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Time to 90 Percent Consolidation

Hardtime rate of consolidation
A 3-m-thick clay layer drains only from its top and has cv = 1.0 × 10⁻⁷ m²/s. With Tv = 0.848 at 90% consolidation, t90 is most nearly:
  1. A98 days
  2. B883 days
  3. C221 days
  4. D442 days
Show solution

Answer: B. 883 days

Equation: time for consolidation, t = Tv·Hdr² / cv, where Hdr is the longest distance water must travel to reach a draining boundary. Values: Tv = 0.848 is the time factor for 90% consolidation. cv = 1.0 × 10⁻⁷ m²/s is given. The clay is 3 m thick with free-draining sand above and impervious rock below, so water can only leave through the top. That makes Hdr the full thickness, 3 m. Step 1: Hdr² = 3² = 9 m². Step 2: t90 = 0.848 × 9 / (1.0 × 10⁻⁷) = 7.63 × 10⁷ s. Step 3: convert to days, 7.63 × 10⁷ / 86,400 = 883 days. Using Hdr = 1.5 m, as if the layer drained both ways, gives 221 days.
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