Question 5 of 5

Question 5 (25 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.

(a) Number of boreholes required

Unlike a single building footprint, a 10 km linear alignment needs boreholes distributed along its entire length, not clustered at one point, and the count is governed by several factors: the along-alignment spacing adopted (typically 30–100 m for an urban tunnel, tightened toward the lower end in variable or high-risk ground and relaxed toward the upper end in well-understood, uniform ground with corroborating geophysics between holes); a much higher density at stations, cross-passages, ventilation shafts, and portals, where the excavation is largest and the consequence of a missed condition is greatest; targeted additional holes at any known geological complexity crossed by the alignment (faults, karst, buried channels, contaminated ground); and the acceptable residual risk the owner is willing to carry, since exploration density and residual ground-condition risk trade off directly against each other.

As an illustrative order-of-magnitude estimate for this 10 km alignment: adopting a mid-range 75 m along-alignment spacing gives approximately 10{,}000/75 + 1 ≈ 134 boreholes along the running tunnel; adding roughly 3 boreholes at each of 8 stations (a typical station spacing of ∼1.2–1.5 km on a 10 km urban line) contributes 24 more; and 2 boreholes at each of 2 shaft/portal structures contributes a further 4 — a total on the order of 160 boreholes for this alignment, before any additional holes triggered by a known fault crossing, a river/utility crossing, or an environmentally sensitive area named in the question. This figure is illustrative of the method, not a fixed design rule; the actual count is finalized once the desk study identifies the specific ground hazards the alignment crosses.

(b) Zone of influence — determination, factors, soil vs. rock, and effect on the investigation plan

The zone of influence (ZOI) is the volume of ground around a tunnel excavation within which the ground movements and stress changes induced by that excavation are large enough to matter to something at or near the surface — an existing structure, a utility, or a sensitive environmental feature. It is determined using a combination of empirical methods and numerical modelling: the widely used Peck (1969) empirical settlement-trough method idealizes the surface settlement profile above a soft-ground tunnel as a Gaussian curve, whose width is set by a trough-width parameter (proportional to the depth to the tunnel axis and a soil-type coefficient) and whose depth/volume is set by the volume loss ratio achieved by the excavation method (typically well under 1–2% for a well-controlled modern EPB/slurry TBM); numerical modelling (finite element/finite difference) is used where the geometry is complex — multiple tunnels, a station box, or an adjacent structure with its own stiffness that interacts with the ground movement — since the empirical trough method assumes a simple, isolated single tunnel. Factors that influence the ZOI's extent include tunnel depth (a deeper tunnel spreads its settlement trough wider but shallower at surface) and diameter, the ground's stiffness and structure, the excavation method and the volume loss it achieves, groundwater drawdown accompanying the excavation (which itself causes settlement beyond the mechanical ZOI), and the presence and stiffness of nearby structures, which can either concentrate or spread the movement they experience relative to greenfield predictions.

Soil versus rock produces a genuinely different ZOI character, not just a different magnitude. In soil, the ZOI is governed by the smooth, empirically well-characterized settlement trough described above, typically extending laterally to roughly 2–2.5 times the tunnel depth at surface, and is driven primarily by volume loss and groundwater drawdown. In rock, by contrast, the ZOI is normally far narrower and governed instead by discontinuity-controlled block movement and the elastic stress redistribution around the opening (the Kirsch tangential-stress concentration at the excavation boundary) rather than a smooth trough; ground movement in sound rock is often negligible at surface unless the rock is weak, closely fractured, karstic, or shallow-cover, in which case its behaviour can converge toward the soil case. This distinction directly affects the site investigation plan: for a soil tunnel, the investigation must extend boreholes and instrumentation laterally beyond the alignment centreline to cover the full predicted settlement-trough footprint at every sensitive structure, with dense groundwater monitoring to separate mechanical settlement from drawdown settlement; for a rock tunnel, the investigation instead concentrates on discontinuity mapping, in-situ stress measurement (Question 3(b)), and targeted geophysics to find the weak/fractured/karstic zones where the ZOI could unexpectedly widen, since a uniform borehole spacing calibrated to "typical" sound rock would miss exactly the anomaly that matters most.

(c) Site investigation plan differences: soil versus rock excavation

If the tunnel is excavated in soil, the investigation plan emphasizes continuous stratigraphic and geotechnical-parameter profiling (CPT/SPT at close, regular intervals per part (a)), groundwater characterization and control design (dewatering feasibility or ground-freezing where required), and face-stability/support-pressure design for an earth-pressure-balance or slurry TBM — all of which need closely and regularly spaced boreholes because soil variability over short distances is typically high and support pressure must be actively controlled in real time during excavation. If the tunnel is excavated in rock, the plan instead emphasizes rock-mass characterization (RQD, discontinuity spacing/orientation/condition feeding an RMR or Q-system classification), in-situ stress measurement, and groundwater inflow through discontinuities (assessed with packer/Lugeon testing rather than a general permeability test) to size grouting and lining requirements; boreholes are typically fewer but deeper and more specialized, with oriented coring and surface geophysics (seismic refraction/resistivity) used to map the rock head and locate weak, fractured, or faulted zones between the sparser hole locations. In short: soil tunnelling drives the investigation toward density/continuity of coverage, while rock tunnelling drives it toward depth of characterization at fewer, carefully targeted locations, supplemented by geophysics to fill the gaps between them.

(d) Defining "accuracy" and the extent to which the investigation is accurate

Accuracy is how close a measured or interpreted value is to its true value — distinct from precision, which is how repeatable or closely clustered a set of measurements are, regardless of whether they are close to the truth. Applied to a site investigation, "accuracy" has two layers: a point measurement (a borehole log, a lab test result, an instrument reading) can be highly accurate at the specific location and depth it was taken, while the interpreted ground model built by interpolating between those points is inherently a lower-confidence inference, because a linear 10 km alignment's boreholes sample only a very small fraction of the total ground volume the tunnel will actually pass through. The extent to which the investigation's results can accurately determine the ground's true extents is therefore governed by the exploration spacing relative to the true (unknown) geological variability: where the ground is genuinely uniform between two boreholes, the interpolated interpretation is accurate; where an undetected fault, lens, or contact sits between two widely spaced holes, it is not, and no amount of care in the individual borehole logs can compensate for a gap in coverage. Good practice manages this honestly rather than hiding it: cross-validating boreholes against surface geophysics and geological mapping increases confidence between exploration points; every interpreted contact or boundary is reported with an explicit statement of confidence or a stated tolerance (e.g., "interpreted contact ± a few metres") rather than as an exact line; and the observational method — instrumented monitoring during construction (Question 2) — is the mechanism that closes the residual gap between the interpreted model and the ground actually encountered, converting an unavoidable interpretive uncertainty into a managed construction-stage risk rather than a surprise.