# An airport runway fill needs 8,50,000 m3 of soil compacted to a void ratio of 0.7. The required soil is to be taken from a borrow pit having an in situ void ratio of 0.8. If the transportation cost is ₹ 10 per m3, the estimated cost for the filling work is (in ₹):

An airport runway fill needs 8,50,000 m3 of soil compacted to a void ratio of 0.7. The required soil is to be taken from a borrow pit having an in situ void ratio of 0.8. If the transportation cost is ₹ 10 per m3, the estimated cost for the filling work is (in ₹):

#### SOLUTION

The main concept is that while excavating the soil from the borrow pit and after that compacting it, the mass of solids and its specific gravity will not change, and hence, the volume of solids remains constant even after compaction.

The volume of solids, Vs is given by:

${{\rm{V}}_{\rm{s}}} = \frac{{{\rm{Total}}\:{\rm{Volume}}\:\left( {\rm{V}} \right)}}{{1\: + \:{\rm{e}}}}$

During fill:

Given:  e = 0.7 and V = 8,50,000 m3

${{\rm{V}}_{\rm{s}}} = \:\frac{{8,50,000}}{{1 + 0.7}}$ = 500000 m3

During Excavation:

The volume of solids will be same as that of during fill i.e. Vs = 500000 m3

Void ratio, e = 0.8 (given)

Let the volume of excavated soil is V:

Now, we know that

${{\rm{V}}_{\rm{s}}} = \frac{{{\rm{Total}}\:{\rm{Volume}}\:\left( {\rm{V}} \right)}}{{1\: + \:{\rm{e}}}}$

$500000 = \:\frac{V}{{1 + 0.8}}$

V =900,000 m3

Cost = 10 × 900,000 = ₹ 9000000

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