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The bitumen content in the Marshal specimen of bitumenous concrete is 5% of the total weight of the mix.
The theoretical and measured unit weights of the mix are 2.5 g/cm3 and 2.4 g/cm3 respectively. The bitumen has specific gravity of 1. The percentage voids in mineral aggregates filled with bitumen (VFB) are:
The theoretical and measured unit weights of the mix are 2.5 g/cm3 and 2.4 g/cm3 respectively. The bitumen has specific gravity of 1. The percentage voids in mineral aggregates filled with bitumen (VFB) are:
- a)50%
- b)70%
- c)75%
- d)85%
Correct answer is option 'C'. Can you explain this answer?
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To find the percentage voids in the mineral aggregates filled with bitumen (VFB), we need to use the following formula:
VFB = [(Gmb - Gt) / Gmb] * 100
Where:
VFB = Percentage voids in mineral aggregates filled with bitumen
Gmb = Measured unit weight of the mix
Gt = Theoretical unit weight of the mix
Let's calculate the VFB using the given values:
Given:
Gmb = 2.4 g/cm3
Gt = 2.5 g/cm3
1. Calculate the difference between the measured and theoretical unit weights:
Gmb - Gt = 2.4 - 2.5 = -0.1 g/cm3
2. Calculate the percentage voids in mineral aggregates filled with bitumen:
VFB = [(-0.1) / 2.4] * 100 ≈ -4.17%
The calculated VFB is a negative value, which doesn't make sense in this context. Therefore, we need to re-evaluate the calculation.
Upon reviewing the question, we realize that there might be a mistake in the given values. The bitumen content is stated to be 5% of the total weight of the mix. However, the specific gravity of the bitumen is given as 1, which is not realistic. The specific gravity of bitumen is usually between 0.97 and 1.02.
Let's assume that the specific gravity of the bitumen is actually 1.0 and recalculate the VFB using this assumption:
Given:
Gmb = 2.4 g/cm3
Gt = 2.5 g/cm3
Bitumen content = 5% of total weight
1. Calculate the weight of the bitumen:
Weight of bitumen = (5/100) * Total weight
2. Calculate the weight of the mineral aggregates:
Weight of mineral aggregates = Total weight - Weight of bitumen
3. Calculate the specific gravity of the mix:
Gmix = [(Weight of bitumen * 1) + (Weight of mineral aggregates * Gmb)] / Total weight
4. Calculate the percentage voids in mineral aggregates filled with bitumen:
VFB = [(Gmix - Gmb) / Gmix] * 100
Now let's calculate step by step:
Step 1: Calculate the weight of the bitumen:
Assume the total weight of the mix is 100 units.
Weight of bitumen = (5/100) * 100 = 5 units
Step 2: Calculate the weight of the mineral aggregates:
Weight of mineral aggregates = 100 - 5 = 95 units
Step 3: Calculate the specific gravity of the mix:
Gmix = [(5 * 1) + (95 * 2.4)] / 100
Gmix = (5 + 228) / 100
Gmix = 233 / 100
Gmix ≈ 2.33 g/cm3
Step 4: Calculate the percentage voids in mineral aggregates filled with bitumen:
VFB = [(2.33 - 2.4) / 2.33] * 100
VFB = (-0.07 / 2.33) * 100
VFB ≈ -3%
Again, we get a negative value for VFB, which doesn
VFB = [(Gmb - Gt) / Gmb] * 100
Where:
VFB = Percentage voids in mineral aggregates filled with bitumen
Gmb = Measured unit weight of the mix
Gt = Theoretical unit weight of the mix
Let's calculate the VFB using the given values:
Given:
Gmb = 2.4 g/cm3
Gt = 2.5 g/cm3
1. Calculate the difference between the measured and theoretical unit weights:
Gmb - Gt = 2.4 - 2.5 = -0.1 g/cm3
2. Calculate the percentage voids in mineral aggregates filled with bitumen:
VFB = [(-0.1) / 2.4] * 100 ≈ -4.17%
The calculated VFB is a negative value, which doesn't make sense in this context. Therefore, we need to re-evaluate the calculation.
Upon reviewing the question, we realize that there might be a mistake in the given values. The bitumen content is stated to be 5% of the total weight of the mix. However, the specific gravity of the bitumen is given as 1, which is not realistic. The specific gravity of bitumen is usually between 0.97 and 1.02.
Let's assume that the specific gravity of the bitumen is actually 1.0 and recalculate the VFB using this assumption:
Given:
Gmb = 2.4 g/cm3
Gt = 2.5 g/cm3
Bitumen content = 5% of total weight
1. Calculate the weight of the bitumen:
Weight of bitumen = (5/100) * Total weight
2. Calculate the weight of the mineral aggregates:
Weight of mineral aggregates = Total weight - Weight of bitumen
3. Calculate the specific gravity of the mix:
Gmix = [(Weight of bitumen * 1) + (Weight of mineral aggregates * Gmb)] / Total weight
4. Calculate the percentage voids in mineral aggregates filled with bitumen:
VFB = [(Gmix - Gmb) / Gmix] * 100
Now let's calculate step by step:
Step 1: Calculate the weight of the bitumen:
Assume the total weight of the mix is 100 units.
Weight of bitumen = (5/100) * 100 = 5 units
Step 2: Calculate the weight of the mineral aggregates:
Weight of mineral aggregates = 100 - 5 = 95 units
Step 3: Calculate the specific gravity of the mix:
Gmix = [(5 * 1) + (95 * 2.4)] / 100
Gmix = (5 + 228) / 100
Gmix = 233 / 100
Gmix ≈ 2.33 g/cm3
Step 4: Calculate the percentage voids in mineral aggregates filled with bitumen:
VFB = [(2.33 - 2.4) / 2.33] * 100
VFB = (-0.07 / 2.33) * 100
VFB ≈ -3%
Again, we get a negative value for VFB, which doesn
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The bitumen content in the Marshalspecimen of bitumenous concreteis 5% of the total weight of the mix.The theoretical and measured unitweights of the mix are 2.5 g/cm3and 2.4 g/cm3 respectively. Thebitumen has specific gravity of 1.The percentage voids in mineralaggregates filled with bitumen (VFB) are:a)50%b)70%c)75%d)85%Correct answer is option 'C'. Can you explain this answer?
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