18-Geol-A5 Rock Mechanics · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams, December 2015 — 04-Geol-A5, Rock Mechanics. Open-book, 3-hour exam; 5 questions of 20 marks each; candidates were instructed to answer only 4 of the 5 — all 5 are answered below as a complete study resource.
Reference texts for this subject:
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.
Groundwater. A rising water table or an undrained rainfall event raises the pore pressure acting on a potential failure plane (a bedding surface, joint or fault daylighting into the pit). Because the Mohr-Coulomb shear strength of a discontinuity is τf = c + (σn − u)tanφ, any increase in pore pressure u directly lowers the effective normal stress σn′ = σn−u and therefore the available shear resistance — this is the detrimental case, and it is exactly the mechanism analyzed quantitatively in Question 4 of this paper, where filling the tension crack with water drops the factor of safety from 1.15 (dry) to 0.60 (saturated) on the same geometry. Water can also act beneficially, or at least neutrally: a well-drained pit wall with horizontal drain holes or a toe drainage blanket keeps the phreatic surface low and the pore pressure near zero regardless of rainfall, so the slope's factor of safety stays at its dry value; more directly beneficial, dewatering wells that actively lower the water table below a marginal slope can raise the factor of safety above what it was even before mining began, by removing a natural artesian pressure that pre-dated the excavation.
Ground acceleration (blasting or seismic). A pseudo-static horizontal acceleration khg adds a body force khW acting outward (down-slope) on a potential sliding block, which both increases the driving (shear) force along the failure plane and reduces the normal force resisting it — a poorly designed production blast with excessive powder factor close to a final wall, or a nearby seismic event, can push a slope that was stable under static loading (FoS > 1) into instantaneous failure, particularly on steeply dipping, already near-limiting discontinuities. Conversely, a controlled perimeter blast (pre-split or smooth-wall blasting, reduced-charge trim rows) is a deliberate application of the same physical mechanism used beneficially: the controlled vibration and gas pressure create a clean, planar final wall with minimal blast-induced fracturing behind it, which preserves the intact rock bridge strength between joints and leaves the final wall MORE stable than an uncontrolled bulk blast to the same line would. Similarly, in some jointed rock masses a moderate vibration can beneficially loosen and re-seat a marginally interlocked block into a more stable, lower-centre-of-gravity position without triggering full failure — though this is the exception, not something a designer should rely on.
Ground support in an underground excavation performs two distinct structural functions, and the choice of medium follows directly from which function is needed.
Reinforcement of the near-excavation rock mass (internal function). Reinforcement increases the rock mass's own load-carrying capacity by tying blocks together across joints and mobilizing the rock's internal shear and interlock strength, rather than simply holding a surface skin in place. Typical media are mechanically or resin-anchored rock bolts, fully grouted rebar (dowels), cable bolts (for longer, higher-capacity reinforcement in weaker or more deeply stressed ground), and friction-set (Split Set/Swellex) bolts for rapid, low-cost temporary reinforcement. Reinforcement works by (i) suturing individual blocks into a thicker, stiffer composite beam or arch that spans the opening (the beam-building action exploited directly in Table 2 of this paper, where systematic bolt length and spacing scale with rock mass class), and (ii) increasing the effective normal stress and hence the frictional shear strength across discontinuities that the bolt crosses (dowel/pinning action).
Surface support (external function). Surface support does not reinforce the rock mass itself; it retains loose or raveling material at the excavation surface, prevents progressive unraveling between reinforcement elements, and (for shotcrete/mesh in particular) applies a confining pressure that helps preserve the rock's own residual strength. Typical media are welded wire mesh, chain-link mesh and straps (retention only, no arching capacity of their own), and shotcrete (plain, fibre-reinforced or mesh-reinforced), which additionally provides some genuine membrane/arching strength once cured, unlike mesh alone. In practice the two functions are combined systematically — bolts (or cables) reinforce the rock mass, while mesh and/or shotcrete applied over the bolted face retain the rock between bolt collars and prevent it from raveling out of the reinforced zone; Table 2's progression from “spot bolting only” (Class I) through bolts with occasional mesh (Class II) to systematic bolts with wire mesh and shotcrete (Classes III–V) is precisely this combined-function logic scaling up with deteriorating rock mass quality.
