Abstract Toe design is an important task for coastal engineers as it ensures the stability of the main armor layer and prevents scour in front of the armor slope. Several laboratory experiments have been conducted to investigate the toe stability using different testing approaches, i.e. damage due to a single test condition and cumulative damage due to a number of conditions. In addition, the methods of measuring and reporting damage to the toe are not the same as some researchers have counted only stones that were washed away from the toe; while others counted all the stones that have been displaced. Several formulas with different levels of success have been developed based on these studies. However, the scatter in the results is large and effects of some parameters are disregarded. The aims of this study are (a) to briefly review the abovementioned differences and exiting formulas, and (b) to develop a and physically sound formula for common design conditions, which considers the effect of all governing parameters. To achieve this, first a comprehensive data base from existing reliable studies was collected. Then nondimensional parameters which capture effects of governing parameters such as wave height, wave period, water depth, toe depth, toe width and foreshore slopes were deployed to develop a stability formula using physical reasoning and regression analysis. The new formula outperforms existing formulae for toe stability. The coefficient of variation of the formula was also determined to be used for probabilistic design applications. Finally, some design hints are provided for practitioners.

中文翻译：

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论碎石堆结构的趾部稳定性

摘要 趾部设计是海岸工程师的一项重要任务，它保证了主装甲层的稳定性，防止了装甲坡前的冲刷。已经进行了几个实验室实验以使用不同的测试方法来研究脚趾稳定性，即由于单一测试条件造成的损坏和由于多种条件造成的累积损坏。此外，测量和报告脚趾损伤的方法也不尽相同，因为一些研究人员只计算从脚趾上冲走的石头；而其他人则计算所有被转移的石头。在这些研究的基础上，已经开发了几个具有不同成功程度的公式。但是，结果的分散性很大，并且忽略了某些参数的影响。本研究的目的是 (a) 简要回顾上述差异和现有公式，以及 (b) 为常见设计条件开发一个物理上合理的公式，该公式考虑了所有控制参数的影响。为了实现这一目标，首先从现有的可靠研究中收集了一个综合数据库。然后，利用物理推理和回归分析，利用无量纲参数捕捉控制参数的影响，例如波高、波浪周期、水深、趾深、趾宽和前滨坡度，以开发稳定性公式。新配方优于现有的脚趾稳定性配方。公式的变异系数也被确定用于概率设计应用。最后，为从业者提供了一些设计提示。