16-Civ-B3 Geotechnical Design · December 2016

Question 6 of 9: Design axial capacity of a belled drilled pier in clay

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

Notes on this paper

Paper format. Professional Engineers Ontario / Engineers Canada National Examinations, December 2016 — 98-Civ-B3 Geotechnical Design. Three hours, OPEN BOOK, any non-communicating calculator. Section A carries five discussion questions of 7 marks each (answer any four); Section B carries four design questions of 24 marks each (answer any three); the examinable total is 4 × 7 + 3 × 24 = 100 marks. All nine questions are worked below, because the set is a study resource rather than a timed attempt.

Reference texts (98-Civ-B3 / 16-Civ-B3 Geotechnical Design).

B. M. Das, Principles of Foundation Engineering, 9th ed. — subsurface exploration (Ch. 2), bearing capacity of shallow foundations (Ch. 3), settlement of shallow foundations including Schmertmann's strain-influence method (Ch. 5), retaining walls (Ch. 8), pile foundations (Ch. 11), drilled shafts (Ch. 12).
B. M. Das, Principles of Geotechnical Engineering, 9th ed. — shear strength (Ch. 12), lateral earth pressure (Ch. 13), slope stability (Ch. 15).
Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed. — the governing Canadian practice document for site investigation, in-situ testing, bearing resistance, deep foundations and earth-retaining structures.
R. F. Craig, Craig's Soil Mechanics, 9th ed. — effective stress, undrained versus drained behaviour, earth pressure, and the total-stress circular-arc slope analysis.
M. J. Tomlinson & J. Woodward, Pile Design and Construction Practice, 6th ed. — shaft adhesion in clay and under-reamed (belled) bored piles.
P. K. Robertson & K. L. Cabal, Guide to Cone Penetration Testing, 6th ed. — CPT interpretation and CPT-versus-SPT selection.

Sources of design charts and assumed values (page-1 Note 6). Note 6 requires the candidate to identify the source of every design chart and of every value assumed where the paper supplies none. They are named at the point of use and collected here:

Adhesion factor α = 0.55 for a drilled shaft in clay (Q6) — O'Neill and Reese (1999), reproduced in Das, Principles of Foundation Engineering, 9th ed., Section 12.9; the exclusion of the top 1.5 m and of one shaft diameter above the bell comes from the same source.
Bearing-capacity factor N_c^* = 9 (Q6) — Skempton (1951), as tabulated in Das, Section 11.11.
Overburden correction C_N = √(p_a/σ'_o) (Q7) — Liao and Whitman (1986), Das Principles of Geotechnical Engineering, Section 17.6.
SPT-to-friction-angle correlation (Q7) — Peck, Hanson and Thornburn (1974) as fitted by Wolff (1989); cross-checked against Kulhawy and Mayne (1990). Both are tabulated in Das, Principles of Foundation Engineering, 9th ed., Section 2.9.
Bearing-capacity factors and shape/depth factors (Q7) — Vesic (1973) and De Beer (1970), Das Sections 3.6 and 3.7.
Strain-influence diagram and the C₁, C₂ factors (Q7) — Schmertmann, Hartman and Brown (1978), Das Section 5.6; the modulus correlation E_s = 500(N₆₀ + 15) kPa is Bowles (1996), reproduced in the same section.
Rankine active coefficient for an inclined backfill (Q9) — Das, Principles of Geotechnical Engineering, 9th ed., Eq. (13.35); the base friction and adhesion reductions k₁ = k₂ = 2/3 are Das Section 8.4.
Unit weight of the submerged backfill (Q9) — assumed equal to the printed moist unit weight, 18 kN/m³, in the absence of a saturated value; the consequence of that assumption is bounded in the Q9 callout.

Section A

Section B

Question 6: Design axial capacity of a belled drilled pier in clay (24 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.

Given.

Quantity	Symbol	Value
Shaft diameter	D_s	1.0 m
Bell (base) diameter	D_b	2.0 m
Total length to base	L	12 m (8 m + 4 m)
Height of the under-ream	h_b	1.0 m (from 11 m to 12 m)
Undrained strength, upper clay	c_u1	50 kPa
Undrained strength, lower clay	c_u2	50 kPa
Factor of safety	FS	2

Find. The allowable (design) axial compressive capacity of the pier, that is Q_all = Q_ult / 2, stating and justifying every assumption the figure does not supply.

[Figure not reproduced: Figure 6.1 — The belled drilled pier of Figure 1, redrawn to scale. Shaft adhesion acts over the straight shaft only; end bearing acts on the full 2.0 m diameter of the under-ream. See the official exam paper.]

Approach. Treat the member as a drilled shaft (bored pier) in clay under undrained conditions: compute end bearing on the bell base from Skempton's N_c^* = 9, compute shaft resistance by the α method over the length of straight shaft that O'Neill and Reese permit to be counted, add them, and divide by the factor of safety.

The figure shows a widened base, which is the signature of a machine-excavated, under-reamed drilled shaft rather than a driven pile, so the drilled-shaft rules apply throughout. Both clay layers have the same undrained strength, so the layering affects only the bookkeeping, not the result.

Establish the base area. End bearing is mobilised on the full projected area of the under-ream, not on the shaft: $$A_p = \frac{\pi}{4}D_b^2 = \frac{\pi}{4}(2.0)^2 = 3.1416\ \text{m}^2$$ The embedment ratio to the base is $L/D_b = 12/2.0 = 6 > 4$, which is the condition for the deep-foundation bearing factor to have reached its limiting value.
Compute the ultimate end bearing. For a foundation in saturated clay loaded undrained, with $\phi_u = 0$, $$Q_p = A_p\,N_c^{*}\,c_{u2} = 3.1416 \times 9 \times 50 = 1413.7\ \text{kN}$$ Skempton's $N_c^{*} = 9$ is used because the base is more than four diameters below ground (Das, Section 11.11). This is a net resistance: the overburden term $q' A_p$ is deliberately omitted because it is cancelled by the weight of the pier itself, which is treated below.
Select the adhesion factor. With $c_u/p_a = 50/101.3 = 0.49 \le 1.5$, O'Neill and Reese (1999) give $$\alpha = 0.55$$ for a drilled shaft in clay. This is lower than the value that would be used for a driven pile in the same clay, and deliberately so: the excavation of a bored shaft softens and remoulds the clay at the interface and the fluid concrete does not restore the original horizontal stress.
Establish the length over which shaft adhesion may be counted. The same source excludes the top 1.5 m, where seasonal effects and construction disturbance make the adhesion unreliable, and excludes one shaft diameter immediately above the top of the bell, because the soil there moves with the bell rather than shearing along the shaft. The bell begins at 11 m, so $$L_{\text{eff}} = 11.0 - 1.5 - 1.0 = 8.5\ \text{m}$$ No adhesion is taken on the sloping surface of the under-ream itself.
Compute the shaft resistance. Over that length the clay strength is uniform at 50 kPa, so a single term suffices: $$Q_s = \alpha\,c_u\,(\pi D_s)\,L_{\text{eff}} = 0.55 \times 50 \times (\pi \times 1.0) \times 8.5 = 734.4\ \text{kN}$$ The perimeter is that of the straight shaft, 3.1416 m, not that of the bell.
Assemble the ultimate capacity. Summing the two components, $$Q_{ult} = Q_p + Q_s = 1413.7 + 734.4 = 2148.1\ \text{kN}$$ End bearing supplies 66 per cent of the total, which is the expected balance for an under-reamed pier — the bell exists precisely to make it so.
Apply the factor of safety. With FS = 2 as instructed, $$Q_{\text{all}} = \frac{Q_{ult}}{FS} = \frac{2148.1}{2} = 1074\ \text{kN}$$ so the design axial capacity is $$\boxed{Q_{\text{all}} \approx 1.07 \times 10^{3}\ \text{kN} \ \ (\text{say } 1070\ \text{kN})}$$
Check the self weight of the pier. The shaft volume is $\frac{\pi}{4}(1.0)^2(11.0) = 8.639\ \text{m}^3$ and the under-ream, a frustum from 0.5 m to 1.0 m radius over 1.0 m, adds $\frac{\pi}{3}(1.0)\left(1.0^2 + 1.0 \times 0.5 + 0.5^2\right) = 1.833\ \text{m}^3$, a total of 10.47 m³ weighing about 251 kN at 24 kN/m³. Because the concrete displaces soil of very nearly the same unit weight, the net additional load is small (of the order of 40 to 50 kN) and, consistent with omitting the overburden term from $Q_p$ in Step 2, it is not deducted. Stating this explicitly is what makes the omission legitimate rather than an oversight.

Quantity	Value
Base area of the under-ream, A_p	3.1416 m²
Ultimate end bearing, Q_p	1413.7 kN
Adhesion factor, α	0.55
Effective shaft length, L_eff	8.5 m
Ultimate shaft resistance, Q_s	734.4 kN
Ultimate axial capacity, Q_ult	2148.1 kN
Design (allowable) axial capacity, FS = 2	1074 kN, say 1070 kN

Check: the assumptions this answer rests on, and how much they are worth.

Drilled shaft, not driven pile. The under-ream can only be formed by a belling tool in a bored hole, so α = 0.55 with the O'Neill and Reese exclusions is the correct family of rules. If the member were instead treated as a driven pile with α ≈ 0.7 over the full 11 m, the answer would rise to about 1310 kN. The bored interpretation is the conservative and the defensible one.
Adhesion factor. Taking Skempton's classic bored-pile value α = 0.45 over the same 8.5 m gives Q_all = 1007 kN; taking α = 0.55 over the full 11 m of shaft (that is, ignoring the two exclusion zones) gives 1182 kN. The design value is therefore bracketed within roughly ±10 per cent by any defensible choice, which is the useful thing to be able to say.
Undrained (short-term) condition. Both layers are described only by c_u, so the total-stress α method is the only method the data support. A long-term effective-stress (β) check would need φ' and the horizontal stress state, neither of which is given; in a stiff clay the long-term capacity is normally the larger of the two, so the undrained result governs.
Settlement is not checked. A factor of safety of 2 on a drilled shaft is modest, and drilled shafts typically need 4 to 5 per cent of the base diameter — here 80 to 100 mm — to mobilise full end bearing. In service the working settlement would be far less than that, but on a real project the load-settlement response, not the ultimate capacity, would set the design load.
Group effects. The question asks for a single pier. If piers of this size were spaced at less than about three base diameters, block failure and group settlement would have to be checked separately.

Topic. Undrained axial capacity of an under-reamed (belled) drilled shaft in clay by the α method.

Key relations. $Q_{ult} = Q_p + Q_s$; $Q_p = A_p N_c^{*} c_u$ with $N_c^{*} = 9$ for $L/D_b \ge 4$; $Q_s = \sum \alpha c_u (\pi D_s)\,\Delta L$ with $\alpha = 0.55$ for $c_u/p_a \le 1.5$; $A_p = \tfrac{\pi}{4}D_b^2$; $Q_{\text{all}} = Q_{ult}/FS$.

Why this works. The bell converts a slender member into one with a large bearing area at depth, and it does so in the one soil type where a bell will stand open long enough to be concreted. Because clay is loaded undrained, its bearing resistance is a fixed multiple of c_u and is independent of depth once the failure mechanism is fully confined — that is what the constant N_c^* = 9 expresses. Shaft adhesion, by contrast, is a fraction of c_u that reflects how much the construction process degraded the interface, which is why the bored-pile α is well below unity and why the disturbed top and the zone above the bell are excluded outright.

Common pitfall. Using the bell diameter for the shaft perimeter, which inflates Q_s by a factor of two; and counting adhesion over the entire 12 m, which ignores both exclusion zones and the fact that no adhesion at all can be mobilised on the under-ream. A third error is to add the overburden pressure to the end bearing while also ignoring the weight of the pier, which double-counts the same 250 kN.

Source. Das, Principles of Foundation Engineering, 9th ed., Section 12.9 (drilled shafts in clay; O'Neill and Reese α and the exclusion lengths) and Section 11.11 (point bearing in saturated clay); Tomlinson and Woodward, Pile Design and Construction Practice, 6th ed., Section 4.2; CFEM, 4th ed., Ch. 18.

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