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

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. Constant-displacement 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 magma-chamber inflation is estimated at the order of 10¹⁴ J (0.1 PJ). For comparison, the surface energy needed to form a typical feeder dike is of the same order of magnitude, or 10¹⁴ 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 magma-chamber 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.