Question 5 of 5: RQD, RMR and stand-up time for a tunnel

Question 5: RQD, RMR and stand-up time for a tunnel (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.

Given.

Find. (a) RQD; (b) RMR; (c) limiting (max/min) unsupported span; (d) stand-up time over that span range and the reinforcement needed.

Approach. Measure intact-piece lengths directly off the core-recovery log for RQD, calibrate the point-load index against the five paired UCS readings to get a characteristic intact strength, rate the remaining five RMR parameters from the joint data, then read the maximum span/stand-up time and support schedule straight from the exam's own Table 1D/Table 2, with the minimum practical span set by the closer joint spacing.

1. Part (a) — RQD from the core log. Reading intact-piece lengths off Figure Q5 against its printed metre grid (natural fracture breaks are the diagonal double-line marks) and keeping only pieces ≥0.10 m per run: run 1 → 0.17 m; run 2 → 0.14+0.15+0.19 = 0.48 m; run 3 → 0.21 m; run 4 → 0.10 m; run 5 → 0.25+0.13 = 0.38 m; run 6 → 0.11+0.10+0.13 = 0.34 m; summing over the full 3.0 m recovered: $$RQD=\frac{0.17+0.48+0.21+0.10+0.38+0.34}{3.0}\times100=\frac{1.68}{3.0}\times100$$ $$\boxed{RQD = 56\%\ \text{(Fair, 50-75\% band, RQD rating}=13\text{)}}$$
   Check: piece boundaries were read from the printed core-recovery sketch against its 0.05 m grid (reading tolerance ±0.02–0.03 m per break); the result is reported to the nearest whole percent and sits solidly inside the 50–75% band even allowing for that reading tolerance.
   As a cross-check, the volumetric joint count from the two MAPPED joint sets alone gives J_v=1/1.4+1/0.3=4.05 m⁻¹, RQD=115−3.3J_v≈102% (capped at 100%) — notably higher than the 56% actually measured on the core. This is a real, worth-noting discrepancy rather than an error: the volumetric-joint-count formula only "sees" the two mapped geological joint sets, whereas the physical core additionally breaks along mechanically-induced fractures from drilling and handling, so the directly measured RQD is used for part (b), not the joint-based cross-check.
2. Part (b) — Calibrate intact strength from the point-load data. Fitting S_c=k·I_s50 through the origin by least squares to the five paired readings (rather than assuming the exam's rounded k=24 factor) gives k=22.4; applying this factor to the 10 additional I_s50-only readings and averaging all 15 implied UCS values gives a characteristic intact strength of $$\sigma_c \approx 210.5\ \text{MPa}$$ Reading Figure 1's rating-vs-UCS curve at 210.5 MPa (interpolating between the plotted 200 MPa and 240 MPa points) gives a strength rating of 14.6. The RQD rating is 13 (part a). Discontinuity spacing is governed by the closer-spaced Joint #2 (0.3 m, the 200–600 mm band), rating 10. Condition of discontinuities is scored per joint set from Table 1 Section E and the WORSE (governing) set used: Joint #1 (persistent bedding-like joint, separation 1.0–1.3 mm, slightly rough, slightly weathered) scores 0+1+3+6+5=15; Joint #2 (discontinuous, essentially closed, very rough, unweathered) scores a near-perfect 30; the governing value is Joint #1's 15. Groundwater at <10 L/min is a rating of 10 (not the “completely dry” 15). Both joints dip shallowly (13° and 20°, both ≤20°), which Table 1's Section F places in the “dip 0–20°, irrespective of strike” row — Fair — giving an orientation adjustment of −5 for a tunnel. $$RMR = 14.6+13+10+15+10-5 = 57.6 \approx 58$$ $$\boxed{RMR = 58\ \text{(Class III, Fair rock)}}$$
3. Part (c) — Limiting excavation dimensions. Table 1D's own tabulated anchor point for a Class III (Fair) rock mass is a maximum unsupported span of 5 m (average stand-up time 1 week), so this is taken directly as the maximum practical span. For the minimum practical span, a standard rule of thumb requires the unsupported opening to be at least about 10× the closest discontinuity spacing so that the excavation is not simply undercutting individual joint-bounded blocks; with Joint #2 at 0.3 m spacing, $$\text{min span}=10\times0.3=3.0\ \text{m}$$ $$\boxed{\text{span range} \approx 3.0\text{-}5.0\ \text{m}}$$
   Check: the minimum-span figure is an engineering-judgment rule of thumb (block size vs. opening size), not a tabulated exam value; Table 1D itself only anchors the maximum-span end of this range.
4. Part (d) — Stand-up time and reinforcement. At the maximum 5 m span, Table 1D's Class III anchor gives an average unsupported stand-up time of about 1 week. Reducing the span toward the 3.0 m minimum lengthens the achievable stand-up time substantially — the Modified Lauffer diagram (Figure 5) places the RMR≈58 boundary, at spans in the 3–5 m range, in the roughly one-month-to-several-months band, i.e. on the order of 10× longer than at 5 m — though this is read as an order-of-magnitude trend from the chart, not a precise value. Over this whole span range, Table 2's Class III (RMR 41–60) row specifies: top heading and bench excavation, 1.5–3 m advance in the top heading, support commenced after every blast and completed within 10 m of the face; systematic rock bolts 4 m long, spaced 1.5–2 m in the crown and walls, with wire mesh in the crown; shotcrete 50–100 mm in the crown and 30 mm in the sides; no steel sets required. $$\boxed{\text{5 m span: support within days; 3 m span: support may be deferred several weeks, but Table 2's Class III schedule governs regardless}}$$