Relationship between Brittleness Index and Crack Initiation Stress Ratio for Different Rock Types

Brittleness and crack initiation stress (σ_ci) are important rock mechanical properties and intrinsically related to rock deformation and failure. We establish the relationship betweenσ_ciand uniaxial tensile strength (σ_t) based on the Griffith stress criterion of brittle failure and introduce brittleness indexesB₁–B₄based on the ratio of uniaxial compressive strength (σ_c) toσ_t. The crack initiation stress ratio (K) is defined as the ratio ofσ_cito crack damage stress. The relationship between brittleness index andKis obtained from laboratory mechanics tests including uniaxial compression and Brazilian splitting tests. The results show thatB₁andB₂have an inversely proportional and variant inversely proportional relationship withK, respectively, whereas no apparent relationship is observed betweenB₃andB₄andK. The fitting of experimental data from igneous, metamorphic, and sedimentary rocks shows thatB₁andB₂have a power and linear relationship withK, respectively, whereas no functional relationship is observed betweenB₃andB₄andK. We collected 70 different types of uniaxial compression test data for igneous, metamorphic, and sedimentary rocks and obtained laws that are consistent within each rock type. The experimental data are used to verifyKestimations using a specified constantαbased on the experimental data. According to results of the limestone tests,α = 3 forσ_c < 60 MPa (high porosity),α = 5 for 60 MPa ≤ σ_c ≤ 90 MPa (moderate porosity), andα = 8 forσ_c > 90 MPa (low porosity) as well as for igneous and metamorphic rocks. Estimates ofKfor 127 different rock types using the newly defined brittleness index are in good agreement with the experimental results. This study provides an important new brittleness index calculation method and a simple and reliable method for estimatingK.

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