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16-Civ-B3 Geotechnical Design · December 2013

Question 2 of 9: Choice of method for the short-term capacity of a pile in soft clay

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. National Examinations, December 2013 — 98-Civ-B3 Geotechnical Design. Three hours, open book, any non-communicating calculator. Section A holds five 7-mark discussion questions (answer any four); Section B holds four 24-mark design questions (answer any three), so the examinable total is 4 × 7 + 3 × 24 = 100 marks. Every one of the nine questions is answered here, because the set is a study resource rather than a sitting.

Reference texts. B. M. Das, Principles of Foundation Engineering (9th ed.) and Principles of Geotechnical Engineering (9th ed.); Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM, 4th ed.) — the governing Canadian reference for foundation practice; R. F. Craig, Craig's Soil Mechanics (9th ed.); D. P. Coduto, Foundation Design: Principles and Practices (3rd ed.).

Sources of design charts and assumed values (paper Note 6). The paper requires every chart and assumed value to be identified. Bearing-capacity factors are Terzaghi’s (Das, Foundation Engineering, Table 3.1, with Nγ after Kumbhojkar 1993); the pile end-bearing factor Nq* is read from Meyerhof’s chart (Das Fig. 11.14) and cross-checked against Janbu’s closed-form expression; the adhesion factor α is Das Table 11.5 (Terzaghi, Peck & Mesri); the strain-influence distribution is Schmertmann, Hartman & Brown (1978). Assumed values — specific gravity of solids Gs = 2.65 for the Question 8 backfill, base friction δ = ⅔φ′ and base adhesion ca = ⅔c′ (CFEM §24), and a driving-parameter value K = 1.4K0 for a high-displacement driven pile (Das §11.11) — are flagged where they are used.
Check — Question 6 text and figure disagree. The printed text of Question 6 states a 1 m × 1 m square footing with γ = 20 kN/m³ and φ = 36°, while Figure 3 is drawn for a 2.5 m footing with γ = 18 kN/m³ and φ′ = 38°. The question text governs (it is the instruction to the candidate); the figure is used only for the embedment Df = 1.5 m and for the CPT modulus profile, which the text does not restate. The alternative reading is noted at the end of the answer.

Question 2: Choice of method for the short-term capacity of a pile in soft clay (7 marks)

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.

For the short-term capacity of a single pile in a soft saturated clay I would use the $\alpha$ (total-stress) method. Short term means that the excess pore pressures generated by driving and by the applied load have not dissipated, so the clay behaves in an undrained manner and its strength is the undrained shear strength $c_u$. The unit shaft resistance is taken as a fraction of that strength, $f = \alpha c_u$, and the base resistance as $q_p = 9\,c_u$ — both expressed in total stress, which is the only consistent way to describe a soil whose pore pressures are unknown and changing.

The $\beta$ method is an effective-stress formulation, $f = \beta \sigma^{\prime}_v$ with $\beta = K \tan \delta^{\prime}$, and it describes the long-term, fully drained condition once the driving-induced pore pressures have dissipated and the clay has reconsolidated against the shaft. Applying it to the short term would require knowing the effective stress on the shaft immediately after driving, which is precisely the quantity that is unknown. The $\lambda$ method, $f_{av} = \lambda(\bar{\sigma}^{\prime}_v + 2\bar{c}_u)$, is a useful hybrid calibrated on driven pipe piles in normally consolidated clay, but it gives only a single average unit friction over the whole embedded length and so cannot represent a layered profile; it is best kept as a check.

Information required. From the field: a continuous profile of undrained shear strength with depth from the field vane (with Bjerrum’s plasticity correction applied) and from CPT / CPTu using cu = (qt − σv0)/Nkt; layer thicknesses and the depth to any bearing stratum; the piezometric profile; and, on a project of any size, a static load test with a dynamic (PDA) check on production piles. From the laboratory: unconsolidated undrained (UU) triaxial tests on tube samples for cu, bulk and saturated unit weights, Atterberg limits and water content (which set the plasticity index used to correct the vane and to select α), sensitivity from vane or fall-cone, and consolidation tests if set-up or downdrag is to be estimated.

Strengths. The method is simple, needs only one strength parameter, and $\alpha$ has been back-figured from a very large database of instrumented and load-tested piles, so it is directly anchored in measured behaviour. In soft clay ($c_u \lesssim 25$ kPa) $\alpha$ approaches unity and the answer is insensitive to the choice, which makes it robust exactly where it is most used.

Limitations. $\alpha$ is an empirical lumped factor, not a soil property: it depends on pile material, installation method, overconsolidation ratio, embedment ratio and time after driving, and different codes give visibly different curves for the same $c_u$. The method carries no explicit account of set-up — the capacity of a driven pile in soft clay commonly doubles over weeks as the remoulded, high-pore-pressure annulus reconsolidates — so a short-term estimate is conservative for service loads but may be unconservative for restrike criteria. It also says nothing about downdrag from a consolidating layer, about group effects, or about the settlement of the pile, and it is only as good as the $c_u$ profile, which in soft sensitive clay is itself uncertain by 20–30 %. For those reasons the $\alpha$ estimate should be confirmed by load-testing roughly one pile in ten, as Canadian practice requires.