Longitudinal spreading of granular flow in trapezoidal channels

Nochoke flow in a trapezoidal channel with a change in bed elevation is analyzed assuming there is no change in channel sections before and after the transition. The energy and continuity equations...

is very suitable to design a channel transition from the point of view of a no-choke condition. In this study, the condition of choke-free flow for two types of transitions in trapezoidal channels subject to a rise in bed elevation is considered. Based on the critical flow occurring downstream of the transition zone, the energy equation is solved with the aid of numerical methods to determine explicit equations for the maximum permitted bed rise under a given approaching regime. The presented procedure herein can also be used to determine end sill height in triangular and trapezoidal channel sections to assure hydraulic jump occurrence in stilling basins. Moreover, to determine the limits of upstream-flow depths (the choke-free regions) a suitable dimensionless specific energy equation is presented. This equation can be utilised to choose the operating ranges of upstream flow depths for choke-free flow in subcritical and supercritical upstream flow conditions. Finally energy loss in the transition zone is considered by applying it in the proposed equations.

Debris flows in mountainous regions are of great concern because they present a serious threat to the residents and infrastructures in downstream areas as a result of their long runout distances. However, the mechanisms of debris-flow runout are still unclear because of many factors influencing debris-flow mobility. This study focuses on two major factors, namely, particle size and slurry viscosities. A series of experimental model tests were conducted in a rectangular inclined flume connected to a final horizontal plain. Results reveal that the debris-flow mobility is significantly influenced by the slurry viscosities. The runout distance initially increases and then decreases as the slurry viscosities increase. Also, runout distance for debris flows contain large particle sizes is longer than that of debris flows contain small particle sizes. The depositional widths are almost unchanged in the experimental test, which suggests that the debris flows are constrained by the fixed channel boundaries. The results of this study can improve the understanding the behavior and the deposition features of debris flows.

Geophysical granular flows, such as snow avalanches and debris flows, represent a great hazard to man and infrastructures. These natural phenomena are characterized by the rapid flow of a granular solid phase, embedded in an ambient fluid. Since such events occur with little warning, in addition to investigating the triggering conditions, it is of crucial interest to predict their propagation and run-out distances. The main purpose of the present research is to better understand the flow dynamics of dry granular flows, in the presence of no-slip bottom boundary conditions, and predict their propagation by using a depth-averaged approach. In this case, a stratification of different flow regimes, such as quasi-static and dense collisional, occurs and makes the utilization of the classical single layer depth-averaged models insufficient, because of important uncertainties about the velocity and shear stress distributions along the flow depth. In the first part of the present work, an experimental-numerical study on dam-break flows of dry granular material is reported. It has been found that a modification to the formula, proposed in the Savage-Hutter model for calculating the earth-pressure coefficient, leads to an improved agreement with experimental data, in presence of no-slip bottom conditions. In the second part, an experimental study on steady state velocity profiles of dry granular flows is reported. The granular material, used in this experimental research, was Ottawa sand (ASTM C-778 20/30). The velocity profiles at the side walls and free surfaces have been obtained, through granular PIV techniques. The measurements are in accordance with other experimental works on different granular materials and suggest the occurrence of a rheological stratification along the flow depth, in case of no-slip bottom condition. In order to better describe such a complex flow dynamics, a two-layer depth-averaged model has been proposed. The dynamics of the two layers, ideally corresponding to dense-collisional and quasi-static regimes, have been considered independently. As well, mass exchanges between the layers have calculated through a physically based closure equation. The well-known mathematical issue of the hyperbolicity loss in two-layer models has been carefully addressed. In order to overcome it, a local modification of source terms of the original mathematical model has been proposed. Such a treatment consists of introducing an extra resistance at the interface, if necessary, to avoid the hyperbolicity loss. This approach has been found to be robust and yields reasonable results, as long as the asymptotic steady state solution and boundary conditions fulfil the hyperbolicity requirements of the original model. Through comparisons with experimental data, the two-layer approach turns out to be very promising to describe the complex flow dynamics in case of no-slip bottom boundary conditions, although a more detailed description of the basal shear stress seems to be required. In the third part of the present dissertation, the same two-layer approach has been used in order to rewrite the mathematical model in a curvilinear coordinates system, attached to the interface between the two layers. The model equations have been obtained, by using the same approach proposed in Tai and Kuo (2008). In the model derivation, the physically negligible quantities are identified in a more rational way than the previous model, by means of a scaling approximation.

Constructing multiple barriers along the predicted flow paths has been recognised as an effective engineering measure to intercept large volumes of debris flows. In the field, barriers usually have a basal clearance, which is an opening between the channel bed and the base of the barrier, to allow small discharges pass through the barrier and prevent the accumulation of stream loads. However, the current design of basal clearance is still based on an empirical criterion. The objectives of this research are to investigate the effects of basal clearance on the interaction between debris flow and multiple rigid barriers and to propose and verify a new analytical framework for flow impact on multiple rigid barriers with basal clearance. Findings from this study can serve to improve the current design guidelines on multiple-barrier system. The newly proposed analytical framework consists of an impact equation for barrier with a basal clearance, discharge equations to estimate flow properties of the basal discharge and a landing equation to estimate the flow properties after flow lands on the basal discharge. To verify the proposed framework, physical and numerical modelling were adopted. A series of dry granular flow tests has been carried out with a 5-m flume model to investigate the fundamental impact behaviour of idealised uniform particles on a rigid barrier with basal clearance. A discrete element model was calibrated by the physical tests and a series of numerical parametric studies has been conducted with varying barrier heights and barrier spacing. Furthermore, due to scale dependent nature of debris flow, a 28-m flume facility has been newly developed to investigate the impact dynamics of debris flow on dual rigid barriers with basal clearance. It is found that basal clearance can be designed to optimise barrier size and minimise maintenance work for a multiple-barrier system. Basal clearance with a ratio between clearance height and flow depth, H<sub>c</sub>/h<sub>i</sub>, ranging from 0.5 to 1.0 with Fr = 7 can reduce the impact force and runup height of two-phase debris flow by up to 55% and 43%, respectively. The effectiveness of basal clearance on mitigating impact can be characterised by Friction number, N<sub>fric</sub>, of the flow. A larger N<sub>fric</sub> represents a higher shear resistance among particles that would resist the flow to be discharged and lead the flow tend to be redirected to parallel to the barrier. N<sub>fric</sub> of dry granular flow that is by up to 55 times higher than the two-phase flow leads the basal clearance about 30% less effective on reducing the impact force and runup height of dry granular flow. Characteristic particle size, d<sub>max</sub> that represents the largest particle of the debris material, is found capable of determining the occurrence of jamming at the basal clearance. Basal clearance height H<sub>c</sub>/d<sub>max</sub> ≤ 2.0 and H<sub>c</sub>/d<sub>max</sub> ≥ 3.0 may lead and not lead jamming at the clearance, respectively, and could be adopted for a barrier to regulate debris flow without losing barrier retention and without retaining any debris, respectively. The proposed impact equation can well estimate both dry granular flow and debris flow impact on a rigid barrier with a basal clearance. The proposed landing equation can provide an upper bound for flow depth and velocity near the landing location. However, with an increasing flow distance, the decrease of downstream flow depth may lead that only the discharge equations are needed to estimate the flow properties.

Deposition morphology in large-scale laboratory stony debris flows

Simulation of granular surface flows using incompressible non-Newtonian SPH (INNSPH) method

Debris flow is the gravity-propelled movement of sediment-water mixtures, in which grains are supported above the non-moving bed by the strength and buoyancy of a clay-water matrix. The competence (largest supported grain size) of a debris flow is thereby determined by the magnitudes of matrix strength and density, which vary primarily and directly with matrix clay content. Strength also varies with the type of clay mineral and with the cation content of the water. Experiments reported here indicate that as little as 1.5 to 4 wt. % clay mixed into water is sufficient to support finest sand. The experiments also show that competence is less in flowing debris than in static debris, and that competence decreases with flow duration for durations less than about one hour but remains essent ally constant for durations greater than one hour. Competence apparently is independent of flow velocity or velocity gradient, although low velocities and gradients were not examined here. Calculations based on the experimental data reveal that marine sediments with finest sand as their coarsest material and with bulk clay contents as low as 2 wt. %, or less, can move as debris flows. Sediments with coarsest sand can move as debris flows if they contain as little as 19% clay, or less. Considering that these values are high estimates, many finegrained marine sediments have clay contents great enough in order to move as debris flows. Zones of various competences should exist within a debris flow because of the nature of the velocity profile and the dependence of competence on shear and flow duration. These zones are preserved during deposition and therefore, debris-flow deposits expectably should have layers of various grain sizes, and perhaps be normally and/or inversely graded. Debris flow is discussed in this paper as an idealized concept, where grain support is wholly by strength and buoyancy. In real flows, support also may be provided by graininteraction dispersive pressure and by turbulence, increasing the competence of the flows. Debris-flow mobility, in terms of the forces required to keep the flow moving, was not considered here but is equally significant to competence in evaluating the occurrence of real debris flows.

Gravitational mass movements, such as debris and mud flows, are among the most destructive natural hazards, leading to substantial fatalities and extensive economic damage worldwide. Improving our understanding and modeling of these processes is essential for developing effective risk management and early warning strategies. When debris and mud flows pass through a curved channel, centrifugal forces may cause a difference in flow height between the inner and outer banks of the channel. This height difference, known as superelevation, can be described using analytical models that establish a relationship between the superelevation height and the flow velocity.Analytical models often employ a forced vortex approach, incorporating parameters such as the cross-sectional slope of the flow surface, flow width, and bend radius. These models, however, rely on assumptions such as a linear flow surface between mud deposits on the banks, a rectangular cross-section, and neglect both complex rheological behaviors and solid-fluid interactions. As a result, an empirically determined correction factor is required within the formula. The absence of a clear mechanical rationale for this correction factor presents challenges, as it is currently derived only through field investigations and laboratory experiments.This study presents an enhancement to the existing forced vortex approach by incorporating insights from numerical modeling. A coupled SPH-DEM numerical model is employed, where DEM particles represent coarse solid particles, and SPH accounts for the fluid phase, comprising fines and water. The SPH-DEM coupling is based on the no-slip interaction model, with simulations performed using a GPU-based solver to ensure enhanced computational efficiency. To validate the approach, a parametric test is conducted, initially back-calculating laboratory-scale experiments. The study further involves varying the water content in debris and mud flows to examine its impact on flow behavior and superelevation. Larger water contents lead to an increased superelevation angle. Results from the parametric test reveal a clear correlation between water content and the flow surface shape in curved channels. Specifically, mud flows are characterized by convex upward surface shapes, whereas more granular debris flows typically exhibit concave downward shapes.The distribution of material within the cross-section of the flow is governed by the equilibrium between boundary forces and centrifugal forces acting on the flow, which directly influences the superelevation. Numerical investigations are conducted to determine a correction factor and assess the extent to which inertial effects contribute to this correction factor for different material mixtures. Furthermore, we demonstrate that the effect of the flow surface shape is significant and is currently only accounted for by the empirical correction factor. This study offers new physical insights for the back-calculation of debris flow velocities in curved sections marked by mud deposits. Large-scale SPH-DEM simulations of a real debris flow event at Illgraben (Switzerland) are performed, showing good agreement with field data and its potential for further real-scale modeling.

Numerous landslide that provided abundant material for the mobilization of debris flows were triggered in the Mozi gully on the right bank of Mingjiang River in response to the M8.0 Wenchuan earthquake of May 12, 2008. Following the earthquake, debris flows occurred during July through September of 2008 and again in September of 2009. Five of these events blocked the Mingjiang River. This paper estimates the volume of landslide material contributed to the valley by comparing remote sensing images before and after the quake, and analyzes the resultant landslide dams to estimate the volume ume of material necessary to block the channel. Return periods of debris flows with varying peak discharges are estimated based on empirical formulas and field surveys of the valley. © 2011 Casa Editrice Universita La Sapienza.

A kinematic model is developed to estimate the velocity and runout distance of a gravitative debris flow. The characteristics and the different stages of development of a gravitative flow are first described. The equations governing the motion during the flow are then derived based on the Newtonian translation motion with some simplified assumptions on the erosion process along the flow path. After the motion is initiated, the debris is considered to behave as a frictional material with the friction angle during motion being a function of the distance travelled measured from the initiation point. The equations derived are applied to two well-documented case records to assess their applicability. The application shows that the computed runout distances are slightly higher than the measured values. This slight error on the safe side is consistent with the simplified assumptions used in deriving the equations. The small error is acceptable for engineering designs in areas vulnerable to debris flows. © 2011 Casa Editrice Università La Sapienza.

A novel approach to calculate radiative thermal exchange in coupled particle simulations

Granular flow, such as hopper discharge and debris flows, involves complex multi-scale, multi-phase, and multi-physics coupling, posing significant challenges for numerical simulation. Over the past two decades, methods like the Discrete Element Method (DEM), Smoothed Particle Hydrodynamics (SPH), and Depth-Averaging Method (DAM), have been developed to address these problems. However, their applicability across different scales remains unclear due to differences in physical assumptions and numerical algorithms. Therefore, a comprehensive evaluation is critically needed. This study selects three typical methods (DEM, SPH, and DAM) to examine their convergence behavior, boundary condition implementation, and limitations in physical and numerical modeling. We numerically studied three extreme deformation flow cases with the three chosen methods. These cases include granular column collapse at the particle scale, flow-structure interaction at the laboratory scale, and reconstruction of the 2015 Shenzhen Guangming landslide at the field scale. By comparing the granular flow dynamics, deposition morphology, and structure interactions, and also the simulation accuracy and computational efficiency, we show the applicability of the three models across different scales. Further, we provide practical guidance for model selection in large-deformation flow problems in a granular system of different scales.

The basal friction coefficient, defined as the ratio of basal shear to normal stress, is fundamental to understanding granular avalanche dynamics. Normalized stress fluctuations, quantifying deviations from the mean stress, capture grain-scale interactions, yet their link to bulk friction remains unclear. Through inclined-chute experiments using uniform glass beads under varying slopes and flow thicknesses, we show that the fluctuation intensity systematically decreases as the flow becomes thicker and increases with slope. When both basal friction and stress fluctuations are rescaled by geometric parameters, the data collapse onto a unified curve, revealing a robust power-law trend. This scaling demonstrates that frictional resistance strengthens with enhanced stress variability but weakens with flow depth, offering a quantitative framework for modeling the mobility of landslides and debris flows.

Three-dimensional physics-based cellular automata model for granular shear flow