Defining the Hoek-Brown constant mi for volcanic lithologies

The empirical Hoek-Brown failure criterion is a well-known and commonly used failure criterion for both intact rocks and rock masses, especially in geological engineering. The intact criterion is calculated using experimental triaxial compression test results on intact samples while the rock mass criterion modifies the intact strength using quantified measures of the rock mass quality. The Hoek-Brown failure criterion includes a fitting constant for intact rocks, mi, which controls the steepness and curvature of the failure envelope, and is derived from curve-fitting the failure criterion to triaxial test data. However, because of the existence of tabulated mi values for various rock types, calculated using 1000’s of triaxial experiments, mi values are often extracted from the tables in the literature rather than the more time- and resource-intensive triaxial experiments. Using 100’s of triaxial experiments on variously altered volcanic rocks from volcanoes around the world, we demonstrate that mi varies dramatically based on a complex combination of alteration, lithology and texture, for example ranging from 2-38 for andesites. In contrast, tabulated estimates are typically given as small ranges, for example 25±5 for andesite. This means the failure criteria for volcanic rocks based on tabulated estimates could significantly over or under predict the intact strength, and thereby the rock mass strength, causing errors for stability and deformation assessments for a variety of volcanological and geological engineering purposes, from dome deformation or flank stability to excavation in volcanic rocks. In this research we not only highlight the high variability of mi for volcanic rocks, but by building on published relationships between porosity and strength, we demonstrate that it too is sensitive to porosity. We propose a number of preliminary methods to constrain mi values, including one using porosity.