Abstract Estimation of the required armor size is a major task in the design of coastal structures under wave loading such as breakwaters and revetments. Several semi-empirical formulas have been developed for this purpose. However, these formulas are often either limited to certain water depth conditions or do not incorporate the permeability of the structure in an appropriate way. The main objectives of this study are to (a) develop a unified physically sound formula for the estimation of the required rock size in all relevant water depth conditions and (b) to relate the effects of the permeability of the structure directly to physical parameters. To achieve these, first a comprehensive data base of deep and shallow water experiments within the design conditions was built. Then physical reasoning along with a robust data mining approach, i.e. M5 model tree, were used to develop formulas for armor stability. In the stability formula, wave characteristics such as the significant wave height and spectral energy mean period (Tm-1,0) are invoked while the permeability is incorporated using the ratio between the size of the core material and the armor stones. Accuracy metrics such as discrepancy ratio and scatter index indicated high performance of the model in different conditions. Finally, a probabilistic formula and some guidelines are provided for practicing engineers.

中文翻译：

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岩石装甲碎石堆结构稳定性研究

摘要 估计所需的装甲尺寸是防波堤和护岸等波浪载荷下沿海结构设计中的一项主要任务。为此，已经开发了几个半经验公式。然而，这些公式通常要么限于某些水深条件，要么没有以适当的方式结合结构的渗透性。本研究的主要目标是 (a) 制定统一的物理合理公式，用于估计所有相关水深条件下所需的岩石尺寸，以及 (b) 将结构渗透率的影响直接与物理参数相关联。为了实现这些，首先在设计条件下建立了一个综合的深水和浅水实验数据库。然后是物理推理以及强大的数据挖掘方法，即 M5 模型树，用于开发装甲稳定性公式。在稳定性公式中，调用了有效波高和光谱能量平均周期 (Tm-1,0) 等波浪特征，同时使用芯材和装甲石的尺寸之间的比率来考虑渗透率。差异率和分散指数等准确度指标表明模型在不同条件下的高性能。最后，为实践工程师提供了一个概率公式和一些指导方针。差异率和分散指数等准确度指标表明模型在不同条件下的高性能。最后，为实践工程师提供了一个概率公式和一些指导方针。差异率和分散指数等准确度指标表明模型在不同条件下的高性能。最后，为实践工程师提供了一个概率公式和一些指导方针。