Gravity wall
A gravity retaining wall of mass (plain) concrete or stone masonry, per foot of wall: the earth pressure, the stability of the wall on its base, and the strength of the stem at five sections (plain concrete to ACI 318-19 Chapter 14, or stone masonry by the no-tension rule and an allowable stress).
Inputs of the gravity wall #
- Wall: height H from the base bottom to the top, top width, front batter and back batter (horizontal per vertical; a back batter slopes out under the backfill), an optional base slab (thickness, toe and heel projections), the material (plain concrete with f'c and λ, or stone masonry with the allowable compressive stress of its joints) and its unit weight.
- Backfill and soil: the earth pressure theory: Coulomb on the back of the wall (wall friction δ, 2/3 φ is common; the back's inclination θ comes from the batter) or Rankine on the vertical plane through the heel (the soil over the heel and over a sloped back moves with the wall and counts as weight, the thrust acts parallel to the slope); φ, β, γ, a uniform surcharge (dead or live) and the soil depth in front for passive resistance.
- Stability and bearing: allowable bearing pressure, base friction coefficient μ, the passive reduction factor and the neglected top depth, the factors of safety for sliding and overturning, the eccentricity limit (B/6 keeps the whole base in compression), and the load factor on H for the concrete sections.
Auto-design (editor toolbar) varies the top width (1/2-ft steps), the front batter and the toe and heel of a base slab; the height, slab thickness, soil and loads are kept. Objective: least wall area. Every other input is kept; see Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Earth pressure | Coulomb Ka(φ, δ, β, θ) with the thrust at δ + θ below the horizontal, or Rankine Ka(φ, β) on the vertical plane through the heel; Pa = ½ K γ H² at H/3; surcharge K q H at H/2 (× cos θ / cos(θ − β) for Coulomb with a sloped backfill); drained backfill |
| Sliding | (μN + Pp) / T ≥ FS; a live surcharge over the wall or heel does not resist |
| Overturning | Resisting over overturning moment about the toe ≥ FS (the vertical earth thrust resists) |
| Bearing and eccentricity | Trapezoidal or triangular base pressure under D + H and D + H + L (ASCE 7-22 2.4.1) against the allowable; eccentricity within the entered limit |
| Plain concrete sections | At five levels of the stem, under 1.4D + H, 1.2D + H + 1.6L and 0.9D + H (2.3.1): tension face Mu/Sm − Pu/Ag ≤ φ5λ√f'c (14.5.3.1), shear Vu ≤ φ(4/3)λ√f'c b h (14.5.5.1), φ = 0.60 |
| Masonry joints | At five levels, service: resultant in the middle third (no tension) and the maximum compressive stress against the allowable |
The drawings (screen, report, DXF and PDF sheet) show the wall section (stem and base slab, backfill, soil in front, surcharge, the horizontal earth pressure on the back plane, the height, base and top dimensions) and the service bearing pressure under the base. Drainage, weep holes, joints and any base slab reinforcement are not part of the calculation.
Limitations #
- A drained backfill is assumed: no water pressure or uplift. Seismic earth pressure and global stability are not included.
- Coulomb on the back of the wall is not offered with a heel (the soil over the heel moves with the wall: use Rankine).
- The base slab is taken as part of the mass; its bending strength as a cantilever toe or heel is not checked (keep it thick enough, or design it as a cantilever wall footing).
- ACI 318-19 14.5.1.7 (thickness less 2 in. for concrete cast against soil) is not applied to the stem sections.
Verification examples #
Verification status: 11 values compared in 2 examples (0 published, 2 hand calculations from the cited equations): 11 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: written without the code document on hand, and confirmed only in part through published examples.
No free published gravity-wall example with complete data was available (research/DOCUMENTS_NEEDED.md lists the textbooks and the USACE and NAVFAC manuals). Hand calculations in closed form (backend/tests/test_verify_gravity_wall.py):
| What it checks | Hand | ILX Calcs |
|---|---|---|
| Rankine Ka, φ = 32° | 0.3073 | 0.3073 |
| Rectangular wall 4 × 8 ft: overturning moment / resisting moment ÷ 2 | 3.146 / 4.640 kip-ft | 3.146 / 4.640 |
| Sliding force / toe pressure | 1.180 kip/ft / 2.340 ksf | 1.180 / 2.340 |
| Plain concrete tension at the base, 0.9D + 1.6H | 5.86 psi | 5.86 |
| Coulomb Ka, δ = 21°, vertical back | 0.2751 | 0.2751 |
| Trapezoidal wall: overturning / resisting ÷ 2 | 6.422 / 8.138 kip-ft | 6.422 / 8.138 |
| Sliding force / resistance ÷ 1.5 | 1.798 / 2.176 kip/ft | 1.798 / 2.176 |