Question

The time taken to construct building was from April 1992 to September 1993. In September 1996, the average settlement was found to be 5.16 cm. If the ultimate settlement is estimated to be 25 cm, then the settlement in January 1997 would have been

• A. 6 cm
• B. 7 cm
• C. 8 cm
• D. 9 cm

Answer 1

The correct option is A 6 cm

From September 1993 to September 1996 i.e, in 3 years, the average settlement is 5.16 cm

$i.e.,t_1=3years$

$\Delta h_1=5.16cm$

Then settlement in January 1997 i.e., in 3.25 year will be $\Delta h_2$

$\text{Consolidation in 3 years}=\frac{5.16}{25}=0.2064$

$\therefore T_v=\frac{\pi }{4}{U}^2=0.0034$

$\therefore \frac{C_{v}t}{H^2}=T_v=0.0334$

$\frac{C_v}{H^2}=\frac{0.0334}{3}=0.0113$

Now in 3.25 years

$T_v=\frac{\pi }{4}{U}^2=\frac{C_{v}t}{H^2}$

$=0.0113\times 3.25=0.03618$

U = 0.2146

$\therefore U=\frac{\Delta h_2}{H}$

$0.2146=\frac{\Delta h_2}{25}$

$\therefore \Delta h_2=5.37cm$