Question 5 of 5: RQD, RMR and excavation/support design from core-box and point-load data

Question 5: RQD, RMR and excavation/support design from core-box and point-load data (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. A 3.0 m core-box log (6 runs of 0.5 m), a point-load calibration table (15 readings, 5 with paired UCS), and two joint sets with stated spacing, condition and orientation.

Find. RQD; RMR (with class); the limiting (max/min) unsupported excavation span; stand-up time and reinforcement for those spans.

Approach. Read RQD directly off the core log (sound-piece length ≥ 0.1 m, over the full 3.0 m), calibrate a point-load→UCS conversion constant from the five paired readings and apply it to the rest, assemble RMR from the five Bieniawski parameters (using the closer-spaced, weaker joint set as the governing discontinuity), then read the excavation guidelines (Tables D and 2 supplied with the exam) at the resulting RMR class.

1. (a) RQD from the core-box log. Measuring each 0.5 m run's sound pieces ≥ 0.1 m long against the printed ruler (runs 1–6, left to right) and summing: $$\sum L_{\ge0.1\,\text{m}}=0.48+0.30+0.32+0.10+0.10+0.34=1.64\ \text{m of }3.00\ \text{m}$$ $$RQD=\frac{1.64}{3.00}\times100\approx55\%$$ $$\boxed{RQD\approx55\%}$$ Cross-check via the formula sheet's $RQD=115-3.3J_v$ using the two mapped joint sets alone ($J_v=1/2.5+1/0.25=4.4\ \text{m}^{-1}$) gives $RQD\to100\%$ (capped) — far higher than the measured 55%. This is not a contradiction: drilling-induced mechanical breaks (visible in the core log) reduce the measured RQD below what the widely-spaced geological joints alone would predict, so the directly measured 55% — not the joint-count formula — is used for RMR below.
2. (b) RMR for the development site. Strength: the calibration constant $K=\overline{S_c/I_{s(54)}}\approx22.3$ from the five paired readings, applied to the remaining 10 $I_{s(54)}$ readings and averaged with the 5 known values, gives a mean UCS $\approx210$ MPa — the 100–250 MPa band, rating 12. RQD (55%, the 50–75% band) rates 13. Spacing: the governing (closer, weaker) set is Joint #2 at 0.25 m (200–600 mm band), rating 10. Condition (Table E, using the weaker-governing set): Joint #1 — roughness (slightly rough) 3 + separation (1.0–1.5 mm) 1 + persistence (continuous) 0 + infilling (none) 6 + weathering (slightly weathered) 5 = 15; Joint #2 scores 30 (very rough, unweathered, negligible separation, discontinuous) — the WORSE (lower-rated) set, Joint #1 at 15, governs. Groundwater (damp, <10 L/min) rates 10. $$RMR_{\text{basic}}=12+13+10+15+10=60$$ Both joint sets dip shallowly (12° and 15°, both inside the 0–20° “irrespective of strike” band of Table F), which Table B rates Fair for tunnels/mines (−5): $$RMR=60-5=55$$ $$\boxed{RMR=55\ \text{(Class III, Fair rock)}}$$
3. (c) Limiting excavation dimensions. Table D's own Class III entry gives “1 week for a 5 m span” as the reference unsupported stand-up condition — taken as the practical maximum span for a short (about one week) exposure before support must be in place. A practical minimum span is governed by the rock's own block size, not by stress: an opening much narrower than the governing joint spacing offers no advantage over simply not excavating, so a standard rule of thumb of roughly 10× the closest joint spacing is applied, $10(0.25)=2.5$ m. $$\boxed{\text{span}\approx2.5\ \text{m (min, block-size governed)}\ \text{to}\ 5\ \text{m (max, 1-week stand-up)}}$$
4. (d) Stand-up time and reinforcement. At the reference 5 m span, Table D gives an unsupported stand-up time of about 1 week for Class III; a smaller opening near the 2.5 m minimum would sit further up the same Class III Lauffer-type curve (Figure 5) toward a considerably longer stand-up time, though reading an exact value off that log-log chart beyond its printed anchor points is imprecise and is not relied on here. Table 2's Class III guidelines (both spans) call for top-heading-and-bench excavation (1.5–3 m advance in the top heading, support commenced after each blast, complete support 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, and 50–100 mm of shotcrete in the crown with 30 mm in the sides; no steel sets are required at this class.