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Due to the characteristics of sudden occurrence, fast disaster speed, and severe damage, debris-flow disasters can easily result in the loss of human lives and cause serious damage to property and social infrastructure. In this study, taking the debris-flow events in Liaoning province from 1960 to 2020 as the study period, the natural geographical characteristics and key influencing factors of the debris-flow-prone areas were explored utilizing the self-organization mapping clustering method and nonlinear global sensitivity analysis. The main conclusions were as follows: (1) The key influencing factors of debris flow are the content of clay, sand, and silt; the first type of debris flow is sensitive to the fluctuation in slope and elevation; the second and third types of debris flows are more significantly affected by changes in land use and geomorphology; the third type of debris flow is weakly sensitive the NDVI value, vegetation type, slope direction, and soil type; (2) The first type of debris flow was widely distributed, mainly located in most of the hills of eastern and the southwest part of Liaoning province; the focus of the second type of debris flow focus was further in Xiuyan County and scattered in the hills of northeast Liaoning province; the third type of debris flow was mainly distributed on the peninsula of Liaodong and the southwest of Liaoning province. (3) When the clay content is 12–27%, sand content is 49–70%, silt content is 18–29%, the elevation is 0–500 m, the slope is 0°–30°, and the land use is at the junction of arable land, medium cover grassland, and forested land, etc., debris flow disasters are very likely to occur.