Abstract
Rock failure criteria are key input parameters for models designed to better understand the stability of volcanic rock masses. Cohesion and friction angle are the two defining material variables for the Mohr-Coulomb failure criterion. Although these can be determined from laboratory deformation experiments, they are rarely reported. Tabulated data for volcanic rocks, calculated using published triaxial results, show that cohesion and friction angle decrease with increasing porosity. If porosity is known, these empirical fits can provide laboratory-scale cohesion and friction angle estimations. We present a method to upscale these parameters using the generalised Hoek-Brown failure criterion, discuss the considerations and assumptions associated with the upscaling, and provide recommendations for potential end-users. A spreadsheet is provided so that modellers can (1) estimate cohesion and friction angle and (2) upscale these values for use in large-scale volcano modelling. Better constrained input parameters will increase the accuracy of large-scale volcano stability models.
Highlights
Sensitivity analysis of all of the parameters in a model should be considered best practice, in particular considering the high variability of rocks and rock masses and the inherent uncertainty in the resulting input parameters, as demonstrated by the propagated errors given in Table 1 and the standard error of the estimate (SEE) for the porosity-based relationships developed for the datasets we present here
We provide a Microsoft Excel® workbook with two worksheets, one to calculate intact cohesion and internal friction angle, and a second to calculate rock mass cohesion and friction angle, as well as the generalised Hoek-Brown parameters mb, s, and a
We demonstrate the use of standard errors and propagation of these errors when deriving cohesion and internal friction angle from triaxial data as a way to highlight the uncertainty associated with deriving failure criterion parameters from real rock samples
Summary
Rock physical and mechanical properties are important input parameters in slope stability models. The required input parameters for defining failure criteria, such as the cohesion and internal friction angle for the Mohr-Coulomb failure criterion, of volcanic rocks are rarely reported, as noted by Ball et al [2018]. We first detail a simple method to determine the cohesion and internal friction angle using data from laboratory deformation experiments, which we use to create a table of values for volcanic rocks using published triaxial deformation data. We show how uniaxial compressive strength and Hoek-Brown fitting parameter, (mi), values required to upscale cohesion and internal friction angle to the scale of the rock mass, are derived from laboratory triaxial data. We provide empirical relationships between porosity and uniaxial compressive strength and Hoek-Brown fitting parameter mi, which can be used in the absence of laboratory data.
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