Question

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 Rs.10 per m³, the estimated cost for the filling work is (in Rs.):
1. 85,00,000
2. 90,00,000
3. 50,00,000
4. 82,00,000

Answer 1

Correct Answer - Option 2 : 90,00,000

Concept:

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 Total volume(V) of soil is given by

V = V_v + V_s ...........(i)

Where V = Total volume of soil, V_v = Volume of voids, V_s = Volume of solids

Divide the equation (i) by Vs (Volume of solids)

\({V \over V_s} = {V_v \over V_s}+ {V_s \over V_s}\)

\({V \over V_s} = {V_v \over V_s}+ 1\)

\({V \over V_s} = e+ 1\)

\({ V_s} = {V \over(1+e)}\)

Calculation:

Condition - I: Filling

e_f = 0.7 and V_f = 8,50,000 m³

So, Volume of solids in filling(V_sf)

\({ V_{sf}} = {V_f \over(1+e_f)} = {850000 \over(1+0.7)}\) = 500000 m³

Condition-I: Excavation

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

e_exc = 0.8

So, find the volume of excavated soil(V_exc)

\({ V_{s(exc)}} = {V_{exc} \over(1+e_{exc})} \)

\(500000 = {V_{exc} \over(1+0.8)} \)

\(V_{exc} = {500000 \times (1+0.8)} \) = 900000 m³

The estimated cost for the filling work is (in Rs.) = 10 \(\times\) 900000 = 90,00,000