准确体现原型冲刷的物理模型对桩基冲刷工程设计至关重要。受比尺效应的影响，传统的小比尺波流水槽物理模型通常不能正确体现原型桩基周围的平衡冲刷深度，而基于小比尺模型试验数据的平衡冲刷深度公式的适用性也受到了极大限制。因此该文通过量纲分析和相似理论，分析了波浪条件下比尺对原型与模型之间Shields数的影响，并且分别在泥沙粒径相等和泥沙粒径相似的基础上给出不同紊流情况时比尺与Shields数的关系；此外，通过大比尺模型试验获取不同近底水质点的速度用于改进模型Shields数，从而削弱比尺效应的影响。基于改进后的Shields数，现有平衡冲刷深度和相应冲刷坑体积量的公式的预测精度得到了提升。

Objective: The physical model that accurately reflects the actual scour of the prototype is essential for engineering design. The traditional small-scale flume models usually fail to properly reflect the equilibrium scour depth around monopile foundation of the prototype due to scale effect, and the applicability of equilibrium scour depth formulae based on small-scale model experimental data is greatly limited. This study aims to modify the Shields number to reduce the impact of scale effect and improve the prediction accuracy of existing equilibrium scour depth formula and the corresponding scour hole volume formula by analyzing the impact of scale on the Shields number in different turbulent flow regions. Methods: The impact of scale on the Shields number between the prototype and the model under wave conditions is analyzed based on dimensional analysis and similarity theory. The relationships in different turbulent flow are respectively provided under the condition of equal and similar sediment particle size and verified by experimental data. Moreover, different velocities of water particle at the bottom are obtained through large-scale model tests to modify the definition of the model Shields parameter, thereby reducing the impact of scale effect. The accuracy of the existing formulae for equilibrium scour depth and corresponding scour hole volume is also analyzed, based on the modified Shields parameter. Results: The results of dimensional analysis and similarity theory showed that: 1) The ratio of the Shields number between the prototype and the model is greater than 1 in both rough and smooth turbulent flow under the condition of equal sediment particle size. The Shields number between the prototype and the model is equal only when the scale is 1, and the ratio between them gradually increases as the scale increases. 2) The ratio of the Shields number between the prototype and the model is always 1 in rough turbulent flow under the condition of similar sediment particle size. The ratio is less than 1 in smooth turbulent flow. It is only 1 when the scale ratio is 1, and becomes smaller as the scale increases. 3) Compared with the ratio of the Shields number between the prototype and the model under the condition of equal sediment particle size, the ratio under the condition of similar sediment particle size is closer to 1 in smooth turbulent flow region with the same scale. 4) The mean velocity value and mean value of the one third highest velocities are used respectively to modify the definition of Shields number in both rough and smooth turbulence flow when the sediment particle sizes of the prototype and model are equal, thereby reducing the impact of scale effect and improving the prediction accuracy of the formulae for equilibrium scour depth and scour hole volume. Conclusions: Through the dimensional analysis and similarity theory, the impact of scale on the Shields number between the prototype and model in both rough and smooth turbulent flow under the condition of equal and similar sediment particle size is provided and verified by experimental data. The definition of the Shields number in different turbulent flow under the condition of equal sediment particle size is modified to reduce the impact of scale effect. The prediction accuracy of the existing formulae for equilibrium scour depth and scour hole volume is improved, based on the modified the Shields number.