In order to minimize material waste or borrow, it is necessary to produce what is called a Mass Haul diagram. This is essentially a plot of cumulative volume of soil against distance along the road, often called the chainage. Cut volumes are taken to be positive and fill volumes to be negative.
Calculation of Cross Sectional Area
The first stage in the production of the Mass Haul Diagram is the calculation of the cross sectional areas of cut or fill at different points along the road.
For a cut or fill on horizontal ground.
Figure 1 – Typical Cut Cross Section |
Assuming a cut such as the one above, the cross sectional area is given by:
Area = h.2b + 2nh²/2 = h(2b + nh)
For a cut or fill on sloping ground
Figure 2 – Typical Sloping Cut Cross Section |
Assuming a cut such as the one above, the cross sectional area is found firstly by calculating W_{L} and W_{G}:
W_{L} = S(b+nh)/(S+n)
W_{G} = S(b+nh)/(S-n)
Thus Area = ½(h + b/n)(W_{L} + W_{G}) – b²/n
For more complicated cross sections, simply combine the above. It should be noted that this is NOT part of the design process for the slope stability.
Cumulative Volumes
Once the cross sectional areas are known at various points along the road, it is possible to calculate the cumulative volume along the cut by interpolating between the different points.
The simplest way of doing this is to assume a straight line variation and use the prismatic rule. Other slightly more complicated methods involve using Simpsons rule or similar. Do not forget to take account of the bulking factor or shrinkage factor although care should be taken not to use them both as this will produce incorrect results. If you are using the shrinkage factor then changes in volume due to excavation is accounted for automatically. The same is true for the bulking factor.
EARTHWORK FORMULAS
Area | |
Area by Coordinates | |
Area = [X_{A}(Y_{B} - Y_{N}) + X_{B}(Y_{C} - Y_{A}) + X_{C}(Y_{D} - Y_{B}) + ...+ X_{N}(Y_{A} - Y_{N-1})]/2 | |
Trapezoidal Rule | |
Area = w[(h_{1} + h_{n})/2 + h_{2} + h_{3} + h_{4} + .... + h_{n-1}] w = common interval length | |
Simpson’s 1/3 Rule | |
w = common interval length | |
Volume | |
Average End Area Formula | |
V = L(A_{1} + A_{2})/2 | |
Prismoidal Formula | |
V = L(A_{1} + 4A_{m} + A_{2})/6 | |
Pyramid or Cone | |
V = h(area of base)/3 |
For a more accurate measurement of dike volume on rough ground, you should apply the following formula, known as Simpson’s rule, where: V = (d ÷ 3) x [A_{1} + A_{n} + 4(A_{2} + A_{4} + ... A_{n-1}) + 2(A_{3} + A_{5} + ... A_{n-2})]. Proceed as follows:
(a) Divide the length of the dike into an odd number n of cross-sections at equal intervals of d metres.
(b) Calculate the area A of each cross-section as explained earlier.
(c) Introduce these values into the above formula
Abubakar Mustapha
please send me formulas for calculating the volume fill for earth dikes
PONRAJ
how to draw earthwork cutting sections in excel sheet and how can we calculate total volume by using the excel drawing
Oktay Songur
Excellent
Oguntoye Samuel Oluwaseun
you people are wonderful.
Oguntoye Samuel Oluwaseun
you people are wonderful.
Mohammad Adil
nyc one
Dipun Behera
very nice
Anuj Dubey
works at gref.
Theodory Kisumo
well!
Emmanuel Lugola
very useful and thanks for remind us.
Onuchukwu Ifeanyi
NICE ONE
Sanjay Pandurang Malawade
ok
Ilme Umar
nice one…………
Adugna Gelaw
not enough
Khensani Hlungwani
Very useful manual!
Praveen Karoth
nice effort, may b u can add the methode when n is an even number.
Sulleiman Silver
YAP
Muluken Embiale
yap
Muluken Embiale
it is good running.
Selamawit Ermias
one answer for monday's exam!
Muluken Embiale
ya it may be!!!
Kingsley Armah
Could you please assist with a spreadsheet template for embankment earthwork volume calculations.
Seth Tetteh
Hi nii u'v not been calling me why i míss u try and let me here of u pls.
Kingsley Armah
Ok, I will keep in touch.
Shamsher Singh
I have collect the OGL and compare with FRL, I found some points are showing Cut and Some points showing Fill in section but I want Separate-Separate quantity for cut and fill (for total Cut and Total Cut) in Microsoft excel?