Question 10 of 10: Bearing and Skin Resistance of a Belled Drilled Pier

Question 10: Bearing and Skin Resistance of a Belled Drilled Pier (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 belled drilled pier cast through a silty clay layer with its bell founded in sand.

Find. (a) the net allowable point bearing capacity of the bell with $FS=4$; (b) the skin resistance developed over the top 5 m of shaft in the silty clay; (c) the advantages and disadvantages of drilled piers; (d) an alternative foundation for a heavy structure on this profile.

[Figure not reproduced: Figure 5 (redrawn) — belled drilled pier: 1.00 m shaft through 5.0 m of silty clay, 1.8 m bell bearing 2.5 m into the sand. See the official exam paper.]

Approach. The bell bears in sand, so the point resistance is a deep bearing-capacity problem in a $c'=0$ material driven by the effective overburden at the base and the deep bearing-capacity factor $N_q$; the net capacity subtracts the overburden that was there before the pier was built. The shaft resistance in the clay is a total-stress problem and is taken by the $\alpha$ method with the adhesion factor recommended for drilled shafts.

1. Base area and effective stress at the base. The bell is 1.8 m in diameter, so $$A_p=\frac{\pi}{4}D_b^2=\frac{\pi}{4}(1.8)^2=2.545\ \text{m}^2$$ The base sits at $L_1+L_2=7.5$ m below ground, and no water table is shown, so $$q'=\gamma_cL_1+\gamma_sL_2=20(5.0)+19(2.5)=100.0+47.5=147.5\ \text{kPa}$$
2. Bearing-capacity factor for the sand. Using the Reissner–Prandtl expression, which is the $N_q$ tabulated by Vesic and is the source stated for this calculation, $$N_q=e^{\pi\tan\phi'}\tan^2\!\left(45^\circ+\frac{\phi'}{2}\right)=e^{\pi\tan37.5^\circ}\tan^2 63.75^\circ$$ $$N_q=e^{2.4106}(2.0278)^2=11.14\times4.112=45.81$$ The question's instruction not to reduce $\phi'$ matters here: some texts recommend lowering the friction angle by a few degrees for a bored shaft to allow for stress relief at the base, and doing so would cut $N_q$ by roughly a quarter for every 2° removed.
3. Net ultimate point resistance. For a cohesionless bearing stratum the gross ultimate base pressure is $q_p=q'N_q$, and the net value subtracts the overburden that the excavation removed: $$Q_{p(\text{net})}=A_p\,q'\left(N_q-1\right)=2.545(147.5)(45.81-1)$$ $$Q_{p(\text{net})}=2.545(147.5)(44.81)=16\,820\ \text{kN}$$
4. (a) Net allowable point bearing capacity. Applying the required factor of safety, $$Q_{p(\text{all})}=\frac{Q_{p(\text{net})}}{FS}=\frac{16\,820}{4}=\boxed{Q_{p(\text{all})}\approx4200\ \text{kN}}$$
5. (b) Skin resistance in the silty clay. Shaft resistance in clay is taken by the $\alpha$ method, $f_s=\alpha^{*}c_u$. For drilled shafts the recommended adhesion factor is $\alpha^{*}=0.4$, appreciably lower than the value used for driven piles because boring softens the borehole wall and no set-up from displacement occurs. The shaft perimeter is $$p=\pi D_s=\pi(1.00)=3.142\ \text{m}$$ so over the 5.0 m of clay $$Q_s=\alpha^{*}c_u\,p\,\Delta L=0.4(30)(3.142)(5.0)=\boxed{Q_s=188.5\ \text{kN}}$$ This is barely 1% of the ultimate point resistance — a striking illustration of the point made in Question 1, that for a pier bearing on a competent stratum the shaft contribution through weak overlying soil is small enough to be treated as a reserve rather than as design capacity.

(c) Advantages and disadvantages of drilled piers

Advantages. A single drilled pier commonly replaces a group of driven piles together with its pile cap, which removes both the cap and the group-efficiency reduction, and it can be positioned exactly under a column. The excavation can be inspected — visually, by downhole camera, or by a shaft inspection device — so the founding stratum is confirmed rather than inferred, and the length can be adjusted on site to reach it. Very large capacities are available: a belled pier of the kind analysed here offers thousands of kilonewtons, and rock-socketed shafts far more. Construction generates neither the vibration nor the noise of driving, which matters beside existing structures, in urban settings, and in sensitive clays where driving would remould the soil. There is no heave of the surrounding ground or of adjacent piles, no risk of splicing or of damage during driving, and the reinforcement can be tailored for uplift or for lateral load. A bell can be formed in cohesive soil to multiply the base area — as here, where a 1.8 m bell on a 1.0 m shaft triples the bearing area for a modest increase in excavation.

Disadvantages. Quality depends entirely on workmanship, and the critical surfaces are the ones nobody can see once concrete is placed. Base cleanliness is the recurring problem: loose spoil or slurry left at the bottom produces a soft toe that destroys the very point resistance the design relies on. Caving soils and water-bearing granular strata require temporary casing or a slurry, and slurry left too long forms a filter cake that reduces shaft friction; withdrawing casing carelessly can neck the shaft. Boring relieves lateral stress in the surrounding soil, so shaft friction is systematically lower than for a displacement pile of the same size. Belling cannot be done at all in cohesionless soil, which will not stand unsupported, or below the water table without dewatering — the bell in this problem is formed in sand and is therefore an idealisation to be questioned on the answer paper. Concrete placement under water or slurry must be by tremie and demands care to avoid segregation or inclusions. Spoil disposal is an issue on contaminated sites, and the whole operation is weather-sensitive and generally more expensive per pier than driven piling where driving is feasible. Finally, integrity testing after the fact — low-strain sonic echo or cross-hole sonic logging — is a check rather than a cure, and remediating a defective shaft is expensive.

(d) An alternative foundation for a heavy structure on this profile

The profile is 5 m of soft to firm silty clay ($c_u=30$ kPa) over a dense sand ($\phi'=37.5^\circ$), which is a classic case for transferring load through the weak stratum to the competent one. The natural alternative is a driven pile group with a pile cap — precast concrete or closed-ended steel pipe piles driven 3 to 5 m into the sand. Driving is a displacement process, so it densifies the sand around and beneath the toe and generates far higher shaft resistance in it than boring does; installation is fast, capacity can be verified pile by pile from driving records and dynamic testing, and the sand offers exactly the material in which driving criteria are most reliable. The competing considerations are vibration and noise near existing structures, and the fact that the piles must be designed for downdrag if the silty clay is likely to consolidate under fill.

Other defensible answers, with their conditions: a piled raft, if the structure is a large heavy building — the raft spreads part of the load and the piles control differential settlement, which is usually the governing criterion; a mat (raft) foundation with partial compensation, if the structure has a basement, since excavating 5 m of clay at 20 kN/m³ removes 100 kPa of net pressure and can make the foundation nearly fully compensated; ground improvement — stone columns, deep soil mixing or preloading with wick drains through the silty clay — followed by a conventional raft, where the loads are moderate and programme allows the time; or a group of the drilled piers analysed here, retained on its own merits where vibration must be avoided. A spread footing bearing directly on the silty clay is not a candidate: with $c_u=30$ kPa the net ultimate bearing capacity is only about $5.14(30)\approx154$ kPa, and the consolidation settlement of a heavy structure on 5 m of that clay would be unacceptable long before that pressure was reached.