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Sorting of rocks, boulders, and silt/sand-sized particles according to their size is a characteristic feature of debris flow deposits and is an active process during flow which significantly affects the mobility. The degree at which size sorting occurs in debris flows depends on the relative magnitudes of granular processes such as particle size segregation and diffusion. Since debris flows are fluid-saturated phenomena, accurate modelling of size sorting requires the understanding of the influence of fluids on these processes, which have not been systematically studied. Here, we present simulation results and the associated empirical expressions for particle size segregation and diffusion which take into account fluid effects due to buoyant and drag forces. These expressions are developed through scaling analysis of data obtained from coupled granular-fluid simulations of saturated bi-disperse mixtures under simple shear. We further show that using these scaling relationships, an existing segregation-diffusion continuum equation can be extended to model particle sorting in debris flows with various types of fluids.

Debris flows are gravity-driven phenomena common in mountainous regions that are hazardous to downstream facilities. To mitigate the impacts of these disastrous processes, structural countermeasures such as slit dams are constructed in gullies and along mountain slopes. Existing studies on the impact dynamics of debris flows against slit dams typically focus only on the flow characteristics but fail to take the geometry of the structure into account. Here we develop an analytical model, derived from the momentum approach, that allows for the estimation of the runup height and impact load of debris flows on slit dams. The model is validated against discrete element simulations and small-scale flume experiments. It is found that the runup height is controlled by both the Froude number and slit size. The proposed analytical model can predict the runup height well within a certain range of Froude numbers. Results from experiments further reveal that the fontal dynamic pressure is sensitive to the flow properties whereas the peak dynamic pressure is strongly affected by the slit size.

Abstract We are concerned with general third-order nonlinear boundary value problems. An existence theorem of solution is given under weaker conditions. In the meantime, an iterative algorithm with global convergence is presented. The higher order derivatives of approximate solution is obtained by using this method can approximate the corresponding derivatives of exact solution well.