Design axial capacity of a belled bored pile in clay: 16-Civ-B3 Geotechnical Design, Undated paper, Q7

Question 7: Design axial capacity of a belled bored pile 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. A bored pile with an under-reamed (belled) base, from Figure 2: a 1.0 m diameter straight shaft, 8 m of clay with $c_u=40\ \text{kPa}$ overlying 4 m of clay with $c_u=60\ \text{kPa}$, the pile toe at 12 m, and a bell 1.0 m high flaring the base to 2.0 m diameter. Factor of safety 3.

Find. The ultimate axial compressive capacity and the design (allowable) axial capacity.

The pile of Figure 2 with the three resistance components. Side resistance is not counted over the top 1.5 m, over the bell, or for one shaft diameter above the bell.

Approach. Total-stress (alpha) method: unit side resistance $f=\alpha c_u$ on the mobilised shaft length in each layer, unit base resistance $q_p=9c_u$ on the full bell area, then $Q_{all}=Q_u/\mathrm{FS}$.

Fix the idealisation and the assumptions. The pile is a bored, cast-in-place, under-reamed shaft, so the total-stress method for drilled shafts applies rather than the driven-pile version. Following Reese and O’Neill (1999), as adopted in Das and in the CFEM, the adhesion factor is $\alpha=0.55$ for $c_u/p_a\le 1.5$, which holds here ($60/101.3=0.59$); side resistance is neglected over the top 1.5 m, where the soil is disturbed and seasonally active; and it is neglected over the bell and for one shaft diameter above the bell, because the soil there is disturbed by the under-reamer and moves with the base rather than against the shaft.
Mobilised shaft lengths. The bell occupies 11.0 m to 12.0 m, so its top is at 11.0 m and one shaft diameter above that is 10.0 m. Hence $$\begin{aligned}L_1^{*}&=8.0-1.5=6.5\ \text{m in the upper clay} \\ L_2^{*}&=10.0-8.0=2.0\ \text{m in the lower clay}\end{aligned}$$ The shaft perimeter is $p=\pi(1.0)=3.142\ \text{m}$.
Side resistance, layer by layer. With $f=\alpha c_u$, $$\begin{aligned}f_1&=0.55(40)=22.0\ \text{kPa} \\ Q_{s1}&=22.0(3.142)(6.5)=449\ \text{kN}\end{aligned}$$ $$\begin{aligned}f_2&=0.55(60)=33.0\ \text{kPa} \\ Q_{s2}&=33.0(3.142)(2.0)=207\ \text{kN}\end{aligned}$$ giving a total shaft resistance $Q_s=449+207=\boxed{657\ \text{kN}}$
Base resistance on the bell. The bell bears in the lower clay, and for a deep foundation in clay the bearing-capacity factor has reached its limiting value $N_c^{*}=9$ because the embedment exceeds four base diameters: $$\begin{aligned}A_b&=\frac{\pi}{4}(2.0)^{2}=3.142\ \text{m}^2 \\ q_p&=9c_{u(2)}=9(60)=540\ \text{kPa}\end{aligned}$$ $$Q_p=540(3.142)=\boxed{1697\ \text{kN}}$$
Check the large-base reduction. Because the base diameter exceeds 1.9 m, Reese and O’Neill require the base resistance to be reduced when the settlement needed to mobilise it would be excessive, by $F_r=2.5/(\psi_1 D_b+\psi_2)\le 1$, with $\psi_1=0.0071+0.0021(L/D_b)=0.0197$, capped at 0.015, and $\psi_2=0.45\sqrt{c_u}=3.49$, capped at 1.5. Then $F_r=2.5/(0.015\times 2.0+1.5)=1.63 \gt 1$, so $F_r=1$ and no reduction applies.
Ultimate and design capacity. $$\begin{aligned}Q_u&=Q_s+Q_p \\ &=657+1697 \\ &=2353\ \text{kN}\end{aligned}$$ $$\begin{aligned}Q_{design}&=\frac{Q_u}{\mathrm{FS}} \\ &=\frac{2353}{3} \\ &=\boxed{784\ \text{kN}}\end{aligned}$$
Sanity checks on the answer. The base supplies 72 per cent of the ultimate capacity, which is the expected signature of a bell: doubling the base diameter quadrupled the base area. The structural check on the shaft is comfortable — 784 kN over the 0.785 m² shaft is 1.0 MPa, well inside the working stress of a bored pile in 30 MPa concrete. The self-weight of the pile, about 250 kN of concrete displacing a similar weight of soil, approximately cancels and is neglected.

Check: mobilisation, not strength, is the real limit on a belled pile. Side resistance is fully mobilised at 5 to 10 mm of movement, while base resistance on a 2.0 m bell needs of the order of 5 per cent of the base diameter, that is about 100 mm, to reach the $9c_u$ value used above. At the working load the shaft is therefore already at its limit while the bell is barely engaged. If the structure cannot tolerate the settlement, the design load should be governed by a serviceability check rather than by $Q_u/3$, or the bell should be omitted and the shaft lengthened.

Check: assumptions that a site would have to confirm. The clays are assumed to be intact and non-fissured, so no further reduction of $c_u$ is applied; construction is assumed dry or under a stable slurry, with the bell cleaned before concreting, since debris left in an under-ream destroys the base resistance that carries most of this pile; and $\alpha=0.55$ assumes a hole open for hours rather than days, because prolonged exposure softens the wall of a bored pile in clay and can drop $\alpha$ towards 0.4. Note also that belling is only feasible in a clay that will stand unsupported; it cannot be done under slurry.

Question 7 — results
Component	Symbol	Value
Unit side resistance, upper clay	$f_1=\alpha c_{u1}$	22.0 kPa
Unit side resistance, lower clay	$f_2=\alpha c_{u2}$	33.0 kPa
Shaft resistance, upper clay (6.5 m)	$Q_{s1}$	449 kN
Shaft resistance, lower clay (2.0 m)	$Q_{s2}$	207 kN
Total shaft resistance	$Q_s$	657 kN
Bell base area	$A_b$	3.142 m²
Unit base resistance	$q_p=9c_{u2}$	540 kPa
Base resistance	$Q_p$	1697 kN
Ultimate axial capacity	$Q_u$	2353 kN
Design axial capacity, FS = 3	$Q_{design}$	784 kN

Topic. Axial capacity of a bored pile in clay by the total-stress (alpha) method.

Key relations. $Q_u=Q_s+Q_p=\sum \alpha c_u\,p\,\Delta L + N_c^{*}c_{u(b)}A_b$ with $N_c^{*}=9$ for $L/D_b\ge 4$; $\alpha=0.55$ for $c_u/p_a\le 1.5$ (Reese and O’Neill); exclusions of the top 1.5 m, the bell, and one diameter above it.

Why this works. Boring a hole in clay relieves the horizontal stress on its wall and lets the clay soften, so the adhesion that develops is a fraction of the undrained strength rather than the full value. Wrapping all of that into a single empirical $\alpha$ calibrated against load tests is what makes the method usable, and the exclusion zones encode where load tests show no side resistance develops at all.

Common pitfall. Counting side resistance over the bell and the metre above it. On this pile that would have added about 200 kN of resistance that load tests show is not there, an eight per cent overestimate of capacity for no reason.

Source. Das, Principles of Foundation Engineering, 8th ed., ch. 12 (drilled shafts); Reese and O’Neill, FHWA-IF-99-025; CFEM 4th ed., ch. 18.

Question 7 of 9: Design axial capacity of a belled bored pile in clay

Question 7: Design axial capacity of a belled bored pile in clay (24 marks)