3D multifractal analysis of explosion-induced fractures in bedding shale using μ-CT imaging

To systematically evaluate the spatial anisotropy of fracture propagation in bedding shales under different explosive loads, this study conducted 6 groups of explosion experiments on bedding shales with central drilling. CH₄-O₂ mixed gas with varying initial pressure (P₀, 0.3–2.1 MPa) was used to generate explosive loads at different energy levels. The explosive loads of the combustible gases were quantitatively assessed using the TNT equivalence method. μ-CT images of explosion-induced fractures were acquired to reconstruct the 3D fracture morphology. A multifractal calculation algorithm for fractures was developed to perform spatial heterogeneity evaluation of both binary fracture images and 3D fracture data. To thoroughly investigate the influence of spatial location on 3D fracture propagation, 32 representative elementary volumes (REVs) were extracted under different explosive loads and positions. 3D multifractal analysis was used to quantify the complexity of fractures across various heterogeneities. In addition, the fracture characteristics and absolute permeability of the REVs were subjected to statistical analysis. The results show that varying P₀ of the CH₄-O₂ mixed gas generate explosive loads with TNT equivalence factors ranging from 1.352 kg/m³ to 8.072 kg/m³. As the explosive load increases, the fracture morphology transitions from a bi-wing fracture to multi-radial fractures. The multifractal analysis of the 3D fractures reveals that the generalized dimension spectrum (D(q)-q spectrum) displays an inverse S-shaped monotonic decrease, while the multifractal singularity spectrum (α-f(α) spectrum) exhibits a left-hook shape. These features suggest that explosion-generated fractures in dense areas have smaller heterogeneity and dominate over sparser fracture regions. The fractal dimension of the binary fracture images first increases and then decreases with the slice number. The multifractal results also show that the complexity of fractures in different fracture density increases first and then decreases with the slice number. The statistical results of the fracture characteristic parameters for the 32 REVs indicate that the 3D volume and surface area increase with the explosive load. Under the same explosive load, fracture complexity is highest at the bottom of the wellbore. The multifractal analysis reveals that the more complex the 3D fracture morphology, the more the D(q)-q spectrums shift upwards, and the α-f(α) spectrum shift upwards and to the right. Permeability first increases and then decreases with explosive load, with the highest permeability observed at the center and bottom of the wellbore. Correlation analysis reveals relationships between fracture characteristic parameters and the D(q)-q spectrum parameters as well as the α-f(α) spectrum parameters. Finally, the mechanical mechanism for the spatial anisotropy of fracture extension is discussed, considering the enhancement of the normal reflected detonation waves, the stress concentration at the bottom of the wellbore, and the cross-layer propagation of stress waves. This study also provides a useful example for evaluating the spatial anisotropy of fracture distribution using CT data in other research contexts.