Experimental evidence links volcanic particle characteristics to pyroclastic flow hazard

Earth and Planetary Science Letters 295 (2010) 314–320

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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / e p s l

Experimental evidence links volcanic particle characteristics to pyroclastic flow hazard Pierfrancesco Dellino a,⁎, Ralf Büttner b, Fabio Dioguardi a, Domenico M. Doronzo a, Luigi La Volpe a, Daniela Mele a, Ingo Sonder b, Roberto Sulpizio a, Bernd Zimanowski b a b

Centro Interdipartimentale di Ricerca sul Rischio Sismico e Vulcanico (CIRISIVU) - c/o Dipartimento Geomineralogico, Università di Bari, Via E. Orabona 4, 70125 Bari, Italy Physikalisch Vulkanologisches Labor,Universität Würzburg, Pleicherwall 1, 97070, Würzburg, Germany

a r t i c l e

i n f o

Article history: Received 16 December 2009 Received in revised form 1 April 2010 Accepted 12 April 2010 Available online 8 May 2010 Editor: L. Stixrude Keywords: pyroclastic flows experimental volcanology pyroclastic particles volcanic hazard

a b s t r a c t Pyroclastic flows represent the most hazardous events of explosive volcanism, one striking example being the famous historical eruption of Vesuvius that destroyed Pompeii (AD 79). Much of our knowledge of the mechanics of pyroclastic flows comes from theoretical models and numerical simulations. Valuable data are also stored in the geological record of past eruptions, including the particles contained in pyroclastic deposits, but the deposit characteristics are rarely used for quantifying the destructive potential of pyroclastic flows. By means of experiments, we validate a model that is based on data from pyroclastic deposits. The model allows the reconstruction of the current's fluid-dynamic behaviour. Model results are consistent with measured values of dynamic pressure in the experiments, and allow the quantification of the damage potential of pyroclastic flows. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Sediment density currents are multiphase flows that move by means of the density difference between a fluid-particle mixture and the surrounding free fluid. In geology, the most familiar examples are turbidity currents, which move over the ocean floor, and volcanic pyroclastic flows (Fisher, 1966; Druitt, 1998; Branney and Kokelaar, 2002; Sulpizio and Dellino, 2008). The latter, also known as pyroclastic density currents, can result from the collapse of an eruption column that generates a flow hundreds of meters thick, moving over the ground surface with velocities generally in the range of tens of m/s and temperature of hundreds °C (Sigurdsson et al., 1985; Gurioli et al., 2005; Bursik and Woods, 1996; Iverson and Denlinger, 2001; Neri et al., 2003; 2007; Dellino et al., 2008). Knowledge of the fluid-dynamic behaviour of pyroclastic flows is important for quantifying their destructive power. In particular, dynamic pressure, Pdyn = 1 / 2ρfU2, where ρf and U are flow density and velocity, is a measure of the lateral stress that pyroclastic flows exert over structures (Valentine, 1998), and allows quantification of the expected damage to buildings (Spence et al., 2004). Particle volumetric concentration, C, is also a measure of the threat from such currents, since hot volcanic ash is lethal if people are exposed even to

⁎ Corresponding author. E-mail address: [email protected] (P. Dellino). 0012-821X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2010.04.022

low concentration currents (Baxter et al., 1998; Horwell and Baxter, 2006). We recently proposed a method, based on data from particles contained in the deposit, which allows the calculation of Pdyn and C of a pyroclastic flow (Dellino et al., 2008). Since pyroclastic flows are highly unpredictable and dangerous, it is impossible to fit model calculations with any existing direct measurements. In order to validate our model, we built an experimental facility that produces density currents analogous to natural ones. 2. Experiments The experimental apparatus and its operations are described by Dellino et al. (2007, 2010). Since the irregular shape of volcanic clasts strongly influences gas–particle coupling (Dellino et al., 2005), in order to replicate natural conditions, we used pyroclasts from natural deposits of Vesuvius. The source deposit (Fig. 1) contains a broad size range of particles (sorting, σ, is about 2 phi), the median size, d, is about 0 phi (1 mm). The experimental currents show a striking similarity with natural pyroclastic flows. The flow is initiated by the collapse of the eruption column issuing from the conduit (Fig. 2A), which at the impact with the ground forms a shear current. On impact, a dense underflow forms (Fig. 2B), which expands downcurrent and develops turbulence (Fig. 2C), in this way resembling the lateral evolution from a dense to a dilute highly-turbulent current as postulated for natural pyroclastic density currents (Valentine, 1987; Burgissier, and Bergantz, 2002).

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sized that if model calculation fit experimental measurements well, use of our model could be extended to the natural case. We focused our attention on the shear current, since it is the part where dynamic pressure has maximum values, meaning the highest destructive potential in the natural case. 3. Model validation

Fig. 1. Histogram of the grain-size distribution of the source pyroclastic material used in the experiments. Size is in phi unit, where phi = −log2d, and d is size in mm.

Experiments were performed both at ambient temperature and up to 300 °C, and thermal video cameras were used to visualize the effect of heat (Fig. 2D). Except for the development of a buoyant upper part that lofts fine ash in hot experiments, where particles in the flow stayed at a temperature over 200 °C, the mechanics of the shear current were not much different between hot and cold experiments. Note that in the hot experiments particle temperature, after emplacement, was similar to that at experiment initiation and, because of the low thermal conductivity of pyroclasts, stayed high for some time. For example, in the thickest part (dm range) of deposit, after an hour the temperature had decreased by less than 10 °C from the initial value. Thus there is a high burn risk for items resting in contact with the deposit (Loughlin et al., 2002). Deposits formed from experiments are similar to natural ones, with the proximal layers being massive and thicker (Fig. 2E), while with distance they develop tractional features, similar to ripples (Fig. 2F) as a result of increasing lateral velocity and turbulence. The lateral flow evolution resulted in a selective transportation of particle sizes. In the massive facies (Fig. 3A) the grain-size distribution (Fig. 3B) is very similar to the source material (Fig. 1); whereas, in the tractional layer (Fig. 4A), two modes are clearly visible (Fig. 4B). The coarse mode is to be related to particles moving in contact with the ground; the fine one is related to particles sedimented by turbulent suspension. At a location where the flow reached its maximum downstream velocity (which was known from previous test runs), video cameras were used to visualize the structure of the current and sensors were used to measure the dynamic pressure at various flow heights. The structure of the experimental flows (Fig. 5) shows a great similarity with that postulated for density currents in general (Kneller et al., 1999). It consists of two parts, a bottom one that is characterized by a logarithmic velocity profile akin that of a boundary layer shear flow (Furbish, 1997), which extends up to the velocity maximum, and an upper part in which velocity decreases, similar to the outer region of wall jets (Kneller et al., 1999). Particle volumetric concentration decreases all the way up through current height. Using videos of the flows we measured the velocity at the flow front, the thickness of the shear current, Hsf, and total flow height, Htot. Data show that Hsf ranged from 0.3 to 0.4 of Htot, which is what we expect for sediment density currents (Kneller et al., 1999). Maximum velocity at the top of the shear current ranged from 3.7 to 15 m/s. Dynamic pressure was up to about 500 Pa and the maximum value was always reached inside the shear current. Experimental flows had dynamic pressures in the same order of magnitude of natural events, for which values of a few kPa are reported in the literature (Esposti Ongaro et al., 2002; Baxter et al., 2005; Dellino et al., 2008; Sulpizio et al., 2010a). In addition, at the location where the maximum downstream velocity was reached, the Reynolds number was always higher than 106, so the flow was fully turbulent, with the complete range of turbulent structures replicated by our experiments. We can therefore argue that experiments captured the essential physics of natural flows, and therefore provide data with which to test our model relating deposited particles to flow dynamics. We hypothe-

The deposits of experimental currents were sampled, and grain size, density, and shape factor of particles, which are the input data of our model, were measured in our particle-analysis laboratory. Our model assumes that ash particles settle from suspension when their terminal velocity, w, equals flow shear velocity, u* (Middleton and Southard, 1984) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4gdðρs −ρf Þ = u* w= 3Cd ρf

ð1Þ

where g is gravity acceleration, d is particle size, ρs and ρf are particle and fluid densities respectively, and Cd is particle drag coefficient, which we calculated by the model of Dellino et al. (2005) 3

Cd =

0:69gd ρf ð1:33ρs −1:33ρf Þ  1:6 3 1:0412 μ 2 gψ d ρμf2ðρs −ρf Þ

ð2Þ

where µ is fluid viscosity and ψ is particle shape factor. Coarse particles, at the base of the current, are just able to move when θ = 0.015 (Miller et al., 1977), θ=

ρf u2*

ðρs1 −ρf Þgd1

ð3Þ

where ρs1 and d1 are density and maximum size of particles at the base of the current. When both particles just at initiation of motion and particles deposited from suspension are recognized in the deposit, since they can be discriminated by means of the two modes of the grain-size distribution (Fig. 4b), Eqs. (1) and (3) are combined and the model solves for flow shear velocity and average flow density. Equations are actually arranged in a way to provide a statistical range around an average solution, and the maximum solution is considered as a “safety” value for quantifying the damage potential (Dellino et al., 2008). This safety value is meant to provide the maximum likely stress an object would experience and is potentially useful as a design parameter. The method is summarized in Appendix A. The velocity profile is obtained by means of the law of the wall of boundary layers over a rough substrate (Furbish, 1997), where roughness is related to small-scale irregularities at the flow-substrate boundary, uðyÞ 1 y + 8:5 = ln u* k ks

ð4Þ

where u(y) is time-averaged velocity, ks is ground surface roughness (in our case 2 cm), as related to the size of the coarse particles settling at the base of the current. Note that, since the pre-existing topography was rendered flat before every experiment, it acquired roughness only as a result of flow propagation over the ground. k is the Von Karman constant = 0.4. The concentration profile is calculated by assuming a Rousean gradient (Rouse, 1939), with respect to a reference level, y0, at which concentration, C0, is known, by  CðyÞ = C0

 y0 Htot −y Pn Htot −y0 y

ð5Þ

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Fig. 2. Display mount of images of a representative experiment. A, Gas–particle column issuing from the conduit. B, Formation of an undercurrent upon impact of the collapsing column. C, Expansion of the fully turbulent current. D, Image from a thermal video camera of a hot experiment. On the right side, the temperature scale is in °C. E, Thick deposit in proximal location showing a massive structure. F, Deposit showing the downcurrent development of tractional structures.

where Htot is total flow thickness and Pn is the Rouse number of the suspension population. The reference level is assumed very close to the ground surface, where particles settle from suspension (it is set as median particle size). The reference concentration is close to maximum particle packing, about 0.75. Flow density is related to particle volumetric concentration, C, by ρf = ð1−CÞρg + Cρs where ρg and ρs are gas and particle densities.

ð6Þ

By combining Eqs. (5) and (6), the density profile can be obtained, once Pn is known, which is calculated by ρfavg =

1 H ∫ tot ρ + Htot −y0 y0 g

    y0 Htot −y Pn dy ðρs −ρg ÞC0 Htot −y0 y

ð7Þ

where ρfavg is the average density value of the shear current, as calculated previously, and Htot is total flow thickness, as measured by videos. By combining the velocity and density profiles, the dynamic pressure profile is finally obtained (Fig. 6, Table 1).

P. Dellino et al. / Earth and Planetary Science Letters 295 (2010) 314–320

Fig. 3. Massive facies of the experimental deposit. A, Close-up view of photo 2E, showing a detail of the massive structure of deposit. B, Histogram showing the grainsize distribution of the massive deposit.

The experimental measurements of dynamic pressure lie well within the statistical range of model solutions, and fall close to the average solution, validating our model in terms of its ability to relate particles in deposits to the damage potential of pyroclastic currents. Particle concentration inside the shear current is always higher than 0.001, consistent with values calculated with our method for natural currents (Dellino et al., 2008). This means that unsheltered people caught by such currents, even in distal reaches, where the current's strength diminishes, could not survive. 4. Discussion and conclusion Our model, when applied to real deposits, as for example those of Vesuvius, and compared with values of building resistance for that area (Spence et al., 2004), suggests that only in the very big eruptions of the Plinian type, such as Avellino, 3900 yr BP (Mastrolorenzo et al., 2006; Sulpizio et al., 2010a, in press), and Pompeii, AD 79 (Sigurdsson et al., 1985; Gurioli et al., 2005), would currents have had safety values of dynamic pressure (40 kPa) exceeding the resistance of concrete walls. For smaller eruptions of the sub-Plinian type, similar in size to the AD 472 eruption (Sulpizio et al., 2005) with safety values b6 kPa (Dellino et al., 2008), which

317

Fig. 4. Tractional facies of the experimental deposit. A, Close-up view of photo 2F, showing a detail of the ripple bedforms of the tractional deposit. The arrow marks current direction. B, Histogram of the grain-size distribution of the tractional deposits. The coarse and fine modes are marked.

are the most likely, just openings (windows and doors) could be destroyed by dynamic pressure. In such situations, even though walls might be able to withstand the dynamics pressures, the entrance of pyroclastic flow material into a building could cause thermal damage and casualties, and ignite fires. Thus, a relatively simple mitigating step that could be taken would be to reinforce doors and windows (perhaps with heavy-duty metal shutters). The results show that by applying our model to the pyroclastic deposits of past eruptions, the hazard from pyroclastic flows can be quantified, at least in the case of fully turbulent, dilute, currents. Field workers, by carefully studying the facies architecture of deposits, could identify layers containing tractional features and sample the two size modes recognized in our experimental deposits and also found in natural deposits (Sulpizio et al., 2005; Dellino et al., 2008; Sulpizio et al., 2010a, in press). In this way, and by means of our model, a quantification of the hazard potential of active volcanoes could be obtained from the deposits of past eruption. Our model resulted in statistically significant solutions when applied to natural deposits with the coarse mode ranging in between 4 mm and 10 cm, and the fine mode ranging in between 0.1 mm and 4 mm. Finally, since our model is of general validity for any density current, we think it should be of help for quantifying

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Fig. 5. Close-up view of an experimental current taken at the location where pressure sensors were set. The velocity structure of the current is marked, as also shear current height, Hsf, and total flow thickness, Htot. In the inset the signal from one pressure sensor is shown.

the fluid-dynamic behaviour also of volcaniclastic turbidity currents (Doronzo and Dellino, 2010), which represent a prolongation of pyroclastic flows under the sea, or the remobilization of ash layers over ocean basins.

!! Cd = d

Acknowledgement Research was partially funded by INGV-DPC grant and MUR 06. Sonia Calvari and Enrica Marotta are greatly thanked for providing thermal camera images of hot experimental runs. Michael Ort, Greg Valentine and James White are greatly thanked for the thorough revision. Appendix A. Calculation of the statistical range of model solutions The size of particles in Eq. (1) refers to the suspension population. The average of this population is represented by the median size, d, and the range of variation is expressed by the sorting value, σ, of the grain-size distribution. Also the drag coefficient, Cd, in Eq. (1), which is a function of particle diameter (see Eq. (2)), has a range of variation around the average value. This range of d and Cd must be considered while solving the system of Eqs. (1) and (3), in order to obtain a significant range of shear velocity and flow density. To evaluate this range, we grouped Eqs. (1) and (3), and expressed the ratio Cd/d as a function of flow density Cd 4ðρs −ρf Þ = d d1 θ3ðρs1 −ρf Þ

We then wrote the Cd/d ratio as a function of the square of the shear velocity: 4g ρs −

*

!

:

ð9Þ

θgd1 ρs1 u2 + θgd1

*

Substituting into Eq. (9) the Cd/d values of Cd/d (2 kg/m3) and Cd/d (100 kg/m3), the corresponding values of the squared shear velocity, here named u2* (2 kg/m3) and u2* (100 kg/m3), were calculated. We then found the average Cd/d model ratio by means of 2

3

u ð2 kg = m Þ Cd 1 ∫ *2 avg = 2 3 d u ð2 kg = m3 Þ−u2 ð100 kg = m3 Þ u* ð100 kg = m Þ * * !!

4g ρs − 

θgd1 ρs1 u2 + θgd1

*

θgd1 ρs1 u2 + θgd1

3u2 *

!

ð10Þ 2

du* :

*

Making use of Eq. (2), the average Cd of particles in the 2–100 kg/m3 density range was calculated by means of Cd avg =

ð8Þ

and we searched for the range of Cd/d values compatible with density currents. Since the shear current is expected to be denser than the surrounding atmosphere and since the maximum volumetric particle concentration cannot be over a few percent, we chose a range between 2 and 100 kg/m3. By using Eq. (8), the Cd/d values resulting from this range of density were calculated. The values corresponding to 2 and 100 kg/m3 are named Cd/d (2 kg/m3) and Cd/d (100 kg/m3).

3u2 *

θgd1 ρs1 u + θgd1 2

3 3 1 100 kg = m 0:69gd ρf ð1:33ρs −1:33ρf Þ ∫  1:6 3 1:0412 dρf : 3 2 kg = m3 100 kg = m −2 kg = m μ 2 gψ d ρf ðρs −ρf Þ 3

μ2

ð11Þ From this value, the d model value was obtained by using the Cd/d model average value previously calculated. The d model value can be compared to the actual d value by means of a statistical Student t-test t=

d−dmod qffiffiffiffiffiffiffi σ 1 =n

ð12Þ

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319

Fig. 6. Diagrams representing the statistical range of model solutions of dynamic pressure as compared with data from pressure sensors. For ease of visualization, height normalized to total flow thickness is plot along the vertical and dynamics pressure (the function) is plot along the horizontal. The solid line represents the average model solution. The dashed line represents the maximum solution, which is the safety value. The dotted line represents the minimum solution. Dots represent the value of dynamic pressure as measured by sensors. The diagrams refer to the 4 runs of Table 1.

where the model value, dmod, represents the population mean of the test, and the value of the experimental data, d, represents the sample mean. The standard deviation is the sorting value (σ, phi units) of the grain-size distribution. The number of size classes in the grain-size distribution is n, and the degrees of freedom of the test are n − 1. A two-tails test is formalized, at a cumulative significance level of 0.05, and critical values are found, at the respective degrees of freedom, by the values of the t

distribution. The test value never fell outside the range of critical values for our experimental data. This means that dmod is a significant model of the experimental data. Since the value of dmod, was obtained by calculations that started from an assumption of the density range for the currents, the test actually provides a verification of this assumption. We then proceeded by normalizing model results to experimental data. The average Cd/d model value has an associated average model

Table 1 Experiment results and particle data of the 4 runs reported on Fig. 6. Vmax = maximum velocity measured on top of the shear current. Hsf = height of the shear current. Htot = total flow thickness. d = median size of particle of the suspension population. d1 = maximum size of particle at initiation of motion at the base of the current. ρs = density of the particles of the suspension population. ρs1 = density of the maximum particle at initiation of motion at the base of the current. Ψ = shape factor of particle of the suspension population. Run 1 2 3 4

Vmax

Hsf

Htot

(m/s)

(m)

(m)

d (mm)

d1 (mm)

ρs (kg/m3)

ρs1 (kg/m3)

Ψ (–)

3.7 5.9 5.6 10.5

0.38 0.35 0.25 0.4

1.2 0.85 0.8 1

0.109 0.101 0.276 0.280

5.73 7.81 6.03 6.08

1973 1958 1472 1466

748 739 678 2547

0.37 0.37 0.37 0.37

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density, ρfmod, which is calculated by means of Eq. (8). The settling velocity of dmod and experimental d can be equated, and the following equation results: 4gdðρs −ρf Þ 4gdmod ðρs −ρfmod Þ = 3Cd ρf 3Cd ρfmod

ð13Þ

where the experimental data are used on the left side and model data are used on the right side. In particular, dmod is the value of the average d model and ρfmod is the value of the average flow model density. The unknown is the density, ρf, of the flow normalized to the experimental data. By calculating the normalized flow density, the normalized Cd/d value can be calculated using Eq. (8). This value is then used into Eq. (9), and the normalized average squared shear velocity, associated with the normalized average density, is found. Once the average values of shear velocity and flow density are found, intervals around these values, associated with a certain range of probability, can be calculated. In statistics, this interval is generally expressed by the quantity corresponding to ± one unit of standard deviation around the average. In a Gaussian distribution, the range enclosed in this interval corresponds to the central 68% of probability of the distribution, 34% on the right and 34% on the left of the average, respectively. In order to conform to this standard, we calculated this interval by subdividing the total area enclosed by the function of Cd/d vs. shear velocity over the u2* (2 kg/m3)–u2* (100 kg/m3) range, into two parts, one on the left and the other on the right side of the average value. To each part we assigned a 50% of probability. By means of !! 2

u avg Cd = ∫u*2 ð100 kg=m3 Þ d *

4g ρs −

θgd1 ρs1 u2 + θgd1

*

3u2 *

θgd1 ρs1 u2 + θgd1

!

2

du* :

ð14Þ

*

The total area on the left of the average is found. 68% of this quantity represents the Cd/d value that corresponds to 34% of the probability to the left of the average. This value, when substituted into Eq. (9), results in a shear velocity that represents the minimum value of our range. The same is done on the right side of the average, by using u2* (2 kg/m3) as the upper limit of integration in Eq. (14). The value corresponding to 34% of the right side of the average is then found, and this represents the maximum value of our shear velocity range. Using these values together with the associated Cd/d values in Eq. (8), the associated minimum and maximum densities were calculated. Note that the maximum value of shear velocity is associated with the minimum value of flow density, and the minimum shear velocity is associated with the maximum density. The obtained range of solutions of shear velocity and average density of the shear current were then used to reconstruct the average, minimum and maximum solutions of the velocity and density profiles, and finally the model solutions of the dynamic pressure profiles of Fig. 6. References Baxter, P.J., Neri, A., Todesco, M., 1998. Physical modeling and human survival in pyroclastic flows. Nat. Hazard. 17, 163–176. Baxter, P.J., Boyle, R., Cole, P., Neri, A., Spence, R.S., Zuccaro, G., 2005. The impacts of pyroclastic surges on buildings at the eruption of the Soufrière Hills volcano, Montserrat. Bull. Volcanol. 67, 292–313. Branney, M.J., Kokelaar, P., 2002. Pyroclastic density currents and the sedimentation of ignimbrites. Geol. Soc. Mem. London 27, 1–152. Burgissier, A., Bergantz, G.W., 2002. Reconciling pyroclastic flow and surge: the multiphase physics of pyroclastic density currents. Earth Plan. Sci. Lett. 202, 405–418.

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