16-Civ-B3 Geotechnical Design · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. EGBC / Engineers Canada National Examination 16-Civ-B3 Geotechnical Design, May 2018. Three hours, open book, any non-communicating calculator. Section A — five discussion questions of 7 marks each, answer any four. Section B — four design questions of 24 marks each, answer any three. Examinable total $4\times 7 + 3\times 24 = 100$ marks. Page 1 Note 6 requires the candidate to identify clearly the source of every design chart and assumed value used, so the provenance of each correlation is named where it is used, not only in the concept notes. All nine questions are solved below, because the set is a study resource rather than a three-hour sitting.
Reference texts for this subject. B. M. Das, Principles of Foundation Engineering, 9th ed. (Cengage) — Ch. 3 (subsurface exploration and SPT corrections), Ch. 4 (bearing capacity), Ch. 5 (settlement, Schmertmann), Ch. 8 (retaining walls), Ch. 11–12 (pile foundations and drilled shafts); B. M. Das, Principles of Geotechnical Engineering, 9th ed. — Ch. 8 (shear strength), Ch. 15 (slope stability); R. D. Holtz, W. D. Kovacs & T. C. Sheahan, An Introduction to Geotechnical Engineering, 2nd ed.; Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — the Canadian design authority for the factors of safety and serviceability limits quoted here; L. C. Reese & M. W. O'Neill, Drilled Shafts: Construction Procedures and Design Methods (FHWA-HI-88-042).
Check — figure readings. Two dimensions are read from the drawings, as follows. (1) In Figure 2 the “1 m” dimension is the height of the bell: its arrows point inward at the flare, and scaling against the 4 m dimension on the same figure puts the bell base exactly on the 12 m line. The pile is therefore $L = 12$ m long with the bell top at 11 m, not 11 m long with its base floating 1 m clear of the layer base. (2) In Figure 3 the “0.35 m” label carries extension lines from the top and bottom corners of the base slab, so it is the base thickness; the “0.5 m” at the left is measured to the base underside, so only 0.15 m of soil covers the toe. The toe projection is not dimensioned and follows from the printed values as $4.0 - 0.3 - 2.0 = 1.7$ m. Figure 3 is not drawn to scale — its toe is drawn about half its dimensioned length — so the printed numbers govern, as page 1 Note 1 anticipates.
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 mat (raft) is the right choice when a spread foundation is still viable but individual footings can no longer do the job — either because they would occupy most of the plan area anyway, because differential settlement must be controlled, or because the structure needs the mat for a reason other than bearing. It is preferred to piles whenever the bearing stratum is at or near founding level, since a mat is far cheaper and quicker than a piled solution.
The area rule. The classical trigger is that the required footing area exceeds roughly half the building footprint. If $\sum A_{footing} > 0.5\,A_{building}$ the footings are so close that their stress bulbs overlap, the settlement of each is increased by its neighbours, and the formwork and excavation for many separate footings costs more than one continuous slab. That situation arises whenever column loads are high and the allowable bearing pressure is low — heavy frames on soft to firm clay, or on loose sand.
Control of differential settlement. A mat is stiff in flexure, so it redistributes load away from soft spots and bridges over erratic ground. Question 9 of this paper is exactly the case in point: an “erratic” sandy deposit whose modulus varies by a factor of two and a half from one data set to the next. Isolated footings on such a deposit would settle by wildly different amounts, and it is the differential settlement, not the total, that cracks a structure. A mat converts a differential settlement problem into a total settlement problem plus a tilt, both of which a frame tolerates far better. The same argument applies over old fill, over backfilled channels, over solution cavities in limestone, and where mining subsidence or collapsible loess is possible.
Compensated design. A mat can be founded in an excavation deep enough that the weight of soil removed offsets much of the structure's weight. The net bearing pressure is $q_{net} = Q/A - \gamma D_f$, and a fully compensated raft has $q_{net} = 0$: no new stress reaches the clay, and in principle no consolidation settlement occurs. This is the standard solution for a multi-storey building with two or three basement levels on deep soft clay, and it is unavailable to isolated footings.
Non-bearing reasons. Where a basement extends below the water table, the mat must in any case be a watertight slab designed for hydrostatic uplift $u = \gamma_w h_w$, so it costs little more to make it the foundation as well. A mat also gives a rigid diaphragm that ties column bases together against seismic and wind overturning, resists uplift on a light structure by its own dead weight, and distributes the load of a stiff shear-wall core.
When individual or combined footings remain preferable. On a competent stratum with a high allowable pressure and modest column loads, isolated footings are cheaper, use less concrete and reinforcement, and are far simpler to build. A combined footing is the natural intermediate step when only two or three columns interact — a column on a property line eccentric to its footing, two closely spaced heavily loaded columns, or a strap-beam arrangement that transfers the eccentricity to an interior column. Reach for these before reaching for a mat.
When piles must be used instead. A mat is a shallow foundation and cannot escape the soil beneath it. Piles become necessary when the competent stratum is deep and even a compensated mat would settle excessively; when loads are very heavy or highly concentrated; when there is significant uplift or lateral load (tall towers, transmission structures, marine works); where scour could undermine a shallow foundation; where the surface soil is expansive, collapsible or liquefiable; and where an adjacent excavation or tunnel will remove support. A piled raft — a mat that carries most of the load in bearing with a small number of settlement-reducing piles under the heaviest columns — is often the economical answer when a mat alone is close but not quite adequate.
Summary of the decision. Prefer a mat when the required footing area exceeds about half the footprint, when the deposit is erratic and differential settlement governs, when compensation can be exploited, or when a watertight basement slab is needed anyway. Prefer footings when the ground is good and the loads are light; prefer piles when no shallow solution can meet either the strength or the settlement requirement.
