A Mathematical Model for Debris Flow Blockage Assessment based on Topographical Factors

Abstract

Abstract Debris-flow dams are often associated with the occurrence of debris flows blocking rivers in mountainous areas, posing a great threat to the safety of people's lives and property in downstream areas. To accurately assess the occurrence probability of debris-flow dam disasters, it is necessary to first assess the possibility of complete debris-flow fan blockage. In this paper, on the basis of the debris-flow fan blockage model proposed by previous authors, a mathematical model for determining debris-flow blockage is proposed based on three topographical factors, depositional distance, depositional thickness and depositional volume, taking full account of the influence of topographical factors on the complete blockage of debris flows. The greater the depositional distance, the greater the depositional width and the greater the depositional thickness of the Wenjiagully debris-flow dam calculated by the model are − 2.07%, -5.85% and − 6.40%, respectively, which clearly demonstrated the feasibility of the model. A parametric sensitivity analysis was conducted on the factors influencing the elements of the depositional pattern and the size of the depositional volume of the debris-flow dam. Depositional distance and thickness were positively correlated with rainfall intensity, debris-flow trench catchment area and trench slope and negatively correlated with geotechnical particle density and geotechnical mean particle size; depositional width and volume were positively correlated with rainfall intensity and debris-flow trench catchment area and negatively correlated with trench slope, geotechnical particle density and geotechnical mean particle size before being positively correlated. The proposed model has implications for assessing the possibility of complete blockage of the river by debris-flow fans and formulating corresponding disaster prevention and mitigation measures.