CEE 340 · Advanced Foundation Engineering · Ch. 11

Design of Deep Foundations

When the soil near the surface cannot carry the load, stop trying to spread it and start trying to reach past it. A pile carries load two ways at once — on its tip and along its sides — and knowing which one dominates changes everything about how you design it.

End Bearing Skin Friction α Method Pile Groups Settlement
01

When Shallow Isn't an Option

Piles are expensive. You use them when a spread footing genuinely cannot do the job — and there are five distinct reasons that happens.

Reason 1

Weak soil near surface

The upper strata cannot carry the load at any practical footing size, but a competent layer exists deeper. Reach it.

Reason 2

Intolerable settlement

Bearing capacity might be adequate but a shallow foundation would settle far too much. Piles bypass the compressible layer.

Reason 3

Uplift and lateral loads

Transmission towers, tall buildings under wind, and offshore structures need tension and lateral capacity a footing simply cannot supply.

Reason 4

Scour

Bridge piers must be founded below the depth that flood flow can wash away, which can be many metres.

Reason 5

Expansive / collapsible soil

Piles anchored below the active zone escape seasonal swelling and shrinking that would jack a footing up and down.

The economics

Always check shallow first

Piling can be an order of magnitude more expensive per unit load. It is the answer only after a spread or raft foundation has been shown to fail.

02

Classifying Piles

By load transfer

End bearing vs. friction

End bearing: the tip rests on rock or dense stratum and carries nearly everything. Friction: no competent layer within reach, so load is shed along the shaft. Most real piles are a combination.

By installation

Driven vs. bored

Driven piles displace soil sideways, densifying sand and increasing capacity — but they cause noise and vibration. Bored (cast-in-situ) piles remove soil, so there is no densification and less shaft friction, but they are quiet and can be very large.

By material

Concrete, steel, timber

Precast/prestressed concrete is the workhorse. Steel H-piles and pipe piles drive well through hard layers and splice easily. Timber is cheap and durable if kept permanently below the water table.

Installation method is not just a construction detail. The same pile geometry in the same sand can have noticeably different capacity depending on whether it was driven or bored, because driving changes the soil around it. That is why design correlations distinguish the two — and why a pile load test is worth so much.
03

How a Pile Carries Load

🧭
Push a straw into a thick milkshake. Some resistance comes from the tip pressing on what is beneath it, and some from the drink gripping the sides of the straw all the way down. Push into a glass with a solid bottom and it is nearly all tip. Push into a very deep milkshake with no bottom in reach and it is all sides. Same object, completely different mechanism — and that is the whole classification of piles.
Ultimate capacity
\[ Q_u = Q_p + Q_s \]

Point (end bearing) resistance plus skin (shaft) friction. They mobilise at very different displacements: shaft friction is fully developed after only about 5–10 mm of movement, while end bearing needs 10–25% of the pile diameter. At working loads, friction is doing almost all the work even in a nominally end-bearing pile.

Load Transfer

Q Q_s — skin friction Q_p — end bearing load in pile tip load depth ↓

Axial load in the pile decreases with depth as friction sheds it into the surrounding soil. Whatever is left at the bottom is the end bearing. The shape of that curve tells you immediately which mechanism dominates.

04

Piles in Sand

End bearing
\[ Q_p = A_p q' N_q^* \le A_p\left(0.5\,p_a N_q^*\tan\phi'\right) \]

Nq* is Meyerhof's bearing capacity factor for piles — far larger than the shallow-foundation Nq (81 vs 23 at φ' = 32°) because the failure zone is confined by soil on all sides. The limiting value on the right almost always governs.

Skin friction
\[ f = K\sigma'_v\tan\delta', \qquad Q_s = \sum p\,\Delta L\,f \]

K ≈ 1.4 for driven displacement piles, ≈ 1−sinφ' for bored. δ' ≈ 0.5–0.8φ'. p is the pile perimeter.

Core Idea — the critical depth

Both q' and σ'v stop increasing below a critical depth of roughly 15–20 pile diameters. Arching in the sand means the vertical stress acting on the pile does not keep growing indefinitely with depth. Ignore this and a long pile's capacity is wildly overestimated — the calculator below shows the effect directly.

Consequence: beyond the critical depth, every extra metre of pile adds friction at a constant rate, not an increasing one. Driving deeper still helps — but linearly, not quadratically, and there is a point where a second pile is cheaper than a longer one.
05

Piles in Clay — the α Method

End bearing (undrained, φ = 0)
\[ Q_p = 9\,c_u A_p \]

Nc* = 9 for a deep foundation, against 5.14 for a shallow one — again because the failure surface is fully confined.

Skin friction — α method
\[ f = \alpha c_u, \qquad Q_s = \sum \alpha c_u\, p\,\Delta L \]

α ≈ 1.0 for soft clay (cu < 25 kPa), falling to about 0.5 at cu = 100 kPa and 0.4–0.45 for stiff clay beyond that.

🥣
Why does α fall as the clay gets stiffer? Driving a pile into stiff clay remoulds and softens a thin annulus around the shaft, and can open a gap near the top. The clay right against the pile is therefore weaker than the clay the laboratory tested. Soft clay has less structure to destroy in the first place, so it loses less — hence α near 1.
Core Idea

In clay, friction dominates overwhelmingly. Worked Example 2 gets 634 kN of shaft friction against just 86 kN of end bearing — the tip contributes 12%. Shortening a friction pile is far more damaging than in sand, where the tip matters more.

06

Pile Capacity Calculator

Switch soil type and watch the balance between tip and shaft flip. Try pushing the length well past the critical depth in sand to see friction accumulate linearly rather than quadratically.

07

Pile Groups & Efficiency

Piles are almost never used singly — they come in groups under a common cap. And a group of nine piles does not carry nine times a single pile.

🫒
Drinking straws sharing one milkshake. One straw draws from all the fluid around it. Put nine straws close together and they compete for the same soil — their zones of influence overlap, so each is less effective than it was alone. Spread them further apart and interference falls, which is exactly why minimum spacing rules exist.
Converse–Labarre efficiency
\[ \eta = 1 - \frac{\theta}{90}\cdot\frac{(n-1)m + (m-1)n}{mn} \]

θ = arctan(D/s) in degrees, m × n piles at spacing s. Group capacity Qg = η · (mn) · Qu.

Block failure — the other check

In clay a closely spaced group can fail as one enormous block rather than as individual piles. Compute the capacity of the group perimeter acting as a single deep footing, and take the smaller of the two answers.

\[ Q_{g(block)} = c_u N_c^* (B_g L_g) + \sum \alpha c_u\, p_g \Delta L \]
Minimum spacing is typically 2.5–3.5D, most commonly 3D. Closer and efficiency drops sharply while driving one pile heaves or damages its neighbours; further apart and the pile cap grows expensive. At s = 3D a 3×3 group has η ≈ 0.73 — you lose over a quarter of the theoretical capacity to interference.
08

Negative Skin Friction

Skin friction is normally your friend: the soil grips the pile and holds it up. But if the soil settles more than the pile, that grip reverses direction and starts dragging the pile down.

When it happens

A pile driven through a soft clay layer that is still consolidating — under a new fill, a lowered water table, or its own weight. The clay settles past the pile, and friction along that length becomes a downward load instead of an upward resistance.

The double penalty

You lose the friction you were counting on over that length, and you gain an extra load the pile must carry. A layer that should have contributed +200 kN might instead impose −200 kN — a 400 kN swing. Mitigation: bitumen coating on the shaft through the settling layer, or a sleeve.

Core Idea

Negative skin friction is a load, not a reduction in resistance. Add it to the applied structural load before comparing against allowable capacity — do not simply subtract it from Qu.

09

Settlement of Piles

Capacity answers "will it hold?" — and just as with shallow foundations, that is only half the design. A pile group can be nowhere near failure and still settle enough to distress the structure above it.

📏
Three things squash when you stand on a stilt. The stilt itself shortens a little under the load. The ground under its foot dents. And the ground gripping its sides gets dragged down slightly. Those are exactly the three components of pile settlement — and for a slender concrete pile, the first is almost negligible while the second usually dominates.
Se1 — elastic shortening
\[ S_{e1} = \frac{(Q_{wp} + \xi Q_{ws})L}{A_p E_p} \]

The pile as a compression member. ξ ≈ 0.5 for uniform or parabolic friction distribution, 0.67 for triangular. Small for concrete, larger for long steel piles.

Se2 — from the tip load
\[ S_{e2} = \frac{q_{wp} D}{E_s}(1-\mu_s^2)I_{wp} \]

Soil compressing beneath the point, with qwp = Qwp/Ap and Iwp ≈ 0.85. Usually the largest of the three.

Se3 — from the shaft load
\[ S_{e3} = \left(\frac{Q_{ws}}{pL}\right)\frac{D}{E_s}(1-\mu_s^2)I_{ws} \]

Soil dragged down along the shaft, with \( I_{ws} = 2 + 0.35\sqrt{L/D} \). Typically the smallest term.

Core Idea

\( S_e = S_{e1} + S_{e2} + S_{e3} \). Worked Example 4 gets 1.1 + 8.7 + 0.7 mm — the tip term is 82% of the total. That is the opposite of the capacity picture, where the shaft carried 69%. A pile can get most of its strength from friction while getting most of its settlement from the point.

Group settlement — Vesic
\[ S_g = S_e\sqrt{\frac{B_g}{D}} \]

Bg = width of the pile group. A group settles considerably more than any single pile in it, because their stress bulbs overlap and the group loads a much deeper volume of soil.

The group penalty appears twice. Section 7 showed a 3×3 group loses 27% of its capacity to interaction. Here the same group settles 2.6× as much as a single pile (Example 4). Both effects come from the same overlapping stress zones — and both are why a pile cap can never be designed one pile at a time.
10

The Pile Load Test

Every equation in this chapter is an empirical correlation with real scatter — capacity predictions are commonly off by 30% or more. The load test is the only way to actually find out, and on any significant project it pays for itself.

Procedure

Load in increments

Apply load in steps of roughly 25% of the estimated allowable load, holding each until settlement stabilises, and record the load-settlement curve.

Interpretation

Finding Qu

Sometimes there is a clear plunging failure. More often there is not, so a criterion is used — for example net settlement reaching 10% of the pile diameter, or Davisson's offset line.

Value

Design confidence

A verified capacity permits a lower factor of safety (often 2 instead of 3), which frequently saves more in pile lengths across the site than the test cost.

11

Worked Examples

Example 1

Driven Pile in Sand

Problem: A 0.4 m square precast concrete pile is driven 12 m into sand with γ = 18 kN/m³, φ' = 32°. Take K = 1.4, δ' = 0.7φ', and a critical depth of 15D. Find the allowable capacity with FS = 3.

1
Geometry: \( A_p = 0.4^2 = 0.16\text{m}^2 \), perimeter \( p = 4(0.4) = 1.6\text{m} \), critical depth \( L_c = 15(0.4) = 6.0\text{m} \)
2
Effective stress at the tip is capped at Lc: \( q' = 18(6.0) = 108\text{kPa} \) — not 18(12) = 216 kPa
3
End bearing with Meyerhof's Nq* = 81 at φ' = 32°: \( Q_p = 0.16(108)(81) = 1400\text{kN} \), but the limiting value is \( 0.16(0.5)(100)(81)\tan32^\circ = 405\text{kN} \). The limit governs: Qp = 405 kN.
4
Skin friction, 0 to 6 m (σ'v rising 0 → 108, average 54): \( Q_{s1} = 1.4(54)\tan(22.4^\circ)(1.6)(6) = 299\text{kN} \)
5
Skin friction, 6 to 12 m (σ'v constant at 108): \( Q_{s2} = 1.4(108)\tan(22.4^\circ)(1.6)(6) = 598\text{kN} \)
6
\( Q_u = 405 + 299 + 598 = 1302\text{kN} \), so \( Q_{all} = 1302/3 = 434\text{kN} \)
Answer: Qall ≈ 434 kN. Shaft friction supplies 69% of capacity. Note the lower 6 m contributes twice as much friction as the upper 6 m — not because it is deeper, but because σ'v has already reached its capped value there.
Example 2

The Same Pile in Clay

Problem: The same 0.4 m × 12 m pile is instead driven into clay with cu = 60 kPa. Take α = 0.55. Find the allowable capacity with FS = 3.

1
End bearing: \( Q_p = 9c_u A_p = 9(60)(0.16) = 86.4\text{kN} \)
2
Skin friction: \( Q_s = \alpha c_u\, p L = 0.55(60)(1.6)(12) = 633.6\text{kN} \)
3
\( Q_u = 86.4 + 633.6 = 720\text{kN} \)
4
\( Q_{all} = 720/3 = 240\text{kN} \)
Answer: Qall = 240 kN — only 55% of the same pile in sand. The tip contributes just 12%: in clay this is essentially a friction pile, and its capacity is very nearly proportional to its length.
Example 3

A 3 × 3 Pile Group

Problem: Nine of the clay piles from Example 2 are arranged in a 3 × 3 group at 1.2 m centres (s = 3D). Find the group capacity using Converse–Labarre.

1
\( \theta = \arctan(D/s) = \arctan(0.4/1.2) = \arctan(0.3333) = 18.43^\circ \)
2
\( \eta = 1 - \dfrac{18.43}{90}\cdot\dfrac{(3-1)(3)+(3-1)(3)}{3\times3} = 1 - 0.2048\left(\dfrac{12}{9}\right) = 1 - 0.273 = 0.727 \)
3
Group capacity: \( Q_g = \eta(mn)Q_u = 0.727(9)(720) = 4711\text{kN} \), so \( Q_{g,all} = 4711/3 = 1570\text{kN} \)
4
Also check block failure — the group perimeter is 2.8 m × 2.8 m. In clay this check can govern for closely spaced groups, and the smaller of the two answers must be used.
Answer: Qg ≈ 4711 kN ultimate, 1570 kN allowable — against 9 × 720 = 6480 kN if the piles did not interfere. 27% of the theoretical capacity is lost to group interaction, which is exactly why a pile cap cannot simply be designed pile-by-pile.
Example 4

Settlement of the Sand Pile, Single and in a Group

Problem: The pile of Example 1 (0.4 m square, L = 12 m, Qall = 434 kN) carries its working load. Ep = 21 × 10⁶ kPa, Es = 30,000 kPa, μs = 0.3, ξ = 0.6. Find the settlement of a single pile, then of a 3 × 3 group at 1.2 m centres.

1
Split the working load in the same proportion as the ultimate: tip 405/1302 = 31%, shaft 897/1302 = 69%. So \( Q_{wp} = 135\text{kN} \), \( Q_{ws} = 299\text{kN} \).
2
Elastic shortening: \( S_{e1} = \dfrac{(135 + 0.6\times299)(12)}{0.16(21\times10^6)} = \dfrac{3773}{3.36\times10^6} = 1.12\text{mm} \)
3
From the tip load: \( q_{wp} = 135/0.16 = 844\text{kPa} \), so \( S_{e2} = \dfrac{844(0.4)}{30000}(1-0.3^2)(0.85) = 8.70\text{mm} \)
4
From the shaft load: \( I_{ws} = 2+0.35\sqrt{12/0.4} = 3.92 \), and \( \dfrac{Q_{ws}}{pL} = \dfrac{299}{1.6(12)} = 15.6\text{kPa} \), giving \( S_{e3} = 15.6\dfrac{0.4}{30000}(0.91)(3.92) = 0.74\text{mm} \)
5
Single pile: \( S_e = 1.12 + 8.70 + 0.74 = 10.6\text{mm} \)
6
Group (Vesic): \( B_g = 2(1.2)+0.4 = 2.8\text{m} \), so \( S_g = 10.6\sqrt{2.8/0.4} = 10.6(2.65) = 28.0\text{mm} \)
Answer: Single pile 10.6 mm; the 3×3 group settles 28 mm — 2.6× more. Note the tip term alone is 8.7 of the 10.6 mm (82%), even though the tip supplies only 31% of the capacity. Strength and settlement are governed by different parts of the same pile.
12

Quick Reference & Quick Check

Ultimate capacityQu = Qp + Qs
End bearing, sandApq'Nq* ≤ Ap(0.5paNq*tanφ')
End bearing, clay9cuAp
Skin friction, sandf = Kσ'vtanδ'
Skin friction, clayf = αcu
Critical depth15–20 D
K (driven / bored)≈1.4 / 1−sinφ'
δ'0.5 to 0.8 φ'
Group efficiencyConverse–Labarre η
Minimum spacing2.5–3.5 D (usually 3D)
FS3 (2 with load test)
Negative skin frictionadded as a load, not a strength loss

1. A pile in sand is driven to 30 m instead of 12 m. Why doesn't capacity increase as much as expected?

2. Why does α decrease as clay becomes stiffer?

3. A pile passes through soft clay that is still consolidating under a new fill. What happens to the friction along that length?

4. A 3×3 group at 3D spacing has η = 0.73. What does that mean?

5. In Example 2 the tip supplied only 12% of capacity. What does that imply for design?