A technician reports the liquid limit of an undisturbed clay as 50%. According to Ralph Peck, what will be the estimated compression index of this clay?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 14/11/2022
Detailed Explanation
The compression index Cc is the slope of the straight (virgin) part of the e – log σ′ curve. It tells us how compressible a normally consolidated clay is. Finding it properly needs an oedometer test, but for preliminary estimates engineers use empirical correlations with the liquid limit. The best known is the Terzaghi and Peck (1967) relation for undisturbed clays of low to medium sensitivity.
\[ C_c = 0.009\,(w_L - 10) \]
\[ C_c = 0.009\,(50 - 10) = 0.009 \times 40 = 0.36 \]
Why “0.36” Is Correct
The clay is undisturbed, so the 0.009 coefficient applies, and the liquid limit is entered in percent (50, not 0.5). The result, 0.36, is a typical value for a medium-plasticity clay.
| Soil condition | Empirical relation for Cc | wL = 50% |
|---|---|---|
| Undisturbed (normally consolidated) clay — Terzaghi & Peck | Cc = 0.009 (wL − 10) | 0.36 |
| Remoulded clay — Skempton | Cc = 0.007 (wL − 10) | 0.28 |
wL is the liquid limit in percent. The remoulded value is lower because remoulding destroys the natural structure of the clay.
Why the Other Options Are Wrong
- A. 0.24: 0.24 does not match either standard correlation for w_L = 50%.
- B. 0.12: 0.12 is far too low; it is roughly what you get by forgetting to subtract 10 and also using the wrong coefficient.
- C. 0.48: 0.48 is too high; it would correspond to a liquid limit of about 63% with the undisturbed formula.
Key Point
Undisturbed clay: Cc = 0.009(wL − 10). Remoulded clay: Cc = 0.007(wL − 10). Liquid limit in percent.
Key Concepts for Students
- The relation is usually credited to Terzaghi and Peck; Ralph Peck was the co-author.
- Cc is dimensionless and is used in ΔH = [Cc·H/(1 + e₀)]·log(σ′f/σ′₀) for normally consolidated clays.
- Typical Cc: about 0.2–0.5 for medium clays, much higher for organic clays and peats.
Practice more: this is question 5 in Soil Consolidation MCQs – Part 1. Try the whole set and check every answer instantly.