Flow-induced waterway in a heterogeneous granular material

Viscous flow around three-dimensional macroscopic cavities in a granular material

“…These 3-D results were partially confirmed by Sano et al (2013), who measured the velocity field inside a hemispherical cavity by LDV. If the far upstream velocity U ∞ exceeds a certain critical value U c , the grains at the cavity boundary can no longer sustain the structure, so that the grains of the upstream-side boundary are removed and are carried downstream (see Kaneko & Sano 2005;Sano & Nagata 2006;Sano 2011Sano , 2020. Repetition of these processes create a fluidized region toward the upstream direction, which will be discussed in § 6.…”

“…The interaction of two cavities, in which the asymptotic effect of the other cavity is taken into account, was analysed (see Sano 2020), which also reproduced the experimental findings. As a result of interaction, the critical value U c , where the collapse of cavities results, may be lowered, and the spread of the fluidized region may be enlarged, so that the network formation of the water channel and the onset of a landslide arising from heavy rainfalls may be predicted (see Kaneko & Sano 2005;Sano & Nagata 2006;Sano 2011Sano , 2020, which will be discussed in § 6. We found that the concentration of the flow and the stresses are more pronounced in the 3-D configuration, which is often the case in real situations.…”

A general two‐phase debris flow model

“…The initial triangular mass is divided into two parts: an upper triangle (UT), and a lower triangle (LT), which have either the same or different solid volume fraction. The idea of using different initial solid volume fractions in the front and the back of the debris body is motivated by field observations that the phases can be spatially nonuniformly distributed (see, e.g., Sano [2011]). Initially, some parts of the mixture material may be fully saturated, whereas the other parts may be partially saturated.…”

Viscous flow and collapse of macroscopic cavities in a granular material in terms of a Darcylet

“…If, however, a number of cavities are distributed within a well-interacting distance, the fluidized region will merge to form a long waterway. The details on the flow through a noncircular cavity are given in [7,8], while evolution of the cavity shape, migration and merging of cavities are given in [10][11][12][13][14]. Furthermore, if many such waterways spread sheet-like and slanted, as is often observed on the boundary of impermeable layer of stratum, one side of the granular layer is disconnected to the other side, which can be a cause of landslide at a heavy rainfall.…”

“…Flow concentration enhances the local stress on the upstream-side boundary of the cavity, so that the grains of that part will be eroded and carried to the downstream-side boundary if it exceeds certain criteria. This process effectively causes the migration of the cavity towards the upstream direction, or a narrow waterway formation in the medium as was previously shown [10][11][12][13][14][15]. In this paper, we reformulate the analysis on the fundamental flow through a single cavity, and apply it to the interaction of two cavities.…”