Rankine Earth Pressure Calculator for Retaining Wall Analysis

Input Data

The page is vertically stacked, while the form becomes three columns on large screens, two on medium screens, and one on mobile screens.

Wall Height, H (m)

Soil Friction Angle, φ (degrees)

Backfill Slope, β (degrees)

Dry Unit Weight, γ_d (kN/m³)

Saturated Unit Weight, γ_sat (kN/m³)

Cohesion, c (kPa)

Uniform Surcharge, q (kPa)

Water Table Depth from Surface (m)

Water Unit Weight, γ_w (kN/m³)

Graph Sample Count

Example Data Table

This simple reference case uses level backfill, no cohesion, and no groundwater so you can quickly verify the behavior.

Parameter	Example Value	Comment
Wall Height, H	6.0 m	Reference retaining wall height
Friction Angle, φ	30°	Typical granular backfill
Backfill Slope, β	0°	Level backfill surface
Dry Unit Weight, γ	18 kN/m³	Used across the full height
Cohesion, c	0 kPa	Pure frictional soil example
Surcharge, q	12 kPa	Uniform live load at the surface
Calculated K_a	0.333	For φ = 30° and β = 0°
Calculated K_p	3.000	Reciprocal form for level backfill
Base Active Pressure	40.0 kPa	K_a(γH + q)
Total Active Thrust	132.0 kN/m	K_a(γH²/2 + qH)

Formula Used

Rankine active coefficient for a sloping backfill
K_a = cosβ × [cosβ − √(cos²β − cos²φ)] / [cosβ + √(cos²β − cos²φ)]

Rankine passive coefficient for a sloping backfill
K_p = cosβ × [cosβ + √(cos²β − cos²φ)] / [cosβ − √(cos²β − cos²φ)]

Effective vertical stress
σ′_v = q + γ_dz_dry + γ′z_sub
where γ′ = γ_sat − γ_w

Water pressure below the water table
u = γ_w(z − z_w)

Total lateral stresses
σ_h,a = max(K_aσ′_v − 2c√K_a, 0) + u
σ_h,p = max(K_pσ′_v + 2c√K_p, 0) + u

Resultant force and lever arm
P = ∫σ_hdz, y = [∫σ_h(H − z)dz] / P

The calculator samples the full wall depth numerically, integrates the pressure profile by the trapezoidal rule, and reports the thrust location above the base.

How to Use This Calculator

Enter the wall height and the soil friction angle.
Set the backfill slope angle. Use zero for a level backfill.
Provide dry and saturated unit weights. The saturated value is only used below the water table.
Enter cohesion and surface surcharge when applicable.
Leave the water table blank for dry conditions, or enter its depth below ground surface.
Choose a graph sample count. Higher values create a smoother plot.
Press the calculate button to show coefficients, pressures, thrusts, table values, and the Plotly graph above the form.
Use the CSV and PDF buttons to export the summary and pressure profile.

Engineering Assumptions

Vertical wall face.
Smooth wall with zero wall friction.
Homogeneous soil properties within dry and submerged zones.
Planar ground surface defined by β.
Uniform surcharge over the backfill surface.
Hydrostatic water pressure below the water table.

FAQs

1. What does this calculator estimate?

It estimates Rankine active pressure, passive pressure, net pressure, thrust magnitude, thrust location, water pressure, and tension crack depth for a retaining wall section.

2. When should I use the active result?

Use the active result when the wall can move enough away from the soil to mobilize active conditions. That value is common for retaining wall backfill design checks.

3. When is the passive result important?

Passive resistance matters where soil in front of a wall, key, or embedded toe is compressed. Designers often apply reduction factors because full passive resistance may not always develop.

4. Why does the calculator ask for saturated unit weight?

Below the water table, effective stress uses submerged unit weight, not dry unit weight. The saturated value lets the calculator determine submerged behavior and add hydrostatic pressure correctly.

5. Why can the active pressure near the top become zero?

Cohesion can reduce the calculated active stress near the surface. Negative active values are physically treated as zero, which may indicate a tension crack region in cohesive soils.

6. Does this handle wall friction or Coulomb theory?

No. This page applies Rankine theory for a smooth vertical wall. If wall friction, wall batter, or irregular geometry matters, use a Coulomb or more advanced method.

7. Why is the backfill slope limited?

For the Rankine sloping-ground equations used here, the slope angle must stay below the soil friction angle. Otherwise the square-root term becomes invalid and the theory breaks down.

8. Are the exported files useful for reports?

Yes. The CSV exports numerical results and the full pressure profile, while the PDF summarizes inputs, coefficients, thrusts, and selected depth values for documentation.