Numerical investigation on origin and evolution of polygonal cracks on rock surfaces

We studied the formation and evolution mechanism of polygonal cracks on rock surfaces under cooling by modelling meso-damage mechanics, continuum mechanics and thermodynamics. Factors that affect rock surface damage include ambient temperature, lithology difference and boundary restrictions. We established and simulated a heterogeneous model with a surface weak layer for three types of boundaries. These were biaxial constraint, uniaxial constraint and free boundary. The initiation and propagation of polygonal cracks were reproduced for varying thickness and homogeneity of the weak layer. The results show that the boundary constraints strongly influence the polygonal cracking. Many polygonal or parallel cracks are generated on the rock surface under biaxial or uniaxial constraint. The unconstrained rock surface displays polygonal cracks at the center and parallel cracks in the surrounding areas. The thicker the surface weak layer, the larger the average area of formed blocks. Small blocks and short cracks are more numerous than large blocks and long cracks. As the heterogeneity index increases, the rock layer is more likely to produce blocks with relatively regular shapes. Quadrilateral, pentagonal and hexagonal blocks dominate regardless of changes in layer thickness and heterogeneity. However, the number of edges of the polygonal blocks is sensitive to rock heterogeneity. The polygons tend to become more complex with increasing inhomogeneity. This study contributes to understanding the complex formation mechanisms of polygonal cracks on rock surfaces in nature. Additionally, the simulations of three-dimensional fracture geometry provide a basis for developing algorithms to generate discrete fractures and blocks in discrete fracture network (DFN) analyses