RQD = sum of core pieces >100 mm ÷ total core run × 100. No core? Use RQD = 115 − 3.3 × Jv (Palmstrom). If RQD ≤ 10, use RQD = 10.
Count the number of distinct joint sets present at the site. Random joints add to the count. More joint sets = lower Jn score = worse block size ratio.
Rate the roughness of the least-favorable (worst) joint set. Rough, undulating joints resist sliding. Add 1.0 if joint walls are in contact before shearing.
Rate the weakest filling or coating material on joints. Higher Ja = weaker, more clay-like infilling = worse shear strength. Use the worst joint set.
Water reduces effective normal stress on joints and softens fillings. Rate based on inflow at the tunnel face. If in doubt, select the wetter condition.
SRF accounts for in-situ stress conditions and weakness zones. High stress (rock burst) and low stress (near-surface loosening) both reduce Q. This is the most difficult parameter to assess.
ESR reflects acceptable risk level for the opening type. Used to calculate equivalent dimension De = Span ÷ ESR for support chart. Not needed for Q alone.
How to Use This Calculator
6 simple steps — takes about 5 minutes with your field data and borehole logs ready.
- RQD: From core logs, add all core pieces longer than 100 mm and divide by the total core run length. Multiply by 100 for the percentage. If no core is available, use Palmstrom's formula: RQD = 115 − 3.3 × Jv.
- Jn (Joint Sets): Identify distinct joint families at the site from mapping or core. Count the number of joint sets. Random joints add to the count. More sets = higher Jn = worse block size.
- Jr (Roughness): Assess the least-favourable (weakest) joint set. Rough, undulating surfaces have higher Jr. Smooth, slickensided planar joints have Jr = 0.5.
- Ja (Alteration): Identify the infilling material on the weakest joint set. Unaltered, hard walls score Ja = 1. Soft clay, swelling minerals score Ja = 8–20.
- Jw (Water): Observe inflow at the tunnel face. Dry = Jw = 1.0. Exceptionally high flow = Jw = 0.1. Rate conservatively — conditions worsen during wet season.
- SRF (Stress): Assess whether weakness zones, high stress (rock burst), squeezing, or swelling conditions are present. This is the most difficult parameter — seek specialist input for unusual stress conditions.
Q-System Classification Table
Barton 1974 — nine quality classes. Q ranges from 0.001 to 1000.
| Q Value | Rock Quality Class | Description | Typical Support |
|---|---|---|---|
| 400–1000 | A — Exceptionally Good | Massive, jointing rare | Unsupported |
| 100–400 | B — Extremely Good | Very widely jointed | Spot bolts only |
| 40–100 | C — Very Good | Widely jointed | Spot bolts |
| 10–40 | D — Good | Moderately jointed | Systematic bolts |
| 4–10 | E — Fair | Blocky/disturbed | Bolts + shotcrete |
| 1–4 | F — Poor | Very blocky/disturbed | Shotcrete + steel |
| 0.1–1 | G — Very Poor | Crushed/sheared | Cast concrete lining |
| 0.01–0.1 | H — Extremely Poor | Heavily crushed | Heavy concrete lining |
| 0.001–0.01 | I — Exceptionally Poor | Near soil | Special measures |
Parameter Reference Tables
Quick reference for all Q-System parameter values — Barton, Lien & Lunde 1974.
RQD — Rock Quality Designation
| RQD (%) | Description | Value used |
|---|---|---|
| 0–25 | Very poor | 25 (min. 10) |
| 25–50 | Poor | 25–50 |
| 50–75 | Fair | 50–75 |
| 75–90 | Good | 75–90 |
| 90–100 | Excellent | 90–100 |
Jn — Number of Joint Sets
| Description | Jn Value |
|---|---|
| Massive, no or few joints | 0.5–1 |
| One joint set | 1 |
| One joint set + random | 2 |
| Two joint sets | 3 |
| Two joint sets + random | 4 |
| Three joint sets | 6 |
| Three joint sets + random | 9 |
| Four or more joint sets | 12 |
| Crushed rock, earthlike | 15–20 |
Jr — Joint Roughness / Ja — Joint Alteration
| Jr Description | Jr | Ja Description | Ja |
|---|---|---|---|
| Discontinuous | 4 | Tight healed, hard fill | 0.75 |
| Rough, undulating | 3 | Unaltered walls | 1 |
| Smooth, undulating | 2 | Slightly altered | 2 |
| Slickensided, undulating | 1.5 | Sandy/clay coatings | 3–4 |
| Smooth, planar | 1 | Soft clay fills (<5 mm) | 6–8 |
| Slickensided, planar | 0.5 | Thick clay, swelling | 12–20 |
What is the Q-System? Complete Guide
Everything engineers and students need to know about the Barton 1974 rock tunnel quality system.
The Q Formula Explained
Q = (RQD/Jn) × (Jr/Ja) × (Jw/SRF)
Three ratios: RQD/Jn = block size, Jr/Ja = inter-block shear strength, Jw/SRF = active stress. Multiply them to get Q. Range: 0.001 to 1000. Log scale — Q = 1 to Q = 10 is a 10× improvement in quality.
Q-System vs RMR
Q-System handles stress (via SRF) and joint condition in more detail. RMR is simpler and more widely used in the USA. For important projects, always calculate both and compare using: RMR ≈ 9 × ln(Q) + 44. Significant divergence signals unusual conditions.
When to Use Q-System
- Tunnel support design in all rock types
- High stress environments (deep tunnels)
- Squeezing or swelling ground
- NGI / Norwegian / European practice
- When Jw/SRF stress conditions are a key factor
- Cross-checking RMR classification
Key Advantages over RMR
- Explicitly handles in-situ stress (SRF)
- Distinguishes squeezing and swelling ground
- Wider range (0.001–1000) gives better resolution in poor rock
- Q-support chart gives direct bolt spacing and shotcrete thickness
Common Mistakes
- Using RQD < 10 — always use minimum value of 10
- Rating Jr without considering wall contact
- Underestimating SRF for near-surface loosening
- Ignoring seasonal changes in Jw
- Averaging Q across different rock zones — classify each unit separately
History of the Q-System
Developed by Nick Barton, Reidar Lien, and Johan Lunde at the Norwegian Geotechnical Institute (NGI) in 1974. Based on analysis of 212 tunnel case histories. Updated by Barton in 2002 (Q-prime for TBM use). One of the two most widely used rock classification systems worldwide alongside RMR.
Frequently Asked Questions
Common questions about the Q-System from engineers, students, and tunneling professionals.
| RQD / Jn (Block size) | — |
| Jr / Ja (Shear strength) | — |
| Jw / SRF (Active stress) | — |
| Q Value | — |
| Rock Quality | — |
| De (Equiv. Dim.) | — |
| RMR Correlation | — |
| GSI Estimate | — |
Implements Barton, Lien & Lunde 1974. For final tunnel design, verify with a qualified geotechnical engineer.