Road construction in Civil engineering

Lead and Lift
Computation of Earthwork
Cross Section Area with no transverse slope
Calculation of Quantities of earthwork FOR
Mid Section Formula, - MeanSection Formula, - Prismoidal Formula
Mass Haul Diagram

1. Road Construction Content Lead and Lift Computation of Earthwork Cross Section Area with no transverse slope Calculation of Quantities of earthwork FOR Mid Section Formula, - MeanSection Formula, - Prismoidal Formula Mass Haul Diagram

2. Road Construction What is Road and Why it is needed Specially designed route to allow movement from one place to other. Items in road construction Survey Work, Earthworks (Cutting, Filling), Subgrade, Sub base, Base Course, Bituminous Course Note: In this chapter, we will study Earthworks calculation

3. Road Construction Cutting And Filling Why cutting Filling are required?: Formation Level of Road may be below the actual ground level or may be above ground level, hence to provide all road layers properly executed, sufficient depth/height are needed. Lead and Lift To dispose or dumping soil at suitable place, Transportation and Lifting of soil are required Lead : It’s a horizontal straight practicable distance through earth can be transported from source to place of dumping. When Unit of Lead is 50 m up to 500 m, Lead is measured as separate items:- 0 to 250 m 250 to 500 m

4. Road Construction Lead and Lift Lead ( conti ..) When Unit of Lead is 500 m to 5000 m, Lead is measured as a separate item:- 500 m to 1000 m 1000 m to 1500 m 1500 m to 2000 m… Keep on increasing 500 m When Unit of Lead is beyong 5 KM, Lead is measured as a separate item, starting from 1 km or 1/2km Lead item shall include loading and unloading. Lead is measured from Centre of Exacavted place to Centre of Dumping Place.

5. Road Construction Lead and Lift Lift Height measured from Ground level. Excavation of soil upto 1.5 m meter from ground level and depositing on ground is included in earthwork item rate. Extra lift is measured in unit of 1.5 m or part thereof. Inherent Lift is measured separately (due slope difference in lead beyond 250 m) When earth is to be moved over a bank, dumped beyond it. Lift is measured difference in level of centre of gravity to excavated area and TOP of bank.

6. Road Construction Volume of Earthwork To avoid flooding on Road, The level of formation is designed above the high flood level. So it forms a trapezium to side slopes of the embankment And when Formation level is below ground level, cutting is required side slopes. So both in cutting and filling, trapezium is formed. The height of banking and depth of cutting is designed as per high flood level, ruling gradient and for economy in earthwork To estimate earthwork, longitudinal levels along the centreline of a road are taken at certain distance apart. The distance between two points depends on topography of surface. For Plain surface, distance is 20 to 50 m For Hilly areas, distance is 10 to 20 m The Scale for Drawings:- For Longitudinal Sections : 1 cm = 10 m to 1 cm = 20 m For Cross Section : 1 cm = 1 m to 2 m

7. Road Construction Volume of Earthwork Depth of cutting or banking is difference between ground level and formation level. Slope is Horizontal : Vertical for Sides Will follow the Formulas for Calculation of Earthwork quantity. Mid Section Method Trapezoidal or Average End area or Mean Section method Prismoidal Method as per Simson’s one-third rule

8. Road Construction Volume of Earthwork Mid Section Method: Area of any Section is Bd + Sd ² Volume of Earth between Two sections V = Area of Mid Section x L V = Am X L V = ( Bd + Sdm ²) x L Dm = Mean Depth between two consecutive sections Dm = (d1 +d2) / 2

9. Road Construction Volume of Earthwork Mid Section Method: Table Format for Calculation Station or Chainage Reduced level of Ground Formation Level Depth or Height at Station Area of Centre Portion Area of Sides Total Area Distance Between Stations Quantity Embankment Am x L Cutting Am X L                                         When Due to change in Reduced levels of Ground, Formation level goes up or down with respect to Ground Level then Crossing chainage shall be found out. Check Example below At Chainage CH1 and Depth of Cutting is d1 and At Chainage CH2 the Height of Embankment is h2

10. Road Construction Volume of Earthwork Mid Section Method: IF formation level (FL) has rising gradient (1 : r or in 1 in r distance) in longitudinal direction Then, we can mention:- IF formation level (FL) has down gradient (1 : r or in 1 in r distance) in longitudinal direction Then, we can mention:-

11. Road Construction Volume of Earthwork Mid Section Method : Example : A Single railway track is to be at uniform down gradient from point ‘A’ with formation level of 118.90 to a point ‘B’ with formation level of 118.10. Distance between two points is 320 m. The ground lvel at different chainages are given in table. Estimate cost of earthwork involved, Formation width in cutnig is 5.5 m and Banking is 6.0 m. Side Slope for Cutting 1.5:1 and in Banking 2:1. GL 120.5 120.1 119.7 119.2 118.5 118.2 117.7 117.3 117.5 Chainage 1 2 3 4 5 6 7 8 Station or Chainage Reduced level of Ground Formation Level Depth or Height at Station (GL-FL) Mean Depth dm Area of Centre Portion Bdm Area of Sides Sdm² Total Area Am = Bdm + Sdm² Distance Between Stations L Quantity Embankment Am x L Cutting Am X L 120.5 118.9 1.6               40 120.1 118.8 1.3 1.45 7.975 3.15375 11.12875 40 445.15   80 119.7 118.7 1 1.15 6.325 1.98375 8.30875 40 332.35   120 119.2 118.6 0.6 0.8 4.4 0.96 5.36 40 214.4   160 118.5 118.5 0.3 1.65 0.135 1.785 40 71.4   200 118.2 118.4 -0.2 -0.1 -0.6 -0.02 -0.62 40   -24.8 240 117.7 118.3 -0.6 -0.4 -2.4 -0.32 -2.72 40   -108.8 280 117.3 118.2 -0.9 -0.75 -4.5 -1.125 -5.625 40   -225 320 117.5 118.1 -0.6 -0.75 -4.5 -1.125 -5.625 40   -225 Total 1063.3 -583.6

12. Road Construction Volume of Earthwork Mid Section Method : Example :

13. Road Construction Volume of Earthwork Trapezoidal Formula or Average End Area or Mean Sectional Area Instead of taking Mean Depth of 2 consecutive section, Average of Two consecutive cross sectional area is taken. First Cross section (A ₁ ) = Bd ₁ + Sd ₁² Next Cross section (A ₂ ) = Bd ₂ + Sd ₂² Mean Sectional Area (Am) = (A ₁ + A ₂) / 2 L is length between sections then Volume for n number of sections (V) = V = L ( A ₁ + A ₂ )/2 + L ( A ₂+ A 3)/2 + ………. L (An-1 – An)/2 V = L /2 (A1 + 2A2 + 2A3 + 2A4 + ……..2An-1 +An) That means Volume = Distance between two sections divide by two and multiplied by addition of FIRST, LAST and two times all rest section areas.

14. Road Construction Volume of Earthwork Trapezoidal Formula or Average End Area or Mean Sectional Area Repeat Same Example . Station or Chainage Reduced level of Ground Formation Level Depth or Height at Station (GL-FL)   Area of Centre Portion Bd Area of Sides Sd² Total Area A = Bd + Sd² (A1 + A2)/2 Distance Between Stations L Quantity Embankment Am x L Cutting Am X L 120.5 118.9 1.6   8.8 3.84 12.64         40 120.1 118.8 1.3   7.15 2.535 9.685 11.1625 40 446.5   80 119.7 118.7 1   5.5 1.5 7 8.3425 40 333.7   120 119.2 118.6 0.6   3.3 0.54 3.84 5.42 40 216.8   160 118.5 118.5   1.92 40 76.8   200 118.2 118.4 -0.2   -1.2 -0.08 -1.28 -0.64 40   -25.6 240 117.7 118.3 -0.6   -3.6 -0.72 -4.32 -2.8 40   -112 280 117.3 118.2 -0.9   -5.4 -1.62 -7.02 -5.67 40   -226.8 320 117.5 118.1 -0.6   -3.6 -0.72 -4.32 -5.67 40   -226.8 Total 1073.8 -591.2

15. Road Construction Volume of Earthwork Prismoidal Formula ( Simson rule) Assumption here is that A 1 and A 2 are areas at ends and Am is mid section of them and parallel to them. Then Volume of prism L/6x(A 1 + A 2 +4A m ) is considered Prismoidal Formula Note : Am is not average of A 1 and A 2 First Cross section (A ₁ ) = Bd ₁ + Sd ₁² Next Cross section (A ₂ ) = Bd ₂ + Sd ₂² Mid Section Area (Am) = Bd m + Sd m² L is distance between A 1 and A 2

16. Road Construction Volume of Earthwork Prismoidal Formula Example : Embankment is 120 m long 8 m wide at crest, whose side slopes is 1:2 (Vertical to Horizontal). Central height from 0 to every 30 m intervals are 0.6, 1.2m, 1.6m, 2.0m, 1.3m CH d dm A Am L V (emb) AmL 0.6 5.52 30 1.2 0.9 12.48 8.82 30 266.4 60 1.6 1.4 17.92 15.12 30 454.4 90 2 1.8 24 20.88 30 627.2 120 1.3 1.65 13.78 18.65 30 561.8 sum 1910

17. Road Construction Volume of Earthwork Area of Turfing Area of one side Turfing = L x Sqrt (( sd m ) 2 +d m 2 )) = L x d m x sqrt (s 2 +1) Area of both side turfing = 2Ld m sqrt (s 2 +1) Table Format

18. Road Construction Volume of Earthwork Mass Haul Diagram Why Mass Haul Diagram required:- Haulage distance between excavated place to depositing or filling place varies in construction of road, canal, drainage or longitudinal excavation For economical transportation of excavated soils, Mass haul diagram is required. Most of the times cutting soil is used in filling in nearby sections and sometimes have to have from borrow pits So it is necessary to place the movement of materials from cuts to fills so that haul distance be minimum to reduce the cost of earthwork (specially in undulating areas)

19. Road Construction Volume of Earthwork Mass Haul Diagram What is Mass haul Diagram:- Its is curve representing cumulative volume of earthwork at any point on the curve Or algebraic sum of volume at every chainage . It indicates the balance points of cutting and filling, volume of free haul, overhaul Comparative Economical study can be prepared whether to use cut soil or borrow Figure shows Mass Haul diagram as per chainage and also compare with Longitudinal sections Mass Haul Diagram

20. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) A few Definition to understand detail of MHD:- Haul Distance : Distance to which excavated earth is transported Haul : Sum of products of each load by its haul distance ( = Cum x Meter) Average Haul Distance : Distance from centre of gravity of a cutting to that of the tipped material (lead) Free Haul Distance : Cost of haul within a specified distance is included in earthwork item rate is called Free Haul Distance. Economical Haul : This is limit of profitable haul distance, beyond which it is good to waste and borrow. Cost of excavation and hauling = Cost of excavation and waste + Cost of borrow from pits. Volume XLMA’ hauling to place of NPZB’ can be uneconomical, so better to borrow from pits and waste XLMA’

21. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) A few Definition to understand detail of MHD:- Over Haul Distance : Extra Distance beyond Free haul distance to which price is fixed in contract for haulage. JJ’ and K’K are overhaul distance. J and K point are centroid of XLMA and NPZB’ How to find J and K point : Drop line from mid point of ordinates (at ends of freehaul ), intersecting on curve on both side. Over Haul : Sum of products of products of each load by its overhaul haul distance ( = Cum x Meter) Balancing Lines : Any horizontal lines which intersects curve at two points. Quantity of earthwork for excavation equals to filling between these two points of sections (EF or JJ’ or K’K in figure)

22. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) Characteristics of MHD As curve (A’C) upwards, it shows cutting (+ ve ) and curve reaches at maximum(C). Then curve (CB’) moves downwards it shows filling (- ve ) Take a scale of free haul distance (EF) and insert between curve in such a way that it remains parallel to Baseline(A’B’) and intersects(E & F) to curve at two points, it will show free haul distance and vertical distance(CC’) to upto maximum point(C) is volume to be free haul

23. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) Characteristics of MHD Vertical Distance(EJ’) between two points (E & J) with no maximum & minimum between them, is volume of earth between the length(J”G) of these two points. Similarly JJ” is the volume of earth between point A’ and J” Wherever Curve intersects with Baseline, volume of cut becomes equals to volume of filling up to that point. At B’ the cut volume (XA’Y) equals to fill volume (YB’Z) Algebric sum of volume of cut and fill is zero at intersection point (B’)

24. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) Characteristics of MHD When Curve is above the balance line then volume is be moved from left to right. When curve is below the balance line then volume is to be moved from right to left. Length(A”B”) of balancing line intercepted by a loop of curve, represents the maximum haul distance (A”B”) in that section.

25. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) Preparation of MHD Work out accumulated volume at every station. Positive sign for cutting and Negative sign for filling Draw a horizontal line as abscissa (baseline) and select a scale (1 cm = 20 m or 30 or 50 m). Mark chainage or station points. Select a scale (1 cm = 200 cum, 250/300/500/1000) for quantity of earth work At every station point draw vertical lines equal commulative volume at that point (positive above abscissa and negative below) Join all the ends of ordinates and the baseline by a smooth curve. The whole enclosed area within curve and baseline is called Mass Haul Diagram.

26. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) Example-1 :

27. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) Example-2: Plot the ground profile and mass haul diagram of the road section from the data given below. And calculate a) Economical Haul Distance b) Division points in cut for least possible total haul c) Total Free Hual d) Total Overhaul e)Total borrowed earth f) Total cost of earthwork Following information is given:- Free haul distance is 90 m. Cost of excavation with free haul is Rs 6.00 per cum. Cost of borrowed earth is Rs 7.5 per cum for stage of each. Cost of overhauling is Rs 1.5 per cum for each additional lead of 30 m over free haul distance. Solution is in next slide CH 30 60 90 120 150 180 210 240 270 300 330 360 Volum 350 450 250 100 -350 -550 -625 -475 -175 250 525 500 Accumulated 350 800 1050 1150 800 250 -375 -850 -1025 -775 -250 250

28. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) Example (Solution)

29. Road Construction Volume of Earthwork Mass Haul Diagram (MHD) Example (Solution) Limit of Economical Haul is when cost of overhaul = cost of borrow C 1 (X- ff ) = C 2 x 30 1.5 (X-90) = 7.5 x 30 X = 240 m Total Free haul distance = 90 m, Free haul volume is 1.4x250+2.0x250 = 850 cum Total overhaul distance = (o 1 k 1 + o 2 k 2 ) carrying 800 cum and (o 3 k 3 + o 4 k 4 ) carrying 550 cum = 1.8x 30 = 54 m (in upper loop) = 0.9x 30 = 27 m (in lower loop) Total Borrowed earth = bb 2 = 250 cum Total Cost of Earthwork = Total freehaul cost + Total overhaul cost + Total borrow cost =850 x 6 + (54x800/30+27x550/30) x 1.5 + 250 x 7.5 = 5100 + 2902.5 + 1875 = Rs 9877