US Standards Series · Part 9 of 9

Retaining Wall Design — ACI 318-25 & ASCE 7-22

A complete guide to cantilever retaining wall design: wall type selection, geometry pre-sizing, Rankine and Coulomb active earth pressure, overturning, sliding, and bearing stability checks, Mononobe-Okabe seismic earth pressure, ACI 318-25 stem and footing reinforcement, and drainage requirements. Both US Customary and SI units throughout.

Wall Types & When to Use
Geometry & Pre-Sizing
Earth Pressure — Rankine & Coulomb
Stability Checks
Seismic Earth Pressure — Mononobe-Okabe
Reinforcement Design (ACI 318-25)
Drainage & Practical Considerations

1. Wall Types & When to Use

Type 1

Gravity Wall

Height: H ≤ 3 ft (1 m)

Material: mass concrete or stone

Relies on self-weight; no reinforcement

Type 2

Cantilever Wall

Height: 4–25 ft (1.2–7.5 m)

Most common RC type; T-shaped footprint

Stem acts as cantilever beam; heel/toe in footing

Type 3

Counterfort Wall

Height: > 25 ft (7.5 m)

Counterforts every 8–15 ft reduce stem bending

More economical than thick cantilever for tall walls

Type 4

MSE Wall

Height: unlimited (40+ ft practical)

Mechanically stabilized earth; geosynthetic reinforcement

Common for highway and infrastructure applications

2. Geometry & Pre-Sizing (Cantilever Wall)

The following rules of thumb provide a starting geometry. All dimensions are subject to stability verification.

Dimension	Preliminary estimate	Notes
Footing width B	0.4 – 0.7 × H	Use 0.5H for initial sizing; wider for soft soils
Footing toe length L_t	0.2 – 0.3 × B	Shorter toe → more heel soil stabilizing moment
Footing thickness t_f	H/12 – H/10	Min 12 in (300 mm)
Stem base thickness t_s,base	H/12	Min 8 in (200 mm)
Stem top thickness	6–8 in (150–200 mm)	Taper from base to top
Key depth d_k	H/8 – H/6	Optional; increases passive resistance

3. Earth Pressure — Rankine & Coulomb

3.1 Rankine Active Pressure

Rankine theory assumes a smooth (frictionless) wall and a planar backfill surface. It is conservative and simpler than Coulomb.

Rankine active pressure coefficient K_a

Both K_a = (1 − sinφ) / (1 + sinφ) = tan²(45° − φ/2)

Total active force P_a (level backfill)

US P_a = ½ · K_a · γ_s · H² γs: pcf, H: ft → Pa: lb/ft

SI P_a = ½ · K_a · γ_s · H² γs: kN/m³, H: m → Pa: kN/m

Arm Acts at H/3 from base (triangular distribution)

3.2 Sloped Backfill — Modified K_a

Rankine K_a with backfill slope β

Both K_a = cosβ · [cosβ − √(cos²β − cos²φ)] / [cosβ + √(cos²β − cos²φ)]

β = angle of backfill slope from horizontal; φ = internal friction angle of soil. Valid for β ≤ φ.

3.3 Coulomb Active Pressure

Coulomb theory accounts for wall-soil friction (δ) and is less conservative than Rankine when δ > 0:

Coulomb K_a

Both K_a = sin²(α+φ) / {sin²α · sin(α−δ) · [1 + √(sin(φ+δ)sin(φ−β) / sin(α−δ)sin(α+β))]²}

α = angle of stem from horizontal (90° for vertical wall); δ = wall friction angle (typically 0.5φ – 0.67φ for concrete).

3.4 Passive Pressure and Surcharge

Passive pressure coefficient K_p

Both K_p = (1 + sinφ) / (1 − sinφ) = tan²(45° + φ/2)

Surcharge (uniform load q on backfill surface)

US P_as = K_a · q · H q: psf, H: ft → lb/ft

SI P_as = K_a · q · H q: kN/m², H: m → kN/m

Arm Acts at H/2 from base (rectangular distribution)

Soil type	φ (degrees)	γ_s (pcf)	γ_s (kN/m³)	K_a
Loose sand	28°	100	15.7	0.361
Dense sand	34°	115	18.1	0.283
Granular fill (typical)	30°	110	17.3	0.333
Stiff silty clay	25°	105	16.5	0.406

4. Stability Checks

Three stability modes must be verified at service load level (unfactored forces):

Overturning

FS_ot ≥ 2.0

1.5 seismic

Sliding

FS_sl ≥ 1.5

1.1 seismic

Bearing

q_max ≤ q_a

e ≤ B/6

4.1 Overturning

Factor of safety against overturning (about toe)

Both FS_ot = ΣM_R / ΣM_O ≥ 2.0 (static)

ΣM_R = sum of restoring moments about the toe (wall self-weight, soil on heel, surcharge on heel). ΣM_O = sum of overturning moments about the toe (lateral earth pressure and surcharge).

4.2 Sliding

Factor of safety against sliding

Both FS_sl = (μ · ΣV + P_p) / P_a,h ≥ 1.5 (static)

μ = base friction coefficient ≈ tanφ for granular soil (use 0.45–0.55 for concrete on granular). ΣV = total vertical force on base. P_p = passive resistance from soil in front of footing (often neglected conservatively). P_a,h = horizontal component of active pressure.

4.3 Bearing Pressure

Trapezoidal bearing pressure distribution

Both q_max,min = (ΣV / B) · (1 ± 6e/B)

Eccentricity e = B/2 − x̄_R

x̄_R = location of resultant measured from toe. For no tension at base: e ≤ B/6 (resultant within middle third). q_max must not exceed allowable bearing capacity q_a.

If e > B/6, the heel lifts and a triangular pressure distribution applies over 3(B/2 − e): q_max = 2ΣV / [3(B/2 − e)]. Aim to keep e ≤ B/6 for robust design.

4.4 Numerical Example

Given: H = 12 ft (3.66 m), B = 7 ft (2.13 m), φ = 30°, γ_s = 110 pcf (17.3 kN/m³), level backfill, no surcharge, stem friction μ = 0.45, allowable bearing q_a = 3,000 psf (144 kPa).

Step 1 — Earth pressure coefficient and total force

US K_a = tan²(45° − 30°/2) = 0.333

US P_a = ½ × 0.333 × 110 × 12² = 2,638 lb/ft

SI P_a = ½ × 0.333 × 17.3 × 3.66² = 38.4 kN/m

Arm Acts at H/3 = 4.0 ft (1.22 m) above base

Step 2 — Vertical loads (per foot of wall)

US W_stem = 150 pcf × (8/12) ft × 11.5 ft = 1,150 lb/ft

US W_footing = 150 × (12/12) × 7.0 = 1,050 lb/ft

US W_soil,heel = 110 × 11.5 × 4.5 = 5,693 lb/ft (approx.)

US ΣV ≈ 7,893 lb/ft

Step 3 — Stability checks

Overturning FS_ot = ΣM_R / M_O ≈ 27,700 / 10,553 = 2.65 ✓ (≥ 2.0)

Sliding FS_sl = (0.45 × 7,893) / 2,638 = 1.71 ✓ (≥ 1.5)

Bearing q_max ≈ 2,540 psf < 3,000 psf ✓

All three stability criteria are satisfied for this geometry. Stem design would proceed for M_u = 1.6 × P_a × H/3 at the footing top face, using f'_c = 3,000 psi and f_y = 60,000 psi per ACI 318-25.

5. Seismic Earth Pressure — Mononobe-Okabe

During earthquakes, walls experience an additional dynamic earth pressure increment. The Mononobe-Okabe (M-O) method is the standard approach per ASCE 7-22 Chapter 11 and NCHRP 611.

Seismic horizontal and vertical coefficients

Both k_h = S_DS/2 (typical for retaining walls)

Both k_v = ±k_h/2 (use k_v = 0 conservatively)

Dynamic active pressure increment ΔP_ae

US ΔP_ae = 0.5 · (1 − k_v) · γ_s · H² · (K_AE − K_a) lb/ft

SI ΔP_ae = 0.5 · (1 − k_v) · γ_s · H² · (K_AE − K_a) kN/m

Arm ΔP_ae acts at ≈ 0.6H from base

M-O seismic active earth pressure coefficient K_AE

Both K_AE = cos²(φ−ψ−α) / {cos(ψ)·cos²(α)·cos(δ+α+ψ)·[1+√(sin(φ+δ)sin(φ−ψ−β)/(cos(α−β)cos(δ+α+ψ)))]²}

Where ψ = arctan(k_h / (1 − k_v))

Check	Static FS	Seismic FS
Overturning	≥ 2.0	≥ 1.5
Sliding	≥ 1.5	≥ 1.1
Bearing	q_max ≤ q_a	q_max ≤ 1.33q_a

Simplified seismic check: For most retaining walls in SDC B/C with S_DS ≤ 0.50g, add ΔP_ae at 0.6H and recheck stability with the reduced seismic factors. Full M-O analysis is required for SDC D/E/F.

6. Reinforcement Design — ACI 318-25

6.1 Stem Reinforcement (Vertical, Earth Face)

The stem is designed as a cantilever beam fixed at the footing top. The critical section is at the base of the stem.

Factored moment at stem base

US M_u = 1.6 · P_a · H/3 (for triangular earth pressure) kip·ft/ft

SI M_u = 1.6 · P_a · H/3 kN·m/m

Design the stem as a singly-reinforced beam with b = 12 in (1 m). Vertical bars are placed on the earth (tension) face. Minimum reinforcement per ACI §11.6:

Minimum wall reinforcement ratio

Vertical ρ_l ≥ 0.0015 · b · h §11.6.1

Horizontal ρ_t ≥ 0.0025 · b · h §11.6.1

6.2 Footing Heel and Toe Reinforcement

Footing zone	Net upward pressure	Critical section	Bar face
Heel	q_net,heel = q_soil − γ_s·H (net upward)	At stem back face	Top (tension on top)
Toe	q_net,toe = q_max − γ_c·t_f	At stem front face	Bottom (tension on bottom)

The heel typically governs moment design in cantilever walls with a wide footing. Both sections are designed as one-way slab strips per ACI Chapter 7.

6.3 Shear Key — Design

A shear key cast monolithically with the footing increases passive resistance and is used when the sliding factor of safety is insufficient without it.

Passive force on shear key

US F_p,key = K_p · γ_s · (2d_k·H_b + d_k²) / 2 lb/ft

SI F_p,key = K_p · γ_s · (2d_k·H_b + d_k²) / 2 kN/m

d_k = key depth below footing bottom; H_b = depth of footing bottom from grade in front of wall. Place key at or slightly toward the heel side of the footing centroid.

Reinforcement Design (Cantilever Method)

The key is designed as a short cantilever extending below the footing slab, loaded by the horizontal passive pressure F_p,key:

Factored moment at key base (ACI §5.3.1, U = 0.9D + 1.0H)

Both M_u = 1.6 · F_p,key · (d_k / 2)

Required vertical reinforcement in key

Both A_s,req = M_u / (φ · f_y · (d − a/2))

Min A_s,min = max(3√f'_c/f_y, 200/f_y) · b_k · d US: psi; SI: 0.25√f'c/fy

b_k = key width (= footing thickness t_f at base, in most cases); d = key effective depth = d_k − cover − bar radius.

Construction requirements: The shear key must be cast monolithically with the footing — cold joints at the key base severely reduce passive resistance. Vertical dowels from the footing into the key must develop full A_s,req above the construction joint. Horizontal ties at spacing ≤ 12 in (300 mm) are required per ACI §11.7.

Retaining Wall Calculator (US Customary) → Retaining Wall Calculator (SI) →

7. Drainage & Practical Considerations

7.1 Drainage Requirements

Hydrostatic pressure can be catastrophic for retaining walls. Proper drainage eliminates it entirely:

Weep holes: ≥ 4 in (100 mm) diameter, spaced ≤ 10 ft (3 m) on center along the wall base
Drainage blanket: 12–18 in (300–450 mm) of clean granular fill directly behind the stem, connected to weep holes
Filter fabric: Geotextile between native backfill and drainage blanket prevents clogging

7.2 Hydrostatic Pressure (If Undrained)

If drainage cannot be assured (saturated backfill or design requirement), add hydrostatic pressure to the earth pressure calculation:

Hydrostatic pressure (water table at backfill surface)

US P_w = ½ · γ_w · H² γ_w = 62.4 pcf

SI P_w = ½ · γ_w · H² γ_w = 9.81 kN/m³

For partially saturated backfill, use the submerged unit weight γ' = γ_sat − γ_w below the water table. Add K_a·γ'·H' plus the full hydrostatic head γ_w·H'.

7.3 Additional Practical Notes

Specify minimum concrete: f'_c = 4,000 psi (28 MPa); cover = 2 in (50 mm) for earth face, 1.5 in (38 mm) for formed face
Use a construction joint between the footing and the stem; provide starter bars at ≥ L_d below the joint
Consider settlement — differential settlement between wall and adjacent structure can crack stem; joint or flexible connection may be needed
For walls > 15 ft (4.5 m), require a geotechnical investigation with soil boring for actual φ, γ, and bearing capacity

The single most common cause of retaining wall failure is inadequate drainage, not structural deficiency. Always specify and inspect drainage systems.

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Jump to any article or use the calculators to apply what you've learned:

1. Introduction 2. Materials 3. Loads 4. Seismic 5. Load Combos 6. RC Design 7. Steel Design 8. Serviceability

Disclaimer: This article presents general principles for retaining wall design per ACI 318-25 and ASCE 7-22 for educational purposes. Actual designs require a geotechnical investigation, a licensed structural engineer, and compliance with local codes. Soil conditions vary significantly by site.

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Retaining Wall Design — ACI 318-25 & ASCE 7-22

Contents

1. Wall Types & When to Use

2. Geometry & Pre-Sizing (Cantilever Wall)

3. Earth Pressure — Rankine & Coulomb

3.1 Rankine Active Pressure

3.2 Sloped Backfill — Modified Ka

3.3 Coulomb Active Pressure

3.4 Passive Pressure and Surcharge

4. Stability Checks

4.1 Overturning

4.2 Sliding

4.3 Bearing Pressure

4.4 Numerical Example

5. Seismic Earth Pressure — Mononobe-Okabe

6. Reinforcement Design — ACI 318-25

6.1 Stem Reinforcement (Vertical, Earth Face)

6.2 Footing Heel and Toe Reinforcement

6.3 Shear Key — Design

Reinforcement Design (Cantilever Method)

7. Drainage & Practical Considerations

7.1 Drainage Requirements

7.2 Hydrostatic Pressure (If Undrained)

7.3 Additional Practical Notes

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Related Tools & Guides

3.2 Sloped Backfill — Modified K_a