Wall Verification Calculator — Overturning and Sliding
Once the static and seismic thrusts are known, the retaining wall must satisfy three basic conditions: no overturning, no sliding, and no contact pressures exceeding the allowable bearing capacity of the soil. This calculator determines the factors of safety against overturning (FS_v) and sliding (FS_d) based on the wall geometry, acting forces, and bearing ground resistance, in static and seismic combinations in accordance with BS EN 1997-1 (Eurocode 7) and practices from the Highways Agency Design Manual for Roads and Bridges.
What does it verify and when is it applied?
Three classic failure modes: overturning (rotation about the toe), sliding (translation at the base), and bearing capacity (failure beneath the toe). This calculator focuses on the first two and leaves bearing capacity to the Terzaghi/Vesic tool. It applies to gravity walls of concrete or masonry, reinforced concrete cantilever walls, bridge abutments, and L-shaped walls. It does not cover anchored walls or sheet pile walls, which require specific methods of analysis for penetration and embedment.
Applied Formulas
FS overturning: FS_v = ΣM_stabilising / ΣM_overturning
M_stabilising: self-weight of wall + weight of backfill on heel + passive thrust (if considered)
M_overturning: active thrust + surcharge + seismic thrust ΔPae (applied at 0.6·H)
FS sliding: FS_d = (N · tan δb + c_b · B + Pp) / ΣFh
N = sum of vertical forces (weight + vertical components of thrust)
δb = base-soil friction angle (typically 2φ/3)
c_b = cohesion at the base (typically 2c/3)
Pp = reduced passive thrust (if considered)
ΣFh = total horizontal active thrust
Minimum FS BS EN 1997-1 (Eurocode 7):
Static: FS_v ≥ 1.5; FS_d ≥ 1.5
Seismic: FS_v ≥ 1.2; FS_d ≥ 1.1
Calculation example
| Parameter | Value |
|---|---|
| Wall height H | 4.0 m |
| Base width B | 2.5 m |
| Coping width | 0.6 m |
| Unit weight concrete γc | 24 kN/m³ |
| Unit weight backfill γ | 19 kN/m³ |
| φ backfill | 32° |
| Active thrust Pa | 41.8 kN/m (at H/3) |
| Seismic increment thrust ΔPae | 36.0 kN/m (at 0.6·H) |
| δ base-soil | 2·32/3 = 21° |
Wall weight (approx. trapezoidal): W = γc · (B+coping)/2 · H = 24 · 1.55 · 4 = 148.8 kN/m. Weight of backfill on heel = γ · (B − coping) · H = 19 · 1.9 · 4 = 144.4 kN/m. N = W + W_backfill = 148.8 + 144.4 = 293.2 kN/m. Stabilising moment about the toe (approx. lever arm 1.25 m wall, 1.55 m backfill): M_stab = 148.8 · 1.25 + 144.4 · 1.55 = 186 + 223.8 = 409.8 kN·m/m. Static overturning moment: M_overt = Pa · H/3 = 41.8 · 1.33 = 55.6 kN·m/m. Static FS_v = 409.8 / 55.6 = 7.37 ≫ 1.5 OK. Seismic overturning moment: M_overt_s = 41.8·1.33 + 36.0·2.4 = 55.6 + 86.4 = 142.0 kN·m/m. Seismic FS_v = 409.8 / 142.0 = 2.89 > 1.2 OK. Static sliding: FS_d = 293.2 · tan 21° / 41.8 = 293.2 · 0.384 / 41.8 = 112.6 / 41.8 = 2.69 > 1.5 OK. Seismic: FS_d = 112.6 / (41.8 + 36.0) = 112.6 / 77.8 = 1.45 > 1.1 OK.
Result: Static FS_v = 7.37, FS_d = 2.69 · Seismic FS_v = 2.89, FS_d = 1.45. All comply with BS EN 1997-1 (Eurocode 7).
Interpretation of results
FS_v and FS_d are generous in static but tighter in seismic — a typical pattern in projects in high seismicity zones. If the seismic FS_d had fallen below 1.1, solutions include: increasing base width, adding a shear key to increase Pp, or increasing wall weight with a longer heel. Bearing capacity beneath the toe must be verified separately: high eccentricity can generate contact stresses above qadm even if the overturning and sliding FS pass.
Reference standards
- BS EN 1997-1 (Eurocode 7) — Geotechnical design (minimum static and seismic FS)
- BS EN 1998-5 (Eurocode 8) — Seismic design of structures
- BS 8004 — Code of practice for foundations
- BS EN 1997-1 (Eurocode 7) — Geotechnical design
- Highways Agency Design Manual for Roads and Bridges — Section 11
- BSI standard
Frequently asked questions
Do I include passive thrust in sliding?
Only if the toe is embedded at least 0.5-1.0 m in firm undisturbed soil and it is guaranteed that this earth will not be excavated in the future. Even so, it is recommended to reduce it to 0.3-0.5·Pp due to the displacement required to mobilise it. If in doubt, neglecting it is conservative.
What do I do if the seismic sliding FS is just below 1.1?
Lower-cost alternatives: add a shear key under the base to mobilise additional passive thrust, extend the heel to increase the weight of backfill on the footing, or roughen the base (corrugations) to increase δ_base. Recalculating with these improvements usually resolves the deficit.
How do I calculate eccentricity and verify stresses?
e = B/2 − x_N, where x_N is the position of the resultant relative to the toe. If |e| ≤ B/6, all pressures are compressive and the extreme values are q = N/B · (1 ± 6e/B). If |e| > B/6 there is uplift at one edge and the distribution is triangular. In seismic zones BS EN 1997-1 (Eurocode 7) allows e ≤ B/3.
Is δ base-soil equal to φ of the backfill?
No. δ_base depends on the foundation soil (not the backfill) and is typically taken as 2/3 of φ of that soil. If the base is concrete on dense sand (φ = 36°), δ_base ≈ 24°. If there is a concrete-saturated clay interface, δ is very low and is supplemented by c_b.