Soil erosion in the boundary layer flow along a slope: a theoretical study

Brivois, Olivier; Bonelli, Stéphane; Borghi, R.

doi:10.1016/j.euromechflu.2007.03.006

Cited by 30 publications

(23 citation statements)

References 9 publications

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“…As described in Methods, we study the erosion of soft clay bodies by fast-flowing water, allowing us to witness what is an intractably slow process in nature. We consider unidirectional flow and canonical initial geometries-a thin flat bed of clay, a cylinder, and a sphere-with an eye toward informing mathematical models that intimately link the coevolving flow and shape (12,13). Our experiments typically involve centimeter-scale bodies immersed in flows of 40-70 cm/s, yielding high Reynolds numbers of order 10 4 .…”

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confidence: 99%

“…2C). The Blasius solution describes the boundary-layer thickness along a plate (12), which grows with the streamwise coordinate as δ ∼ x 1=2 , resulting in shear that decreases as U=δ ∼ x −1=2 . If the local erosion rate varies directly with shear stress, then _ h = − Cx −1=2 and thus hðx; tÞ = h 0 − Cx −1=2 t, where hðx; tÞ is the local bed thickness, hðx; 0Þ = h 0 is the initial thickness, and C is a constant.…”

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confidence: 99%

“…law's local validity is crucial for understanding cases in which the coevolving shape and flow strongly influence one another (12,13).…”

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Sculpting of an erodible body by flowing water

Ristroph

Moore

Childress

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

112

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Erosion by flowing fluids carves striking landforms on Earth and also provides important clues to the past and present environments of other worlds. In these processes, solid boundaries both influence and are shaped by the surrounding fluid, but the emergence of morphology as a result of this interaction is not well understood. We study the coevolution of shape and flow in the context of erodible bodies molded from clay and immersed in a fast, unidirectional water flow. Although commonly viewed as a smoothing process, we find that erosion sculpts pointed and cornerlike features that persist as the solid shrinks. We explain these observations using flow visualization and a fluid mechanical model in which the surface shear stress dictates the rate of material removal. Experiments and simulations show that this interaction ultimately leads to selfsimilarly receding boundaries and a unique front surface characterized by nearly uniform shear stress. This tendency toward conformity of stress offers a principle for understanding erosion in more complex geometries and flows, such as those present in nature.R eflecting on his scientific discoveries, Isaac Newton compared himself to a boy on the seashore who marvels at having found a yet smoother stone (1). For pebbles and mountains alike, our curiosity about natural sculptures stems perhaps from the realization that these shapes reflect countless incremental events acting over eons. Morphology is often the only clue available as we attempt to reconstruct the physical history of the Earth as well as of our neighboring worlds (2-6). Recreating geologically inspired situations in the laboratory offers an opportunity to connect the development of structures to the underlying processes at work (7). This approach has been used to study phenomena across many scales, for example, the rounding of rocks by abrasion (8), the formation of rivers (9) and drainage channels (10), and the drift of continental plates driven by mantle convection (11).Rather than mimic a particular geological scenario, we conduct experiments that isolate a central aspect common to all erosive processes: the interdependent evolution of shape and flow (3). As described in Methods, we study the erosion of soft clay bodies by fast-flowing water, allowing us to witness what is an intractably slow process in nature. We consider unidirectional flow and canonical initial geometries-a thin flat bed of clay, a cylinder, and a sphere-with an eye toward informing mathematical models that intimately link the coevolving flow and shape (12, 13). Our experiments typically involve centimeter-scale bodies immersed in flows of 40-70 cm/s, yielding high Reynolds numbers of order 10 4 . Importantly, the solid boundaries recede at rates (approximately centimeters per hour) that are many orders slower than the flow speed, preserving the large separation of time-scales characteristic of natural erosion.Considering first the case of a 3D body, we form a clay sphere of diameter 4.9 cm and support it within a water tunnel with a cro...

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Sculpting of an erodible body by flowing water

Ristroph

Moore

Childress

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

112

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“…Therefore, the solid/flow interface can be considered as a singular interface with a negligible thickness. In this case, the erosion phenomenon is simply described by the flux of eroded mass crossing this interface [5,9].…”

Section: Introductionmentioning

confidence: 99%

Numerical modelling of concentrated leak erosion during Hole Erosion Tests

Mercier

Bonelli

Golay³

et al. 2014

Acta Geotech.

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This study focuses on the numerical modelling of the concentrated leak erosion of a cohesive soil by turbulent flow in axisymmetrical geometry, using the Hole Erosion Test (HET). The numerical model is based on the adaptive remeshing of the water/soil interface to ensure the accurate description of the mechanical phenomena occurring near the soil/water interface. The erosion law governing the interface motion is based on two erosion parameters: critical shear stress and the erosion coefficient. The model is first validated in the case of 2D piping erosion caused by laminar flow. Then, the numerical results are compared with the interpretation model of the HET. Three HETs performed on different soils are modelled with rather good accuracy. Lastly, a parametric analysis of the influence of the erosion parameters on erosion kinetics and the evolution of the channel diameter is performed. Finally, after this validation by comparison with both the experimental results and the interpretation of Bonelli et al.[2], our model is now able to accurately reproduce the erosion of a cohesive soil by a concentrated leak. It also provides a detailed description of all the averaged hydrodynamic flow quantities. This detailed description is essential in order to achieve better understanding of erosion processes.

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“…More refined models try to include the influence of the sediments detached from the soil (see for example (Woodward, 1999;Bonelli et al, 2006;Brivois et al, 2007)), or consider probabilistic models for the erosion factors (Sidorchuk, 2005), however it remains unclear whether the alternatives they provide are truly required with respect to the simpler model of equation [7]. Following (Wan et al, 2004a;Knapen et al, 2007), an approximation can be used to derive the hydraulic shear stress as a function of the gradient of the hydraulic head,…”

Section: Modeling Of Erosionmentioning

confidence: 99%

Numerical modeling of erosion using an improvement of the extended finite element method

Cottereau¹,

Dı́ez²

2011

European Journal of Environmental and Civil Engineering

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ABSTRACT. We present in this paper a numerical model of the erosion of a soil that accounts for both the flow in the open fluid and the flow of fluid through the porous soil. The interface between the open fluid and the soil is represented using a level-set function, and the erosion is controlled by the shear stress vector. The evaluation of the approximate value of this gradient is particularly focused on, and an improved method, called XFE+ method, is presented. Numerical results in 2D and 3D illustrate the accuracy and the potentiality of this method.RÉSUMÉ. Cet article décrit un modèle numérique d'érosion du sol, qui prend en compte à la fois le fluide dans le sol, considéré comme un milieu poreux, et le fluide extérieur. L'interface entre les deux milieux est représentée à l'aide d'une fonction level-set, et l'érosion est contrôlée par le gradient de la vitesse du fluide. Nous nous concentrons particulièrement sur l'évaluation numérique de ce gradient, et introduisons une méthode, appelée méthode XFE+, pour l'améliorer. Des résultats numériques en 2D et 3D montrent la précision et les potentialités de cette mé-thode.

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Soil erosion in the boundary layer flow along a slope: a theoretical study

Cited by 30 publications

References 9 publications

Sculpting of an erodible body by flowing water

Sculpting of an erodible body by flowing water

Numerical modelling of concentrated leak erosion during Hole Erosion Tests

Numerical modeling of erosion using an improvement of the extended finite element method

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