related to the factors affecting the joint rotations. Obviously, the rotational stiffness of the joint directly affected the joint rotation and thus the overall stiffness. However, when the rotational stiffness of several joints decreased to a certain level relative to the segment stiffness, the segmental ring could be thought of as developing into a hinged structure. Consequently, ring deformation or joint rotation was largely affected by external resistance. That is why the overall stiffness turned into almost a constant in the last two tests. Therefore, the overall stiffness of the segmental ring not only depended on the stiffnesses of its joints and segments, but also was affected by the external resistance to ring deformation.

Failure mechanisms of Ring A

Ring A first went through an elastic phase, in which the structural deformation and internal forces generally developed linearly. The relative rotation between adjacent segments occurred at the joint under bending moment, leading to a gradual decrease in the contact area between the joint interfaces and thereby causing concrete cracking at the joint due to stress concentration. Concrete cracking first occurred at joint No. 3, and the ring therefore entered the elastoplastic phase. As the load level increased, the joints bearing relatively large internal forces (especially bending moments) cracked one after another, such as joints Nos. 4, 5, and 6. The slight cracking of these joints, however, had little impact on the ring’s overall stiffness and internal force distribution. The further damage and rotation of joint No. 3 lowered its rotational stiffness, resulting in fewer bending moments shared by joint No. 3 and its adjacent areas and more bending moments shared by joints Nos. 1 and 4 and their adjacent areas. This consequently accelerated the damage of joints Nos. 1 and 4, leading to further redistributions of internal forces. The progressive failure of joints, mainly involving joints Nos. 3, 4, 1, and 6, was accompanied by the frequent redistributions of internal forces. Meanwhile, the overall stiffness gradually decreased until multiple plastic hinges formed at joints Nos. 3, 4, 1, and 6, eventually causing the ring to enter the plastic phase. The load level at the elastic limit was determined to be 39.6% of that at the elastoplastic limit.

The failure of Ring A was caused by joint failure, and joints Nos. 3, 4, 1, and 6 were weak parts for the structure. In contrast, the capacities of the segments were not fully utilized. The horseshoe-shaped segmental ring exhibited similar failure mechanisms to circular ones.

Loading test of Ring B

Test process of Ring B

Figure 15 illustrates the loading process of Ring B. As P_B increased from 0 to 880 kN, the load-displacement curve developed linearly. When P_B reached 1056 kN (①), block EB1 experienced localized concrete cracking at the inside of joint No. 1 due to compressive stress concentration, and the overall stiffness slightly decreased. However, the overall stiffness slightly increased at the next load level, and the curve developed linearly again at higher load levels. When P_B reached 1760 kN (②), block EB2 cracked at the outside of joint No. 3 under compressive stress, but it did not cause a variation in the overall stiffness. When P_B reached 2112 kN (③), concrete cover of block EB2 spalled at the outside of joint No. 3, and that of block EA5 spalled at the inside of joint No. 4, resulting in an obvious decrease of the overall stiffness. In the subsequent loading, the maximum P_B reached up to 2288 kN, and no further structural damage was observed. At this point, Ring B had only undergone the cracking or spalling of the concrete cover at joints Nos. 1, 3, and 4. In comparison, Ring A had entered the plastic phase as P_A reached 1920 kN, and multiple joints had turned into plastic hinges. Therefore, Ring B had a significantly higher bearing capacity owing to the change in the loading condition.

Fig. 15.

Load-displacement curve of Ring B.

Ring A and B loading conditions were compared, and the actual pressure values of the loading points on the right side were employed for the comparison, as listed in Table 5. The pressures exerted on the vault areas, involving loading points Nos. 1, 3, and 5, were basically equal under both conditions. And the invert area, involving loading points Nos. 17, 19, 21, and 23, also had approximately equal pressures on the whole. Significantly, Ring B had greater lateral pressures, mainly involving loading points Nos. 9, 11, and 15. The increase in the lateral pressures significantly raised the bearing capacity of the structure. Ring B has sufficient safety reserves as well as a large optimization space.

Table 5.

Comparison of the loading conditions between Ring A and Ring B.

Loading point	Pressure ratio of Ring B and Ring A
No. 1	0.98–0.99
No. 3	1.01–1.01
No. 5	0.97–0.98
No. 7	0.87–0.88
No. 9	1.25–1.76
No. 11	0.86–1.58
No. 13	0.96–0.97
No. 15	1.19–1.20
No. 17	0.95–0.98
No. 19	0.95–1.01
No. 21	0.89–0.95
No. 23	0.98–1.14

During the loading test of Ring B, the oil pressures of some hydraulic jacks reached approximately 40 MPa, and the concentrated forces of these loading points exceeded 3000 kN, which posed a high safety risk to the test personnel. Judging from the experimental results of Ring A, Ring B might require an especially high load level to enter the plastic phase, which meant a higher safety risk. Finally, the loading test of Ring B was moderately interrupted for safety considerations.

Experimental results of Ring B

Figure 16 showed the effects of the loading condition on structural deformation. Here, horizontal expansion deformation refers to the relative displacement between both sides along the horizontal axis at the maximum span. As the load level (P) increased from 0 to 1080 kN, the vertical convergence deformations of Ring A and Ring B were basically compatible. However, when P exceeded 1080 kN, Ring A had larger convergence deformation, and that of Ring B continued to develope linearly until further structural damage occurred. When P reached approximately 1900 kN, Ring B had a maximum reduction of 28% in the vertical convergence deformation compared with Ring A. On the other hand, the horizontal expansion deformation of Ring B was smaller too, reduced by up to 1 cm.

Fig. 16.

Comparison of load-displacement curves of Ring A and Ring B: (a) vertical convergence deformation, (b) horizontal expansion deformation.

The increased lateral pressures restricted the ring deformation, retarded the joint damage, and maintained the overall stiffness to a higher load level. As a result, it improved the bearing capacity of the ring, since the structural damage of Ring B occurred only at joints too. It is notable that the increase in lateral pressures did not lead to an increase in the overall stiffness of Ring B, which suggests that the overall stiffness of the ring largely depended on the stiffnesses of its own parts when the joints had relatively large rotational stiffnesses.

The loading conditions of the two rings are relatively similar, and Ring B shares many similarities with Ring A in terms of the failure characteristic, convergence deformation, and internal force distribution. To avoid being verbose, no further elaboration is repeated here.

Segment damage during TBM advancement

In the early stages of TBM advancement, there was a frequent occurrence of segment damage at inferior joints following the separation of segmental rings from the TBM tail. The specific positions of ring damage are shown in Fig. 17. The majority of cases involving segment damage were observed at joint No. 7 of either the odd or even ring, and concrete cracking at joints Nos. 5, 6, and 8 occurred approximately one-fifth as frequently as at joint No. 7. It is likely that compressive stress or compression-shear stress caused the segment damage, and the characteristics of such damage are shown in Fig. 18.

Fig. 17.

Damaged positions of the horseshoe-shaped segmental ring: (a) odd ring, (b) even ring.

Fig. 18.

Damage characteristics of segments: (a) joint No. 7, (b) joint No. 8, (c) side surface of joint No. 7.

After conducting a thorough investigation and analysis, the primary factors contributing to segment damage were identified as follows.

1. The lining structure had a significant span and dead-weight, while the TBM was not equipped with a device to maintain the cross-sectional shape of the horseshoe-shaped segmental ring. Additionally, the backfill grout took approximately 8 h to set and could not restrain ring deformation in time. These factors allowed significant oval deformation of the segmental ring to occur (the top and bottom deformed inward, and the middle expanded outward). As the ring deformation was mainly concentrated at joints, the relative rotations at joints led to stress concentration and thereby concrete cracking.

2. Before the grout solidified, the segmental ring, especially the invert area, was subjected to significant buoyancy. And the horseshoe-shaped segmental tunnel lining had a flat inverted arch. Therefore, the joints in the invert area were prone to suffer large shear forces, resulting in compression-shear damage at those joints, as shown in Fig. 18.

3. The longitudinal joint was designed with a tongue-and-groove structure to facilitate the positioning and assembly of segments. However, it was found that the reinforcement of the tongue-and-groove structure was inadequate, and the concrete cover was excessively thick. As a result, the longitudinal joint lacked sufficient strength to bear excessive external forces, particularly shear forces, making it prone to brittle damage.

To address the above problems, the following measures were taken.

1. The solidification of the backfill grout was accelerated to cope with the oval deformation and floating. New polymer materials, designated as materials A and B, were added into the original grout to achieve timely solidification, and the setting time could be regulated by varying the proportions of materials A and B. Meanwhile, optimizing grouting pressure, volume, and positions further improved the restraining for the oval deformation and floating of the lining structure. As a result, the occurrences of segment damage at joints Nos. 5 and 8 significantly decreased. While there was some alleviation of segment damage at joints Nos. 6 and 7, it had not been completely eradicated.

2. For the existing segments, reinforcing bars were embedded in the concrete cover of the longitudinal joint to enhance the shear capacity, as shown in Fig. 19. For the segments that had not yet been manufactured, the reinforcement within the longitudinal joint was further strengthened. Following these improvements in the shear capacity, segment damage at joints Nos. 6 and 7 was effectively suppressed.

Fig. 19.

Embedding reinforcing bars in the longitudinal joint.

Discussion

The results of the full-scale loading tests reveal that the horseshoe-shaped segmental ring had similar deformation and failure mechanisms to those observed in circular ones. The structural failure of the horseshoe-shaped segmental ring mainly occurred in the arch area, indicating that the bearing capacity of the structure was determined by the arch area, while the invert did not prove to be a weak area. Therefore, it can be inferred that there is no significant difference in bearing capacity between the horseshoe-shaped segmental ring and the circular one. Nevertheless, it was revealed in practical applications that segment damage was prone to occur at the inferior segment joints of the horseshoe-shaped segmental ring. The flat inverted arch may induce significant shear forces on the inferior joints, requiring an increased shear capacity for those joints.

On the other hand, each segment in the horseshoe-shaped segmental ring is unique and has a relative fixed spatial position. As such, implementing nonuniform reinforcement design for the segments in a horseshoe-shaped segmental ring is more practical than in a circular one, leading to steel savings. Besides, less concrete volume is required for a horseshoe-shaped ring. In brief, the use of horseshoe-shaped segmental tunnel linings can reduce the consumption of construction materials and lower costs.

In terms of assembly efficiency, the horseshoe-shaped segment ring’s lack of central symmetry required more time for segment positioning. It took a minimum of 120 min to complete a ring in the preliminary stage. With increased proficiency, the average assembly time was reduced to approximately 55 min (Li, 2017).

In conclusion, the segmental tunnel lining with a horseshoe-shaped cross section demonstrates comparable bearing capacity to that with a circular one, while providing significant cost advantages. Further research is needed to assess and compare the comprehensive benefits in design, manufacturing, assembly, service performance, and cost of the two cross-sectional types of segmental tunnel linings. This is also a critical consideration for evaluating the practicability of the horseshoe-shaped TBM method.

Conclusion

The first application of the mechanized method using a horseshoe-shaped EPB-TBM was achieved relying on the Baicheng Tunnel project, but uncertainties remain on the structural behavior of the horseshoe-shaped segmental tunnel lining. This study revealed the mechanical characteristics and mechanisms of this novel lining through the full-scale experiments, and elaborated the main problems exposed during its practical application. The results demonstrated that:

1. The horseshoe-shaped segmental ring exhibited similar deformation and failure mechanisms to circular ones, with the segment joints identified as the weak parts of the structure. The deformation of the ring was mainly attributed to the concentrated rotations at segment joints, and the structural failure was caused by joint failure. Furthermore, the bearing capacity of the horseshoe-shaped segmental ring was largely determined by the arch area, while the invert did not prove to be a weak area.

2. The distribution positions of segment joints significantly affected the specific characteristics of the ring convergence deformation and bending moment distribution, while having limited effects on the axial force. Furthermore, the joint positions also had an effect on the failure progress and bearing capacity of the structure to some extent. Excessive relative rotation at the joint could accelerate the joint damage because of stress concentration, and the damage and failure of a joint could accelerate that of its adjacent joints due to the redistribution of internal forces. Specifically, the progressive failure of joints mainly caused the redistribution of bending moments.

3. The horseshoe-shaped segmental ring could achieve a comparable bearing capacity to the circular one. Nevertheless, practical applications have revealed that segment damage was prone to occur at the inferior segment joints of the horseshoe-shaped segmental ring due to significant shear forces induced by the flat inverted arch, requiring an increased shear capacity for those joints. On the other hand, the use of horseshoe-shaped segmental tunnel linings can significantly reduce the consumption of construction materials, thereby providing superior cost efficiency.

Author contributions

X.F. contributed to Methodology, Investigation, Analysis, and Writing; W.Q., Y.C. and H. contributed to Validation, Resources, and Funding acquisition; J.H. and R. contributed to Investigation and Review editing.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Competing interests

The authors declare no competing interests.