Calculating Cut and Fill Norman W. Garrick CE 4410 Spring 2017 Lecture 8

Average End Area Method Typically used for linear projects such as roads, railroads, canals http://www.latinamericanstudies.org/erie-canal.htm

Find area of Fill and Cut separately for selected cross-sections Volume of Fill (or cut) between Two Cross-sections = [(A1 + A2)/2 ] * L Where: A1 is area of fill for Cross-section 1 A2 is area of fill for Cross-section 2 L is distance between 1 and 2

A refinement to this approach is used when A1 or A2 is an end cross-section (there is not fill or cut) In this case, (A1+A2)/2 * L Over estimates the volume since The shape of the earthwork is more Like a pyramid. In this case a more accurate formula Is [(A1+A2)/3] * L (Note there is an error in text for this formula)

Contour Area Method Calculating Cut and Fill

Determine the cut/fill line

Find the area between the existing and finished contour for cut and fill separately Contour Line Cut Area (sq. ft) Fill Area (sq. ft) 28 26 10000 24 15000 22 30000 20 35000 18 17500 16

Calculate Cut and Fill Volumes Contour Line Cut Area (sq. ft) Fill Area (sq. ft) 28 26 10000 24 15000 22 30000 20 35000 18 17500 16 V = A1*h/3 + (A1+A2)*h/2 + (A2+A3*h/2 +…. (An-1+An)*h/2 + An*h/3

Calculate Cut and Fill Volumes Contour Line Cut Area (sq. ft) Fill Area (sq. ft) 28 26 10000 24 15000 22 30000 20 35000 18 17500 16 Cut V = A1*h/3 + (A1+A2)*h/2 + (A2+A3*h/2 +…. (An-1+An)*h/2 + An*h/3 = 10000*2/3 +(10000+15000)*2/2+(15000+30000)*2/2*30000*2/3 = 97000 cu. Feet = 3600 cubic yard Cut V = A1*h/3 + (A1+A2)*h/2 + (A2+A3*h/2 +…. (An-1+An)*h/2 + An*h/3 = 35000*2/3 +(35000+17500)*2/2+17500*2/3 = 88000 cu. Feet = 3200 cubic yard

Borrow Pit Method Calculating Cut and Fill

Find amount of cut or fill needed to create a terrace at elevation 96 ft Figure 4.5 Textbook

Find amount of cut or fill needed to create a terrace at elevation 96 ft No.1 No.2 No.3 No.4 Figure 4.5 Textbook

Find amount of cut or fill needed to create a terrace at elevation 96 ft Cell No. 1 Cut/Fill at each Corner B3 Cut 99.4 – 96.0 = 3.4 ft B4 Cut 98.4 – 96.0 = 2.4 ft C3 Cut 98.3 – 96.0 = 2.3 ft C4 Cut 97.8 – 96.0 = 1.8 ft Average Cut = (3.4+2.4+2.3+1.8)/4 = 9.9/4 = 2.475 ft Amount of Cut Cell No. 1 = Average Cut * Area = 2.475*10,000 = 24,750 cu. ft = 24,750/27 = 917 cubic yard = 920 cubic yard No.1 No.2 No.3 No.4 Figure 4.5 Textbook

Find amount of cut or fill needed to create a terrace at elevation 96 ft Cell No. 2 Cut/Fill at each Corner B4 Cut 98.4 – 96.0 = 2.4 ft B5 Cut 97.1 – 96.0 = 1.1 ft C4 Cut 97.8 – 96.0 = 1.8 ft C5 Cut 96.7 – 96.0 = 0.7 ft Average Cut = (2.4+1.1+1.8+0.7)/4 = 6.0/4 = 1.5 ft Amount of Cut Cell No. 1 = Average Cut * Area = 1.5*10,000 = 15,000 cu. ft = 15,000/27 = 556 cubic yard = 560 cubic yard No.1 No.2 No.3 No.4 Figure 4.5 Textbook

Find amount of cut or fill needed to create a terrace at elevation 96 ft Cell No. 3 Cut/Fill at each Corner C3 Cut 98.3 – 96.0 = 2.3 ft C4 Cut 97.8 – 96.0 = 1.8 ft B3 Cut 96.7 – 96.0 = 0.7 ft B4 Cut 96.6 – 96.0 = 0.6 ft Average Cut = (2.3+1.8+0.7+0.6)/4 = 5.4/4 = 1.35 ft Amount of Cut Cell No. 3 = Average Cut * Area = 1.35*10,000 = 13,500 cu. ft = 13,500/27 = 500 cubic yard No.1 No.2 No.3 No.4 Figure 4.5 Textbook

Find amount of cut or fill needed to create a terrace at elevation 96 ft Cell No. 4 Cut/Fill at each Corner C4 Cut 97.8 – 96.0 = 1.8 ft C5 Cut 96.7 – 96.0 = 0.7 ft B4 Cut 96.6 – 96.0 = 0.6 ft B5 Cut 96.0 – 96.0 = 0.0 ft Average Cut = (1.8+0.7+0.6+0.0)/4 = 3.1/4 = 0.78 ft Amount of Cut Cell No. 1 = Average Cut * Area = 0.78*10,000 = 7,800 cu. ft = 7.800/27 = 289 cubic yard = 290 cubic yard No.1 No.2 No.3 No.4 Figure 4.5 Textbook

Find amount of cut or fill needed to create a terrace at elevation 96 ft Total Volume Cut Cell 1 – 920 cu. yd. Cell 2 - 560 cu. yd. Cell 3 – 500 cu. yd. Cell 4 - 290 cu. yd. = 2270 cubic yard No.1 No.2 No.3 No.4 Figure 4.5 Textbook

A Calculation Short-cut Find amount of cut or fill needed to create a terrace at elevation 96 ft A Calculation Short-cut Use V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4) Where V – volume of cut or fill A – area of each cell h1 – sum of cuts (or fill) for all grid corners common to one grid h2 – sum of cuts (or fill) for all grid corners common to two grids h3 – sum of cuts (or fill) for all grid corners common to three grid h4 – sum of cuts (or fill) for all grid corners common to four grids No.1 No.2 No.3 No.4 Figure 4.5 Textbook

A Calculation Short-cut Find amount of cut or fill needed to create a terrace at elevation 96 ft A Calculation Short-cut V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4) h1 = (99.4-96)+(97.1-96)+96.7-96)+(96.0-96) = 3.4 + 1.1 + 0.7 + 0 = 5.2 No.1 No.2 No.3 No.4 Figure 4.5 Textbook

A Calculation Short-cut Find amount of cut or fill needed to create a terrace at elevation 96 ft A Calculation Short-cut V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4) h2 = (98.4-96)+(98.3-96)+96.7-96)+(96.6-96) = 2.4 + 2.3 + 0.7 + 0.6 = 6.0 No.1 No.2 No.3 No.4 Figure 4.5 Textbook

A Calculation Short-cut Find amount of cut or fill needed to create a terrace at elevation 96 ft A Calculation Short-cut V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4) h3 = 0 No.1 No.2 No.3 No.4 Figure 4.5 Textbook

A Calculation Short-cut Find amount of cut or fill needed to create a terrace at elevation 96 ft A Calculation Short-cut V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4) h4 = (97.8-96) = 1.8 No.1 No.2 No.3 No.4 Figure 4.5 Textbook

A Calculation Short-cut Find amount of cut or fill needed to create a terrace at elevation 96 ft A Calculation Short-cut h1 = 5.2 h2 = 6.0 h3 = 0 h2 = 1.8 V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4) = (10,000/4)*(1*5.2 + 2*6.0 + 3*0 + 4*1.8) = 2260 cubic yards No.1 No.2 No.3 No.4 Figure 4.5 Textbook

Find amount of cut or fill needed to create a terrace at elevation 97 ft We need to do separate calculations for cut and fill Cut h1 = 2.4+0.1+0+0 h2 = 1.4+1.3+0+0 h3 = 0 h2 = 0.8 V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4) = 1000 cubic yards No.1 No.2 No.3 No.4 Fill h1 = 0+0+0.3+1.0 h2 = 0+0+0.3+0.4 h3 = 0 h2 = 0 V = (A/4)*(1*h1 + 2*h2 + 3*h3 + 4*h4) = 250 cubic yards Figure 4.5 Textbook