Dam foundation is subjected to a larger impact force when debris flow runs up

causing stress concentration and local impact failure. To address this problem

in this study the vertical structures are optimized into arc-shaped dams. Based on the principle of momentum and energy conservation

the theoretical calculations of the impact process of debris flow and arc-shaped dam are carried out

and the formulas of impact force and maximum run-up height of debris flow are deduced. The theoretical formulas are verified through a series of physical model tests of debris flow impact arc-shaped dam. The results show that the results of the physical model are highly consistent with those of the theoretical calculations

indicating that the proposed theoretical formulas are applicable in the calculation of the impact of debris flow on arc-shaped dam. The debris velocity

impact force and the maximum run-up height are proportional to the flume slope of debris flow. The impact force and the maximum run-up height are mainly controlled by Froude number(Fr)

flume slope(?)

and arc-shaped radius(R). Both the impact force and the maximum run-up height have quadratic relationships with the Froude number

and are inversely proportional to the cosine of the flume slope. Compared with the rigid vertical structures

the arc-shaped dams have no signicicant influence on the maximum run-up height

but it can reduce the normal impact force on the dam considerably

and the structure strength can also be enhanced by the strengthening of local structure. This study provides a theoretical and technical support for the dam structure design.