On 6 July 2020, 3 h 40 min after rainfall stopped, a delayed debris-flow disaster occurred due to colluvium deposits in a hollow region (CDH) in the Chenghuangmiao gully, Sichuan Province, China, which resulted in 4 deaths and 27 injuries. This study explores the initiation process of the delayed debris flow and the cause for the delay. Field investigations, catchment geometry interpretation, laboratory tests, theoretical calculations, and fluid-solid coupling numerical simulation were performed to obtain landslide parameters and understand the mechanisms of the event. Results show: (1) The event was a giant low-frequency viscous debris flow. (2) Its initiation was caused by the delayed landslide process under the influence of back-end confluence. (3) The debris-flow discharge in the main gully increased over 19.5 min. (4) The seepage process inside the CDH continued for 3 h 20 min after the rainfall stopped before its pore pressure and reduction in strength was sufficient to initiate the debris flow. This research provides new insights on delayed debris-flow disasters; it is a reference for improving disaster management systems, especially monitoring and early warning systems, thereby avoiding future casualties.

Estimation of velocity profile through mud depth is a long-standing and essential problem in debris-flow dynamics. Until now, various velocity profiles have been proposed based on the regression of experimental measurements, but these are often limited by the observation conditions, such as the number of the configured sensors. Therefore, the resulting linear velocity profiles exhibit limitations in reproducing the nonlinear behavior and its temporal variation during the debris-flow process. In this study, we present a novel approach to explore debris-flow velocity profile in detail upon our previous 3D-HBP-SPH numerical model, i.e., the three-dimensional Smoothed Particle Hydrodynamic model incorporating with the Herschel-Bulkley-Papanastasiou rheology. Specifically, we propose a stratification statistical algorithm for interpreting the details of SPH particles, which enables the recording of temporal velocities of debris flow at different mud depths. To regress the velocity profile, we introduce a logarithmic-based nonlinear function with two empirical parameters, that controlling the shape of velocity profile and concerning its temporal evolution. We verify the proposed velocity profile and explore its sensitivity using 34 sets of velocity data from three individual flume experiments in previous literatures. Our results demonstrate that the proposed temporal-varying and depth-nonlinear velocity profile outperforms the previous ones.