Geotechnical Resource

Retaining Wall Stability Calculations

Calculation frameworks for retaining-wall sliding, overturning, eccentricity and base pressure, without prescribing design acceptance criteria.

Table of contents

External stability calculations for a gravity or cantilever retaining wall commonly include sliding, overturning or resultant location, base pressure, bearing resistance and global stability.

Topic guide: For background, method selection and related checks, see Retaining Wall Design.

The calculations must use one consistent free-body diagram and load combination. A favourable force should not be counted unless it can be relied upon for the design condition.

Force schedule

List each force separately with:

horizontal and vertical components
point of application
lever arm to the selected moment point
stabilising or destabilising role
permanent or variable classification
characteristic, factored or service value
groundwater and drainage condition

Common actions include wall weight, soil above the footing, earth pressure, surcharge, water pressure, uplift and structural loads.

Sliding check

A generic force ratio is:

$$ FS_{\mathrm{slide}}= \frac{\sum R_h}{\sum D_h} $$

Where $\sum R_h$ is the dependable horizontal resistance and $\sum D_h$ is the driving horizontal action.

Possible resistance components depend on the selected design framework and may include base shear, adhesion, keys or passive resistance. Passive resistance should never be included automatically.

Overturning moment ratio

Where a moment-ratio check is applicable:

$$ FS_{\mathrm{OT}}= \frac{\sum M_{\mathrm{resisting}}} {\sum M_{\mathrm{overturning}}} $$

The moment point and sign convention must be stated. Some design frameworks assess resultant location and bearing pressure rather than use a simple overturning factor.

Resultant location and eccentricity

Let total vertical force be $V$ and the net moment about the toe be $M_{\mathrm{toe}}$. The resultant distance from the toe is:

$$ \bar{x}=\frac{M_{\mathrm{toe}}}{V} $$

For base width $B$, eccentricity from the centre is:

$$ e=\frac{B}{2}-\bar{x} $$

The sign convention must remain consistent.

Base pressure for full contact

For a rectangular base with length $L$ and uniaxial eccentricity:

$$ q_{\mathrm{avg}}=\frac{V}{BL} $$ $$ q_{\mathrm{max,min}}= \frac{V}{BL} \left(1\pm\frac{6e}{B}\right) $$

This linear full-contact expression is applicable only while the assumed contact condition remains valid. If $q_{\mathrm{min}}<0$, a no-tension contact model or another selected method is required.

Compact worked framework

Assume:

$B=3.0$ m
$L=1.0$ m per metre length of wall
$V=300$ kN/m
resultant distance from toe $\bar{x}=1.35$ m

$$ e=1.50-1.35=0.15\ \mathrm{m} $$ $$ q_{\mathrm{avg}}=\frac{300}{3(1)}=100\ \mathrm{kPa} $$ $$ q_{\mathrm{max}}=100\left(1+\frac{6(0.15)}{3}\right)=130\ \mathrm{kPa} $$ $$ q_{\mathrm{min}}=100\left(1-\frac{6(0.15)}{3}\right)=70\ \mathrm{kPa} $$

These pressures are inputs to further bearing and settlement assessment. They are not proof of wall adequacy.

Separate checks still required

External wall calculations do not replace:

structural design
bearing-capacity assessment
settlement
global slope stability
drainage design
internal stability of reinforced systems
seismic assessment
construction-stage checks
scour or erosion assessment

Calculation controls

The tool should:

display a force and moment table
preserve load combinations
show included and excluded resistance
state the moment point
calculate resultant location and pressure
flag loss of full contact
link to the selected bearing method
avoid default acceptance limits

Related resources

Authoritative references

Final wall design requires an applicable design framework, complete load cases and coordinated geotechnical and structural review.