Correlating mechanical properties to fractal dimensions of shales under uniaxial compression tests

With the rapid increase in world energy consumption and exhaustion of conventional energy reserves, shale gas, as the most promising unconventional resource, has attracted worldwide attention. It is of great theoretical and practical significance to study the mechanical properties and fracture behavior of shale for the evaluation and development of deep shale gas. To study the mechanical behaviors of shales under uniaxial compression tests, two fractal dimensions F-s and F-b are used, in which F-s is calculated by the size distribution of fragmentations and F-b is calculated by box-counting method based on the fracture distribution on the surface of damaged shale samples. A total of 100 shale samples are prepared and uniaxial compression tests are carried out using the servo-controlled MTS816 testing system. The micro-CT scanning technology is employed to exhibit the structures of cracks and to interpret the relationship between mechanical properties and fractal dimensions of shales. The results show that the value of F-s ranges from 1.3049 to 2.0605, and the larger F-s indicates a larger number of fragments. The F-b representing the complexity of the cracks varies from 1.2486 to 1.4303, and a larger F-b indicates that the shales are more seriously damaged. Both the peak strength and elastic modulus can be predicted using F-s and F-b, following linear and power-law relationships, respectively. The micro-CT scanning results show that although the locations of slices are different, the distributions of main cracks are almost the same because the initial weak planes are parallel to the axial direction of the sample. The main cracks are generated through the sample with relatively large apertures. Sample No. 20 has a larger mean F-b of slices and a larger peak strength than sample No. 14, due to its larger volume and/or volume percentage of cracks. This well explains that mechanical behaviors such as peak strength and elastic modulus can be strongly correlated with the fractal dimensions representing the distribution of fragmentations and crack patterns on the surface of broken samples. This research can provide new ideas for the study of the mechanical properties and failure characteristics of shale, and also provide scientific guidance for the exploration and development of shale oil and gas.