A consistent debris flow model with intergranular friction and dynamic pore-fluid pressure

This work presents the thermodynamically consistent development of a scaled, depth-integrated model for granular-fluid flows. Considering a general topography, the model is used for the numerical simulation of debris flows in different scenarios. With regard to important physical mechanisms in such flows and the underlying dynamics, additional fields are included, an extra pore-fluid pressure and hypoplastic, intergranular friction. The combined recourse to these two fields takes place in the context of a derivation with the entropy principle, beginning with general laws of thermodynamics, and ends with the application to real, large-scale debris flow events. As a starting point, within the framework of mixture theory and the entropy principle, a continuum model for a general granular-fluid mixture is derived. Amending the basic fields of mass, momentum and energy, as well as a balance equation for the volume fraction, an additional field for the intergranular contact forces is considered, together with, newly introduced in the context of thermodynamic consistent modeling, a dynamic partial pressure. Assuming a shallow, saturated flow, the derived model is then non-dimensionalized and depth-integrated. The resulting model is further transferred into general coordinates. This allows for the easy representation of debris flows on real mountainous topography. Implemented with a shock-capturing NOC scheme, several numerical simulations are performed, ranging from parameter studies on a laboratory scale and the comparison with a dam break experiment to a large-scale event. The numerical parameter studies confirm the expected behavior of the additional physical fields. Since the extra pore-fluid pressure arises from the interaction of the granular skeleton and the pore-fluid, it interferes with the hydrostatic pressure and is able to push the granular particles apart, thus reducing their apparent friction and prolongating the movement of the bulk mass. It accelerates the whole mixture and prevents the mass from settling, while the intergranular friction helps the granular structure to maintain its form, hindering it from dissolving like a fluid and accounting for the non-linear, anelastic behavior of granular material. It should be emphasized that the presented modeling establishes a transfer from investigations on granular materials in the context of the entropy principle to the more practically orientated class of depth-integrated models. With this, the additional fields can be seen as the incorporation of information on the granular skeleton, i.e. the microstructure, in its interdependency with the fluid phase - something that is usually not depicted similarly in the framework of mixture theory. A central aim here is therefore to provide a consistent debris flow model, developed with regard to these additional fields, which is applicable for numerical studies