Computing Elastic Moduli of Igneous Rocks Using Modal Composition and Effective Medium Theory

Abstract

Elastic constants of rock materials are the basic parameters required for modeling the response of rock materials under mechanical loads. Experimental tests for determining these properties are expensive, time-consuming and suffer from a high uncertainty due to both experimental limitations and the heterogeneous nature of rock materials. To avoid such experimental difficulties, in this paper a method is suggested for determining elastic constants of rock materials by determining their porosity and modal composition and employing effective medium theory. The Voigt–Reuss–Hill average is used to determine effective elastic constants of the studied igneous rocks according to the elastic moduli of their mineral constituents. Then, the effect of porosity has been taken into account by considering rock as a two-phase material, and the Kuster–Toksoz formulation is used for providing a close estimation of different moduli. The solutions are provided for different isotropic igneous rocks. This sustainable method avoids destructive tests and the usage of energy for performing time-consuming and expensive tests and requires simple equipment.