Inputs
Example Data Table
| H (m) | γ (kN/m³) | φ (deg) | q (kPa) | B (m) | Lt (m) | μ | FS Sliding | FS Overturning | qmax (kPa) |
|---|---|---|---|---|---|---|---|---|---|
| 3.0 | 18 | 30 | 10 | 2.2 | 0.7 | 0.55 | ~1.6 | ~2.2 | ~160 |
| 4.0 | 19 | 32 | 15 | 2.8 | 0.9 | 0.50 | ~1.5 | ~2.0 | ~190 |
Formula Used
- Rankine active pressure coefficient: Ka = tan²(45° − φ/2).
- Active lateral force (soil): Pa,soil = 0.5 × Ka × γ × H².
- Active lateral force (surcharge): Pa,q = Ka × q × H.
- Overturning moment about toe: Mo = Pa,soil(H/3) + Pa,q(H/2).
- Resisting moments: Mr = Σ(Wi × xi) − U × (B/2).
- Sliding resistance: R = μV + Pp,reduced.
- Factors of safety: FSslide = R / Pnet, FSOT = Mr / Mo.
- Resultant and eccentricity: x = (Mr − Mo)/V, e = B/2 − x.
- Bearing pressures: qmax/min = (V/B) × (1 ± 6e/B) when |e| ≤ B/6.
How to Use This Calculator
- Enter wall height, soil properties, and surcharge loading.
- Provide base geometry: base width, toe length, and thicknesses.
- Set friction coefficient and decide whether to include soil over heel.
- Optionally include passive resistance with a conservative reduction factor.
- Optionally include uplift using water heights at heel and toe.
- Adjust acceptance criteria, then run the calculation.
- Review pass/fail checks and download CSV or PDF reports.
Technical Notes: Wing Wall Stability
1) What the checks represent
Wing walls behave like short retaining walls tied into an abutment or headwall. This tool evaluates three core service-stability checks: sliding, overturning, and bearing. For typical granular backfill, an internal friction angle of 28–36° often produces an active pressure coefficient Ka near 0.45–0.27, respectively. As height increases, lateral force grows with H2, so stability margins can change rapidly.
2) Lateral earth and surcharge loading
Active earth pressure is modeled using a Rankine approach with a horizontal backfill surface. The soil force is triangular, acting at H/3 above the base, while uniform surcharge creates a rectangular component acting at H/2. As a quick reference, a 10 kPa surcharge is equivalent to 10 kN per square meter of plan area, which can be significant for approach slabs, traffic, or construction staging loads.
3) Resisting weight and lever arms
Resisting moment is dominated by self‑weight and any soil over the heel. Normal‑weight concrete is commonly approximated at 24 kN/m³. Small geometry edits matter: shifting the centroid toward the toe increases resisting moment and reduces eccentricity. This calculator computes the resultant location from net moment and vertical load, then checks whether the middle‑third rule (|e| ≤ B/6) is satisfied.
4) Sliding resistance and passive soil
Sliding resistance combines base friction (μV) with optional passive resistance at the toe. Friction coefficients for concrete on compacted granular material often fall around 0.5–0.7, but project conditions vary. Passive pressure can be reduced to reflect uncertainty and potential excavation; conservative reduction factors (for example 0.3–0.7) are commonly used to avoid over‑reliance on passive support.
5) Interpreting factors of safety
The output reports FS for sliding and overturning, plus bearing pressure limits. Many designers target FSslide ≥ 1.5 and FSOT ≥ 2.0 for service conditions, then confirm geotechnical bearing capacity separately. If qmin becomes negative, partial uplift or tension is implied and the base configuration typically needs revision through geometry, keying, backfill changes, or drainage measures.
FAQs
1) Is this suitable for curved or skewed wing walls?
It is intended for straight wall segments using per‑meter (or per‑foot) strip analysis. For curved, tapered, or skewed geometry, use the tool for preliminary screening, then complete a project‑specific 3D or segmented check.
2) Which soil friction angle should I enter?
Use the effective friction angle for the retained backfill at service conditions. If you have lab or in‑situ data, use those. Otherwise, select a conservative value consistent with the specified backfill and compaction level.
3) What does “soil over heel” change?
Including soil over the heel increases vertical load and resisting moment, which usually improves sliding and overturning checks. Only include it when that soil is reliably present, compacted, and not expected to be excavated later.
4) Should I always include passive resistance?
Not always. Passive resistance can be reduced by future trenching, erosion, or poor compaction. If you include it, apply a conservative reduction factor and confirm site conditions and detailing (toe embedment, protection) support that assumption.
5) How do I interpret negative qmin?
A negative minimum bearing pressure indicates the resultant falls outside the middle third and part of the base would be in tension. In practice, adjust geometry, add weight, change backfill, or improve drainage to restore compression across the base.
6) Does uplift include full hydrostatic pressure?
The uplift model is simplified, using heel and toe water heights to form a linear pressure distribution. For critical structures, confirm groundwater levels, drainage provisions, and uplift assumptions with geotechnical inputs and site monitoring data.
7) Are the reported bearing pressures “allowable”?
The calculator reports contact pressures from statics. “Allowable” bearing depends on geotechnical capacity and settlement criteria. Compare qmax to a project‑approved allowable value, and verify settlement for the chosen foundation material.