07-Str-B1 · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Examinations — May 2019 — 07-Str-B1 Geotechnical Design. Three-hour, OPEN-BOOK exam; any calculator is permitted provided the candidate records its make and model. Format: Section A carries five discussion questions of 7 marks each, of which the candidate answers any four; Section B carries four problems of 24 marks each, of which the candidate answers any three (4 × 7 + 3 × 24 = 100 marks). Every question is worked here, because the set is a study resource rather than a marked script.
Reference texts: Das, B.M., Principles of Foundation Engineering (9th ed., Cengage) — SPT-based allowable bearing pressure, Terzaghi bearing capacity, drilled-shaft capacity, retaining walls, sheet-pile walls; Das, B.M., Principles of Geotechnical Engineering (9th ed., Cengage) — effective stress, shear strength, lateral earth pressure; Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM, 4th ed., 2006) — Canadian practice for site investigation, SPT and CPT interpretation, tolerable settlement, raft and deep foundations; Craig, R.F. / Knappett, J.A., Craig's Soil Mechanics (8th ed., CRC Press) — undrained strength, slope stability, anchored sheet-pile design; Reese, L.C. and O'Neill, M.W., Drilled Shafts: Construction Procedures and Design Methods (FHWA) — the alpha method for shafts in clay.
Assumptions declared once, applied throughout. Unit weight of water $\gamma_w = 9.81\ \text{kN/m}^3$; atmospheric reference pressure $p_a = 101.3\ \text{kPa}$; the SPT blow counts quoted in Question 6 are already corrected to $N_{60}$, as the paper states, so no further energy or overburden correction is applied. All wall and sheet-pile results are per metre run of wall. Where the paper says "make suitable assumptions providing justification", the assumption is stated in a highlighted note beside the step that uses it, in the form the exam rubric asks for.
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: Figure 1 (redrawn): the family of in situ devices offered by the exam figure. In a sand deposit the choice is effectively between the SPT and the cone, because the ground cannot be sampled undisturbed. See the official exam paper.]
Recommendation. The electric cone penetration test — specifically the piezocone (CPTu), with a seismic module added if the site is in a seismic region. Of the devices drawn in Figure 1 it is the one that yields, in a single continuous sounding, all three things a rational sand design needs: a stratigraphic profile, a strength parameter, and a deformation parameter.
Why the cone, and not the alternatives. Clean sand cannot be recovered undisturbed by any routine sampler, so laboratory testing is not an option and the design must be built on in situ measurements. The cone is pushed at a constant 20 mm/s and logs cone resistance $q_c$, sleeve friction $f_s$ and pore pressure $u_2$ every 10 to 50 mm, which is a hundred times the vertical resolution of a standard penetration test taken at 1.5 m centres. That resolution matters because the thing that governs a shallow foundation in sand is usually not the average deposit but a thin loose or silty seam inside the stress bulb, and an SPT programme can step straight over it. From $q_c$ one obtains relative density and the peak friction angle through well-established correlations, and the constrained modulus for a settlement calculation; from the friction ratio $R_f = f_s/q_c$ one obtains a soil behaviour type classification that separates clean sand from silty sand; and from $u_2$ one obtains the true piezometric surface rather than a water level read from a borehole that has been drilled with mud. The test is also operator-independent and repeatable, which the SPT emphatically is not — hammer efficiency alone moves the raw blow count by a factor of about two, which is exactly why the paper is careful to specify $N_{60}$ in Question 6. Finally, a seismic cone gives the small-strain shear modulus $G_{max}$ from the downhole shear-wave velocity, and $q_{c1N}$ feeds directly into a liquefaction triggering assessment — an unavoidable check for a sand site in most of British Columbia.
Limitations, stated honestly. The cone recovers no sample, so there is no gradation, no Atterberg limits, no chemistry and nothing to look at; a rational programme therefore pairs the soundings with a small number of sampled boreholes for calibration and classification, which is why the exam figure shows drilling and sampling alongside the cone. Penetration refuses in dense gravel, cobbles and boulders, and in glacial soils that refusal can occur within a few metres, which is a real constraint across much of Canada; pre-drilling or a downhole hammer is then needed. The reaction force must come from a 15 to 20 tonne rig, so access, working platform and headroom all constrain the method, and it cannot be used inside a building or on a steep slope without special plant. Every parameter derived from $q_c$ comes through an empirical correlation calibrated on particular sands, and ageing, cementation, over-consolidation, carbonate content and compressibility all shift those correlations, so the derived $\phi'$ carries a genuine uncertainty of a few degrees. Deep soundings suffer rod bending and verticality error, and the cone measures nothing at all in rock. None of these is a reason to prefer another single device; they are reasons to specify the cone as the backbone of the investigation and support it with boreholes, standpipe piezometers and laboratory index testing.
