Non-linearity in multidirectional P-wave velocity: confining pressure behaviour based on real 3D laboratory measurements, and its mathematical approximation
R. Přikryl, Karel Klíma, T. Lokajíček, Z. Pros, 2005. "Non-linearity in multidirectional P-wave velocity: confining pressure behaviour based on real 3D laboratory measurements, and its mathematical approximation", Petrophysical Properties of Crystalline Rocks, P. K. Harvey, T. S. Brewer, P. A. Pezard, V. A. Petrov
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Experimental laboratory measurements of P-wave velocity confirm the superposition of linearity over non-linearity by a progressive increase in confining pressure. The increase in confining pressure diminishes the influence of microcracks that are partly or totally closed. At a certain stress level, the trend of P-wave velocity with applied confining pressure approaches that of a solid without cracks, and a linear increase in elastic wave velocity occurs under high confinement.
Several studies have focused on the problem of mathematical approximation of this phenomenon (Carlson & Gangi 1985; Wepfer & Christensen 1991; Greenfield & Graham 1996; Meglis et al. 1996). Although successful within a certain degree of error, they provide neither a multidirectional solution nor the comparison of results with rock fabric. In this study, an analytical relation was applied to describe the P-wave velocity-confining pressure behaviour of quasi-isotropic rocks (granites) and their anisotropic equivalents (orthogneisses). Two parameters of this relationship reflect the elastic properties of the rock matrix, and two others are related to the presence of microcracks, their density and genesis. The results of a mathematical approximation of the P-wave velocity-confining pressure behaviour show a favourable correlation to the measured data-sets. Comparison of individual fitted parameters with the rock fabric provides an improved understanding of the material's mechanical behaviour.