The loading period for a new building extended from May 1995 to May 1997. In May 2000, the average measured settlement was found to be 11.43 cm. It is known that the ultimate settlement will be about 35.56 cm. Estimate the settlement in May 2005. Assume double drainage to occur.

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Accepted Answer

For the majority of practical cases in which loading is applied over a period, acceptable accuracy is obtained when calculating time-settlement relationships by assuming the time datum to be midway through the loading or construction period.

[latex]S_{t}=11.43 cm ext { when } t=4 ext { years and } S=35.56 cm ext {. }[/latex]

The settlement is required for t = 9 years, that is, up to May2005. Assuming as a starting point that at t = 9 years, the degree of consolidation will be = 0.60. Under these conditions per Eq. (7.48), [latex]U=1.13 \sqrt{T}[/latex].

[latex]T=\frac{\pi}{4} \frac{U \%}{100}^{2}[/latex] (7.48)

If [latex]S_{t_{1}}= ext { settlement at time } t_{1}, S_{t_{2}}= ext { settlement at time } t_{2}[/latex]

[latex]\frac{S_{t_{1}}}{S_{t_{2}}}=\frac{U_{1}}{U_{2}}=\sqrt{\frac{T_{1}}{T_{2}}}=\sqrt{\frac{t_{1}}{t_{2}}} \quad ext { since } \quad T=\frac{c_{ u} t}{H_{d r}^{2}}[/latex]

where [latex]\frac{c_{v}}{H_{d r}^{2}}[/latex] is a constant. Therefore [latex]\frac{11.43}{S_{t_{2}}}=\sqrt{\frac{4}{9}} ext { or } S_{t_{2}}=17.15 cm[/latex]

Therefore at t = 9 years, [latex]U=\frac{17.5}{35.56}=0.48[/latex]

Since the value of U is less than 0.60 the assumption is valid. Therefore the estimated settlement is 17.15 cm. In the event of the degree of consolidation exceeding 0.60, equation (7.50) has to be used to obtain the relationship between T and U.

[latex]T=1.781-0.933 \log (100- U \%)[/latex] (7.50)

Question 7.11: The loading period for a new building extended from May 1995...

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