Application of the 2D Depth-Averaged Model, FLATModel, to Pumiceous Debris Flows in the Amalfi Coast

Abstract

Few studies about modelling pumice debris flows are available in literature. An integrated approach based on field surveys and numerical modelling is here proposed. A pumiceous debris flow, which occurred in the Amalfi Coast (Italy), is reconstructed by the numerical code, FLATModel, consisting of a two-dimensional shallow-water model written in curvilinear coordinates. The morphological evolution of the gully and of the alluvial fan was monitored by terrestrial laser scanner and photo-modelling aerial surveys, providing, in a cost-effective way, data otherwise unavailable, for the implementation, calibration and validation of the model. The most suitable resistance law is identified to be the Voellmy model, which is found capable of correctly describing the friction-collisional resistance mechanisms of pumiceous debris flows. The initial conditions of the numerical simulations are assumed to be of dam-break type: i.e., they are given by the sudden release of masses of pumice, whose shape and depths are obtained by reconstruction of the pre-event slopes. The predicted depths and shape of deposits are compared with the measured ones, where a good agreement (average error smaller than 10 cm) is observed for several dam-break scenarios. The proposed cost-effective integrated approach can be straightforwardly employed for the description of other debris flows of the same kind and for better designing risk mitigation measures.2 of 22 meaning that the computational domain is large and, hence, the choice of the mesh size is crucial. From a practical viewpoint this typically involves vertical integration and averaging of the hydraulic variables, leading to models of the shallow-water type [23][24][25][26].Moreover, the evaluation of the energy losses during the flow has to be suitably addressed. Generally speaking, a debris flow is made up of a heterogeneous mixture of solids and liquids. In nature, the fluid is water or a slurry of water and fine sediments (clay and silt), and the solid phase is represented by natural grain soils, with a size ranging from silt to boulders. The physics governing the mixture behaviour at the micro-scale is fully defined by the classical equations of mechanics, taking into account interactions within the solid phase, solid-fluid interactions and the dynamics of the fluid phase. Yet, modelling one by one every single particle in problems at the field scale becomes highly computationally expensive, and, often, is still beyond the capacities of the existing computational resources. Therefore, a macro-scale rheological approach should be selected, moving from the particle-fluid mechanics to the continuum mechanics. The scientific problem of the debris flow rheology is a consequence of this continuum mechanics approach, e.g., [27,28].The code FLATModel, firstly introduced by [20] and subsequently reformulated in curvilinear coordinates in [29], implements a two-dimensional depth-averaged mathematical model of the shallow-water type, specifically designed to describe the propagation of debris fl...

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