Question 5 of 6: Reinforcement Strategy for a Permanent Excavation

Question 5: Reinforcement Strategy for a Permanent Excavation (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.

[Figure not reproduced: Source cross-section for Question 5 (redrawn): the 6 m wide arched-back excavation and the two dominant structures, each dipping 30°. They intersect 1.73 m above springline, releasing the shaded symmetric prism of rock over the full span of the back. See the official exam paper.]

5.1 — Reinforcement strategy

Given. Permanent 6 m wide excavation at 450 m depth; two dominant, persistent structures, each dipping 30° and dipping towards one another so that they intersect above the back (from the accompanying section); no site-specific joint-strength testing, only the mine's traditional c = 22 kPa, φ = 27°; good-quality rock mass; dry (no water infiltration).

Find. A defensible reinforcement strategy, with assumptions stated explicitly as the question requires.

Approach. With two dominant structure sets and a permanent (long-design-life) opening in otherwise good rock, the governing failure mode is very likely structurally controlled — gravity-driven wedges or blocks formed by the intersection of the two joint sets with the excavation surface — rather than stress-driven yielding of the rock mass itself, so the reinforcement strategy is built around securing kinematically-removable blocks rather than a full stress-based support design.

At 450 m depth the vertical field stress is of order $\gamma H\approx0.027\times450\approx12$ MPa, modest relative to the strength of a good-quality rock mass, confirming that stress-induced (strain-burst or squeezing) failure is unlikely to govern for a 6 m span; the two structures are the dominant hazard. The section fixes that hazard precisely: two structures dipping 30° towards each other over a 6 m back intersect above its centre, and the prism of rock between them and the back is completely released — both joints open as it translates vertically downwards, so it is a free-falling keyblock spanning the full width of the back, not a marginal corner wedge. Its size is therefore not a matter of judgement and can be computed directly.

1. Released roof-prism geometry. The two structures meet at a height $h=\tfrac{W}{2}\tan30^\circ=3\tan30^\circ=\boxed{1.73\ \text{m}}$ above springline, so the prism's cross-section is a triangle of base 6 m and height 1.73 m: $A=\tfrac12(6)(1.732)=\boxed{5.20\ \text{m}^2}$ per metre of drive. Each bounding structure has length $\ell=\dfrac{3}{\cos30^\circ}=3.46\ \text{m}$ within the prism.
2. Dead weight to be carried. Taking $\gamma=27\ \text{kN/m}^3$ (assumption 4 below), $W_{block}=\gamma A=27\times5.196=\boxed{140.3\ \text{kN per metre of drive}}$.
3. Resistance available from the structures alone. A symmetric prism with its apex upwards separates from both joints as it falls, so the normal stress on them — and with it the frictional $\tan\phi$ term — vanishes at the instant of detachment; only cohesion resists: $R_c=c(2\ell)=22\times6.928=152.4\ \text{kN/m}$, giving $FS=\dfrac{152.4}{140.3}=\boxed{1.09}$ unsupported.
4. Required support. FS ≈ 1.09 is unacceptable for a permanent opening (target 1.5–2.0), and it rests entirely on a joint cohesion that is assumed rather than measured — exactly the quantity Question 4 shows to be the most damaging to lose. The defensible design therefore discounts joint cohesion altogether and suspends the full dead weight: $T_{req}=FS\times W_{block}=1.5\times140.3=\boxed{210\ \text{kN per metre of drive}}$ (281 kN/m at FS = 2.0).
5. Bolt pattern. A 1.5 m × 1.5 m pattern across the 6 m back gives $\dfrac{6/1.5}{1.5}=2.67$ bolts per metre of drive, i.e. $\dfrac{210}{2.67}=\boxed{79\ \text{kN per bolt}}$ — comfortably within the capacity of a standard 20 mm fully resin-grouted rebar bolt (≈150 kN), leaving margin for the FS = 2.0 case. The bolts must anchor well above the apex: minimum length $1.73+1.0\ \text{m of anchorage}=2.73\ \text{m}$, so specify 3.0 m bolts.

Stated assumptions. (1) The traditional c = 22 kPa, φ = 27° joint strength is representative of both structure sets in the absence of site testing — a conservative choice given it is described as "traditional" rather than measured for this specific excavation. (2) No water pressure acts on any joint (consistent with the stated dry condition), so no uplift/thrust terms are needed in any block-stability check. (3) "Good quality rock mass" is taken to mean the intervening rock blocks themselves are strong enough that block sliding/toppling on the two structures, not intact rock fracture, controls stability. (4) The rock unit weight is not restated in this question, so $\gamma=27\ \text{kN/m}^3$ is adopted from Question 4 of the same paper; the block weight and the required bolt load scale linearly with it, so a 10% error in $\gamma$ moves $T_{req}$ by 10%.

Proposed strategy. (a) Install systematic pattern rock bolting, fully resin-grouted for a permanent opening, on a 1.5 m × 1.5 m pattern with 3.0 m bolts, sized as computed above to suspend the released roof prism at FS ≥ 1.5 (79 kN per bolt) without relying on joint cohesion. (b) Confirm the section's 30°/30° geometry by oriented core or scanline mapping plus a kinematic (stereonet) analysis before final design: the dip directions are not given, and if either structure strikes obliquely to the drive the released body is a plunging wedge rather than the two-dimensional prism assumed here, which lengthens the bolts required along the line of intersection. (c) Apply welded wire mesh or shotcrete between bolts to retain smaller, ravelling blocks that are too small to key individually but can still fall from between the two dominant structure sets. (d) Because only the traditional strength parameters are available (no site testing), specify a monitoring and re-mapping programme (convergence stations, periodic scanline remapping) so the design can be verified and, if needed, upgraded once real joint-strength data are collected — standard practice for a permanent opening supported on assumed rather than measured parameters. (e) Given the excavation is dry, no drainage measures are required now, but the design should note that a future change in water condition would require the block-stability checks in (b) to be revisited with uplift/thrust terms added, since cohesion loss and water pressure are the two factors shown in Question 4 to be most damaging to block/wedge stability.