07-Str-B1 · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Examinations — May 2013 — 07-Str-B1 Geotechnical Design. Three-hour, OPEN-BOOK exam; any non-communicating calculator permitted (the candidate must record its make and model). Format: Section A carries five short-answer questions of 7 marks each, of which any FOUR are to be answered; Section B carries the long design questions at 24 marks each, of which any THREE are to be answered. The paper instructs candidates to state any interpretive assumptions and to identify the source of every design chart or assumed value used. Every question in both sections is worked below, because the set is intended as a study resource.
Reference texts: Das, B.M., Principles of Foundation Engineering (9th ed., Cengage) — shallow foundations, consolidation settlement, sheet-pile walls, retaining walls and drilled shafts; Das, B.M., Principles of Geotechnical Engineering (9th ed., Cengage) — method of slices, lateral earth pressure, consolidation theory; Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM, 4th ed., 2006) — Canadian practice for SPT interpretation, pile design, limit-states design and tolerable settlement; Craig, R.F. / Knappett, J.A., Craig's Soil Mechanics (8th ed., CRC Press) — effective stress, shear strength and slope stability; Duncan, J.M., Wright, S.G. & Brandon, T.L., Soil Strength and Slope Stability (2nd ed., Wiley) — choice of strength parameters and factors of safety for short- and long-term analyses.
NOTE 1 — question numbering in the source. The printed paper labels the retaining-wall problem (Figure 4) and the drilled-pier problem (Figure 5) both as "Question 9", while the Section B heading reads "answer any THREE of the following FOUR questions". Section B therefore contains five printed problems under four numbers. They are set out below as Question 9 (retaining wall) and Question 10 (drilled pier) in printed order, so that each can be referred to unambiguously; the marks shown are those printed against each problem.
NOTE 2 — dimensions scaled from Figure 1. Figure 1 is a hand-drawn slope on a 1 m × 1 m grid with no written dimensions other than $R=10$ m. The geometry used in Question 6 was scaled from that grid: slope height 7 m over a 9 m horizontal run, a 3 m thick lower layer, and the centre of the trial circle 1.4 m horizontally beyond the toe and 8.0 m above it. Every one of these values reproduces the drawing to within about 0.2 m (one fifth of a grid square). Check against the original if the paper is used for marking rather than study.
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.
All three methods predict unit shaft resistance from a soil parameter measured before the pile exists, and none of them models what installation does to the soil. Driving a displacement pile into clay remoulds an annulus one to two diameters thick, generates excess pore pressures approaching the total overburden stress, and is followed by weeks or months of reconsolidation during which capacity commonly rises by 50 to 100% — the "set-up" or "freeze" effect. Bored piles move the other way: stress relief and softening at the borehole wall, and any polymer or bentonite cake left on it, reduce shaft resistance below the value the same soil would give a driven pile. A static load test is the only routine measurement that sees the pile as built, in the ground as disturbed, at the age at which it will be loaded.
The second reason is the scatter of the methods themselves. Predictions of shaft capacity in clay from $\alpha$, $\beta$ or $\lambda$ routinely differ from measured capacity by 30 to 60%, and differ from one another by a similar margin on the same profile, because each was calibrated on a particular population of piles and a particular way of measuring $s_u$. There is no way to know from the calculation alone which end of that range a given site sits at.
The third reason is economic and codified. Canadian limit-states practice attaches the resistance factor to the level of verification: CFEM and CSA S6 allow a materially higher geotechnical resistance factor for axial compression when capacity is confirmed by static load testing than when it rests on a static analysis alone — roughly $\varphi\approx0.6$ against $\varphi\approx0.4$. On a large piling contract that difference in pile length or number pays for the tests several times over. Testing about one pile in ten also gives statistical control over site variability, verifies that the driving criterion or the boring procedure actually delivers the assumed capacity, and provides the load–settlement curve that the empirical methods cannot supply at all — which matters because piled foundations are very often governed by settlement rather than by capacity.
The β (effective-stress) method is the appropriate and more reliable choice for long-term capacity.
Long-term means drained. By the time the excess pore pressures generated by installation have dissipated and the soil around the shaft has reconsolidated, the shear resistance available at the pile–soil interface is a frictional resistance governed by the effective normal stress acting on the shaft. That is exactly what the β method expresses: $$f_s=\beta\,\sigma'_v,\qquad \beta=K\tan\delta'$$ with $K$ the horizontal stress coefficient after reconsolidation and $\delta'$ the interface friction angle, which for a remoulded clay against a pile is close to the critical-state angle $\phi'_{cv}$. Every term is a drained, effective-stress quantity, so the formulation matches the drainage condition it is being asked to describe, and it automatically accounts for changes in groundwater level over the design life.
The α method, $f_s=\alpha s_u$, is a total-stress formulation. It was calibrated against load tests carried out relatively soon after installation and it inherits every difficulty of measuring $s_u$ — which test, at what strain rate, on what quality of sample. It is the right tool for the short-term, end-of-construction check on a driven pile in clay, and it remains the standard practical method for that case, but it says nothing about the effective stresses that will actually be acting a decade later.
The λ method of Vijayvergiya and Focht, $f_s=\lambda(\bar\sigma'_v+2\bar s_u)$, is a hybrid: it mixes an effective stress with an undrained strength and applies a single coefficient $\lambda$ over the whole embedded length, so it cannot represent a layered profile and it cannot be applied incrementally. It was derived from load tests on long driven steel pipe piles in the Gulf of Mexico and its reliability outside that population — in particular for bored piles or for short piles in stiff clay — is poor. It is a useful rapid check, not a long-term design method.
Check: the printed question is degraded at this point and reads "α; or ...t"; the three methods named in the opening sentence are α, β and λ, and the comparison has been answered on that basis.
