Question 2 of 5: Empirical rock mass classification systems

Question 2: Empirical rock mass classification systems (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) The four classification systems in routine practice.

Rock Quality Designation (RQD) — Deere (1964). RQD is the percentage of a core run recovered as sound pieces ≥ 100 mm long, divided by the total run length: $$RQD=\frac{\sum L_{i\ge100\,\text{mm}}}{L_{\text{total}}}\times100\%$$ It is the simplest index — a single number describing core fracture intensity — and is also one input parameter to both RMR and Q below (worked numerically in Question 5a).

Rock Mass Rating (RMR) — Bieniawski (1976, revised 1989). RMR sums five weighted parameters (intact strength, RQD, discontinuity spacing, discontinuity condition, groundwater), each read from a ratings table, then applies a discontinuity-orientation adjustment: $$RMR=\sum_{i=1}^{5}(\text{parameter rating})_i+(\text{orientation adjustment})$$ RMR runs 0–100 and sorts the rock mass into five classes (I–V, Very Good–Very Poor), each linked directly to an excavation/support guideline table (Question 5 below).

Rock Tunnelling Quality Index (Q) — Barton, Lien & Lunde (1974, NGI). Q multiplies three ratios describing block size, inter-block shear strength, and active stress: $$Q=\frac{RQD}{J_n}\times\frac{J_r}{J_a}\times\frac{J_w}{SRF}$$ where $J_n$ = joint-set number, $J_r$/$J_a$ = joint roughness/alteration, $J_w$ = water-reduction factor, $SRF$ = stress-reduction factor. Q spans several orders of magnitude (0.001–1000) and is read directly into a support chart (bolt spacing, shotcrete thickness) via the equivalent dimension $D_e=\text{span or height}/ESR$.

Geological Strength Index (GSI) — Hoek, Kaiser & Bawden (1995). GSI is a qualitative chart (block structure vs. discontinuity-surface condition) read visually from an exposure or core photograph, with no separate numeric sub-ratings. Its purpose is not excavation/support selection directly, but to scale the Hoek–Brown strength criterion from intact rock to rock mass: $$m=m_i\exp\!\left(\frac{GSI-100}{28}\right),\qquad s=\exp\!\left(\frac{GSI-100}{9}\right)$$ — the same functional form used with RMR in Question 3 below (GSI and RMR coincide for RMR > 23 in undisturbed rock, per Hoek's own correlation, but GSI extends to very poor rock where RMR's groundwater/orientation terms become unreliable).

(b) Strengths and limitations of each.

RQD — Strength: trivial to measure from any core run, needs no judgement calls, and is universally reported. Limitation: insensitive to joint orientation, roughness, or infilling — two rock masses with identical RQD can have completely different stability (e.g. clay-filled vs. clean joints at the same spacing); also direction-dependent (a core drilled parallel to a joint set records artificially high RQD).

RMR — Strength: directly linked to a practical excavation/support table (Question 5), well validated on decades of tunnelling case histories, and its ratings are individually auditable (each of the five parameters is checked separately). Limitation: was calibrated on tunnels/mines of moderate span; the orientation-adjustment table is coarse (only five qualitative bands) and the system loses resolution at the very poor end (Class V, RMR < 21) where a few points of ratings error can flip the recommended support category.

Q-system — Strength: explicitly incorporates in-situ stress (via SRF) and water pressure (via $J_w$), which RMR handles only coarsely, and its logarithmic scale resolves both very good and very poor ground without saturating. Limitation: six input parameters means more judgement calls (and more opportunity for inconsistency between raters) than RMR's five, and the support chart was developed from Scandinavian hard-rock case histories, so its shotcrete/bolt recommendations need local calibration in very different rock/stress environments.

GSI — Strength: purpose-built to feed the Hoek–Brown criterion directly (Question 3), works across the full range from massive to highly disturbed rock (unlike RMR, which becomes unreliable below RMR ≈ 25), and a single visual chart reading is fast in the field. Limitation: purely qualitative/visual — there is no numeric sub-score to audit, so two engineers can legitimately read the same exposure differently, and it is not linked to a support-design table the way RMR/Q are (it feeds a strength criterion, not a support chart).