One of the goals of fracture mechanics in the analysis of problems containing cracks is to study the growth and propagation of cracks. Each crack grows and propagates only in the environment according to the geometry and loading conditions, which can be under pure modes or under mixed modes. The pattern of crack growth and propagation under these conditions is specific and corresponds to the failure mode. One of the most important factors affecting the failure of structures is the phenomenon of cracking of structural elements. Given the importance of the subject, the study of cracks in structures began in the early second half of the twentieth century in the form of experimental and definite relations and continued with the introduction of various models such as the Griffith, Paris-Erdogan, Forman, Newman, etc. models. With the observation of significant and non-negligible dispersions in the results of existing tests, the study of this issue began statistically with Weibull research in this field, and now, over the course of more than three decades, researchers have presented various methods and models to analyze the phenomenon of cracks and their growth. In this study, using Abaqus software and using the finite element method and based on the principles of fracture mechanics, the phenomenon of cracking and crack growth and the stress intensity factor of rough and smooth cracks and the crack propagation of Barton roughness profiles have been investigated. The study conducted in this study shows that the crack roughness in the rock has an important effect on the crack propagation and stress intensity factor at the crack tip in the disk specimen, and numerical observations show that with an increase in the crack roughness factor, the deviation of the fin cracks from the initial pre-crack decreases.