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

Abstract

Brittleness and crack initiation stress (σci) are important rock mechanical properties and intrinsically related to rock deformation and failure. We establish the relationship between σci and uniaxial tensile strength (σt) based on the Griffith stress criterion of brittle failure and introduce brittleness indexes B1–B4 based on the ratio of uniaxial compressive strength (σc) to σt. The crack initiation stress ratio (K) is defined as the ratio of σci to crack damage stress. The relationship between brittleness index and K is obtained from laboratory mechanics tests including uniaxial compression and Brazilian splitting tests. The results show that B1 and B2 have an inversely proportional and variant inversely proportional relationship with K, respectively, whereas no apparent relationship is observed between B3 and B4 and K. The fitting of experimental data from igneous, metamorphic, and sedimentary rocks shows that B1 and B2 have a power and linear relationship with K, respectively, whereas no functional relationship is observed between B3 and B4 and K. 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 verify K estimations using a specified constant α based on the experimental data. According to results of the limestone tests, α = 3 for σc < 60 MPa (high porosity), α = 5 for 60 MPa ≤ σc ≤ 90 MPa (moderate porosity), and α = 8 for σc > 90 MPa (low porosity) as well as for igneous and metamorphic rocks. Estimates of K for 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 estimating K.