Correct Answer - Option 1 : 6 cm
Concept:
Correction For Construction Period:
- Settlement begins only when the applied load exceeds the weight of the excavated soil. The corrected settlement may be obtained adopting Terzaghi’s approximate method (also adopted by IS: 8009 – Part 1, 1976).
- This is based on the following assumptions:-
- The actual settlement at the end of the construction time is the same as that resulting from the total load acting for half of the loading time.
- The load–time relationship is linear.
Thus, the settlement at the end of the loading period is equal to the settlement on the instantaneous load curve corresponding to one-half of the total loading period.
Time of loading will be considered from the mid-way through the construction of loading.
Calculation:
Duration of construction April 1992 to September 1993 = 1.5 years
Duration of loading from sept 1993 to sept 1996 = 3 years
∴ Considered duration of loading = Duration of loading + ½ (Duration of construction) = 3.75 years
Ultimate settlement = 25 cm
Average settlement in 3.75 years = 5.16 cm
∴ \(Degree\;of\;consolidation\;U = \frac{{5.16}}{{25}} \times 100 = 20.64\% \)
Since, U< 60%
∴ \({T_v} = \frac{\pi }{4}{U^2} = \frac{{3.14}}{4} \times {0.2064^2} = 0.0334\)
We know,
\({T_v} = \frac{{{C_v}t}}{{{H^2}}}\)
⇒ \(\therefore \;\frac{{{C_v}t}}{{{H^2}}} = 0.0334\)
⇒ \(\frac{{{C_v}}}{{{H^2}}} = \frac{{0.0334}}{{3.75}} = 0.008906\;Yea{r^{ - 1}}\)
Now, For Settlement in January 1997,
Addition duration of loading from sept 1996 to Jan 1997 = 4 months = 4/12 years
∴ Total duration of loading = (3.75 + 4/12) years = 4.0833 years
Now,
Time factor,
\({T_v} = \frac{{{C_v}t}}{{{H^2}}} = 0.008906 \times 4.0833 = 0.003636\; \le 0.2826\)
∴ \({T_v} = \frac{\pi }{4}{U^2} \Rightarrow U = \;\sqrt {\frac{{4 \times 0.003636}}{{3.14}}} = 0.2151 \approx 21.51\% \)
Also,
\(U = \frac{{settlement\;in\;given\;time}}{{ultimate\;settlement}} \times 100\)
∴ Settlement, \(\Delta h = 0.2151 \times 25 = 5.3 cm\)
