Terzaghi's virgin compression curve (one-dimensional consolidation) Given initial effective pressure σ0' with corresponding void ratio e0, and an increased effective pressure σ' with corresponding void ratio e. If Cc is the (dimensionless) compression index, choose the correct empirical expression for the virgin compression curve.

Introduction / Context:
In soil consolidation (one-dimensional loading), the relationship between void ratio and effective stress in the virgin compression range is commonly represented by a straight line on a semi-log plot. Terzaghi and Peck introduced an empirical equation using the compression index Cc to describe this e–log σ' relationship.

Given Data / Assumptions:

• Initial effective pressure = σ0' with void ratio e0.
• Increased effective pressure = σ' with void ratio e.
• Compression index Cc is constant over the considered virgin compression range.
• Logarithm base 10 is used.

Concept / Approach:

The virgin compression curve is linear in e versus log10 σ'. As stress increases, void ratio decreases, so the formula must reduce e when σ' > σ0'. The correct relationship is e = e0 − Cc * log10(σ'/σ0').

Step-by-Step Solution:

Verification / Alternative check:

On an e–log σ' plot, the slope magnitude equals Cc. The sign convention requires a decrease in e with increasing σ', exactly captured by the minus sign.

Why Other Options Are Wrong:

Option (a) predicts e increases with stress (non-physical). Options (c) and (d) rearrange terms incorrectly or with wrong signs relative to the standard form.

Common Pitfalls:

Confusing log base e (natural log) with log base 10; missing the minus sign; applying the formula outside the virgin compression range.

Final Answer:

e = e0 − Cc log10(σ'/σ0')