Basement wall

A restrained (basement) retaining wall of concrete, per foot of wall, spanning vertically between the floor diaphragm at the top and the slab on grade or footing at the base: lateral earth, water and surcharge pressure, axial load from above, reactions to the diaphragm and the base, and the wall designed to ACI 318-19 (Chapters 6, 11 and 22).

Inputs of the basement wall #

• Wall: the span L between the base support and the diaphragm, the retained soil height (up to the span: grade may be below the floor), the thickness h, and the span condition: a propped cantilever (fixed at the footing, pinned at the floor) or a simple span (pinned at both). The real base lies between fixed and pinned; the choice is the engineer's. The wall is analysed as a one-way vertical strip of constant stiffness.
• Lateral pressure: an equivalent fluid pressure from the geotechnical report (with a second value below the water table that includes the water), at rest K0 = (1 − sin φ) OCR^sin φ (Jaky; Mayne and Kulhawy for an overconsolidated or compacted backfill, as in FHWA GEC 2 and AASHTO 3.11.5.2), or Rankine / Coulomb active for a wall that can yield (sloped backfill allowed, horizontal component used). A restrained wall does not move enough for active pressure; at rest or the report's value is the usual choice. With K, the water table adds hydrostatic pressure and the soil below it takes its effective unit weight. A uniform surcharge (dead or live) adds K q (with an equivalent fluid pressure, q × EFP / γ: the surcharge as an equivalent height of soil); compaction pressure can be entered the same way (2 ft of soil is common for short walls).
• Axial load from above: dead and live line loads at the top and their eccentricity toward the interior face (a moment P e at the top, tension on the exterior face); the wall's own weight is added below the top.
• Concrete and reinforcement: f'c, fy, λ, one or two layers of vertical bars (exterior and interior face, or one centered layer), covers, horizontal bars, and whether the wall is a single-story basement wall (the 11.7.2.3 exception to two layers).
• Code options: the load factor on H (1.6 prefilled, ASCE 7-22 2.3.1), the effective length factor k and the unsupported height ℓu for slenderness (k = 1.0 is permitted for nonsway members, 6.6.4.4.3), and the shear critical section (at d from the supports where the reaction compresses the member end, or at the supports).

Auto-design (editor toolbar) varies the wall thickness (2-in. steps) and the vertical bars of each face and the horizontal bars (size and spacing); the span, soil, water, loads and span condition 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 with the floor diaphragm and the slab or footing as stubs by others, the backfill grade, the water table, the surcharge, the vertical bars of each face and the horizontal bars at their spacings, and the service lateral pressure on the wall; beside it the factored shear and moment along the height under the combination with the largest moment. The floor, the footing, the slab on grade, dowels, splices, waterproofing and drainage are not part of the calculation.

Limitations #

• The footing (bearing, sliding) is not designed: the slab and the footing carry the reactions the calculation reports (see the wall footing and spread footing calculations).
• Seismic earth pressure, two-way action near corners and openings, crack control, deflection and the dowels into the footing are not included. Bar spacing follows Chapter 11 (11.7), which does not call for Table 24.3.2; ACI MNL-17(21) Retaining Walls Example 1 nevertheless checks Table 24.3.2 crack control on its basement wall. Whether to add that check here is an open item for the owner. Compaction pressure is entered as a surcharge or within the equivalent fluid pressure.
• At-rest and equivalent fluid pressures are for level backfill (a sloped backfill raises them by an amount the geotechnical engineer gives); Coulomb's vertical component of the thrust is not added to the axial force (conservative for a tension-controlled wall).
• A masonry (TMS 402) basement wall is not offered: TMS 402-22 is not on file (only TMS 402-13), and its slender wall provisions belong to the masonry wall calculations.

Verification examples #

Verification status: 25 values compared in 4 examples (2 published, 2 hand calculations from the cited equations): 21 within tolerance, 4 recorded deviations. Thin: only 2 published examples. Code basis: not determined. The code is cited, but no record shows a section-by-section read for this module.

Published worked example (backend/tests/test_verify_basement_wall.py): ACI E702.4, Buried Concrete Basement Wall Design (ACI E702 Example Problems, 2013, free from concrete.org): 12 in. wall, fixed base and pinned top, 15 ft between supports, equivalent fluid pressure 60 pcf with 2 ft of soil as surcharge, D = 2.5 and L = 1.5 kip/ft, #6 at 8 in. each face, f'c = 4000 psi. The example is written to ACI 318-11; the analysis values and the factored moment do not depend on the edition.

Hand calculations: a simple span under at-rest pressure (reactions W/3 and 2W/3, maximum moment 2WL/(9√3) and its factored value) and a propped wall under an eccentric top load (the carry-over moment −Mt/2 at the fixed base and the reaction (Mb − Mt)/L), all within 0.1 %.