Hoek-Brown Failure Criterion Lookup Table (Excel)

The Hoek-Brown Failure Criterion is a widely adopted empirical model for estimating the nonlinear shear strength envelope of rock masses under varying stress conditions. Unlike Mohr-Coulomb, which assumes linear strength behavior, Hoek-Brown accounts for rock mass heterogeneity, jointing, weathering, and disturbance through three key empirical inputs: the Geological Strength Index (GSI), the intact rock uniaxial compressive strength (σ_ci), and the rock mass disturbance factor (D). The Excel-based lookup table operationalizes the 2018 updated Hoek-Brown equations by precomputing values of the rock mass constant m_b = m_i * exp[(GSI − 100)/28(1 + D/2)] and the equivalent rock mass UCS σ_cm = σ_ci * [(m_b * σ_ci / σ_ci + s)^a], where s and a are derived from GSI and D. This eliminates the need for real-time numerical solving or coding, making it accessible to practitioners without advanced computational tools. The table typically includes tabulated ranges of GSI (0–100), σ_ci (e.g., 1–300 MPa), and D (0.0–1.0), with interpolated outputs for m_b, s, a, σ_cm, and sometimes derived Mohr-Coulomb equivalents (c_mb, φ_mb) for compatibility with common geotechnical software. Its primary value lies in speed, consistency, and auditability—critical for time-sensitive mine design reviews, back-analysis of failures, and regulatory documentation in underground and open-pit mining contexts.