Structural Engineering & Statics
where the load goes
Concept

Pile — where it appears

A slender foundation element driven or bored into the ground to carry load below the surface, in shaft friction, in end bearing, or in both. Which of the two dominates decides how it behaves in settling ground and how much of it is available to resist uplift.

Named by 4 essays across one field — each of them below, with the objects they name alongside it.

A pile has no length until the ground gives it one. Deflection, bending moment and soil reaction down a 0.6 m pile carrying 150 kN at a free head, in ground whose modulus grows by 0.005 N/mm³ per millimetre of depth. The one length in the problem is T, the fifth root of EI over n_h, which is 1.89 m here; the head moves 20.5 mm, the worst moment of 219 kNm is at 2.50 m — 1.32 T — and below about four T nothing happens at all. The classical coefficients come out of the finite differences rather than a table: 2.430 against Matlock and Reese's 2.435, and 0.772 against their 0.772.

A pile has no length until the ground gives it one

Almost every other structural member is handed a length by the drawing. A pile goes into the ground until it stops, and what decides how much of it is working is a fifth root of the ratio between its own stiffness and the soil's.

internal-forces · Lateral pile The worst force in a pile is not at the top of it. A 0.75 m pile 30 m long through ground that is settling, carrying 1200 kN at its head. Above the neutral plane the soil moves down past the shaft and the friction acts downward, so the axial force grows with depth; below it the friction acts upward in the ordinary way and the force falls again to the 600 kN the base takes. The maximum is 2331.39 kN at 18.86 m — 1.94 times the load applied, and it is at a depth where nothing is applied, nothing is connected and nothing can be inspected. A pile section chosen for the head load is under-sized by that factor over the middle third of its length.

The coating that takes the resistance with it

The cure for downdrag is to make the pile slippery, and it works — a bitumen slip layer takes the drag on this pile from 1,131 kN to 34. It also removes the shaft friction that was holding the pile up, in the same proportion and over the same length, and past a certain smoothness there is no neutral plane to find because there is no equilibrium.

internal-forces · Downdrag Where the pile and the ground settle alike. For a pile 24 m long and 600 mm across, carrying 800 kN, in ground whose top 18 m settles — by 100 mm at the surface, less with depth — over a toe that resists by moving: on the left, how far the ground (dashed) and the pile (solid) settle down the pile's length; on the right, the force in the pile. Above 15.9 m the ground settles more than the pile and hangs on it; below, the pile settles more and the ground holds it up. The force peaks there, at 1,407 kN against the 800 kN applied, and the toe, settling 10.6 mm, mobilises 623 kN; the head settles 13.6 mm.

The plane where the pile and the ground agree

Downdrag is usually found by equilibrium: the ground hangs on the pile above a neutral plane, holds it up below, and the plane is where those balance the load and the toe's resistance. But the toe's resistance is not a number the designer can supply. It is whatever the toe's own settlement mobilises, and the toe settles because the ground drags the pile down. Solved by compatibility instead — the plane where the pile and the ground settle by the same amount — the drag, the neutral plane, the toe's force and the pile's own settlement all turn out to grow with how far the ground goes, and each kilonewton put on the head costs the pile three quarters of one, not half.

internal-forces · Downdrag Heave puts the pile in tension where settlement put it in compression. For a 24 m pile 600 mm across carrying 200 kN, in clay whose top 18 m moves, by 100 mm at the surface: the axial force down the pile, compression positive, when the ground heaves (solid) and when it settles as far (dashed). Settling, the pile's compression peaks at 910 kN at 17.2 m and its toe carries 324 kN. Heaving, it is in tension below 8.9 m, peaking at 520 kN at 17.3 m, and its toe carries nothing: lifted, it parts from the soil beneath, so everything holding the pile down comes from the shaft below the plane.

The pile the ground pulls apart

Clay that swells after its trees are felled rises past the piles in it, and the same compatibility that put a pile into compression in settling ground puts it into tension in heaving ground, at nearly the same depth. Nearly everything else changes. A lifted toe parts from the soil and holds nothing, so the shaft alone anchors the pile; the head load that added to the downdrag now subtracts from the tension; and the tension peaks 17 metres down, far below the short cage a lightly loaded pile is given. A house's piles in swelling clay are tension members nobody reinforced.

internal-forces · Downdrag

Named alongside it

The objects these essays reach for when they reach for this one.

DowndragLoad pathNeutral planeCompatibilityEquilibriumFrictionSettlementBending momentBoundary layerCharacteristic lengthEffective stressElastic foundation

All concepts