ACI 318 Concrete Retaining Wall Calculator

This professional-grade retaining wall design calculator helps civil and structural engineers rapidly evaluate a cantilever concrete wall per ACI 318 stability checks. It computes active earth pressure (Rankine), stem base moment, sliding and overturning factors of safety, and bearing pressures—optimized for mobile, keyboard, and screen reader users.

Authoritative Data Source and Methodology

Primary codes and references:

  • ACI Committee 318. “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary.” 2019. https://www.concrete.org/store/productdetail.aspx?ItemID=31819
  • USACE. “Retaining and Flood Walls (EM 1110-2-2502).” 1994. https://apps.dtic.mil/sti/pdfs/ADA284320.pdf

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formulas Explained

Backfill assumed horizontal, wall friction neglected (Rankine):
Ka = (1 - sin φ) / (1 + sin φ) = tan²(45° − φ/2)

Active earth force (soil):
P_a = 1/2 · K_a · γ_s · H²
Surcharge-induced force:
P_q = K_a · q · H
Total lateral force: P = P_a + P_q

Overturning moment about toe:
M_o = P_a · (H/3) + P_q · (H/2)

Component weights (per unit length): W_i = γ · A_i; Resisting moment:
M_r = Σ(W_i · x_i) with x_i measured from the toe

Safety factors:
FS_ot = M_r / M_o, FS_sl = μ · ΣW / P

Resultant location and bearing (base width B):
x_R = (M_r − M_o)/W, e = |x_R − B/2|
q_max,q_min = (W/B) · (1 ± 6e/B)

Stem base moment (cantilever from base):
M_st = (K_a γ_s H³)/6 + (K_a q H²)/2

Glossary of Variables

  • H: wall height (m or ft)
  • a_toe, a_heel: toe and heel widths (m or ft)
  • t_stem, t_base: stem and base slab thicknesses (m or ft)
  • γ_s, γ_c: unit weights of soil and concrete (kN/m³ or pcf)
  • φ: soil friction angle (degrees)
  • q: uniform surcharge (kPa or psf)
  • μ: base friction coefficient (–)
  • K_a: Rankine active earth pressure coefficient (–)
  • P_a, P_q: lateral forces from soil and surcharge per unit length (kN/m or kips/ft)
  • M_o, M_r: overturning and resisting moments about toe per unit length (kN·m/m or kip·ft/ft)
  • W: total stabilizing vertical weight per unit length (kN/m or kips/ft)
  • B: total base width B = a_toe + t_stem + a_heel
  • e: resultant eccentricity from base centerline (m or ft)
  • qmax, qmin: extreme bearing pressures (kPa or ksf)
  • M_st: base moment in the cantilever stem (kN·m/m or kip·ft/ft)

How It Works: A Step-by-Step Example

Assume SI units and the defaults: H=4.0 m, a_toe=1.0 m, t_stem=0.35 m, a_heel=1.8 m, t_base=0.50 m, γ_s=18 kN/m³, γ_c=24 kN/m³, φ=32°, q=5 kPa, μ=0.5.

  1. Compute Ka: Ka = (1 − sin 32°)/(1 + sin 32°) ≈ 0.307.
  2. Earth forces: Pa = 0.5·0.307·18·4² ≈ 44.2 kN/m; Pq = 0.307·5·4 ≈ 6.1 kN/m; P ≈ 50.3 kN/m.
  3. Overturning: Mo = 44.2·(4/3) + 6.1·(4/2) ≈ 78.6 kN·m/m.
  4. Base width: B = 1.0 + 0.35 + 1.8 = 3.15 m. Weights:
    • W_base = 24 · (3.15 · 0.50) = 37.8 kN/m at x=1.575 m.
    • W_stem = 24 · (0.35 · 4.0) = 33.6 kN/m at x=1.0 + 0.175 = 1.175 m.
    • W_soil(heel) = 18 · (1.8 · 4.0) = 129.6 kN/m at x=1.0 + 0.35 + 0.9 = 2.25 m.
    ΣW ≈ 201.0 kN/m; Mr = Σ(W·x) ≈ 37.8·1.575 + 33.6·1.175 + 129.6·2.25 ≈ 356.6 kN·m/m.
  5. Stability: FS_ot = 356.6 / 78.6 ≈ 4.54; FS_sl = 0.5·201.0 / 50.3 ≈ 2.00.
  6. Bearing: x_R = (356.6 − 78.6)/201.0 ≈ 1.38 m; e = |1.38 − 3.15/2| ≈ 0.195 m ≤ B/6 (0.525 m). q0 = 201.0/3.15 ≈ 63.8 kPa; qmax ≈ 63.8·(1 + 6e/B) ≈ 63.8·(1 + 0.371) ≈ 87.3 kPa; qmin ≈ 40.3 kPa.
  7. Stem moment: M_st = Kaγ_sH³/6 + Ka q H²/2 ≈ 0.307·18·64/6 + 0.307·5·16/2 ≈ 58.9 + 12.3 ≈ 71.2 kN·m/m.

These results meet common preliminary criteria (FS_sl ≥ 1.5, FS_ot ≥ 1.5, e ≤ B/6, bearing within limits). Adjust inputs to fit your project requirements.

Frequently Asked Questions (FAQ)

What wall type does this calculator cover?

A cast-in-place cantilever retaining wall with a base slab (toe–stem–heel) and level backfill. It reports per-unit-length results (1 m or 1 ft).

Does it check reinforcement per ACI 318?

This tool focuses on global stability and stem base moment. Use the reported M_st to design reinforcement per ACI 318 detailing and strength provisions.

Can I include passive pressure or a shear key?

Not in this simplified tool. For conservatism, passive pressure and keys are excluded. You can increase sliding capacity by adding a key and rechecking with detailed analysis.

Are water pressures considered?

No. Design proper drainage behind the wall to avoid hydrostatic pressure. If groundwater is expected, include hydrostatic loads in your analysis.

What are acceptable safety factors?

Typical preliminary targets: FS against sliding ≥ 1.5, FS against overturning ≥ 1.5, resultant within middle third (e ≤ B/6), and bearing pressures within geotechnical limits. Follow your governing code and geotechnical report.

How accurate is this for non-level backfill?

This calculator assumes horizontal backfill with negligible wall friction. Use Coulomb theory or a geotechnical program for sloping backfill or wall friction effects.

Tool developed by Ugo Candido. Content verified by CalcDomain Engineering Editorial.
Last reviewed for accuracy on: .