Skip to content

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

\[ Q = \frac{RQD}{J_n} \cdot \frac{J_r}{J_a} \cdot \frac{J_w}{SRF} \]

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 \(\sigma_c\):

\[ Q_c = Q \cdot \frac{\sigma_c}{100} \]

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):

\[ \varphi' = \arctan\!\left(\frac{J_r \cdot J_w}{J_a}\right) \]

Cohesive component (approximation of the cohesion of the rock mass):

\[ c' = \frac{RQD}{J_n} \cdot \frac{1}{SRF} \cdot \frac{\sigma_c}{100} \]

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 \(RMR = 9\ln(Q) + 44\):

\[ E_m = 10^{\frac{RMR - 10}{40}} \quad [\text{GPa}] \]

Found an error on this page? Let us know.