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Clay φ’ from PI Calculator

Estimate effective friction angle (φ’) of clay from Plasticity Index using Kenney (1959), Bjerrum & Simons (1960), and Gibson (1953) correlations.

Last updated 16 June 2026

About this tool

Estimate the effective friction angle (φ’) of clay from Plasticity Index using three published correlations: Kenney (1959), Bjerrum & Simons (1960), and Gibson (1953). Enter PI and get three estimates to inform engineering judgement.

These correlations are for normally consolidated, reconstituted clays. They provide useful first estimates when no triaxial test data is available, particularly at feasibility or preliminary design stage.

How to use this tool

1. Enter the Plasticity Index (PI) — from Atterberg limit testing (PI = LL - PL).

2. Compare the three estimates — use the range to inform judgement, not a single value.

Technical information

Kenney (1959): sin(φ’) = 0.814 - 0.233 × log₁₀(PI)

Bjerrum & Simons (1960): φ’ = 18 + 0.18 × (100 - PI)

Gibson (1953): φ’ = 39 - 11.3 × log₁₀(PI)

All correlations apply to normally consolidated, reconstituted clays. Overconsolidated clays may have higher peak φ’ but lower residual φ’r.

Limitations

These are empirical correlations with significant scatter. Use triaxial test data for detailed design. The correlations are not valid for overconsolidated, cemented, or structured clays.

The Bjerrum & Simons correlation is only applicable for PI ≥ 10%. For low-plasticity soils, Kenney and Gibson are more appropriate.

Residual friction angle (φ’r) is generally lower than peak φ’ and is not estimated by these correlations. For slopes with pre-existing shear surfaces, use ring shear or reversal shear box data.

Revision history

16 June 2026: Initial release

Disclaimer

This tool is provided for educational and general information purposes only. It is not a substitute for professional engineering advice, design or verification.

Diggy and its contributors are not licensed engineering consultants and no results generated by this tool should be used directly for construction, design or safety-critical decisions.

All values and outputs are based on published empirical correlations and should be independently checked and confirmed by a qualified geotechnical engineer before use.

By using this tool, you accept full responsibility for how you interpret and apply the information provided.

Spotted an error? Let us know.

Plasticity Index (PI)

Typical range: 5-100%

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