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.
The governing comparison is with spread footings first. The standard screening rule is geometric: size the individual footings for the allowable bearing pressure, add up their plan areas, and if that total exceeds roughly half the building footprint, adopt a mat. Below that threshold the footings are separate elements and each one is cheap; above it they crowd, the excavation between them becomes uneconomic, the formwork and the reinforcement laps multiply, and a single continuous slab is both cheaper and simpler to build. Question 6 of this paper is a good illustration of how quickly the threshold is approached: 25 footings of 3.0 m square occupy 225 m2 of a 600 m2 plan, which is 37.5 per cent, and a tolerable settlement any tighter than 15 mm, or an SPT profile any weaker, would push that past 50 per cent.
Where a mat is preferred on performance rather than economy. The first case is weak or erratic ground. On a soft, loose or variable deposit, individual footings become very large and, more importantly, they settle by different amounts because each one sees its own local soil. A mat is a single stiff element: it redistributes load away from the soft spots, bridges local weaknesses such as an old fill pocket, a buried channel, a karst cavity or abandoned workings, and it reduces differential settlement to roughly half of the value that footings on the same soil would experience for the same total settlement. Since it is differential and not total settlement that damages a frame, that is often the decisive argument.
The second case is a compensated or floating design. Excavating a basement removes the weight of the soil taken out, so the net increase in pressure at founding level is the gross structural pressure minus $\gamma D_f$. A raft under a deep basement can therefore be designed for a very small — even zero — net pressure, and since settlement responds to net pressure, this is the only shallow foundation strategy that can carry a heavy building on a compressible soil with acceptable movement. Individual footings cannot do this, because the excavation between them is backfilled.
The third case is water. Below the water table a mat serves simultaneously as the bearing element and as the watertight base of the substructure, and its weight plus the weight of the structure above is what resists hydrostatic uplift on the basement. A group of pad footings with a suspended slab between them cannot do either job. The fourth case is heavy, closely spaced or eccentric loading: shear-wall cores in tall buildings, silos, tanks, transformer and machine bases, and any structure where overturning must be resisted by mobilising the weight of a large area of substructure. The fifth is simply that piling is precluded — by vibration and noise limits next to sensitive neighbours, by contaminated ground where creating vertical pathways is unacceptable, by limited headroom, or by cost, where no competent stratum lies deep enough to justify the mobilisation.
When a mat is the wrong answer and piles are preferred. A mat spreads pressure over a larger area, which means its stress bulb extends far deeper than that of an individual footing. If the compressible layer is thick and continues well below the building width, a mat mobilises the whole of it and the total settlement can be large regardless of how the load is distributed; a piled or piled-raft solution that transfers load below the compressible layer is then the only route to acceptable movement. A mat is likewise the wrong choice where the ground has insufficient capacity even at a fully compensated net pressure, where net uplift or large lateral loads demand tension and shear capacity that only piles can supply, and where scour or seasonal shrink and swell would undermine or heave a shallow element. Finally, a mat is a highly redundant and stiff element whose design requires a soil-structure interaction analysis with a defensible modulus of subgrade reaction; on a site where that modulus cannot be characterised with confidence, the apparent simplicity of the mat is deceptive.
