Practice Question: Soil Volume Calculation Considering Swell and Shrinkage

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Solution

The average end-area method for earthwork calculates volume “V” between two consecutive cross sections as the average of their areas multiplied by the distance between them:

\(V=L\left(\frac{A_1+A_2}{2}\right)\)

 

L=Distance between \(A_1\)  and \(A_2\)

\(L_{AB}=1,250-1,200=50ft\)

\(L_{BC}=1,300-1,250=50ft\)

 

\(V_{Fill\left(A-B\right)}=\frac{\left(40+0\right)}{2}\times 50=1,000\ ft^3\)

 

\(V_{Cut\left(A-B\right)}=\frac{\left(0+60\right)}{2}\times 50=1,500\ ft^3\)

 

 

\(V_{Fill\left(B-C\right)}=\frac{\left(0+30\right)}{2}\times 50=750\ ft^3\)

 

\(V_{Cut\left(B-C\right)}=\frac{\left(60+20\right)}{2}\times 50=2,000\ ft^3\)

 

 

\(Total\ Volume\ of\ Excavation=\ V_{Exc}=1,500+2,000=3,500\ ft^3\)

 

 

\(Total\ Volume\ of\ Embankment=\ V_{Emb_{(compacted\ volume)}}=1,000+750=1,750\ ft^3\)

 

 

\({V_{Emb}}_{(bank\ volume)}=\frac{V_{Emb_{(compacted\ volume)}}}{1-S_h}\ =\frac{1,750}{1-0.15}=2,059\ ft^3\)

 

This is the required amount of soil at bank after excavation.

 

The remaining volume between required bank volume and excavation is the amount of soil that will not be used:

\(V_B=V_{Exc}-{V_{Emb}}_{(bank\ volume)}=3,500-2,059=1,441\ ft^3\)

 

The remaining volume of excavated soil after swelling (loose volume, \(V_L\)) that should be hauled out of the site:

\(V_L=V_B\times \left(1+S_w\right)\ =1,441\times (1+0.25)=1,801\ ft^3\)

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