Cagnoli, Bruno

The results of three-dimensional discrete element modeling (DEM) presented in this paper confirm the grain size and flow volume effects on granular flow mobility that were observed in laboratory experiments where batches of granular material traveled down a curved chute. Our numerical simulations are able to predict the correct relative mobility of the granular flows because they take into account particle interactions and, thus, the energy dissipated by the flows. The results illustrated here are obtained without prior fine tuning of the parameter values to get the desired output. The grain size and flow volume effects can be expressed by a linear relationship between scaling parameters where the finer the grain size or the smaller the flow volume, the more mobile the centre of mass of the granular flows. The numerical simulations reveal also the effect of the initial compaction of the granular masses before release. The larger the initial compaction, the more mobile the centre of mass of the granular flows. Both grain size effect and compaction effect are explained by different particle agitations per unit of flow mass that cause different energy dissipations per unit of travel distance. The volume effect is explained by the backward accretion of the deposits that occurs wherever there is a change of slope (either gradual or abrupt). Our results are relevant for the understanding of the travel and deposition mechanisms of geophysical flows such as rock avalanches and pyroclastic flows.

Flows of angular rock fragments are released down a concave upward chute in the laboratory to study their mobility which is measured considering the travel distance of the centre of mass of the granular masses. The prediction of flow mobility is necessary, in volcanic and mountain regions, to assess natural hazards caused by pyroclastic flows and rock avalanches. The longitudinal profile of our chute is similar to that of the flanks of Mayon volcano in the Philippines. Our flows are dry and they have different masses (30 and 60 g) and different grain size ranges (0.5-1, 1-2 and 2-3 mm). The values of all the other variables that can affect the travel distance are held constant. Flow mobility is measured as the reciprocal of the apparent coefficient of friction that is equal to the ratio of the vertical drop of the centre of mass to its horizontal distance of travel. Our dimensional analysis generates a functional relationship between the apparent coefficient of friction and a scaling parameter that contains grain size and flow volume.

Rapid mass movements of rock fragments are among the most hazardous natural phenomena. The ability to foresee their mobility is important when assessing natural hazards in volcanic regions. The dynamics of granular flows is however a challenging multivariate problem. Among the variables that affect their mobility we can include grain size and flow volume. Unfortunately, there are no generally accepted scaling laws describing these phenomena with the certainty to have taken into consideration all important aspects of nature. There are also different ways to assess mobility. Some authors, for example, adopt the distance travelled by the flow front or other arbitrary distances which are inappropriate for energy budget considerations because these flows deform during motion and deposition. Because of the difficulties inherent in direct field observations of these catastrophic events, we resort to laboratory experiments where granular material is released down a chute whose shape is similar to the profile of Mayon Volcano in the Philippines. Our experiments show that in flows of angular rock fragments, the smaller the grain size (all the other things equal), the larger is mobility. Importantly, this mobility is assessed measuring the distance travelled by centres of mass. Particle image velocimetry analysis of high speed video camera images shows also that the smaller the grain size, the smaller is the agitation of the fragments. This can explain the increase of runout distance as grain size decreases because fragments that are less agitated dissipate less energy. This should also explain why larger flow volumes are known to be more mobile. The larger the volume, the relatively smaller is the mass of a fragment with respect to the total mass of the flow so that fragments of larger flows are less agitated and for this reason dissipate less energy.

Granular mass flows of rock fragments are studied in the lab by means of a high-speed video camera at 2000 frames per second. These granular flows are generated using beds of pumice fragments positioned on a rough rotating disk, whose angular velocity is controlled by a motor. The experimental apparatus allows an understanding of the arrangement of the particles in granular mass flows with relatively small and relatively large values of the Savage number (the Savage number represents the ratio between grain collision stresses and gravitational grain contact stresses). In particular, these flows develop a basal layer of agitated and colliding particles underneath a relatively rigid upper layer. Our experimental results suggest the validity, on average, of the Coulomb’s relationship between shear and normal forces at the base of granular mass flows irrespective of their Savage number value. In Coulomb’s equation the shear stresses do not depend on the shear rate. We expect the Coulomb friction law to be valid also in moving pyroclastic flows. Our experiments suggest that the collisions and subsequent comminution of pumice fragments in moving pyroclastic flows could provide ash for the overriding ash clouds. In our experiments the amount of ash generated by particle-particle and particle-boundary interactions increases as the value of the Savage number increases. In nature, part of this ash may also simply move toward the base of the flows because of kinetic sieving.

We present here a new hypothesis to explain the high mobility of same rapid mass movements of rock fragments. We suggest that oscillations of flows with a quasi-rigid plug can result in reduction of their apparent coefficient of friction. This coefficient is computed as the ratio between drop in elevation and horizontal distance of travel. In our model, the effective friction during a downhill journay is a combination of the friction forces acting on the plug during the ascending and descending parts of its slope-normal oscillations. As a consequence of oscillations, the decreased contact with ground surface reduces the apparent coefficent of friction. Channel lateral surfaces can also support a portion of plug weight giving another contribution in the reduction of this coefficient. The support of lateral surfaces requires a relatively narrow channel such as a gully or the presence of levees whereas the reduced basal contact can be important also in larger channels that do not provide lateral support. We suggest that slope-normal oscillations are generated by ground asperities. The true coefficent of friction are larger than the apparent one because they account energetically for the oscillations that reduce basal contact. Thus we can say that our model is able to explain long runout distances as long as the energy dissipated by oscillations is accounted for by the true coefficents of friction that enter the calculations. Field and experimental investigation of several ideas discussed in this paper constitutes important aspects of future research that will improve the understanding of granular flows mobility.

We simulate granular flows of angular rock fragments by means of a three-dimensional discrete element modeling to study the basal stresses that these flows exert on the subsurface. These granular flows have different grain sizes and different flow volumes and they model dry rock avalanches and dense pyroclastic flows. These flows travel on four different concave–upward chutes that represent channels on a mountainside or on the flank of a volcano. Each chute has a different width. The stress data demonstrate the validity of a linear relation between two scaling parameters: D and ψ. Parameter D is a scaled basal stress deviation that is equivalent to a scaled particle agitation. Particle agitation is ultimately responsible for the energy dissipation that governs the mobility of dense geophysical flows in nature. Parameter ψ contains grain size, flow volume and channel width. This second parameter is equal to the product of the reciprocal of characteristic numbers of fragments in granular flows. Since these numbers of particles are dimensionless, the linear relation is valid at any scale, either in the laboratory or in nature.

The ability to predict the mobility of rock avalanches is necessary when designing strategies to mitigate the risks they pose. A popular mobility indicator of the flow front is the Heim’s apparent friction coefficient muH. In the field, muH shows a decrease in value as flow volume V increases. But this correlation has been a mystery as to whether it is due to a causal relationship between V and mobility since: (1) field data of muH do not collapse onto a single curve because typically widely scattered and (2) laboratory experiments have shown an opposite volume effect on the center of mass mobility of miniature flows. My numerical simulations confirm for the first time the existence of a functional relationship of scaling parameters where muH decreases as V increases in unsteady and nonuniform 3D flows. Data scatter is caused by muH that is affected by numerous other variables besides V. The interplay of these variables produces different granular regimes with opposite volume effects. In particular, muH decreases as V increases in the regime characterized by a relatively rough subsurface. The relationship holds for large-scale flows that, like rock avalanches, consist of a very large number of fine clasts traveling in wide channels. In these dense flows, flow front mobility increases as flow volume increases, as channel width increases, as grain size decreases, as basal friction decreases and as flow scale increases. Larger-scale flows are more mobile because they have larger Froude number values.

Non-fluidised, dry granular mass flows are obtained with rock fragments located on a rough rotating disk. In these flows that develop a quasi-rigid upper layer and a basal layer of colliding particles, dense clasts sink whereas light ones rise when surrounded by particles with intermediate density. Our experiments demonstrate that the presence of a quasi-rigid upper layer in granular mass flows does not prevent vertical segregation and that the formation of coarse-tail grading in pyroclastic flows does not require fluidising gases. High-speed videos reveal that vertical segregation in granular mass flow of rock fragments is generated by inertia differences between segregating clasts and matrix when they are both pushed upward by collisions with the basal layer. Coarse-tail grading occurs because the average segregation velocity of smaller clasts is smaller than that of larger clasts.

In this paper, we illustrate laboratory experiments whose purpose is to study the vertical segregations that are commonly observed in deposits of dense geophysical flows (such as pyroclastic flows and rock avalanches). In these experiments, we use rock cuboids with 5 mm long edges as matrix and rock cuboids with 2 cm long edges as segregating clasts. A rotating disk is used to apply frictional stresses at the base of the granular masses. In our experiments, segregating cuboids with density smaller than or equal to that of the matrix particles rise whereas segregating cuboidswith density larger than that of the matrix particles sink. The granular flows are imaged through the glass container of the experimental apparatus by a high-speed video camera at 2000 fps. By means of particle image velocimetry analysis of the movies, we study the vertical gradient of particle agitation that exists within the granular flows where agitation increases downward because of the interaction with the subsurface asperities. The high-speed movies show that it is the particle agitation within the flows that exerts an upward force and that, when this force is larger than theweight of the segregating clast, the clast riseswhereas, when it is smaller, the clast sinks. The most important result in our set of experiments is that the threshold which separates the values of density of the segregating clasts that segregate upward and the values of density of the segregating clasts that segregate downward is larger than the density of the matrix particles. This explains the upward segregation of dense lithics that is frequently observed in deposits of geophysical flows. This upward segregation is due to the fact that the resultant of the collisions exerted by the matrix particles is a force strong enough to push upward also dense and heavy fragments.

Rapid mass movements of rocks fragments (pyroclastic flows and rock avalanches for example) can be considered among the most hazardous natural phenomena because of their large momentum content.