Primary consolidation time estimate (double drainage) A structure rests on an impervious clay layer of thickness 12 m. Drainage is possible at both the top and bottom surfaces (double drainage). The coefficient of consolidation is Cv = 0.015 cm²/min. For 50% consolidation (time factor Tv ≈ 0.20), estimate the time required in days.

Introduction / Context:Consolidation time estimates are essential for predicting settlement rates and scheduling construction. For one-dimensional primary consolidation, the nondimensional time factor Tv links elapsed time to the square of the drainage path length and coefficient of consolidation Cv.

Given Data / Assumptions:

• Clay thickness H = 12 m = 1200 cm.
• Double drainage ⇒ drainage path Hdr = H/2 = 600 cm.
• Cv = 0.015 cm²/min.
• Target degree of consolidation U = 50% ⇒ Tv ≈ 0.20 (often tabulated as 0.197).

Concept / Approach:

The fundamental relation is: t = Tv * Hdr² / Cv Convert the resulting minutes to days by dividing by 1440.

Step-by-Step Solution:

Verification / Alternative check:

Both computations give roughly 3.3 × 10³ days. Among the provided discrete options, 3313 days is the closest realistic value and reflects small variations due to Tv rounding and field variability.

Why Other Options Are Wrong:

3123 and 3233 days deviate more from the 3283–3333 day band; “33331 days” appears to be a typographical error one order of magnitude too large; 2999 is too small for the given parameters.

Common Pitfalls:

Using total thickness instead of drainage path; mixing units (m vs cm); forgetting to convert minutes to days; misreading Tv from charts.

Final Answer:

3313 days