The influence of porosity and vesicle size on the brittle strength of volcanic rocks and magma

Abstract

Volcanic rocks and magma display a wide range of porosity and vesicle size, a result of their complex genesis. While the role of porosity is known to exert a fundamental control on strength in the brittle field, less is known as to the influence of vesicle size. To help resolve this issue, here, we lean on a combination of micromechanical (Sammis and Ashby's pore-emanating crack model) and stochastic (rock failure and process analysis code) modelling. The models show, for a homogenous vesicle size, that an increase in porosity (in the form of circular vesicles, from 0 to 40 %) and/or vesicle diameter (from 0.1 to 2.0 mm) results in a dramatic reduction in strength. For example, uniaxial compressive strength can be reduced by about a factor of 5 as porosity is increased from 0 to 40 %. The presence of vesicles locally amplifies the stress within the groundmass and promotes the nucleation of vesicle-emanating microcracks that grow in the direction of the applied macroscopic stress. As strain increases, these microcracks continue to grow and eventually coalesce leading to macroscopic failure. Vesicle clustering, which promotes the overlap and interaction of the tensile stress lobes at the north and south poles of neighbouring vesicles, and the increased ease of microcrack interaction, is encouraged at higher porosity and reduces sample strength. Once a microcrack nucleates at the vesicle wall, larger vesicles impart higher stress intensities at the crack tips, allowing microcracks to propagate at a lower applied macroscopic stress. Larger vesicles also permit a shorter route through the groundmass for the macroscopic shear fracture. This explains the reduction in strength at higher vesicle diameters (at a constant porosity). The modelling highlights that the reduction in strength as porosity or vesicle size increases is nonlinear; the largest reductions are observed at low porosity and small vesicle diameters. In detail, we find that vesicle diameter can play an important role in dictating strength at low porosity but is largely inconsequential above 15 % porosity. Vesicle clustering and stress lobe interaction are implicit at high porosity, regardless of the vesicle diameter. In the case of an inhomogeneous vesicle size, the microcracks grow from the largest vesicles, and brittle strength is closer to that of the largest vesicle end-member. The results of this study highlight the important role of vesicle size, and the complex interplay between porosity and vesicle size, in controlling the brittle strength of volcanic rocks and magma.