Question 10 of 10: Belled drilled pier: point bearing, skin resistance and selection

Question 10: Belled drilled pier: point bearing, skin resistance and selection (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 passing through $L_1 = 5.0$ m of silty clay ($\gamma_c = 20$ kN/m$^3$, $c_u = 30$ kPa) into $L_2 = 2.5$ m of sand ($\gamma_s = 19$ kN/m$^3$, $\phi' = 37.5^{\circ}$, $c' = 0$). Shaft diameter $D_s = 1.00$ m, bell diameter $D_b = 1.8$ m, base at 7.5 m depth. No water table is shown, so total and effective stresses coincide.

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

[Figure not reproduced: Figure 5 (redrawn). Belled drilled pier carried through 5.0 m of silty clay and 2.5 m of sand, with the bell formed in the sand. See the official exam paper.]

Approach. For (a), take the effective vertical stress at the base level, apply the deep bearing capacity factor for the given friction angle, and subtract the overburden term so the answer is a net capacity. For (b), use the total-stress (alpha) method with the shaft perimeter and Das's recommended adhesion factor for drilled shafts.

1. Part (a): effective vertical stress at the base of the bell. The base sits at $L_1 + L_2 = 7.5$ m. With no water table, $$q' = \gamma_c L_1 + \gamma_s L_2 = 20(5.0) + 19(2.5) = 100.0 + 47.5 = 147.5\ \text{kPa}$$
2. Bearing capacity factor for the sand. The question directs that $\phi'$ is not to be reduced, so the deep bearing capacity factor is taken directly at $\phi' = 37.5^{\circ}$ from the Reissner expression that underlies the tabulated values: $$N^*_q = e^{\pi\tan\phi'}\tan^2\!\left(45^{\circ}+\frac{\phi'}{2}\right) = e^{\pi\tan 37.5^{\circ}}\tan^2 63.75^{\circ} = 45.8$$This is consistent with the standard tabulation, which gives $N_q = 42.92$ at $37^{\circ}$ and $48.93$ at $38^{\circ}$; the value used sits between them as it must.
3. Net ultimate point bearing capacity. The bell area is $$A_p = \frac{\pi}{4}D_b^2 = \frac{\pi}{4}(1.8)^2 = 2.5447\ \text{m}^2$$and the net resistance subtracts the overburden that the soil was already carrying, which is what the $(N^*_q - 1)$ term does: $$Q_{p(net)} = A_p q'\left(N^*_q - 1\right) = 2.5447(147.5)(45.81 - 1) = 16820\ \text{kN}$$
4. Apply the factor of safety. With $FS = 4$, $$Q_{all(net)} = \frac{Q_{p(net)}}{FS} = \frac{16820}{4} = \boxed{4205\ \text{kN}}$$or about 4.20 MN, corresponding to a net allowable base pressure of 1652 kPa.
5. Part (b): skin resistance in the silty clay by the alpha method. For drilled shafts in clay the unit skin friction is taken as a fraction of the undrained strength, $f = \alpha^* c_u$, with $\alpha^* = 0.4$ recommended for bored piles (lower than for driven piles because boring softens the shaft wall): $$f = 0.4(30) = 12.0\ \text{kPa}$$The shaft perimeter over that length is $p = \pi D_s = \pi(1.00) = 3.1416$ m, so $$Q_s = \alpha^* c_u\, p\, L_1 = 12.0(3.1416)(5.0) = \boxed{188.5\ \text{kN}}$$Note how small this is beside the base resistance: the pier is overwhelmingly an end-bearing element, which is exactly the situation described in Question 1.
6. Part (c): advantages and disadvantages of drilled piers. The advantages first. A single drilled pier replaces a group of driven piles and its pile cap, which is usually cheaper and always simpler. Its diameter and length can be varied to suit conditions found during drilling, and the bell can be enlarged to two or three times the shaft diameter to pick up a large base area in a competent stratum. Installation causes almost no vibration and little noise, so drilled piers are the natural choice next to existing structures and in urban Canadian sites; there is no driving heave to disturb neighbouring foundations, and no ground displacement to damage adjacent services. The soil at the base and along the shaft can be inspected or sampled during construction, which is a form of verification no driven pile offers, and the large section gives high resistance to lateral load and moment.
7. Part (c) continued: the drawbacks. Quality depends almost entirely on workmanship and inspection. In caving granular soils or below the water table a casing or a drilling fluid is essential; if the fluid is not properly conditioned, filter cake and trapped slurry reduce both shaft friction and base contact. Base cleanliness is the classic problem: loose spoil left at the bottom of the hole produces large settlements before the designed end bearing is mobilized, which is why some codes discount end bearing unless the base is inspected. Boring relieves lateral stress and softens the shaft wall, so shaft friction is smaller than for a displacement pile of the same size, which the $\alpha^* = 0.4$ factor above reflects. Belling cannot be done in cohesionless soil that will not stand unsupported, nor under slurry. Concreting must be continuous and by tremie under water, and defects are hidden, so integrity testing (sonic echo, cross-hole sonic logging) is normally specified. Finally, the plant is heavy and needs a working platform, and spoil disposal from a large-diameter shaft in contaminated ground can be a significant cost.
8. Part (d): an alternative foundation for a heavy structure. The profile is a soft to firm silty clay only 5 m thick over a dense sand, with no rock within reach. A group of driven precast or steel H piles taken through the clay and driven to set in the sand is the obvious alternative and is in several ways better suited to a heavy structure. Driving displaces and densifies the sand instead of loosening it, so the end bearing is mobilized at smaller settlement and can be verified pile by pile with a driving formula or a pile-driving analyser; capacity per unit cost is high and quality is far less dependent on inspection. A group under a common cap also gives redundancy that a single pier does not. The penalties are noise, vibration and possible heave, which may rule the option out on a constrained urban site — the same trade-off that produced the drilled pier in the first place.
9. Part (d) continued: the other candidates. If the structural loads were more modest, a piled raft or even a raft on the sand after excavating the clay would be worth pricing, since removing 5 m of clay and replacing it with compacted granular fill converts the problem into a shallow foundation one. Where the clay is soft and the structure is genuinely heavy, a group of belled piers or barrettes gives the same end bearing with greater redundancy than one large pier. Ground improvement — stone columns or deep soil mixing through the clay — is a further option that would allow a raft, and is increasingly used in Canadian practice where pile driving is restricted. The choice is settled by the load, the tolerable settlement, the proximity of neighbours and the local availability of plant, not by capacity alone.