Experimental and Theoretical Study on the Crack Defect Effect on the Bearing Capacity of a Rectangular Culvert
Abstract
:1. Introduction
2. Experimental Study on External Pressure of Rectangular Culvert with Crack Defects
2.1. Experiment Ideas
2.2. Experiment Method and Procedure
2.2.1. Specimen Preparation
2.2.2. Stress and Displacement Measurement
2.2.3. Loading
2.3. Test Results and Analysis
2.3.1. Specimen Failure Mode
2.3.2. Influence of Crack Depth on Rectangular Culvert UBC
3. Calculation Model of UBC of Rectangular Culvert with Crack Defects
3.1. UBC Calculation Model of Non-Defective Rectangular Culvert
- θA—Point A’s angular displacement;
- θC—Point C’s angular displacement;
- a—Average length of the rectangular culvert section, m;
- b—Average width of the rectangular culvert section, m;
- c—Longitudinal length of the rectangular culvert, m;
- i1—AM and CN rod line stiffness; see Formula (2);
- i2—AC rod line stiffness; see Formula (2);
- MAC—A-end bending moment of the AC rod;
- MCA—C-end bending moment of the AC rod;
- MAM—A-end bending moment of the AM rod;
- MMA—M-end bending moment of the AM rod;
- MNC—N-end bending moment of the CN rod;
- MCN—C-end bending moment of the CN rod;
- F—M, N point load, N.
- As—The combined cross-sectional area of stirrups within the section’s tensile zone, mm2;
- fcc—Compressive strength of concrete, MPa;
- frt—Stirrup tensile strength, MPa;
- frc—Stirrup compressive strength, MPa;
- x—Compression zone height, mm;
- α1—The equivalent rectangular stress coefficient in the concrete compression zone is 1.0 for concrete grades of C50 or lower.
- Mu—Section under the bending moment, N·m;
- As1—Total stirrup cross-sectional area in the section’s compression zone, mm2;
- h0—Section’s effective depth, mm;
- h—Sectional height, mm;
- as—Thickness of the inner protective layer of the rectangular culvert, mm;
- as1—Thickness of the outer protective layer of the rectangular culvert, mm.
- Fmax—The maximum load of the rectangular culvert, N;
- Mmax—Maximum bending moment of the cross-section, N·m.
3.2. UBC Calculation Model for Cracked Rectangular Culvert
- Mu1—The maximum bending moment of the rectangular culvert section with crack defects, N·m;
- kc—Reduction coefficient of the concrete compressive strength;
- kr—Compressive strength reduction factor of the concrete/steel bar (the reduction in the tensile strength of the steel bar is roughly equivalent to that of the compressive strength);
- kcr—The bond strength reduction coefficient between the concrete and steel bar;
- t—Fracture depth, mm;
- x1—Crack defect section concrete compression zone height, mm.
4. Conclusions
- In the trilateral external load test, the failure process of the rectangular culvert can be categorized into three distinct phases: the initial stage with no visible cracks, the crack progression stage, and the final failure stage. During the intact stage, the load applied to the rectangular culvert increased proportionally with displacement. In the crack progression phase, the load continued to grow as the displacement increased, with a decreasing curvature of the load–displacement curve, and cracks gradually appeared and expanded along the culvert wall. In the final failure stage, the rectangular culvert’s structural integrity was compromised, with the load first increasing and then declining.
- Because the change in crack depth will change the bond strength between reinforced concrete, it is necessary to discuss the reduction coefficient kcr of the bond strength between reinforced concrete. Based on the comparison between the test results and the theoretical calculation of the rectangular culvert’s UBC, it can be inferred that the reduction coefficient kc for the bond strength of reinforced concrete is linked to the ratio of the crack depth to the protective layer thickness. The error between the theoretical calculation correction value and the test value obtained by this calculation method is about 10%, so the calculation formula is suitable for the calculation model of the UBC of the crack defect pipeline considering only the single influence factor of the crack depth.
- The effect of crack depth on the bearing capacity of rectangular culverts can be considered as a reduction in the wall thickness. When the crack depth is less than or equal to the thickness of the concrete protective layer, the UBC of the rectangular culvert reduces as the crack depth increases. When the crack depth equals the protective layer’s thickness, both the test value and calculated value of the UBC decrease by 31%, with an error of less than 10%. This study demonstrates that an increasing crack depth leads to a substantial reduction in the bearing capacity, with implications for the design and maintenance of urban drainage structures. In the follow-up monitoring of components, if cracks are found, surface repair, injection repair, replacement repair, paste repair, and other technologies can be used to treat the cracks according to their different causes and characteristics.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Testing Material | Material Type and Model |
---|---|
Cement | Normal Portland cement (P.I.42.5) |
Sand | Manufactured sand (60–80 mesh) |
Longitudinal bar | Hot rolled plain steel bars (5 mm) |
Stirrup | Hot rolled plain steel bars (5 mm) |
Compressive strength of concrete | 23.4 MPa |
Stirrup tensile strength | 650 MPa |
Groups | Influencing Factors of Defects | Defection Evaluation | Quantity |
---|---|---|---|
A1 | Undamaged | Zero defect | 1 |
C1 | Crack depth | Two cracks are positioned on the inner side of the upper and lower surfaces (ULSs) of the rectangular culvert, and two cracks are arranged on the outer side of the left and right surfaces. The depth is 1/3 of the protective layer thickness, with a width of 0.2 mm. | 1 |
C2 | Crack depth | Two cracks are positioned on the inner side of the ULSs of the rectangular culvert, and two cracks are arranged on the outer side of the left and right surfaces. The depth is 2/3 of the protective layer thickness, with a width of 0.2 mm. | 1 |
C3 | Crack depth | Two cracks are positioned on the inner side of the ULSs of the rectangular culvert, and two cracks are arranged on the outer side of the left and right surfaces. The depth is the protective layer thickness, with a width of 0.2 mm. | 1 |
Groups | Displacement at UBC (mm) | UBC (N) |
---|---|---|
A1 | 9.65 | 7768.24 |
C1 | 8.42 | 6738.31 |
C2 | 16.98 | 6389.86 |
C3 | 15.57 | 5218.53 |
Groups | Bond Strength Reduction Factor of Reinforced Concrete | The Theoretical Calculation Value of the UBC (N) |
---|---|---|
A1 | 1 | 7176.17 |
C1 | 0.9 | 6418.77 |
C2 | 0.8 | 5670.65 |
C3 | 0.7 | 4931.63 |
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Wang, W.; Peng, S.; Chen, X.; Mi, R.; Wu, Q.; Zhang, P. Experimental and Theoretical Study on the Crack Defect Effect on the Bearing Capacity of a Rectangular Culvert. Buildings 2024, 14, 3755. https://doi.org/10.3390/buildings14123755
Wang W, Peng S, Chen X, Mi R, Wu Q, Zhang P. Experimental and Theoretical Study on the Crack Defect Effect on the Bearing Capacity of a Rectangular Culvert. Buildings. 2024; 14(12):3755. https://doi.org/10.3390/buildings14123755
Chicago/Turabian StyleWang, Wanqiong, Shouhai Peng, Xiaolong Chen, Rongxi Mi, Qingqing Wu, and Peng Zhang. 2024. "Experimental and Theoretical Study on the Crack Defect Effect on the Bearing Capacity of a Rectangular Culvert" Buildings 14, no. 12: 3755. https://doi.org/10.3390/buildings14123755
APA StyleWang, W., Peng, S., Chen, X., Mi, R., Wu, Q., & Zhang, P. (2024). Experimental and Theoretical Study on the Crack Defect Effect on the Bearing Capacity of a Rectangular Culvert. Buildings, 14(12), 3755. https://doi.org/10.3390/buildings14123755