General Assembly 2017 Vienna | Austria | 23 – 28 April 2017
Daniel Zugliani(1), Matteo Pasqualini(2) and Giorgio Rosatti(3) CUDAM University Center for Advanced Studies on Hydrogeological Risk in Mountain Areas Department of Civil, Environmental and Mechanical Engineering - University of Trento
1: Problem description Debris flow or hyper-concentrated flow is composed by a mixture of fluid and solid phase, usually water and sediment. When this flow propagate over loose beds, particles constituting the mixture of water and sediments strongly interact with the ones forming the bed, leading to erosion or deposition. However, there are lots of other situations when the mixture flows over rigid bedrocks or over artificially paved transects, so there is no mass exchange between bed and mixture. The two situations are usually referred to as, respectively, mobile- and fixed-bed conditions. Such flow, in its path, encounters both conditions as reported in figure 1. In Rosatti & Zugliani 2015, the mathematical and numerical description of the transition between fixed- and mobile-bed was successfully resolved, for the case of low sediment transport phenomena, by the introduction of a suitable erodibility variable and satisfactory results were obtained. The main disadvantage of the approach is related to the erodibility variable, that changes in space, based on bed characteristics, but remains constant in time. However, the nature of the bed can change dynamically as result of deposition over fixed bed or high erosion over mobile bed.
(1)
[email protected] (2)
[email protected] (3)
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3: Numerical approach
2: Mathematical approach Mobile bed
Introducing of a specific source term in the erodibility equation based on the physic of the problem. The remaining part of the system is equal to the static transition.
Fixed bed
Fixed- to mobile-bed transition
Mobile- to fixed-bed transition
1) Update the conserved variables at non-conservative step as they are evaluated as fixed or mobile with fixed-bed fluxes
1) Compare the bed elevation obtained as mobile bed with the minimum bed elevation possible
Erodibility
Mobile bed Fixed bed
2) Split time interval in mobile-bed and fixed-bed 2) Compare transported concentration of fixed bed with equilibrium concentration of mobile bed Fixed bed Mobile bed
+ Composite system with dynamic transition
3) Update the erobility 4) Evaluate new fluxes and conserved variables for fixedbed interval
3) Update the erodibility
4: Analytic solution for sedimentation over fixed bed The fixed-mobile shock problem
Generalized Rankine-Hugoniot relation
A wave of sediment propagates upstream over the fixed bed causing a dynamic transition between fixed and mobile bed. Fixed bed
Figure 1: Examples of transition between fixed- and mobile-bed.
Essential bibliography G. Rosatti and D. Zugliani. Modelling the transition between fixed and mobile bed conditions in two-phase free-surface flows: The composite Riemann problem and its numerical solution. J. Comput. Phys., 285:226 – 250, 2015 F. Rulot, B.J. Dewals, S. Erpicum, P. Archambeau, and M. Pirotton. Modelling sediment transport over partially non-erodible bottoms. Int. J. Numer. Meth. Fluids, 70(2):186 – 199, 2012 N. Strukisma. Mathematical modelling of bedload transport over nonerodible layers. 1st RCEM, 1:89 – 98, Sept. 1999.
Acknowledgement This work has been supported and funded by CARITRO Foundation – Cassa di Risparmio di Trento e Rovereto (Italy)
Unknown flux and source term but physic is known
Numerical solution
S
Mobile bed
The difference of erodibility flux must be equal to the speed of the shock sediment wave.
5: Trench evolution over partially erodible bed Example of the evolution of a trench over an non-erodible bump covered by erodible material. Concentration around 0.25 in order to simulate an hyperconcentrated flow with fast morphological variation.
Similar result as laboratory data. Not the same simulation due to lack of data necessary to reproduce the same phenomena.
Modified from Strukisma 1999
European Geosciences Union
DYNAMIC TRANSITION BETWEEN FIXED- AND MOBILE-BED: MATHEMATICAL AND NUMERICAL ASPECTS
