Question 11 of 11: Pit Slope Geotechnics — Characterization, Design, Monitoring and Remediation

Question 6: Pit Slope Geotechnics — Characterization, Design, Monitoring and Remediation (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.

6.1.1 — initial rock strength and discontinuity characterization. At feasibility stage, geotechnical data comes primarily from oriented diamond drill core, supplemented by any available outcrop mapping. Intact rock strength is measured by uniaxial compressive strength (UCS) and point-load index testing on core samples, giving direct input to the Hoek–Brown failure criterion's intact strength parameter $\sigma_{ci}$. Discontinuity (joint, fault, bedding) orientation, spacing, roughness and infill are logged from oriented core using acoustic or optical televiewer imaging (which recovers true 3-D orientation that unoriented core cannot), supplemented by scanline or window mapping of any accessible outcrop or exploration adit. These feed rock-mass classification systems (RMR, Q-system, GSI) that in turn set the rock-mass strength used in slope-stability analysis. Accuracy at feasibility stage is inherently limited — drill-hole spacing samples only a small fraction of the eventual pit volume, and near-surface weathering/blast damage means results from a single early campaign are treated as a first-pass domain model, always scheduled for confirmation drilling and pit-wall mapping once the pit is actually excavated and structure is directly observable.

6.1.2 — water and pit wall stability. Water reduces effective normal stress on a potential failure surface (via pore pressure) and can soften weak infill materials, both of which reduce shear strength directly, so its distribution must be characterized before slope angles are finalized. Measurement equipment includes standpipe piezometers and, increasingly, vibrating-wire piezometers installed at multiple depths in a single hole to resolve the vertical pore-pressure profile, together with packer (Lugeon) testing to characterize rock-mass permeability by domain. Typical recommendations flowing from this data include depressurization via horizontal drain holes drilled from the pit wall, vertical dewatering wells ahead of mining, or, where permeability is very low, simply designing the slope angle conservatively to accept the pore pressure that cannot practically be removed. In every case, the wall-slope design process treats the pore-pressure regime as a design input on the same footing as rock strength and structure — not as an afterthought.

6.1.3 — wedge failure potential. A wedge failure occurs where two discontinuity sets intersect within a pit wall such that their line of intersection daylights (plunges out of the slope face) at an angle shallower than the wall itself, releasing a wedge-shaped rock mass bounded by the two planes. Presence of such structures is determined by systematic structural mapping (orientation, persistence and spacing of each joint set, by domain) and is displayed graphically using a stereonet (equal-area or equal-angle projection): each discontinuity set plots as a great circle (or its pole), the intersection of any two sets plots directly as a point whose plunge and trend can be read off the net, and overlaying the pit-wall face orientation and its friction-angle cone identifies, at a glance, which specific set-pairs produce a kinematically feasible (daylighting, low-friction) wedge and which do not.

6.1.4 — the two suggested wall-slope figures. The two numbers given are not independent design choices — they describe the same slope geometry from two different levels (overall wall vs. individual bench). Check: computed directly — $\arctan(2) = 63.435^\circ$ exactly, and combining a 30 m double-bench height at that 2:1 batter with a 14 m berm gives an overall (inter-ramp) angle of exactly $\arctan\!\big(30/(30/2+14)\big)=\arctan(30/29)=45.971^\circ$ — matching the paper's stated overall figure to three decimal places. In other words, 63.435° is very likely a deliberately clean 2:1 (horizontal:vertical run) batter slope chosen for the individual bench face, and 45.971° is the resulting overall wall angle once the 14 m safety berm required at every double bench is folded in — not two independently-derived numbers. As a design figure, a 2:1 batter is a common, achievable value in competent hard rock but would need to be checked against the site's actual GSI/Hoek–Brown rock-mass strength and structural fabric (6.1.1–6.1.3) before being adopted; the resulting 46° overall angle is a realistic, moderately conservative figure for a large, long-life pit wall, but its practicality depends entirely on whether the assumed berm width is sufficient to catch the design rockfall volume for the actual bench height and rock competency, which a single trigonometric back-calculation cannot confirm on its own. Role of water: the derivation above is a purely geometric (dry) construction; a saturated wall carries reduced effective normal stress on any daylighting structure, so the practical batter/berm combination the pore-pressure data (6.1.2) can support is typically flatter than this dry-geometry figure unless drainage measures (horizontal drains, dewatering wells) are implemented — remediation can be quantified directly by re-running the same slope-stability analysis with the piezometric surface lowered by the amount the drainage system is designed to achieve, and comparing the resulting factor of safety against the dry-design target.

6.2 — determining pre-ramp, post-ramp and inter-ramp slopes. The bench (pre-ramp) face angle is set first, purely from bench-scale rock strength and structure (6.1.1, 6.1.3) with no ramp interruption. The inter-ramp angle (the angle of a multi-bench stack between successive ramps, as computed in 6.1.4) is then set from the bench angle, bench height and berm width, checked against a limit-equilibrium or numerical stability analysis for the specific pushback geometry — each economic pushback, being a nested pit outline with its own footprint and depth, can carry a different inter-ramp angle where its own rock domain and pushback height justify it. The overall (post-ramp) slope angle is finally set by adding the horizontal offset every ramp consumes (ramp width divided by the vertical interval between ramp switchbacks) to the inter-ramp geometry, which is always flatter than the inter-ramp angle alone. Ramp location is chosen, wherever the pit geometry allows a choice, in the structurally most favourable sector of the pit wall — away from adversely-oriented, daylighting joint sets or known wedge-forming intersections (6.1.3) and away from the weakest rock-type domain identified in the geotechnical model — because a ramp cut into an already-marginal sector both adds a stress concentration at the ramp corners and removes the width available for the wedge or bench-scale failure's own runout catchment; where the favourable sector migrates as successive pushbacks deepen the pit, ramp location is re-optimized pushback by pushback rather than fixed for the pit's life.

6.3.1–6.3.2 — modern pit slope monitoring. Current practice layers several complementary tools rather than relying on one: slope stability radar (SSR) scans the entire active wall face every few minutes from a fixed setup, measuring millimetre-scale surface displacement over the whole monitored area without needing prisms on the rock; robotic total-station prism monitoring tracks discrete survey prisms at critical locations at high precision and lower area coverage; satellite or ground-based InSAR extends coverage over the whole pit (or region) at lower temporal frequency, useful for detecting broad-scale, slow deformation trends outside the SSR's immediate field of view; and extensometers and time-domain reflectometry (TDR) cable installed in monitoring boreholes measure sub-surface displacement directly across a known failure surface, which the surface-only methods cannot see. Results are analysed in near-real-time against velocity and inverse-velocity (Fukuzono) thresholds: a wall segment whose displacement rate is accelerating (inverse velocity trending to zero) triggers an escalating response — increased monitoring frequency, restricted access, and ultimately evacuation and equipment withdrawal — timed against the projected time-to-failure the inverse-velocity trend itself estimates.

6.4 — wall support/remediation and regional destabilization. (6.4.1) Off-loading reduces the driving force on a failure surface by removing mass from the head of an unstable slope (cutting back the crest), lowering both the driving weight and, often, the height of the potential failure. (6.4.2) Buttressing adds resisting mass or structure at the toe of a potential failure — a waste-rock berm, engineered fill, or in extreme cases a structural buttress — directly increasing the resisting force in the limit-equilibrium factor-of-safety calculation. (6.4.3) Dewatering lowers pore pressure on the failure surface (the remediation quantified numerically in 6.1.4), increasing effective normal stress and therefore shear strength without moving any rock. (6.4.4) Mechanical support — rock bolts, cable bolts, or shotcrete/mesh on smaller or more localized instabilities — adds a direct resisting force or confines a jointed rock mass so it behaves closer to intact rock. In practice these are combined: dewatering is usually the first, cheapest measure attempted, with off-loading and buttressing reserved for larger, already-moving masses, and mechanical support for bench-scale or structurally-controlled instabilities where wholesale mass movement is impractical. Regional destabilization (earthquakes): pit design in seismically active regions adds a pseudo-static horizontal acceleration coefficient (or, for higher-consequence walls, a full dynamic/Newmark sliding-block analysis) to the standard limit-equilibrium stability check, sized from the site's seismic hazard assessment; because the added driving force from even a moderate design earthquake is significant relative to a pit wall's normal factor of safety margin, this typically means either flattening the design slope angle in seismically active ground beyond what static analysis alone would require, or explicitly budgeting for post-event inspection and remediation as an accepted operating risk rather than designing it out entirely.