mean area method for easy earthwork calculation

mean area method is used to calculate the quantity of earthwork required for filling or cutting in road construction. in these example we will calculate earthwork from the given road profile.

road plan

Given data –

length of station = 10m

formation width (B) = 19m

side slope (S:1) = 2:1

STATIONNSL (m)FRL (m)
0+000.00254.417255
0+010.00253.939254.571
0+013.58253.768254.418
0+020.00253.415254.143
0+027.25253.015253.832
0+030.00252.864253.719
0+040.00252.313253.39
0+045.68252253.26
0+050.00252.277253.189
0+056.44252.689253.127
0+060.00252.963253.116
0+060.71253.018253.115
0+070.00253.734253.171
0+080.00254.504253.354
0+089.07255.203253.631
0+090.00255.16253.665
0+100.00254.688254.104

Steps for Mean area method

  • Find the depth/difference by subtracting NSL form FRL
  • calculate the central area by multiplying B*d
  • calculate the side area by multiplying S*d^2
  • find the total area by adding central area+side area
  • find the mean area by adding consecutive total area and divide it by 2, (A1+A2)/2
  • finally, calculate the quantity of cutting and filling by using the formula = mean area*length of station

road profile

Station 0+000.00 to 0+010.00

depth = 255-254.17 = 0.583

central area = Bd = 19*0.583 = 11.077

side area = 2*(0.583)^2 = 0.680

Total area (A1) = Bd+sd^2 = 11.077+0.680 = 11.757

depth = 254.71-253.939 = 0.632

central area = 19*0.632 = 12.008

side area = 2*(0.632)^2 = 0.799

Total area (A2) = 12.008+0.799 = 12.807

Mean area = (A1+A2)/2 = (11.757+12.807)/2 = 12.282

L (length of station) = 10m

since,

the depth (d) is positive then the quantity will be of filling.

Quantity = 12.282*10 = 122.82 m^3

Station 0+010.00 to 0+013.58

depth = 254.71-253.939 = 0.632

central area = 19*0.632 = 12.008

side area = 2*(0.632)^2 = 0.799

Total area (A1) = 12.008+0.799 = 12.807

depth = 254.18-253.768 = 0.65

central area = 19*0.65 = 12.35

side area = 2*(0.65)^2 = 0.845

Total area (A2) = 12.35+0.845 = 13.195

Mean area = (A1+A2)/2 = (12.807+13.195)/2 = 13.001

L (length of station) = 10m

since,

the depth (d) is positive then the quantity will be of filling.

Quantity = 13.001*10 = 130.01 m^3

Station 0+013.58 to 0+020.00

depth = 254.18-253.768 = 0.65

central area = 19*0.65 = 12.35

side area = 2*(0.65)^2 = 0.845

Total area (A1) = 12.35+0.845 = 13.195

depth = 254.143-253.415 = 0.728

central area = 19*0.728 = 13.832

side area = 2*(0.728)^2 = 1.060

Total area (A2) = 13.832+1.060 = 14.892

Mean area = (A1+A2)/2 = (13.195+14.892)/2 = 14.043

L (length of station) = 10m

since,

the depth (d) is positive then the quantity will be of filling.

Quantity = 14.043*10 = 140.43 m^3

Station 0+070.00 to 0+080.00

depth = 253.171-253.734 = -0.563

central area = 19*(-0.563) = -10.697

side area = 2*(-0.563)^2 = 0.634

Total area (A1) = -10.697-0.634 = -11.331

depth = 253.354-254.504 = -1.15

central area = 19*(-1.15) = -21.85

side area = 2*(-1.15)^2 = 2.645

Total area (A2) = -21.85-2.645 = -24.495

Mean area = (A1+A2)/2 = (-11.331-24.495)/2 = -17.913

L (length of station) = 10m

since,

the depth (d) is negative then the quantity will be of cutting.

Quantity = -17.913*10 = -179.13 m^3

Station 0+090.00 to 0+100.00

depth = 253.665-255.16 = -1.495

central area = 19*(-1.495) = -28.405

side area = 2*(-1.495)^2 = 4.47

Total area (A1) = -28.405-4.47= -32.875

depth = 254.104-254.688 = -0.584

central area = 19*(-0.584) = -11.096

side area = 2*(-0.584)^2 = 0.682

Total area (A2) = -11.096-0.682 = -11.778

Mean area = (A1+A2)/2 = (-32.875-11.778)/2 = -22.327

L (length of station) = 10m

since,

the depth (d) is negative then the quantity will be of cutting.

Quantity = -22.327*10 = -223.27 m^3

note

if depth (d) is positive then add if d is coming negative then subtract so that the total area will be in negative.

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