16-Civ-B3 Geotechnical Design · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examinations, December 2019 — 16-Civ-B3 Geotechnical Design. Three hours, open book, any non-communicating calculator. Section A holds five discussion questions worth 7 marks each (answer any four); Section B holds four design questions worth 24 marks each (answer any three). The examinable total is therefore 4 × 7 + 3 × 24 = 100 marks. Page-1 Note 3 sets the answer-any-four / any-three rule, and Note 6 requires the candidate to name the source of every design chart and of every assumed value — so every chart read, correlation and assumption below is attributed where it is used. All nine questions are solved here, because the set is a study resource rather than a timed sitting.
Reference texts. B. M. Das, Principles of Foundation Engineering, 9th ed. (bearing capacity, elastic settlement, retaining walls, drilled shafts); B. M. Das, Principles of Geotechnical Engineering, 9th ed. (shear strength, lateral earth pressure, slope stability); Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. (Canadian practice, factors of safety, in-situ testing); R. F. Craig, Craigʹs Soil Mechanics, 9th ed. (effective stress, undrained strength); D. P. Coduto, Foundation Design: Principles and Practices, 2nd ed. (shallow-foundation design, settlement serviceability).
Check — conventions used throughout this paper. Unit weights printed on the figures are treated as bulk (saturated below any water table); effective unit weights use γw = 9.81 kN/m3. Reinforced concrete is taken at γc = 24 kN/m3 (CFEM 4th ed.; the exam gives no value), and Question 8 shows that the conclusion is unchanged anywhere in the 23–25 kN/m3 range. Where the paper omits a number the solution needs, the assumption is stated at the point of use and its influence on the answer is quantified, as page-1 Notes 1 and 7 invite.
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 — or raft — is a single continuous footing carrying all the columns and walls of a structure. Choosing it over spread footings is mostly a question of area and uniformity; choosing it over piles is mostly a question of where the competent stratum is. Both comparisons are made below.
Preferred over individual or combined footings when… The classical trigger is that the required footing area becomes a large fraction of the building footprint. When the soil is weak enough, or the column loads heavy enough, that the individual footings would occupy more than roughly half the plan area, it is cheaper to excavate and concrete one slab than to form many footings with the strips of untouched ground between them — and at that spacing the footings are no longer independent anyway, because their pressure bulbs overlap and each one settles into its neighbourʹs stress field. A mat is also preferred where the soil is erratic: pockets of soft material, old fill, buried channels, organic lenses or karst cavities produce differential settlement between adjacent footings, whereas a stiff raft bridges the weak zone and redistributes the load, converting differential settlement into a smaller overall tilt. That makes it the natural choice for a structure sensitive to differential movement — a building with brittle cladding or finishes, a machine foundation, or a structure over ground subject to subsidence from mining or groundwater lowering.
Three further cases favour the mat for reasons that have nothing to do with bearing capacity. Where there is a basement below the water table, a raft is needed anyway as a watertight floor able to resist hydrostatic uplift, so extending it to carry the columns costs little. Where the excavation is deep enough, the mat allows a compensated (floating) design: the weight of soil removed offsets part or all of the building weight, so the net increase in stress at founding level — and hence the settlement — can be reduced to almost nothing. And where uplift or overturning from wind or seismic action must be resisted, a mat mobilises the whole building footprint and its overburden rather than isolated pads. Very heavy or very unequal column loads on compressible ground also point to a mat, because the slab can be thickened or stiffened locally to spread them.
Preferred over a pile foundation when… A mat is the better choice when the soil immediately beneath the structure is adequate — that is, when the bearing capacity is sufficient and the estimated total and differential settlements are tolerable at the pressures the raft will apply. Piles become necessary when the competent stratum is deep and the near-surface material is too weak or too compressible to satisfy those checks at any practical raft thickness, when settlement of a raft would exceed the serviceability limit, when the loads must be carried through fill or organic soil, when scour or seasonal volume change could undermine a shallow foundation, or when large tensile or lateral loads must be taken. A mat is also preferred where driving or boring is impracticable — a congested urban site with vibration-sensitive neighbours, or a site underlain by boulders — and where the cost and programme of a piling rig cannot be justified for a low-rise structure. Between the two lies the piled raft, in which the raft carries most of the load and a modest number of piles are added beneath the heaviest columns purely to control differential settlement; it is the economical answer for many tall buildings and should be named as the middle option rather than treating the choice as binary.
When a mat is the wrong answer. Where the soil is competent and the loads modest, individual spread footings remain much cheaper — a mat commits the whole footprint to excavation, reinforcement and concrete, and a thick, heavily reinforced slab is expensive. Where the column layout is very irregular or the loads very unequal on a soil of low stiffness, a mat may attract large bending moments and prove less economical than combined footings or strap footings on the few columns that need them. And where the underlying stratum is deeply compressible, a mat simply loads the whole compressible thickness over the entire footprint, which increases total settlement rather than reducing it — the stress from a large loaded area reaches far deeper than that from a small one, which is precisely the case where piles or a piled raft become the right choice.
