Calculator Inputs
Example Data Table
Sample inputs and typical results for a granular backfill case (per unit wall length). Adjust values for your project criteria.
| Scenario | Inputs | Key outputs |
|---|---|---|
| Granular, level backfill |
H = 6 m γ = 18 kN/m³ φ = 30° , c = 0 q = 10 kPa β = 0° , δ = 0° , θ = 0° Water = No |
Rankine Ka ≈ 0.333 P ≈ 0.5·Ka·γ·H² + Ka·q·H Resultant ≈ near H/3 from base |
| With groundwater |
Same as above, plus: Water = Yes WT depth = 3 m γsat = 20 kN/m³ γw = 9.81 kN/m³ |
Higher base pressure due to hydrostatic component. Resultant location shifts upward slightly. Verify drainage and relief details. |
Formula Used
1) Basic lateral pressure model
Total lateral pressure at depth z is computed as:
p(z) = p′(z) + pw(z)
Effective (soil) component
p′(z) = max(0, K·(σ′v(z) + q) − 2c√K)
Where σ′v is vertical effective stress from soil weight. For dry soil: σ′v = γ·z.
With groundwater, submerged unit weight is approximated as γ′ = γsat − γw below the water table.
Hydrostatic water component
If the water table is at depth zw from the top:
pw(z) = γw·(z − zw) for z > zw.
2) Earth pressure coefficient K
- Rankine (level backfill): Ka = tan²(45° − φ/2), Kp = tan²(45° + φ/2).
- Rankine (sloping backfill β): Ka = cosβ·(cosβ − √(cos²β − cos²φ)) / (cosβ + √(cos²β − cos²φ)).
- Coulomb (general form): Ka = cos²(φ − θ) / [cos²θ·cos(δ+θ)·(1 + √( sin(δ+φ)·sin(φ−β) / (cos(δ+θ)·cos(β−θ)) ))²].
- At-rest: K0 = 1 − sinφ (Jaky), or user K0 override.
3) Resultant force and location
The calculator numerically integrates the pressure diagram:
P = ∫ p(z) dz and M = ∫ p(z)·(H − z) dz.
Resultant location from base: y = M / P.
How to Use This Calculator
- Select the unit system used on your drawings and calculations.
- Choose an earth pressure method (Rankine for quick checks, Coulomb for wall friction/batter).
- Set the soil state (active for yielding walls, at-rest for restrained walls, passive for resistance).
- Enter the retained height H and backfill properties (γ, φ, and cohesion if applicable).
- Add any surcharge q that represents traffic, live loads, or compaction effects.
- If groundwater is relevant, enable groundwater and provide water table depth and weights.
- Press Calculate. Review K, resultant force, and point of application for stability checks.
- Use Download CSV or Download PDF for documenting your design notes.
Abutment Earth Pressure Article
1) Earth pressure components and outputs
Abutment backwalls retain approach embankments and transfer lateral loads into the foundation. For preliminary sizing, the lateral pressure diagram can be idealized as a depth‑varying stress p(z) that produces a resultant force P and an overturning moment about the base. This calculator reports P per unit wall length and its point of application, which typically falls near H/3 for a simple triangular distribution. Include backfill height changes from roadway profiles carefully.
2) Selecting the earth pressure coefficient
Earth pressure coefficients convert vertical stress into lateral stress. Rankine is widely used for level or uniformly sloped backfill where wall friction is neglected. Coulomb extends the model by including wall friction δ and wall batter θ, often reducing active pressure when interface friction is mobilized. For restrained abutments, at‑rest pressure K0 is appropriate because wall movements may be insufficient to reach the active state.
3) Surcharge loading and practical ranges
Uniform surcharge q represents traffic, approach slab effects, construction equipment, and compaction energy. In the lateral model, surcharge contributes a rectangular pressure increment K·q that adds linearly to the force. Even modest q values can noticeably increase the upper third of the pressure diagram, influencing coping reinforcement, wingwall demands, and bearings near the abutment seat.
4) Groundwater, buoyancy, and drainage risk
Groundwater can dominate abutment demand if drainage is compromised. The calculator separates soil effective stress from hydrostatic water pressure, adding p_w(z)=γ_w(z−z_w) below the water table. Submerged unit weight γ′=γ_sat−γ_w reduces effective stress, yet the added water pressure often increases total lateral stress at depth. Always verify drain details, weep paths, and realistic worst‑case water levels.
5) Using results in design checks
Use the outputs for sliding, overturning, bearing, and structural design checks under the governing code load combinations. Apply resistance factors or safety factors to soil parameters, and document assumptions for φ, γ, K selection, and groundwater. Exporting CSV/PDF summaries supports design reviews and helps maintain consistent calculations across multiple abutments and staged construction sequences.
FAQs
1) Which method should I use for most abutments?
Use Rankine for quick checks with vertical walls and minimal wall friction. Use Coulomb when wall batter or interface friction is significant. Use K0 for stiff or restrained abutments where movements are limited.
2) Does the calculator replace a geotechnical report?
No. It applies standard earth pressure relationships using your inputs. Use project geotechnical parameters, drainage assumptions, and code requirements. Treat the results as a check or documentation tool, not a substitute for site investigation.
3) How is surcharge handled in the results?
Surcharge q adds a constant lateral component K·q along the wall height. This increases force and moment without changing the soil unit weight. Model traffic and compaction surcharges per your bridge and geotechnical guidance.
4) What happens when groundwater is enabled?
The model adds hydrostatic water pressure below the water table and uses submerged unit weight for effective stress. Total lateral pressure usually increases at depth. Verify drainage reliability and consider worst‑case water levels for design.
5) Can I use cohesion for cohesive backfills?
You can enter cohesion, but cohesive backfill behind abutments is often avoided. The calculator applies a common cohesion reduction term and prevents negative pressures. Confirm whether your design standards permit cohesion and whether long‑term conditions reduce it.
6) Why does passive pressure sometimes look very large?
Passive resistance can be high because Kp is much larger than Ka. In practice, passive mobilization requires significant movement and may be reduced by disturbance, slope effects, and code limits. Apply appropriate reduction factors and detailing.
7) What does the resultant location mean?
It is the height above the base where the combined lateral force acts, computed from the pressure diagram. Use it to calculate overturning moment, stem reinforcement demands, and foundation checks under your governing load combinations.