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: Recall the volumetric quantities needed.
Marshall mix design defines: \(G_t\) = theoretical maximum specific gravity (mix with zero air voids), \(V_a\) = air voids (%), \(V_b\) = volume of bitumen (%), \(VMA\) = voids in mineral aggregate \(= V_a+V_b\), and \(VFB = \dfrac{V_b}{VMA}\times100\), the fraction of the VMA actually filled by the binder.

Step 2: Find the theoretical maximum specific gravity, \(G_t\).
For 100 kg of mix, using the given percentages by weight and specific gravities of each ingredient,
\[ G_t = \frac{100}{\dfrac{58}{2.68}+\dfrac{25}{2.45}+\dfrac{12}{2.42}+\dfrac{5}{1.15}} \]
Compute each term: \(58/2.68=21.642\), \(25/2.45=10.204\), \(12/2.42=4.959\), \(5/1.15=4.348\). Sum \(=41.153\).
\[ G_t = \frac{100}{41.153}=2.430 \]

Step 3: Find the air voids, \(V_a\).
Air voids compare the actual (bulk) specific gravity \(G_m=2.2\) with the zero-void value \(G_t\):
\[ V_a = \frac{G_t-G_m}{G_t}\times100 = \frac{2.430-2.2}{2.430}\times100=9.47\% \]

Step 4: Find the volume of bitumen, \(V_b\).
\[ V_b = \frac{G_m\times W_b}{G_b} = \frac{2.2\times5}{1.15}=\frac{11}{1.15}=9.57\% \]
where \(W_b=5\) is the percent bitumen by weight of the total mix and \(G_b=1.15\) its specific gravity.

Step 5: Find VMA, then VFB.
\[ VMA = V_a+V_b=9.47+9.57=19.03\% \]
\[ VFB = \frac{V_b}{VMA}\times100=\frac{9.57}{19.03}\times100=50.3\% \]

Final Answer:
Rounded to the nearest integer, roughly half of the void space between the aggregate particles is filled with bitumen.
\[ \boxed{VFB \approx 50\%} \]