Since MPJ & JAS tunnel is a novel and special elemental structure, it is necessary to carry out FE analysis and bending test to study and verify the structure performance as well as to determine the physical characteristics, failure behavior and strength for design.

Bending test

Experimental design

The specimen is a segment of MPJ & JAS tunnel structure composed of five steel pipe elements, as shown in Fig. 14. The main design parameters of the specimen are as follows: the steel plate thickness is 16 mm; the filled concrete strength grade in the specimen is C50; shear connectors with a spacing of 300 mm are arranged in the specimen as an optional constructional measure so the steel plate and the concrete cooperatively work; in addition, the steel plate and the shear connectors in the specimen are made of Q235 steel, and the high-performance grouting material (see in “High-performance grouting material for joints” section) is poured into the CT-shaped integrated joint.

The bending test specimen is supported by simple supports and is subjected to a four-point bending strength test. During the test, the load is applied by hydraulic jack and distribution beam. Before formally conducting the test, preloading is applied with loads of no more than 100 kN, with each load stage at 10 kN, and the load holding time is 5 min. Prior to structural cracking, each load stage is increased to 20 kN, and the load holding time is 5 min. From the onset of structural cracking until the cracks approach through penetration, each load stage is set at 100 kN, with a loading rate not exceeding 10 kN/s, and the load holding time is 5 min. From the point where the cracks approach through penetration to structural failure, the loading is controlled by displacement, with each stage at 4 mm, a loading rate not exceeding 0.5 mm/s, and the load holding time is 5 min.

Experimental measurements

As shown in Fig. 15a, displacement meters WYJ1, WYJ2, and WYJ3 are arranged at the lower edge of the CT-shaped integrated joints under tension at the pure bending section and at the mid-span of the steel plate under tension to monitor the deflection of the specimen. Steel plates, under tension and compression at the pure bending section, are evenly arranged with the strain gauges SC1, SC2, SC3, ST1, ST2, and ST3 at a spacing of 300 mm to monitor their strain. The strain gauges JG1 and JG2 are arranged on the mid-span surface of the shear connector to consider its possible shear failure. The strain gauges JC1, JC2, JT1, and JT2 are arranged on the surface of the CT-shaped integrated joints at the pure bending section to monitor their damage. As shown in Fig. 15b, the surface of the pure bending section is sprayed with a speckle pattern, and a binocular vision camera system (two Optronis CL600 high-speed cameras) is adopted. Based on videogrammetric measurement technology, the three-dimensional full field strain of the pure bending section is monitored through stereoscopic matching and target tracking to investigate whether the plane section assumption is tenable²⁵.

Finite element model

Considering the influence of steel plate thickness, filled concrete strength, and shear connector spacing on the structure performance, as shown in Table 3, a total of 15 FE models were set, of which FE model W14 is consistent with the bending test specimen.

As shown in Fig. 16, establish FE models according to the bending test specimen (Fig. 14). Steel plates, filled concrete, grouting material, and shear connectors are meshed using C3D8R elements (a linear brick element with reduced integration). Steel plates and shear connectors are made of Q235 steel, a nonlinear isotropic/kinematic hardening model in the ABAQUS material library is used for the steel²⁶. The mass density of steel material is 7.85 × 10^–9 g/mm³. For the elastic behavior of steel material, the elastic Young’s modulus and Poisson’s ratio are defined as 200 GPa and 0.3. For the plastic behavior of steel material, the yield strength, ultimate strength and plastic Young’s modulus are defined as 235 MPa, 420 MPa and 2 GPa. The constitutive model of filled concrete and grouting material adopts the concrete damage plasticity model in the ABAQUS material library. The mass density of concrete material is 2.5 × 10^–9 g/mm³. The Young’s modulus ranges from 31.5 to 36.0 GPa, and the Poisson’s ratio is 0.2. For the concrete damaged plasticity, the dilation angle of 30°, flow potential eccentricity of 0.1, the ratio of biaxial/uniaxial compressive strength of 1.16, invariant stress ratio of 0.667 and viscosity parameter of 0.005 are set respectively.

The interactions among the steel, concrete, and grouting material are simulated by surface-to-surface contact pairs, followed by the hard contact in the normal direction to the interacting surface and the friction coefficient of 0.6 in the tangential direction to the interacting surface²⁷. Shear connectors are embedded in the whole model. To prevent stress concentration at the support and loading positions, steel cushion blocks (10 mm thick) are set at the corresponding positions, and the elastic modulus is 100 times that of the steel. The contact between the steel plates and the cushion blocks are constrained by the “Tie” constraint in ABAQUS. FE models adopt the simply supported mode to carry out the four-point bending loading test. The bottom of the steel cushion block located on the left side of the bottom of the structure is restrained against moving in any directions, while the one on the right side is restrained only in Y and Z directions. Two reference points are established on the surfaces of the steel cushion blocks at the top of the structure, and these points come in contact with the blocks by the coupling constraint. By applying vertical displacements to these reference points, the displacement-controlled loading mode is applied, which is conducive to the convergence of FE models.

Test and FE model results

Failure models

Figure 17 shows that the failure models and deformed shapes of the MPJ & JAS tunnel structure of the FE simulation are completely consistent with that of the bending test. The MPJ & JAS tunnel structure shows three typical deformed shapes: shape 1 is the void deformation between the longitudinal plate and the filled concrete, it generates firstly and becomes more serious with the increase of load; shape 2 is the torsional deformation of the top CT-shaped integrated joint under compression, and the compression steel plate tends to buckle slightly with the joint torsion intensifies; shape 3 is the severe tensile failure of the bottom CT-shaped integrated joint under tension, the severe joint deflection deformation results in the grouting material being crushed and the joint finally fail in a state of void and opening. Figure 18 shows that the axial forces of midspan bottom CT-shaped integrated joints when structure fails are 1558.438 kN to 1602.454 kN, which is 194.805–200.307 MPa when converted into the average section stress (section area: 500 mm × 16 mm). The average section stress is almost the same as that of 207.708 MPa in the joint tensile test (tensile strength: 99.7 kN; section area: 30 mm × 16 mm), further demonstrating that the CT-shaped integrated joint is in a tensile failure state. Judging from bending test and FE analysis results, the CT-shaped integrated joint is obviously the weakest part of the MPJ & JAS tunnel structure, and its tensile failure directly induces the structure’s failure.

Crack behaviors

According to the bending test, the first crack occurred at the bottom shear connectors under the loading points when loaded to 851 kN. When loaded to 996 kN, cracks were generated from CT-shaped integrated joints and spread to the surrounding. Meanwhile, voids formed between the longitudinal plate and the filled concrete. When loaded to 1440 kN, cracks were generated from the bottom shear connectors of the pure bending section and spread obliquely upward to the loading points. As the loading continues, more and more cracks developed from the outer bottom shear connectors. The experimental crack distribution is shown in Fig. 19a, it was found that almost all cracks were generated from CT-shaped integrated joints and bottom shear connectors due to stress concentration, and those at bottom shear connectors developed obliquely upward in a direction about 45° deviated from the horizontal axis. Figure 19b shows the cracks observed from the FE analysis. The contour plot of the tensile damage variable, i.e., DAMAGET is used to represent the tensile cracks in the concrete. Comparing the crack distribution of test and FE analysis, it shows that the FE model can capture the most of cracks in the concrete.

Load–deflection response and stress–strain distribution

The load–deflection curves obtained from the bending test specimen and the FE model W14 are generally similar in form, especially in the elastic stage, as is shown in Fig. 20. In the bending test, the mid-span deflection where the structure fails is 22.86 mm; this is only 0.3% different from the 22.93 mm result from the FE analysis, indicating that the FE analysis can effectively predict the structural deformation. However, the ultimate load obtained from the bending test and the FE analysis are 2305.19 and 1863.53 kN, respectively (a difference of 19%). This is mainly because the FE analysis does not consider the characteristics of the high-performance grouting material. Therefore, the strength of the grouting material is underestimated, resulting in a decrease in the strength of the CT-shaped integrated joint and causing a conservative ultimate load in the FE analysis. Overall, the bending test result verifies the reliability of the FE analysis.

The strain measurement results of the bending test are shown in Fig. 21. The top steel plate (under compression) does not yield when the structure fails, and the bottom steel plate (under tension) begin to yield, but the yield strain remains small. The top CT-shaped integrated joints of the pure bending section do not yield, and the strain is small. However, the bottom CT-shaped integrated joints of the pure bending section do yield, and the yield strain is large. The shear connections do not yield, and the strains are almost negligible. As shown in Fig. 22, the stress distribution of the FE results can more clearly show that the stress of the top steel plate on both sides of the joint is generally greater than that of the top CT-shaped integrated joint, and neither of them yields. Conversely, the stress of the bottom CT-shaped integrated joint is generally greater than that of the bottom steel plate, all bottom CT-shaped integrated joints and midspan bottom steel plate yield, especially the yield stress of the midspan joints is serious. The strain distribution results of bending test and the stress distribution results of FE model are mutually corroborated. This stress–strain distribution is consistent with the failure modes of torsional deformation of compression joints and tensile failure of tension joints, indicating that special attention should be paid to the improvement of CT-shaped integrated joint performance in order to improve the MPJ & JAS tunnel structure performance.

According to the videogrammetric measurement result shown in Fig. 23, it found that the strain field distribution in the pure bending section is basically linear along the section height, indicating that the plane section assumption is tenable.

Influence parameters

The failure models, crack behaviors, load–deflection response, and stress–strain distribution of the FE model W14 agreed with the bending test results. Hence, FE models can be used to analyze the influences of steel plate thickness, filled concrete strength, and shear connector spacing on the MPJ & JAS tunnel structure performance.

The influences of the steel plate thickness are shown in Fig. 24. The yield load increases linearly as the steel plate thickness increases, but the steel plate thickness exhibits little effect on the yield deflection. When the steel plate thickness is small (≤ 16 mm), the structure fails due to excessive buckling deformation of the steel plate. Increasing the steel plate thickness improves the ultimate load to a certain extent, as the ultimate load increases linearly along with the increase in steel plate thickness. However, when the steel plate thickness is large (> 16 mm), the ultimate load is mainly controlled by the performance of the CT-shaped integrated joint because the failure of the joint precedes the buckling failure of the steel plate. Therefore, as the steel plate thickness continues to increase, the ultimate load increases only minimally. Little difference is found in the ultimate deflection when the steel plate thickness is lower than 16 mm. However, when the steel plate thickness does exceed 16 mm, the ultimate deflection suddenly decreases linearly, and the structure is in brittle failure. This is primarily due to the increase in structural stiffness as the steel plate thickness increases. In conclusion, it is not necessarily better to have thicker steel plates, a 16 mm thick steel plate is suitable for the MPJ & JAS tunnel structure, ensuring that the requirements of structural bearing capacity and ductile failure are met.

The influences of filled concrete strength are shown in Fig. 25. When the filled concrete strength is low (< C50), the tensile steel plate does not yield, and the structure mainly fails by concrete shear failure. Therefore, the ultimate load increases as the filled concrete strength increases. However, when the filled concrete strength is high (≥ C50), the structure fails primarily due to the bending yield of the steel plate, and increasing the filled concrete strength results in little effect on the ultimate load.

The influences of shear connector spacing are shown in Fig. 26. The deflection without the shear connector is large, and the buckling deformation of the steel plate and the void between the steel plate and the filled concrete are severe. The shear connectors can transmit the interface shear force between the steel plate and the concrete as well as provide a strong pull-out resistance; in turn, this improves the stability of the steel plate by ensuring that the steel plate and the concrete are closely connected so they work cooperatively. Shear connectors reduce both the degree of buckling deformation of the steel plate and the structural deflection deformation; however, they hardly affect the ultimate load, and the shear connector spacing demonstrates negligible influence on the ultimate load. Therefore, shear connectors can be used as a constructional measure to reduce structural deformation.