Question 10 of 13: Pit-Wall Slope Monitoring

Question 4: Pit-Wall Slope Monitoring (15 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.

Pit-wall slope monitoring is a purely observational/essay topic in this exam – there is no calculation to verify, so the answer below is presented as continuous prose rather than the numbered-steps calc shape.

4.1 – Evolution of slope monitoring, 1965 to present (3 marks). In the mid-1960s, pit-wall monitoring was almost entirely manual: survey crews re-measured a small number of fixed prism targets by theodolite and tape at weekly-to-monthly intervals, adequate only for detecting slow, long-term deformation and essentially blind to a rapidly accelerating failure. The 1970s–1980s introduced Electronic Distance Measurement (EDM) and, later, motorized total stations, cutting survey time enough to allow daily or shift-based prism rounds and the first crude displacement-rate (mm/day) trending. The 1990s brought automated, robotic total stations that could unattended-cycle a large prism network every 15–60 minutes, and the same decade saw the first application of slope-stability radar (SSR), which removed the need for line-of-sight prisms entirely and could scan an entire wall face continuously. The 2000s–2010s matured GPS/GNSS-based continuous monitoring (fixed receiver arrays on the crest), InSAR satellite deformation monitoring for regional-scale trends, and further-generation ground-based interferometric radar with sub-millimetre precision and near-real-time (minute-scale) update rates – today’s state of practice integrates several of these systems (radar, robotic survey, GNSS, extensometers, piezometers) into one automated Trigger Action Response Plan (TARP), rather than relying on any single method.

4.2 – Automated survey (robotic total station / prism) vs. slope-stability radar (9 marks).

Accuracy and repeatability (4.2.1). Robotic total stations, sighting a discrete retro-reflective prism, achieve very high point accuracy – typically sub-millimetre to a few millimetres in each of horizontal angle, vertical angle and slope distance once corrected for atmospheric refraction – but only at the prism’s exact fixed location. Radar measures line-of-sight displacement (not full 3-D vector) over a continuous grid of natural-surface pixels at coarser per-pixel precision (sub-millimetre to a few millimetres in the radar line-of-sight direction, but with no independent cross-slope component at a single pixel), trading point precision for complete spatial coverage.

X, Y, Z change assessment (4.2.2). A prism network resolves the full 3-D displacement vector at each target directly from its angle/distance observations, so translational, rotational and differential movement between targets can be computed explicitly. Radar resolves only the component of movement toward or away from the instrument (range change); estimating true 3-D movement from radar alone requires either a second radar at a different azimuth or fusing the radar data with a sparse prism or GNSS network for ground-truth vector information.

Cost and unit count (4.2.3). A prism network needs one robotic total station per unobstructed sight-line sector of the pit (often 2–4 units to cover all walls of a large pit without shadowing) plus a prism installed at every monitored point, each prism being low-cost but requiring periodic re-siting as benches retreat; total capital cost is moderate but scales with the number of monitored points and sectors. A radar unit is a much larger single capital cost per unit but each unit can scan an entire wall face (hundreds of metres) with no discrete targets to install or maintain, so fewer units (often 1 per major wall, sometimes 1 covering multiple walls from a central position) are needed for full-wall coverage; radar’s higher unit cost is offset by eliminating prism installation/maintenance labour.

All-weather capability (4.2.4). Optical total stations require line of sight and are degraded or blocked entirely by heavy rain, fog, dust and blast smoke, and cannot operate at night without illuminated targets. Ground-based radar operates through rain, fog, dust and darkness (it is an active microwave sensor, not optical), making it the more reliable all-weather, 24-hour system – a major reason it has become the primary tool for imminent-failure detection.

Evacuation planning (4.2.5). Both systems feed a Trigger Action Response Plan built on displacement-rate thresholds (e.g. mm/hour) and, more powerfully, on the inverse-velocity method (plotting 1/velocity vs. time, which trends to zero at the predicted failure time for an accelerating creep failure) – radar’s continuous, whole-wall, high-update-rate data is generally better suited to real-time inverse-velocity forecasting and automatic alarm/evacuation triggering, while a prism network provides a valuable independent check at specific critical points and can continue operating as a backup if radar coverage is lost.

Surface movement as an indicator of internal conditions, and independent internal monitoring (4.2.6). Accelerating surface displacement is the visible symptom of a developing internal failure surface, but neither survey nor radar directly measures what is happening below the face – a slope can show little surface movement while a deep-seated failure surface develops, or surface movement can be superficial (raveling) rather than indicative of a mass failure. Independent internal monitoring uses inclinometers (borehole casings read periodically or with an in-place string of sensors, showing the depth and rate of a developing shear surface directly), time-domain reflectometry (TDR) cable (a coaxial cable grouted in a borehole that shows a signal reflection at the depth a shear plane deforms it, cheap and can be automated), piezometers (pore-pressure, since rising pore pressure is a common failure driver independent of visible surface movement), and microseismic monitoring (detecting the acoustic emissions of internal rock fracturing before it manifests as measurable surface displacement).

4.3 – Factor of Safety vs. Probability of Failure (3 marks). Factor of Safety (FoS) is the deterministic ratio of resisting to driving forces (or moments) along a critical failure surface, computed from single best-estimate (or intentionally conservative) values of shear strength, pore pressure and geometry; a slope is designed to a target FoS (commonly 1.2–1.5 for an interim pit wall, higher for a permanent/critical structure such as a haul road or civil facility). FoS is simple to compute and communicate but says nothing about how confident that single number is – two slopes with the same FoS = 1.3 can have very different real risk if one has tightly constrained, well-understood geotechnical parameters and the other has widely scattered, poorly sampled data. Probability of Failure (PoF) instead treats the input parameters (strength, pore pressure, geometry) as statistical distributions and propagates that uncertainty (via Monte Carlo simulation or first-order reliability methods) through the same limit-equilibrium model to report the probability that FoS falls below 1.0, directly quantifying the confidence behind the design and allowing risk-based (rather than purely deterministic) decisions – e.g. accepting a lower FoS on a temporary, low-consequence wall where a calculated PoF is still acceptably small, while requiring both a high FoS and a low PoF on a wall whose failure would threaten personnel or critical infrastructure. Modern large-pit slope design typically reports both criteria together, since FoS alone cannot distinguish a well-characterized slope from a poorly characterized one carrying the same nominal safety margin.