Time for 80% consolidation vs thickness: scaling with drainage path A clay layer 2 m thick reaches 80% consolidation in 10 years. For another stratum of the same clay 8 m thick under similar drainage conditions, estimate the time for 80% consolidation.

Introduction / Context:Primary consolidation time depends on the drainage path length through the coefficient of consolidation Cv and the time factor Tv. For the same clay and the same degree of consolidation, Tv is constant and time scales with the square of the maximum drainage path Hdr.

Given Data / Assumptions:

• Same clay ⇒ same Cv.
• Same degree U = 80% ⇒ same Tv.
• Similar drainage condition for both layers (e.g., both double-drained or both single-drained).

Concept / Approach:

Time t is related by t = Tv * (Hdr^2 / Cv). Hence, for identical Cv and Tv, t ∝ Hdr^2. For double drainage, Hdr = thickness/2. Increasing thickness by a factor of 4 increases Hdr by 4, and time by 4^2 = 16.

Step-by-Step Solution:

Verification / Alternative check:

This holds for either both single-drained or both double-drained as long as drainage conditions are the same; the scaling with the square of drainage path remains valid.

Why Other Options Are Wrong:

Other answers ignore the square-law dependence and underpredict the large increase due to thickness.

Common Pitfalls:

Using linear scaling with thickness; confusing thickness with drainage path (half-thickness for double drainage).

Final Answer:

160 years