16-Civ-B3 Geotechnical Design · May 2017

Question 6 of 9: Design axial capacity of a belled bored pile in layered clay

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

Notes on this paper

Paper format. National Examinations, May 2017 — 16-Civ-B3 Geotechnical Design; three hours, open book, any non-communicating calculator. Section A holds five discussion questions worth 7 marks each of which four are marked; Section B holds four design questions worth 24 marks each of which three are marked, so 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 marked script.

Reference texts. B. M. Das, Principles of Foundation Engineering, 7th–9th ed. (Cengage); B. M. Das, Principles of Geotechnical Engineering; R. F. Craig, Craig's Soil Mechanics, 8th ed. (Knappett & Craig); Canadian Geotechnical Society, Canadian Foundation Engineering Manual (CFEM), 4th ed.; J. E. Bowles, Foundation Analysis and Design; ASTM D1586 (SPT) and D5778 (CPT).

Source of charts and assumed values (page 1, Note 6). Every design coefficient used below is named where it is used: Terzaghi bearing-capacity factors from Das, Principles of Foundation Engineering, Table 3.1 (values computed by Kumbhojkar, 1993); Vesic/Reissner factors and the shape, depth and inclination factors from Das Table 3.4 and Eqs. (3.19)–(3.26); drilled-shaft adhesion factor alpha* = 0.55 from Reese & O'Neill (1989) as tabulated by Das, Chapter 12; bearing factor Nc* = 9 from Skempton (1951); earth-pressure coefficient for downdrag K' = 1 − sin(phi') from Das, Chapter 11; Janbu's bearing-capacity number for the pile point from Das Eq. (11.33). Assumed values (adhesion ratio, pile spacing, rigidity index) are stated in a callout beside the step that uses them.

Question 6: Design axial capacity of a belled bored pile in layered 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. A bored (drilled) pile with a belled base founded in two clay strata, dimensioned from Figure 2; the required factor of safety is 2.

Given data (Figure 2)
Quantity	Symbol	Value
Shaft diameter	D_s	1.0 m
Bell (base) diameter	D_b	2.0 m
Total pile length below ground (8 m + 4 m, to the underside of the bell)	L	12 m
Vertical height of the bell	L_b	1 m (from 11 m to 12 m)
Upper clay, ground level to 8 m	c_u,1	60 kPa
Lower clay, 8 m to below the base	c_u,2	40 kPa
Factor of safety	FS	2

Find. The allowable (design) axial compressive load the pile may carry, that is the ultimate capacity divided by 2.

[Figure not reproduced: Figure 2 redrawn: 1.0 m shaft to 11 m, 2.0 m bell from 11 m to the base at 12 m, founded in the c u = 40 kPa clay. See the official exam paper.]

Approach. Both strata are clay, so the governing case is short-term (undrained) loading: compute the ultimate capacity as the sum of the side resistance mobilised on the straight shaft, using the drilled-shaft adhesion factor, and the base resistance of the bell from Skempton's Nc* = 9, then divide the total by the required factor of safety.

Assumptions, with justification (page 1, Notes 1, 6 and 7). (1) Construction method. The enlarged base identifies this as a bored and under-reamed pile, not a driven one, so the drilled-shaft adhesion factor applies rather than the alpha factor for driven piles. (2) Adhesion factor. alpha* = 0.55, from Reese and O'Neill (1989), valid where c_u/p_a is not greater than 1.5; here the worst case is 60/101.3 = 0.59, comfortably inside the range. (3) Inactive lengths. Following the same reference, no side resistance is counted over the top 1.5 m (seasonal moisture change, desiccation, casing and the concrete slump zone) nor over a length equal to one shaft diameter immediately above the bell, because the clay there moves away from the shaft as the bell is loaded; no side resistance is counted on the flared face of the bell itself. (4) Undrained analysis. Total-stress (phi = 0) analysis governs a pile in clay at end of construction; the position of the water table therefore does not enter the calculation. (5) No group effects — a single pile is analysed as drawn. (6) Reading of Figure 2. The 8 m and 4 m dimensions run from the ground surface to the line on which the underside of the bell sits, and the small “1m” dimension, with inward-pointing arrows at the flare, is the height of the bell itself; the pile is therefore 12 m long with the bell occupying 11 m to 12 m.

Set the geometry and the shaft perimeter. The straight shaft runs from ground level to the top of the bell at 11 m; the bell occupies the last metre, down to 12 m. The perimeter of the straight shaft is $$p=\pi D_s=\pi(1.0)=3.1416\ \text{m}$$ and the plan area of the base is $$A_b=\frac{\pi}{4}D_b^{2}=\frac{\pi}{4}(2.0)^{2}=3.1416\ \text{m}^{2}$$
Identify the length of shaft that actually delivers side resistance. Discounting the top 1.5 m and one shaft diameter (1.0 m) above the top of the bell at 11 m leaves the interval from 1.5 m to 10.0 m. That interval is split by the stratum boundary at 8 m into 6.5 m in the upper clay and 2.0 m in the lower clay.
Accumulate the adhesion over the two strata. With f = alpha* c_u acting over each sub-length, $$\sum c_u \Delta L=(60)(6.5)+(40)(2.0)=390+80=470\ \text{kPa}\cdot\text{m}$$
Evaluate the side resistance. Multiplying by the adhesion factor and the perimeter, $$Q_s=\alpha^{*}p\sum c_u\Delta L=(0.55)(3.1416)(470)$$ $$\boxed{Q_s=812.1\ \text{kN}}$$
Evaluate the base resistance of the bell. The bell is founded in the lower clay, so c_u = 40 kPa applies. The embedment ratio L/D_b = 12/2 = 6.0 is well above 4, so Skempton's factor is at its full value, $$N_c^{*}=6\left[1+0.2\frac{L}{D_b}\right]=6[1+1.20]=13.2\ \Rightarrow\ N_c^{*}=9\ \text{(upper limit)}$$ $$Q_p=A_b N_c^{*}c_{u,2}=(3.1416)(9)(40)$$ $$\boxed{Q_p=1131.0\ \text{kN}}$$
Combine and apply the factor of safety. Adding the two contributions, $$Q_u=Q_s+Q_p=812.1+1131.0=1943.1\ \text{kN}$$ and dividing by the required factor of safety of 2, $$\boxed{Q_{\text{design}}=\frac{Q_u}{FS}=\frac{1943.1}{2}=972\ \text{kN}}$$
Check the result for engineering sense. The bell contributes 58 per cent of the capacity and the shaft the remainder, which is what the under-ream is for: without it the base area would fall from 3.14 m² to 0.79 m² and the base resistance from 1131 kN to 283 kN, cutting the ultimate capacity by about 44 per cent. The mobilised shaft adhesion, 33 kPa in the upper clay and 22 kPa in the lower, is a reasonable magnitude for a bored pile in firm clay.

Final results — Question 6
Quantity	Symbol	Value
Effective shaft length for side resistance	—	1.5 m to 10.0 m (8.5 m total)
Ultimate side resistance	Q_s	812.1 kN
Ultimate base resistance of the bell	Q_p	1131.0 kN
Ultimate axial capacity	Q_u	1943.1 kN
Design (allowable) axial capacity, FS = 2	Q_design	972 kN (say 970 kN)

Check — sensitivity of the assumptions. If the top 1.5 m is not deducted, Q_s rises to 968 kN, Q_u to 2099 kN and the design load to 1049 kN — about 8 per cent higher; if the whole 11 m straight shaft is counted (neither inactive length deducted), Q_s = 1037 kN, Q_u = 2168 kN and the design load 1084 kN, about 12 per cent higher. The deductions are retained because it is the recommended practice for under-reamed shafts and because the discounted zones are the least reliable part of the interface. A second caveat concerns serviceability: a base diameter of 2.0 m exceeds the 1.9 m threshold above which the settlement required to mobilise the full base resistance becomes a significant fraction of the base diameter, so the design load should be confirmed by a settlement calculation (or by reducing the base contribution) rather than by the factor of safety alone. Finally, this capacity is a gross capacity; subtracting the buoyant weight of the concrete would reduce the net available load by roughly 150 kN, which is conventionally offset against the weight of soil displaced and ignored.

Topic. Ultimate axial capacity of a bored pile in cohesive soil (alpha method with an under-reamed base).

Key relations. Q_u = Q_s + Q_p; side resistance Q_s = sum over strata of alpha* c_u p delta-L with alpha* = 0.55 for c_u/p_a not greater than 1.5; base resistance Q_p = A_b N_c* c_u with N_c* = 6[1 + 0.2 L/D_b] limited to 9; design load Q_design = Q_u/FS.

Why this works. In a saturated clay loaded quickly the strength available at the pile–soil interface and beneath the base is the undrained strength, which does not depend on the normal effective stress. The capacity therefore separates cleanly into an interface term proportional to the contact area and a bearing term proportional to the base area, and both are linear in c_u. The adhesion factor is less than one because boring softens a thin annulus of clay against the borehole wall and because the concrete does not develop the full undrained strength of the intact clay across the interface. The base factor 9 is the deep-foundation limit of the phi = 0 bearing-capacity solution: once the embedment exceeds about four base diameters the failure mechanism is fully contained in the soil and no longer reaches the surface, so N_c stops growing.

Common pitfall. Counting side resistance on the flared face of the bell and on the shaft immediately above it. As the base is pushed down the clay directly above the under-ream is dragged away from the shaft, so that zone contributes nothing; including it can overstate the capacity by ten per cent or more. A second pitfall is applying the driven-pile alpha chart (alpha near 1.0 for soft clay) to a bored pile, which overstates the shaft resistance substantially.

Source. Das, Principles of Foundation Engineering, Chapter 12 (drilled shafts), Eqs. (12.20)–(12.24) and Table 12.2 after Reese & O'Neill (1989); Skempton (1951) for N_c* = 9; Canadian Foundation Engineering Manual, 4th ed., Chapter 18.

← Question 5 Next: Question 7 →