Behavior of the Vault in Column-Free Large-Span Metro Stations Under Asymmetric Loading
Abstract
1. Introduction
2. Engineering Background
3. Experimental Method and Results
- Arch segments A and B were precast in a factory. After reaching the required concrete strength, they were transported to the construction site.
- The precast segments were assembled on site to form a three-hinged arch, as shown in Figure 3a. Cast in situ concrete was then placed on top of the precast layer to form an integral arch.
- The test was carried out using a force–displacement hybrid control method [27]. In this test, the horizontal ground pressure was set to zero, while the vertical ground pressure was increased by a safety factor of 1.35. A total of 46 iron blocks were placed on the upper surface of the arch to simulate vertical ground pressure, as illustrated in Figure 4c. By adjusting both the applied load and the prescribed displacement, the internal forces and deformations of the stacked arch were analyzed.
3.1. Test Scheme
- A crane was used to stack 46 iron blocks in sequence from the fixed arch foot to the arch crown according to the numbering (see Figure 4b for the stacking order). By adjusting the jack load, the displacement of the sliding support was controlled to remain within the range of 1 mm from the initial position during the reloading process until the half-span stacking load was completed.
- After the completion of the half-span stacking load, the horizontal sliding of the left arch foot was achieved by controlling the jack, with an average speed of 0.3 mm per loading level, and the total displacement could reach 3 mm (see Figure 4b). The right arch foot was clamped. The sliding displacement was applied by adjusting the cable tension. Finally, the sliding arch foot was fixed with a restraint, marking the completion of the experiment.
- The counterweight blocks were unloaded in the reverse order of the stacking order, and the support displacement was adjusted back to the initial position.
3.2. Test Equipment
3.3. Monitoring Items
3.4. Structural Deformation
3.5. Structural Stresses
3.5.1. Precast Layer
3.5.2. Cast In Situ Layer
4. Structural Analysis
4.1. Deflection Analysis of the Arch Element
4.2. Analytical Solution of the Clamped Circular Arch Under Asymmetric Loads
4.3. Internal Force Analysis of the Arch Element
5. Discussion
6. Conclusions
- When the weight of the steel blocks reaches 1.35 times of the vertical ground pressure, the vertical displacement of the arch crown and arch foot, as well as the staggered value and opening value of the joint change slightly. It indicates that the precast layer and cast in situ layer can work together as a whole. When the prescribed displacement of the arch foot is increased to 3 mm, this deflection of the vault crown of 3.79 mm is only 0.02% of the span of the vault. Cross sectional stiffness of the vault combined with precast and cast in situ method is acceptable.
- In the half span loading stage, the full section is compressed, and the arching effect is obvious. When the prescribed displacement of sliding foot is increased further, the arch effect gradually weakened. The maximum tensile stress and compressive stress of the rebars occur at one half of the left and right arches. The change in-internal force of the rebars is basically within the range of −30 MPa and 20 MPa. The results are less than the yield stress of the rebars. It is proven that the stacked arch has a large safety reserve, and there is room for optimal design of the structure.
- The computed value results in an increase in the maximum deflection of the arch by 13.67%, compared to the experimental results, which indicates that the reliability of the numerical simulation method is verified under the same boundary conditions.
- In order to check the validity of the derived analytical solutions of the clamped arch for ground pressure resulting from the vertical ground pressure. Compared to the numerical simulation, the maximum error range is 7.32% to 30.14%. The results are in good agreement with each other. It is verified the reliability of the analytical solution of the clamped circular arch under the asymmetric loads derived from the tested arch. The consistency demonstrated by the mutual verification of full-scale test results, numerical simulation results, and analytical solutions also provides strong support for the reliability of the numerical model and the general applicability of the conclusions.
- During this test, the response of the stacked arch structure to the arch feet displacement is obvious. Therefore, the lateral displacement of arch feet is an important index to control the safety of underground arch structures.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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Load Form | Control Variable | Deflection at the Crown | ||
---|---|---|---|---|
Prescribed Displacement of the Sliding Foot (mm) | Load (kN) | Experimental Measurement (mm) | Numerical Simulation (mm) | |
Half span load | 3.0 | Vertical ground pressure × 1.35 | 3.79 | 4.39 |
Material | Cross-Section (m2) | Constraint Condition | Uniformly Distributed Line Load (kN/m) | Circular Distributed Line Load (kN/m) |
---|---|---|---|---|
Concrete (C40) | 1.0 | fixed constraints | 99.78 | 120.48 |
Safety Threshold | Internal Force | Crack Width (mm) | ||
---|---|---|---|---|
Displacement Calculation Value (mm) | Bending Moment (kN·m) | Axial Force (kN) | ||
2.29 | 244.38 | 224.92 | 0.02 | Cracks visible |
6.76 | 723.00 | 665.40 | 0.20 | Maximum limit [33] |
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Zhang, J.-L.; Qiao, G.-H.; Zhou, Z.; Li, C. Behavior of the Vault in Column-Free Large-Span Metro Stations Under Asymmetric Loading. Appl. Sci. 2025, 15, 10944. https://doi.org/10.3390/app152010944
Zhang J-L, Qiao G-H, Zhou Z, Li C. Behavior of the Vault in Column-Free Large-Span Metro Stations Under Asymmetric Loading. Applied Sciences. 2025; 15(20):10944. https://doi.org/10.3390/app152010944
Chicago/Turabian StyleZhang, Jiao-Long, Guan-Hua Qiao, Zheng Zhou, and Cao Li. 2025. "Behavior of the Vault in Column-Free Large-Span Metro Stations Under Asymmetric Loading" Applied Sciences 15, no. 20: 10944. https://doi.org/10.3390/app152010944
APA StyleZhang, J.-L., Qiao, G.-H., Zhou, Z., & Li, C. (2025). Behavior of the Vault in Column-Free Large-Span Metro Stations Under Asymmetric Loading. Applied Sciences, 15(20), 10944. https://doi.org/10.3390/app152010944