Numerical modeling of deformation and stress fields around a magma chamber: Constraints on failure conditions and rheology Gilda Currenti a,⇑ , Charles A. Williams b a Istituto Nazionale di Geofisica e Vulcanologia – Osservatorio Etneo, Sezione di Catania, Italy b GNS Science, Lower Hutt 5040, New Zealand article info Article history: Received 29 November 2012 Received in revised form 7 October 2013 Accepted 6 November 2013 Available online 15 November 2013 Edited by M. Jellinek Keywords: Magma chamber Inelastic rheology Failure condition Gravitational loading Numerical modeling Volcano unrest abstract We present a stress–strain analysis using the Finite Element Method to investigate failure conditions of pressured magma chambers embedded in an inelastic domain. The pressure build-up induces variations in the stress field until failure conditions are reached. Therefore, the definition of the failure conditions could have a significant impact on the volcano hazard assessment. Using a numerical approach, we ana- lyze the stresses in a gravitationally loaded model assuming a brittle failure criterion, to determine the favorable conditions for magma chamber failure in different source geometries, reference stress states, pore fluid pressures, rock rheologies and topographic profiles. The numerical results allow us to pinpoint the conditions promoting seismicity near the magma chamber. The methodology places a limit on the pressure that a magma chamber can sustain before failing and provides a quantitative estimate of the uplift expected at the ground surface. Thermally-activated ductile regimes, which may develop in the region surrounding a heated magma chamber, are also investigated. The stress relaxation in a ductile shell may prevent the wall rupture, favoring the growth of large overpressured chambers, which could lead to considerable deformation at the ground surface without significant seismicity. The numerical results suggest that a spherical source, compressive regime, gentle edifice topography, and growth of a ductile shell are important factors for the initial formation and the mechanical stability of magma storage systems. On the other hand, an elongated ellipsoidal source, extensional regime, steep volcano topogra- phy and high pore fluid pressure lower the overpressure necessary for inducing failure. These findings could help in gaining insights on the internal state of the volcano and, hence, in advancing the assessment of the likelihood of volcano unrest. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Ground deformation and other surface observations in volcanic areas are often interpreted in terms of overpressure changes in magma chambers. Since they represent the storage of magma ris- ing from depth, and their growth and evolution regulate the trans- port of magma toward the surface, investigations on magma chamber stability are of particular interest. When a magma cham- ber is present, the condition for the onset of an eruption is the fail- ure of its walls. To assess the likelihood of a volcanic eruption, it should be determined if the chamber is prone to rupture (Gudmundsson, 2006). The definition of the conditions for cham- ber failure is therefore of primary interest in understanding the factors that lead to chamber wall failure, possibly triggering an eruption. The magma overpressure that the wall of a chamber can sustain before failing depends complexly on the medium rheology, the mechanical rock properties, the stress distribution around the chamber, the volcanic edifice loading, and the source geometry (Sartoris et al., 1990; Grosfils, 2007; Hurwitz et al., 2009; Long and Grosfils, 2009; Martí and Geyer, 2009). When failure conditions are investigated, a preliminary analysis of stability is required and total pressures, rather than simple internal overpressures, have to be considered (Grosfils, 2007; Gerbault et al., 2012). Usually simple elastic models, which repre- sent the magma chamber as a cavity within an unloaded elastic medium, have been used to estimate wall ruptures (Gudmundsson, 2006; Pinel and Jaupart, 2004; Martí and Geyer, 2009), without making any assumptions about the total pressure acting on its wall. Recently, Grosfils (2007) demonstrated that the estimate of the value of the overpressure for tensile failure using gravitation- ally loaded models can be considerably different than that estimated using unloaded elastic models. The location and occur- rence of ruptures was estimated by determining the regions where the elastic stresses exceed the tensile strength of the rocks. In vol- canic regions many factors make the rocks deviate from elastic behavior and may strongly affect the estimate of source overpres- sure. A more realistic representation of rocks surrounding a magma chamber would be as brittle material in which fracture is con- trolled by a brittle failure criterion that is dependent on the net 0031-9201/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.pepi.2013.11.003 ⇑ Corresponding author. Tel.: +39 0957165800. E-mail address: gilda.currenti@ct.ingv.it (G. Currenti). Physics of the Earth and Planetary Interiors 226 (2014) 14–27 Contents lists available at ScienceDirect Physics of the Earth and Planetary Interiors journal homepage: www.elsevier.com/locate/pepi