A study on distribution parameters for individual wave overtopping volume at vertical walls
-
摘要: 基于Weibull分布估算最大单波越浪量，关键在于准确确定其分布参数—形状参数和越浪率—的取值。现有研究多集中于深水与中等水深条件，对破波带内的分布参数特性尚缺乏系统分析。本文通过将实验水深范围扩展至相对水深0.9～4，覆盖破波带、中等水深与深水工况，重点考察相对水深、相对顶高、波陡和床面坡度4个无量纲变量对分布参数的影响，并建立适用于该扩展条件的参数估算方法。实验发现，在涵盖破波带的实验区间内，形状参数和越浪率随相对水深的变化均呈现类孤立波形态的单峰特征。基于这一现象，本文借鉴类孤立波函数形式，构建了分布参数的计算公式，进而实现对最大单波越浪量的预测。与现有模型相比，本文所提方法在实验范围内均表现出更低的预测误差，尤其在破波带浅水区域优势更为显著。Abstract: Estimating the maximum individual wave overtopping discharge based on the Weibull distribution crucially depends on the accurate determination of its parameters—namely, the shape parameter and the overtopping percentage. Existing research has primarily focused on deep and intermediate water depth conditions, with a lack of systematic analysis on the characteristics of these distribution parameters within the surf zone. This study extends the experimental range of relative water depths to 0.9−4, covering conditions in the surf zone, intermediate depths, and deep water. It specifically investigates the influence of four dimensionless variables—relative water depth, relative crest freeboard, wave steepness, and seabed slope—on the distribution parameters, and establishes a parameter estimation method applicable to these extended conditions. Experimental results indicate that within the range covering the surf zone, both the shape parameter and the overtopping percentage exhibit a unimodal characteristic, resembling the form of solitary waves, as the relative water depth changes. Based on this observation, the study draws on the solitary-wave-like functional form to formulate calculation formulas for the distribution parameters, thereby enabling the prediction of the maximum individual wave overtopping discharge. Compared to existing models, the proposed method demonstrates lower prediction errors across the experimental range, with its advantages being particularly significant in the shallow water regions of the surf zone.
-
图 2 实验布置的侧面图（a）和平面图（b）
Fig. 2 The side (a) and plane (b) views of the experiment set-up
图 3 基于液压传感器信号分析越浪量的示例
Fig. 3 A typical example of the analysis result from the signals of the pressure sensors
图 4 采用式(6)拟合单波越浪量数据在两种不同条件下的示例
Fig. 4 Examples of the typical fitting result of overtopping volume distribution with Eq. (6)
图 5 参数a的实验值分别与式（2）（a）和式（2'）（b）的计算值的比较
Fig. 5 Comparison between the values of a tested and predicted by Eq. (2) (a) and Eq. (2') (b)
图 6 b的实验值相对于相对水深ht/Hs0的整体分布情况
Fig. 6 The overall respones of b to relative water depth ht/Hs0
图 7 b值关于不同变量的均值和对该均值的直接拟合结果（点划线），以及公式化拟合结果（实线）
Fig. 7 Averaged values of b over different variables along with the direct (dot-dash) and fomulated fittings (solid)
图 8 b的实验值与式（11）预测值间的对比
Fig. 8 Comparison between the values of b tested and predicted by Eq. (11)
图 9 Pow的实验值相对于相对水深ht/Hs0的整体分布情况
Fig. 9 The overall respones of Pow to relative water depth ht/Hs0
图 10 Pow的实验值与式（13）预测值间的对比
Fig. 10 Comparison between the values of Pow tested and predicted by Eq. 13
图 11 Vmax实验值 与各模型预测值的比较
Fig. 11 Comparison between the values of Vmax tested and predicted by different models
表 1 试验条件安排
Tab. 1 The arrangement of test conditions
tan θ R0/cm ht/cm Hs0/cm T1/3/s Rc/Hs0 ht/Hs0 so N 1/10, 1/30 90, 92.5, 95 10.2～18.9 4.3～12.5 1.06～2.77 0.7, 1.0, 1.3 0.9, 1.1, 1.4, 2, 3, 4 0.015, 0.025, 0.035 108 
下载: 导出CSV
表 2 各模型关于Vmax预测值的误差参数结果
Tab. 2 Results of the error indexes for the estimate of Vmax by different models
公式 r μ R2 EurOtop 0.78 0.06 0.4 Victor 0.85 −0.1 −0.03 Nørgaard 0.86 −0.02 0.52 本文 0.91 0.01 0.85
下载: 导出CSV
-
[1] Franco L, de Gerloni M, van der Meer J W. Wave overtopping on vertical and composite breakwaters[C]//Proceedings of the 24th International Conference on Coastal Engineering. Kobe: ASCE, 1994: 1030−1045. [2] van der Meer J W, Janssen J P F M. Wave run-up and wave overtopping at dikes and revetments[R]. Delft Hydraulics, 1994. [3] Besley P. Wave overtopping of seawalls, design and assessment manual[R]. Oxfordshire: HR Wallingford Ltd, 1999. [4] Victor L, van der Meer J W, Troch P. Probability distribution of individual wave overtopping volumes for smooth impermeable steep slopes with low crest freeboards[J]. Coastal Engineering, 2012, 64: 87−101. doi: 10.1016/j.coastaleng.2012.01.003 [5] Hughs S, Thornton C, van der Meer J W, et al. Improvement in describing wave overtopping progresses[C]//Proceedings of the 33rd International Conference on Coastal Engineering 2012. [6] Nørgaard J Q H, Andersen T L, Burcharth H F. Distribution of individual wave overtopping volumes in shallow water wave conditions[J]. Coastal Engineering, 2014, 83: 15−23. doi: 10.1016/j.coastaleng.2013.09.003 [7] Gallach-Sánchez D. Experimental study of wave overtopping performance of steep low-crested structures[D]. Ghent: Ghent University, 2018. [8] Salauddin M, O’Sullivan J J, Abolfathi S, et al. New insights in the probability distributions of wave-by-wave overtopping volumes at vertical breakwaters[J]. Scientific Reports, 2022, 12(1): 16228. doi: 10.1038/s41598-022-20464-5 [9] Zanuttigh B, van der Meer J W, Bruce T, et al. Statistical characterisation of extreme overtopping wave volumes[C]//Allsop W, Burgess K. From Sea to Shore—Meeting the Challenges of the Sea: (Coasts, Marine Structures and Breakwaters 2013). London: ICE Publishing, 2013. [10] Mares-Nasarre P, Molines J, Gómez-Martín M E, et al. Individual wave overtopping volumes on mound breakwaters in breaking wave conditions and gentle sea bottoms[J]. Coastal Engineering, 2020, 159: 103703. doi: 10.1016/j.coastaleng.2020.103703 [11] Goda Y. Random Seas and Design of Maritime Structures[M]. 2nd ed. Singapore: World Scientific Publishing, 2000: 356−359. [12] Lashley C H, Brown J M, Yelland M J, et al. Comparison of deep-water-parameter-based wave overtopping with wirewall field measurements and social media reports at Crosby (UK)[J]. Coastal Engineering, 2023, 179: 104241, doi: 10.1016/j.coastaleng.2022.104241 [13] Goda Y. A performance test of nearshore wave height prediction with CLASH datasets[J]. Coastal Engineering, 2009, 56(3): 220−229. doi: 10.1016/j.coastaleng.2008.07.003 [14] Li Xiaoliang, Huang Guibiao. Study on effectiveness of solitary-wave-like form based on overtopping data from irregular wave tests[J]. China Ocean Engineering, 2024, 38(4): 701−710. doi: 10.1007/s13344-024-0055-5 [15] 李晓亮. 测深法: 基于液压传感器的越浪量测量方法[J]. 水运工程, 2017(2): 123−129. doi: 10.16233/j.cnki.issn1002-4972.2017.02.022Li Xiaoliang. Sounding method: a technique of wave overtopping measurement based on the hydraulic pressure sensors[J]. Port & Waterway Engineering, 2017(2): 123−129. doi: 10.16233/j.cnki.issn1002-4972.2017.02.022 [16] Li Xiaoliang. Formula of overtopping discharge of vertical seawall with a form similar to solitary wave function[J]. China Ocean Engineering, 2022, 36(5): 802−807. doi: 10.1007/s13344-022-0071-2 [17] EurOtop. Manual on Wave Overtopping of Sea Defences and Related Structures: An Overtopping Manual Largely Based on European Research, But for Worldwide Application[M]. 2nd ed. 2018. [18] Battjes J A, Groenendijk H W. Wave height distributions on shallow foreshores[J]. Coastal Engineering, 2000, 40(3): 161−182. doi: 10.1016/S0378-3839(00)00007-7 [19] Li Xiaoliang. A complete formulation of the Goda graph in a single form[J]. Ocean Engineering, 2023, 288: 115916. doi: 10.1016/j.oceaneng.2023.115916 -
计量
- 文章访问数: 98
- HTML全文浏览量: 45
- PDF下载量: 6
- 被引次数: 0
