In a bituminous mix, the percentage by weight of coarse aggregate, fine ag gregate, filler, and bituminous binder is 58, 25, 12, and 5, respectively. The cor responding 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).

The correct answer is 50.

Step 1: Identify the given data
The percentages by weight of the individual constituents in the bituminous mix are:
- Coarse aggregate (ca): P_ca = 58%
- Fine aggregate (fa): P_fa = 25%
- Filler (f): P_f = 12%
- Bitumen binder (b): P_b = 5%
The specific gravity (G) of each material is given as:
- Coarse aggregate: G_ca = 2.68
- Fine aggregate: G_fa = 2.45
- Filler: G_f = 2.42
- Bitumen: G_b = 1.15
The bulk specific gravity of the total mix (G_m) is:
- G_m = 2.2

Step 2: Calculate the theoretical maximum specific gravity of the mix (G_t)
The theoretical maximum specific gravity (G_t) assuming zero air voids is calculated using the following relation:

$$G_t=\frac{100}{\frac{P_{\mathrm{ca}}}{G_{\mathrm{ca}}}+\frac{P_{\mathrm{fa}}}{G_{\mathrm{fa}}}+\frac{P_f}{G_f}+\frac{P_b}{G_b}}$$

Substituting the given values into the equation:

$$G_t=\frac{100}{\frac{58}{2.68}+\frac{25}{2.45}+\frac{12}{2.42}+\frac{5}{1.15}}$$

Calculate each individual term in the denominator:
- 58 / 2.68 = 21.6418
- 25 / 2.45 = 10.2041
- 12 / 2.42 = 4.9587
- 5 / 1.15 = 4.3478

Summing the values:
Denominator = 21.6418 + 10.2041 + 4.9587 + 4.3478 = 41.1524

Therefore, we get:

$$G_t=\frac{100}{41.1524}\approx 2.430$$

Step 3: Calculate the percentage of air voids (V_v) in the mix
The volume percentage of air voids (V_v) is given by:

$$V_v=\left(\frac{G_t-G_m}{G_t}\right)\times 100$$

Substituting the values:

$$V_v=\left(\frac{2.430-2.2}{2.430}\right)\times 100\approx 9.465\%$$

Step 4: Calculate the volume percentage of bitumen (V_b)
The percentage volume of bitumen binder in the mix (V_b) is given by:

$$V_b=\frac{P_b\times G_m}{G_b}$$

Substituting the values:

$$V_b=\frac{5\times 2.2}{1.15}=\frac{11}{1.15}\approx 9.565\%$$

Step 5: Calculate the Voids in Mineral Aggregate (VMA)
VMA is the total volume of voids present within the aggregate structure, which includes both the volume of air voids and the volume of effective bitumen.

$$\mathrm{VMA}=V_v+V_b$$

Substituting the values:

$$\mathrm{VMA}=9.465+9.565=19.03\%$$

Step 6: Calculate Voids Filled with Bitumen (VFB)
VFB represents the percentage of the voids in the mineral aggregate framework that are filled with bitumen:

$$\mathrm{VFB}=\left(\frac{V_b}{\mathrm{VMA}}\right)\times 100$$

Substituting the calculated values:

$$\mathrm{VFB}=\left(\frac{9.565}{19.03}\right)\times 100\approx 50.26\%$$

Rounding off to the nearest integer, we get:
VFB = 50%