Concept

Retaining wall — where it appears

A wall that holds back ground at a change of level, resisting its pressure by its own weight, by bending from its base, or by anchors. Its load depends on how far it is allowed to move and on how the fill behind it was placed and compacted.

Named by 6 essays across 2 fields — each of them below, with the objects they name alongside it.

The prop load is decided by the digging, not by the hole. Prop forces in a 12 m excavation propped at 3 levels, with the force each prop reaches at any stage of the sequence drawn thick and the force the finished arrangement gives it drawn thin. The pale dots are the individual stages. The middle prop reaches 214 kN while the dig is at 9.5 m and finishes at 88 — a factor of 2.44 between the two, and the larger one is not in the final analysis anywhere. Terzaghi and Peck's apparent pressure diagram, a rectangle of 49.4 kN/m², reproduces the total of the staged maxima to 2% — which is what it is: an envelope of measured prop loads, back-figured into a pressure, and a shape nothing on a wall is ever loaded with.

Every prop has its own worst day

A braced excavation has no finished state worth analysing. It is dug in stages, a level of props goes in at each stage, and a prop's force is largely fixed the moment it is installed — so the force to design it for is the largest it sees during a sequence that appears on no calculation sheet, and which for the middle prop here is nearly two and a half times what the finished arrangement gives.

structures · Propped excavation

The roller's pressure, not the soil's. Horizontal pressure down the back of a wall, for backfill of 20 kN/m³ and φ′ = 30° behind a wall 3.0 m high, compacted by a roller of 60 kN per metre of its width. Dashed, the soil's own active pressure, Kₐ·γz (Kₐ = 0.33), and at-rest pressure, K₀·γz (K₀ = 0.50). Solid, Ingold's compaction envelope: rising as the passive limit γz/Kₐ to 27.6 kPa at 0.46 m, then constant at √(2pγ/π) = 27.6 kPa all the way down, since the active pressure would not reach it until 4.15 m. Its thrust is 76.6 kN per metre of wall against the active 30.0, and its moment about the base 106.3 kN·m against 30.0.

The pressure the roller leaves behind

A retaining wall is designed for the pressure of the soil it holds, a triangle growing with depth. The soil behind most walls was not tipped there. It was placed in layers and rolled, and each pass of the roller pushed the soil sideways against the wall harder than the soil's own weight ever could, and left most of that push locked in when it moved on. Behind a 3 m wall compacted by an ordinary vibrating roller the locked-in pressure is a constant 28 kPa from half a metre down, the thrust two and a half times the active triangle's and the moment at the base three and a half.

equilibrium · Lateral pressure

The stem that bends away from the roller

A roller compacting backfill against a wall leaves a lateral pressure behind it that the soil's weight alone would never make, and for a wall that cannot move that residual is Ingold's envelope. A cantilever stem moves as the fill goes up, and a residual locked in against it relaxes as the stem bends away. But not everywhere: the base never moves, so it keeps its pressure, and the last lifts have nothing placed after them, so they keep theirs. A 300 mm stem sheds an eighth of the rigid wall's base moment and the softest stem a third — never more, because the two ends of the stem are where the relief cannot reach.

equilibrium · Lateral pressure

Propped before it is filled, the stem keeps the roller's pressure. For a 3 m stem of stiffness 67,500 kN·m² a metre, fixed at its base, propped at its top by a slab cast first, backfilled in 250 mm lifts with a 60 kN/m roller: the lateral pressure on the stem after the last lift, in kPa, against depth — propped at its top before the fill (solid), the same stem as a free cantilever (dashed), a stem too stiff to move (dotted) and the active pressure. The propped stem moves at most 0.15 mm, in its middle, where the free cantilever's top moved 2.61 mm; it relaxes almost nothing, and its pressure lies on the stiff stem's along the whole height — the roller's residual, 27 kPa from half a metre down, four times the active pressure at mid-height.

The prop that holds what the roller left

A basement wall whose ground-floor slab is cast before the backfill spans between its base and the slab, and as the fill is compacted against it the wall bows by a sixth of a millimetre. A free cantilever stem leaned sixteen times as far and shed an eighth of the roller's pressure; the propped wall sheds one per cent. Its base moment falls to a third, which looks like a gain, but the pressure has not gone: the slab now carries 22.6 kN a metre against the 6 an active-pressure design gives it and the 9 of soil at rest.

equilibrium · Lateral pressure

The slab that shrinks away from the wall

A basement wall propped by its ground-floor slab before it is backfilled keeps the roller's pressure, and its slab takes it. Then the slab dries. Two millimetres of shrinkage at each end — about a year for a 30 m slab indoors — and a slab that only bears on the wall has let go of it, leaving a stem designed as propped to carry 2.6 times the base moment it was given. Tying the slab into the wall to stop that makes it worse: the slab goes on shrinking and pulls, and the base moment passes the free cantilever's.

equilibrium · Lateral pressure

The seasons ride on the shrinkage. How far the slab's end has moved away from the fill since the fill was finished, over six years, for slabs 10, 20, 30 m between walls at 60 per cent humidity, swinging 3.0 K either way each year, propping a 3 m stem fixed at its base, its top held by the slab cast before its fill went up in 250 mm lifts rolled at 60 kN/m. The slab lets go of the stem at 2.08 mm (dashed). 10 m: a seasonal swing of ±0.15 mm on shrinkage reaching 1.28 mm by year six; it still touches the stem in the sixth year. 20 m: a seasonal swing of ±0.30 mm on shrinkage reaching 2.55 mm by year six; it last touches the stem 3.4 years on. 30 m: a seasonal swing of ±0.45 mm on shrinkage reaching 3.83 mm by year six; it last touches the stem 1.3 years on.

The seasons that stop reaching the wall

A ground-floor slab that has shrunk away from the basement wall it propped moves with the seasons as well, a few tenths of a millimetre at each end every year. It looks like a ratchet waiting to happen: each winter the slab presses the stem back into its fill, and each push might lock a little more pressure in. On a 30 m slab it never gets the chance — the seasons ride on a shrinkage ten times larger, and the slab last touches the wall sixteen months after the fill is finished. On a 10 m slab it touches every year for good, and the stem still loses most of its prop.

equilibrium · Lateral pressure

Named alongside it

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

Compaction Active pressure Earth pressure Lateral pressure Residual stress At rest pressure Load path Passive pressure Propped cantilever Shrinkage Stiffness Apparent pressure

All concepts