| Case | Method | Pressure (kPa) | Settlement (mm) | k (kN/m³) | k (MN/m³) |
|---|---|---|---|---|---|
| A | Direct | 200 | 4.0 | 50,000 | 50.0 |
| B | Plate Load (300 mm) | 250 | 5.0 | 50,000 | 50.0 |
| C | Elastic (E=60 MPa, ν=0.35, d=300 mm) | — | — | ~ 724,000 | ~ 724 |
- k = p / s, where p is contact pressure (kPa) and s is settlement (m).
- Plate load test pressure: p = P / A, with A = π(d/2)².
- Elastic equivalent stiffness (approx.): k ≈ (π·Es) / (2·(1−ν²)·a) × α.
- Select a method matching your available test data.
- Enter values and choose units for each input field.
- Pick an output unit for quick reporting or comparison.
- Press Calculate Modulus to view results above the form.
- Download CSV or PDF to share results with your team.
Meaning of Subgrade Reaction Modulus
The subgrade reaction modulus, k, is a Winkler spring constant that links contact pressure to vertical deformation. It is reported as pressure per unit settlement, typically kN/m³ or MN/m³. Because it depends on stress level, plate size, and moisture, k is best treated as a project-specific parameter derived from consistent measurements.
Direct Pressure–Settlement Use
In direct mode, the calculator converts the entered pressure to kPa and settlement to meters, then applies k = p / s. For example, 250 kPa at 5 mm produces 50,000 kN/m³. Enter paired values taken at the same loading stage, and avoid mixing peak pressure with residual settlement.
Plate Load Test Workflow
For plate testing, pressure is computed from load and plate area: p = P / A with A = π(d/2)². A 300 mm plate has an area of about 0.0707 m². If P = 150 kN, the pressure is roughly 2,123 kPa, and dividing by measured settlement yields k. Use the same diameter when comparing locations.
Elastic Estimate for Quick Checks
The elastic option estimates an equivalent k from soil modulus Es, Poisson’s ratio ν, and plate radius a using k ≈ (πEs)/(2(1−ν²)a) × α. This is useful for sensitivity studies, such as checking how k changes when Es varies from 30 to 80 MPa. Calibrate α when field data is available.
Interpreting Results for Design
Higher k indicates stiffer support and smaller settlements under the same pressure. Slab-on-grade, mat foundations, and pavement models often require k in consistent units. If you must shift units, remember that kPa/m equals kN/m³ and that pci is a convenient legacy unit for some specifications. On granular subgrades, k often increases with stress, while fine-grained soils may soften after yield. When specifications require a reference level, compute k at a chosen settlement, such as 1.25 mm or 2.5 mm, for consistent sitewide comparisons.
Quality Controls and Reporting
Check that k values trend logically with increasing load and that repeated tests at nearby stations fall within an acceptable spread. Large jumps can signal seating errors, variable saturation, or inconsistent plate contact. Use the built-in history, exports, and Plotly charts to document assumptions, keep traceability, and communicate results clearly.
FAQs
1. What does the modulus k physically represent?
It represents a spring-like stiffness of the supporting soil: how much pressure is needed to create one unit of settlement. It is an idealized parameter that summarizes a pressure–deflection response for a given loading area and stress range.
2. Which method should I choose?
Use Direct when you already have pressure and settlement pairs. Use Plate Load when you measured load, plate size, and settlement. Use Elastic for quick sensitivity checks when you only have an estimated soil modulus and Poisson’s ratio.
3. Why does k change with plate size?
The stress bulb and the volume of soil mobilized increase with plate diameter, so the measured stiffness is scale-dependent. Smaller plates often report higher k than larger plates on the same deposit, especially in layered profiles.
4. Is the elastic estimate a replacement for testing?
No. It is a simplified equivalent stiffness for a rigid circular plate on an elastic half-space. It helps with comparisons and preliminary design, but site testing or calibrated correlations are preferred for final k values.
5. How do I interpret pci versus metric units?
The calculator reports k in kN/m³ and MN/m³, and also converts to pci (lb/in³) for legacy specifications. Use a single unit system throughout your design model to avoid accidental scaling errors.
6. What should I export in a design submittal?
Include the method, input units, assumed plate diameter or reference settlement, and the final k used for design. Attach the CSV or PDF output as evidence, and add brief notes about groundwater, moisture, and test conditions.