IAVCEI 2013 Scientific Assembly - July 20 - 24, Kagoshima, Japan
Forecasting Volcanic Activity - Reading and translating the messages of nature for society

1W_3D-P3

Date/Time: July 21 Poster

Finite element analysis of conduit wall rock stresses associated with steady flow models
Jonathan B Hanson1 , Alison C Rust1 , Martyn J Pavier1 , Jeremy C Phillips1 , Antonio Costa2
1

University of Bristol, United Kingdom, 2 INGV - Bologna, Italy
E-mail: jonathan.hanson@bristol.ac.uk

Conduit erosion (i.e. the permanent removal of wall-rock) modifies conduit geometry during eruptions and affects
eruption dynamics. However, there has been very little modelling of conduit wall-rock failure and none couplingerosion and fluid dynamic models.

Finite element analysis is a powerful tool to elucidate the behaviour of the wall-rock during both dynamic
and static loading and is capable of dealing with inherently non-linear and complex systems. Initial investigations
using the FEA package Abaqus have focused on conduit wall-rock loading based on the pressure profiles
determined by the steady 1-D explosive eruption dynamics models of Costa et al., 2009. Their models assume a
6000 m conduit linking the chamber (of variable pressure) to the vent with a cylindrical, dyke-like or hybrid (dikethat transitions to a cylinder) geometry. The fluid pressures in their set of simulations range from +30MPa to-106MPa, with respect to lithostatic.

FE models loading the conduit walls with the stress from the simulated fluid pressures suggest significant
wall-rock failure would occur for all geometries modelled. For example, the pressure profile for a cylindricalconduit in an elastic medium (Youngs modulus = 40 GPa, Poissons ratio = 0.25, and yield strength = 20 MPa)
results in damaged volumes of 107 m3 . Damage is focused around, and particularly important in, areas of conduit
underpressures, as this material will implode into the conduit; erosion of damaged overpressured areas requires afurther mechanism to remove material (e.g. magmatic shear stress or particle collisions). The forecasted yielded
volumes exceed that of the conduit by an order of magnitude, suggesting that significant wall-rock failure would
inhibit the development of the modelled steady flow pressure profiles. FE analyses with a dyke-like geometry
suggest that significant failure would be focused near the dyke tips. Results for a dyke underpressure of 50 MPa(properties as above) indicate yielded cross-sectional areas of hundreds of square meters. Due to the spatial
relationship between this damaged material and the dyke, this material would not easily be removed, although
increased permeability through damage could be important in promoting magma-water interaction.

The amount of damaged material strongly depends on the initial size of the conduit and the assumed rockrheology. For increasingly complicated, quasi-steady models coupling 1-D flow and evolving conduit geometry
based on FE wall-rock failure, an elastic-plastic wall-rock rheology may be more appropriate. In the static loading
done to date, adjusting the rheology from elastic to elastic-plastic increases the damaged volume by orders ofmagnitude.

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