Abstract
Flow-like landslides are one of the most catastrophic types of natural hazards due to their high velocity and long travel distance. They travel like fluid after initiation and mainly fall into the ‘flow’ movement type in the updated Varnes classification (Hungr et al., 2014). In recent years, depth-averaged models have been widely reported to predict the velocity and run-out distance of flow-like landslides. However, most of the existing depth-averaged models present different shortcomings for application to real-world simulations. This paper presents a novel depth-averaged model featured with a set of new governing equations derived in a mathematically rigorous way based on the shallow flow assumption and Mohr-Coulomb rheology. Particularly, the new mathematical formulation takes into account the effects of vertical acceleration and curvature effects caused by complex terrain topographies. The model is derived on a global Cartesian coordinate system so that it is easy to apply in real-world applications. A Godunov-type finite volume method is implemented to numerically solve these new governing equations, together with a novel scheme proposed to discretise the friction source terms. The hydrostatic reconstruction approach is implemented and improved in the context of the new governing equations, providing well-balanced and non-negative numerical solutions for mass flows over complex domain topographies. The model is validated against several test cases, including a field-scale flow-like landslide. Satisfactory results are obtained, demonstrating the model's improved simulation capability and potential for wider applications.
Highlights
Flow-like landslides are one of the most catastrophic types of natural hazards due to their high velocity and long travel distance
Savage and Hutter (1989) made the first attempt to develop a depth-averaged model for granular flows based on the Mohr-Coulomb internal rheology law and constant Coulomb bed friction
The corresponding homogeneous equations of Eqs.(1)–(3) are strictly hyperbolic when h≠0. This implies that the new depth-averaged mass flow governing equations can be numerically solved using a range of Godunov-type numerical schemes that have been widely developed for the shallow water equations
Summary
Flow-like landslides are one of the most catastrophic types of natural hazards due to their high velocity and long travel distance. To avoid this, Bouchut and Westdickenberg (2004) introduced a shallow water flow model on an arbitrary coordinate system for simulations over topographies with small curvatures Their overall governing equations were derived on a fixed Cartesian coordinate system while the variables were defined on a local reference coordinate system aligning with the local topography, i.e. the flow depth is normal to and the velocities are parallel to the bed. Compared with the Bousinessq-type models, the numerical implementation of these shallow water type models can be much easier to achieve and many well-documented numerical schemes developed for shallow flow hydrodynamics can be directly used These models have proven to be successful for certain applications, they have not been fully justified in a mathematically rigorous way and all of them do not consider the effect of the centrifugal force induced by bed curvatures which may become significant for applications involving complex topographies. A glossary of notations is provided at the end of the manuscript
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