Abstract: A rational constitutive model is critical for numerical simulation of rheological behavior of debris-flow. It is also one of the key issues that determine the accuracy of numerical simulation of its dynamic process. The numerical models based on Bingham and Cross constitutive models has been observed failing to simulate the shearing thickening and thinning phenomenon of the rheological behavior of debris-flow that belongs to multi-phase mixture of fluid and debris. We discuss the numerical divergence problem of using the Bingham model with low shear strain rate. To simulate the dynamic flow process of diluted debris-flow, the 3D numerical model is set up, applying an alternative solution of the Herschel-Bulkley-Papanastasiou(HBP) constitutive model with the smoothed particle hydrodynamic(SPH) method. Comparing to the traditional two-dimensional numerical model based on the hypothesis of shallow water wave, the proposed method in this paper solves Navier-Stokes equations describing the debris-flow with the SPH in three-dimension, thus the velocity field and deposition pattern of debris flow can be simulated. The proposed method incorporates the HBP constitutive model, ensuring the numerical convergence, can perform well to reveal the non-linear variation of stress-strain relationship of debris flow at transition phase of plastic yield and large shear rate. The proposed method is verified by a flume experiment. It indicates that the simulation results match well with the experimental measurements.

Key words: debris flow, non-newtonian fluid, Herschel-Bulkley-Papanasiou(HBP) model, smoothed particle hydrodynamic(SPH), numerical simulation