Concept:
1) Percent Air voids (Vv)
\({{\rm{V}}_{\rm{V}}}{\rm{ = }}\frac{{\left( {{{\rm{G}}_{\rm{t}}}{\rm{ - }}{{\rm{G}}_{\rm{m}}}} \right)}}{{{{\rm{G}}_{\rm{t}}}}}{\rm{ \times 100}}\)
Gt = theoretical specific gravity of mixture
Gm = bulk density or mass density of the specimen
2) Percent voids in mineral Aggregate (VMA)
VMA = Vv + Vb
Where Vv = volume of air voids, %
Vb = Volume of bitumen, %
\({{\rm{V}}_{\rm{b}}} = {{\rm{G}}_{\rm{m}}} \times \frac{{{{\rm{W}}_{\rm{b}}}}}{{{{\rm{G}}_{\rm{b}}}}}\)
Where
Wb = % of bitumen by weight
Gb = Specific gravity of bitumen
3) Percent voids filled with bitumen (VFB)
\({\rm{VFB = }}\frac{{{{\rm{V}}_{\rm{b}}}}}{{{\rm{VMA}}}}{\rm{ \times 100}}\)
Calculation:
Given:
Gt = 2.441
Gm = 2.324
Wb = 5%
Therefore,
\({{\rm{V}}_{\rm{b}}} = {{\rm{G}}_{\rm{m}}} \times \frac{{{{\rm{W}}_{\rm{b}}}}}{{{{\rm{G}}_{\rm{b}}}}}\)
\({{\rm{V}}_{\rm{b}}} = {{\rm{2.324}}{\rm{}}} \times \frac{{{{\rm{5}}{\rm{}}}}}{{{{\rm{1.10}}{\rm{}}}}}=10.56 \%\)
The volume of air voids is,
\({{\rm{V}}_{\rm{V}}}{\rm{ = }}\frac{{\left( {{{\rm{G}}_{\rm{t}}}{\rm{ - }}{{\rm{G}}_{\rm{m}}}} \right)}}{{{{\rm{G}}_{\rm{t}}}}}{\rm{ \times 100}}\)
\({V_v} = \left( {\frac{{2.441 - 2.324}}{{2.441}}} \right) \times 100\)
Vv = 4.793%
We know that,
VMA = Vv + Vb
VMA = 4.793 + 10.56 = 15.35%
Now,
\({\rm{VFB = }}\frac{{{{\rm{V}}_{\rm{b}}}}}{{{\rm{VMA}}}}{\rm{ \times 100}}\)
\({\rm{VFB = }}\frac{{{{\rm{10.56}}_{\rm{}}}}}{{{\rm{15.35}}}}{\rm{ \times 100}}\)
VFB = 68.76%
Hence the void filled with the bitumen (VFB) in the Marshall sample (in %) is 68.76