Olsen Curve Calculator: What It Does

The Olsen curve calculator estimates the percentage of a soil sample that passes through a given sieve size based on particle diameter, using the Olsen (or modified) particle-size distribution equation. You enter the particle diameter (in mm) and the soil’s coefficient of uniformity (Cu), and it returns the percent passing, a key value in geotechnical engineering for classifying soil gradation.

Formula

The Olsen curve is a power-law approximation of a grain-size distribution curve. It is expressed as:

P = 100 × (D / D_ref)^−α

Where:

• P = percent passing (%), the fraction of soil finer than diameter D.
• D = particle diameter (mm) – the sieve opening size you are evaluating.
• D_ref = reference diameter, typically 0.075 mm (the No. 200 sieve).
• α = a shape parameter related to the coefficient of uniformity, Cu, by α = 0.5 × log10(Cu) / log10(2).

The coefficient of uniformity (Cu) is defined as D₆₀ / D₁₀, where D₆₀ and D₁₀ are the particle diameters at which 60% and 10% of the soil are finer, respectively. For a well-graded soil, Cu > 4 (for gravels) or Cu > 6 (for sands).

Worked Example

Using the default values: particle diameter D = 0.1 mm, Cu = 5.

1. Calculate α: α = 0.5 × log10(5) / log10(2) ≈ 0.5 × 0.69897 / 0.30103 ≈ 1.16096.
2. Compute the ratio D/D_ref = 0.1 / 0.075 = 1.3333.
3. Raise to the power −α: 1.3333^−1.16096 ≈ 0.7224.
4. Multiply by 100: P ≈ 72.2%.

The calculator returns 72.2% passing, matching the manual calculation.

When to Use the Olsen Curve

The Olsen curve is most useful in preliminary geotechnical analysis when you have only a few known points from a sieve analysis and need to estimate the full gradation curve. It is commonly applied in:

• Soil classification for engineering purposes (e.g., AASHTO or USCS).
• Design of filters and drainage layers.
• Estimating hydraulic conductivity from grain size.
• Checking if a soil meets gradation specifications for construction.

The curve is an approximation, not a substitute for a full laboratory sieve analysis, but it is handy for quick checks and when only partial data are available.

How to Choose the Coefficient of Uniformity

Cu is a measure of the spread of particle sizes. To use the calculator, you need a value for Cu. If you have a sieve analysis, compute Cu = D₆₀/D₁₀. If not, you can estimate it from soil type:

• Uniform sand (e.g., beach sand): Cu ≈ 2–3.
• Well-graded sand: Cu > 6.
• Gravelly soil: Cu often 5–20.
• Silty or clayey soil: Cu may be higher, but the Olsen model is less accurate for cohesive soils.

If you do not have a measured Cu, using a value of 5 is a reasonable default for many sands.

Common Mistakes and Misconceptions

One frequent error is mixing up D_ref. The Olsen curve is calibrated to the No. 200 sieve (0.075 mm). If you use a different reference, the results shift. Another mistake is using the diameter in microns instead of millimeters – always convert to mm (1 mm = 1000 µm). Also, the curve assumes a log-linear relationship in the range of sand and gravel; it does not work well for clay particles (less than 0.002 mm) because those follow different settling behavior.

A common misconception is that the Olsen curve gives the exact grain-size distribution. It is an empirical model, and real soils often deviate, especially if they are gap-graded (missing a range of sizes). Always verify with actual sieve data when possible.

Limitations of the Model

The Olsen curve is a simplification. It assumes a continuous, well-graded distribution, so it may not represent soils with a bimodal distribution or those containing significant fines (silt/clay). It also does not account for particle shape, which affects settling and compaction. For engineering design, always rely on measured data, not just the model.

Alternatives to the Olsen Curve

If you need a more accurate grain-size distribution, you can use:

• Full sieve analysis (mechanical sieving) for particles larger than 0.075 mm.
• Hydrometer analysis for fines (silt and clay).
• Software tools like Gradistat or the USDA texture triangle for classification.
• Other empirical curves, such as the Fredlund model, which handles a wider range of soil types.

For a quick estimate, the Olsen curve is fine, but for critical projects, perform a standard ASTM D6913 sieve test.

Frequently Asked Questions

What is the Olsen curve used for?

It is used to estimate the percentage of soil passing a given sieve size from a single point and the coefficient of uniformity. It helps in preliminary soil classification and in assessing whether a soil meets gradation specs without running a full sieve analysis.

How do I find the coefficient of uniformity (Cu)?

Cu is calculated from a sieve analysis: Cu = D₆₀ / D₁₀, where D₆₀ and D₁₀ are the particle diameters at which 60% and 10% of the sample are finer. If you do not have that data, you can estimate Cu from typical values for the soil type.

Can I use this calculator for clay soils?

Not reliably. The Olsen curve is based on sieve analysis, which is valid for particles larger than 0.075 mm. Clay particles are much smaller and require a hydrometer test. For clay, use a different model or a hydrometer analysis.

Why does the calculator use 0.075 mm as the reference?

0.075 mm is the opening of the No. 200 sieve, a standard boundary between sand and silt in geotechnical engineering. The Olsen curve is normalized to that sieve, meaning it assumes 100% passing at 0.075 mm.

What if my soil has a gap in grain sizes?

The Olsen curve assumes a continuous distribution. If your soil is gap-graded (missing a range of sizes), the curve will overestimate or underestimate the percent passing in that gap. In such cases, you should use actual sieve data instead of the model.

Is the Olsen curve the same as the gradation curve from a sieve test?

No. The Olsen curve is an approximation. A sieve test gives actual measured percentages for each sieve. The Olsen curve is a mathematical fit that can be used when only limited data are available, but it is not a substitute for laboratory testing.

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in d | Particle diameter | mm | 0.1 | 0
in cu | Coefficient of uniformity (Cu) | - | 5 | 1
out pct | Percent passing | % | 100 * (d / 0.075)^(-0.5 * log10(cu) / log10(2)) | 1