Question 1 of 5: RQD, RMR and Unsupported Stand-up Time for a Tunnel in Jointed Rock

Question 1: RQD, RMR and Unsupported Stand-up Time for a Tunnel in Jointed Rock (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. Core recovery log (Figure Q1) — six 0.5 m runs, total 3.0 m; point-load/UCS calibration pairs and 10 further point-load-only readings (table below); two joint sets with the strike/dip/spacing/roughness/separation data quoted above; groundwater inflow < 5 L/min (< 10 L/min per 10 m tunnel length bracket); Bieniawski (1989) RMR Tables 1–2 and the Modified Lauffer stand-up-time relationship (Table D / Figure 5) supplied with the exam.

*calibration pairs (used to establish the site-specific $S_c/I_{s54}$ ratio, then applied to the remaining ten $I_{s54}$-only readings).

Find. (a) RQD from the core log. (b) RMR (Bieniawski 1989) for the rock mass. (c) The maximum and minimum practicable unsupported excavation span. (d) The unsupported stand-up time over that span range, and the corresponding rock-bolt/shotcrete/steel-set support range.

Approach. Count intact core-piece lengths ≥ 100 mm directly off the recovery log for RQD (the direct-measurement definition, since the actual core is available — the empirical $RQD=115-3.3J_v$ formula is reserved for cases with no core to inspect). Sum the five RMR parameters (strength, RQD, spacing, condition, groundwater) from Tables 1 and the discontinuity-condition guidelines, plus the tunnel-orientation adjustment, to get RMR and the rock-mass class (Table 1C). Use the class's own Table 1D benchmark span/stand-up-time pair as the primary (non-graphical) quantitative anchor for parts (c)/(d), supplemented by Table 2's excavation/support guidance for that class.

1. Part (a) — RQD from the core log. Each of the six 0.5 m (500 mm) runs is broken into intact pieces by its mapped fractures; pieces ≥ 100 mm count toward RQD. Run 1: pieces of 120, 80, 180, 60 mm → 120+180=300 mm qualifies. Run 2: 220, 240 mm (both qualify) → 460 mm. Run 3: 80, 140, 120, 100 mm → 140+120+100=360 mm qualifies (the 80 mm piece is excluded). Run 4: 40, 280, 80, 40 mm → only 280 mm qualifies. Run 5: 40, 180, 200 mm → 180+200=380 mm qualifies. Run 6: 340, 80, 40 mm → only 340 mm qualifies. $$\sum(\text{pieces}\ge100\text{mm}) = 300+460+360+280+380+340 = 2120\ \text{mm}$$ $$RQD=\frac{2120}{3000}\times100=\boxed{70.7\%}$$ By Table 1 (parameter 2), 70.7% falls in the 50–75% bracket → RQD rating = 13.
2. Part (b) — intact rock strength rating. The five calibration pairs give a site-specific ratio $S_c/I_{s54}$ of 22.4, 21.7, 22.2, 23.1 and 21.9 (mean $k=22.3$) — close to, but more reliable than, the exam's generic $S_c=24\,I_{s54}$ correlation because it is fitted to this rock. Applying $k=22.3$ to the ten further $I_{s54}$ readings and averaging all fifteen $S_c$ values (5 measured + 10 estimated) gives a mean intact-rock UCS of $\boxed{209.8\ \text{MPa}}$. By Table 1 (parameter 1), 100–250 MPa → strength rating = 12.
3. RMR — spacing, condition and groundwater ratings. Two joint sets are present with different governing spacings and conditions, so each RMR sub-parameter is scored from the set that controls it. Spacing: Joint #2 (0.3 m = 300 mm) is the closer, governing set — Table 1 bracket 200–600 mm → rating 10 (Joint #1's 1.5 m spacing would instead rate 15, but the closer-spaced set governs local block size). Condition: Joint #1's 1.0–1.5 mm continuous separation places it in the "Separation 1–5 mm, Continuous" bracket → rating 10; Joint #2 (very rough, discontinuous, separation << 0.1 mm) would rate 30, so Joint #1 is again the governing (weaker) set. Groundwater: < 5 L/min is inside the < 10 L/min per 10 m bracket ("damp") → rating 10.
   Check: with two joint sets rating differently on spacing and condition, the WORSE (governing) rating from either set is taken for each sub-parameter independently — the conventional conservative treatment when a table gives no explicit rule for combining multiple joint families.
4. RMR — orientation adjustment and total. Joint #1 (the continuous, weaker-condition set) strikes parallel to the tunnel axis and dips only $15^{\circ}$ — Table 1B/F's "Dip 0–20°, irrespective of strike" row rates this "Fair" for tunnels & mines, an adjustment of $-5$. $$RMR = 12\ (\text{strength}) + 13\ (\text{RQD}) + 10\ (\text{spacing}) + 10\ (\text{condition}) + 10\ (\text{water}) - 5\ (\text{orientation}) = \boxed{50}$$ By Table 1C, RMR 50 (41–60 bracket) places this rock mass in Class III — Fair rock.
5. Part (c) — limiting excavation dimensions. Table 1D's own Class III benchmark is a 5.0 m span at an average 1-week unsupported stand-up time — taken as the practical maximum unsupported span for this rock mass, since larger spans on the same RMR-contoured Lauffer curve (Figure 5) stand up for much less than a week. A practical minimum is set by Joint #2's 0.3 m spacing: for the rock mass to behave as the continuum the RMR classification assumes (rather than as a few discrete blocks), the opening should span at least about ten discontinuity spacings, i.e. $10\times0.3=\boxed{3.0\ \text{m}}$. $$\boxed{3.0\ \text{m} \le \text{span} \le 5.0\ \text{m}}$$
   Check: the 5.0 m maximum is read directly from the exam's own Table 1D (no digitization needed); the 3.0 m minimum applies the standard "span ≫ dominant block size" rule of thumb for RMR/Q continuum validity, since the source provides no explicit minimum-span table.
6. Part (d) — stand-up time and support range. At the 5.0 m maximum span, Table 1D gives an unsupported stand-up time of about 1 week for Class III. At the 3.0 m practical minimum, the same Class-III Lauffer curve (Figure 5) is markedly flatter at smaller spans, so the stand-up time is materially longer — qualitatively several weeks to a few months rather than a specific digitized value. Table 2's Class III (RMR 41–60) guidance applies across this whole span range: excavate top heading and bench (1.5–3 m advance in the heading), commence support after each blast and complete support within 10 m of the face; systematic rock bolts 4 m long spaced 1.5–2 m in crown and walls with wire mesh in the crown; 50–100 mm shotcrete in the crown and 30 mm in the sides; no steel sets required.