Retaining wall

A cantilever retaining wall, per foot of wall: earth pressures, stability under service loads, and the stem, heel and toe designed to ACI 318-19 (13.3.6, Chapters 7, 22, 24 and 25).

Inputs of the retaining wall #

• Wall: stem height above the footing (the backfill is level with the top of the stem), stem thickness at the top and base (the back face is vertical, a thicker base batters the front face), footing thickness, toe and heel lengths, and an optional shear key (depth, width, position).
• Backfill and soil: the earth pressure theory (Rankine active with a sloped backfill, Coulomb active with the wall friction δ on the vertical plane through the heel, or at rest K0 = 1 − sin φ for level backfill), φ, β, γ, the water table above the base with the saturated unit weight, a uniform surcharge (dead or live), and the soil over the toe (its weight can be counted or ignored).
• Loads on the stem top: dead and live line loads.
• Stability and bearing: allowable pressure, base friction μ, the passive resistance factor and the top depth neglected, factors of safety for sliding and overturning (1.5 per IBC 1807.2.3), and whether the resultant must be in the middle third.
• Concrete and reinforcement: covers, stem vertical bars (earth face), heel top and toe bottom bars, stem horizontal and footing longitudinal bars; the load factor on H (1.6 prefilled) and λs for the toe and heel.

Auto-design (editor toolbar) varies the heel and toe (1/2-ft steps), stem base and footing thickness (2-in. steps) and every bar mat (size and spacing); the height, key, soil and loads are kept. Objectives: lowest cost index (concrete, formwork, reinforcement); least concrete, then cost. Every other input is kept; see Auto-design.

Checks performed #

The drawings (screen, report, DXF and PDF sheet) show the wall section: stem (battered front face), toe, heel and key, the backfill (level or sloped), the soil over the toe, the water table and the surcharge; the stem vertical bars with their standard hook into the footing, the heel top and toe bottom bars, the stem horizontal bars (one or both faces) and the footing longitudinal bars at their spacings; the service lateral pressure (earth + water + surcharge) on the vertical plane through the heel; and the service bearing pressure under the base, aligned under the section. Bar lengths, cut-offs, splices, the hook direction, key reinforcement, drainage and joints are not part of the calculation and are not drawn.

Limitations #

• Seismic earth pressure (Mononobe-Okabe), compaction pressures, cohesive backfill and global (slope) stability are not included; the key's own strength is not designed; counterfort walls are not covered.
• The backfill reaches the top of the stem; at-rest pressure is for level backfill only.
• The uplift distribution (full at the heel, zero at the toe) is an assumption for a drained toe.
• The ASCE 7-22 load factors on H (1.6 adding, and H at 1.0 in the service combinations) are entered as inputs; they are marked for verification against the ASCE 7-22 text, which is not on file. IBC 1807.2.3 (FS 1.5) is quoted from memory and marked the same way.

Verification examples #

Published worked example (backend/tests/test_verify_retaining_wall.py): the free StructurePoint example (ACI 318-19) that reproduces Darwin, Dolan and Nilson, Design of Concrete Structures, 16th Ed., Example 16.8: 13.5 ft tapered stem, 9.75 ft × 18 in footing, key, φ = 30°, 400 psf surcharge, f'c = 4500 psi. The example's stem is battered on the earth side and the program's on the front face, so the weights, the overturning factor of safety, the base pressures and the toe and heel moments are not compared.

Hand calculation of the default wall: 12 ft stem, 3 ft toe, 6 ft heel, 24 in key, Rankine, 250 psf live surcharge.