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 Standard Penetration Test survives because it is cheap, universally available and directly linked to a large body of empirical correlation — not because it is a good measurement. Its limitations fall into three groups: what the test does to itself, what it cannot see, and what the correlations built on it can and cannot support.
The measurement is equipment- and operator-dependent. The blow count reflects the energy actually delivered to the rods, and delivered energy varies from about 45% of the theoretical free-fall energy for a rope-and-cathead donut hammer to 80% or more for an automatic trip hammer. Two rigs on the same borehole can differ by a factor of nearly two in raw $N$. That is why every modern correlation is written in terms of $N_{60}$, and why $N$ must be corrected for hammer energy ratio, rod length below about 10 m, borehole diameter above 115 mm, and the presence or absence of a sampler liner. Poor borehole practice adds more error: if the water level in the casing is allowed to fall below the piezometric level, the base blows or loosens and $N$ collapses; a bentonite cake or an unwashed cuttings plug at the base inflates it.
Overburden dependence. $N$ increases with confining stress even at constant relative density, so a raw blow count cannot be compared between depths or between sites without normalising to a reference stress of 100 kPa through $C_N$. The normalisation itself is empirical and becomes unreliable at very shallow depth, where $C_N$ is capped, and at high stress.
Soil types where the test does not apply. In gravels, cobbles and fills containing oversize particles the 51 mm split spoon simply meets individual stones and returns a meaningless high count. In soft sensitive clays $N$ is near zero and offers no resolution, and the test is destructive of exactly the structure that governs behaviour. In silts and clayey silts penetration is partly drained, so the count reflects an undefined mixture of drained and undrained response. Below the water table in fine sands and silts, dilation or the generation of excess pore pressure during driving distorts the result.
What it cannot see. The test is a point measurement, normally at 1.5 m centres, so a thin soft seam or a laminated layer between test depths is missed entirely — and thin weak layers frequently govern settlement and slope stability. It measures no pore pressure, unlike the piezocone, so it locates neither the drainage boundaries nor the true stratigraphy between samples. The sample recovered is fully disturbed: it serves for classification, water content and Atterberg limits, and for nothing else. No strength, stiffness, permeability or consolidation parameter can be measured directly on it.
The correlations are the real limitation. $N_{60}$ is not a soil property; it is an index from which properties are inferred through empirical relations — Peck, Hanson and Thornburn or Schmertmann for $\phi'$, Skempton for relative density, Meyerhof or Burland and Burbidge for footing settlement on sand, and the Youd et al. framework for liquefaction triggering. Each of those relations was calibrated on a particular soil population and carries scatter of the order of ±30 to 50%. Applying an $N$–$s_u$ correlation to a clay is the least defensible of all, since the undrained strength of clay depends on stress history and plasticity in ways the blow count cannot resolve; CFEM is explicit that SPT results in clay should be treated as an index only.
In Canadian practice the SPT is therefore used to profile the site, to identify strata and to provide the input for well-established sand correlations, and it is supplemented by the piezocone for continuous profiling, by field vane or CU triaxial testing for undrained strength in clay, and by pressuremeter or plate load testing where stiffness matters — never used alone for the design of an important foundation.
