Behind the long runout of deadly pyroclastic density currents

As worldwide population growth continues, the threat from volcanic events intensifies. Over 600 million individuals live in regions at risk of deadly pyroclastic density currents, making it essential to understand the elements responsible for their extensive reach.
Behind the long runout of deadly pyroclastic density currents
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Origin story

It was a dark and stormy night in Berkeley, California, when Dr. Walsh and I, both participants in the CIDER program, found ourselves deep in discussion after an intense day of researching viscous granular flows. The program, aimed at fostering collaboration among early-career geoscientists studying volcanic processes, had brought us together to explore the connections between various natural avalanches, both volcanic and non-volcanic.

Granular interactions are crucial in the initiation, transportation, and deposition of mass flows, such as turbidity currents, snow avalanches, rock avalanches, landslides, debris flows, and pyroclastic flows, among others. Interestingly, all these flows share a common characteristic: the larger the flow, the farther it travels. This observation may seem obvious, but what captures our attention is the fact that when we scale the runout (the distance traveled from the source) to the drop height (which provides potential energy), we find that the mobility increases with the flow size. This trend appears to be universal, even observed in extraterrestrial landslides.

While the search for a universal volume-dependent mechanism that reduces friction and enhances the mobility of mass flows is an ongoing area of research in geophysics, planetary sciences, and soft-matter physics, volcanic flows stand out as the most mobile gas-particle granular flows on Earth. Their unique composition, a multiphase mixture of blocks, ash, and gas, combined with high temperatures (typically 200-600 degrees Celsius), offers clues to their exceptional mobility. But how does the gas phase influence the rheology of these granular mixtures?

Fluidisation

Enter fluidisation: a process in which a fluid flows through a porous granular medium in a direction opposing gravity, reducing both normal stress and subsequently effective shear stress, and ultimately diminishing the effective friction. Fluidisation is widely used in industry to facilitate chemical reactions, heat transfer, and the transportation of granular materials by forcing an external fluid flow through a granular bed. However, in most cases, such external fluid flow is not expected to occur in pyroclastic density currents (PDCs). Instead, the creation of excess pore-fluid pressure (fluidisation) and its diffusion (defluidisation) can result from the compaction of the mixture, a phenomenon known as pore pressure feedback. 

Sketch of the pore pressure feedback in multiphase flows (Adapted from Lube et al. 2020)

Through a combination of observations, theories, and experiments at various scales, we have come to understand that the low permeability of volcanic mixtures, which are highly polydisperse and rich in fines, coupled with their formation mechanism (e.g. collapse of a dilute volcanic column that failed to become buoyant or sedimentation at the base of a dilute ash cloud) can lead to the partial fluidisation of the dense granular layer at the base of PDCs. This, in turn, can sustain excess pore pressure for an extended duration, further elucidating the remarkable mobility of volcanic granular flows.

Thought experiment

A few weeks before our intriguing conversation with Dr. Walsh, I had begun working on a Nature Reviews article on pyroclastic density currents (PDCs) and found myself grappling with the understanding of a specific type of PDC and the processes leading to its fluidisation. The PDC in question, known as block-and-ash flows, typically consists of bimodal mixtures of blocks and powder (ash) formed by dome collapses. These flows are prevalent in volcanoes that erupt highly viscous lava, creating a "plug" or dome at the top of the conduit. Pressure builds up beneath the lava dome, causing extrusion and eventual collapse, often due to destabilization on slopes steeper than 40°. The video below illustrates a recent dome-fed PDC descending the slopes of Indonesia's Merapi volcano at a velocity exceeding 50 m/s. Such flows are both common and extremely hazardous.

Dense granular avalanches, which drive the current, are usually confined to valleys. However, the more dilute turbulent overriding ash-cloud behaves like a gravity current, capable of spilling out of valleys and potentially engulfing populated areas. Block-and-ash flows begin as a mixture dominated by large blocks formed by fragmentation of the dome upon impact on the steep slope. The question that arises is: how quickly do these flows acquire their characteristic grain-size distribution, and how does this affect the interstitial gas phase?

While previous studies have examined attrition and particle rounding (e.g. Dufek et al. 2008), existing PDC models in the dense regime have either assumed incompressibility (constant particle volumetric concentration) or a constant maximum random packing value, regardless of the transported grain-size distribution. Both assumptions overlook a critical aspect of PDCs: how pore fluid pressure responds to fragmentation of the granular mixture.

We then considered a thought experiment: the widening of the grain-size distribution would lead to the compaction of the granular avalanche on steep slopes, subsequently increasing pore-fluid pressure and reducing the mixture's effective shear stress. With a hypothesized mechanism in mind, we sought evidence in past volcanic eruptions.

Example of block-and-ash flow deposit from Mont Hood volcano, Oregon, USA.

Having a suspected mechanism, we sought the evidence in past volcanic eruptions

Years later, we examined natural PDCs, focusing on well-studied flows produced by Merapi volcano. Collaborating with my colleague Dr. Charbonnier, an expert on block-and-ash flows, we tested our hypothesis on grain-size data collected from Merapi PDCs. The deposits were sampled from proximal areas (about 2 km from source) to the final runout of the flows (7-15 km) and showed remarkable invariance with distance. We analyzed three main events from 2006 and 2010 and found striking similarities in grain-size distribution (GSD) between them. The self-similar fragmentation mechanism appeared to be self-limiting, as the flow of blocks transformed into a flow of block-and-ash but did not become a flow composed solely of ash. But why?

We turned to soft-matter physics for answers. In a mixture with two size fractions, the fines create the matrix, meaning the coarse fraction (blocks) does not directly contact each other. Using the discrete element method, researchers demonstrated that contact stresses are almost entirely carried by the fine fraction once about 30% of the solid volume is occupied by fines (Shire et al. 2014). Consequently, the fines act as a shielding material, preventing further fragmentation of blocks within the flow.

With an understanding of why the material's grain-size does not change drastically past ~2 km from source, it became evident that significant GSD changes occur within the first 2 km of the runout. The remaining question thus arises: How does this affect the flow rheology?

Why does the random-close packing value matter?

Granular media's rheology in a specific state is heavily influenced by its proximity to jamming (Kostynick et al. 2022). We thus explored the concept of time-variant jamming points (a particular particle-volumetric concentration) in granular mixtures in the laboratory, using block-and-ash flow mixtures. By measuring the highest particle volumetric concentration at jamming as a function of grain-size distribution, we discovered that existing mathematical descriptions for spherical mixtures could be adapted to account for the non-sphericity of natural grains. Dr. T Giachetti and I investigated how the random-close packing of natural scale mixtures would evolve with distance, inferring that it must have increased proximally and then remained relatively constant. The change in the mixture's jamming point, due to the transformation of the transported grain-size, implies that the distance to jamming would increase with time if the flow did not respond to such changes. Instead, the flow would respond by compacting.

While we might expect the flows on steep slopes like those at Merapi (15-40°) to be quite diluted granular flows, the large thickness of the flows and associated confining normal stress actually make the flow quite dense, with concentrations reaching around 80 vol.% as it acquires its "final" bimodal grain-size distribution (GSD).

Numerical investigation

Pr. Dufek and I utilized a multiphase flow code to examine the interplay between Reynolds dilatancy, compaction arising from GSD changes, and the influence on pore-fluid pressure. We studied the balance between compaction (source) and diffusion of excess pore-fluid pressure (sink) as the mixture permeability (dependent on GSD and porosity) and flow thickness evolved in time. Employing the Eulerian-Eulerian (continuum) approach, we investigated the impact of fragmentation rates and initial flow thickness on the fragmentation-induced fluidisation (FIF) mechanism.

Our simulations yielded a variety of feasible fragmentation rates and predicted the partial fluidisation of PDC mixtures at Merapi. They also illustrated the significant effect of volume on the FIF process concerning flow mobility, as larger and thicker flows fragmented more quickly and defluidized at a slower pace. Upon acquiring the final GSD, flows are primarily governed by diffusion, with runout mainly dictated by flow thickness.

These findings served as inputs for a depth-averaged model simulating PDCs traversing volcanic topography. Although such models do not encompass the full physics of the flows, they are highly effective in evaluating flow behaviour over complex 3D topography. This allows for rapid PDC hazard assessment, epistemic uncertainty exploration, and even the creation of probabilistic hazard maps.

By examining the FIF process's efficacy at Merapi, we demonstrated its capacity to replicate the extent of natural events, and deduced that the fragmentation-induced fluidisation mechanism plays a crucial role in generating highly mobile block-and-ash flows.

Interestingly, the FIF process also facilitates the elutriation of fine particles, supplying the overriding ash-cloud. As the mixture compacts, the forced upward airflow transports well-coupled fine particles, shedding light on the highly time-dependent and dominant nature of the elutriation flux in the proximal region.

Other processes that can aid the FIF process

The discovery of the FIF mechanism enhances our comprehension of other flows, such as those resulting from the collapse of coarse proximal material accumulated on steep slopes (Charbonnier et al. 2023). This is relevant to PDCs produced by Fuego volcano during the eruption on June 3, 2018, since the deposits exhibit numerous similarities to the BAFs generated by dome collapses. Consequently, the FIF process likely contributed to the increased mobility of these flows, leading to devastating outcomes.

While the FIF mechanism plays a crucial role in transforming highly frictional granular media into partially fluidised mobile pyroclastic mixtures, additional processes can further boost PDC mobility. These include vaporization of water (liquid or as snow) present on the substrate, compaction as flows encounter large topographic barriers (e.g. steps), and potential degassing of gas-rich portions of the lava dome.

Future implications

In conclusion, the discovery of the fragmentation-induced fluidisation (FIF) mechanism has shed new light on the complex dynamics of pyroclastic density currents. By investigating the role of FIF in various volcanic settings, we could better understand the mobility and hazards associated with these powerful and destructive phenomena. As we persist in honing our models and observations, we aim to improve our abilities to evaluate and reduce the risks associated with PDCs, ultimately bolstering our efforts to safeguard communities near active volcanoes.

Personal perspective

A frontier in Volcanology lies in the in-situ measurement of physical properties of PDCs, a task that presents numerous engineering challenges. However, overcoming these obstacles and obtaining accurate measurements will be crucial in settling long-standing paradigms, ultimately making a significant impact on our understanding of pyroclastic density currents.

References:

Charbonnier, S. J., Garin, F., Rodríguez, L. A., Ayala, K., Cancel, S., Escobar-Wolf, R., ... & Calder, E. S. (2023). Unravelling the dynamics and hazards of the June 3rd, 2018, pyroclastic density currents at Fuego volcano (Guatemala). Journal of Volcanology and Geothermal Research, 107791.

Dufek, J., & Manga, M. (2008). In situ production of ash in pyroclastic flows. Journal of Geophysical Research: Solid Earth113(B9).

Lube, G., Breard, E. C., Esposti-Ongaro, T., Dufek, J., & Brand, B. (2020). Multiphase flow behaviour and hazard prediction of pyroclastic density currents. Nature Reviews Earth & Environment1(7), 348-365.

Kostynick, R., Matinpour, H., Pradeep, S., Haber, S., Sauret, A., Meiburg, E., ... & Jerolmack, D. (2022). Rheology of debris flow materials is controlled by the distance from jamming. Proceedings of the National Academy of Sciences119(44), e2209109119.

Shire, T., O’Sullivan, C., Hanley, K. J., & Fannin, R. J. (2014). Fabric and effective stress distribution in internally unstable soils. Journal of geotechnical and geoenvironmental engineering140(12), 04014072.

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