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Retaining Wall Design: worked example
A cantilever retaining wall checked for sliding, overturning, bearing and the stem, toe and heel reinforcement.
EN 1997-1:2004 — Eurocode 7: Geotechnical design + EN 1992-1-1:2004 — Eurocode 2 (RC design) · SI units · Calculator v1.0
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Inputs
| Wall type | Cantilever |
| Active earth pressure theory | Rankine |
| Stem height | 3 m |
| Footing thickness / stem thickness | 400 / 300 mm |
| Toe / heel length | 1.2 / 2.6 m |
| Embedment depth | 0.6 m |
| Base width | 1.8 m |
| Backfill unit weight γ | 18 kN/m³ |
| Friction angle φ / cohesion c | 30° / 0 kPa |
| Surcharge | 10 kPa |
| Backfill slope β / wall friction δ | 0° / 20° |
| Water table | No |
| Passive resistance | Not included |
| Concrete | C16/20 |
| Reinforcing steel | B500B |
| Cover | 50 mm |
| Stem / toe / heel bars | φ16 / φ16 / φ14 |
Design checks All checks pass
| Check | Required | Provided | Utilisation | Result |
|---|---|---|---|---|
| Overturning | 58.6 kN·m/m | 503.0 kN·m/m | 23.3% | PASS |
| Sliding | 49.4 kN/m | 59.8 kN/m | 82.7% | PASS |
| Bearing capacity | 53.2 kPa | 191.7 kPa | 27.7% | PASS |
| Middle-third (uplift) | e = 157 mm | B/6 = 683 mm | 23.0% | PASS |
| Stem flexure | 595 mm² | 603 mm² | 98.7% | PASS |
| Stem shear | 51.5 kN/m | 89.4 kN/m | 57.6% | PASS |
| Toe flexure | 445 mm² | 603 mm² | 73.7% | PASS |
| Toe shear | 24.8 kN/m | 112.2 kN/m | 22.1% | PASS |
| Heel flexure | 1144 mm² | 1232 mm² | 92.9% | PASS |
| Heel shear | 125.8 kN/m | 126.8 kN/m | 99.2% | PASS |
Calculation steps
Overturning stability (5 steps)
—
Active thrust components (soil / surcharge / water), unfactored
F = Σ ∫σ(z) dz, resolved at ψ from horizontal
ψ = β = 0.0°
Ph = 46.0 kN/m (soil 34.7 + surcharge 11.3 + water 0.0)
—
Resisting moment about the toe
Mr = ΣWi·xi + Pv·B
Mr = 503.0 + 0.0
Mr = 503.0 kN·m/m
—
Overturning moment about the toe
Mo = Ph-component heights × force, taken about the toe
Mo = 58.6 kN·m/m
EN 1997-1 §6.5.4(4) note / conventional practice
Factor of safety against overturning
FoS = Mr / Mo
FoS = 503.0/58.6
FoS = 8.59 ✓ (min 2)
EN 1997-1
Note
EC7 does not itself verify a rigid-body overturning limit state for a spread-footing retaining wall — it is subsumed by the eccentricity limit (below). This FoS is shown as a conventional cross-check, common in European practice, not a formal EC7 GEO/EQU verification.
Eccentricity & bearing pressure (3 steps)
—
Vertical resultant
N = ΣWi + Pv
N = 39.4 + 21.6 + 140.4 + 0.0
N = 201.4 kN/m
EN 1997-1 §6.5.4(4)
Eccentricity from footing centreline
e = B/2 − (Mnet/N)
e = 2050 − 444.4/201.4
e = -157 mm, B/6 = 683 mm ✓ within middle third
—
Base pressures
q = N/B·(1 ± 6e/B)
q,toe = 37.8 kPa, q,heel = 60.4 kPa
Sliding resistance (3 steps)
NAVFAC DM-7.2 / Das (conservative default)
Base friction & adhesion
δb = (2/3)φ, ca = 0.5c
δb = 16.5°, ca = 0.00 kPa
EN 1997-1 §6.5.3
Sliding resistance
R = N·tanδb + ca·B + Pp(reduced)
R = 201.4×tan(16.5°) + 0.0 + 0.0
R = 59.8 kN/m
EN 1997-1 §2.4.7.3.2 (DA1-C2: A2)
Design driving force (A2 action factors)
Hd = γG·(Ph,soil+Ph,water) + γQ·Ph,sur
Hd = 1.0×34.7 + 1.3×11.3
Hd = 49.4 kN/m, utilization = 82.7%
Ultimate bearing capacity (4 steps)
EN 1997-1 Annex D.3
Bearing capacity factors
Nq = e^(πtanφ)·tan²(45+φ/2), Nc = (Nq−1)cotφ, Nγ per code
φd = 24.8°
Nq = 10.43, Nc = 20.42, Nγ = 8.71
Vesic (1973)
Load-inclination factors (H parallel to B, strip footing m=2)
iq=(1−H/(V+A′c·cotφ))^m, iγ=(...)^(m+1)
V=201.4, H=49.4
iq = 0.569, iγ = 0.430, ic = 0.524
EN 1997-1 Annex D
Ultimate bearing resistance (strip, shape/depth factors = 1)
qult = c·Nc·ic + q·Nq·iq + 0.5·γ·B′·Nγ·iγ
B′ = B−2|e| = 3786 mm
qult = 191.7 kPa
EN 1997-1 §6.5.2.1
Utilization
Vd/(qult·A′) ≤ 1.0
qapplied = V/A′ = 201.4/3.786
= 53.2/191.7 = 27.7%
Stem design (critical section at footing top) (5 steps)
EN 1990 (γG=1.35, γQ=1.5)
Factored shear & moment at stem base
Mu = ψ-resolved factored thrust over Hstem
Hstem = 3000 mm
Mu = 59.0 kN·m/m, Vu = 51.5 kN/m
EC2 6.1
Stem base flexure: section design
K = MEd/(b·d²·fck); z = d·[0.5+√(0.25−K/1.134)] ≤ 0.95d
K = 59.0×10⁶/(1000×242²×16)
z = 228 mm
EC2 6.1
Stem base flexure: required steel
As = MEd/(fyd·z), fyd = fyk/1.15
As = 59.0×10⁶/(435×228)
As,req = 595 mm²
EC2 9.2.1.1 / 9.3.1.1
Minimum reinforcement
As,min = max(0.26·fctm/fyk, 0.0013)·b·d
As,min = 315 mm² → provide 3φ16 @ 333 mm
EC2 6.2.2
One-way shear at the stem base
k = 1.909, ρl = 0.246%, vRd,c = 0.369 MPa
VRd,c = 89.4 kN/m vs Vu = 51.5 kN/m
Toe design (critical section at stem front face) (4 steps)
—
Net factored upward pressure (gross bearing − self-weight)
qnet = qu − γG·γconc·tFooting
q,tip = 39.9 − 13.0 = 26.9; q,face = 45.3 − 13.0 = 32.3
Mu = 20.7 kN·m/m, Vu(d from face) = 24.8 kN/m
EC2 6.1
Toe flexure: section design
K = MEd/(b·d²·fck); z = d·[0.5+√(0.25−K/1.134)] ≤ 0.95d
K = 20.7×10⁶/(1000×342²×16)
z = 325 mm
EC2 6.1
Toe flexure: required steel
As = MEd/(fyd·z), fyd = fyk/1.15
As = 20.7×10⁶/(435×325)
As,req = 146 mm²
EC2 9.2.1.1 / 9.3.1.1
Minimum reinforcement
As,min = 445 mm² → provide 3φ16 @ 333 mm
Heel design (critical section at stem back face) (5 steps)
—
Net factored downward load (backfill + self-weight + surcharge − upward reaction)
wnet = γG·(γsoil·Hstem + γconc·tFooting) + γQ·qs − qu
w,tip = 100.9 − 58.3 = 42.5; w,face = 100.9 − 46.6 = 54.2
Mu = 156.9 kN·m/m, Vu(at face) = 125.8 kN/m
EC2 6.1
Heel flexure (tension at top): section design
K = MEd/(b·d²·fck); z = d·[0.5+√(0.25−K/1.134)] ≤ 0.95d
K = 156.9×10⁶/(1000×343²×16)
z = 316 mm
EC2 6.1
Heel flexure (tension at top): required steel
As = MEd/(fyd·z), fyd = fyk/1.15
As = 156.9×10⁶/(435×316)
As,req = 1144 mm²
EC2 9.2.1.1 / 9.3.1.1
Minimum reinforcement
As,min = 446 mm² → provide 8φ14 @ 125 mm
EC2 6.2.2(6)
Shear critical section
Checked at the face — net load is downward, no compression-strut relief to the stem
Design basis and assumptions
- National Annex: none applied as a whole — the EN recommended values are used, except where noted below. There is no National Annex selector; check the values against the annex for your project.
- Stem, toe and heel flexure reuse Foundation’s engine: the αcc = 0.85 lever-arm form, with fyd = fyk/1.15.
- Actions on the structure γG = 1.35, γQ = 1.5 (EN 1990 recommended).
- Active earth pressure uses classical Rankine or Coulomb theory — both assume a rigid wall and a homogeneous, drained backfill, not staged construction or wall flexibility.
- Soil unit weight, friction angle and cohesion must come from a geotechnical report, never assumed — bearing capacity is computed from those via the Meyerhof/Terzaghi general bearing equation (EC7 mode: EN 1997-1 Annex D); always cross-check against the report’s stated allowable pressure.
- Batter (sloped stem/wall faces) is not modeled — the stem is assumed uniform thickness.
- Water-table uplift beneath the footing base is not modeled — verify separately when a high water table is present.
- Passive resistance, if included, is reduced by a user-set mobilization factor since full passive resistance only develops after wall movement most designs don’t allow for.
- The footing (toe/heel) reuses Foundation’s own flexure and one-way-shear engine.
Example values for illustration only. Results are checked against a published validation suite; for real projects, have a licensed engineer review the results.