Learn: Classical retaining-wall overturning FS
A retaining wall needs a consistent balance against overturning. This traditional overall factor of safety compares the supplied resisting total with the supplied driving total; it does not derive those totals from geometry.
What the formula is saying
Divide resisting moment by overturning moment, both taken about the same chosen pivot.
Read the symbols in plain language
- ΣMR
- Resisting moments
Resisting moments. Only compatible, available and correctly referenced resistance components belong in this total.
kN·m/mUse kN·m/m as the base unit shown here. Both totals use kN·m/m, on the same per-metre wall basis, so the final ratio is dimensionless. Use nonnegative resisting magnitude and a strictly positive driving magnitude.
- ΣMO
- Overturning moments
Overturning moments. Divide matching force or moment totals to obtain the stated global safety ratio.
kN·m/mUse kN·m/m as the base unit shown here. Both totals use kN·m/m, on the same per-metre wall basis, so the final ratio is dimensionless. Use nonnegative resisting magnitude and a strictly positive driving magnitude.
- FSOT
- Result to find
Classical retaining-wall overturning FS. Divide matching force or moment totals to obtain the stated global safety ratio.
ratio / no unit
Sort out the units first
Both totals use kN·m/m, on the same per-metre wall basis, so the final ratio is dimensionless. Use nonnegative resisting magnitude and a strictly positive driving magnitude.
Assumptions before calculating
This is an idealized study model with supplied soil parameters and loading. Ground investigation, drainage condition, groundwater, geometry and the governing design approach must be established by the responsible geotechnical design process.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find FSOT and explain the result in the stated output unit.
- ΣMR · Resisting moments
- 800 kN·m/m
- ΣMO · Overturning moments
- 300 kN·m/m
Identify the justified resisting total
Only compatible, available and correctly referenced resistance components belong in this total.
(800) = 800 kN·m/mCompare with the driving total
Divide matching force or moment totals to obtain the stated global safety ratio.
(800) ÷ (300) ≈ 2.666666667
Does this worked answer make sense?
A ratio of 1 means equality of the supplied resisting and driving totals, not automatic design acceptance. Doubling the driving total halves the ratio if resistance stays fixed.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- ΣMR · Resisting moments
- 1200 kN·m/m
- ΣMO · Overturning moments
- 500 kN·m/m
Identify the justified resisting total
Only compatible, available and correctly referenced resistance components belong in this total.
(1200) = 1200 kN·m/mCompare with the driving total
Divide matching force or moment totals to obtain the stated global safety ratio.
(1200) ÷ (500) = 2.4
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- ΣMR · Resisting moments
- 900 kN·m/m
- ΣMO · Overturning moments
- 400 kN·m/m
Find: Learn: Classical retaining-wall overturning FS
A hint, not the answer
Divide resisting moment by overturning moment, both taken about the same chosen pivot.
Both totals use kN·m/m, on the same per-metre wall basis, so the final ratio is dimensionless. Use nonnegative resisting magnitude and a strictly positive driving magnitude.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the justified resisting total
Only compatible, available and correctly referenced resistance components belong in this total.
(900) = 900 kN·m/mCompare with the driving total
Divide matching force or moment totals to obtain the stated global safety ratio.
(900) ÷ (400) = 2.25
Avoid the common trap
Do not reverse resistance and demand or combine factored and unfactored totals without a coherent design method. Do not compare moments about different pivots or omit the lever arm of water pressure.
When this method applies — and when it does not
This is a global-factor study check, not an automatic Eurocode partial-factor verification. All forces and lever arms must use the same pivot, and stabilizing actions may require different treatment from destabilizing actions. Bearing, contact, settlement, structural resistance and overall stability remain separate.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Classical retaining-wall overturning FS. Read the relevant soil phase, seepage, earth-pressure, settlement or foundation topic. Effective stress, drainage and idealized geometry determine whether the relationship applies.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.