Question

In a bituminous mix, the percentage by weight of coarse aggregate, fine aggregate, filler, and bituminous binder is 58, 25, 12, and 5, respectively. The corresponding specific gravity of these materials is 2.68, 2.45, 2.42, and 1.15. The bulk specific gravity of the mix is 2.2. The Voids Filled with Bitumen (VFB, in percentage) is ______ (rounded off to the nearest integer).

Hint:

Find \(G_t\) from the weighted specific gravities, then \(V_a\), \(V_b\), \(VMA=V_a+V_b\), and \(VFB=100V_b/VMA\).

Answer 1

Correct Answer: 50

Step 1: Take 100 g of the compacted mix as the basis.
Total mass $=100$ g. Using the bulk specific gravity $G_m=2.2$, the total (bulk) volume of this 100 g of compacted mix is
$V_{mix} = \dfrac{100}{2.2} = 45.455$ cm$^3$

Step 2: Find the actual solid volume of each ingredient (no internal voids in a solid).
Coarse aggregate: mass $=58$ g, volume $=58/2.68=21.642$ cm$^3$.
Fine aggregate: mass $=25$ g, volume $=25/2.45=10.204$ cm$^3$.
Filler: mass $=12$ g, volume $=12/2.42=4.959$ cm$^3$.
Bitumen: mass $=5$ g, volume $=5/1.15=4.348$ cm$^3$.
Total solid+binder volume (zero air) $=21.642+10.204+4.959+4.348=41.153$ cm$^3$. This is also $100/G_t$, confirming $G_t=100/41.153=2.430$.

Step 3: Find the air void volume by subtraction.
Since the actual bulk volume (45.455 cm$^3$, Step 1) is larger than the zero-void volume (41.153 cm$^3$, Step 2), the extra volume is air trapped in the compacted mix:
$V_{air} = 45.455-41.153=4.302$ cm$^3$, or as a percentage of bulk volume, $V_a = \dfrac{4.302}{45.455}\times100=9.47\%$

Step 4: Express the bitumen volume as a percentage of the bulk mix volume.
$V_b = \dfrac{4.348}{45.455}\times100=9.57\%$

Step 5: VMA is everything that is not solid aggregate: air plus bitumen.
$VMA = V_a+V_b = 9.47+9.57=19.03\%$
Fraction of that space occupied by bitumen:
$VFB = \dfrac{V_b}{VMA}\times100=\dfrac{9.57}{19.03}\times100=50.3\%$
\[ \boxed{VFB \approx 50\%} \]