A model of volcanic explosions at Popocatépetl volcano (Mexico): Integrating fragmentation experiments and ballistic analysis

Summary The dynamics of magma fragmentation is a controlling factor
in the behavior of explosive volcanic eruptions. Fragmentation
changes the eruption dynamics from a system of bubbly flow to one
of gas-particle flow. To date, the influence of the fragmentation
process itself on the eruption dynamics has been largely neglected
in eruption models. This is understandable, as the explosive
expansion of mixtures of pressurized gases and pyroclasts in
volcanic eruptions is a complex process that cannot be studied
directly. The dynamics of the gas-particle mixture resulting after
magma fragmentation in volcanic eruptions was experimentally
investigated in a shock-tube apparatus. We performed fragmentation
experiments with natural volcanic samples with diverse porosities
(10 – 67 vol. %), different applied pressures (4-20 MPa) and
distinct temperatures (room temperature and 850°C). Two different
types of experiments were performed. In the first type, we measured
the ejection velocity of a plate placed loosely on top of a
volcanic sample in order to account for the ejection of the caprock
in Vulcanian eruptions. In the second type we simultaneously
measured the fragmentation speed and the ejection velocity of the
gas-particle mixture in the absence of a plate. In both cases the
results are in good agreement with a general model for Vulcanian
eruptions based on 1-D shock-tube theory, including magma
fragmentation, and considering the specific conditions of each
experiment. Our results show that the fragmentation process plays
an important role in the dynamics of the gas-particle mixture. The
reasons include the following: 1) the energy consumed by
fragmentation reduces the energy available to accelerate the
gas-particle mixture; 2) the fragmentation speed controls the
pressure available for the ejection of the gas-particle mixture
which in turn determines the velocity, density and mass discharge
rate; 3) the grain-size distribution produced during fragmentation
controls the mechanical and thermal coupling between the gas phase
and the particles; 4) the fragmentation process may produce
heterogeneities in the concentration of particles. In volcanic
eruptions all these factors can affect the eruption dynamics
significantly. The model presented herein is consistent with the
experimental results and is capable of describing the dynamics of
brittle fragmentation in Vulcanian eruptions and yielding more
realistic initial pressures at the onset of fragmentation than
previous models. We applied this model to recent Vulcanian
eruptions of Popocatépetl and Colima volcanoes (Mexico) and
estimated the initial gas pressure required to disrupt the caprock,
fragment the underlying magma and eject ballistic projectiles to
the observed distances. Further, the model is used in concert with
a ballistic model to relate initial pressure and gas content with
ballistic range. This coupled model was calibrated and validated
with field and video observations of ballistics ejected during
different Vulcanian eruptions at Popocatépetl Volcano. The model
relates the zones which could be affected by the impact of
ballistic projectiles to the initial pressure that can be estimated
from seismic and geophysical monitoring, providing valuable
information for more refined short-term hazard assessment at active
explosive volcanoes. Finally, a general methodology to delimit the
zones that can be affected by ballistic projectiles is presented
and applied to Popocatépetl Volcano. Three explosive scenarios with
different intensities have been defined according to the past
activity of the volcano and parameterized considering the maximum
kinetic energy associated with ballistic projectiles ejected during
previous eruptions. For each explosive scenario, the ballistic
model is used to calculate the maximum range of the projectiles
considering the optimum launch conditions. Our results are
presented in a ballistic hazard map with topographic profiles that
depict the likely maximum ranges of ballistic projectiles
(horizontally and vertically) under the three explosive scenarios
defined specifically for Popocatépetl Volcano. The multi-level
hazard zones shown on the map are intended to allow the responsible
authorities to plan the definition, development and mitigation of
restricted areas during volcanic crises.