The particle image velocimetry (PIV) is a well-established non-invasive optical technique for measuring the velocity field in fluids. Recently, the PIV approach has been extended to granular flows, where the medium under investigation is composed of a discrete number of grains that are typically non-transparent and of super-millimetric size. Granular PIV (g-PIV) still represents a non-standard application, as some accuracy concerns arise. In particular, since granular flows can be highly sheared, the choice of appropriate interrogation windows for the PIV analysis is not trivial. As well, owing to the spatially-averaged nature of the PIV approach, the estimation of second-order statistics remains a very challenging task. Here, we report a laboratory investigation on dry granular flows composed of glass spheres in a rotating drum. The velocity measurements at the sidewall are obtained by using a window deformation multi-pass PIV approach, where the open-source code PIVlab has been specifically used. Different combinations of the number of PIV passes and of interrogation windows are investigated. A slightly modified version of PIVlab allowed us to carry out g-PIV calculations with an arbitrary number of passes (i.e. greater than 4). Comparisons among different analyses helped us to identify reliable settings for g-PIV applications.

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.

The description of geophysical granular flows, like avalanches and debris flows, is a challenging open problem due to the high complexity of the granular dynamics, which is characterized by various momentum exchange mechanisms and is strongly coupled with the solid volume fraction field. In order to capture the rich variability of the granular dynamics along the avalanche depth, we present a well-posed multilayer model, where various layers, made of the same granular material, are advected in a dynamically coupled way. The stress and shear-rate tensors are related to each other by the μ(I) rheology. A variable volume fraction field is introduced through a relaxation argument and is governed by a dilatancy law depending on the inertial number, I. To avoid short-wave instabilities, which are a well-known issue of the conditionally hyperbolic multilayer models and also of three-dimensional models implementing the μ(I) rheology, a physically based viscous regularization using a sensible approximation of the in-plane stress gradients is proposed. Linear stability analyses in the short-wave limit show the suitability of the proposed regularization in ensuring the model well-posedness and also in providing a finite cutoff frequency for the short-wave instabilities, which is beneficial for the practical convergence of numerical simulations. The model is numerically integrated by a time-splitting finite volume scheme with a high-resolution lateralized Harten–Lax–van Leer (LHLL) solver. Numerical tests illustrate the main features and the robust numerical stability of the model.