Abstract:
Abstract: Scattered root stone loss under the action of water flow is one of main reasons causing bank instability. Drag force is an important parameter for understanding the related mechanisms. In this paper, we investigated the effects of shape and Reynolds number on the drag force coefficient of root stone under the action of water flow. Scattered root stones on Yellow River bank had the width-height ratio of 1.01-2.55, the length-height ratio of 1.29-3.40, and unit weight of 17.70-26.20 kN/m3. Based on these investigated results, samples of different shapes (block and ball) and sizes were prepared. A set of force measurement system was developed for determining velocity and pressure signals simultaneously, which could measure horizontal drag force under the action of water flow on balls and different sizes of blocks by controlling water flow of sloping flume. Based on the analysis on the relationship between Reynolds number, shape and drag force, drag coefficient function of block was calibrated. Results showed that the drag force coefficients of underwater balls or balls were not influenced by the flow and shape. Their drag force coefficients were 0.40-0.56. However, the drag force coefficient of blocks was affected by the water flow and object shape. When the Reynolds number of block was less than 3×104, the drag force coefficient changed in hyperbolic shape.When the Reynolds number of block was greater than 3×104, if the width-height ratio of upstream face was less than or equaled to the length-height ratio of upstream of side elevation, the drag coefficients tended to be constant values of 0.80-0.90, or if the width-height ratio of upstream face was more than the length-height ratio of upstream of side elevation, the drag coefficients tended to be constant values of 1.00-1.10. Considering the interaction effects of the Reynolds number and block shape, the horizontal drag force coefficient formula of block stone could be obtained under 7 combination conditions. Based on the measured data, the drag coefficients under different application conditions were fitted by least square method. The formulas of drag force coefficients of block stone were presented under the influence of Reynolds number and shape parameters. And then the horizontal drag force calculation formula was suggested with the projected area of different objects in the flow direction. It could more accurately reflect the force characteristics of the underwater root stone. The goodness of fit of drag force coefficient reached above 0.90, and the mean of relative error was 8.7%. After correction the mean of relative error of drag force was only 7.5%. Compared to the regular method considering the drag coefficient as a constant of 0.45 (the mean relative error of drag force), the corrected method had a higher accuracy, indicating that the modification in this study is reasonable and the formula established is useful for block root stones. The research results make up for inadequacy of theoretical basis for drag force analysis of underwater root stones in the process of revetment engineering stability calculation. These results can be applied to planning and designing revetment projects in water conservancy projects.