Consolidation Time Scaling – Effect of thickness, permeability, and compressibility A clay layer reaches 90% consolidation in 15 years. If the layer becomes twice as thick, three times more permeable, and four times more compressible (all else same), what is the new time for 90% consolidation?

Introduction / Context:
Primary consolidation time depends on drainage path, permeability, and compressibility. For a given degree of consolidation (e.g., 90%), the time scales with the square of the drainage path and inversely with the coefficient of consolidation Cv. This question checks proportional reasoning without requiring tables of Tv.

Given Data / Assumptions:

• Initial time to 90% consolidation t₀ = 15 years.
• New thickness = 2 × original; drainage conditions unchanged (so H_dr doubles).
• Permeability increases 3×; compressibility (mv) increases 4×.
• Water unit weight constant; one-dimensional consolidation.

Concept / Approach:

For a fixed U (degree of consolidation), t ∝ H_dr^2 / Cv. Also, Cv = k / (mv * gamma_w). If k → 3k and mv → 4mv, then Cv_new = (3/4) Cv_old. With H_dr doubling, H_dr^2 scales by 2^2 = 4. Therefore the new time factor multiplies by 4 / (3/4) = 4 * (4/3) = 16/3 ≈ 5.333.

Step-by-Step Solution:

Verification / Alternative check:

Since U is fixed, Tv cancels. The strong dependence on H_dr^2 explains why doubling thickness dominates the increase in time even though permeability improves.

Why Other Options Are Wrong:

70, 75, and 85 years reflect partial consideration (e.g., using only H^2 or only Cv changes) but not both. 60 years would require higher Cv or smaller H than stated.

Common Pitfalls:

Using total thickness instead of drainage path, ignoring whether single or double drainage applies, or forgetting Cv depends on both k and mv.

Final Answer:

80 years