Managing complexity in high-concentration flow modelling aimed at hazard assessment: numerical and practical aspects

High-concentration flows are complex phenomena typical of Alpine mountain areas. Essentially, they are free-surface flows with intense sediment transport, often caused by intense rainfall events and involving large volumes of solid material. Because of the amount of sediments moved, the intense erosion and deposition processes typically observed and the quite unexpected character, these phenomena represent a serious hazard in populated mountain areas, where reliable and effective hazard-management and -protection strategies are required. In mountain-hazard management, high-concentration flows modelling represents a key factor, since it allows to evaluate impacts of possible hazard scenarios and the effectiveness of possible protection and mitigation measures. However, the intrinsic phenomenon complexity makes high-concentration flow modelling and hazard assessment quite challenging. In this thesis, some of the effects of high-concentration flow complexity on modelling are experienced directly and suitable solutions are proposed, to make the phenomenon description more reliable and straightforward. Among very different modelling approaches present in the literature, this work embraced the quasi-two phase, mobile-bed approach proposed in Armanini et al. (2009b) and in Rosatti and Begnudelli (2013a), which is implemented in the TRENT2D model. TRENT2D is a quite sophisticated model that solves a system of Partial Differential Equations over a Cartesian mesh by means of a finite-volume method with Godunov-type fluxes. By means of TRENT2D, the back-analysis of a couple of real debris-flow events occurred in Italy was first performed. These applications revealed clearly some troublesome "complexity issues", i.e. modelling issues generated by phenomenon complexity that may affect hazard assessment. Because of the public importance of the subject, four of the "complexity issues" identified were then faced directly. According to the purpose of this thesis, possible solutions to the issues were proposed, to ensure a proper description of the flow behaviour and possibly limit intricacy in the model use. The first complexity issue is "operational" and regards the use of the TRENT2D model and, more in general, the amount of work necessary to perform a complete hazard-assessment job about high-concentration flows. Because of the phenomenon complexity and the sophisticated character of the model, the operational chain necessary to assess hazard by means of TRENT2D appears quite demanding. The large efforts required in terms of handwork, computational charge and resources may divert the user attention from the physical meaning of the hazard-assessment process, possibly leading to inaccurate results. To overcome this issue, a possible solution is proposed, based on the use of a loosely-coupled Service Oriented Architecture approach. The aim is to develop a unique, user-friendly working environment able to support high-quality, cost-effective hazard assessment and, in perspective, the possible development of a Decision Support System for mountain hazard. The second complexity issue is "geometrical" and "numerical" and concerns morphology representation. Because of the strong interaction between high-concentration flows and bed morphology, these phenomena require bed morphology to be described with the right level of detail, especially where heterogeneity is outstanding. This is typically the case of urbanised mountain areas, with their characteristic terrain shapes, buildings, infrastructures, embankments and mitigation structures. A believable representation of these geometrical constraints may be fulfilled acting on the computational mesh used to solve model equations, preferably avoiding regular Cartesian meshes. In this work, a new version of the TRENT2D model is developed, based on the use of Delaunay, triangular unstructured meshes. To reach second order accuracy, a MUSCL-Hancock approach is considered, with gradient computation performed by means of the multidimensional method proposed in Barth and Jespersen (1989) for Euler equations. The effects of different gradient limiters are also evaluated, aiming at a proper description of the flow dynamics in heterogeneous morphology contexts. The third complexity issue is both "geometrical" and "mathematical". It concerns the effects of artificial structures, i.e. artificial geometrical constraints, on the flow dynamics. Among different structures aimed expressly at controlling the high-concentration flow behaviour, attention was paid to sluice gates, which can be used in channels and hydropower reservoirs to control sediment routing. In the literature, the effects of sluice gates have been studied especially with reference to clear water flows over fixed beds, while knowledge about the influence on high-concentration flows over mobile beds is still limited. Here, a rough, bread new mathematical description is proposed, in order to take into account the 3D morphodynamics effects caused by sluice gates in high-concentration flow modelling. The last complexity issue is pretty "numerical" and arises from the challenge of numerical models to comply with the phenomenon complexity. Generally speaking, reliable numerical models are expected to catch the main characteristics of the physical processes at both a general and a local spatial scale, although with a certain level of approximation, depending on the numerical scheme. Sometimes it may be hard to close the gap between the local phenomenon complexity and its numerical representation, leading to non-physical numerical results that could affect hazard assessment. In this work, a particular numerical issue is investigated, which was identified through a thorough analysis of TRENT2D model results. In particular, it was observed that the direction of the numerical mixture-mass flux is occasionally opposite to the direction of numerical solid-mass flux, despite the isokinetic approach which the model is based on. This incoherence was studied with a rigorous method, trying to fix the source of the problem. However, the question turned out to be quite tricky, due to the sophisticated character of the model. These four, deliberately heterogeneous, "complexity issues" allow to perceive clearly the size of complexity effects on high-concentration modelling. Furthermore, they give the measure of how much diffcult is reaching the right level of detail in describing and modelling high-concentration flows. The research of solutions that are accurate and as much simple as possible was not straightforward and required a quite large effort. Nonetheless, possible solutions were found in the end for three of the four "complexity issues", therefore the goal of the thesis can be considered as achieved.