A brittleness evaluation method of rock constitutive relationship with Weibull distribution based on double-body system theory

Brittleness of rocks plays an important role in the evaluation of unconventional oil and gas reservoir network fracturing and many rock engineering application fields. However, there is still no commonly accepted definition of the concept of brittleness. In this study, the brittleness differences between rocks are understood as the differences of internal microunit strength cracking characteristics under an external load. Because rock ruptures are regarded as a fracturing problem of a double body system, the region where no cracking occurs during the uniaxial compression loading process is regarded as a body I system with elastic deformation characteristics; the region that breaks first and induces the integral fracture of the rock is regarded as a body II system in which the structural strength of the microunit follows the deformation characteristic of the Weibull distribution. An energy quasi-static equilibrium equation for rock fractures of a double body system under an external load was established. A new index for evaluating brittleness was established based on the energy mutation process of the quasi-static equilibrium equation of double body system. Sandstone, red sandstone, mudstone, sandy mudstone, shale, limestone, and granite were selected as the research objects, while the correlation curve between the new brittleness index, the Weibull distribution characteristic parameters, and the mutation break point was calculated. The brittleness index studied in this paper reveals the evolution process of integral fractures induced by the internal fractures of rocks, which is important for further understanding the essence of brittleness. These results can provide a new method for further studying the formation process of local fracture networks.