Sample 1
21 sections · length 500.00 m · pavement 4 layers
1. Basis of the estimate and standard template
Quantities of earthwork and pavement layers worked out from the existing ground levels of the cross-section survey and the proposed finished road levels (FRL). The finished surface has a crown camber across the carriageway and paved shoulders and a steeper cross fall on the earthen shoulders (IRC:73 - at least 0.5 % steeper than the carriageway). The pavement layers are parallel to the finished surface; the formation (top of subgrade) lies the total pavement thickness below it. Side slopes run from the shoulder edge to the ground.
| Project | - |
|---|---|
| Client | - |
| Location | - |
| Length | 0/000 to 0/500 = 500.00 m, 21 cross sections |
| Carriageway | 3.75 m, crown camber 3 % (IRC:73 / IRC:SP:73) |
| Shoulders | paved 0 m at the camber; earthen 1.875 m at 4 % cross fall (each side) |
| Roadway (formation) width | 7.5 m |
| Side slopes | embankment 2 H : 1 V, cutting 1 H : 1 V |
| Total pavement thickness | 320 mm |
| Proposed profile | vertical intersection points with parabolic vertical curves |
Pavement layers of the template
| Layer | Thickness (mm) | Extends over | Extra width each side (m) | Width (m) | Area of section (m2) |
|---|---|---|---|---|---|
| PMC 20 mm | 20 | Carriageway only | 0 | 3.750 | 0.0750 |
| WBM Gr III | 75 | Carriageway only | 0 | 3.750 | 0.2812 |
| WBM Gr II | 75 | Carriageway only | 0 | 3.750 | 0.2812 |
| GSB | 150 | Full roadway (incl. earthen shoulders) | - | 7.500 | 1.1250 |
- Areas of cut and fill at each section by the coordinate (exact) method between the ground line and the earthwork boundary - formation level under the roadway and the side slopes beyond; mixed sections are split at the cross-over points.
- Pavement layer areas = layer thickness x layer width (constant along the road).
- Volumes between sections by the trapezoidal (average end area) rule V = L (A1 + A2) / 2 and by the prismoidal rule V = h / 3 (A1 + 4 A2 + A3) over pairs of equal intervals (IS 1200 Part 1 measurements of earthwork; the prismoidal correction is shown for comparison).
- Earthen shoulder fill above formation level and the subgrade layer are listed separately.
2. Longitudinal section - levels
Vertical profile - VIPs and vertical curves (K = L / A)
| VIP chainage | VIP level (m) | Grade in % | Grade out % | A = g2 - g1 % | Curve L (m) | K | Type | BVC - EVC |
|---|---|---|---|---|---|---|---|---|
| 0/175 | 102.600 | +0.800 | -0.857 | -1.657 | 120 | 72.4 | summit | 0/115 - 0/235 |
| 0/350 | 101.100 | -0.857 | +0.867 | +1.724 | 100 | 58.0 | valley | 0/300 - 0/400 |
Level on a vertical curve: y = y(BVC) + g1 x + (g2 - g1) x^2 / (2 L), x measured from the BVC. The K value (length per % change of grade) is to be checked against the stopping / intermediate sight distance needs of IRC:SP:23 for the design speed.
Centre line levels
| Chainage | Existing GL (m) | Proposed FRL (m) | Formation (m) | Fill (m) | Cut (m) |
|---|---|---|---|---|---|
| 0/000 | 100.508 | 101.200 | 100.880 | 0.692 | |
| 0/025 | 101.399 | 101.400 | 101.080 | 0.001 | |
| 0/050 | 101.866 | 101.600 | 101.280 | 0.266 | |
| 0/075 | 101.879 | 101.800 | 101.480 | 0.079 | |
| 0/100 | 101.582 | 102.000 | 101.680 | 0.418 | |
| 0/125 | 101.220 | 102.193 | 101.873 | 0.973 | |
| 0/150 | 101.023 | 102.315 | 101.995 | 1.292 | |
| 0/175 | 101.105 | 102.351 | 102.031 | 1.246 | |
| 0/200 | 101.417 | 102.301 | 101.981 | 0.884 | |
| 0/225 | 101.770 | 102.165 | 101.845 | 0.395 | |
| 0/250 | 101.928 | 101.957 | 101.637 | 0.029 | |
| 0/275 | 101.721 | 101.743 | 101.423 | 0.022 | |
| 0/300 | 101.123 | 101.529 | 101.209 | 0.406 | |
| 0/325 | 100.278 | 101.368 | 101.048 | 1.090 | |
| 0/350 | 99.439 | 101.315 | 100.995 | 1.876 | |
| 0/375 | 98.867 | 101.371 | 101.051 | 2.504 | |
| 0/400 | 98.722 | 101.533 | 101.213 | 2.811 | |
| 0/425 | 99.000 | 101.750 | 101.430 | 2.750 | |
| 0/450 | 99.537 | 101.967 | 101.647 | 2.430 | |
| 0/475 | 100.093 | 102.183 | 101.863 | 2.090 | |
| 0/500 | 100.455 | 102.400 | 102.080 | 1.945 |
3. Areas at each cross section
Cross-sectional areas (m2)
| Chainage | Cut | Fill | Catch L - R (m) | PMC 20 mm | WBM Gr III | WBM Gr II | GSB | Earthen shoulder (above formation) | Subgrade (500 mm, full roadway) |
|---|---|---|---|---|---|---|---|---|---|
| 0/000 | 0.000 | 2.960 | -4.86 / 4.89 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/025 | 2.721 | 0.000 | -3.86 / 3.82 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/050 | 4.719 | 0.000 | -4.14 / 4.02 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/075 | 3.189 | 0.000 | -3.99 / 3.78 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/100 | 0.114 | 0.994 | -4.13 / 4.92 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/125 | 0.000 | 6.396 | -5.03 / 6.18 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/150 | 0.000 | 9.844 | -5.51 / 6.77 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/175 | 0.000 | 8.898 | -5.32 / 6.50 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/200 | 0.000 | 4.609 | -4.66 / 5.59 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/225 | 0.375 | 0.306 | -3.85 / 4.42 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/250 | 2.955 | 0.000 | -4.02 / 3.84 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/275 | 2.924 | 0.000 | -3.96 / 3.88 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/300 | 0.100 | 0.330 | -4.23 / 4.27 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/325 | 0.000 | 7.306 | -5.65 / 5.81 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/350 | 0.000 | 18.127 | -7.22 / 7.80 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/375 | 0.000 | 28.922 | -8.47 / 9.47 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/400 | 0.000 | 34.810 | -9.01 / 10.28 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/425 | 0.000 | 33.298 | -8.70 / 10.13 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/450 | 0.000 | 26.848 | -7.83 / 9.28 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/475 | 0.000 | 20.632 | -6.98 / 8.35 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
| 0/500 | 0.000 | 17.877 | -6.60 / 7.82 | 0.075 | 0.281 | 0.281 | 1.125 | 0.637 | 3.750 |
4. Volumes by the trapezoidal (average end area) rule
Worked example - first intervalOK
| Reference | Description | Calculation | Result | |
|---|---|---|---|---|
| Trapezoidal rule | Cutting V = L (A1 + A2) / 2 | 25 x (0.000 + 2.721) / 2 | 34.01 m3 | |
| Trapezoidal rule | Filling V = L (A1 + A2) / 2 | 25 x (2.960 + 0.000) / 2 | 36.99 m3 |
Volumes between consecutive sections (m3)
| Stretch | L (m) | Earthwork in cutting | Earthwork in embankment / filling | PMC 20 mm | WBM Gr III | WBM Gr II | GSB | Earthen shoulder (above formation) | Subgrade (500 mm, full roadway) |
|---|---|---|---|---|---|---|---|---|---|
| 0/000 - 0/025 | 25 | 34.01 | 36.99 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/025 - 0/050 | 25 | 93.00 | 0.00 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/050 - 0/075 | 25 | 98.85 | 0.00 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/075 - 0/100 | 25 | 41.29 | 12.43 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/100 - 0/125 | 25 | 1.43 | 92.38 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/125 - 0/150 | 25 | 0.00 | 203.00 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/150 - 0/175 | 25 | 0.00 | 234.27 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/175 - 0/200 | 25 | 0.00 | 168.83 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/200 - 0/225 | 25 | 4.69 | 61.44 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/225 - 0/250 | 25 | 41.62 | 3.83 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/250 - 0/275 | 25 | 73.49 | 0.00 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/275 - 0/300 | 25 | 37.80 | 4.12 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/300 - 0/325 | 25 | 1.25 | 95.44 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/325 - 0/350 | 25 | 0.00 | 317.90 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/350 - 0/375 | 25 | 0.00 | 588.11 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/375 - 0/400 | 25 | 0.00 | 796.66 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/400 - 0/425 | 25 | 0.00 | 851.35 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/425 - 0/450 | 25 | 0.00 | 751.82 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/450 - 0/475 | 25 | 0.00 | 593.49 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| 0/475 - 0/500 | 25 | 0.00 | 481.36 | 1.88 | 7.03 | 7.03 | 28.12 | 15.94 | 93.75 |
| Total | 500 | 427.43 | 5,293.42 | 37.50 | 140.62 | 140.62 | 562.50 | 318.75 | 1,875.00 |
5. Volumes by the prismoidal rule
Prismoidal (Simpson's) rule over pairs of equal intervals V = h / 3 (A1 + 4 A2 + A3); an unpaired last interval or unequal intervals by the trapezoidal rule.
Earthwork by the prismoidal rule (m3)
| Stretch | Rule | Cutting - calculation | Cutting | Filling |
|---|---|---|---|---|
| 0/000 - 0/050 | prismoidal | 25 / 3 x (0.00 + 4 x 2.72 + 4.72) | 130.02 | 24.66 |
| 0/050 - 0/100 | prismoidal | 25 / 3 x (4.72 + 4 x 3.19 + 0.11) | 146.57 | 8.28 |
| 0/100 - 0/150 | prismoidal | 25 / 3 x (0.11 + 4 x 0.00 + 0.00) | 0.95 | 303.52 |
| 0/150 - 0/200 | prismoidal | 25 / 3 x (0.00 + 4 x 0.00 + 0.00) | 0.00 | 417.04 |
| 0/200 - 0/250 | prismoidal | 25 / 3 x (0.00 + 4 x 0.38 + 2.95) | 37.13 | 48.61 |
| 0/250 - 0/300 | prismoidal | 25 / 3 x (2.95 + 4 x 2.92 + 0.10) | 122.93 | 2.75 |
| 0/300 - 0/350 | prismoidal | 25 / 3 x (0.10 + 4 x 0.00 + 0.00) | 0.83 | 397.32 |
| 0/350 - 0/400 | prismoidal | 25 / 3 x (0.00 + 4 x 0.00 + 0.00) | 0.00 | 1,405.22 |
| 0/400 - 0/450 | prismoidal | 25 / 3 x (0.00 + 4 x 0.00 + 0.00) | 0.00 | 1,623.74 |
| 0/450 - 0/500 | prismoidal | 25 / 3 x (0.00 + 4 x 0.00 + 0.00) | 0.00 | 1,060.43 |
| Total | 438.43 | 5,291.58 |
Comparison of the two rules (m3)
| Item | Trapezoidal | Prismoidal | Difference % |
|---|---|---|---|
| Earthwork in cutting | 427.43 | 438.43 | +2.57 |
| Earthwork in embankment / filling | 5,293.42 | 5,291.58 | -0.03 |
6. Mass haul
Cumulative volume of cut x 1 less fill x 1 (factors for bulking / shrinkage and compaction). A rising line is surplus (cutting), a falling line deficit (filling); a horizontal balance line cuts the curve at the points between which cut and fill balance.
Mass ordinates
| Chainage | Cumulative (m3) |
|---|---|
| 0/000 | 0.0 |
| 0/025 | -3.0 |
| 0/050 | 90.0 |
| 0/075 | 188.9 |
| 0/100 | 217.7 |
| 0/125 | 126.8 |
| 0/150 | -76.2 |
| 0/175 | -310.5 |
| 0/200 | -479.3 |
| 0/225 | -536.1 |
| 0/250 | -498.3 |
| 0/275 | -424.8 |
| 0/300 | -391.1 |
| 0/325 | -485.3 |
| 0/350 | -803.2 |
| 0/375 | -1,391.3 |
| 0/400 | -2,188.0 |
| 0/425 | -3,039.3 |
| 0/450 | -3,791.1 |
| 0/475 | -4,384.6 |
| 0/500 | -4,866.0 |
7. Summary of quantities
Abstract of quantities
| No. | Item | Unit | Trapezoidal | Prismoidal |
|---|---|---|---|---|
| 1 | Earthwork in cutting | m3 | 427.43 | 438.43 |
| 2 | Earthwork in embankment / filling | m3 | 5,293.42 | 5,291.58 |
| 3 | PMC 20 mm | m3 | 37.50 | 37.50 |
| 4 | WBM Gr III | m3 | 140.62 | 140.63 |
| 5 | WBM Gr II | m3 | 140.62 | 140.63 |
| 6 | GSB | m3 | 562.50 | 562.50 |
| 7 | Earthen shoulder (above formation) | m3 | 318.75 | 318.75 |
| 8 | Subgrade (500 mm, full roadway) | m3 | 1,875.00 | 1,875.00 |
| 9 | PMC 20 mm - top surface (prime / tack coat, surface dressing) | m2 | 1,875.00 | 1,875.00 |
| Adopted rule | trapezoidal (prismoidal shown for comparison) |
|---|---|
| Surplus (+) / deficit (-) of earth | -4,866.0 m3 (trapezoidal, with factors) |
8. Drawings
Longitudinal section sheets followed by the cross-section sheets (A3).