1 Introduction
Prefabricated technology has emerged, as a solution to the labor shortage crisis in the construction industry, due to its high mechanization and low manpower requirements. Furthermore, this environmentally friendly and low-carbon technology has been rapidly promoted in recent years [
1–
5]. With the fast development of rail transit infrastructure in China, many big cities have explored and implemented prefabricated technology in subway station construction [
6–
9]. However, compared to traditional cast-in-place subway stations, prefabricated stations consist of many components that are connected by joints, which are often considered to be weak links [
10–
12]. Previous study has indicated that the strength and stiffness of joints are lower than those of continuous structures constructed by the cast-in-place method [
13]. The deformation and opening of joints in prefabricated stations, mainly caused by bending moment, can lead to groundwater leakage and disrupt the normal operation of the subway. Therefore, the flexural performance of joints is critical in determining the overall mechanical performance and waterproofing ability of the structure. It is essential to explore more reasonable types of joint to enhance flexural performance in the design and research of prefabricated subway station structures.
The segmental joint has been successfully used in different types of shield tunnels. Although shield tunnels have good mechanical performance due to their circular shape, their joints are highly susceptible to tunnel diseases, such as tunnel leakage and lining cracking [
14]. Therefore, the joints for prefabricated subway stations, which usually have a rectangular or quasi-rectangular shape and large geometric dimensions, should be carefully investigated. Yang et al. [
15] proposed the grouted mortise-tenon joint, consisting of tenon and groove (TG), pre-tightening rod, and joint grouting, and this has been applied in prefabricated subway stations in Changchun and Qingdao, China [
16,
17]. Ye et al. [
18] proposed a new type of steel-concrete composite joint, consisting of TG, four channel steels (CSs), and two H-beams, and such joints have been applied in a prefabricated subway station in Guangzhou, China. However, these prefabricated subway stations were constructed using the open-cut method, and any potential lack of strength or waterproofing performance of the joint can be supplemented by the underground diaphragm wall and the concrete fill surrounding the station structure. For prefabricated subway stations constructed using trenchless methods, such as pipe-jacking and shield methods [
19,
20], where there is a high demand for mechanical performance, there is a lack of research on suitable joints. The ultra-high performance concrete (UHPC) joint, which connects prefabricated components of underground structures, is also a feasible option [
21]. However, its construction time is prolonged due to its cast-in-site construction. Therefore, more research is necessary to investigate joint forms that have a high mechanical performance.
Since the opening of the joint is mainly due to bending moment, the mechanical performance of joints has traditionally been investigated with a focus on their flexural behavior. There are three primary research methods used to investigate the flexural performance of joints: full-scale tests [
22–
25], numerical simulations [
26–
28], and theoretical research [
10,
11,
13]. For prefabricated structures for engineering projects, full-scale tests are the primary and most direct research method. Yang et al. [
15] developed a new experimental system and loading strategy to perform a set of 1:1 prototype experiments to investigate the bending resistance characteristics of a proposed grouted mortise-tenon joint. Wang et al. [
21] carried out a series of full-scale tests to investigate the bending performance of ultra-high concrete joints reinforced by various bolt types. Qiu et al. [
29] conducted a full-scale experimental study to investigate the bending behavior of assembled joints for prefabricated two-wall-in-one diaphragm walls. However, conducting a series of full-scale tests under different loading conditions can be costly, and obtaining enough reliable data from tests is difficult. Therefore, numerical simulation has become a necessary complementary method to investigate the mechanical performance of joints [
30–
32]. Guo et al. [
33] established a three dimensional (3D) numerical calculation model, which was validated by full-scale tests, to study the deformation and damage behavior of segmental joints under ultimate compression-bending loads. Ding et al. [
27] established a refined numerical model for the new segmental joint containing double rows of bolts to investigate the flexural behavior and bearing mechanism of the joint.
After comparing the flexural performance of existing joints, a combination of steel, high-strength bolt, and TG appears to be a promising choice for a new high-performance joint. However, the mechanical properties of the contact interface between steel and concrete are difficult to define and may significantly influence the flexural performance of the joint. Ding et al. [
27] established a 3D finite element (FE) model in which the steel plate and concrete interface were simulated using a tie constraint. However, this method cannot account for the detachment of the steel-concrete interface. The viscous contact in ABAQUS software that is capable of simulating the bonding and detachment characteristics of the interface between the steel and concrete at the joint, provides an effective solution to the numerical simulation of such joints whose mechanical performance is susceptible to the behavior of the steel-concrete interface.
In this study, a new channel steel-bolt (CB) joint is proposed for a test-case station, a prefabricated subway station, on Shenzhen Rail Transit Line 12, which was constructed using the pipe-jacking method. The flexural performance of the CB joint is investigated through a combination of full-scale tests and numerical simulations. Viscous contact is used to simulate the interface between the CSs and concrete in the 3D FE model established using the ABAQUS software, and the simulation is then validated using experimental data. The flexural behavior of the CB joint, including its deformation characteristics, failure mode, and bearing mechanism, is analyzed based on the experimental and numerical results. Additionally, the effects of the axial force and preload of the bolt are also discussed in detail.
2 Project overview
As shown in Fig.1, Shasan Station is an underground double-layer station on Line 12 of the Shenzhen Metro. The main structure of the station is 212 m in length and is divided into three sections based on the construction method used: the prefabricated section in the middle and the cast-in-place sections at each end. The prefabricated section spans 70 m and is constructed using the pipe-jacking method to pass under a large rainwater box culvert. The prefabricated station structure comprises many components that are connected by CB joints, a newly proposed form of joint that consists of a pair of CSs connected by ten high-strength bolts on both sides and a TG in the middle. The joints are designed to be located on the sidewall of the station structure, including the upper and lower joints (Fig.1). Additionally, the station has a width and height of 22.6 and 13.53 m, respectively, and the longitudinal spacing of the station columns is 8 m. Due to the large section of the prefabricated station structure, it is necessary to carefully examine the flexural performance of the CB joint before its application in the station.
The CB joint is designed with a width of 2000 mm, as illustrated in Fig.2. The thickness of the CB joint is designed to be 900 mm, based on the designed forces of the upper and lower joints, which have been obtained from preliminary calculations [
34]. The joint consists of two pairs of large and small CSs, each of them connected by ten high-strength bolts of 10.9-grade M30, with a spacing of 0.2 m. A TG is placed in the middle of the joint surface to improve the shear performance of the joint and enhance assembly accuracy and efficiency. It is worth mentioning that a 5 mm gap is designed between the TG to prevent their direct contact during assembly, which may damage the concrete of the TG. The gap will be filled with grout through the pre-buried grouting pipe from the inner side of the joint. Waterproof belts are positioned on the inner and outer sides of the tenon to ensure waterproofing performance, while the belts on the lateral sides are designed to prevent water leakage between the ring structures.
3 Flexural test of the channel steel-bolt joint
To obtain more reliable results for the flexural performance of the CB joint, two sets of full-scale tests were carried out. These tests aimed to determine the flexural capacity of the CB joint, which is intended for use in the test-case station.
3.1 Test specimen
The test specimens utilized for the flexural test were manufactured in accordance with the CB joint design. However, the width of the test specimen was half that of the width of the CB joint, in order to not only reduce the demand on the loading equipment but also lower the test cost. As shown in Fig.3, the flexural test specimen consisted of TG parts with a total length of 3 m, the length of each part was 1.5 m. The concrete grade of the test specimens was C50, and the reinforcements were designed according to the design bending moment of the joint. The diameter of the anchor bar for the big CSs of the tenon part was 32 mm, while that of the groove part was 28 mm. The big and small CSs were connected by five high-strength bolts with a spacing of 200 mm. The bolt mounting hole was oval-shaped to ease bolt installation. The heights of big and small CS were 200 and 130 mm, respectively, while their widths are both 120 mm. The gap on the flange of the big and small CSs was designed to be welded after installation to improve the waterproof performance of the joint. Fig.4 shows the reinforcements and produced specimens of TG parts. The assembled test specimen weighed around 6.75 t, with hooks designed to facilitate hoisting, transportation, and assembly.
3.2 Test setup
Fig.5 depicts the loading test platform used for the flexural tests, and it was primarily composed of the loading frame, the jack loading system, and the loading beams. The loading frame was responsible for providing counterforce for both the vertical loading jack (VLJ) and the supporting beams. The jack loading system included the VLJ and the horizontal loading jacks (HLJs). The VLJ applied two equal vertical forces on the test specimen through the vertical loading beam. Two HLJs, symmetrically arranged on both sides of the specimen, provided the axial force through the horizontal loading beams connected by steel strands. The HLJs could provide a maximum axial force of 2000 kN, while the VLJ could provide a maximum force of 5000 kN, both of which satisfy the loading requirements for the tests.
3.3 Loading and measuring schemes
As shown in Fig.6, the vertical load (
P) was applied to the top of the test specimen, and the distance between the loading point and the bearing roller was 1.16 m. Testing loads for the joint specimen were derived from the preliminary design axial force and bending moment of the joint, obtained from the FE model of the station structure with the assumption that the section of side wall was continuous [
34]. Based on the simulation results, the maximum design moment of the joint was approximately 1072 kN·m, and the axial forces for the upper and lower joints were approximately 2112 and 2406 kN, respectively. Since the test specimen was half the size of the CB joint, the design moment and axial force for the test specimen were half of those for the CB joint. Consequently, the values of the design moment (
Md), and axial forces for the lower and upper joint (
Nd1 and
Nd2) in the flexural tests were 536 kN·m, 1056 and 1203 kN, respectively. Additionally,
P could be preliminarily calculated as follows:
P =
M/1.16. It is worth mentioning that the bending moment-rotational angle (
M–
θ) curve presented in Sections 5 and 6 takes into account the influence of the weight of the specimen and axial force on the bending moment.
The loading procedure is presented in Fig.7, which corresponds to the loading scheme proposed by Yang et al. [
15,
16]. This procedure can help to obtain more test results from a test specimen. The procedure consisted of four stages of varying load. In the first stage (S1),
Nd1 was larger than
Nd2, and
Md were simultaneously and proportionally applied to the specimen. At the end of S1, the moment reaches the
Md, and the corresponding value of the vertical load was 462 kN. In the second stage (S2), the axial force was held constant at
Nd2 while increasing the vertical load until the bending moment reached 2
Md, and the corresponding value of vertical load was 924 kN. The results of this loading stage could help to investigate the flexural performance of the lower joint. During the third stage (S3), the axial force was reduced to half of
Nd2, while
P was kept constant. During the fourth stage (S4), the axial force was maintained at
Nd2, while
P continued to increase until the specimen failed. The loading stages could help to obtain the flexural performance of both the upper and lower joints, as well as investigate the flexural capacity of the CB joint.
During the flexural test, the vertical displacement (VD) and opening of the joint, and the strain of the high-strength bolt, were monitored and recorded, as illustrated in Fig.6. Ten displacement sensors (D1–D10) were located on the front and back sides of the specimen, where D1–D4 measured the joint opening, while D5–D10 measured the VD of the joint. The strain of the middle high-strength bolt on the tensile side of the specimen was measured by a strain gauge installed on the groove in the bolt.
3.4 Experiment results
3.4.1 Results of joint deformation
Fig.8 illustrates the evolution of VD of the CB joint with increasing vertical load; S1 to S4 were consistent with the four loading stages shown in Fig.7. The test results of the two sets of flexural tests were in agreement with each other, indicating the reliability of the test results. Generally, the VD value increased nonlinearly with the increase of P, with the growth rate gradually increasing until the failure of the test specimens. When the value of P was less than Pd, the vertical load corresponding to Md in S1, the VD increased linearly with the increase of P, indicating that the specimens were in an elastic state. At the end of S1, the values of VD for tests 1 and 2 were 1.26 and 1.8 mm, respectively. In S2, the axial force remained constant at 1203 kN, while the value of P increased from Pd to 2Pd, causing the P-VD curve to gradually change from showing linear to showing nonlinear growth, and also causing the growth of VD to accelerate. This indicated that the specimens were gradually transforming from an elastic state to a plastic state. In S3, the axial force was reduced from 1203 to 1056 kN. Correspondingly, the values of VD increased slightly from 4.78 to 5.56 mm and from 6.16 to 6.8 mm, respectively, demonstrating that the axial force was beneficial for restricting the joint deformation. In S4, the axial force remained constant at 1056 kN, while the value of P gradually increased until the failure of the test specimens. As the plasticity of the test specimen developed, the growth rate of VD increased rapidly. Finally, the values of P for Tests 1 and 2 reached 1591 and 1486.7 kN, and the corresponding values of VD were 60.2 and 33.9 mm, respectively.
As shown in Fig.9, the variation in joint opening of the test specimen mirrored the vertical load-displacement curve. At a P value of 462 kN, the joint opening values were recorded as 0.01 and 0.38 mm, respectively. Disparities in joint opening can be attributed to the potential inconsistencies present among test specimens during their production. As the value of P surpassed 462 kN, the growth rate of joint opening gradually escalated until the failure of the test specimens. At a P value of 924 kN, the joint opening values in the two tests increased to approximately 2.9 mm. Beyond this point, the joint opening values for the two tests converged, displaying a similar pattern.
3.4.2 Results of strain of bolt
The high-strength bolts connecting the TG parts play a vital role in the flexural performance of the CB joint. Fig.10 illustrates the strain of the bolt monitored in Test 1 during the four loading stages. Notably, the strain monitoring of the bolt began after applying preload, and therefore, the strain induced by preload is not considered. The linear growth of the strain of the bolt with the increase of P in S1 to S3 indicates the elastic state of the high-strength bolt. At the end of S1, when the value of P reached 462 kN, the strain of the bolt increased linearly to 154.6 × 10−6. The low value of bolt strain could be attributed to the beneficial effect of axial force in the initial loading stage. In S2, the growth rate of bolt strain was higher than that observed in S1, and the strain of the bolt increased linearly to 1426.9 με by the end of S2. During S3, the strain of the bolt increased to 1681.3 με when the value of axial force decreased to 1056 kN. At the beginning of S4, the P-strain curve also showed a linear growth trend, and the growth rate remained basically unchanged compared to that of S2. When the value of P reached 1359 kN, the strain of the bolt increased to 2777.7 με. Subsequently, the strain of the bolt showed a noticeable nonlinear growth, indicating that the bolt was in a plastic state. Finally, the strain of the bolt reached 5994.4 με when the value of P was 1565.6 kN, after which the strain sensor was damaged.
3.4.3 Failure process and mode
Fig.11 presents the crack development and failure process of the specimen during the flexural test. As shown in Fig.11(a), at a load of 673.3 kN, no significant joint opening occurred, but cracks appeared on both the tensile and compression sides of the groove part. The absence of concrete in the groove part impaired its strength, causing larger deformations of the concrete and CSs, which induced cracks near the CSs. Stress concentration due to the vertical load possibly caused cracks parallel to the anchor bars near the big CSs and loading pad on the compression side. On the tensile side, the inclined crack was mainly due to the shear force induced by the CS flange, with the anchor bar tension also contributing to cracking near the anchor bar. At P = 769 kN, as depicted in Fig.11(b), slight joint opening was observed on the tensile part of the joint, with a monitored opening of 2.1 mm. The interface between the web of the big CS and concrete was also slightly detached due to the inward bending of the web under bolt tension. The cracks on the compression side slightly expanded, while those on the tensile side developed further. The inclined cracks near the large and small CSs were induced by the shear forces between the flanges of the CSs and concrete, with the groove causing the crack above the big CS to incline toward the end of the groove. At P = 1060.3 kN, the monitored joint opening increased to 8.1 mm, and the detachment between the web of the big CS and concrete became more pronounced, as shown in Fig.11(c). The cracks on the tensile side continued to develop, with the number of cracks near the big CS doubling and their length increasing. At P = 1413.8 kN, the monitored joint opening increased to 19.5 mm, and both the big and small CS webs bended and detached from the concrete, as shown in Fig.11(d). The new cracks on the tensile side mainly occurred above the big CS, with the intense cracks on the concrete between the groove and big CS indicating that the concrete was close to being crushed. As shown in Fig.11(e), the test specimen failed at a load of 1591 kN with the high-strength bolt breaking.
Fig.11(f) displays the TG parts of the specimen after the flexural test. The concrete on the compression side of the groove part was crushed under compression, while the tenon showed a shear failure induced by the large contact force between the TG in the later stage of loading, where the VD of the tenon rapidly increased and contacted the groove.
4 Numerical simulation
A 3D FE model of the joint specimen was created using ABAQUS software to further analyze its flexural performance. The simulation results can provide more insight into the bearing mechanism of CB joints.
4.1 Geometry and mesh
In Fig.12, a 3D FE model of the test specimen is presented, including the big and small CSs, bolts, TG, and reinforcements. The gap between the TG was set to 5 mm, which was consistent with the test specimen. To simulate joint concrete, bolts, and CSs, C3D8R elements were adopted, while T2D2 elements were used for reinforcements. The mesh size was determined according to the size of each component, with minimum and maximum values of 5 and 80 mm. Additionally, a high mesh density was set in the loading and boundary areas of the specimen. Consequently, the 3D FE model comprised a total of 91000 elements. The simulation results, which were verified by the test results (see Fig.13), can help to better reveal the bearing mechanism of CB joints.
4.2 Material parameters
The concrete grade of the specimen was C50, with a compressive strength of 43.8 MPa and an elastic modulus of 35.7 MPa, determined through compressive tests of concrete cubes. To better simulate the plastic and failure behavior of the test specimen, the concrete damage plastic (CDP) constitutive model proposed by Lubliner et al. [
35] and Lee and Fenves [
36] was employed. This model could be directly used in ABAQUS software, and the stress-inelastic strain of concrete could be derived from the code for design of concrete structures (GB 50010-2010). The input parameters for the CDP model in ABAQUS were the same as those introduced by Guo et al. [
33]. In addition, a bilinear constitutive model was adopted for the CSs, bolts, and reinforcements, which considered both the elastic and plasticity strengthening stages of steel [
37]. The mechanical parameters of steel in the 3D FE model are presented in Tab.1. According to Chinese standard (GBT 1591-2018), the yield strength of steel plate (Q355) with a thickness between 16 and 40 mm is 345 MPa. In addition, the yield and ultimate stresses of the reinforcement were obtained from tensile tests.
4.3 Loads and constrains
The loads in the FE model were determined based on the loading process of the flexural test, as shown in Fig.7. It is important to note that the preload of bolts, which could be implemented using the bolt load function in ABAQUS, was applied prior to the loading of axial and vertical forces. The value of bolt preload was set to be 188.9 kN, in accordance with the actual loading situation. The loading areas of the axial and vertical forces were also consistent with the locations of the horizontal loading beam and the vertical loading pad, respectively.
The contacts in the model consisted of six types: concrete to concrete, CS to CS, CS to bolt, concrete to reinforcement, CS to anchor bar, and CS to concrete. The concrete-to-concrete, CS-to-CS, and CS-to-bolt contacts were set as face-to-face [
38]. The normal model for these contacts was set as hard contact, and the friction model of the contact surface was set as a penalty. The friction coefficient for concrete-to-concrete contact was 0.55 [
39], while the values for CS to CS and CS to bolt were both 0.3. The reinforcements were set to be embedded in the concrete, and the ends of anchor bars that were welded together with CSs were also set to be embedded in the CSs. It was important to accurately simulate the contact between CSs and concrete, as the deformation of CSs could cause detachment from the concrete, as revealed in the experimental results. Viscous contact in ABAQUS was a preferable choice, since it could simulate the bonding, slip, and detachment behavior of the contacts. The tensile and shear strength of the contact interface between CSs and concrete were set to 0.8 and 0.28 MPa, respectively [
40]. As for the boundary of the model, a hinge constraint was set at the center of the bearing pad, which could simulate the constraints of bearing bars.
4.4 Results from finite element model
4.4.1 Results of joint deformation
The VDs of the test specimen obtained from the 3D FM model and experimental results are compared in Fig.13. The good agreement between the numerical simulation and experimental results indicates that the 3D FM model is capable of effectively predicting the bending deformation of the CB joint. However, it should be noted that when the value of P fell between 950 and 1000 kN, the simulated VD was slightly smaller than the experimental results. This may be attributed to the fact that the specimen exhibited obvious cracks during the loading period (as shown in Fig.11), resulting in a decrease in the stiffness of the joint.
In S1, the VD of the joint increased linearly with the vertical load, indicating that the 3D FE model was in an elastic state. In S2, the VD exhibited linear growth with the increase in vertical load, except for the later stage of S2, where the growth curve gradually changed from linear to nonlinear, indicating that the FE model gradually entered the elastic-plastic stage. In S3, a slight increase in VD could be observed when the axial force decreased from 1203 to 1056 kN. In S4, the VD of the joint showed a clear nonlinear increasing trend with the increase in vertical load, and the increasing speed became progressively faster, indicating that the joint in the model entered the plastic stage. In general, the variation law of the simulated VD of the joint was consistent with the experimental results.
Previous studies have indicated that the mechanical performance of prefabricated structures is different from that of cast-in-place structures [
16,
41], so it was necessary to compare the flexural performance of the CB joint and the continuous beam that had the same geometric parameters and reinforcements. As shown in Fig.13, in S1, the ratio between the slope of the curve for the CB joint and that of the curve for the continuous beam was approximately 18%, indicating the reduction rate of flexural rigidity for the CB joint. The values for S2 was higher, reaching around 26%.
In addition, the deformation of the simulated results at each loading stage was assessed, and the joint deformation under a load of 1413.8 kN was compared with the experimental result, as shown in Fig.14. At the end of S1, the maximum VD of the joint was 1.44 mm. Due to the 5 mm gap between the tenon and the mortise, the displacement of the tenon was unconstrained under vertical loading. In S2, the maximum VD appeared at the tenon position, reaching 5.33 mm, while the displacement at the joint was slightly smaller, at 4.87 mm. Additionally, it was observed that the VD of the web of the big CS was obviously larger than that of the flange and the connecting concrete, indicating that the bending deformation of the web gradually detached the contact interface between the CS and the concrete. In S4, when the value of P reached 1413.8 kN, the simulated maximum VD, located at the web of the big CS, increased to 37.4 mm. The simulated opening of the joint interface was 21 mm, compared to 19.5 mm from the experimental result. Fig.14(c) illustrates that the deformation characteristic of the simulated joint was highly consistent with the experimental results, further demonstrating the reliability of the 3D FE model.
4.4.2 Results of stresses
1) Stresses of steel
Fig.15 presents the stresses of the CSs, bolts, and anchor bars of the CB joint on the tensile side, which are essential in understanding the deformation behavior of the joint. The stress contour of steel at the end of S1 is shown in Fig.15(a). The maximum stress for the CSs was 346.9 MPa, caused by stress concentration induced by the contact of CSs and bolts. However, the stresses for the rest of the regions were significantly lower than the yield stress of CS (345 MPa). The maximum stress for the bolts was 660.5 MPa, which was lower than their yield stress of 900 MPa. Therefore, all the components were in an elastic state in S1.
By the end of S2, the maximum stress for the CSs increased to 390.6 MPa, while the stress for the anchor bars was 293.1 MPa. Stress concentration near the bolt holes of CSs was induced by the tensile load of bolts, causing these areas of the flanges of CSs to enter the plastic state. The maximum stress for bolts appeared at the head of the bolt and reached 910.8 MPa, which was also a result of stress concentration. Generally, most of the steel components were in an elastic state at the end of S2, except for the areas near the contact surface of bolt and CS. The stress state in S3 was similar to that of S2, so no further analysis is conducted here.
At the end of S4, the stresses for CSs and bolts reached the ultimate stress, while the maximum stress for anchor bars was 513.4 MPa, which was lower than their ultimate stress of 599.2 MPa. Additionally, the maximum stresses for the web of CSs on the tensile and compression side were 415.2 and 348 MPa, respectively. As a result, both sides of the joint were in the plastic state at the end of S4. Meanwhile, the maximum stress for the bolt rod reached 904.3 MPa.
2) Stresses of concrete
Fig.16 displays the maximum principal stress of the joint concrete at the end of stages S1, S2, and S4. At the end of S1, the web of CSs exhibited a large stiffness and thus the maximum compressive stress was found at the contact surface between the concrete and the end of the web of CSs, with a maximum value of 13.1 MPa. At the end of S2, the stress concentration became more prominent, and the maximum compressive stress reached 27 MPa. Furthermore, the compressed area of the joint interface was further reduced. At the end of stage S3, the maximum compressive stress of the concrete reached 52 MPa, and was located in the areas that made contact with the corner of the CSs. It is worth noting that the distribution area of the maximum compressive stress on the concrete was reduced due to the asymmetry of the test specimen. The asymmetrical stress contour was consistent with the failure characteristics of the test specimen, as depicted in Fig.11.
5 Bearing mechanism and four-stage simplified model
The testing loads of the flexural test are derived from the preliminary designed forces of the joints in the Shasan station. To facilitate the application of the CB joint in the other prefabricated structures, the validated 3D FE model can be used to obtain more general results on the flexural behavior of CB joints. The vertical loads were typically applied to the specimen after the axial force had been applied, and the M–θ curve was employed to assess the flexural performance of the joint. Therefore, the M–θ curve of the CB joint could be obtained from the 3D FE model, and the bearing mechanism of the joint could also be further investigated.
The bending moment and rotational angle of the joint can be calculated by Eqs. (1) and (2) [
21,
33].
where P is the vertical load, a is the distance between the joint and bearing roller (1.16 m), G is the weight of the tenon or groove part (approximately 33.75 kN), L is the length tenon or groove part (1.5 m), b is the distance from the loading end of specimen to the bearing roller (0.1 m), N is the axial force, and Vd is the VD of the joint. These symbols can be seen in Fig.6.
5.1 Bearing mechanism analysis
Based on the simulation results from the FE model, with an axial force value of 1000 kN, the bearing mechanism of the CB joint can be analyzed by evaluating the M–θ curve. Fig.17 illustrates that the M–θ curve has three critical points, with the critical bending moments, M1, M2, and M3, being 222, 1175, and 1455 kN·m, respectively. The critical points for M1 and M3 are the inflection points (CP1 and CP3) of M–θ curve, which can be easily identified. The simulation results showed that the yield of around 70% of the large CS web would lead to a more rapid decrease in the M–θ curve, and that is where CP2 is defined. The value of M2 can be calculated by Eq. (1) when the vertical load at CP2 is identified. Additionally, the stress and deformation of the joint under the critical bending moments are also presented in Fig.17.
For values of M lower than M1, the M–θ curve exhibited linear growth. The stress contour of CP1 showed that the concrete stress on the bottom of the tensile side of the joint interface was nearly zero, suggesting that the tensile force on the bottom of the joint, caused by the bending moment, was roughly equivalent to the compressing force induced by the axial force. When M was between M1 and M2, the M–θ curve still displayed linear growth but with a decreased slope, indicating that the value of rotational stiffness was reduced. In this stage, the joint on the tensile side gradually opened up, and the bolts and CSs began to bear tensile loads induced by the bending moment. The stress contour of CP2 shows that the stress of the web of the CSs reached the yield stress of 345 MPa, resulting in the appearance of CP2 in the M–θ curve. When M increased from M2 to M3, the M–θ curve started to exhibit a nonlinear change trend, because the yielding area of the web of the CSs gradually increased, thereby decreasing the slope of the curve. Then, the curve showed a linear increasing trend again. At CP3, the TG of the CB joint started to make contact, as illustrated by the compression stress on the root of the tenon. When M exceeded M3, the M–θ curve generally displayed a linear increasing trend, with a slightly decreased slope.
It is noteworthy that M2 can be considered as the flexural capacity of the joint when the joint is under the critical point of entering the plastic stage. Therefore, for an axial force of 1000 kN, the flexural capacity is about twice the value of the designed moment of the CB joint (536 kN·m).
Considering the force transmission mechanism between different components of the CB joint, the numerical and experimental results showed that the flexural performance of the CB joint was primarily influenced by the CSs, bolts, and anchor bars on the tensile side. Before reaching CP1, the CSs were tightly compressed by bolt preload, leading to excessive tensile force induced by the vertical load applied to the specimen. During this stage, the interface between the web of CSs and the concrete underwent a shear force, while the interface between the flange plate and concrete experienced a tensile force. The displacement of the joint was mainly caused by the relative movements at the interfaces between CS and concrete. As the tensile load increased, the connection between the web of CSs and concrete gradually weakened, leading to a noticeable joint opening, while the flange plates of CSs were secured by anchor bars. At CP2, most of the web of the larger CS yielded, whereas the bolts and anchor bars remained in an elastic state. Transitioning from CP2 to CP3, the anchor bars and bolts gradually entered the plastic state. Upon reaching CP3, an increased VD of the joint caused the TG to come into contact, sharing the bending moment applied to the joint until the joint eventually failed.
5.2 Four-stage simplified model
Based on the analysis presented above and prior research [
27], a simplified four-stage model for the bending stiffness of the CB joint is proposed, as shown in Fig.18. The
M–
θ curve is divided into four stages, and each stage can be approximated by a straight line, with the slope representing the rotation stiffness (
Kθ). In stage 1, the curve shows a linear elastic growth trend, primarily influenced by the axial force. Stage 2 represents the elastic-to-plastic development stage, where the
M–
θ curve can also be approximated by a straight line. Stage 3 represents the plastic stage of the CB joint, where the web of CSs is under plastic deformation, and a straight line can be used to fit the
M–
θ curve in this stage. Stage 4 is the ultimate failure stage, where the TG make contact, and the bolts are under plastic deformation. While there may be some deviation in fitting the
M–
θ curve in stages 3 and 4 with two straight lines, these slight differences are deemed acceptable in engineering applications.
6 Parametric study
6.1 Axial force
In the 3D FE model, axial forces of 500, 1000, 1500, 2000, and 2500 kN were applied to investigate their effect on the flexural behavior of the CB joint. Following the completion of axial loading, a vertical load was applied to the specimen. The resulting M–θ curves for different axial forces are presented in Fig.19. The M–θ curves demonstrate that the flexural performance of the joint increased with the increase of axial force, and the variations of the M–θ curve under different axial forces are similar to each other. As discussed in Section 5, the axial force predominantly influenced the flexural performance of the joint in stage 1, as evidenced by the expansion of the curve in this stage with increasing axial force. It should be noted that the slopes of the curves in stages 2, 3, and 4 exhibit minimal differences, indicating that the axial force had a negligible effect on the bending stiffness in these stages.
Tab.2 presents the rotational stiffness of a CB joint in each stage under different axial forces. These values can be readily incorporated into the beam-spring model [
42,
43], shell-spring model [
44], and solid cross-section spring model [
34], thereby facilitating the utilization of the new CB joint in prefabricated structures.
6.2 Preload of the bolt
Fig.20 illustrates the impact of bolt preload on the flexural performance of the CB joint, where the axial force in the FE model is set at 1000 kN. It is evident that the flexural capacity of the CB joint gradually improves with increasing preload of the bolt, though the increase is relatively limited. Specifically, when the value of M is below 800 kN·m, the four curves overlap substantially, mainly due to the impact of the axial force, which renders the effect of bolt preload insignificant.
Tab.3 presents the maximum joint opening with different bolt preload when the bending moment equals the design moment. It is evident that joint opening significantly decreases as bolt preload increases, a percentage decrease of 18.7% when the value of bolt preload (T) increases from 0 to 300 kN. However, when the value of T surpasses 200 kN, further increases in T only minimally affect the joint opening.
Generally, while the preload of the bolt has little influence on the flexural performance of the CB joint, a higher bolt preload can help minimize the joint opening and improve waterproofing performance. As a result, it is advisable to set the bolt preload at values exceeding 200 kN.
7 Conclusions
In this study, a novel CB joint is proposed for prefabricated subway stations, comprising a pair of CSs connected by ten high-strength bolts on both sides and a TG in the middle. The flexural behavior of the CB joint is investigated through both experimental tests and numerical simulations. A four-stage simplified model is proposed based on the bearing mechanism analysis of the joint to illustrate the piecewise linearity of the M–θ curve. Furthermore, the effects of axial force and bolt preload on the flexural behavior of the CB joint are examined. The main conclusions are as follows.
1) The flexural behavior of the CB joint exhibits obvious nonlinear characteristics, with the bending stiffness gradually decreasing as the bending moment increases. Three critical points are identified, which correspond to the detachment of the tensile side of the joint, the yield of CSs, and the contact of the TG.
2) The bending moment-rotational angle curves of the CB joint can be divided into four stages: elastic growth stage, elastic-plastic development stage, plastic stage, and ultimate failure stage. The proposed four-stage simplified model provides an effective method for estimating the bending stiffness of the CB joint.
3) Axial force can improve the flexural capacity of the CB joint, but it has a limited effect on the bending stiffness, especially in the latter three stages. Bolt preload has a negligible effect on the flexural performance of the CB joint.
4) The flexural capacity of the CB joint is approximate twice the value of the designed bending moment, demonstrating that the design of the CB joint is reasonable and suitable for the test-case station.
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