16-Civ-B3 Geotechnical Design · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations (Engineers Canada / EGBC), 16-Civ-B3 Geotechnical Design — 3 hours, open book, any non-communicating calculator permitted (the candidate must write its make and model on the left-hand sheet). The paper prints nine questions in two sections: Section A holds five short questions of 7 marks and asks for any four; Section B holds four design questions of 24 marks and asks for any three. Only the first four of Section A and the first three of Section B are marked, so a complete paper is 4 × 7 + 3 × 24 = 100 marks. Note 1 urges the candidate to state any assumptions made, Note 6 requires the source of every design chart to be identified, and Note 7 permits assumed values provided the source is stated. All nine questions are solved below, because the set is a study resource rather than a sitting.
Reference texts. B. M. Das, Principles of Foundation Engineering, 8th ed. (bearing capacity ch. 3, settlement of shallow foundations ch. 5, drilled shafts ch. 12, retaining walls ch. 8, sheet pile walls ch. 9); B. M. Das, Principles of Geotechnical Engineering, 9th ed. (shear strength, lateral earth pressure, slope stability); R. F. Craig and J. A. Knappett, Craig’s Soil Mechanics, 8th ed. (effective stress, undrained strength, anchored walls); D. P. Coduto, Foundation Design: Principles and Practices, 2nd ed.; and in the Canadian frame the Canadian Foundation Engineering Manual (CFEM), 4th ed., Canadian Geotechnical Society — ch. 4 for site investigation and in-situ testing, ch. 10 for shallow foundations, ch. 18 for deep foundations and ch. 25 for earth retaining structures. Test standards are quoted as ASTM/CSA where the CFEM adopts them (SPT: ASTM D1586; CPT: ASTM D5778; field vane: ASTM D2573).
Source-quality note.
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 area rule comes first. The standard screening test is to size the individual footings for the allowable bearing pressure and add up their plan area. If that total exceeds roughly half the building footprint, the mat is normally the cheaper structure: the formwork, excavation, reinforcement laps and the cost of forming and inspecting dozens of separate pits start to exceed the cost of one continuous slab, and once the footings are within a metre or so of one another their stress bulbs overlap anyway, so they are behaving as a mat without any of a mat’s stiffness. Question 6 of this paper lands close to that boundary: 25 pads of 3.0 m take 225 m2 of a 600 m2 footprint, 37.5 per cent, on a 4.9 m grid.
Then the soil conditions. A mat is preferred where the allowable bearing pressure is low — soft or normally consolidated clay, loose sand, uncontrolled fill — because spreading the load over the whole footprint reduces the applied pressure to something the soil can carry. It is preferred where the deposit is erratic: pockets of soft material, old foundations, filled channels, karst or thawing ground produce large differential settlements between isolated footings, and a stiff mat bridges over them and redistributes the load, so what would have been a differential settlement becomes a bending moment in the slab. That is the real argument for a mat — it controls differential settlement even when it does not much reduce total settlement.
Then the groundwater and the basement. Where there is a basement below the water table, the slab has to be there anyway to keep the water out and to resist uplift, so making it structural costs little extra; individual footings would need a separate watertight slab spanning between them. Where buoyancy governs, the mat is the element that mobilises the weight of the whole structure against it. And a mat makes the compensated or floating foundation possible: excavating to a depth at which the weight of soil removed matches a large part of the building weight leaves a small net pressure increase, which on soft clay may be the only way to keep settlement acceptable.
When to stay with individual or combined footings. Competent near-surface soil, a modest and fairly uniform column grid, no basement, and a deep water table — here spread footings are the cheapest thing that works, and the mat would be paying for stiffness nobody needs. Combined and strap footings occupy the middle ground and are the right answer for the local problems that create them: two columns too close to have separate pads, or a property-line column whose pad cannot be centred under it.
When to go to piles instead. Piles take over when the problem is depth rather than area: the competent stratum lies well below any practicable excavation; a mat would still settle more than the structure can tolerate because the compressible layer is thick and the mat loads it to great depth; there is significant uplift, overturning or lateral load (towers, tall shear walls, waterfront structures); scour or future adjacent excavation could remove the support of a shallow foundation; or the near-surface soil is liquefiable, collapsible, or expansive, so it must be bypassed altogether. A piled raft is the intermediate solution and is often the economical one: the raft carries most of the load and a modest number of piles are added as settlement reducers under the heaviest columns, rather than designing the piles to carry everything.
