Paper:

# Numerical Simulations of Dome-Collapse Pyroclastic Density Currents Using faSavageHutterFOAM: Application to the 3 June 1991 Eruption of Unzen Volcano, Japan

## Hiroyuki A. Shimizu

National Research Institute for Earth Science and Disaster Resilience

3-1 Tennodai, Tsukuba, Ibaraki 305-0006, Japan

Corresponding author

Pyroclastic density currents (PDCs) are one of the most dangerous but least understood phenomena of volcanic eruptions. An open-source numerical depth-averaged model of dense granular currents controlled by physical processes such as energy dissipation, basal deposition, and erosion (faSavageHutterFOAM) was applied to investigate the basal concentrated region of a dome-collapse PDC generated on June 3, 1991 at Unzen volcano (Japan) to assess the effects of the physical processes (and their interplay) on the flow dynamics and run-out area of the PDC. Numerical simulations show that energy dissipation process decreases the flow velocity and increases the basal deposition rate, which reduces the run-out distance. The simulations also reveal that erosion process during flow propagation decreases the flow velocity and increases the run-out distance. The numerical results are sensitive to the parameters of energy dissipation (dry friction coefficient μ and collisional or turbulent friction coefficient χ) and erosion (specific erosion energy e_{b}). The results are fitted to field data for run-out distance and flow velocity when μ is between 0.01 and 0.1 with χ∼10^{3} m^{-1} s^{-2} (or when χ is between 10^{4} and 10^{5} m^{-1} s^{-2} with μ∼0.2) and e_{b}∼10^{2} m^{2} s^{-2}. The estimated value of e_{b} suggests that re-entrainment of deposit mass played an important role in controlling the flow dynamics and run-out area of the PDC. The estimated values of μ and χ are correlated, but the estimation of these parameters might be improved by further constraints from field data. The presented results serve as a basis to make further quantitative estimations of the model parameters (μ, χ, and e_{b}) for applying the faSavageHutterFOAM model to hazard assessments of PDCs.

*J. Disaster Res.*, Vol.17 No.5, pp. 768-778, 2022.

- [1] A. Freundt, S. N. Carey, and C. J. Wilson, “Ignimbrites and block-and-ash flow deposits,” H. Sigurdsson, B. Houghton, S. McNutt, H. Rymer, and J. Stix (Eds.), “Encyclopedia of Volcanoes,” 1st Edition, pp. 581-600, Academic Press, 2000.
- [2] M. J. Branney and P. Kokelaar, “Pyroclastic Density Currents and the Sedimentation of Ignimbrites,” Geological Society of London, 2002.
- [3] J. Dufek, T. Esposti Ongaro, and O. Roche, “Pyroclastic density currents: Processes and models,” H. Sigurdsson (Eds.), “Encyclopedia of Volcanoes,” 2nd Edition, pp. 617-629, Academic Press, 2015.
- [4] S. Nakada and T. Fujii, “Preliminary report on the activity at Unzen Volcano (Japan), November 1990–November 1991: Dacite lava domes and pyroclastic flows,” J. Volcanol. Geotherm. Res., Vol.54, Issues 3-4, pp. 319-333, 1993.
- [5] T. Yamamoto, S. Takarada, and S. Suto, “Pyroclastic flows from the 1991 eruption of Unzen volcano, Japan,” Bull. Volcanol., Vol.55, Issue 3, pp. 166-175, 1993.
- [6] T. Fujii and S. Nakada, “The 15 September 1991 pyroclastic flows at Unzen Volcano (Japan): A flow model for associated ash-cloud surges,” J. Volcanol. Geotherm. Res., Vol.89, Issues 1-4, pp. 159-172, 1999.
- [7] S. Nakada, H. Shimizu, and K. Ohta, “Overview of the 1990–1995 eruption at Unzen Volcano,” J. Volcanol. Geotherm. Res., Vol.89, Issues 1-4, pp. 1-22, 1999.
- [8] R. Saucedo, J. L. Macías, M. F. Sheridan, M. I. Bursik, and J. C. Komorowski, “Modeling of pyroclastic flows of Colima Volcano, Mexico: Implications for hazard assessment,” J. Volcanol. Geotherm. Res., Vol.139, Issues 1-2, pp. 103-115, 2005.
- [9] E. Macorps, S. J. Charbonnier, N. R. Varley, L. Capra, Z. Atlas, and J. Cabré, “Stratigraphy, sedimentology and inferred flow dynamics from the July 2015 block-and-ash flow deposits at Volcán de Colima, Mexico,” J. Volcanol. Geotherm. Res., Vol.349, pp. 99-116, 2018.
- [10] V. M. Zobin, C. Navarro, and A. Tellez, “Insight into lava dome extrusion dynamics from seismic signatures of pyroclastic flows and incandescent rockfalls: Volcán de Colima, México, 1998–2017,” Bull. Volcanol., Vol.83, Issue 7, Article No.44, 2021.
- [11] B. Voight and M. J. Davis, “Emplacement temperatures of the November 22, 1994 nuée ardente deposits, Merapi Volcano, Java,” J. Volcanol. Geotherm. Res., Vol.100, Issues 1-4, pp. 371-377, 2000.
- [12] B. Voight, E. K. Constantine, S. Siswowidjoyo, and R. Torley, “Historical eruptions of Merapi volcano, central Java, Indonesia, 1768–1998,” J. Volcanol. Geotherm. Res., Vol.100, Issues 1-4, pp. 69-138, 2000.
- [13] S. J. Charbonnier and R. Gertisser, “Field observations and surface characteristics of pristine block-and-ash flow deposits from the 2006 eruption of Merapi Volcano, Java, Indonesia,” J. Volcanol. Geotherm. Res., Vol.177, Issue 4, pp. 971-982, 2008.
- [14] J.-C. Komorowski, S. Jenkins, P. J. Baxter, A. Picquout, F. Lavigne, S. Charbonnier, R. Gertisser, K. Preece, N. Cholik, A. B. Santoso, and Surono, “Paroxysmal dome explosion during the Merapi 2010 eruption: Processes and facies relationships of associated high-energy pyroclastic density currents,” J. Volcanol. Geotherm. Res., Vol.261, pp. 260-294, 2013.
- [15] K. Kelfoun, A. B. Santoso, T. Latchimy, M. Bontemps, I. Nurdien, F. Beauducel, A. Fahmi, R. Putra, N. Dahamna, A. Laurin, M. H. Rizal, J. T. Sukmana, and V. Gueugneau, “Growth and collapse of the 2018–2019 lava dome of Merapi volcano,” Bull. Volcanol., Vol.83, Issue 2, Article No.8, 2021.
- [16] P. D. Cole, E. S. Calder, T. H. Druitt, R. Hoblitt, R. Robertson, R. S. J. Sparks, and S. R. Young, “Pyroclastic flows generated by gravitational instability of the 1996–97 lava dome of Soufriere Hills Volcano, Montserrat,” Geophys. Res. Lett., Vol.25, Issue 18, pp. 3425-3428, 1998.
- [17] S. R. Young, R. S. J. Sparks, W. P. Aspinall, L. L. Lynch, A. D. Miller, R. E. Robertson, and J. B. Shepherd, “Overview of the eruption of Soufriere Hills volcano, Montserrat, 18 July 1995 to December 1997,” Geophys. Res. Lett., Vol.25, Issue 18, pp. 3389-3392, 1998.
- [18] E. S. Calder, P. D. Cole, W. B. Dade, T. H. Druitt, R. P. Hoblitt, H. E. Huppert, L. Ritchie, R. S. J. Sparks, and S. R. Young, “Mobility of pyroclastic flows and surges at the Soufriere Hills Volcano, Montserrat,” Geophys. Res. Lett., Vol.26, Issue 5, pp. 537-540, 1999.
- [19] B. P. Kokelaar, “Setting, chronology and consequences of the eruption of Soufrière Hills Volcano, Montserrat (1995–1999),” T. H. Druitt and B. P. Kokelaar (Eds.), “The Eruption of Soufrière Hills Volcano, Montserrat, from 1995 to 1999 (Geological Society Memoirs No.21),” pp. 1-43, Geological Society of London, 2002.
- [20] H. Gunawan, A. Budianto, O. Prambada, W. McCausland, J. Pallister, and M. Iguchi, “Overview of the eruptions of Sinabung Volcano, 2010 and 2013–present and details of the 2013 phreatomagmatic phase,” J. Volcanol. Geotherm. Res., Vol.382, pp. 103-119, 2019.
- [21] S. Nakada, A. Zaennudin, M. Yoshimoto, F. Maeno, Y. Suzuki, N. Hokanishi, H. Sasaki, M. Iguchi, T. Ohkura, H. Gunawan, and H. Triastut, “Growth process of the lava dome/flow complex at Sinabung Volcano during 2013–2016,” J. Volcanol. Geotherm. Res., Vol.382, pp. 120-136, 2019.
- [22] J. Pallister, R. Wessels, J. Griswold, W. McCausland, N. Kartadinata, H. Gunawan, A. Budianto, and S. Primulyana, “Monitoring, forecasting collapse events, and mapping pyroclastic deposits at Sinabung volcano with satellite imagery,” J. Volcanol. Geotherm. Res., Vol.382, pp. 149-163, 2019.
- [23] G. A. Valentine, “Damage to structures by pyroclastic flows and surges, inferred from nuclear weapons effects,” J. Volcanol. Geotherm. Res., Vol.87, Issues 1-4, pp. 117-140, 1998.
- [24] P. J. Baxter, R. Boyle, P. Cole, A. Neri, R. Spence, and G. Zuccaro, “The impacts of pyroclastic surges on buildings at the eruption of the Soufrière Hills volcano, Montserrat,” Bull. Volcanol., Vol.67, Issue 4, pp. 292-313, 2005.
- [25] A. Neri, T. Esposti Ongaro, B. Voight, and C. Widiwijayanti, “Pyroclastic density current hazards and risk,” J. F. Shroder and P. Papale (Eds.), “Volcanic Hazards, Risks and Disasters,” pp. 109-140, Academic Press, 2015.
- [26] R. Sulpizio, P. Dellino, D. M. Doronzo, and D. Sarocchi, “Pyroclastic density currents: State of the art and perspectives,” J. Volcanol. Geotherm. Res., Vol.283, pp. 36-65, 2014.
- [27] J. Dufek, “The fluid mechanics of pyroclastic density currents,” Annu. Rev. Fluid Mech., Vol.48, pp. 459-485, 2016.
- [28] G. Lube, E. C. P. Breard, T. Esposti-Ongaro, J. Dufek, and B. Brand, “Multiphase flow behaviour and hazard prediction of pyroclastic density currents,” Nat. Rev. Earth Environ., Vol.1, pp. 348-365, 2020.
- [29] K. Kelfoun, “A two-layer depth-averaged model for both the dilute and the concentrated parts of pyroclastic currents,” J. Geophys. Res., Vol.122, Issue 6, pp. 4293-4311, 2017.
- [30] T. Takahashi and H. Tsujimoto, “A mechanical model for Merapi-type pyroclastic flow,” J. Volcanol. Geotherm. Res., Vol.98, Issues 1-4, pp. 91-115, 2000.
- [31] C. Chedeville and O. Roche, “Autofluidization of pyroclastic flows propagating on rough substrates as shown by laboratory experiments,” J. Geophys. Res., Vol.119, Issue 3, pp. 1764-1776, 2014.
- [32] C. Chédeville and O. Roche, “Influence of slope angle on pore pressure generation and kinematics of pyroclastic flows: Insights from laboratory experiments,” Bull. Volcanol., Vol.77, Issue 11, Article No.96, 2015.
- [33] A. Fries, O. Roche, and G. Carazzo, “Granular mixture deflation and generation of pore fluid pressure at the impact zone of a pyroclastic fountain: Experimental insights,” J. Volcanol. Geotherm. Res., Vol.414, Article No.107226, 2021.
- [34] L. Girolami, T. H. Druitt, O. Roche, and Z. Khrabrykh, “Propagation and hindered settling of laboratory ash flows,” J. Geophys. Res. Solid Earth, Vol.113, Issue B2, Article No.B02202, 2008.
- [35] L. Girolami, O. Roche, T. H. Druitt, and T. Corpetti, “Particle velocity fields and depositional processes in laboratory ash flows, with implications for the sedimentation of dense pyroclastic flows,” Bull. Volcanol., Vol.72, Issue 6, pp. 747-759, 2010.
- [36] L. Girolami, T. H. Druitt, and O. Roche, “Towards a quantitative understanding of pyroclastic flows: Effects of expansion on the dynamics of laboratory fluidized granular flows,” J. Volcanol. Geotherm. Res., Vol.296, pp. 31-39, 2015.
- [37] S. Montserrat, A. Tamburrino, O. Roche, Y. Niño, and C. F. Ihle, “Enhanced run-out of dam-break granular flows caused by initial fluidization and initial material expansion,” Granul. Matter, Vol.18, Issue 1, Article No.11, 2016.
- [38] O. Roche, “Depositional processes and gas pore pressure in pyroclastic flows: An experimental perspective,” Bull. Volcanol., Vol.74, Issue 8, pp. 1807-1820, 2012.
- [39] O. Roche, M. Gilbertson, J. C. Phillips, and R. S. J. Sparks, “Experiments on deaerating granular flows and implications for pyroclastic flow mobility,” Geophys. Res. Lett., Vol.29, Issue 16, pp. 40-1–40-4, 2002.
- [40] O. Roche, M. A. Gilbertson, J. C. Phillips, and R. S. J. Sparks, “Experimental study of gas-fluidized granular flows with implications for pyroclastic flow emplacement,” J. Geophys. Res. Solid Earth, Vol.109, Issue B10, Article No.B10201, 2004.
- [41] O. Roche, S. Montserrat, Y. Niño, and A. Tamburrino, “Experimental observations of water-like behavior of initially fluidized, dam break granular flows and their relevance for the propagation of ash-rich pyroclastic flows,” J. Geophys. Res., Vol.113, Issue B12, Article No.B12203, 2008.
- [42] O. Roche, S. Montserrat, Y. Niño, and A. Tamburrino, “Pore fluid pressure and internal kinematics of gravitational laboratory air-particle flows: Insights into the emplacement dynamics of pyroclastic flows,” J. Geophys. Res. Solid Earth, Vol.115, Issue B9, Article No.B09206, 2010.
- [43] O. Roche, M. Attali, A. Mangeney, and A. Lucas, “On the run-out distance of geophysical gravitational flows: Insight from fluidized granular collapse experiments,” Earth Planet. Sci. Lett., Vol.311, Issues 3-4, pp. 375-385, 2011.
- [44] O. Roche, Y. Niño, A. Mangeney, B. Brand, N. Pollock, and G. A. Valentine, “Dynamic pore-pressure variations induce substrate erosion by pyroclastic flows,” Geology, Vol.41, No.10, pp. 1107-1110, 2013.
- [45] P. J. Rowley, O. Roche, T. H. Druitt, and R. Cas, “Experimental study of dense pyroclastic density currents using sustained, gas-fluidized granular flows,” Bull. Volcanol., Vol.76, Issue 9, Article No.855, 2014.
- [46] G. M. Smith, R. Williams, P. J. Rowley, and D. R. Parsons, “Investigation of variable aeration of monodisperse mixtures: Implications for pyroclastic density currents,” Bull. Volcanol., Vol.80, Issue 8, Article No.67, 2018.
- [47] G. Smith, P. Rowley, R. Williams, G. Giordano, M. Trolese, A. Silleni, D. R. Parsons, and S. Capon, “A bedform phase diagram for dense granular currents,” Nat. Commun., Vol.11, Article No.2873, 2020.
- [48] A. K. Patra, A. C. Bauer, C. C. Nichita, E. B. Pitman, M. F. Sheridan, M. Bursik, B. Rupp, A. Webber, A. J. Stinton, L. M. Namikawa, and C. S. Renschler, “Parallel adaptive numerical simulation of dry avalanches over natural terrain,” J. Volcanol. Geotherm. Res., Vol.139, Issues 1-2, pp. 1-21, 2005.
- [49] K. Kelfoun and T. H. Druitt, “Numerical modeling of the emplacement of Socompa rock avalanche, Chile,” J. Geophys. Res. Solid Earth, Vol.110, Issue B12, Article No.B12202, 2005.
- [50] M. de’ Michieli Vitturi, T. Esposti Ongaro, G. Lari, and A. Aravena, “IMEX_SfloW2D 1.0: A depth-averaged numerical flow model for pyroclastic avalanches,” Geosci. Model Dev., Vol.12, Issue 1, pp. 581-595, 2019.
- [51] S. J. Charbonnier and R. Gertisser, “Numerical simulations of block-and-ash flows using the Titan2D flow model: Examples from the 2006 eruption of Merapi Volcano, Java, Indonesia,” Bull. Volcanol., Vol.71, Issue 8, pp. 953-959, 2009.
- [52] S. J. Charbonnier and R. Gertisser, “Evaluation of geophysical mass flow models using the 2006 block-and-ash flows of Merapi Volcano, Java, Indonesia: Towards a short-term hazard assessment tool,” J. Volcanol. Geotherm. Res., Vols.231-232, pp. 87-108, 2012.
- [53] V. Gueugneau, S. Charbonnier, T. Esposti Ongaro, M. de’ Michieli Vitturi, M. Peruzzetto, A. Mangeney, F. Bouchut, A. Patra, and K. Kelfoun, “Synthetic benchmarking of concentrated pyroclastic current models,” Bull. Volcanol., Vol.83, Issue 11, Article No.75, 2021.
- [54] K. Kelfoun, “Suitability of simple rheological laws for the numerical simulation of dense pyroclastic flows and long-runout volcanic avalanches,” J. Geophys. Res. Solid Earth, Vol.116, Issue B8, Article No.B08209, 2011.
- [55] K. Kelfoun, P. Samaniego, P. Palacios, and D. Barba, “Testing the suitability of frictional behaviour for pyroclastic flow simulation by comparison with a well-constrained eruption at Tungurahua volcano (Ecuador),” Bull. Volcanol., Vol.71, Issue 9, Article No.1057, 2009.
- [56] M. Rauter and Ž. Tuković, “A finite area scheme for shallow granular flows on three-dimensional surfaces,” Comput. Fluids, Vol.166, pp. 184-199, 2018.
- [57] M. Rauter, A. Kofler, A. Huber, and W. Fellin, “faSavageHutterFOAM 1.0: Depth-integrated simulation of dense snow avalanches on natural terrain with OpenFOAM,” Geosci. Model Dev., Vol.11, pp. 2923-2939, 2018.
- [58] M. Rauter and A. Köhler, “Constraints on entrainment and deposition models in avalanche simulations from high-resolution radar data,” Geosciences, Vol.10, No.1, Article No.9, 2020.
- [59] OpenCFD Ltd., OpenFOAM – The Open Source CFD Toolbox – User Guide, 2004, https://www.openfoam.com/documentation/user-guide/ [accessed May 30, 2022]
- [60] M. Rauter, faSavageHutterFoam – README, 2018, https://bitbucket.org/matti2/fasavagehutterfoam/src/master/README.md [accessed May 30, 2022]
- [61] V. Gueugneau, K. Kelfoun, O. Roche, and L. Chupin, “Effects of pore pressure in pyroclastic flows: Numerical simulation and experimental validation,” Geophys. Res. Lett., Vol.44, Issue 5, pp. 2194-2202, 2017.
- [62] R. M. Iverson and C. Ouyang, “Entrainment of bed material by Earth-surface mass flows: Review and reformulation of depth-integrated theory,” Rev. Geophys., Vol.53, Issue 1, pp. 27-58, 2015.
- [63] R. Delannay, A. Valance, A. Mangeney, O. Roche, and P. Richard, “Granular and particle-laden flows: From laboratory experiments to field observations,” J. Phys. D: Appl. Phys., Vol.50, No.5, Article No.053001, 2017.
- [64] M. Rauter, J.-T. Fischer, W. Fellin, and A. Kofler, “Snow avalanche friction relation based on extended kinetic theory,” Nat. Hazards Earth Syst. Sci., Vol.16, Issue 11, pp. 2325-2345, 2016.
- [65] A. Voellmy, “Über die Zerstörungskraft von Lawinen,” Schweizerische Bauzeitung, Vol.73, No.15, pp. 212-217, 1955 (in German).
- [66] J.-T. Fischer, A. Kofler, W. Fellin, M. Granig, and K. Kleemayr, “Multivariate parameter optimization for computational snow avalanche simulation,” J. Glaciol., Vol.61, Issue 229, pp. 875-888, 2015.
- [67] T. Chikashige, I. Ohshiro, and F. Yamaguchi, “Construction of chronological high-density 3D terrain models and analysis methods of terrain variation – Spatial analysis in Mt. Unzen-Fugen area –,” Pap. Proc. Geogr. Inf. Syst. Assoc., Vol.17, pp. 225-228, 2008 (in Japanese).
- [68] S. Nakada, “Lava domes and pyroclastic flows of the 1991–1992 eruption at Unzen volcano,” T. Yanagi, H. Okada, and K. Ohta (Eds.), “Unzen Volcano, The 1990–1992 Eruption,” pp. 56-66, The Nishinippon and Kyushu University Press, 1992.
- [69] H. A. Shimizu, T. Koyaguchi, and Y. J. Suzuki, “The run-out distance of large-scale pyroclastic density currents: A two-layer depth-averaged model,” J. Volcanol. Geotherm. Res., Vol.381, pp. 168-184, 2019.
- [70] H. A. Shimizu, T. Koyaguchi, Y. J. Suzuki, E. Brosch, G. Lube, and M. Cerminara, “Validation of a two-layer depth-averaged model by comparison with an experimental dilute stratified pyroclastic density current,” Bull. Volcanol., Vol.83, Article No.73, Issue 11, 2021.
- [71] J. F. Richardson and W. N. Zaki, “Sedimentation and fluidisation: Part I,” Trans. Inst. Chem. Eng., Vol.32, pp. 35-52, 1954.

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