This study presents the quantitative evaluation of heterogeneity using the characteristic dimension. We propose the modified two-point correlation method to extract the ‘characteristic and representative size’ embedded in rocks applicable to both gray-level and binary images from 3D x-ray computed tomographic images. The method is validated by using a wide range of synthetic images and is applied to 6 rock specimens collected in Korea. Results highlight that the proposed method enables quantitatively defining the representative size in rocks.

1. Introduction

Naturally existing heterogeneity of rock often hampers the precise determination of geophysical key parameters (Blair and Cook, 1998; Torquato, 2002; Lan et al., 2010; Schoen, 2011). Heterogeneity exists in multi-scale from micro (ex. mineral grain) to macro (ex. tectonic stratification) (Torquato, 2002). Heterogeneity are originated from pore geometry (ex. porosity and tortuosity), grain geometry (ex. size and shape), and inter-particle contact (ex. spatial configuration and packing) (Torquato, 2002). Inherent heterogeneity of rock governs the stress localization behavior which lead fracture development mechanisms (Blair and Cook, 1998; Lan et al., 2010). In addition, size and spatial configuration of heterogeneity influence the conduction phenomena such thermal, and elastic conduction (Torquato, 2002). Previous studies have relied on qualitative description of microstructures with the lack of deterministic and dimensional analysis. The two-point correlation method is one of the most general method to characterize heterogeneity of materials based on the two phase image (binarized image) (Blair et al. 1996; Chung & Han 2010). To do that, preprocessing is necessary for the acquired raw image. Recent development of 3D X-ray Computed Tomography (XCT) provide 16 bit scaled physical contrast image of materials using CT number. Physical density of materials governs CT number by Beer-Lambert law. Due to the advantage of XCT which is can visualize internal structure based on physical density, XCT image is frequently applied to the characterization of heterogeneity of materials. However, there is limitations of two-point correlation method owing to the preprocessing for the two-phase system. Generating representative two-phase system for various rock composing minerals is difficult. Also, separation of minerals which has similar densities is challenging. So, this study propose modified two-point correlation method to directly evaluate heterogeneity of rocks based on 16 bit gray images from 3D XCT.

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