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Sieve Analysis Test According to ASTM | Complete Lab Procedure & Calculation
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Estimation of 1 km Asphalt Road

1. Given Data / Assumptions

Length (L) = 1000 m
Width (W) = 7 m
Thickness (t) = 0.05 m

Density of asphalt mix = 2.35 t/m³
Bitumen content (OBC) = 5.17%
Wastage = 5%

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2. Volume of Asphalt Layer

Volume = L × W × t

Volume = 1000 × 7 × 0.05
Volume = 350 m³
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3. Total Weight of Mix

Weight = Volume × Density

Weight = 350 × 2.35
Weight = 822.5 tons
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4. Bitumen Quantity

Bitumen = (5.17 / 100) × 822.5

Bitumen = 42.53 tons
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5. Aggregate Quantity

Aggregate = Total Mix − Bitumen

Aggregate = 822.5 − 42.53
Aggregate = 779.97 tons
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6. Add 5% Wastage

Total Mix = 822.5 × 1.05 = 863.6 ≈ 864 tons

Bitumen = 42.53 × 1.05 = 44.66 ≈ 44.7 tons

Aggregate = 779.97 × 1.05 = 818.97 ≈ 819 tons

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7. Rate Analysis (Example)

Bitumen rate = 700 USD/ton
Aggregate rate = 20 USD/ton
Mixing & laying = 15 USD/ton

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8. Cost Calculation

Bitumen cost = 44.7 × 700 = 31,290 USD

Aggregate cost = 819 × 20 = 16,380 USD

Mixing & laying cost = 864 × 15 = 12,960 USD

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9. Total Cost

Total Cost = 31,290 + 16,380 + 12,960

Total Cost = 60,630 USD
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✅ Final Answer

For 1 km asphalt road:

Total Mix = 864 tons
Bitumen = 44.7 tons
Aggregate = 819 tons

Total Estimated Cost ≈ 60,630 USD

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Important Formulas

Volume = L × W × t

Weight = Volume × Density

Bitumen = (% / 100) × Total Mix

Aggregate = Total Mix − Bitumen

Wastage = Total × 1.05

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Asphalt Mix Design (Marshall Method – MS-2)

1. Given Data

Bitumen grade = 60/70
Aggregate specific gravity (Gsb) = 2.65
Bitumen specific gravity (Gb) = 1.03

Trial bitumen contents (Pb):
4.0%, 4.5%, 5.0%, 5.5%, 6.0%

Compaction = 75 blows per side

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2. Observations (Example for 5% Bitumen)

Weight in air (Wair) = 1200 g
SSD weight (Wssd) = 1220 g
Weight in water (Wwater) = 700 g

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3. Bulk Specific Gravity (Gmb)

Formula:

Gmb = Wair / (Wssd − Wwater)

Calculation:

Gmb = 1200 / (1220 − 700)
Gmb = 1200 / 520
Gmb = 2.31

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4. Theoretical Maximum Specific Gravity (Gmm)

Formula:

Ps = 100 − Pb

Gmm = 100 / [(Pb/Gb) + (Ps/Gsb)]

Calculation:

Pb = 5
Ps = 100 − 5 = 95

Gmm = 100 / [(5/1.03) + (95/2.65)]
Gmm = 100 / (4.85 + 35.85)
Gmm = 100 / 40.7
Gmm = 2.46

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5. Air Voids (Va)

Formula:

Va = [(Gmm − Gmb) / Gmm] × 100

Calculation:

Va = [(2.46 − 2.31) / 2.46] × 100
Va = (0.15 / 2.46) × 100
Va = 6.10%

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6. Voids in Mineral Aggregate (VMA)

Formula:

VMA = 100 − [(Gmb × Ps) / Gsb]

Calculation:

VMA = 100 − [(2.31 × 95) / 2.65]
VMA = 100 − (219.45 / 2.65)
VMA = 100 − 82.83
VMA = 17.17%

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7. Voids Filled with Bitumen (VFB)

Formula:

VFB = [(VMA − Va) / VMA] × 100

Calculation:

VFB = [(17.17 − 6.10) / 17.17] × 100
VFB = (11.07 / 17.17) × 100
VFB = 64.4%

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8. Marshall Stability and Flow

Stability = 12 kN
Flow = 3.5 mm

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9. Results Table (Prepare for All Bitumen Contents)

Pb(%) | Gmb | Gmm | Va | VMA | VFB | Stability | Flow
----------------------------------------------------
4.0 | ... | ... | ...| ... | ... | ... | ...
4.5 | ... | ... | ...| ... | ... | ... | ...
5.0 | 2.31|2.46 |6.1 |17.2 |64.4 |12 |3.5
5.5 | ... | ... | ...| ... | ... | ... | ...
6.0 | ... | ... | ...| ... | ... | ... | ...

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10. Optimum Bitumen Content (OBC)

Formula:

OBC = (B1 + B2 + B3) / 3

Where:

B1 = bitumen at maximum stability
B2 = bitumen at maximum density
B3 = bitumen at 4% air voids

Calculation:

OBC = (5.0 + 5.2 + 5.3) / 3
OBC = 15.5 / 3
OBC = 5.17%

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11. MS-2 Requirements Check

Stability ≥ 9 kN ✔
Flow = 2–4 mm ✔
Air Voids = 3–5% ✔
VMA ≥ 15% ✔
VFB = 65–75% ✔

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12. Final Result

Optimum Bitumen Content (OBC) = 5.17%

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13. Important Formulas (For Study)

Ps = 100 − Pb

Gmb = Wair / (Wssd − Wwater)

Gmm = 100 / [(Pb/Gb) + (Ps/Gsb)]

Va = [(Gmm − Gmb) / Gmm] × 100

VMA = 100 − [(Gmb × Ps) / Gsb]

VFB = [(VMA − Va) / VMA] × 100

OBC = (B1 + B2 + B3) / 3

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Note (Understanding)

Low air voids → durable mix

High stability → strong pavement

Proper VMA → enough space for bitumen

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