Ground engineering · Rock mechanics
Q-system & support calculator
Q = (RQD/Jn)(Jr/Ja)(Jw/SRF), equivalent dimension De = span/ESR, Q–RMR correlation and unsupported span.
Standard: Barton, Lien & Lunde (1974) · Grimstad & Barton
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 |
|---|---|---|
| RQD | 65 | % |
| Joint set number Jn | 9 | |
| Joint roughness Jr | 1.5 | |
| Joint alteration Ja | 1 | |
| Water reduction Jw | 1 | |
| Stress reduction SRF | 1 | |
| Span | 10 | m |
| ESR | 1.0 road & rail tunnels |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Q | 10.83 | |
| De = span/ESR | 10.00 | m |
| RMR ≈ 9 ln Q + 44 | 65.44 | |
| Max unsupported span 2 ESR Q^0.4 | 5.19 | m |
- ✗ Span unsupported OK
Method, formulas and assumptions
- Q = MAX(10,65)/9*1.5/1*1/1 = 10.833
- De = span/ESR = 10/1 = 10 m
- RMR ≈ 9 ln Q + 44 = 9*LN(10.833)+44 = 65.444
- Max unsupported span 2 ESR Q^0.4 = 2*1*10.833^0.4 = 5.1872 m
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…
- Hoek–Brown rock mass strength (GSI) — mb, s, a from GSI, mi and D; rock mass UCS, tensile strength, global strength and modulus.
- 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.