Structural Engineering & Statics
where the load goes
Concept

Pile group — where it appears

Several piles under one cap, whose settlement and capacity are not those of a single pile multiplied by their number. The overlapping stress bulbs make a group settle several times as much as one pile at the same load per pile, and the corner piles carry the largest share.

Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.

The group is not weaker; it is very much softer. A 3 × 3 pile cap on the left, with each pile's share of 9.0 MN and 4.5 MNm in meganewtons — N/n plus M·y/Σy², the same three terms in the same order as a bolt group under an eccentric load and a section under biaxial bending. The corner piles take 1.25 times the average and a pile added at the centroid would change that by nothing at all, because it adds to neither second moment. On the right is the effect a bolt group cannot have: the piles share ground, so the stress bulbs overlap and the group settles 3.9 times as much as a single pile at the same load per pile, rising to 14.2 for 144 of them. The capacity check everyone makes — block failure against the sum of the piles — comes out at 4.54 here and does not govern at all. The check nobody tabulates is the one that does.

Nine piles, and four times the settlement

A pile cap divides its load between its piles by the same three terms a bolt group uses and a section under biaxial bending uses. What a bolt group does not have is neighbours it shares ground with — and the group effect that matters is not the strength check everybody makes, but a stiffness effect nobody tabulates.

structures · Pile group Most of a long pile is doing nothing. Head deflection against embedded length, both measured in the pile's own characteristic length T = 14.67 m. A pile shorter than about two T is a lever with nothing holding its foot and deflects several times as much; past four T the curve is flat to within a per cent, because the ground below that depth is never asked for anything. A lateral check is a check on the top four T of a pile, however deep it goes for its axial load — and adding length to fix a lateral deflection is the one remedy that does not work.

The pile that is too short to bend

A laterally loaded pile is long or short in its own characteristic length, and the two are different structures. The slender pile bends and the ground below four characteristic lengths never hears about it; the monopile is two lengths deep, rotates about a point, and every tabulated coefficient written for the first case is wrong for the second.

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 Closer piles add pull-out the block cannot pay for. For 600 mm piles 15 m long under a 20 × 30 m raft, in ground whose shaft friction is 0.30 of the effective vertical stress and whose submerged unit weight is 10 kN/m³: the summed pull-out of every pile on a square grid (thin, rising steeply as the spacing closes), the submerged weight of the block of ground the group would lift (dashed, 90 MN whatever the spacing), and the group's capacity, the lesser (solid). The two meet at 2.06 m — 3.4 pile diameters — where s² = π·d·β·L/2. Closer than that the group lifts the block and the extra piles add nothing; the most piles worth having is about 142.

The piles that would lift the ground

A basement too light to stay down can be pinned down with tension piles, each holding by the friction on its shaft. Add enough of them, close enough together, and the ground between them stops being something they grip and becomes something they carry: the group lifts out as a block, and the block's weight is all it can hold. For 600 mm piles 15 m long that happens closer than 2.06 m apart, a spacing with no raft, no water and no load in it — and every pile past that point is paid for twice.

equilibrium · Uplift Where the shelter is decides whether the leading row works harder. The share of the cap's shear the leading row and the last row of three rows carry, as a multiple of the average pile's, against the thickness of soft ground over stiffer, in characteristic lengths, with the row factors applied at every depth (solid) or in the soft layer only (dashed). With the factors at every depth the leading row carries 1.24 and the last 0.83 at 2.0 lengths; in the soft layer only, 1.07 and 0.96. In uniform ground the usual reading gives 1.35 and 0.75.

The shelter that stops at the interface

Piles in a group shelter one another, and practice counts the shelter as a factor on each row's soil, calibrated on groups in uniform ground. Put the same group in soft ground over stiff and the calibration has to be read one of two ways — the shelter at every depth, or only where the ground is soft — and the two readings disagree about which row works hardest. The first gives the leading pile 17 per cent more moment at the cap; the second gives the last pile 24 per cent more in the ground.

internal-forces · Lateral pile

Named alongside it

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

Bending momentCharacteristic lengthDowndragEffective stressElastic foundationFree bodyLateral pileLimit stateSettlementShaft frictionStiffnessSubgrade modulus

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