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A theoretical, experimental and numerical study of the formation of coarse dry granular fronts and spontaneously self-channelizing levees in debris flows

Periodic Reporting for period 1 - GraFrontLev (A theoretical, experimental and numerical study of the formation of coarse dry granular fronts and spontaneously self-channelizing levees in debris flows)

Reporting period: 2018-11-01 to 2020-10-31

This project looks at (1) the mechanism of the formation of dry granular fronts in debris flows and (2) their feedback on the dynamics of debris flows. The MSCA Research Fellow conducting this research is particularly interested in the development of a depth-averaged model to account for the formation of dry granular fronts and validation of this proposed model by comparing numerical results with experimental measurements.

These topics are of interest to fluid dynamicists, civil engineers, geophysicists, and geologists working on the practical mitigation of natural hazards. The formation of large amplitude dry bouldery flow fronts is a spectacular and counterintuitive effect, that is directly responsible for the increased destructive power of debris flows. These poorly understood phenomena are often observed in the field (e.g. Pierson (1986)), large-scale experiments (e.g. Iverson et al. (2010) and Johnson et al.(2012)), and small-scale experiments (e.g. Haas et al. (2015) and Lanzoni et al. (2017)). The traditional geological perspective asserts that the coarse grains are segregated to the top of the flow and they are then preferentially sheared forwards and recirculated by particle-size segregation to develop a dry front. Nevertheless, recent laboratory experiments of mono-disperse flows of grains and water, e.g. Davies (1990) and Taylor (2020), also exhibit such phenomena, which motivated us to explore new formation mechanisms in this project.

Formal objectives of this MSCA have been to

(1) establish a model by deriving depth-averaged mass and momentum balance equations for the granular and water phases, respectively;
(2) perform numerical computations by extending the available numerical code;
(3) design an experiment to validate the proposed model;
(4) conduct interdisciplinary training through research and skills acquisition;
(5) and foster the development of an independent researcher.
In this project, the objectives and goals have been addressed via six specific work packages (WPs): (1) development of a mathematical model to describe granular fronts; (2) numerical simulation of the established model equations; (3) design of an experiment and validation of the proposed model; (4) project management; (5) training; and (6) dissemination.

Work Package 1: Development of a mathematical model to describe granular fronts

The intention of WP1 was to develop a depth-averaged model to account for the formation of granular fronts. In WP1, the derivation of the model has taken into account the layered development, i.e. under-saturated and over-saturated regions, see figure 1. The model has the advantage of incorporating shear that plays a crucial role in the formation of a dry snout. This enables the proposed model to account for the experimental phenomena in Davies's (1988, 1990) moving bed flume experiments.

Work Package 2: Perform numerical computation by extending the available numerical code

Given that the derived model equations are hyperbolic Partial Differential Equations (PDEs), discontinuous solutions can develop naturally in the system. Hence, a solver that is capable of capturing shock waves is required. In this case, the shock-capturing scheme developed by Kurganov and Tadmor (2000) is employed, since it does not require the solution of Riemann problems. The fellow has extended the PDE solver developed during his PhD to numerically simulate the model equations.

The fellow has simulated an inclined flow for wet granular flows. The numerical results have been depicted in section 1.2.2 in Part B of the periodic technical report.

Work Package 3: Design of an experiment and validation of the proposed model

Due to the disruption of the Covid-19 pandemic, the host's lab has either been closed or very difficult to access from March 2020 up until the end of the grant. Thus, the fellow could not conduct any experiments. To circumvent this challenge, the supervisor has helped the fellow with collecting the experimental data from Prof. Tim Davies from the University of Canterbury in New Zealand and from Prof. Andy Take from the University of Queen in Canada. The model has been validated against the moving-bed laboratory experiment documented in Davies (1990). For more details, see section 1.2.3 in Part B of the periodic technical report.

Work Package 4: Project management

The fellow has received relevant training to project management from the New Academics Programme (NAP) which supported the fellow in completing a continuing career development plan and future project management.

Work Package 5: Training

The purpose of WP5 was to increase the fellow's research skills and encourage him to share his own knowledge and skills with others. The MSCA application listed seven training goals to be completed by the end of the grant period. Via this MSCA grant, the fellow has received high-quality research training and vibrant interaction with the host's group. The fellow has received the necessary and sufficient training described in section 1.2.5 in Part B of the periodic technical report.

Work Package 6: Dissemination

The MSCA application promised to participate in (1) Engagement@Manchester lunchtime meeting, (2) Big Bang UK Young Scientists & Engineers Fair, and (3) Manchester Science Festival 2019 for the purpose of dissemination. The fellow has joined Engagement@Manchester lunchtime meetings to learn necessary knowledge and strategies about public engagement. Nevertheless, due to the disruption caused by the Covid-19 pandemic, the fellow has not been able to conduct any effective dissemination activities. To minimize the influence, the fellow participated in the General Assembly of European Geosciences Union (EGU) 2021 online session to share the results of this project with researchers.
Impacts anticipated from the MSCA are increased and improved due to the fact that the new model works surprisingly well for the steady-flows experiments (see Davies (1990)) as well as for time-dependent flows (see Taylor-Noonan (2020)). The work conducted during this fellowship helps to clarify the point that the formation of dry granular fronts in debris flows does not necessarily arise from particle-size segregation. Instead, shear plays a crucial role. Furthermore, to the best of our knowledge, none of the existing debris-flow models are capable of capturing the dynamic grain and water surfaces simultaneously. The model derived in this project does this job remarkably. Thus, it is reasonable to think that this project yields a substantial advancement towards deeply understanding the physics of debris flows.
Two-dimensional schematic diagram of wet granular flows