Practice Question: Relative Compaction Based on Test Data

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Solution

Answer: A) 78%

Refer to PE Civil Reference handbook Section 3.8.3 for weight-volume relationships for soil.

The relative compaction is based on the in-situ dry density and max dry density:
\[\text{Relative compaction =} \frac{\gamma_{dry\ in-situ}}{\gamma_{dry \ max}}\\\]

Optimum water content should be determined to know the relative compaction percentage.

First, determine the total density and dry density for each sample:

\[\gamma_{dry} =  \frac{\gamma_{t}}{1+w} \\\]
\[\gamma_{t} =  \frac{moist\ soil\ weight\ of\ sample}{volume\ of\ sample} \\\]

Volume of Sample (\(ft^3\))	Weight of moist soil sample (lb)	Water content %	\[\gamma_{t}\\(lb/ft^3)\]	\[\gamma_{d}\\( lb/ft^3)\]
1/40	2.93	10	87.9	106.5
1/40	3.15	12	94.5	112.5
1/40	3.4	14	102	119.3
1/40	3.2	16	96	110.3
1/40	3.05	18	91.5	103.4
1/40	2.85	20	85.5	95.0

\[\text{From table } \to \gamma _{dry\ max} = 119.3 PCF\]

\[\gamma _{t\ in-situ}=\frac{Total\ in-situ\ Sample\ weight}{Total\ undisturbed\ in-situ\ Sample\ Volume}\]\[= \frac{5}{\frac{1}{20}} = 100\ PCF\\\]
\[\frac{\gamma _{t\ in-situ}}{1+w}  = \frac{100}{1+ 8 \%} = 92.6\ PCF \\\]
\[Relative\ compaction = \frac{γ_{dry in-situ}}{γ_{dry max}} =\frac{92.6}{119.3}=77.6\%\]
 

 

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