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In a Marshall sample, the bulk specific gravity of mix and aggregates are 2.324 and 2.546 respectively. The sample includes 5% of bitumen (by total weight of mix) of specific gravity 1.10. The theoretical maximum specific gravity of mix is 2.441. The void filled with the bitumen (VFB) in the Marshall sample (in %) is _______

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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 = V+ Vb

Where V= 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 = V+ 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

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