In Marshall method of mix design, the coarse aggregate, fine aggregate, fines and bitumen having respective values of specific gravity 2.60, 2.70, 2.65 and 1.01, are mixed in the relative proportions (% by weight) of 55.0, 35.8, 3.7 and 5.5 respectively. The theoretical specific gravity of the mix and the effective specific gravity of the aggregates in the mix respectively are:

This question was previously asked in

GATE CE 2015 Official Paper: Shift 2

Option 1 :

2.42 and 2.63

CT 1: Ratio and Proportion

2846

10 Questions
16 Marks
30 Mins

**Concept:**

**Determination of the specific gravity**

\({{\rm{G}}_{\rm{t}}} = \frac{{100}}{{\frac{{{{\rm{W}}_1}}}{{{{\rm{G}}_1}}} + \frac{{{{\rm{W}}_2}}}{{{{\rm{G}}_2}}} + \frac{{{{\rm{W}}_3}}}{{{{\rm{G}}_3}}} + \frac{{{{\rm{W}}_4}}}{{{{\rm{G}}_4}}}}}\)

Where,

W_{1}, W_{2}, W_{3}, and W_{4} are the percentage by weights of the coarse aggregate, fine aggregate, fines and bitumen respectively.

G_{1}, G_{2}, G_{3}, and G_{4} are the specific gravity of the coarse aggregate, fine aggregate, fines and bitumen respectively.

**Effective specific gravity of aggregates (coarse + fine) is given by**

\({\rm{G' = }}\frac{{\left( {{{\rm{W}}_{\rm{1}}}{\rm{ \times }}{{\rm{G}}_{\rm{1}}}} \right){\rm{ + }}\left( {{{\rm{W}}_{\rm{2}}}{\rm{ \times }}{{\rm{G}}_{\rm{2}}}} \right)}}{{{{\rm{W}}_{\rm{1}}}{\rm{ + }}{{\rm{W}}_{\rm{2}}}}}\)

Where,

W1, and W2 are the percentage by weights of the coarse aggregate and fine aggregate respectively.

G1, and G2 are the specific gravity of the coarse aggregate and fine aggregate respectively.

**Calculation:**

Given,

W_{1} = 55.0, W_{2} = 35.8, W_{3} = 3.7,and W_{4} = 5.5

G1= 2.6, G2 = 2.7, G3 = 2.65 and G_{4} = 1.01

Theoretical specific gravity

\(\begin{array}{*{20}{l}} {{{\rm{G}}_{\rm{t}}} = \frac{{100}}{{\frac{{{{\rm{W}}_1}}}{{{{\rm{G}}_1}}} + \frac{{{{\rm{W}}_2}}}{{{{\rm{G}}_2}}} + \frac{{{{\rm{W}}_3}}}{{{{\rm{G}}_3}}} + \frac{{{{\rm{W}}_4}}}{{{{\rm{G}}_4}}}}}}\\ {{{\rm{G}}_{\rm{t}}} = \frac{{100}}{{\frac{{55}}{{2.6}} + \frac{{35.8}}{{2.7}} + \frac{{3.7}}{{2.65}} + \frac{{5.5}}{{1.01}}}} \\ {{\rm{G}}_{\rm{t}}}= 2.42} \end{array}\)

Effective specific gravity of aggregates (coarse + fine) is given by

\({\rm{G'}} = \frac{{\left( {55 \times 2.6} \right) + \left( {35.8 \times 2.7} \right)}}{{55 + 35.8}} = 2.639 = 2.64\)

**∴ Theoretical specific gravity of the mix = G _{t} = 2.42 and the effective specific gravity of the aggregates = G' = 2.64**