Coulomb Earth Pressure Calculator

Calculator Inputs

Pressure case

Choose the lateral condition to evaluate.

Wall height, H (m)

Vertical retained height of soil.

Soil friction angle, φ (deg)

Use the drained angle for long-term checks.

Wall friction angle, δ (deg)

Usually not greater than φ.

Wall face angle, α from horizontal (deg)

Use 90 for a vertical wall back face.

Backfill slope angle, β (deg)

Use 0 for level backfill.

Dry unit weight, γdry (kN/m³)

Used above the water table.

Saturated unit weight, γsat (kN/m³)

Used below the water table.

Water table depth from top (m)

Leave blank for dry conditions.

Uniform surcharge, q (kPa)

Covers traffic, slab, or storage surcharge.

Cohesion, c (kPa)

Included with a standard cohesion correction.

Water unit weight, γw (kN/m³)

Default fresh water value is 9.81.

Wall length out of plane (m)

Use 1 for force per meter run.

Integration points

More points create a smoother plot.

Reset Form

Example Data Table

These sample inputs help you test common retaining wall conditions.

Case	Mode	H (m)	φ (deg)	δ (deg)	α (deg)	β (deg)	γdry	γsat	q (kPa)	c (kPa)	Water depth (m)
Trial 1	Active	6.0	30	15	90	0	18.0	20.0	10	0	Blank
Trial 2	Active	8.0	32	12	85	8	18.5	20.5	25	5	3.0
Trial 3	Passive	5.0	34	10	90	0	19.0	21.0	0	0	1.5

Formula Used

Coulomb active coefficient

K_a = sin²(α + φ) / [sin²α · sin(α − δ) · (1 + √((sin(φ + δ) · sin(φ − β)) / (sin(α − δ) · sin(α + β))))²]

Coulomb passive coefficient

K_p = sin²(α − φ) / [sin²α · sin(α + δ) · (1 − √((sin(φ + δ) · sin(φ + β)) / (sin(α + δ) · sin(α + β))))²]

Effective vertical stress

Above the water table: σ′_v(z) = q + γ_dryz
Below the water table: σ′_v(z) = q + γ_dryz_w + (γ_sat − γ_w)(z − z_w)

Lateral stress used for plotting

Active: σ_h(z) = K_aσ′_v(z) − 2c√K_a + u(z)
Passive: σ_h(z) = K_pσ′_v(z) + 2c√K_p + u(z)
where u(z) = γ_w(z − z_w) below the water table.

Resultant thrust and line of action

P = ∫σ_h(z)dz
y = [∫σ_h(z)(H − z)dz] / P
The calculator evaluates these integrals numerically along the wall height.

How to Use This Calculator

Select the active or passive pressure case.
Enter wall height, soil friction, wall friction, wall angle, and backfill slope.
Provide dry and saturated unit weights.
Add the water table depth only when groundwater is present.
Enter surcharge and cohesion if those loads exist.
Use wall length of 1 meter to obtain force per meter run.
Click the calculate button to show the result block above the form.
Review the coefficient, resultant force, line of action, moment, table, and plot.
Use the export buttons to download the CSV summary or a PDF report.

Important Notes

This tool applies standard Coulomb earth pressure relationships with surcharge, cohesion correction, and hydrostatic water pressure.
It assumes homogeneous soil properties over the retained height.
For layered soils, seismic loads, compaction loads, and wall movement compatibility, use a detailed geotechnical design check.
Negative active effective soil pressure is clipped to zero for plotting, which mimics tension crack behavior near the top.

FAQs

1) When should I use active pressure?

Use active pressure when the wall can move slightly away from the backfill and mobilize the lower lateral state. Cantilever walls often approach this condition after enough outward deflection.

2) When is passive pressure appropriate?

Use passive pressure when soil in front of the wall is compressed by wall movement into the soil. It usually provides resistance for sheet piles, keying, and toe embedment checks.

3) What does the wall face angle mean?

The calculator uses the angle of the wall back face measured from the horizontal. A vertical wall back face is 90 degrees, which is the most common retaining wall input.

4) Why include wall friction?

Wall friction changes the soil-wall interaction and can materially affect the Coulomb coefficient. A rough wall usually lowers active pressure and changes passive resistance compared with a smooth surface.

5) How does groundwater affect the result?

Groundwater reduces the effective vertical stress below the water table but adds hydrostatic pressure. That combination often shifts the line of action and can increase total lateral load significantly.

6) Does cohesion always reduce active pressure?

Cohesion lowers active effective soil pressure in the short term and may create a tension zone near the top. Long-term design often uses reduced or zero cohesion if durability is uncertain.

7) What unit system does the calculator expect?

It uses a consistent metric stress-force system: meters, degrees, kPa, and kN/m³. If wall length is 1 meter, the thrust result is the force per meter run.

8) Can I use this for final structural design?

It is useful for preliminary sizing, checking trends, and generating reports. Final design should still confirm code load combinations, drainage assumptions, stability, and structural detailing.