Barton — Q index¶
Developed in 1974 at the Norwegian Geotechnical Institute essentially for underground works, Barton's classification was later extended to different fields; in 2002 Barton himself proposed a comprehensive revision.
Computing the Q index¶
where the six indices are:
- RQD — Rock Quality Designation, accounts for the subdivision of the rock mass;
- \(J_n\) — Joint Set Number, depends on the number of joint sets;
- \(J_r\) — Joint Roughness Number, depends on the roughness of the most unfavourable set;
- \(J_a\) — Joint Alteration Number, depends on the degree of alteration and on the infilling, for the most unfavourable set;
- \(J_w\) — Joint Water Number, depends on the hydrogeological conditions;
- SRF — Stress Reduction Factor, a function of the stress state or of tectonic disturbance.
The three ratios have a physical meaning: \(RQD/J_n\) is related to block size, \(J_r/J_a\) to the shear strength between blocks, \(J_w/SRF\) to the active stress state.
More recently Q has been normalised with respect to the uniaxial compressive strength of the rock \(\sigma_c\):
Input parameters¶
The parameters \(J_n\), \(J_r\), \(J_a\), \(J_w\) are defined in the common tables:
For RQD its nominal value is used; if \(RQD < 10\) a value of 10 is assumed anyway (see RQD).
SRF factor (Stress Reduction Factor)¶
Weakness zones intersecting the excavation¶
| Definition | SRF |
|---|---|
| Multiple weakness zones with clay or chemically disintegrated rock, very loose surrounding rock | 10 |
| Single weakness zones with clay or disintegrated rock (overburden ≤ 50 m) | 5 |
| Single weakness zones with clay or disintegrated rock (overburden > 50 m) | 2.5 |
| Multiple shear zones in competent rock, loosening of the surrounding rock | 7.5 |
| Single shear zone in competent rock (overburden ≤ 50 m) | 5 |
| Single shear zone in competent rock (overburden > 50 m) | 2.5 |
| Heavily fractured zones intersected by open and continuous discontinuities | 5 |
If the weakness zones influence but do not directly intersect the excavation, SRF should be reduced by 25–50%.
Competent rock mass with geostatic stress problems¶
| Definition | \(\sigma_c/\sigma_1\) | \(\sigma_\theta/\sigma_c\) | SRF |
|---|---|---|---|
| Low stress field, near surface | > 200 | < 0.01 | 2.5 |
| Favourable stress conditions | 200 – 10 | 0.01 – 0.3 | 1 |
| High stress field (favourable in the crown, unfavourable at the sidewalls) | 10 – 5 | 0.3 – 0.5 | 0.5 – 2 |
| Moderate rock bursts after more than one hour, massive rock | 5 – 3 | 0.5 – 0.65 | 5 – 50 |
| Almost immediate rock bursts, massive rock | 3 – 2 | 0.65 – 1 | 50 – 400 |
where \(\sigma_c\) is the compressive strength of the rock, \(\sigma_\theta\) the maximum tangential stress at the excavation boundary, \(\sigma_1\) and \(\sigma_3\) the major and minor principal stresses.
If \(\sigma_1/\sigma_3\) is between 5 and 10, reduce \(\sigma_c\) to \(0{,}75\,\sigma_c\); if > 10, reduce to \(0{,}5\,\sigma_c\). If the depth of the crown below ground level is less than the width of the excavation, Barton suggests SRF = 5. The last three rows apply to very hard, massive rocks, with \(RQD/J_n\) between 50 and 200.
Squeezing rock mass¶
| Definition | SRF |
|---|---|
| Moderately squeezing rock mass | 5 – 10 |
| Strongly squeezing rock mass | 10 – 20 |
Swelling rock mass¶
| Definition | SRF |
|---|---|
| Moderately swelling rock mass | 5 – 10 |
| Strongly swelling rock mass | 10 – 15 |
Characterisation away from the excavation
To characterise the rock mass away from the influence of the excavation, the SRF values (5 – 2.5 – 1.0 – 0.5) can be assumed as a function of the overburden heights (0–5; 5–25; 25–250; > 250 m).
Rock mass classes¶
The Q index ranges from 0.001 to 1000 and is divided into 9 classes:
| Q | Class | Description |
|---|---|---|
| 0.001 – 0.01 | IX | Exceptionally poor |
| 0.01 – 0.1 | VIII | Extremely poor |
| 0.1 – 1 | VII | Very poor |
| 1 – 4 | VI | Poor |
| 4 – 10 | V | Fair |
| 10 – 40 | IV | Good |
| 40 – 100 | III | Very good |
| 100 – 400 | II | Extremely good |
| 400 – 1000 | I | Exceptionally good |
Characteristic rock mass parameters¶
Two strength components are extrapolated from Q:
Frictional component (approximation of the friction angle of the rock mass):
Cohesive component (approximation of the cohesion of the rock mass):
The static deformation modulus of the rock mass is determined according to the expression of Serafim and Pereira (1983) derived from RMR, obtaining the equivalent RMR with \(RMR = 9\ln(Q) + 44\):
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