The pile the ground pulls apart

The ground that hangs on instead of holding up introduced downdrag: ground that settles past a pile hangs on it, adding to the load the pile carries, down to a neutral plane below which the ground holds the pile up instead. The plane where the pile and the ground agree solved it by compatibility. Friction is mobilised by how far the pile moves against the ground; the toe’s resistance by how far the toe itself is pushed down; and the neutral plane is simply where the pile and the ground move alike. Every quantity — the plane, the drag, the toe’s force — came out of the movements, and none had to be assumed.

Every movement in those essays was downward. Their last section named the ground that goes the other way. A clay that takes up water after the trees on it are felled, or after a basement removes its overburden, swells, and it rises past the piles in it. The same compatibility then puts the pile in tension above a neutral plane at the depth where pile and ground rise alike, and the toe that resisted settlement by being pushed down is now being pulled up. The essay asked whether the heave plane sits where the settlement plane did, mirrored, or whether the toe’s different behaviour in uplift moves it.

It sits almost exactly where the settlement plane did. That turns out to be the least interesting fact about it.

The same pile, the ground going up #

The pile is the earlier essay’s: 24 m long and 600 mm across, in clay whose top 18 m moves with depth from its full amount at the surface to nothing at 18 m. Shaft friction reaches its full value, three-tenths of the effective overburden pressure, after 5 mm of relative movement. The toe is pushed into stiffer ground beneath and mobilises its resistance hyperbolically, half of its 1,500 kN after 15 mm. Two things change for heave. The ground moves up instead of down. And the toe, if it is pulled upward, parts from the soil under it and holds nothing — there is no suction or adhesion to rely on beneath a straight shaft.

The load on the head changes too, for a reason that is the point of the whole problem. Piles are put into swelling clay precisely because the clay moves, and the buildings that need them are the ones too light to ride it out on shallow footings: houses, single storeys, light industrial sheds. So the head carries 200 kN, a quarter of the earlier essay’s 800.

Settling by 100 mm, the pile’s compression grows from its 200 kN at the head to 910 kN at 17.2 m — the drag of the ground above — and falls below it to the 324 kN its toe carries. Heaving by 100 mm, the force falls from the head’s 200 kN compression, through zero at 8.9 m, to 520 kN of tension at 17.3 m, and back to nothing at a toe that has lifted off the soil beneath it.

The planes are 0.1 m apart. Mirrored in depth, the two problems are almost the same. Mirrored in force, they are nothing like each other.

Why the plane hardly moves and the force does #

The plane is where the pile and the ground move alike, and in both cases the pile hardly moves at all compared with the ground. Settling, the pile’s head goes down by a few millimetres while the ground goes down by a hundred; heaving, it goes up by four while the ground goes up by a hundred. The ground’s movement falls linearly to nothing at 18 m, so it crosses a pile that barely moves near the bottom of the moving layer, either way. The plane is set by the shape of the ground’s movement, and the shape is the same.

The force is set by what has to balance at the plane, and that is where heave and settlement differ.

Settling, the plane’s compression is the head load plus the drag above it, and it is balanced below by the friction of the stable ground and by the toe. The head load and the drag add. Heaving, the plane’s tension is the uplift above it minus the head load, balanced below by the friction of the stable ground alone, because the toe has lifted. The head load subtracts from the tension it added to in compression, and the toe that carried a third of the load in settlement contributes nothing in heave.

That is the answer to the earlier essay’s question, stated properly. The toe’s different behaviour in uplift moves the plane by tenths of a metre, and not always the same way: with 200 kN on the head the heave plane is 0.1 m deeper than the settlement plane, with nothing on the head 0.4 m shallower, the anchorage below needing more shaft once the toe gives none and the head load deciding how much anchorage there is to provide. What the toe changes is how much of the pile is working in which direction: in settlement the toe shares the work; in heave the bottom 6.7 m of shaft does all of it.

A pile that rises nearly as one piece #

Drawn as movements, the problem is simple to see. The ground rises 100 mm at the surface and less with depth, to nothing at 18 m. The pile rises 4.1 mm at its head and 3.8 mm at its toe, stretching by 0.3 mm under its own tension. Above 17.3 m the ground moves up past the pile and its friction pulls the pile up; below, the pile moves up past ground that is not moving and its friction holds the pile down. The toe has lifted 3.8 mm off the soil beneath, and that gap is the toe’s whole contribution.

The pile’s rise is small, and the building on it rises with it — 4 mm, against the 100 mm a shallow footing in the same clay would ride. That is what the pile is for. It is doing its job by being pulled apart.

The light buildings are the ones at risk #

Every kilonewton on the head comes off the tension, because the head load pushes down against the uplift the ground provides. With nothing on the head the pile carries 693 kN of tension; at 200 kN, 520; and past about 800 kN, the uplift the heaving clay can mobilise above the plane is less than the head load, and the pile never goes into tension at all.

The order matters. In settling ground the most heavily loaded piles have the worst of it, because the drag adds to their load. In heaving ground the most lightly loaded do, because nothing on their heads counters the pull. A heavy building on swelling clay holds its piles in compression; a house on the same clay hangs its piles from the ground. The piles that are most likely to be lightly designed are the ones heave loads hardest.

The tension saturates as the friction does #

How much the clay will heave is the hardest number in the problem to know: it depends on how much water the clay takes up and how deep, which depends on what was growing on the site and how long since it was cleared. The calculation is kind to that uncertainty. The tension rises steeply over the first few tens of millimetres — 331 kN at 25 mm — and then flattens, to 585 kN at nearly 300 mm. Once the ground near the surface has moved past the pile by more than the 5 mm that mobilises full friction, the friction there is at its limit whatever the movement. Further heave only extends the length of shaft over which friction is fully mobilised, down towards the plane.

So the tension is governed by the friction the clay can supply and the length of shaft it acts on, much more than by the heave itself. Doubling an uncertain heave estimate from 100 to 200 mm raises the tension by under a tenth. That is the same saturation the drag showed in settlement, and the same reason: compatibility only decides how much of the friction is mobilised, and beyond a few millimetres of relative movement all of it is.

Anchoring the toe #

The standard response to heave is to anchor the pile below the moving layer, often with an under-reamed base — a bell cut into the stiff ground at the toe, whose shoulders resist being pulled up. Given an uplift resistance at the toe, the pile rises less: with 1,000 kN of toe resistance, 2.1 mm at the head instead of 4.1. But the tension in it does not fall. It rises slightly, from 520 to 553 kN, and the plane moves a little deeper.

The reason is the general one from one support too many: a stiffer restraint attracts more force. An anchored pile resists the ground’s pull more firmly, and the ground’s pull on it is correspondingly larger, because the ground slides past it further. An under-ream reduces the pile’s movement — which is what the building cares about — and leaves the pile’s own tension where it was or makes it worse.

Steel where nobody put any #

The consequence that matters is where the tension is. A lightly loaded bored pile in compression is often reinforced only in its top few metres, where it connects to the building and where any bending from lateral load is: a pile has no length until the ground gives it one showed that a pile’s bending dies out within a few diameters of its head. Below that, the concrete is in compression and needs no steel.

In heaving clay the tension starts at 8.9 m and peaks at 17.3 m, near the bottom of the moving layer, and it asks for 1,196 mm² of steel there — six 16 mm bars, or four 20s. Every millimetre of it is below a 6 m cage. Without it, the concrete at 17 m carries 1.8 N/mm² of tension across its whole section. The strength that is never used made the case that concrete’s tensile strength is never relied on in design, because it is unreliable in exactly the places that matter; a cast shaft has construction joints where the concrete was topped up, soil inclusions where the bore was not clean, and the shrinkage cracks of its own curing. Any one of them at 17 m is a pile that has parted.

It would part without anyone knowing. The pile above the break carries its building down to the break and rides with the heaving ground; the pile below stays put. The building rises with the clay as if it were on shallow footings, by a large share of the heave, and the cause is 17 metres down in a pile that passed every compression check.

Sleeving the part that moves #

The other standard response is to stop the moving clay from gripping the pile at all: a slip sleeve or a coating over the top of the shaft, through the clay that swells, so that its friction there is a small fraction of what it would be. The coating that takes the resistance with it found the same remedy in settling ground, and the same trap: a coating that cuts the drag also cuts the shaft’s support wherever it reaches.

In heave the trap is in where the friction is. Shaft friction grows with depth, as the effective overburden does, so the top few metres of a pile carry very little of it. A sleeve over the top 6 m — the depth the cage reaches, the depth a contractor might sleeve by instinct — cuts the pile’s friction there to a tenth and its tension only from 520 to 446 kN, and the tension still starts at 10.6 m. Sleeved to 9 m it is 354 kN; to 12 m, 226; to 15 m, 61. To relieve a heaving pile the sleeve has to go most of the way down the moving layer, because that is where the moving layer grips.

The pile’s rise falls with the sleeve as well, from 4.1 mm to 0.2 mm at 15 m, and that is the second thing a sleeve buys: a building that does not move with its ground. Both effects come from the same cause. Every metre of sleeve is a metre of shaft that the swelling clay no longer pulls, and the pile is held down by an unchanged length of stable ground below the plane, so the balance at the plane shifts towards the stable ground.

A sleeve that deep is a real cost — it is most of a 24 m pile’s length in swelling clay sleeved — and it is the honest alternative to reinforcing the pile for its tension. One or the other is owed. The figure for the cage says which one a pile with neither has been given by default.

Ground beams and the space beneath them #

The piles are not the only part of a foundation the heaving clay pushes. A ground beam spanning between pile caps sits on the clay that is swelling, and the clay pushes it up with a pressure the beam was never designed for, onto piles that are already in tension. The usual detail is a compressible void former under every ground beam and suspended slab, so that the clay can rise into a gap rather than against the structure, and the piles then carry only what their own shafts collect.

That is the same logic as the sleeve, applied horizontally. The structure in swelling clay is made to touch the clay in as few places, and as far down, as it can. The pile reaches down to stable ground and is the only thing that does; everything above that level is either sleeved, voided or strong enough in tension to take what the clay hands it.

What the calculation takes for granted #

The heave is a known profile. It is taken as linear from the surface to the bottom of the moving layer, which is the shape a uniformly wetted clay would take. Real swelling is concentrated where the water arrives — near the surface if from rain, around a broken drain, at depth beneath a felled tree’s root zone — and a heave concentrated deeper moves the plane down and lengthens the tension zone.

The friction is the same up as down. Shaft friction mobilised by the ground moving up past the pile is taken equal to that mobilised by the ground moving down. In a swelling clay the effective stresses are changing as it swells, and the friction may be less; that would reduce the tension and the plane’s depth together.

The pile is elastic and continuous. A concrete pile in tension cracks, and a cracked pile is less stiff, which changes the movements slightly and the forces hardly at all, since the forces come from friction at its limit. Stiffer than its cracked section says is the right correction for the stiffness; for the strength there is none.

Nothing happens in the time between. Clay swells over seasons and years, the building’s load arrives once, and the piles are cast before either. The calculation is of the final state; a pile that is in tension before its building is complete, because the clay began to swell when the site was cleared, carries the full uplift with no head load at all — the 693 kN of the first point on the load figure.

Still open: a group whose piles shelter one another #

Every number here is for one pile. Piles in swelling clay come in groups, under strip foundations and ground beams, and the clay between closely spaced piles is held by all of them: it cannot rise past one pile without rising past its neighbours, which pull it back. Nine piles, and four times the settlement found that a group in settling ground interacts through the soil between its piles. Whether a group in heaving ground shares its uplift, so that each pile carries less tension than a pile alone, or whether the corner and edge piles, with clay rising freely on their outer sides, carry more than a single pile would, is the question that turns this one pile into the foundation of a house.