Continuum Modeling of Pressure‐Balanced and Fluidized Granular Flows in 2‐D: Comparison With Glass Bead Experiments and Implications for Concentrated Pyroclastic Density Currents

Abstract

Granular flows are found across multiple geophysical environments and include pyroclastic density currents, debris flows, and avalanches, among others. The key to describing transport of these hazardous flows is the rheology of these complex multiphase mixtures. Here we use the multiphase model MFIX in 2‐D for concentrated currents to examine the implications of rheological assumptions and validate this approach through comparison to experiments of both frictional and fluidized flows made of glass beads (Sauter mean grain‐size of 75 μm). Because the rheology of highly polydisperse, highly angular, polydensity granular mixtures is poorly known, we focus on simplified monodisperse or bidisperse mixtures described by the frictional flow theory of Schaeffer (1987, https://doi.org/10.1016/0022-0396(87)90038-6) and Srivastava‐Sundaresan, often referred to as the Princeton model (Srivastava & Sundaresan, 2003, https://doi.org/10.1016/S0032-5910(02)00132-8). We show that simulations including the latter model replicate well the flow shape, kinematics, and pore fluid pressure that match well‐constrained dam‐break experiments of initially fluidized or pressure‐balanced granular flows. Simulations reveal that pore fluid pressure is intrinsically modulated by dilation and compaction of the flow and hence can be generated in concentrated pyroclastic density currents. We use these simulations to interpret basal pore pressure signals from local flow properties (mixture density, solid velocity, and pore fluid pressure). Rheological changes retard these simulated flows considerably near the predicted runout, but most continuum models cannot inherently predict a zero velocity. We suggest an inertial number parameter that can be used to approximate deposition, and this approach could be a valuable tool used to validate simulations against natural pyroclastic current examples.

Granular mixture deflation and generation of pore fluid pressure at the impact zone of a pyroclastic fountain: Experimental insights

“…Figure S2). This underpressure was likely generated by the slip of the granular material along the channel walls, as shown by earlier studies (Breard et al, 2019;Roche, 2012;Roche et al, 2010) but we acknowledge that we did not quantify the local velocity of the granular mixture at the impact zone. Synchronization of the pore pressure measurements with the high-speed videos permitted us to correlate the pressure signals to the stages of particle accumulation (Figure 5).…”

“…These include in particular the mechanisms of the pyroclastic mixture deflation at the impact zone and the formation of the emerging lateral flows. Recent numerical simulations, however, reveal that the dynamics of the impinging fountain and of the resulting lateral flows depend fundamentally on the degree of gas-particle coupling, which controls the particle size segregation and the flow solid concentration (Breard et al, 2019;Sweeney and Valentine, 2017;Valentine, 2020), and on the velocity of the falling mixture, so that shocks and overpressured lateral jets form in supersonic conditions (Valentine and Sweeney, 2018). Rapid differential motion between the gas and the particles and associated drag force can generate interstitial pore fluid pressure (Breard et al, 2018;Valentine, 2020).…”

Modelling pyroclastic density currents from a subplinian eruption at La Soufrière de Guadeloupe (West Indies, France)

“…Many aspects of PDC dynamics remain difficult to investigate, because of the lack of knowledge on the constitutive properties of gas-particle mixtures and the spatial resolution of the numerical simulations. In particular, it is still challenging to describe the rheology of concentrated granular mixtures in 3D (Breard et al 2019) and to correctly reproduce vertical stratification when the vertical grid size is comparable to or larger than the thickness of the basal layer. Our model-based estimates of PDC runout, temperature, and dynamic pressure should then be taken as relative measures and are intended as average values over the first 10-20 m above the topography.…”

Supplemental Material: Explosive caldera-forming eruptions and debris-filled vents: Gargle dynamics

“…The model equations are implemented in the open-source code MFIX (v. 2020.3.1, see mfix.org for the code and full documentation), which uses a finite volume approach to solve the governing equations. Valentine and Sweeney (2018) summarize code validation that supports the application of the model to explosive eruptions and pyroclastic currents, which has since been bolstered by the work of Breard et al (2019).…”