“…Fracture development and distribution in underground rocks strongly influence rock properties, so understanding the fracture system is critical to oil and gas reservoir detection and production, groundwater resource, underground waste storage, mining, seismology and CO 2 capture and storage. Due to the heterogeneity over many scales, from micrometer cracks to hectometres fractures (Barbier et al ., 2012; Zhang et al ., 2019; Ding et al ., 2020), the characterization of carbonate reservoirs to describe the fracture network is a complex task (Luo et al ., 2017; Qin et al ., 2018b; Meng et al ., 2020). Fluid permeability, which is associated with pore size and fracture size, is also dependent on the fracture scale in fractured rocks (Johnson et al ., 1986; Katz and Thompson, 1986; Bernabé, 1995; Glover et al ., 2006; Walker and Glover, 2010).…”