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A rational rheology model is critical for the numerical simulation of debris-flow behavior. The Bingham model commonly used in many current studies has failed to simulate the shear thickening and thinning phenomenon in experiments. We report an alternative solution by incorporating the Herschel-Bulkley-Papanastasiou (HBP) model with the smoothed particle hydrodynamic (SPH) method. The SPH simulation is based on the open-source DualSPHysics scheme, upon which we built a development by the Bingham-based rheology model in our previous study. In this paper, a straightforward improvement is made such that the HBP model is incorporated to describe the constitutive law between particles, extending the compatibility of the simulation to dilatant and pseudoplastic fluids. To illustrate the performance of the HBP-based SPH method, first, a sensitivity analysis was performed to investigate the influence of important rheological coefficients. The proposed method was then verified by a dam-break experiment of water-clay mixtures and the case study of the 2010 Yohutagawa debris-flow event in Japan. The results indicate a good accordance between simulation and observation. A discussion regarding the potential and limitations of the current method concludes the paper. • An HBP-based SPH method is proposed for numerical simulation of debris flows. • Shear thickening and thinning phenomenon of debris-flow mixture can be simulated. • A sensitivity analysis on the HBP rheological model is conducted. • The performance of the proposed method has been verified by experiment and case study. [ABSTRACT FROM AUTHOR]