We propose a physical model for the high‐frequency (>1 Hz) spectral distribution of seismic power generated by debris flows. The modeled debris flow is assumed to have four regions where the impact rate and impulses are controlled by different mechanisms: the flow body, a coarser‐grained snout, a snout lip where particles fall from the snout on the bed, and a dilute front composed of saltating particles. We calculate the seismic power produced by this impact model in two end‐member scenarios, a thin‐flow and thick‐flow limit, which assume that the ratio of grain sizes to flow thicknesses are either near unity or much less than unity. The thin‐flow limit is more appropriate for boulder‐rich flows that are most likely to generate large seismic signals. As a flow passes a seismic station, the rise phase of the seismic amplitude is generated primarily by the snout while the decay phase is generated first by the snout and then the main flow body. The lip and saltating front generate a negligible seismic signal. When ground properties are known, seismic power depends most strongly on both particle diameter and average flow speed cubed, and also depends on length and width of the flow. The effective particle diameter for producing seismic power is substantially higher than the median grain size and close to the 73rd percentile for a realistic grain size distribution. We discuss how the model can be used to estimate effective particle diameter and average flow speed from an integrated measure of seismic power. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.

International audienceEntrainment of underlying debris by geophysical flows can significantly increase the flow deposit extent. To study this phenomenon, analog laboratory experiments have been conducted on granular column collapse over an inclined channel with and without an erodible bed made of similar granular material. Results show that for slope angles below a critical value θc, between 10° and 16°, the run out distance rf depends only on the initial column height h0 and is unaffected by the presence of an erodible bed. On steeper slopes, the flow dynamics change fundamentally, with a slow propagation phase developing after flow front deceleration, significantly extending the flow duration. This phase has characteristics similar to those of steady uniform flows. Its duration increases with increasing slope angle, column volume, column inclination with respect to the slope and channel width, decreasing column aspect ratio (height over length), and in the presence of an erodible bed. It is independent, however, of the maximum front velocity. The increase in the duration of the slow propagation phase has a crucial effect on flow dynamics and deposition. Over a rigid bed, the development of this phase leads to run out distances rf that depend on both the initial column height h0 and length r0. Over an erodible bed, as the duration of the slow propagation phase increases, the duration of bed excavation increases, leading to a greater increase in the run out distance compared with that over a rigid bed (up to 50%). This effect is even more pronounced as bed compaction decreases

The seismic signals generated by rockfalls can provide information on their dynamics and location. However, the lack of field observations makes it difficult to establish clear relationships between the characteristics of the signal and the source. In this study, scaling laws are derived from analytical impact models to relate the mass and the speed of an individual impactor to the radiated elastic energy and the frequency content of the emitted seismic signal. It appears that the radiated elastic energy and frequencies decrease when the impact is viscoelastic or elastoplastic compared to the case of an elastic impact. The scaling laws are validated with laboratory experiments of impacts of beads and gravels on smooth thin plates and rough thick blocks. Regardless of the involved materials, the masses and speeds of the impactors are retrieved from seismic measurements within a factor of 3. A quantitative energy budget of the impacts is established. On smooth thin plates, the lost energy is either radiated in elastic waves or dissipated in viscoelasticity when the impactor is large or small with respect to the plate thickness, respectively. In contrast, on rough thick blocks, the elastic energy radiation represents less than 5% of the lost energy. Most of the energy is lost in plastic deformation or rotation modes of the bead owing to surface roughness. Finally, we estimate the elastic energy radiated during field scale rockfalls experiments. This energy is shown to be proportional to the boulder mass, in agreement with the theoretical scaling laws.

To be published in Journal of Sound and VibrationEstimating the energy lost in elastic waves during an impact is an important problem in seismology and in industry. We propose three complementary methods to estimate the elastic energy radiated by bead impacts on thin plates and thick blocks from the generated vibration. The first two methods are based on the direct wave front and are shown to be equivalent. The third method makes use of the diffuse regime. These methods are tested for laboratory experiments of impacts and are shown to give the same results, with error bars from 40% to 300% for impacts on a smooth plate and on a rough block, respectively. We show that these methods are relevant to establish the energy budget of an impact. On plates of glass and PMMA, the radiated elastic energy increases from 2% to almost 100% of the total energy lost as the bead diameter approaches the plate thickness. The rest of the lost energy is dissipated by viscoelasticity. For beads larger than the plate thickness, plastic deformation occurs and reduces the amount of energy radiated in the form of elastic waves. On a concrete block, the energy dissipation during the impact is principally inelastic because only 0.2% to 2% of the energy lost by the bead is transported by elastic waves. The radiated elastic energy estimated with the presented methods is quantitatively validated by Hertz's model of elastic impact

We simulate here dry granular flows resulting from the collapse of granular columns on an inclined channel (up to 22°) and compare precisely the results with laboratory experiments. Incompressibility is assumed despite the dilatancy observed in the experiments (up to 10%). The 2-D model is based on the so-called μ(I) rheology that induces a Drucker-Prager yield stress and a variable viscosity. A nonlinear Coulomb friction term, representing the friction on the lateral walls of the channel, is added to the model. We demonstrate that this term is crucial to accurately reproduce granular collapses on slopes ≳10°, whereas it remains of little effect on the horizontal slope. Quantitative comparison between the experimental and numerical changes with time of the thickness profiles and front velocity makes it possible to strongly constrain the rheology. In particular, we show that the use of a variable or a constant viscosity does not change significantly the results provided that these viscosities are of the same order. However, only a fine tuning of the constant viscosity (η=1 Pa s) makes it possible to predict the slow propagation phase observed experimentally at large slopes. Finally, we observed that small-scale instabilities develop when refining the mesh (also called ill-posed behavior, characterized in the work of Barker et al. [“Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow,” J. Fluid Mech. 779, 794–818 (2015)] and in the present work) associated with the mechanical model. The velocity field becomes stratified and the bands of high velocity gradient appear. These model instabilities are not avoided by using variable viscosity models such as the μ(I) rheology. However we show that the velocity range, the static-flowing transition, and the thickness profiles are almost not affected by them.

Granular column collapse experiments have been conducted on a flat rough surface tilted at various angles with synchronous measurements of the flow dynamics and the emitted seismic signal. Our results show that the ratio of radiated seismic energy to potential energy lost by the granular flows decreases slightly from 0.033% to 0.017% with increasing slope angle on a poly(methyl methacrylate) (acrylic) plate. This is about 90 times lower than for the impact of a single particle of the same diameter. The experimental granular flows generated signals with frequencies lower than 20 kHz, with a mean value around 5 kHz, which are shown to be similar to the frequencies emitted by a single‐particle impact. The rise phase and maxima of the amplitude and frequencies of the seismic signals generated by our experimental granular flows are mostly controlled by flow motion in the direction normal to the slope, while their decay phase depends on downslope particle speeds. The granular flow regime changes from dense to more agitated flows above a critical slope angle that is about half the friction angle of the granular material. This change is reflected in (1) the shape of the temporal variation of the seismic amplitude and frequencies, with a decay phase lasting much longer and (2) the shape of the cumulative radiated seismic energy, which changes above the same critical slope angle. Implications of these results for the interpretation of seismic emissions from experimental and natural granular flows are discussed.

The elastic waves generated by impactors hitting rough and erodible surfaces are studied. For this purpose, beads of variable materials, diameters, and velocities are dropped on (i) a smooth PMMA plate, (ii) stuck glass beads on the PMMA plate to create roughness, and (iii) the rough plate covered with layers of free particles to investigate erodible beds. The Hertz model validity to describe impacts on a smooth surface is confirmed. For rough and erodible surfaces, an empirical scaling law that relates the elastic energy to the radius R b and normal velocity V z of the impactor is deduced from experimental data. In addition, the radiated elastic energy is found to decrease exponentially with respect to the bed thickness. Lastly, we show that the variability of the elastic energy among shocks increases from some percents to 70% between smooth and erodible surfaces. This work is a first step to better quantify seismic emissions of rock impacts in natural environment, in particular on unconsolidated soils.

We present a novel method for measuring the fluctuating basal normal and shear stresses of debris flows by using along-channel seismic recordings. Our method couples a simple parameterization of a debris flow as a seismic source with direct measurements of seismic path effects using empirical Green's functions generated with a force hammer. We test this method using two large-scale (8 and 10 m 3) experimental flows at the U.S. Geological Survey debris-flow flume that were recorded by dozens of three-component seismic sensors. The seismically derived basal stress fluctuations compare well in amplitude and timing to independent force plate measurements within the valid frequency range (15-50 Hz). We show that although the high-frequency seismic signals provide band-limited forcing information, there are systematic relations between the fluctuating stresses and independently measured flow properties, especially mean basal shear stress and flow thickness. However, none of the relationships are simple, and since the flow properties also correlate with one another, we cannot isolate a single factor that relates in a simple way to the fluctuating forces. Nevertheless, our observations, most notably the gradually declining ratio of fluctuating to mean basal stresses during flow passage and the distinctive behavior of the coarse, unsaturated flow front, imply that flow style may be a primary control on the conversion of translational to vibrational kinetic energy. This conversion ultimately controls the radiation of high-frequency seismic waves. Thus, flow style may provide the key to revealing the nature of the relationship between fluctuating forces and other flow properties. Few monitoring sites rely solely on seismic methods, in part due to the lack of clear quantitative links between seismic signals and flow characteristics. By necessity, most sites combine seismic sensors with nonseismic monitoring methods such as tripwires, pendulums, cameras, flow depth sensors, and manned watch stations (e.g.,