Numerical Investigation of Extreme Wave-Induced Loading on Box Girder in Marine Environment
Abstract
:1. Introduction
2. Numerical Model
2.1. Governing Equations
2.2. Boundary Conditions
- (1)
- Boundary conditions at the wave-inlet: Based on the analytical solutions and the laboratory measurement of wave theory, the values of wave vertical velocity (v), horizontal velocity (u), surface displacement (η), k and ε are given on the wave-inlet (inlet wave maker) boundary.
- (2)
- Boundary conditions at the water bottom: On the bottom boundary, no-slip boundary is applied.
- (3)
- Rigid wall boundary conditions: The near wall function method was used along the rigid wall boundary in this numerical model [28]. The box girder boundary was taken as the rigid wall boundary.
- (4)
- Outlet boundary conditions: On the outlet boundary, in order to absorb the wave energy and make the wave going out of the outlet boundary without significant reflection, the Sommerfeld radiation conditions and a sponge layer was adopted. Larsen and Dancy proposed the sponge layer, which have very broad banded damping characteristics to absorb the wave energy [29]. In particularly, on the right of outlet boundary, the gradient of all hydrodynamic variables were assumed to be zero.
- (5)
- Boundary conditions at the free surface of water: In the present model, the actual pressure at the water surface should be equal to the atmospheric pressure and the relative pressure at the wave surface should be zero.
3. Model Verification
4. Results and Discussion
4.1. Effects of Wave Characteristic
4.1.1. Effects of Wave Height
4.1.2. Effects of Wave Period
4.2. Effects of Water Depth
5. Applications for Engineering Practice
- (1)
- Based on the given wave characteristics, we can determine the value of H/(gT2).
- (2)
- With the given water depth and by calculating the submerged coefficient from the submerged depth of the bridge, we can determine three coefficients, (a, b, c) from Figure 14.
- (3)
- The FHma and Fvmax can be calculated from Equations (7) and (8) with the coefficients, (a, b, c) obtained from Figure 15.
6. Conclusions
- (1)
- As shown in the validations, the present model overall agrees well with the experimental data under the same conditions;
- (2)
- The existence of a box girder can significantly affect the wave field around the box girder. Wave surges, wave breakings and wave run-up may occur on the surface of the box girder. Meanwhile, variations of wave pressure and wave profile around the box girder are quite different from the pressure contours and wave profile of T girder. It is necessary to investigate this type of coastal bridge girder under extreme wave conditions;
- (3)
- The maximum values of horizontal and vertical wave force increase with the increment of wave heights (H). With the increment of wave periods (T), the maximum horizontal force gradually decreases and thereafter, force gradually tends to stably increase. The maximum vertical (uplift) force increases first and then decreases, finally tending to stably decrease with the increment of wave periods (T). The increment of water depth (d) has negative effects on maximum horizontal forces. However, the effects of water depth (d) on maximum vertical force are much smaller than the effects on maximum horizontal force;
- (4)
- The mechanisms of extreme wave-induced wave forces on box girder may be different due to the variations of the submerged coefficients. Based on the present numerical model, the authors suggest a simplified procedure to estimate the horizontal and vertical of wave forces on coastal bridge box girder under various extreme wave conditions. The estimates of wave forces could provide a reference for the design and protection of the box girder coastal bridge under extreme wave conditions.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Different conditions | d = 10.59 m, H = 3 m, T = 11.2 s, Cs = 1 | d = 15.99 m, H = 4 m, T = 11.2 s, Cs = 0 | d = 15.99 m, H = 6 m, T = 11.2 s, Cs = 1 | d = 20.04 m, H = 4 m, T = 11.2 s, Cs = 1 | d = 20.04 m, H = 7 m, T = 11.2 s, Cs = 2 |
Proposed method (kN/m) | 25.64 | 26.82 | 51.05 | 35.15 | 43.74 |
Experimental data (kN/m) | 27.7093 | 28.5566 | 55.6371 | 36.9048 | 47.9507 |
Error | −7.52% | −6.08% | −8.24% | −4.75% | −8.78% |
Different conditions | d = 10.59 m, H = 3 m, T = 11.2 s, Cs = 1 | d = 15.99 m, H = 4 m, T = 11.2 s, Cs = 0 | d = 15.99 m, H = 6 m, T = 11.2 s, Cs = 1 | d = 20.04 m, H = 4 m, T = 11.2 s, Cs = 1 | d = 20.04 m, H = 7 m, T = 11.2 s, Cs = 2 |
Proposed method (kN/m) | 356.06 | 299.86 | 528.84 | 438.55 | 652.61 |
Experimental data (kN/m) | 361.9094 | 295.8260 | 520.5083 | 426.9431 | 666.6768 |
Error | −1.62% | 1.36% | 1.60% | 2.72% | −2.11% |
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Xiang, B.; Yang, Z.; Zhu, B.; Yin, R. Numerical Investigation of Extreme Wave-Induced Loading on Box Girder in Marine Environment. J. Mar. Sci. Eng. 2018, 6, 16. https://doi.org/10.3390/jmse6010016
Xiang B, Yang Z, Zhu B, Yin R. Numerical Investigation of Extreme Wave-Induced Loading on Box Girder in Marine Environment. Journal of Marine Science and Engineering. 2018; 6(1):16. https://doi.org/10.3390/jmse6010016
Chicago/Turabian StyleXiang, Baoshan, Zhiying Yang, Bing Zhu, and Ruitao Yin. 2018. "Numerical Investigation of Extreme Wave-Induced Loading on Box Girder in Marine Environment" Journal of Marine Science and Engineering 6, no. 1: 16. https://doi.org/10.3390/jmse6010016
APA StyleXiang, B., Yang, Z., Zhu, B., & Yin, R. (2018). Numerical Investigation of Extreme Wave-Induced Loading on Box Girder in Marine Environment. Journal of Marine Science and Engineering, 6(1), 16. https://doi.org/10.3390/jmse6010016