Evaluation of 3-D Strain Distribution in Lignite Based on Image Analysis

Evaluation of three dimensionally non-uniform strain distribution in rocks under various conditions such as in water or under freeze-thaw cycles is of significant importance to understand their complex deformations and fracturing mechanisms. For this purpose, we developed an image analysis method which can evaluate or “measure” the three dimensional (3-D) strain distribution in rocks. The proposed method utilizes the 3-D images of rock under initial and deformed configurations, which are obtained by some imaging techniques such as X-ray computed tomography (X-rayCT). In the proposed method, the obtained 3-D images are divided into multiple sub-regions of interest. For each sub-region, the strain is evaluated utilizing 3-D affine transform with unknown coefficients to be determined. In the first step, 3-D voxel level displacements at multiple representative points in each sub-region are computed by 3- D digital volume correlation technique between the comparison images and the initial-guess of the transform coefficients are obtained. In the second step, referring to the initial-guess of unknown transform coefficient, they were optimized in sub-voxel level by finding optimum digital volume correlation between the comparison images, which can evaluate the transform coefficients with higher precision. From the calculated transform coefficients, the strain was directly obtained through the spatial derivative of displacement based on affine transform. In this paper, along with the description of the proposed method, the evaluation of deformation in a lignite specimen due to immersion in water was presented as an application example. As the 3-D imaging technique, micro-focus X-rayCT was applied. The result showed that the induced dilatational strain field due to the initiation and extension of cracks in the specimen was clearly captured. Therefore, authors believe that the proposed method can be applicable to various problems in rock mechanics.