Impact failure models and application condition of trees in debris-flow hazard mitigation

Forestry has played an important role in hazard mitigation associated with debris flows. Most forest mitigation measures refer to the experience of soil and water conservation, which disregard the destructive effect of debris flows, causing potentially serious consequences. Determination of the effect of a forest on reducing debris-flow velocity and even stopping debris flows requires distinguishing between when the debris flow will destroy the forest and when the trees will withstand the debris-flow impact force. In this paper, we summarized two impact failure models of a single tree: stem breakage and overturning. The influences of different tree sizes characteristics(stem base diameter, tree weight, and root failure radius) and debris-flow characteristics(density, velocity, flow depth, and boulder diameter) on tree failure were analyzed. The observations obtained from the model adopted in this study show that trees are more prone to stem breakage than overturning. With an increase in tree size, the ability to resist stem breakage and overturning increases. Debris-flow density influences the critical failure conditions of trees substantially less than the debrisflow velocity, depth, and boulder diameter. The application conditions of forests in debris-flow hazard mitigation were proposed based on the analysis of the model results. The proposed models were applied in the Xiajijiehaizi Gully as a case study, and the results explain the destruction of trees in the forest dispersing zone. This work provides references for implementing forest measures for debris-flow hazard mitigation.