Q-System Calculator: Barton's Rock Mass Quality Online
This free online Q-System calculator implements the rock mass quality index developed by Barton, Lien, and Lunde at the Norwegian Geotechnical Institute in 1974. The Q-System is one of the two most widely used rock mass classification methods in geotechnical engineering, alongside the Rock Mass Rating (RMR) system. Enter your six field parameters below to calculate the Q-value, determine the rock mass quality class, and view the approximate RMR correlation. For additional rock mass assessment tools, visit our Rock Mass Tools hub.
Enter Q-System Parameters
All six Barton 1974 parameters. Results update in real time.
1 Rock Quality Designation (RQD)
Percentage of intact core pieces longer than 100 mm. Use 10 as minimum for calculation when RQD is measured as 0.
2 Joint Set Number (Jn)
Number and type of joint sets present in the rock mass.
3 Joint Roughness Number (Jr)
Surface roughness and waviness of the most unfavorable joint set.
4 Joint Alteration Number (Ja)
Degree of alteration or filling of the most unfavorable joint set.
5 Joint Water Reduction Factor (Jw)
Water inflow and pressure conditions along joints.
6 Stress Reduction Factor (SRF)
In-situ stress state, faulting, squeezing, or swelling conditions.
What is the Q-System?
The Q-System is a rock mass classification method developed by Nick Barton, Reidar Lien, and Jan Lunde at the Norwegian Geotechnical Institute (NGI) and published in 1974. It was created to provide a quantitative method for classifying rock masses and selecting appropriate tunnel support based on the analysis of over 200 case histories of underground excavations in Scandinavia. The system has since been applied to thousands of tunnelling projects worldwide and forms the basis of the Norwegian Method of Tunnelling (NMT).
Unlike the additive approach used in RMR, the Q-System uses a multiplicative formula that produces values spanning several orders of magnitude, from 0.001 for exceptionally poor rock to 1000 for exceptionally good rock. This logarithmic scale reflects the observation that differences in rock mass behavior become more pronounced at the extremes of quality, where small changes in parameter values can have large effects on excavation stability and support requirements.
Q-System Parameters Explained
The Q-value is calculated from six parameters grouped into three quotients, each representing a distinct aspect of rock mass behavior. The three quotients are: block size (RQD/Jn), inter-block shear strength (Jr/Ja), and active stress (Jw/SRF).
| Parameter | Symbol | Range | Represents |
|---|---|---|---|
| Rock Quality Designation | RQD | 0 – 100 (use 10 minimum) | Degree of jointing from core data |
| Joint Set Number | Jn | 0.5 – 20 | Number of joint sets present |
| Joint Roughness Number | Jr | 0.5 – 4 | Joint wall roughness and waviness |
| Joint Alteration Number | Ja | 0.75 – 12 | Joint wall alteration and filling |
| Joint Water Reduction | Jw | 0.1 – 1.0 | Groundwater inflow and pressure |
| Stress Reduction Factor | SRF | 0.5 – 20 | In-situ stress, faulting, squeezing |
The first quotient, RQD/Jn, is an indicator of the relative block size in the rock mass. A high RQD divided by a low Jn produces large values, indicating a rock mass composed of large, intact blocks with few joint sets. The second quotient, Jr/Ja, represents the inter-block friction and dilatancy characteristics. Rough, unaltered joints yield high Jr/Ja ratios, meaning strong resistance to shearing. The third quotient, Jw/SRF, describes the effect of water pressure and stress state on the rock mass, with dry conditions and moderate stress producing values near 1.0 and high water inflow or extreme stress significantly reducing the overall Q-value.
Q Classification Table
The Q-value maps to nine rock mass quality classes spanning four orders of magnitude. The classification below follows Barton's original 1974 publication with the boundary values adopted in current NGI practice.
| Q-Value Range | Quality Class | Description |
|---|---|---|
| 400 – 1000 | Exceptionally Good | Massive, unjointed rock. No support required for most spans. |
| 100 – 400 | Extremely Good | Very few joints, excellent quality. Minimal support if any. |
| 40 – 100 | Very Good | Few joints, competent rock mass. Spot bolting may suffice. |
| 10 – 40 | Good | Moderately jointed. Systematic bolting typically required. |
| 4 – 10 | Fair | Significantly jointed. Bolting plus shotcrete typical support. |
| 1 – 4 | Poor | Very jointed or weathered. Heavy bolting and thick shotcrete. |
| 0.1 – 1 | Very Poor | Highly jointed, clay-filled joints. Fiber-reinforced shotcrete and bolts. |
| 0.01 – 0.1 | Extremely Poor | Crushed or swelling rock. Cast concrete lining often needed. |
| < 0.01 | Exceptionally Poor | Squeezing or swelling ground. Heavy concrete lining required. |
Q vs RMR Correlation
Bieniawski (1976) established the most widely cited empirical relationship between the Q-System and Rock Mass Rating: RMR = 9 ln(Q) + 44. This correlation was derived from case history data collected at tunnel sites where both classification systems had been applied independently. The equation provides a useful cross-check between the two systems but has inherent scatter, with a standard deviation of approximately 9 to 13 RMR points depending on the dataset.
The correlation works best in the mid-range of both scales (Q values of 1 to 100, RMR values of 40 to 80) and becomes less reliable at the extremes. This is partly because RMR has a bounded range of 0 to 100 while Q spans several orders of magnitude. For reliable rock mass classification, both systems should be applied independently using field data, and the correlation should be used as a reasonableness check rather than a substitute for proper classification. Our calculator displays the approximate RMR alongside the Q-value to facilitate this comparison.
Frequently Asked Questions
The Q-System formula is Q = (RQD/Jn) x (Jr/Ja) x (Jw/SRF), where RQD is Rock Quality Designation, Jn is joint set number, Jr is joint roughness number, Ja is joint alteration number, Jw is joint water reduction factor, and SRF is stress reduction factor. The three quotients represent block size (RQD/Jn), inter-block shear strength (Jr/Ja), and active stress (Jw/SRF) respectively. These three ratios are multiplied together to produce the final Q-value.
The most widely used correlation between Q and RMR is the empirical equation RMR = 9 ln(Q) + 44, developed by Bieniawski in 1976. This calculator performs this conversion automatically. However, the correlation has a standard deviation of about 9 to 13 RMR points, so both systems should ideally be applied independently for reliable classification rather than relying solely on conversion between them.
In Barton's Q-System classification, rock mass quality is rated as Good when Q falls between 10 and 40. Very Good rock has Q values of 40 to 100, Extremely Good ranges from 100 to 400, and Exceptionally Good covers Q values from 400 to 1000. Values below 10 indicate Fair (4-10), Poor (1-4), Very Poor (0.1-1), Extremely Poor (0.01-0.1), or Exceptionally Poor (less than 0.01) conditions requiring increasingly heavy support measures.