This study proposes a scour equation for abutments that is based on a combination of Newton’s second law and a turbulence model comprised of a pair of isotropic vortices. A control volume of the scour hole is considered on which the sum of forces equals nil. The effect of abutments on local scour is usually modelled by an empirical K-factor for which there is no physical description available. Here, we deduce a relation between abutment shape and the maximum scour depth by using engineering tools from turbulence science. We pay attention to the scour effects of several types of abutments, such as submerged, non-submerged, permeable and impermeable and the impact of bed protection. We consider the highly nonlinear combination of constriction and local scour. The unknowns in the proposed scour equation are calibrated and validated with several scour tests.

本研究提出了一个基台冲刷方程，该方程基于牛顿第二定律和由一对各向同性涡流组成的湍流模型的组合。考虑冲刷孔的控制体积，其上的力之和等于零。基台对局部冲刷的影响通常由经验K建模- 没有可用物理描述的因素。在这里，我们使用湍流科学的工程工具推导出桥台形状和最大冲刷深度之间的关系。我们关注几种类型的基台的冲刷效果，例如浸没式、非浸没式、透水和不透水以及床保护的影响。我们考虑收缩和局部冲刷的高度非线性组合。提议的冲刷方程中的未知数通过几个冲刷测试进行校准和验证。