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Settlement 4 cm in 2 months, time for 10 cm

Short answer

For U < 60%, time is proportional to U². Degrees of consolidation are U1=20%, U2=50%. Required time = 2 months × (50/20)² = 12.5 months.

A compressible layer whose total settlement under a given loading is expected to be 20 cm settles 4 cm at the end of 2 months. How many months will be required to reach a settlement of 10 cm? Assume double drainage.

Settlement is proportional to the degree of consolidation UU, and time is proportional to TvT_v. For U<60%U < 60\%, Tv=π4U2T_v = \frac{\pi}{4}U^2, so t∝U2t \propto U^2 (same layer, same cvc_v and drainage).

Step 1: Degrees of consolidation

U1=420=20%,U2=1020=50%U_1 = \frac{4}{20} = 20\%, \qquad U_2 = \frac{10}{20} = 50\%

Both are below 60%, so the parabolic relation applies.

Step 2: Time ratio

t2t1=(U2U1)2=(5020)2=6.25\frac{t_2}{t_1} = \left(\frac{U_2}{U_1}\right)^2 = \left(\frac{50}{20}\right)^2 = 6.25 t2=6.25×2=12.5 monthst_2 = 6.25 \times 2 = 12.5\ \text{months}

Answer: about 12.5 months from the start of loading. The double drainage condition does not change the ratio, because HdrH_{dr} is the same in both cases.

✓ Answer checked by Claude Opus 5.5 (high effort)

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