Modeling Debris Flow: On the Influence of Pore Pressure Evolution and Hypoplasticity

For granular debris flows, two characteristics play a crucial role in their dynamic behavior: the pore- pressure feedback, which reduces the intergranular friction and, therefore, enhances the mobility of the whole mixture, and the non-linear deformational behavior that stems from the internal contact stress between grains. In a previous work, the entropy principle based on the formulation of Müller and Liu was exploited in order to find restrictions on the constitutive equations of a general grain-fluid multiphase mixture, including two additional internal variables. In this report, a thermodynamically consistent model for debris flows is depth-integrated and employed for numerical simulation.

Including extra pore-pressure and hypoplastic stress, internal variables that are, respectively, described by a pressure diffusion equation and a transport equation related to the hypoplastic material, are considered. Comparison of the obtained results with those from classical debris flow models shows that the proposed thermodynamic model provides a phenomenological insight into the influence of the pore-pressure feedback and intergranular friction in the flow dynamics.

To better understand the significance of the pore-pressure feedback and the intergranular friction, a simple grain-fluid material sliding on a slope with runout is numerically investigated by using depth- integrated model equations. A non-oscillatory, shock-capturing central-upwind scheme with the total variation diminishing property is applied for this purpose. Numerical results indicate the significant importance of the pore-pressure feedback and the hypoplastic behavior on determining the flow dynamics of debris flows.