Ground engineering · Rock mechanics
Hoek–Brown rock mass strength (GSI) calculator
mb, s, a from GSI, mi and D; rock mass UCS, tensile strength, global strength and modulus.
Standard: Hoek, Carranza-Torres & Corkum (2002) · Hoek & Diederichs (2006)
Open the live calculator → All ground engineering calculators
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Intact UCS σci | 60 | MPa |
| mi | 12 | |
| GSI | 50 | |
| Disturbance D | 0 | |
| Intact modulus Ei | 25000 | MPa |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| mb = mi e^((GSI−100)/(28−14D)) | 2.01 | |
| s = e^((GSI−100)/(9−3D)) | 0.004 | |
| a = ½ + (e^(−GSI/15) − e^(−20/3))/6 | 0.506 | |
| Rock mass UCS σci s^a | 3.61 | MPa |
| Tensile −s σci/mb | -0.115 | MPa |
| Global strength | 11.41 | MPa |
| Erm = Ei(0.02 + (1 − D/2)/(1 + e^((60 + 15D − GSI)/11))) | 7,680 | MPa |
- ✓ GSI in 10–100
Method, formulas and assumptions
- mb = mi e^((GSI−100)/(28−14D)) = 12*EXP((50-100)/(28-14*0)) = 2.0121
- s = e^((GSI−100)/(9−3D)) = EXP((50-100)/(9-3*0)) = 0.0038659
- a = ½ + (e^(−GSI/15) − e^(−20/3))/6 = 0.5+(EXP(-50/15)-EXP(-20/3))/6 = 0.50573
- Rock mass UCS σci s^a = 60*0.0038659^0.50573 = 3.6136 MPa
- Tensile −s σci/mb = -0.0038659*60/2.0121 = -0.11528 MPa
- Global strength = 60*(2.0121+4*0.0038659-0.50573*(2.0121-8*0.0038659))*(2.0121/4+0.0038659)^(0.50573-1)/(2*(1+0.50573)*(2+0.50573)) = 11.41 MPa
- Erm = Ei(0.02 + (1 − D/2)/(1 + e^((60 + 15D − GSI)/11))) = 25000*(0.02+(1-0/2)/(1+EXP((60+15*0-50)/11))) = 7679.6 MPa
Related ground engineering calculators
- Point load index (rock) — Is and size-corrected Is(50) for diametral or axial/block tests, AS 1726 strength term and estimated UCS.
- Rock wedge stability (3-D, Hoek & Bray) with stereonet — Tetrahedral wedge formed by two discontinuities, the slope face and the upper ground surface. Geometry by…
- Rock slope kinematic analysis (planar, wedge, toppling) — Discontinuity sets mapped in a rock cut are tested against the slope face. Planar sliding needs a set…
- Rock Mass Rating (RMR89) — Ratings for UCS, RQD and spacing from values, plus joint condition, groundwater and orientation adjustment…
- Q-system & support — Q = (RQD/Jn)(Jr/Ja)(Jw/SRF), equivalent dimension De = span/ESR, Q–RMR correlation and unsupported span.
- Joint shear strength (Barton–Bandis) — Peak shear strength τ = σn tan(φr + JRC log10(JCS/σn)) and equivalent friction angle.
- Block sliding / toppling criteria — Mode of a block of width b and height h on a plane of dip ψ with friction φ: stable, sliding, toppling or…
- Rock bolt pattern for a loose block / wedge — Bolt load from suspending a loosened zone of height h over the bolt tributary area, with bolt length guidance.
For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.