Strengths and strain energies of volcanic edifices: implications for eruptions, collapse calderas, and landslides

Abstract

Abstract. Natural hazards associated with volcanic edifices depend partly on how fracture resistant the edifices are, i.e. on their strengths. Observations worldwide indicate that large fluid-driven extension fractures (dikes, inclined sheets), shear fractures (landslides), and mixed-mode fractures (ring dikes and ring faults) normally propagate more easily in a basaltic edifice (shield volcano) than in a stratovolcano. For example, dike-fed eruptions occur once every few years in many basaltic edifices but once every 10 2−3 yr in many stratovolcanoes. Large landslides and caldera collapses also appear to be more common in a typical basaltic edifice/shield volcano than in a typical stratovolcano. In contrast to a basaltic edifice, a stratovolcano is composed of mechanically dissimilar rock layers, i.e. layers with mismatching elastic properties (primarily Young's modulus). Elastic mismatch encourages fracture deflection and arrest at contacts and increases the amount of energy needed for a large-scale edifice failure. Fracture-related hazards depend on the potential energy available to propagate the fractures which, in turn, depends on the boundary conditions during fracture propagation. Here there are two possible scenarios: one in which the outer boundary of the volcanic edifice or rift zone does not move during the fracture propagation (constant displacement); the other in which the boundary moves (constant load). In the former, the total potential energy is the strain energy stored in the volcano before fracture formation; in the latter, the total potential energy is the strain energy plus the work done by the forces moving the boundary. Constantdisplacement boundary conditions favor small eruptions, landslides, and caldera collapses, whereas constant-load conditions favor comparatively large eruptions, landslides, and collapses. For a typical magma chamber (sill-like with a diameter of 8 km), the strain energy change due to magmachamber inflation is estimated at the order of 10 14 J (0.1 PJ).For comparison, the surface energy needed to form a typical feeder dike is of the same order of magnitude, or 10 14 J. There are several processes besides magma-chamber inflation that may increase the strain energy in a volcano before eruption. Thus, during a typical unrest period with magmachamber inflation, the added strain energy in the volcano is large enough for a typical feeder dike to form. An injected dike, however, only reaches the surface and becomes a feeder if it is able to propagate through the numerous layers and contacts that tend to deflect or arrest dikes. The strong elastic mismatch between layers that constitute stratovolcanoes not only encourages fracture arrest, but also the storage of more strain energy (than in a typical basaltic edifice/shield volcano) before fracture formation and failure. It is thus through producing materials of widely different mechanical properties that stratovolcanoes become strong and resilient.

Basaltic feeder dykes in rift zones: geometry, emplacement, and effusion rates

“…The propagation is commonly through crustal layers that are stresshomogenised, that is, behave as essentially a single mechanical layer at the time of feeder-dyke emplacement. By contrast, when the crustal layers are not stress-homogenised, they may develop local stresses that are unfavourable for dyke propagation, or have contacts that are similarly unfavourable, in which case the dykes would become arrested and not reach the surface to become feeders (Gudmundsson, 2012a). However, the geometries of the feeder and the nonfeeder dykes are commonly different, particularly close to the surface, as indicated by the results presented here and in other works (Keating et al, 2008;Geshi et al, 2010Geshi et al, , 2012.…”

“…Dykes induce stresses and displacements at and close to the Earth's surface when approaching it (Pollard and Holzhausen, 1979;Pollard et al, 1983;Rubin and Pollard, 1988;Bonafede and Olivieri, 1995;Rubin, 1995;Bonafede and Danesi, 1997;Acocella and Neri, 2003;Gudmundsson, 2003;Gudmundsson et al, 2008). Hence, surface deformation takes place before the eruption as well as at the moment the feeder intersects the Earth's surface.…”

“…While some magma chambers, particularly small sill-like chambers, may be totally molten, most chambers are likely to be only partially molten and behave as poroelastic bodies. For a poroelastic magma chamber, the total volume of magma transported by a feeder dyke to the surface (and including the volume of the feeder itself) during an eruption may be estimated as follows (e.g., Gudmundsson, 2012a):…”

“…The solidification of magma inside these conduits forms plugs and feeder dykes, respectively. Many plugs, however, are composed of dense clusters of dykes (Gudmundsson, 2012a). In rift zones, magma conduits are usually tabular or sheet-like subvertical dykes, and when they reach the surface they form eruptive fissures whose trends coincide with those of the associated feeder dykes.…”

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“…We know that the energetic investment by the magma on this path will be the minimum and that it will be parallel to the trajectory of the main principal stress and normal to the minimum principal stress (Gudmundsson, 2008(Gudmundsson, , 2012. However, we do not have any direct criteria that enable us to determine this route a priori since we lack detailed 3-D knowledge of the stress field of the area.…”