Earth Pressure at Rest Calculator
Compute at-rest lateral earth pressure using Jaky, OCR-adjusted, or manual K0 methods.
Earth Pressure at Rest Is Calculated By Understanding K0, Vertical Stress, and Soil State
In geotechnical engineering, the phrase earth pressure at rest is calculated by using a lateral pressure coefficient and vertical effective stress appears in almost every retaining or underground structure design workflow. At-rest pressure is the condition where the soil mass is not allowed to strain laterally. In practical terms, this means the wall or structure is too stiff to move enough to mobilize active pressure, and not pushed enough to develop passive pressure. Typical examples include basement walls, rigid culverts, braced excavations in initial loading, deep foundations against soil, and buried utility structures with constrained deformation.
The core design equation is:
σh0 = K0 × σv
where σh0 is lateral stress at rest, K0 is the at-rest earth pressure coefficient, and σv is vertical stress (often effective stress in drained design). If surcharge is present, engineers commonly use:
σh0 = K0 × (γz + q)
with γ as unit weight, z depth, and q uniform surcharge. This calculator applies exactly that framework and helps you visualize pressure growth with depth.
Why At-Rest Pressure Is Different from Active and Passive Pressure
Earth pressure states depend on wall movement. If a wall yields away from backfill, lateral stress drops toward active pressure. If it pushes into soil, stress rises toward passive pressure. At-rest pressure sits between these conditions and is normally closer to active than passive for many granular soils, though this depends heavily on stress history and overconsolidation.
- Active: wall moves away, soil expands laterally, lower lateral stress.
- At rest: minimal wall movement, no lateral strain, intermediate stress.
- Passive: wall pushes into soil, lateral compression, high lateral stress.
This distinction is not academic. Using active pressure when a wall is essentially fixed can underpredict loads and reinforcement demand. In many serviceability-controlled structures, at-rest assumptions are safer and more realistic.
Most Common Equations Used for K0
The value of K0 is the heart of the problem. For normally consolidated soils, the most common estimate is Jaky’s relation:
K0 = 1 – sin(φ’)
For overconsolidated soils, a frequently used adjustment is:
K0(OC) = (1 – sin(φ’)) × OCRsin(φ’)
where OCR is overconsolidation ratio. This relation captures the field reality that overconsolidated soils can exhibit significantly higher at-rest lateral stresses than normally consolidated soils with the same friction angle.
- Choose an appropriate φ’ from lab and site interpretation.
- Determine whether soil is normally consolidated or overconsolidated.
- Select K0 model (Jaky, OCR-adjusted, or project-specific calibration).
- Compute vertical stress profile and apply K0 to each depth.
- Check sensitivity using lower and upper bound parameter sets.
Typical Engineering Ranges Used in Preliminary Design
Preliminary geotechnical calculations often start with reasonable soil parameter ranges before final lab correlation and field back-analysis. The table below summarizes typical values widely used in practice.
| Soil Class | Typical φ’ (degrees) | Jaky K0 = 1 – sin(φ’) | Typical Unit Weight γ (kN/m³) |
|---|---|---|---|
| Loose Sand | 28 to 32 | 0.53 to 0.47 | 16.5 to 18.0 |
| Dense Sand | 34 to 40 | 0.44 to 0.36 | 18.0 to 20.0 |
| Normally Consolidated Clay | 20 to 28 | 0.66 to 0.53 | 16.0 to 19.0 |
| Silty Soil | 26 to 34 | 0.56 to 0.44 | 17.0 to 19.0 |
These are representative ranges for preliminary work and should be replaced by site-specific values from CPT, lab tests, stress history evaluation, and local experience. For final design, use governing standards and project geotechnical reports.
How Overconsolidation Changes At-Rest Pressure
Overconsolidation can significantly increase K0. To illustrate the scale of this effect, the following comparison uses φ’ = 30 degrees, where sin(φ’) = 0.5 and Jaky K0 for NC soil equals 0.50.
| OCR | K0 (NC Baseline) | K0 OCR-Adjusted | Increase vs NC |
|---|---|---|---|
| 1 | 0.50 | 0.50 | 0% |
| 2 | 0.50 | 0.71 | 42% |
| 4 | 0.50 | 1.00 | 100% |
| 8 | 0.50 | 1.41 | 182% |
This is why stress history is central in design. If you ignore OCR in heavily preloaded soils, you can materially underestimate structural loads.
Step-by-Step Worked Example
Suppose you have a rigid basement wall with the following conditions: φ’ = 30 degrees, γ = 18 kN/m³, depth z = 6 m, surcharge q = 10 kPa, and normally consolidated backfill.
- Compute K0 using Jaky: K0 = 1 – sin(30) = 1 – 0.5 = 0.50.
- Compute vertical stress at depth: σv = γz + q = (18 × 6) + 10 = 118 kPa.
- Compute lateral at-rest pressure: σh0 = K0 × σv = 0.50 × 118 = 59 kPa.
If the same soil were overconsolidated with OCR = 4 and using OCR-adjusted K0, then K0 becomes about 1.00 and lateral stress rises to roughly 118 kPa. That is a large design difference for reinforcement, concrete sections, and serviceability checks.
Effective Stress vs Total Stress
Engineers often perform earth pressure calculations in effective stress space for drained conditions, then superimpose pore water pressure separately when groundwater is present. In short-term undrained analyses, total stress approaches may be used depending on project requirements. Be explicit in your assumptions:
- Drained long-term: use effective parameters and add hydrostatic pressure separately.
- Undrained short-term: consider total stress behavior and undrained shear parameters.
- Layered profiles: compute stress increment layer by layer, not with one average γ.
Common Mistakes to Avoid
- Using active pressure for very stiff walls with negligible lateral movement.
- Ignoring surcharge or applying surcharge outside the loaded influence width.
- Using one global φ’ for mixed soil strata.
- Assuming OCR = 1 without reviewing site loading history.
- Confusing total and effective unit weights below groundwater.
- Skipping construction stage effects where temporary bracing can alter stress paths.
How to Use This Calculator Correctly
The calculator above is structured for practical design screening and concept-level decisions:
- Select method: Jaky, OCR-adjusted, or manual K0.
- Enter φ’, OCR, unit weight, depth, and surcharge.
- Click Calculate to obtain K0, vertical stress, and lateral pressure.
- Review chart outputs showing how vertical and at-rest pressure vary with depth.
- Run sensitivity scenarios with lower and upper bound φ’ and OCR values.
Because pressure increases approximately linearly with depth for constant γ, charting gives immediate quality control. If results look nonphysical, check input units first. Most field errors in early design come from mixing kPa, kN/m², and psf or from entering saturated unit weight where effective unit weight is required.
Design Context Where At-Rest Pressure Is Often Preferred
- Rigid basement walls in urban structures.
- Braced excavation walls before substantial deflection develops.
- Embedded structures with strict movement limits.
- Pipes, culverts, and boxes where deformation compatibility controls loading.
- Existing structures sensitive to settlement and lateral movement.
Recommended Technical References
For standards, guidance, and deeper background, review:
Federal Highway Administration Geotechnical Engineering Resources (.gov)
MIT OpenCourseWare Soil Behavior and Geotechnics (.edu)
Geotechnical Data Notes and K0 Compilations (industry reference)
Final Takeaway
If you remember one thing, remember this: earth pressure at rest is calculated by multiplying vertical stress by an appropriate K0 that reflects both soil friction and stress history. The formula is simple, but choosing the correct K0 is where engineering skill matters. Jaky gives a robust baseline for normally consolidated soils, OCR adjustments account for stress history, and field-calibrated values can refine final design. Used carefully, this approach gives reliable lateral load estimates for stiff or movement-restricted structures.