Valley incision by debris flow is an important process in creating and maintaining the topography of a valley, in addition to explaining the significant growth of the magnitudes of debris flow hazards. In this paper, we introduce a semi-empirical method to quantitatively estimate the valley incision process by debris flows over complex bed surface. We first reproduce natural bed surface across the valley by a polyline, and use a hydrograph of discharge versus time to represent the temporal variation of debris flow process. The presented method subsequently predicts the debris flow behavior over an irregular bed surface. A dynamic erosion law considers the solved debris flow behavior and estimates an instantaneous erosion rate. Finally, the accumulative incision depth of bed sediment is calculated, reshaping the initial bed surface across the valley. The presented method is simple and therefore notably beneficial for practical work. The performance of the proposed method has been tested using two case study applications. Results demonstrate that the presented method estimates comparable incision depth as revealed in the in-situ survey and the numerical simulation.
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