Three-dimensional topography of debris-flow fan

Study on debris-flow fan configurations lays the groundwork for hazard zone mappings of debris flow disasters. This paper aims to identify the morphological similarity of debris-flow fans based on a series of laboratory experiments and field investigations. The maximum length L-c, width B-m, and thickness Z(o) of debris-flow fans are adopted as the characteristic parameters in the analysis of morphological similarity of debris-flow fans. This analysis demonstrates that the nondimensional longitudinal and transverse profiles of debris-flow fans can be described by Gaussian curves, while a circular curve can be used to fit the nondimensional plan form of the debris-flow fans. By combining the three nondimensional curves mentioned above, the volume for all of a debris-flow fan can be related to the maximum length L-c, maximum width B-m, and maximum thickness Z(o) by for all = alpha L(c)B(m)Z(o), via an empirical coefficient alpha. The parameter alpha is approximately 0.275 for a natural stony debris-flow fan and greater than 0.275 for a natural mud debris-flow fan. In addition, the three-dimensional topography of debris-flow fans can be easily derived based on the parameters L-c, B-m, and Z(o) using three morphological similarity formulae.