Earth Pressure Calculator

Rankine coefficients (horizontal backfill, smooth wall assumption):

• Ka = tan²(45° − φ/2)
• Kp = tan²(45° + φ/2)
• Ko = 1 − sinφ (Jaky, normally consolidated)

Effective stress approach (if a water table is provided):

• Above water table: σ′v = γ·z + q
• Below water table: σ′v = γ·zw + (γsat − γw)(z − zw) + q
• Hydrostatic pressure below water table: u = γw(z − zw)

Horizontal pressure (Rankine c–φ approximation):

• Active: σh = Ka·σ′v − 2c√Ka + u
• Passive: σh = Kp·σ′v + 2c√Kp + u
• At-rest: σh ≈ Ko·σ′v − 2c√Ko + u

For active and at-rest, negative values are set to zero to represent loss of contact.

1. Select the earth pressure state: active, passive, or at-rest.
2. Enter wall height, soil friction angle, unit weight, and surcharge.
3. If soil has cohesion, enter c; otherwise keep it at zero.
4. If groundwater is present, enable water and enter zw and γsat.
5. Click Calculate to show pressures, resultant force, and location.
6. Use the download buttons to save results as CSV or PDF.

1) Why earth pressure matters

Retaining walls commonly fail by sliding, overturning, bearing overstress, or global instability. Lateral pressure is the driver for these checks. For preliminary sizing, engineers often express the resultant lateral force per meter of wall. This calculator reports that resultant and its line of action.

2) Typical input ranges from field practice

Granular backfill friction angles often fall near 28–38°, while cohesive fills can be lower if moisture increases. Moist unit weight is frequently 16–20 kN/m³, and saturated unit weight is often 19–22 kN/m³. Uniform surcharges for traffic or storage are commonly 5–20 kPa, depending on use.

3) Active, passive, and at-rest conditions

Active pressure represents the reduced lateral stress after the backfill yields slightly and mobilizes shear strength. Passive pressure is the opposite; it requires wall movement into the soil and can be difficult to fully mobilize. At-rest pressure applies when movement is restrained, such as basement walls braced by slabs.

4) How coefficients shape the pressure diagram

Rankine coefficients convert vertical effective stress into horizontal effective stress. Increasing φ lowers Ka and raises Kp, strongly influencing design loads. For example, increasing φ from 28° to 34° can noticeably reduce active pressures for the same height and unit weight, affecting reinforcement and footing dimensions.

5) Surcharge effects are simple but important

A uniform surcharge adds a constant vertical stress, which becomes a constant horizontal component after multiplying by the chosen coefficient. This creates a rectangular “block” on the pressure diagram that can dominate short walls. Always include temporary construction loads if heavy equipment will be near the wall.

6) Groundwater changes both stresses and pressures

When the water table rises within the retained height, buoyancy reduces effective vertical stress below the water line using the submerged unit weight (γsat − γw). At the same time, hydrostatic pressure adds directly to the wall. Proper drainage can reduce total pressure and improve long-term performance.

7) Cohesion: helpful in theory, cautious in design

The Rankine c–φ approach can reduce active pressures through the 2c√K term, but relying on cohesion for permanent support is risky because cohesion can degrade with wetting, cracking, and time. Many designs use c = 0 for conservative permanent conditions, then check sensitivity.

8) Using resultants for design checks

The calculator integrates the pressure distribution to obtain the resultant force and its location. The resultant typically acts near one-third of the height above the base for triangular-like distributions, but water and surcharge shift it upward. Use the reported line of action to compute overturning moments and to size keys, bases, and reinforcement.

1) Which earth pressure state should I choose?

Use active for most cantilever retaining walls that can yield slightly. Use at-rest for basement or braced walls with limited movement. Use passive for resistance in front of walls, but confirm movement and construction conditions.

2) What does “per meter wall length” mean?

Pressures are integrated over height to give force per meter out of the page. If your wall segment is 8 m long, multiply the reported resultant (kN/m) by 8 to estimate total lateral force.

3) Why does the calculator set negative active pressure to zero?

Cohesion can mathematically produce tension near the top under active conditions. Soil cannot sustain significant tension, so designers often assume separation or cracking and set negative values to zero for a realistic contact pressure model.

4) What if the water table is deeper than the wall height?

If zw is below the retained height, hydrostatic pressure does not act on the wall within that height. The calculator effectively treats it as “no internal water table,” using moist unit weight throughout the height.

5) Is Rankine always appropriate?

Rankine is a common starting point for level backfill and smooth-wall assumptions. If you need wall friction, sloping backfill, seismic effects, or complicated geometry, consider Coulomb theory or detailed geotechnical analysis.

6) How do I choose Ko?

Jaky’s Ko = 1 − sinφ is widely used for normally consolidated soils. For overconsolidated soils or special conditions, project data may justify a custom Ko; use the custom option to match that value.

7) Can I use cohesion to reduce required reinforcement?

Be cautious. Apparent cohesion may drop with seasonal moisture, cracking, or long-term softening. Many designs set c to zero for permanent loading and use cohesion only for short-term checks with clear justification.