In assessing the potential effects of pyroclastic flow at Pompeii, it is clear that the direction and kinetic energy of the flow resulting from the 79 A.D. eruption cannot be predicted precisely. Nevertheless, it is possible to establish quantitative bounds on the velocity and density of the flow based on published research, particularly studies of the volcanic deposits, numerical simulations of pyroclastic flow at Vesuvius, and general theoretical studies. The following discussion reviews this research and seeks to identify credible bounds for the velocity and density of pyroclastic flow resulting from a large eruption of Vesuvius.
Considering velocities resulting from the eruption of Vesuvius, Dobran  did a particularly important study with respect to the hazard potential of pyroclastic flow. Dobran performed numerical simulations to estimate the extent and rate of pyroclastic flow due to large, medium, and small volcanic eruptions of Vesuvius. For a large eruption, Dobran predicts the following sequence of events along the south-east face of Vesuvius [1994, p. 553]:
|0 sec.||Beginning of eruption|
|20 sec.||The eruptive column collapses, after rising to a height of 3 km. The collapse initiates pyroclastic flow.|
|60 sec.||The pyroclastic flow reaches a distance of 2 km from the vent.|
|120 sec.||The pyroclastic flow reaches a distance of 4 km from the vent.|
|300 sec.||The pyroclastic flow reaches a distance of 7 km from the vent, entering the Tyrrhenian Sea to the east.|
|A chronology of the spread of pyroclastic flow, based on numerical simulations of a large eruption of Vesuvius [Dobran 1994, p. 553].|
The study area for this chronology is the south-east quadrant of Vesuvius, indicated on the figure below. The dotted contours indicate the extent of pyroclastic flow at different points in time, measured in seconds. Note that the city of Pompeii lies just outside the study area, slightly to the east, approximately 9 km from the vent.
|Time contours indicating the rate of spread of pyroclastic flow for a large eruption of Vesuvius [Dobran 1994, p. 553, figure 2a]|
Based on Dobran's chronology of times and distances, it is possible to estimate the velocity of the flow simply by dividing the distance travelled by the elapsed time. The table below summarizes this calculation.
|Total Time||Total Distance||Time Increment||Distance Increment||Average Velocity||Incremental Velocity|
|Average and incremental velocities based on Dobran's chronology . Note that the distance is zero during the first 20 seconds because the eruptive column is rising during that time. [Dobran 1994, p. 553]|
The average velocity (5) is calculated as the total distance (2) divided by the total time (1), while the incremental velocity (6) is calculated as the distance travelled during the time increment (4), divided by the duration of the increment (3). Note that the distance is zero during the first 20 seconds because the eruptive column is rising during that time.
This chronology reveals two points: first, the velocities are relatively low, but are consistent with observed velocities at other events; second the velocity decreases rapidly with distance, so that Pompeii, at a distance of 9,000 m from the vent, would experience velocities still lower than those listed. The graph below shows the three incremental velocities derived from Dobran's data as a function of distance, the graph also includes two extrapolated values, one corresponding to 8 m/s and a higher value of 12 m/s, at a distance of 9000 m.
|A graph of incremental velocity of pyroclastic flow as a function of distance from the vent. The solid line is based on data derived from Dobran . The dotted lines are extrapolations to a distance corresponding to the location of Pompeii; The lower value is 8 m/s at 9000m, and the higher value is 12 m/s.|
Based on this extrapolation, it is reasonable to conclude that pyroclastic flow resulting from the collapse of a large eruptive column, as happened in 79 AD, would reach the city of Pompeii at a velocity in the range of 8 to 12 m/s (18 to 28 MPH). These values contrast sharply with the much higher theoretical values discussed by Sparks , however Sparks analysis is not specific to Vesuvius, as Dobran's study is, and Sparks assumes values for vent diameter and gas velocity at the vent that are much larger than Dobran uses in his analysis of Vesuvius. Sparks analyses include vent radii ranging from 100 to 600 m , and vent velocities ranging from 400 to 600 m/s [1978, p. 1733]. Dobran uses much smaller values of 50 m for the vent radius, and 118 m/s for the vent velocity [1994, p. 552]. Dobran's much smaller predicted flow velocities are consistent with the much smaller assumed values for vent radius and gas velocity at the vent.
The kinetic energy of the flow depends on both velocity and density. As with velocity, there are many uncertainties in estimating the density of a flow; in fact, the uncertainties are greater since velocities, at least average global velocities, can be measured and observed directly, while densities cannot. Estimates of density must be based on the observed behavior of the eruption and the flow, on the nature of the deposits, and the effects of the flow. In addition, density varies throughout the flow; it is common for the lower part of a flow to be composed of higher density materials, overridden by a lower density more turbulent layer.
Flow density depends on two basic factors: the density of the solids, and the percentage of the flow volume which the solid particles occupy. The density of the gaseous medium surrounding the particles is not a significant factor, since the mass of the particles dominates the overall flow density, even when the solids occupy only 1 percent of the total volume.
Concerning the density of the solids, there are two basic types: pumice, and lithics. Pumice typically has density less than or equal to that of water. In theoretical studies of pyroclastic flow including pumice particles, Sparks [1978, p. 1734] assumed a density of 1.0 g/cm3; Pumice with even lower density, approximately 0.7 g/cm3, fell on Pompeii during the air-fall phase of the 79 AD eruption. Lithics are stone particles with a much higher density; Sparks [1978, p. 1734] assumes a value of 2.5 g/cm3 (156 lb/ft3).
At Pompeii, there are a variety of flow deposits with varying mixtures of pumice and lithics. Sigurdsson [1985, p. 352] describes the most destructive surge as follows:
The deposit consists of distinct lower and upper units. The lower unit is relatively massive and flowlike and contains a higher proportion of pumice in a brown silty-to-sandy matrix. This poorly sorted unit also contains tiles and other building fragments, evidence of its destructive force.
Approximate bounds of the flow density can be established by estimating reasonable high and low bounds of the solid density, and the solid concentration, and calculating the resulting densities. Assuming that the pumice content of the solids ranges from 20 percent to 40 percent, leads to the conclusion that the solids have an average density of 2.2 g/cm3 to 1.9 g/cm3 (137 to 118 lb/ft3).
There is little published data on the density of the flow itself. In his numeric studies of Vesuvius, Dobran [1994, p. 552] estimates the particle volumetric fraction at the eruption vent at 0.067 for a large eruption. Sparks [1978, p. 1732] estimated that the initial void fraction of a pyroclastic flow resulting from eruption column collapse was in the range of 0.97 to 0.995, corresponding to particle volumetric fractions of 0.03 to 0.005. As the flow moves away from the source, the flow will tend to become more dense, particularly close to the ground, as heavier particles segregate toward the bottom and gas escapes from the flow [Sparks 1978, p. 1733]. For approximate calculations, it is probably reasonable to choose 10 percent and 5 percent as upper and lower bounds for the particle volumetric fraction.
Combining the estimated bounds for particle density and particle volumetric fraction leads to the following bounds on the density.
|Average particle density||Particle volume fraction||Average flow density|
|g/cm3 (lb/ft3)||g/cm3 (lb/ft3)|
|High bound||2.2 (137)||0.1||0.22 (13.7)|
|Low bound||1.9 (118)||0.05||0.095 (5.9)|
|Estimated upper and lower bounds of flow density based on estimates of the particle density and particle volume fraction.|
Although this estimate represents a wide range, with the maximum more than five times larger than the minimum, it establishes a useful basis for estimating loads in the structural investigation.