# Large-scale volcanic deposit fluidization by dilute pyroclastic density currents

Karim Kelfoun, Antonio Proaño

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Karim Kelfoun, Antonio Proaño. Large-scale volcanic deposit fluidization by dilute pyroclastic density currents. Nature Geoscience, 2023, 16 (6), pp.499-504. 10.1038/s41561-023-01190-7. hal-04215005

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Large-scale volcanic deposit fluidisation
by dilute pyroclastic density currents

Published in Nature Geoscience, 2023

DOI - https://doi.org/10.1038/s41561-023-01190-7

Karim Kelfoun¹, Antonio Proaño¹,²

1. Université Clermont Auvergne, CNRS, IRD, OPGC, Laboratoire Magmas et Volcans, F-63000 Clermont-Ferrand, France. Corresponding author: karim.kelfoun@uca.fr

2. Instituto de Investigación Geológico y Energético (IIGE), Quito 170503, Ecuador

**Introductory paragraph**

There is increasing evidence that fine-grained deposits of pyroclastic density currents can be remobilized on a large scale, resulting in concentrated flows. These flows can be a major hazard: for example, at Soufrière Hills Volcano (Montserrat) in 1997, some travelled beyond the designated danger zone to inhabited areas. Despite their hazard potential, the scale and generation mechanism of these flows are poorly understood. Here we demonstrate using laboratory experiments and numerical modelling that decompression following the passage of dilute pyroclastic density currents can cause rapid deposit fluidization over areas of several square kilometres and to depths of tens of centimetres. The fluidized volume can be substantially greater than that deposited by the triggering pyroclastic density current because of remobilization of previously emplaced deposits, and the fluidized volume can flow even on slopes of a few degrees. The capacity for remobilization of a deposit is limited by its particle cohesion, which rapidly increases with atmospheric humidity. This mechanism of fluidisation should alert us to an under-appreciated volcanic hazard of long-runout pyroclastic flows that can be generated by remobilisation very rapidly and with little warning.

**Main**

Ground-hugging pyroclastic density currents (PDCs) are made up of a mixture of gas and volcanic particles. They cover a broad spectrum of densities from dilute to concentrated. Dilute currents, also called nuées ardentes and pyroclastic surges¹⁻³, transport particles predominantly by turbulent suspension⁴. These currents may originate at an eruptive vent or as the turbulent cloud atop a concentrated PDC. Their particle concentrations are relatively low (< 5%⁵⁻⁷) except close to the ground, where they increase² and where particles are deposited through bed-load mechanisms (such as saltation, traction and rolling)³. Dilute PDCs easily escape any valley topography to cover the interfluves over large areas (several km²)⁸⁻¹¹.

Field evidence such as slumps, overturned deposit laminations and block sag structures (ref¹² and therein) show that the deposits formed by dilute PDCs can experience a fluid behaviour locally. The deposits can be in such a fluid state that coarse ash grains falling onto them forms tiny sag structures¹³. At a much larger scale, the fluidity could affect extensive areas, up to several hundred square metres, and, on slopes, the remobilized deposit could evolve into a concentrated flow able to move hundreds to thousands of metres independent of the parent dilute PDC. This phenomenon, called surge-derived pyroclastic flow, was observed particularly well at Montserrat in 1997¹⁴,¹⁵, and where also documented at Mount St Helens¹⁶,¹⁷, Montagne Pelée¹⁸, Merapi¹¹ and at phreatomagmatic Ubehebe Crater¹²,¹³,¹⁹. Among the various mechanisms evoked for localised fluidisation (ref¹² and therein), the role of pore gases is thought to be highly influential. Field evidence, such as segregation pipes and surface craters, indicate gas defluidisation after emplacement³,¹¹,¹⁶,²⁰. The current explanation for large-scale remobilisation is that gases are trapped during rapid sedimentation of the dilute PDC¹³,¹⁵. As with the dramatic large-scale liquefaction by water²¹⁻²⁷, the pressure gradient between the pressurized interior of the deposit and the surface could counterbalance the weight of the particles²⁸⁻³⁴. The normal stress between the particles drops and, consequently, the resisting shear stress decreases too. If the pressure gradient is steep enough, then the deposit behaves as a fluid and, especially on steep slopes, can begin to flow. However, it is not clear how such an
overpressure builds up. Indeed, while a densely-packed deposit of fine particles can retain gases³²,³⁵, the spaces between the particles probably allow the gas to escape when the particles settle out of the dilute PDC except at very high settling rates³⁴,³⁶ that seem incompatible with their runouts and the mass of particles transported.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Emplacement of a dilute PDC. (a) The pressure of the gas, at its base, is higher than atmospheric pressure. Consequently, it is higher in the resulting deposit. This induces deposit fluidisation in the aftermath of the PDC, when the surface pressure drops back down rapidly enough.</figcaption></figure>

One characteristic of dilute PDCs has not been studied up to now: due to their depth, density and velocity, the gas pressure at their base is higher than atmospheric pressure. The pressure of the interstitial gas in the deposits they form is thus also higher (Fig 1). After the passage of a PDC, the pressure of the gas at the surface must drop back to atmospheric pressure. A gas pressure gradient is thus temporarily created between the interior of the deposit and its surface. Is this pressure gradient enough to fluidise the deposit? What might the consequences of this type of fluidisation be?

To answer these questions, we designed an experimental pressurized tank (see Methods) filled with granular material (Fig 2). Pressure sensors in the granular bed measure the air pressure at different depths. To ensure that the observed phenomena reproduce conditions that could also occur in the field, the experiment setup has been scaled to nature in terms of overpressure, deposit thickness and particle permeability. We also developed a numerical model to further explore the larger range of parameters found in actual volcanic fields.

## Range of parameters studied

Particles deposited by dilute PDCs typically ranges from tens of microns to a few millimetres¹¹,²⁰,³⁷. The gas permeability K, related to the particle size, can be as low as $10^{-13}$–$5 \times 10^{-12}$ m² in ignimbrite and pumice deposits³⁵,³⁸. For deposits of dilute PDC and surge-derived pyroclastic flows, K has been estimated between $10^{-11}$ and $10^{-10}$ m² although the finest particles found in these deposits ($< 20$ µm) can significantly lower this value¹¹,²⁰,³⁸,³⁹. Dilute PDC deposits is typically of some centimetres to tens of centimetres thick¹¹,¹⁹,²⁰. Because they may overlie previous deposits into which the gas can diffuse, we have explored deposit thicknesses H of up to 10 m. We have also explored a large range of deposit densities ρ, between 500 to 2000 kg/m³. The air viscosity is between $\mu = 1.85 \times 10^{-5}$ (at 20°C) and $4.5 \times 10^{-5}$ Pa s (at 950°C).
The maximal static gas pressure at the base of a moderate PDC and its unloading time (i.e. the time to drop back from the maximal static pressure to atmospheric pressure) can be estimated indirectly through numerical simulations of PDC emplacement at Merapi⁴⁰ and Montserrat⁴¹ at 5–10 kPa and 5–30 s, respectively. However, the total gas pressure at the base of a PDC must also include the dynamic pressure which depends on the PDC density ρ_s and its velocity u_s, and is given by $\frac{1}{2} \rho_s u_s^2$. The maximal particle concentration carried by turbulence in a dilute PDC is about 5% vol.⁵⁻⁷ i.e. a density of about ρ_s = 70 kg/m³. With a velocity of 40 m/s⁴²,⁴³, the dynamic pressure increases by more than 50 kPa at certain places where the current meets rises in topography. Moreover, turbulence can create fluctuations in pressure of up to three times that of the mean dynamic pressure⁴⁴. These pressure fluctuations can also cause higher than expected unloading rates. To take these uncertainties into account, we have explored a large range of initial basal pressures P_s0 (1–100 kPa) over the atmospheric pressure (P_atm), a large range of unloading times Δt (0–300 s) and, consequently, a large range of unloading rates (10 Pa/s to >20 kPa/s).

<figure><img src="image_3.png" /><figcaption>**Figure 2:** The experimental device made to simulate the unloading of a dilute PDC. (a) (1) the sealed tank partially filled with granular material, (2) pump, (3) vertical pipe filled with water for sensor calibration, (4) acquisition device, (5) computer and our dedicated acquisition software, (6) LED for synchronisation of videos and pressure measurements, (7) depressurisation valve, (8) pierced caps. (b) Locations of the pressure sensors, numbered 1–8. (c) Schematic representation of one of the sensors used to measure the gas pressure at various depths in the granular bed (located on 2b). (d) Initially, the air between the particles and that above is at atmospheric pressure. (e) The air is then pressurised (using a pump (2) in (2a) and diffuses between the particles. (f) When the pressure is equalized, the valve (7) in (2a) is opened. A cap (8) in (2a) screwed on to the valve controls the decompression rate. Decompression is slower between the particles than above them. (g) This creates a pressure gradient that can fluidise the particle bed.</figcaption></figure>

## Experimental results

The experimental procedure is described in the Methods section. The air is first pressurized above the granular material, leading to a gas pressure increase between the particles. After the valve is opened, the pressure of the air above the granular bed drops (Fig. 2d–g and Fig. 3). The pressure of the air in the bed itself drops in turn, but with a time delay that depends on the bed's permeability, its total thickness and on the distance to the bed surface. The difference between
the pressure within the bed and at its surface increases rapidly (Fig. 3b), creating a gas pressure gradient that can counterbalance the weight of the particles. For low decompression rates (e.g. < 2 kPa/s, see how this value is calculated in Methods), the gas pressure drops in the bed but no movement of the granular material is detected. For intermediate decompression rates (between 2 kPa/s and 8 kPa/s, Fig. 4a), the decompression causes an expansion of the granular material. Experiments with different slope angles show granular flow occurring even on a slope of a few degrees, which indicates partial fluidisation of the granular material. Bubbles can be observed in the bed. For high decompression rates (>8 kPa), the granular material exhibits very fluid behaviour: it flows even on very gentle initial slopes (5°) and forms waves that oscillate before coming to a standstill on a nearly horizontal surface (Fig. 3c). Bubbles, whose size increases with the decompression rate, form in the granular bed and burst at its surface (Fig. 3f-g) forming degassing craters.

<figure><img src="image_4.png" /><figcaption>**Figure 3:** Results of the decompression experiments. (a) Evolution of the pressure with an initial slope of 10° (d, e and f), an initial overpressure $P_{s0}$ of 25 kPa and a maximal decompression rate of ~11 kPa/s (mean 5 kPa/s) for the three sensors shown in (d). The letters in the black circles refer to the locations of figures d-g. (b) Gas pressure difference between sensors 3 and 8, and the granular bed surface (sensor 1). The horizontal dashed lines show the pressure difference needed to fully fluidise the flows, or to enable flow on a 10° slope. (c) Evolution of the slope with time, from an initial angle of 10° to horizontal after fluidisation. (d) Initial geometry of the granular bed before decompression. (e) Flow of the granular bed before bubble genesis. (f) Bubble formation. The decompression rate makes that only the top half of the bed is able to fully fluidise (see caption (b)). (g) Full fluidisation of the whole granular bed and high bubble formation at lower initial pressure (17 kPa) but with a higher decompression rate (79 kPa/s).</figcaption></figure>

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Movies of some experiments synchronized with pressure data are given in Data availability.

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Similar results have been obtained using natural material at high temperature (>100°C).

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However, below 100°C, the natural material is very sensitive to temperature, probably due to

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interaction with air humidity, and cohesive behaviour can be observed: cracks form during

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decompression that coalesce to form preferential paths by which the gas escapes, carrying with

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it the smallest particles and forming fine-depleted degassing pipes while reducing the

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effectiveness of fluidisation.

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## Numerical simulation of the fluidisation

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To explore the whole ranges of unloading (i.e. decompression) conditions ($P_{s0}$, $\Delta t$, $\mu$) and of

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deposit characteristics ($K$, $H$, $\rho$) defined in the section *Range of parameters studied*, we have

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written a numerical model for defluidisation (downloadable in *Code availability*) inspired by

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the work of ref$^{35}$. We have validated the numerical model against our experimental results in

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terms of the evolution of the pressure with time and the capacity of the granular bed to flow on

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a slope. Then we have used the model to explore a broader range of conditions (see *Methods*

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and *Extended Data Fig. 1*).

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Analysis of the numerical results shows that the system is controlled by two dimensionless

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numbers. $\Pi_1 = \frac{\rho gH}{P_{s0}}$ controls the maximal depth of fluidisation with respect to the PDC

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pressure, with $g$ as gravity. $\Pi_2 = \frac{H^2 \mu}{K \bar{P}_s \Delta t}$ is a ratio of the characteristic defluidisation time of the

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granular bed over the unloading time $\Delta t$ of the dilute PDC, with $\bar{P}_s$ the mean value of gas

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pressure during unloading approximated by $\bar{P}_s = P_{atm} + P_{s0}/2$ (see *Methods*).

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The maximal gradient of the gas pressure is systematically at the surface of the granular bed

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and this explains why the fluidisation (number of bubbles and granular flow) is higher at the

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surface of our experiments than at the bottom. We use the term ‘full fluidisation’ where the

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pressure gradient of the gas equals that of the particles and where, consequently, friction between the particles is zero. Full fluidisation can affect the entire bed or the upper part alone.

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*Fig 4a* (and *Extended Data Fig. 2*) shows the ratio $H_f/H$ of the fully fluidised depth, $H_f$,

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(from the surface) over the total bed thickness, $H$, according to $\Pi_1$ and $\Pi_2$. $\Pi_1 = 1$ is the limit

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for the full fluidisation of the entire bed and, at higher values (thicker deposits or lower

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pressures), the upper part of the granular material alone is fluidised.

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A thin or very permeable deposit loses its gas rapidly (dark grey domain, Fig. 4a) while a thick

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or low permeability deposit (light grey and white domains) retains the gas longer, maintaining

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the pressure difference needed for full fluidisation of its upper part. Analysis of $\Pi_1$ and $\Pi_2$

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shows that low permeability deposits ($K = 10^{-12} \text{ m}^2$) are fluidised relatively easily except at low

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thicknesses (<10 cm) or over long unloading times. For example, with $P_{s0} = 10 \text{ kPa}$, $\rho = 1500$

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kg/m$^3$ and $\mu = 3 \times 10^{-5} \text{ Pa s}$, a deposit of 20.4 cm, 68 cm and 4 m experiences full fluidisation at

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its surface for unloading times, $\Delta t$, of less than 23s, 76s and 234 s respectively (Fig. 4a, point

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$\alpha$: $\Pi_1=0.3$ and $\Pi_2=0.5$, point $\beta$: $\Pi_1=1$ and $\Pi_2=1.7$, point $\gamma$: $\Pi_1=6$ and $\Pi_2=20$). For $\Pi_1=0.3$, the

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deposit is entirely fluidised for $\Pi_2>2$, i.e. for $\Delta t<5.8$s. Figure 4a also gives the values of $t_{f10}/\Delta t$,

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the ratio of $t_{f10}$ (the period of full fluidisation of the upper 10 centimetres of the granular bed,

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Fig. 4c), over the unloading time. In extreme cases, the bed can remain fluidised for several

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minutes after the passage of the dilute PDC. For example, with $H=5\text{m}$, $\rho=1000 \text{ kg/m}^3$ and $P_{s0}$

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= 50kPa, $\Pi_1 = 0.98$ (point $\varepsilon$). With $K=10^{-12} \text{ m}^2$ and $\Delta t=120 \text{ s}$, $\Pi_2 = 49.5$. The deposit is thus
fluidised over nearly its whole thickness and $t_{f10}/\Delta t \approx 8$ indicates that the upper 10 centimetres are fluidised for more than 15 minutes by gas escaping from below. The higher permeabilities ($K = 10^{-11} m^2$) require thicker deposits, higher pressures or shorter unloading times to achieve fluidisation, but a significant depth of material can become fully fluidised. For example, with $P_{s0} = 50 \text{ kPa}$, $\Delta t = 60 \text{ s}$ and $\rho = 1500 \text{ kg/m}^3$ (Fig. 4b-c), 35% of the deposit is fully fluidised (i.e. down to a depth of 1.75 m) for a deposit thickness of 5 m (point $\zeta$: $\Pi_1 = 1.47$, $\Pi_2 = 9.90$). The upper 10 centimetres are fully fluidised for about 40 s ($t_{f10}/\Delta t \approx 66\%$). Finally, it should be noted that full fluidisation is not required to initiate a flow. For the previous example ($H = 5 \text{ m}$, $P_{s0} = 50 \text{ kPa}$, $\Delta t = 60 \text{ s}$), the upper 10 cm can flow for 80 s on a 10° slope and 80% of the deposit thickness (i.e. 4 m) can be remobilized ($\varphi = 10°$, white line Fig. 4c, see Methods for explanation of the apparent friction angle $\varphi$). The prediction of the deposit thickness that can flow on a given slope is predicted by a shift in the curves (white curves, Fig 4a).

<figure><img src="image_5.png" /><figcaption>**Figure 4:** Results of the numerical study of the fluidisation by the unloading of a dilute PDC. (a) Evolution of the ratio $H_f/H$ using to $\Pi_1$ and $\Pi_2$. The black curves give the values of $H_f/H$ for a full fluidisation ($\varphi=0°$). The white curves, which are slightly shifted black curves, give $H_f/H$ that flow on a 10° slope ($\varphi=10°$). The dashed curves give the value of $t_{f10}/\Delta t$. Greek letters refer to explanations in the text. The two experimental decompression rates used as examples in the text are also reported ($\Pi_1 = 0.116$). (b) Evolution of the gas pressure imposed at the surface of the deposit for point $\zeta$. (c) Evolution of the friction angle of the deposit with time for $P_{s0}=50 \text{ kPa}$, $K=10^{-11} m^2$ and $\Delta t=60 \text{ s}$ (point $\zeta$). Total fluidisation ($\varphi = 0°$) affects a depth of 1.75 m and the upper part of the deposit is fluidised for 40 s. Material can flow down slopes greater than 10° to a maximal depth of 4 m and the upper 10-cm can flow over this slope for about 80 s.</figcaption></figure>
Implications of large-scale fluidisation

The capacity of a dilute PDC to trigger remobilisation of the underlying deposits is mainly related to the permeability of the deposit and, consequently, the size of its particles³⁸,⁴⁵. We show that for a permeability of 10⁻¹² m² or less, realistic conditions of dilute PDC unloading and deposit thickness are compatible with deposit fluidisation and resulting concentrated flow on a slope. For a permeability of more than 10⁻¹¹ m², full fluidisation only occurs at the surface of thick deposits (>1 m). Are these conditions realistic for volcanic environments? Deposits in nature are rarely emplaced onto an impermeable basement and instead tend to be emplaced onto volcaniclastic deposits from previous activity (ash fall or PDC deposits). When the dilute PDC flows over such deposits, its pressure diffuses down into them, and they can exhibit the behaviour described above after the unloading due to the passage of the current. Thus, 10, 20 or 50 cm of a deposit can be totally fluidised for a period of tens of seconds if a dilute PDC moves over a thick sequence of previous permeable deposits.

We conclude that deposit fluidisation by dilute PDC unloading could be a relatively common phenomenon. We think that it was the cause of the concentrated surge-derived pyroclastic flows observed at Montserrat in 1997¹⁴,¹⁵ and our model is fully compatible with the ‘ash boiling’ described¹⁵. It is also compatible with observations at Ubehebe Crater¹³,¹⁹ and particularly the conclusion that the deposit was inflated and soft shortly after deposition¹⁹. The fact that surge-derived pyroclastic flows are not very commonly described in the literature is probably due to the difficulty of identifying them, since the topography generally causes these secondary concentrated flows to move into channel bottoms and blend with primary concentrated flows in process, making it difficult to distinguish between the two. Our study proposes a new physical framework for the interpretation of this kind of deposits. Note that our mechanism is still compatible with local preservation of the sedimentary structures (dune, lamination, etc.) observed in the field: it affects the deposit after deposition and only where the unloading conditions are compatible with fluidisation.

The capacity for remobilization by the new mechanism revealed by our study is limited by particle cohesion, which is rapidly increased by rain or atmospheric humidity. In these conditions, the gas escapes through fractures, limiting the possibility for particles to flow, as shown in the low temperature ignimbrite experiments. Thus, it seems unlikely that a PDC could remobilize very large volumes of soil or old volcanic deposits. However, during an eruptive phase, the particles might not be affected by atmospheric humidity. Each dilute PDC can pass over several square kilometres of deposit⁸,⁹,¹¹,²⁰,⁴⁰,⁴¹. If thicker, denser or faster-moving PDC develops, fluidisation conditions can be reached. Huge volumes of material accumulated over large areas during a period of a number of days could suddenly be remobilized over an area of several square kilometres. Thick concentrated flows of fine particles could then be generated across the whole area covered by the dilute PDC and could reach long distances with little warning on volcanic slopes, destroying areas previously considered to be safe. Volcanic phenomena are complex and unknown mechanisms clearly pose a challenge for hazard assessment. Our study shows that a dilute PDC can mobilize significantly more material than it has deposited. This new hazard and the associated risks must be taken into account for future estimates of volcanic threats.

Acknowledgements

This is contribution no. 590 of the ClerVolc program of the International Research Center for Disaster Sciences and Sustainable Development of the University Clermont Auvergne. We thank Thierry Latchimy, Edouard Régis, Eric Brut, Jean-Louis Fruquière and Cyrille Guillot for their help in the construction of the experimental devices. The comments of Pr. Greg Valentine contributed significantly to the improvement of the article.

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270 **Author contributions**

271 Conceptualization: K.K. Laboratory experiments: K.K. & A.P. Numerical code: K.K.

272 Writing—original draft: K.K. & A.P. Writing—review and editing: K.K. Funding acquisition:

273 K.K.

274

275 **Competing interests Statement**

276 The authors declare that they have no known competing financial interests or personal

277 relationships that have influenced the work reported.

278

279 **Figure captions**

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281 **Figure 1:** Emplacement of a dilute PDC. (a) The pressure of the gas, at its base, is higher than

282 atmospheric pressure. Consequently, it is higher in the resulting deposit. This induces deposit

283 fluidisation in the aftermath of the PDC, when the surface pressure drops back down rapidly

284 enough.

285

286 **Figure 2:** The experimental device made to simulate the unloading of a dilute PDC. (a) (1) the

287 sealed tank partially filled with granular material, (2) pump, (3) vertical pipe filled with water

288 for sensor calibration, (4) acquisition device, (5) computer and our dedicated acquisition

289 software, (6) LED for synchronisation of videos and pressure measurements, (7)

290 depressurisation valve, (8) pierced caps. (b) Locations of the pressure sensors, numbered 1–8.

291 (c) Schematic representation of one of the sensors used to measure the gas pressure at various

292 depths in the granular bed (located on 2b). (d) Initially, the air between the particles and that

293 above is at atmospheric pressure. (e) The air is then pressurised (using a pump (2) in (2a) and

294 diffuses between the particles. (f) When the pressure is equalized, the valve (7) in (2a) is opened.

295 A cap (8) in (2a) screwed on to the valve controls the decompression rate. Decompression is

296 slower between the particles than above them. (g) This creates a pressure gradient that can

297 fluidise the particle bed.

298

299 **Figure 3:** Results of the decompression experiments. (a) Evolution of the pressure with an

300 initial slope of 10° (d, e and f), an initial overpressure $P_{s0}$ of 25 kPa and a maximal

301 decompression rate of ~11 kPa/s (mean 5 kPa/s) for the three sensors shown in (d). The letters

302 in the black circles refer to the locations of figures d–g. (b) Gas pressure difference between

303 sensors 3 and 8, and the granular bed surface (sensor 1). The horizontal dashed lines show the

304 pressure difference needed to fully fluidise the flows, or to enable flow on a 10° slope. (c)

305 Evolution of the slope with time, from an initial angle of 10° to horizontal after fluidisation. (d)

306 Initial geometry of the granular bed before decompression. (e) Flow of the granular bed before

307 bubble genesis. (f) Bubble formation. The decompression rate makes that only the top half of

308 the bed is able to fully fluidise (see caption (b)). (g) Full fluidisation of the whole granular bed

309 and high bubble formation at lower initial pressure (17 kPa) but with a higher decompression

310 rate (79 kPa/s).

311

312 **Figure 4:** Results of the numerical study of the fluidisation by the unloading of a dilute PDC.

313 (a) Evolution of the ratio $H_f/H$ using to $\Pi_1$ and $\Pi_2$. The black curves give the values of

314 $H_f/H$ for a full fluidisation ($\varphi=0^\circ$). The white curves, which are slightly shifted black curves,

315 give $H_f/H$ that flow on a 10° slope ($\varphi=10^\circ$). The dashed curves give the value of $t_{f10}/\Delta t$.

316 Greek letters refer to explanations in the text. The two experimental decompression rates used

317 as examples in the text are also reported ($\Pi_1 = 0.116$). (b) Evolution of the gas pressure imposed

318 at the surface of the deposit for point $\zeta$. (c) Evolution of the friction angle of the deposit with

319 time for $P_{s0}=50$ kPa, $K=10^{-11} m^2$ and $\Delta t=60$ s (point $\zeta$). Total fluidisation ($\varphi=0$) affects a depth
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of 1.75 m and the upper part of the deposit is fluidised for 40 s. Material can flow down slopes greater than 10° to a maximal depth of 4 m and the upper 10–cm can flow over this slope for about 80 s.

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## Methods

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### Experimental fluidisation by decompression

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The experimental device is composed of an ~7 litre (length 40 cm, width 6 cm, height 30 cm) sealed tank partly filled with granular material (Fig 2a–b). Experiments were carried out with various thicknesses *H* (< 25 cm) of either particles from a natural deposit (ignimbrite from Neschers³⁵) or glass beads with a granulometry close to the fine matrix of dilute PDC deposits (40–70 µm). The air pressure inside the tank could be raised (via the “in” hole, Fig 2b) up to *P*₀ = 30 kPa above atmospheric pressure (Fig. 2e–f). The pressurized air also pushed up a water column in a connected vertical pipe, providing an independent check on the pressure of the tank with an accuracy <10 Pa. A valve located above the granular material allowed the air to be decompressed to atmospheric pressure (“out” hole, Fig 2b). Decompression rates, from 0 to 100 kPa/s, were controlled by caps pierced with holes of different diameters and screwed onto the valve. Seven pressure sensors were sunk into the granular material and measured the air pressure *P* at different depths. An eighth sensor (sensor 1, Fig. 2b) measured the air pressure *P*<sub>s</sub> + *P*<sub>atm</sub> above the particle bed. The pressure sensors were 86–005G–C (for sensors 1, 3, 5 and 8, Fig 2b) and 86–015G–C (for the others) of TE–Connectivity, with a maximal pressure range of 5 psi (~ 34 kPa) and 15 psi (~ 103 kPa) respectively and an accuracy of ~ 23 Pa and ~ 70 Pa. The sensors were recalibrated before each experiment with water levels in the vertical pipe to correct for potential instrumental drift. The measurements were taken at 1000 Hz. An LED lit up when acquisition was triggered to synchronize the measurements with the videos (25 Hz and 500 Hz). To make the bubbles more visible, some experiments were done with the box tilted slightly backwards to force the bubbles to move across the tank window.

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Because the decompression rate is quasi exponential, it varies with time. For a comparison with the numerical results, the values given in the *Experimental Results* section are the mean value, *P̅*<sub>s</sub> (defined as the point at which the air overpressure is half that of the initial overpressure).

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The maximal decompression rate ranges from the mean value itself (for the highest decompression rates) up to 3 times the mean value (for the lowest decompression rates). A total of 270 experiments were carried out using the glass beads, varying the slope of the tank and/or the granular bed (0, 2, 10, 15, 20°), the initial gas overpressure (from 5 to 30 kPa), the decompression rate (0 to 100 kPa/s), the bed thickness (15, 20, 25 cm) and the temperature

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469 (20°C to 60°C). A total of 50 experiments were carried out using the ignimbrite ($H=10$ cm to 470 $H=20$ cm, slopes from 0 to 30°, temperature from 20°C to 150°C).

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## 472 Numerical model

473 The numerical model follows the development of ref³⁵ and is given in Code availability. We 474 simplified the problem by assuming that the granular bed is non-expansive (as observed for 475 slow decompression rates). Mass conservation of the gas implies that:

$$476 \qquad \frac{\partial}{\partial t}(\varepsilon \rho_g) + \frac{\partial}{\partial z}(\varepsilon \rho_g u_g) = 0 \qquad (1)$$

477 where $t$ is time, $\varepsilon$ the porosity of the granular bed, $\rho_g$ is gas density, $z$ the elevation and $u_g$ the 478 gas velocity in the pores. The velocity in the pores is related to the Darcy velocity $u_D$ (i.e. the 479 volumetric rate of flow per unit area) with:

$$480 \qquad u_g = \frac{u_D}{\varepsilon} = -\frac{K}{\varepsilon\mu} \left( \frac{\partial P}{\partial z} - \rho_g g \right) \qquad (2)$$

481 where $\mu$ is the gas viscosity, $K$ is the gas permeability in the granular bed and $g$ is gravity.

482 The link between the gas density $\rho_g$ and its pressure $P$ is deduced from the perfect gas law:

$$483 \qquad \rho_g = \rho_{atm} \frac{P}{P_{atm}} \qquad (3)$$

484 with $\rho_{atm}$ the density of the air (1.2 kg/m³) at atmospheric pressure $P_{atm}$ (101.3 kPa).

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486 To reproduce the experiments, the initial overpressure $P_{s0}+P_{atm}$ was set for the whole deposit. 487 Then, a decrease in surface pressure $P_s+P_{atm}$ was imposed following the experimental 488 measurements from sensor 1. The pressure evolution in the granular bed was calculated by 489 solving equations 1, 2 and 3. We explored various values for the permeability $K$, constant or 490 varying in time and space. Numerical results were then compared to the experimental results to 491 estimate the value of $K$ and its range of variation (Extended Data Fig. 1). For low decompression 492 rates, the bed expansion was small (little variation in the volume of space between the grains) 493 and the whole defluidisation process was simulated with a constant value of $K$ ($2 \times 10^{-12}$ m² for 494 glass beads and $3 \times 10^{-12}$ m² for the ignimbrite). For higher decompression rates, which induce 495 fluidisation, the model showed that although the permeability varied in time and space, it 496 remained within a relatively small range of values (e.g. between 2 and $4 \times 10^{-12}$ m² for most 497 experiments with glass beads, Fig. 4) except for the highest decompression rates with a large 498 pressure gradient and bubbles, where $K$ sometimes temporarily reached more than $10^{-11}$ m². 499

500 To predict if the granular material remains stable or if it flows, we calculated the apparent 501 friction angle $\varphi$. A granular material can be stable on a slope due to friction between its 502 constituent particles. This is described by a mechanical property called the friction angle. The 503 friction angle $\delta$ of the material used is $27^\circ \pm 0.5^\circ$ for the glass beads and $36^\circ \pm 0.5^\circ$ for ignimbrite. 504 The pressure gradient of the gas, by partially or totally sustaining the weight of the particles, 505 lowers the friction and the apparent friction angle $\varphi$ is given by:

$$505 \qquad \tan \varphi = \left( 1 - \frac{P - (P_s + P_{atm})}{\rho g h} \right) \tan \delta \qquad (4)$$

506 where $P$ is the air pressure at depth $h$, $P_s$ is the air overpressure at the bed surface (and at the 507 base of the PDC) that decreases from $P_{s0}$ to 0, $g$ is gravity and $\rho$ the mean density of the granular 508 bed. With no gas pressure gradient, $\varphi=\delta$. This means that for slopes $\alpha$ of the bed surface lower 509 than $\varphi$, non-cohesive material is stable. Above this value ($\alpha>\varphi$), it flows until stability is 510 reached. The bed is fully fluidised above the depth $h$ when the air pressure $P$ rises sufficiently
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to create a value of $P - (P_s + P_{atm})$ that is equal to the pressure of the particles above, so that $\varphi$
equals 0. The bed flows like a fluid in a slope.

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Fig. 4a, has been compiled using the results of 5000 simulations (shown in Extended Data Fig. 2), either by varying the parameters controlling the defluidisation ($P_{s0}$, $H$, $\rho$, $K$, $\mu$, $\Delta t$) or by choosing sets of parameters, automatically and randomly, that give the imposed values of $\Pi_1$ and $\Pi_2$. We applied ranges of values characteristic of natural deposits for various parameters: permeability ($K=10^{-13}$ to $10^{-10}$ m$^2$), gas viscosity ($\mu$ = 1.85 at 20°C and $4.5 \times 10^{-5}$ at 950°C), deposit thickness ($H$ = 10 cm to 10 m), deposit density ($\rho$ from 500 to 2000 kg/m$^3$), unloading times ($\Delta t$ from 0 to 300 s) and basal overpressures of PDC ($P_{s0}$ from 1 to 100 kPa). The surface overpressure $P_s$ decreases linearly from $P_{s0}$ to 0 (Fig. 4b). The maximal depth of fluidisation $H_f$, for $\varphi$=0 and $\varphi$=10° and the time of fluidisation of the upper 10 centimetres are then used to calculate $H_f/H$ and $t_{f10}/\Delta t$. $\bar{P}_s$, in the definition of $\Pi_2$, is the mean value of the gas pressure at the base of the PDC and acts on the defluidisation by changing the gas density through its compressibility $\beta$. It is approximated by $\bar{P}_s = P_{atm} + P_{s0}/2$ but because the gas pressure in the deposit changes in time and space in a non-linear way, this approximation induces an error in the prediction of $H_f/H$ of up to 20% for low thicknesses ($\Pi_2<1$) and between simulations done at high and low pressure (see Extended Data Fig. 2).

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Data availability

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Videos and synchronized pressure data (text files) of characteristic experiments can be
downloaded here: https://doi.org/10.25519/TF5A-8291

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Code availability

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The numerical code used (open source) is available here: https://doi.org/10.25519/TF5A-8291

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The estimation of the pressure and the decompression rate in the field has been done with the version “Pyroclastic flows and surges” of VolcFlow downloadable here: https://lmv.uca.fr/volcflow/

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Corresponding author

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Correspondence to Karim Kelfoun (karim.kelfoun@uca.fr)

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559 Extended data:

<figure><img src="image_6.png" /></figure>

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**Extended data Figure 1:** Numerical simulation of one laboratory experiment. (a) Pressure evolution in the deposit for $K = 2 \times 10^{-12}$, $3 \times 10^{-12}$ and $4 \times 10^{-12}$ m$^2$. The experimental measurements are given by the white circles. Where the particle pressure is equal to or lower than the gas pressure, the granular material is fully fluidised locally. (b) Evolution of the apparent friction angle $\delta$ with time for $K = 3 \times 10^{-12}$ m$^2$. During decompression, the flow is fully fluidised down to about 12 cm beneath the surface and the apparent friction angle of less than 10° shows that all the material can flow on steeper slopes for more than 1 s (and the upper surface for 4 s). Because the geometry change induced by the flow was not simulated, results are compared with experiments carried out on the horizontal but the time of fluidisation coincides with the flow duration of experiments carried out on a slope and in the same conditions.
<figure><img src="image_7.png" /><figcaption>Extended data Figure 2: Evolution of the ratio $H_f/H$ according to $\Pi_1$ and $\Pi_2$. The colours give the values of $H_f/H$ of each of the 5000 simulations used to draw the curves (some points overlap exactly). The data used to make the figure are available here: https://doi.org/10.25519/TF5A-8291. They have been made with the numerical code available in the same repository.</figcaption></figure>