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.
The statement is a design convention rather than a statement of physical fact. Some shaft resistance is certainly generated in the weak overlying soils; the manual's point is that a designer must not count on it, and there are four independent reasons why.
Displacement compatibility. Shaft friction and end bearing are not mobilised at the same pile movement. The full shaft resistance of a pile in soft or loose soil develops at a very small relative displacement — typically 5 to 10 mm, essentially independent of pile diameter — and in sensitive or normally consolidated material it is strain-softening beyond that peak. End bearing on a dense gravel, by contrast, requires a tip movement of the order of 5 to 10% of the pile diameter to approach its ultimate value, which for a 400 mm pile is 20 to 40 mm. At the working displacement of a pile founded on rock or dense gravel, the shaft in the weak layers has therefore already passed its peak and may be shedding load. Summing peak shaft resistance and ultimate end bearing would double-count resistances that never coexist.
Negative skin friction is the more likely outcome. The weak layers are, by definition, the compressible ones. Any fill placed at the surface, any adjacent loading, any dewatering, and in many cases simply the reconsolidation of the soil disturbed by driving, will cause those layers to settle more than the pile does. The relative movement then reverses sign and the layers hang on the pile as downdrag, adding to the load carried at the toe instead of relieving it. A design that credited positive shaft friction in the same layers would be wrong twice over: once in the resistance it claimed, and once in the load it omitted.
The contribution is small but the uncertainty is large. A soft clay with $s_u = 20$ kPa and an adhesion factor near unity offers perhaps 20 kPa of unit shaft resistance, against several megapascals of end bearing available on dense gravel; the weak layers contribute a few percent of capacity while carrying most of the parameter uncertainty in the calculation. Installation makes this worse — driving remoulds a sensitive clay and generates excess pore pressures, and boring under bentonite leaves a softened annulus — so the value at the time of loading is neither the intact value nor reliably predictable.
Robustness over the design life. Ignoring the weak layers makes the capacity insensitive to events the designer cannot control: seasonal groundwater change, scour at a bridge pier, a future basement excavation or service trench beside the pile, or the consolidation caused by a neighbour's fill. Whatever happens in those layers, the pile still stands on the gravel. This is precisely the argument the Canadian Foundation Engineering Manual makes when it separates a "point-bearing pile", whose load path is deliberately a single competent stratum, from a "floating pile", whose capacity is distributed and therefore has to be justified layer by layer.
The corollary matters as much as the rule itself: because the weak layers are excluded from resistance, they must still be included in loading wherever downdrag is credible, and the pile section and the competent stratum must be checked for the sum of structural load and dragload at the neutral plane.
