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## Earthwork Volume Estimation

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**Enabling Learning Objective B**ACTION: Estimate earthwork volume. CONDITIONS: In a classroom environment given a PowerPoint presentation, student handout and calculator (supplied by student). STANDARDS: Estimate earthwork volume by determining the area of cut and/or fill at each cross section to within +/- ten percent accuracy of the provided solutions and using the average end area method to determine the total amount of material to be cut or filled between the cross sectional areas.**Earthwork Volume Estimation**Student Handout – Page 3**What are we going to do?**• Determine the area of a cross section to be cut or filled in square feet. • Multiply the area by the length in feet between areas to determine the volume in cubic feet. • Convert the volume from cubic feet to cubic yards.**What is a Cross Section?**A cross section is a vertical illustration of a section of road perpendicular to the centerline at the stations. It shows the relation of the proposed grade to existing grade.**3**C 2.5 1 L 39.3 23.5 Surveyor Notation Proposed Grade Existing Grade**3**C 2.5 1 L 39.3 23.5 Elevation of the Point ELEVATION OF THIS POINT**3**C 2.5 1 L 39.3 23.5 Horizontal Distance HORIZONTAL DISTANCE FROM CENTERLINE**3**C 2.5’ 1 L 39.3 23.5 Determine Notation ? ?**3**C 2.5’ 1 L 39.3 23.5 Determine Notation 41.8 ? 1. Add 2.5 to elevation (39.3) = 41.8**3**C 2.5’ 1 L 39.3 23.5 Determine Notation 41.8 7.5’ 2. Multiply change in elevation (2.5) by horizontal distance of slope ratio (3) , 2.5 X 3 = 7.5**3**C 2.5’ 1 L 39.3 23.5 Determine Notation 41.8 16.0 7.5’ 16.0’ 23.5’ 3. The 7.5 is subtracted from 23.5 to get our distance from the centerline. 23.5 - 7.5 = 16.0**Determining Volume**Volume between stations is determined by multiplying the average end areas of two cross sections by the distance between them. To convert cubic feet to cubic yards we divide by 27 V = (A1 + A2) 2 Distance L 27 x**End Area**22 + 00 22 + 00 We will use the AVERAGE of the two end areas. 21 + 00 H 21 + 00 W**Station Distance**22 + 00 L 21 + 00 L = Length between stations**Station Distance**One station = 100 ft (by definition). Stations begin numbering from 0+00. For example, Station 20+00 is 2,000 ft from the beginning of the project which starts at 0+00. HINT: Just remove the “+” sign when doing calculations. Cross sections can be drawn at any station as needed.**b x h**A = 2 b1 + b2 A = h 2 Methods for Calculating the Area of a Cross-Section Trapezoidal Method – Accuracy is +/- 10% Area of a triangle: Area of a trapezoid: How many and what type???**b x h**A = 2 h b1 b2 b B1 + b2 h A = h 2 Trapezoidal Method h h h h A 1 A 4 A 2 A 3 b b b END AREA = A1 + A2 + A3 + A4**64.1**62.6 61.1 58.3 58.1 30.8 21.0 0 21.0 24.8 Trapezoidal Method A 1 A 2 A 3 A 4 54.3 55.2 54.3 21.0 21.0 0 Given the above surveyor notations, we will compute the area of the cross-section using the Trapezoidal method.**Trapezoidal Method**Demonstration The difference between the top numbers in the surveyor notations determines the vertical line lengths. The difference between the bottom numbers in the surveyor notations determines the horizontal line lengths.**64.1**62.6 61.1 58.3 58.1 30.8 21.0 O 21.0 24.8 x 30.8 - 21.0 = 9.8 height A1 =62.6 - 54.3 = 8.3 base (b1) 8.3 x 9.8 = 81.34 / 2 = 40.7 (END AREA OF A1) Trapezoidal Method A1 A4 A1 A2 A3 b1 b2 b3 54.3 55.2 54.3 21.0 21.0 0 A1 = (B x H) / 2**64.1**62.6 58.3 58.1 30.8 21.0 21.0 24.8 B1 + B2 x H A2 = 2 =62.6 - 54.3 = 8.3 (b1) + 61.1 - 55.2 = 5.9 (b2) = (8.3 + 5.9) / 2 = 7.1 = 7.1 x 21.0 = 149.1 (END AREA OF A2) Trapezoidal Method 61.1 0 A1 A4 A2 A3 b1 b2 b3 54.3 55.2 54.3 21.0 21.0 0**Calculate Areas A3 & A4Hint: Dimension the areas first.**Practical Exercise 1 Page 4 of SH**Draw a sketch !**? ? ? ? ? ? ?**64.1**62.6 61.1 58.3 58.1 30.8 21.0 O 21.0 24.8 A2 149.1 ft A1 40.7 ft 2 2 Practical Exercise 1 A 4 A 4 A 3 54.3 55.2 54.3 21.0 21.0 0 Given the Surveyor notations above, compute for areas 3 & 4, then determine the total area of the cross section Hint: Round to nearest 0.1**9.8**21.0 21.0 3.8 8.3 5.9 4.0 Correct Dimensions (feet)**Solutions**A1 = 40.7 ft A2 = 149.1 ft A3 = (61.1 - 55.2)+(58.3 - 54.3) x 21.0 = 104.0 ft 2 A4 = (58.3 - 54.3) (24.8 - 21.0) ÷ 2 = 7.6 ft End Area = A1(40.7) + A2(149.1) + A3(104.0) + A4(7.6) End Area = 301.4 ft 2 2 2 2 2 Any Questions on the Trapezoidal Method?**Cross Section SheetsWhat’s our Map Scale?**Scales can be exaggerated to show terrain: ex., 1” = 2’ Vertical, 1” = 10’ Horizontal**Methods for Calculating the Area of a Cross-Section**Stripper Method – Accuracy is +/- 10% The moment you’ve all been waiting for… Bring on the strippers!!! Page 5 of SH**Stripper Method**Before you can use your stripper, you will need to write the scale along one edge. Every 1” is enough (the darkest lines). The other lines are 0.10” apart.**3.O**1.O 2.O Stripper Method Step 1: Subdivide the cross-section into vertical strips.**3.O**1.O 2.O Stripper Method**3.O**1.O 2.O Stripper Method**3.O**1.O 2.O Stripper Method**3.O**2.O 1.O Stripper Method**3.O**2.O 1.O Stripper Method**3.O**1.O 2.O Stripper Method**1.1**1.1 1.0 1.3 1.2 1.1 3.O 3.O 3.O 3.O 3.O 3.O 1.O 1.O 1.O 1.O 1.O 2.O 2.O 2.O 2.O 2.O 2.O 1.O Stripper Method Step 2: Measure each line.**Stripper Method**Step 3: Add together the lengths of the lines. 1.1 + 1.0 + 1.1 + 1.3 + 1.2 + 1.1 = 6.8 in 1.1 1.0 1.3 1.2 1.1 1.1**3.O**1.O 2.O Stripper Method Step 4: Multiply the sum of the lines by the width of the stripper. 6.8 in x 1.0 in = 6.8 in2 The area of the cross section is 6.8 in2 1 in 1 in**Stripper Method**Step 5: Multiply the area by the map scale. Map Scale: 1.0 in = 5.0 ft Horizontal. 1.0 in = 5.0 ft Vertical. (I.E., 5.0 ft per inch in both directions) Therefore, 1.0 in2 = (5.0 ft horiz. X 5.0 ft vert.) 1.0 in2 = 25.0 ft2**Stripper Method**Step 5: Multiply the area by the map scale. Area of Lines x Map Scale 6.8 in2 x 25.0 ft2 / in2 = 170.0 ft2 End Area = 170.0 ft2 Any Questions on the Stripper Method?**Methods for Calculating the Area of a Cross-Section**Counting Squares Method - Accuracy is +/- 10% Step 1: Count 50%-100% full squares, Do not count the rest! SCALE: 1” = 6’ H & V Example: 95 squares Page 5 of SH**5 squares high x 5 squares wide = 25 squares / in**2 Counting Squares Method Step 2:Count the number of squares in a square inch.**Counting Squares Method**Step 3:Divide the number of squares (Step 1) by the number of squares per square inch (step 2). 95 squares / 25 squares per square inch = 3.8 in2 of area**Counting Squares Method**Step 4:Multiply the area (Step 3) by the map scales (Horizontal & Vertical) to convert to square feet. 3.8 in2 X (6.0 ft per in. horiz. x 6.0 ft per in. vert.) = 3.8 in2 X 36.0 ft2 / in2 = 136.8 ft2 of end area. Are there any questions concerning this method?**Methods for Calculating the Area of a Cross-Section**Planimeter Method – Accuracy is +/- 4% Instrument is used to measure the area by tracing its perimeter. Page 5 of SH**Methods for Calculating the Area of a Cross-Section**Terramodel (TM) fromPLUS3 (CAD) – Extremely Accurate • TM is a full-feature software package (CAD). • It is capable of drawing road, building, sewer, and drainage construction projects. • It calculates volumes and produces site maps and plans. • It is fielded in the Army with the Geodimeter total station survey instrument to Engineer units. • 51T’s (21T’s) in AIT are taught Terramodel and total station basics. Page 5 of SH**Midpoint Review**• Cross sections. • Surveyors notations. • Stationing. • Methods for determining areas. • Questions???**Midpoint Review**• What is a vertical illustration of a section of road perpendicular to the centerline at the stations? • What does the top and bottom number of the surveyors notations represent? • How far would station number 22+50 be from the start point? • What are some methods for determining end areas? • What is the most accurate method for calculating the area of a cross section?