The strength of heterogeneous volcanic rocks: A 2D approximation

Abstract

Volcanic rocks typically contain heterogeneities in the form of crystals and pores. We investigate here the influence of such heterogeneity on the strength of volcanic rocks using an elastic damage mechanics model in which we numerically deform two-dimensional samples comprising low-strength elements representing crystals and zero-strength elements representing pores. These circular elements are stochastically generated so that there is no overlap in a medium representing the groundmass. Our modelling indicates that increasing the fraction of pores and/or crystals reduces the strength of volcanic rocks, and that increasing the pore fraction results in larger strength reductions than increasing the crystal fraction. The model also highlights an important weakening role for pore diameter, but finds that crystal diameter has a less significant influence for strength. To account for heterogeneity (pores and crystals), we propose an effective medium approach where we define an effective pore fraction ϕp′=Vp/(Vp+Vg) where Vp and Vg are the pore and groundmass fractions, respectively. Highly heterogeneous samples (containing high pore and/or crystal fractions) will therefore have high values of ϕp′, and vice-versa. When we express our numerical samples (more than 200 simulations spanning a wide range of crystal and pore fractions) in terms of ϕp′, we find that their strengths can be described by a single curve for a given pore diameter. To provide a predictive tool for the strength of heterogeneous volcanic rocks, we propose a modified version of 2D solution for the Sammis and Ashby (1986) pore-emanating crack model, a micromechanical model designed to estimate strength using microstructural attributes such as porosity, pore radius, and fracture toughness. The model, reformulated to include ϕp′ (and therefore crystal fraction), captures the strength curves for our numerical simulations over a sample heterogeneity range relevant to volcanic systems. We find that published experimental data (for which the porosity and crystal fraction is known) correlate well with our modelled curves, adding validity to our approach. We present herein a 2D analytical tool to estimate the strength of volcanic rock that can be used when the porosity, crystal fraction, and maximum pore diameter are known.