Structural Engineering & Statics
where the load goes
Concept

Compaction — where it appears

Densifying placed soil by rolling or vibrating it in layers, which raises its strength and stiffness. Against a wall it also leaves a horizontal pressure behind each pass of the roller, which can exceed the pressure the soil's own weight would make.

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

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 Where a bending stem sheds its compaction pressure. The share of the rigid build-up's pressure shed at each depth by a cantilever stem 3 m high, bending stiffness 67,500 kN·m² a metre (a concrete stem about 300 mm thick), backfilled in 250 mm lifts of soil at 20 kN/m³ and 30°, each compacted by a roller of 60 kN a metre: nothing at the base, which does not move; little in the top lift, which nothing is placed after; most, 20 per cent, at 0.9 m down, where the pressure was locked early and the stem went on moving away from it.

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

Named alongside it

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

Active pressureEarth pressureRetaining wallAt-rest pressureBackfillLateral pressureLoad pathLocked in stressPassive pressureResidual stressStiffness

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