ACI 318 Concrete Retaining Wall Calculator

Professional retaining wall design calculator. Preliminary ACI 318-based checks for cantilever concrete retaining walls: active earth pressure, overturning, sliding, bearing, and heel soil weight with surcharge.

Full original guide (expanded)

ACI 318 Concrete Retaining Wall Calculator

Run preliminary cantilever retaining wall checks for earth pressure, sliding, overturning, and bearing using ACI 318 aligned inputs.

Data Source and Methodology

Authoritative references for the underlying methods:

  • ACI 318 (Building Code Requirements for Structural Concrete) – concrete design provisions and detailing philosophy. Official source
  • ASCE 7-22 (Minimum Design Loads) – load combinations and surcharge concepts. Official source
  • Rankine Active Earth Pressure – classical earth pressure theory.

All calculations are strictly based on the formulas and data provided by these sources.

The Formulas Explained

Active coefficient (Rankine, level backfill): \\( K_a = \\tan^2\\!(45^\\circ - \\tfrac{\\varphi}{2}) \\)

Lateral earth pressure at base (no cohesion): \\( \\sigma_a = K_a\\,\\gamma\\,H \\)

Triangular resultant: \\( P_t = \\tfrac{1}{2} K_a\\,\\gamma\\,H^2 \\) acting at \\( H/3 \\) above base.

Uniform surcharge \\( q \\) adds a rectangle: \\( P_q = K_a\\,q\\,H \\) acting at \\( H/2 \\).

Total: \\( P_a = P_t + P_q \\). Overturning moment about toe: \\( M_{ot} = P_t\\tfrac{H}{3} + P_q\\tfrac{H}{2} \\).

Sliding: \\( FS_{sl} = \\dfrac{\\mu \\sum V}{P_a} \\). Overturning: \\( FS_{ot} = \\dfrac{\\sum M_{res}}{M_{ot}} \\).

Eccentricity at base: \\( e = \\dfrac{M_{res} - M_{ot}}{\\sum V} - \\tfrac{B}{2} \\) (sign per toe at \\(+x\\)).

Base pressure (no tension assumption): \\( q(x) = \\dfrac{\\sum V}{B} \\left(1 \\pm \\dfrac{6e}{B}\\right) \\Rightarrow q_{min}, q_{max} \\).

Glossary of Variables

  • H: retained height (m)
  • B: base width (m); toe: toe projection (m)
  • γ: unit weight of soil (kN/m³)
  • φ: friction angle (deg); μ: base–soil friction coefficient (–)
  • q: uniform surcharge (kPa = kN/m²)
  • Pa: total active lateral force (kN/m)
  • FSot, FSsl: safety factors for overturning and sliding
  • qmin, qmax: base contact pressures (kPa)
  • e: eccentricity of resultant from base centerline (m)
  • qallow: allowable soil bearing pressure (kPa)

How It Works: A Step-by-Step Example

Inputs: H=3.0 m, B=2.0 m, toe=0.6 m, stem=0.3 m, base=0.5 m, γ=19 kN/m³, φ=30°, q=10 kPa, μ=0.55, qallow=200 kPa; heel soil included.

  1. Compute \\(K_a = \\tan^2(45^\\circ-15^\\circ) = \\tan^2(30^\\circ) \\approx 0.333\\).
  2. \\(P_t=0.5\\times 0.333\\times 19\\times 3^2 \\approx 28.5\\,\\text{kN/m}\\); \\(P_q=0.333\\times 10\\times 3 \\approx 10\\,\\text{kN/m}\\).
  3. \\(P_a \\approx 38.5\\,\\text{kN/m}\\). Overturning moment: \\(M_{ot}\\approx P_t\\cdot H/3 + P_q\\cdot H/2\\).
  4. Stabilizing vertical \\(\\sum V\\): self-weight of concrete base+stem plus heel soil weight.
  5. Check \\(FS_{sl}=\\mu\\,\\sum V / P_a\\), \\(FS_{ot}=\\sum M_{res}/M_{ot}\\), and base pressures.

Frequently Asked Questions (FAQ)

Does this tool design reinforcement?

No. It provides preliminary geometry and stability checks. Final design requires flexural and shear design per ACI 318, bar selection, and detailing.

Can I model sloped backfill or seismic?

This version assumes level backfill and static conditions. For sloped backfill or seismic (e.g., Mononobe–Okabe), extend the earth pressure model and combinations per ASCE 7.

What safety factors should I target?

Common practice: FSot ≥ 2.0, FSsl ≥ 1.5, no tension at base, and qmax ≤ qallow. Always verify project-specific criteria.

How accurate are base pressures?

The linear distribution assumes rigid base and elastic soil reaction. Use geotechnical recommendations for settlement and bearing capacity.

Why include heel soil weight?

Soil above the heel increases stabilizing vertical load and resisting moment, improving sliding and bearing checks.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted text)
Active coefficient (Rankine, level backfill): \\( K_a = \\tan^2\\!(45^\\circ - \\tfrac{\\varphi}{2}) \\) Lateral earth pressure at base (no cohesion): \\( \\sigma_a = K_a\\,\\gamma\\,H \\) Triangular resultant: \\( P_t = \\tfrac{1}{2} K_a\\,\\gamma\\,H^2 \\) acting at \\( H/3 \\) above base. Uniform surcharge \\( q \\) adds a rectangle: \\( P_q = K_a\\,q\\,H \\) acting at \\( H/2 \\). Total: \\( P_a = P_t + P_q \\). Overturning moment about toe: \\( M_{ot} = P_t\\tfrac{H}{3} + P_q\\tfrac{H}{2} \\). Sliding: \\( FS_{sl} = \\dfrac{\\mu \\sum V}{P_a} \\). Overturning: \\( FS_{ot} = \\dfrac{\\sum M_{res}}{M_{ot}} \\). Eccentricity at base: \\( e = \\dfrac{M_{res} - M_{ot}}{\\sum V} - \\tfrac{B}{2} \\) (sign per toe at \\(+x\\)). Base pressure (no tension assumption): \\( q(x) = \\dfrac{\\sum V}{B} \\left(1 \\pm \\dfrac{6e}{B}\\right) \\Rightarrow q_{min}, q_{max} \\).
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

ACI 318 Concrete Retaining Wall Calculator

Run preliminary cantilever retaining wall checks for earth pressure, sliding, overturning, and bearing using ACI 318 aligned inputs.

Data Source and Methodology

Authoritative references for the underlying methods:

  • ACI 318 (Building Code Requirements for Structural Concrete) – concrete design provisions and detailing philosophy. Official source
  • ASCE 7-22 (Minimum Design Loads) – load combinations and surcharge concepts. Official source
  • Rankine Active Earth Pressure – classical earth pressure theory.

All calculations are strictly based on the formulas and data provided by these sources.

The Formulas Explained

Active coefficient (Rankine, level backfill): \\( K_a = \\tan^2\\!(45^\\circ - \\tfrac{\\varphi}{2}) \\)

Lateral earth pressure at base (no cohesion): \\( \\sigma_a = K_a\\,\\gamma\\,H \\)

Triangular resultant: \\( P_t = \\tfrac{1}{2} K_a\\,\\gamma\\,H^2 \\) acting at \\( H/3 \\) above base.

Uniform surcharge \\( q \\) adds a rectangle: \\( P_q = K_a\\,q\\,H \\) acting at \\( H/2 \\).

Total: \\( P_a = P_t + P_q \\). Overturning moment about toe: \\( M_{ot} = P_t\\tfrac{H}{3} + P_q\\tfrac{H}{2} \\).

Sliding: \\( FS_{sl} = \\dfrac{\\mu \\sum V}{P_a} \\). Overturning: \\( FS_{ot} = \\dfrac{\\sum M_{res}}{M_{ot}} \\).

Eccentricity at base: \\( e = \\dfrac{M_{res} - M_{ot}}{\\sum V} - \\tfrac{B}{2} \\) (sign per toe at \\(+x\\)).

Base pressure (no tension assumption): \\( q(x) = \\dfrac{\\sum V}{B} \\left(1 \\pm \\dfrac{6e}{B}\\right) \\Rightarrow q_{min}, q_{max} \\).

Glossary of Variables

  • H: retained height (m)
  • B: base width (m); toe: toe projection (m)
  • γ: unit weight of soil (kN/m³)
  • φ: friction angle (deg); μ: base–soil friction coefficient (–)
  • q: uniform surcharge (kPa = kN/m²)
  • Pa: total active lateral force (kN/m)
  • FSot, FSsl: safety factors for overturning and sliding
  • qmin, qmax: base contact pressures (kPa)
  • e: eccentricity of resultant from base centerline (m)
  • qallow: allowable soil bearing pressure (kPa)

How It Works: A Step-by-Step Example

Inputs: H=3.0 m, B=2.0 m, toe=0.6 m, stem=0.3 m, base=0.5 m, γ=19 kN/m³, φ=30°, q=10 kPa, μ=0.55, qallow=200 kPa; heel soil included.

  1. Compute \\(K_a = \\tan^2(45^\\circ-15^\\circ) = \\tan^2(30^\\circ) \\approx 0.333\\).
  2. \\(P_t=0.5\\times 0.333\\times 19\\times 3^2 \\approx 28.5\\,\\text{kN/m}\\); \\(P_q=0.333\\times 10\\times 3 \\approx 10\\,\\text{kN/m}\\).
  3. \\(P_a \\approx 38.5\\,\\text{kN/m}\\). Overturning moment: \\(M_{ot}\\approx P_t\\cdot H/3 + P_q\\cdot H/2\\).
  4. Stabilizing vertical \\(\\sum V\\): self-weight of concrete base+stem plus heel soil weight.
  5. Check \\(FS_{sl}=\\mu\\,\\sum V / P_a\\), \\(FS_{ot}=\\sum M_{res}/M_{ot}\\), and base pressures.

Frequently Asked Questions (FAQ)

Does this tool design reinforcement?

No. It provides preliminary geometry and stability checks. Final design requires flexural and shear design per ACI 318, bar selection, and detailing.

Can I model sloped backfill or seismic?

This version assumes level backfill and static conditions. For sloped backfill or seismic (e.g., Mononobe–Okabe), extend the earth pressure model and combinations per ASCE 7.

What safety factors should I target?

Common practice: FSot ≥ 2.0, FSsl ≥ 1.5, no tension at base, and qmax ≤ qallow. Always verify project-specific criteria.

How accurate are base pressures?

The linear distribution assumes rigid base and elastic soil reaction. Use geotechnical recommendations for settlement and bearing capacity.

Why include heel soil weight?

Soil above the heel increases stabilizing vertical load and resisting moment, improving sliding and bearing checks.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted text)
Active coefficient (Rankine, level backfill): \\( K_a = \\tan^2\\!(45^\\circ - \\tfrac{\\varphi}{2}) \\) Lateral earth pressure at base (no cohesion): \\( \\sigma_a = K_a\\,\\gamma\\,H \\) Triangular resultant: \\( P_t = \\tfrac{1}{2} K_a\\,\\gamma\\,H^2 \\) acting at \\( H/3 \\) above base. Uniform surcharge \\( q \\) adds a rectangle: \\( P_q = K_a\\,q\\,H \\) acting at \\( H/2 \\). Total: \\( P_a = P_t + P_q \\). Overturning moment about toe: \\( M_{ot} = P_t\\tfrac{H}{3} + P_q\\tfrac{H}{2} \\). Sliding: \\( FS_{sl} = \\dfrac{\\mu \\sum V}{P_a} \\). Overturning: \\( FS_{ot} = \\dfrac{\\sum M_{res}}{M_{ot}} \\). Eccentricity at base: \\( e = \\dfrac{M_{res} - M_{ot}}{\\sum V} - \\tfrac{B}{2} \\) (sign per toe at \\(+x\\)). Base pressure (no tension assumption): \\( q(x) = \\dfrac{\\sum V}{B} \\left(1 \\pm \\dfrac{6e}{B}\\right) \\Rightarrow q_{min}, q_{max} \\).
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

ACI 318 Concrete Retaining Wall Calculator

Run preliminary cantilever retaining wall checks for earth pressure, sliding, overturning, and bearing using ACI 318 aligned inputs.

Data Source and Methodology

Authoritative references for the underlying methods:

  • ACI 318 (Building Code Requirements for Structural Concrete) – concrete design provisions and detailing philosophy. Official source
  • ASCE 7-22 (Minimum Design Loads) – load combinations and surcharge concepts. Official source
  • Rankine Active Earth Pressure – classical earth pressure theory.

All calculations are strictly based on the formulas and data provided by these sources.

The Formulas Explained

Active coefficient (Rankine, level backfill): \\( K_a = \\tan^2\\!(45^\\circ - \\tfrac{\\varphi}{2}) \\)

Lateral earth pressure at base (no cohesion): \\( \\sigma_a = K_a\\,\\gamma\\,H \\)

Triangular resultant: \\( P_t = \\tfrac{1}{2} K_a\\,\\gamma\\,H^2 \\) acting at \\( H/3 \\) above base.

Uniform surcharge \\( q \\) adds a rectangle: \\( P_q = K_a\\,q\\,H \\) acting at \\( H/2 \\).

Total: \\( P_a = P_t + P_q \\). Overturning moment about toe: \\( M_{ot} = P_t\\tfrac{H}{3} + P_q\\tfrac{H}{2} \\).

Sliding: \\( FS_{sl} = \\dfrac{\\mu \\sum V}{P_a} \\). Overturning: \\( FS_{ot} = \\dfrac{\\sum M_{res}}{M_{ot}} \\).

Eccentricity at base: \\( e = \\dfrac{M_{res} - M_{ot}}{\\sum V} - \\tfrac{B}{2} \\) (sign per toe at \\(+x\\)).

Base pressure (no tension assumption): \\( q(x) = \\dfrac{\\sum V}{B} \\left(1 \\pm \\dfrac{6e}{B}\\right) \\Rightarrow q_{min}, q_{max} \\).

Glossary of Variables

  • H: retained height (m)
  • B: base width (m); toe: toe projection (m)
  • γ: unit weight of soil (kN/m³)
  • φ: friction angle (deg); μ: base–soil friction coefficient (–)
  • q: uniform surcharge (kPa = kN/m²)
  • Pa: total active lateral force (kN/m)
  • FSot, FSsl: safety factors for overturning and sliding
  • qmin, qmax: base contact pressures (kPa)
  • e: eccentricity of resultant from base centerline (m)
  • qallow: allowable soil bearing pressure (kPa)

How It Works: A Step-by-Step Example

Inputs: H=3.0 m, B=2.0 m, toe=0.6 m, stem=0.3 m, base=0.5 m, γ=19 kN/m³, φ=30°, q=10 kPa, μ=0.55, qallow=200 kPa; heel soil included.

  1. Compute \\(K_a = \\tan^2(45^\\circ-15^\\circ) = \\tan^2(30^\\circ) \\approx 0.333\\).
  2. \\(P_t=0.5\\times 0.333\\times 19\\times 3^2 \\approx 28.5\\,\\text{kN/m}\\); \\(P_q=0.333\\times 10\\times 3 \\approx 10\\,\\text{kN/m}\\).
  3. \\(P_a \\approx 38.5\\,\\text{kN/m}\\). Overturning moment: \\(M_{ot}\\approx P_t\\cdot H/3 + P_q\\cdot H/2\\).
  4. Stabilizing vertical \\(\\sum V\\): self-weight of concrete base+stem plus heel soil weight.
  5. Check \\(FS_{sl}=\\mu\\,\\sum V / P_a\\), \\(FS_{ot}=\\sum M_{res}/M_{ot}\\), and base pressures.

Frequently Asked Questions (FAQ)

Does this tool design reinforcement?

No. It provides preliminary geometry and stability checks. Final design requires flexural and shear design per ACI 318, bar selection, and detailing.

Can I model sloped backfill or seismic?

This version assumes level backfill and static conditions. For sloped backfill or seismic (e.g., Mononobe–Okabe), extend the earth pressure model and combinations per ASCE 7.

What safety factors should I target?

Common practice: FSot ≥ 2.0, FSsl ≥ 1.5, no tension at base, and qmax ≤ qallow. Always verify project-specific criteria.

How accurate are base pressures?

The linear distribution assumes rigid base and elastic soil reaction. Use geotechnical recommendations for settlement and bearing capacity.

Why include heel soil weight?

Soil above the heel increases stabilizing vertical load and resisting moment, improving sliding and bearing checks.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted text)
Active coefficient (Rankine, level backfill): \\( K_a = \\tan^2\\!(45^\\circ - \\tfrac{\\varphi}{2}) \\) Lateral earth pressure at base (no cohesion): \\( \\sigma_a = K_a\\,\\gamma\\,H \\) Triangular resultant: \\( P_t = \\tfrac{1}{2} K_a\\,\\gamma\\,H^2 \\) acting at \\( H/3 \\) above base. Uniform surcharge \\( q \\) adds a rectangle: \\( P_q = K_a\\,q\\,H \\) acting at \\( H/2 \\). Total: \\( P_a = P_t + P_q \\). Overturning moment about toe: \\( M_{ot} = P_t\\tfrac{H}{3} + P_q\\tfrac{H}{2} \\). Sliding: \\( FS_{sl} = \\dfrac{\\mu \\sum V}{P_a} \\). Overturning: \\( FS_{ot} = \\dfrac{\\sum M_{res}}{M_{ot}} \\). Eccentricity at base: \\( e = \\dfrac{M_{res} - M_{ot}}{\\sum V} - \\tfrac{B}{2} \\) (sign per toe at \\(+x\\)). Base pressure (no tension assumption): \\( q(x) = \\dfrac{\\sum V}{B} \\left(1 \\pm \\dfrac{6e}{B}\\right) \\Rightarrow q_{min}, q_{max} \\).
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).