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.
When. Undrained parameters are appropriate whenever the rate of loading is fast compared with the rate at which the soil can drain, so that the water content of the soil does not change while the load is applied. In practice this means a saturated clay or clayey silt of low permeability ($k \lesssim 10^{-8}$ m/s), loaded over days or weeks rather than years. The analysis is then carried out in total stresses with $\phi_u = 0$ and $s_u = c_u$, and no pore-pressure prediction is needed — which is the whole attraction of the method, because pore pressures during construction are the hardest thing in geotechnics to forecast.
A practical example. A 12 m diameter steel storage tank is to be founded on a raft over 9 m of soft, normally consolidated marine clay in the Fraser delta, and it will be hydrotested to full height within about ten days of completion. The governing check is bearing capacity at the end of that hydrotest, before any consolidation has occurred: with $q_u = 5.14\,c_u\,F_{cs}F_{cd} + q$ the whole resistance comes from $c_u$. The long-term drained bearing capacity is much larger, because consolidation under the tank raises the clay's strength — which is why staged filling with a rest period is the standard remedy when the undrained check fails. The same logic governs an embankment raised quickly on soft clay, a footing on clay under a crane surcharge, and the capacity of a driven pile immediately after driving.
Laboratory determination. The unconsolidated–undrained (UU) triaxial test shears a saturated specimen at constant water content under a cell pressure representing the in-situ total stress; the deviator stress at failure gives $c_u = q_f/2$, and a set of UU tests at different cell pressures returns a horizontal total-stress envelope, confirming $\phi_u = 0$. The unconfined compression test is the same test with zero cell pressure, $c_u = q_u/2$; it is quick and cheap but valid only for a fully saturated, intact clay that will stand unsupported. The laboratory vane suits very soft clays too weak to trim. A consolidated–undrained (CU) triaxial test with pore-pressure measurement is the most informative of all, because a single specimen returns $c_u$ for the total-stress analysis and $c'$, $\phi'$ for the drained analysis, and allows the specimen to be consolidated to its in-situ effective stress first, recovering some of the strength lost to sampling. Direct simple shear gives the strength on a horizontal plane, which is the relevant orientation under the middle of an embankment.
Field determination. The field vane shear test is the standard for soft to firm clays: a four-bladed vane is pushed below the borehole base and rotated, and $c_u = T/[\pi d^2(h/2 + d/6)]$ for a rectangular vane. It tests a large, undisturbed volume in place, gives a continuous profile, and also yields the remoulded strength and hence the sensitivity; but it shears fast, on a vertical cylindrical surface, and it must be corrected for plasticity by Bjerrum's factor $\lambda$, which falls from about 1.0 at $PI = 20$ to about 0.6 at $PI = 60$. The piezocone (CPTu) gives a near-continuous profile from $c_u = (q_t-\sigma_{v0})/N_{kt}$ with $N_{kt} \approx 10$–$20$; it is fast, repeatable and excellent at finding thin soft layers, but it is a correlation and $N_{kt}$ must be calibrated locally against vane or triaxial data. The pressuremeter derives $c_u$ from the limit pressure and is one of the few in-situ tests usable in stiff clays and glacial tills. The flat dilatometer gives $c_u$ from the horizontal stress index. The SPT should be used for clay only as a crude index — it is a dynamic test intended for granular soils.
The common limitation. Every one of these methods measures $c_u$ on a particular surface, at a particular rate, after a particular amount of disturbance, and $c_u$ is not a constant of the soil. Sampling relieves the in-situ stress and reduces the measured strength; fast shearing raises it by roughly 10 per cent per log cycle of strain rate; anisotropy means compression, simple shear and extension strengths differ by a factor of two in a soft clay; and a fissured clay gives a mass strength well below any small specimen. Sound practice therefore runs at least two independent methods — in the tank example above, a field vane profile corrected by Bjerrum's factor, checked against CPTu with a locally calibrated $N_{kt}$ and against UU triaxial tests on piston samples — and adopts the lower bound of the three.
