Scaling relation between fluctuating stress and basal friction in granular flows down rough inclines

The basal friction characteristics of granular materials are quite different from those of common solid. We carried out a series of sliding friction tests to investigate the effect of grain size distribution(i.e. particle size and mass percentage) on the basal dynamic friction coefficient of granular materials. Based on the analysis of video images and curve fitting method, the fitting function of displacement and time was established, which was used to deduce the dynamic friction coefficient by the analysis of acceleration in the sliding process. Experimental results indicate the following characteristics. The basal dynamic friction coefficient of granular materials decreases linearly with time. For monodisperse granular materials, the basal dynamic friction coefficient of fine particles is higher than that of coarse particles. For bidisperse granular materials, the basal dynamic friction coefficient of granular materials decreases sharply until reaching a minimum value(content of fine particles, CFP≤40%), then increases sharply(CFP 40% ~60%), and increases slowly with further increasing content of fine particles(CFP≥60%).

Experimental investigation on rheological behavior of dry granular mixtures based on direct measurement of basal friction

In mountainous regions, risk mitigation requires an understanding of sediment‐transport processes. We present new experiments conducted on a steep slope (33%) to study the transition from bedload to debris flow. The flume design was adapted to mimic alpine streams: instead of studying the mobility of a channel bed composed of uniform‐sediments, we generate pulses of sediment by injecting water over a self‐formed deposit of poorly sorted mixtures located at the flume entrance. The setup comprises ultrasonic sensors measuring the height of the water‐sediment mixture and a force sensor measuring normal and tangential forces exerted on the bed. The experiments show that the highest discharges generate bedload. At lower discharges, mass failure of the deposit generates two regimes: a “static‐dynamic” regime, where a granular pulse propagates without a clear water phase, and a “full‐dynamic” regime, where concentrated pulses are driven by water flows. In both regimes, pulses are vertically and longitudinally sorted: the front contains coarse particles, the tail contains finer particles, and the body a mix, with coarser particles concentrated near the surface. Force analysis shows that, in the static‐dynamic regime, mobility is governed by resistance at the front and thrust from body weight. In the full‐dynamic regime, weight alone cannot explain the observed stresses, suggesting roles for additional factors, such as non‐hydrostatic water pressure, acceleration, and vertical transfers. In both regimes, front resistance controls pulse mobility. Basal friction coefficient () analysis further shows that the transition to bedload occurs at the threshold discharge required to mobilize coarse particles alone in the channel.

Longitudinal spreading of granular flow in trapezoidal channels

Seismo-acoustic wave radiated from debris flows motion is one of the main properties used for its monitoring and detection. Understanding the Seismo-acoustic wave using geophone recordings may give us great insight into the physical process of debris flows such as flow velocity and flow rate. To connect the seismo acoustic observation to the debris flows motion, vibration signal recorded from fixed geophones were analysed. In this study, a small-scale granular flow of volume 0.2 m3 consisting of material with average particle diameter 3.34 mm was simulated in a hydraulic flume with cross section of 0.5 m X 0.5 m through granular bed to simulate the debris flow. A series of three-axis geophones were buried along channel bed to record the vibrations produced by granular flows. The discrete Fourier transform was used to decompose vibrations into frequency spectrum and the weighted non-linear least square regression was adopted to isolate the dominant frequency functions and peak frequency. Meanwhile, the physical parameters including front profile, surface velocity, flow depth and discharge were tracked through video recordings and were compared with respect to isolated peak frequency. Assuming the radiated peak frequency in the moving granular flow is within 20-50 Hz and normally distributed, the isolated peak frequency shift in the fixed geophone location was analysed with the tracked flow parameters. Results shows that the peak frequency shift seems to have a non-linear relation with the surface velocity.

Geophysical granular flows, like avalanches and debris flows, are hazardous phenomena for infrastructures and human activities. The complex dynamics of granular systems, involved in these phenomena, poses important challenges to their reliable mathematical modelling. In this context, laboratory investigations on granular flows and non-invasive optical measuring methods are irreplaceable tools for getting a deeper insight into the granular dynamics, as they provide useful information for model calibration and validation. Frictional and collisional momentum flux exchanges coexist in dense granular flows. These resistance mechanisms and their complex interplay with the boundary conditions generate non-negligible fluxes of translational and fluctuation energies along the flow domain, which also influence the kinematics of the free surface. In this work we study steady granular flows in a chute geometry over a fixed bed, specifically focusing on the spatial fluctuations of the free surface. Several tests have been carried out by systematically varying the mass flow rate, the chute inclination and the basal roughness. The experimental apparatus, consisting of a narrow Plexiglas flume, is equipped with a load cell to measure the mass flow rate and a high-speed camera to get non-invasive optical measurements of the free surface fluctuations. A harmonic analysis, employing the Welch method, is performed on a time-series signal obtained from suitably binarized digital images of the free surface fluctuations, recorded at a sampling frequency of 1 kHz. Subsequently, the power spectral densities and the power content of different frequency intervals are analysed. Meaningful correlations are observed between these power components and other relevant measurements, such as the mass flow rates and the flow depths. These preliminary results may be useful for a better understanding of the momentum exchange mechanisms in granular flows and the related fluctuation energy fluxes.

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.

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.

Bed topography is a key control on the evolution of the Antarctic Ice Sheet, influencing ice flow, grounding line retreat and the rate and timing of ice mass loss. To assess the sensitivity of ice sheet evolution to bed variability in ice sheet models, synthetic gridded bed topography datasets are often used. Here, we review methods commonly used to generate synthetic beds, their associated uncertainties and the influence of the approach on the characteristics of the resulting bed. Using the Aurora Subglacial Basin in East Antarctica as a case study, we evaluate the impact of five synthetic bed generation methods on projected ice mass loss under a high emission scenario. Sea-level rise estimates vary by up to 11% (SSP5-8.5 forcing scenario) and 32% (RCP2.6) at 2300 CE when basal friction coefficients from the friction law are optimized for each bed, and by up to 23% (SSP5-8.5) and 51% (RCP2.6) at 2300 CE when using non-optimized coefficients. Our results highlight the importance of relatively small bed variations on the timing and extent of grounding line retreat and the need for process-informed representation of the basal friction in decadal- to centennial-scale sea-level projections. This article is part of the Theo Murphy meeting issue 'Next generation ice-sheet bed measurements'.

Jakobshavn Isbræ (JI), on the West coast of Greenland, is one of the fastest flowing outlet glaciers of the Greenland Ice Sheet, draining 7% of the ice sheet area. Since the late 1990s it has dramatically accelerated, thinned and retreated in a series of phases alternating with periods of quiescence. It exhibits strong seasonal variations in flow speed and calving front position. Between 2012 and 2015, JI attained its point of furthest retreat and flow speeds in excess of 17 km/yr. Since 2016 it has modestly thickened, concurrent with deceleration and readvance of the calving front.The very fast flow and strong annual and interannual variability present significant challenges for ice sheet modellers. We model the evolution of JI between 2009 and 2018 using the BISICLES ice sheet model. The standard modelling technique of assimilating surface velocity observations to infer a power law basal friction coefficient for a snapshot in time fails to account for rapidly changing basal conditions, underestimating the annual variability. We implement a time-series inverse method in which regular velocity observations are assimilated throughout the study period to produce a time-evolving basal friction coefficient. This method is able to reproduce the large annual variations in flow speed much more accurately than the static method.This reliance on regular observations to drive the model poses a problem for future projections. We compare a range of sliding laws applied with the normal snapshot inverse method. A modern regularized Coulomb friction sliding law is better able to reproduce JI’s annual variations in flow speed due to its ability to modulate the basal friction in response to movement of the grounding line. As a result, it may be a more appropriate choice of sliding law for modelling the future evolution of fast-flowing outlet glaciers.

This paper describes a simple thermal model of an actively deforming critically tapered fold‐and‐thrust belt. The model determines the steady state temperature distribution and heat flow, as well as the pressure‐temperature‐time histories of rocks that outcrop at the surface. The main parameters controlling the thermal structure are the accretion and erosion rates, the undisturbed geothermal gradient at the toe, and the amount of frictional heating. Both shear heating on the decollement fault and internal strain heating within the deforming brittle wedge are incorporated in a mechanically consistent manner, and they dominate the effect of radiogenic heating, except in fold‐and‐thrust belts with significantly overpressured pore fluids. The mean stresses, temperatures, and surface heat flow all increase with an increase in the basal and internal coefficients of friction, and this dependence is used to constrain the level of friction on the decollement fault beneath the steady state fold‐and‐thrust belt in Taiwan. Rocks outcropping in the core of the Central Mountain Range of Taiwan experience maximum theoretical temperatures in excess of 400° C and maximum mean pressures in excess of 500 MPa if the coefficient of basal friction is μb = 0.5. Qualitatively, these conditions are in good agreement with the observed high greenschist facies metamorphism. The theoretical surface heat flow, which increases from 95 mW/m2 at the front of the fold‐and‐thrust belt to 240 mW/m2 at the rear, is in excellent agreement with the results of a recent geothermal survey of Taiwan, and theoretical cooling histories are in good agreement with fission track and other geochronologic studies. Taken together, these results provide strong evidence that sliding on the basal decollement fault beneath Taiwan is governed by a coefficient of friction in the range of typical laboratory measurements, μb = 0.5 ± 0.2. Approximately 35% of the total surface heat flux of 3 GW is heat conducted into the base of the wedge from the top of the basal decollement fault, and somewhat more than 30% is heat advected into the toe by accretion. The remaining heat is generated internally, about 25% by internal strain heating and about 10% by radiogenic heating. Either an increase in the coefficient of basal friction μb or a reduction in the pore fluid pressure ratio λ = λb leads to an increase in the surface heat flow, because of the increased frictional heating within the wedge and on the basal decollement fault. The overall balance of energy in a steady state fold‐and‐thrust belt is described by the equation , where Ė is the rate at which both mechanical and heat energy are added from external sources, is the rate at which work is performed against gravitational body forces in a reference frame attached to the overriding plate, and Q is the rate at which waste heat flows out of both the upper and lower boundaries. The total power input into the Taiwan fold‐and‐thrust belt is approximately 4.2 GW. The mechanical work being done on the base and front of the fold‐and‐thrust belt accounts for 3 of these 4.2 GW. In addition, 0.9 GW of heat are being advected from the subducting plate into the toe by accretion; the remaining 0.3 GW are being supplied by in situ radiogenic heating. The outgoing energy is dominated by the 3 GW of heat conducted out the top in the surface heat flow; however, another 0.8 GW are conducted down beneath the rear portion of the basal decollement fault, to heat the underlying subducting slab. Only 0.4 of the incoming 4.2 GW do useful mechanical work against gravity within the wedge; the efficiency of brittle frictional mountain building in Taiwan is therefore 10%.

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.

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.

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.

The 2011 Tohoku-Oki earthquake (Mw 9.0) produced a fault rupture that extended to the toe of the Japan Trench. The deformation and frictional properties beneath the forearc are keys that can help to elucidate this unusual event. In the present study, to investigate the frictional properties of the shallow part of the plate boundary, we applied the critically tapered Coulomb wedge theory to the Japan Trench and obtained the effective coefficient of basal friction and Hubbert-Rubey pore fluid pressure ratio (λ) of the wedge beneath the lower slope. We extracted the surface slope angle and decollement dip angle (which are the necessary topographic parameters for applying the critical taper theory) from seismic reflection and refraction survey data at 12 sites in the frontal wedges of the Japan Trench. We found that the angle between the decollement and back-stop interface generally decreases toward the north. The measured taper angle and inferred effective friction coefficient were remarkably high at three locations. The southernmost area, which had the highest coefficient of basal friction, coincides with the area where the seamount is colliding offshore of Fukushima. The second area with a high effective coefficient of basal friction coincides with the maximum slip location during the 2011 Tohoku-Oki earthquake. The area of the 2011 earthquake rupture was topographically unique from other forearc regions in the Japan Trench. The strain energy accumulation near the trench axis may have proceeded because of the relatively high friction, and later this caused a large slip and collapse of the wedge. The location off Sanriku, where there are neither seamount collisions nor rupture propagation, also has a high coefficient of basal friction. The characteristics of the taper angle, effective coefficient of basal friction, and pore fluid pressure ratio along the Japan Trench presented herein may contribute to the understanding of the relationship between the geometry of the prism and the potential for generating seismo-tsunamigenic slips.