Structural Engineering & Statics
where the load goes
Series

Lateral pressure — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. Five loads behind one wall, and the water is the biggest. The horizontal pressure on a 6 m wall retaining soil at 18 kN/m³ with a friction angle of 30°, a surcharge of 10 kPa and the water table 2 m down, drawn once as the profile the wall feels and then once per term. The terms are surcharge 20.0 kN/m at 3.00 m, soil above water 12.0 kN/m at 4.67 m, soil at the water table 48.0 kN/m at 2.00 m, submerged soil 27.2 kN/m at 1.33 m, water 78.5 kN/m at 1.33 m, and they sum to 185.7 kN/m — matched to 7e-8 by integrating the drawn profile numerically. The largest single term is the water, at 78.5 kN/m: water has no shear strength, so its coefficient is exactly one where the soil's is 0.333, and it acts on top of the soil's effective stress rather than instead of it. The combined resultant sits at 1.90 m above the base, 0.317 of the height rather than the third point at 2.00 m that a pure triangle would give.

    The load that depends on what carries it

    Every other load in this collection is a number the structure is given. Retained soil is not — it pushes with a fraction of its own weight, and the fraction is decided by how far the wall moves. Six millimetres of retreat on a six-metre wall takes a third off the load, and being held still puts it back.

    part 1 · equilibrium
  2. 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.

    part 2 · equilibrium

All series