2. Understood Volume Computations Did Not Understand Volume Computations

3. Volume Seminar Summary What is Average End Area (AEA)? Problems with AEA –Gaps in your Survey Data –Non-Parallel Lines in AEA –Material on Inside and Outside of Turns Problems with Non-Parallel Lines in TINs Problems with Thinning Data in AEA and TINs Contour Dredging And Problems in Computation Different Side Slope Treatments in USACE AEA

4. Terminology Left Top of Bank Left Toe Centerline Right Top of Bank Center Channel Right Toe Design Template Overdepth Template Supergrade Template Left Side Slope Right Side Slope Left of Center Right of Center Design Template Overdepth Template Supergrade Template

5. Reported Materials Most methods report quantities as ‘Left Slope, Center, and Right Slope. Most methods report Material Above Design and Overdepth Material. Some methods report Supergrade (3 rd level) material and Norfolk reports a 4 th level.

6. Reported Materials Sometimes, overdepth material is sometimes classified as Pay (V2P) vs Non-Pay (V2NP). Some folks call this ‘Contour’ material.

7. Pre-Dredge versus Post-Dredge Some methods report additional quantities. For example: X1 (L and R): Amount of material available in the side slope overdepth template based on the After Dredge survey. X2 (L and R): Amount of void beneath the overdepth template, measured from the toe inward a specified distance, based on the After Dredge survey. Y1: (Add Back Material) Any area where the After Dredge survey is shoaler than the Before Dredge survey. More about this stuff later….. V1 V2P V2NP X2L Y1

8. Average End Area (AEA) What AEA Computes Volume = L * (Area 1 + Area 2) / 2

9. Things to Ponder AEA has no interest on what happens between the sections. This assumes a ‘uniform’ bottom between sections. AEA doesn’t give any credit for how deep the bottom is beneath the template.

10. AEA Treatment of Soundings Below Design 0+001+002+003+004+005+006+00 Bottom Alternating Above and Below Design 0+001+002+003+004+005+006+00 What AEA ‘Sees’ If the channel is 200m wide: AEA Volume = 50,000m 3 TIN Volume = 25,000m 3 9m 10m 11m 10m 9m

11. AEA: No Credit for Depth Dropping Below Template! In our first section, the bottom is a constant 9’ deep across our 10’ center channel depth. –Center Channel is 200 feet across. –AEA reports an area of 200 ft 2 In the adjacent section, the bottom is a constant 11’ deep across our center channel depth. –Center Channel is 200 feet across. –AEA reports an area of 0 ft 2. There is no ‘ credit ’ for the bottom being beneath the template.

12. Bottom Close to Design In areas where the bottom continues to go above and below the design depth, a TIN MODEL method will give a more accurate result.

13. Lines run Parallel to a Contour AEA methods treat each sounding as if it was collected along the planned line. This can create errors in the volume computation if the lines are not perpendicular to the slopes.

14. Lines Non-Parallel to the Slope Line run 10’ to the west of the planned line. (Purple) Line run exactly along the planned line. (Blue) Line 1: Area = 22.55 ft2 Line 2: Area = 36.59 ft2 It’s a small difference in this example, but can be a significant amount of material in cases where the lines are almost parallel to the side slopes.

15. Gaps In Survey Data Exterior Gaps Interior Gaps Pre-Dredge versus Post-Dredge Coverage

16. Incomplete Survey Data: Exterior Gaps Not completing a section results in a loss of computed material. You don’t want to ‘create’ the missing data on the end of the section. (Your cell won’t be as nice as Martha Stewart’s.)

17. Incomplete Survey Data: Exterior Line 3 has incomplete survey data. AEA doesn’t care. –V 23 = 100*(A 2 +A 3 )/2 –V 34 = 100*(A 3 +A 4 )/2 –Since A3 is less than it should be, the volume quantity will also be less. –I could use a TIN MODEL and tell it to connect across the gap. It might be more accurate to leave Line 3 out of the computation. –V 24 = 200*(A 2 +A 4 )/2 –Better overall result if the sectional profiles are similar.

18. Incomplete Data: Interior Gaps Interior Gaps: Some people will interpolate across any interior gap (HYPACK for one). Some people will only interpolate across gaps if the distance is less than a specified distance. Spanning across gaps can give a VERY misleading result if the gap spans the toe line. No Data Between Arrows

19. Unequal Coverage: Pre vs. Post Most AEA methods don’t check for coverage differences between Pre-Dredge and Post-Dredge surveys. If I don’t make any ‘adjustments’: –I won’t get any credit for dredging in the ‘B’ area. –I will get credit for removing all of the ‘C’ area.

20. Computing the Distance Between Lines When comparing volumes from different programs: –The Areas generally agree very closely. Provided the sections span the entire channel. (No gaps). –The Distance Between Lines used by each method is where we find the ‘difference’. No difference in parallel lines of equal length. A little difference in parallel lines of unequal length. A lot of difference in non-parallel lines of unequal length.

21. Average End Area Distance Between Lines L Line 1 Line 2 Line 1 VOLUME AEA = L * (A 1 + A 2 ) Parallel Lines of Equal Length: Generally Good Agreement on L Non-Parallel Lines of Unequal Length: Hoo-boy. L???L? Line 1 Line 2 Parallel Lines of Unequal Length: Trouble starts.

22. Distance Between Lines - Methods L = Distance Between Midpoints L = Average Distance Between Endpoints L = Average Distance Between Lines Constructed from Midpoint of Each Line to the Perpendicular Intersection of the Other Line (HYPACK)

23. Mathematical Truth 50m 100m 200m 111.80m 141.42m Line 1 Line 2 Example: We have two non-parallel survey lines that are of different lengths. Material covers the surface to a uniform thickness of 1m. Volume 1 = 2,500m 3 Volume 2 = 5,000m 3 Volume 3 = 5,000m 3 Volume Total = 12,500m 3 Area 1 =.5 x 50 x 100 Area 1 = 2,500 m 2 Area 2 = 50 x 100 Area 2 = 5,000 m 2 Area 3 =.5 x 100 x 100 Area 3 = 5,000 m 2

24. Midpoint to Midpoint 50m 100m 200m 111.80m 141.42m Line 1 Line 2 50m 25m L L = sqr(75 2 + 50 2 ) = 90.14mA1 = 111.80m2 A2 = 200.00m2 AEA = L * (A1 + A2) / 2 AEA = 90.14 * (111.80 + 200.00) / 2 AEA = 14,053m 3 (+12%)

25. Average Distance Between Endpoints 50m 100m 200m 111.80m 141.42m Line 1 Line 2 50m 25m L = (50.00 + 141.42 ) / 2 L = 95.71m A1 = 111.80m2 A2 = 200.00m2 AEA = L * (A1 + A2) / 2 AEA = 95.71 * (111.80 + 200.00) / 2 AEA = 14,921m 3 (+19%) If anybody tries to pull this one on you, just send them to jail.

26. HYPACK ® Method In Theory 50m 100m 200m 111.80m 141.42m Line 1 Line 2 50m 25m L2L2 L = (L 1 + L 2 ) / 2 L1 = Distance from Midpoint of Line 1 to perpendicular intersection of Line 2 L2 = Distance from Midpoint of Line 2 to perpendicular intersection of Line 1 L = (75.00 + 89.44) / 2 = 82.22m A1 = 111.80m2 A2 = 200.00m2 AEA = L * (A1 + A2) / 2 AEA = 82.22 * (111.80 + 200.00) / 2 AEA = 12,818m 3 (+2%) L1L1 50m

27. HYPACK ® Method In Practice 50m 100m 200m 111.80m 141.42m Line 1 Line 2 50m 25m L2L2 A1 = 111.80m2 A2 = 200.00m2 AEA = L * (A1 + A2) / 2 AEA = 82.22 * (111.80 + 200.00) / 2 AEA = 12,818m 3 (+2%) L1L1

28. HYPACK ® TIN MODEL TIN MODEL Volume = 12,499.77 m 3 (0%) With a ‘uniform’ surface, the TIN MODEL gives the best answer when lines are non-parallel and of unequal length.

29. Comparisons MethodVolume (m 3 )Error Mathematical Truth 12,500None Midpoint to Midpoint 14,053+12% Average Distance Between Line Ends 14,921+19% HYPACK ® CS&V 12,818+2% HYPACK ® TIN MODEL 12,499.8-0.002% CONCLUSIONIf you have lines that are non-parallel and/or of different lengths, the TIN MODEL method will give the most accurate result. CONCLUSION: If you have lines that are non-parallel and/or of different lengths, the TIN MODEL method will give the most accurate result.

30. Material on the Inside/Outside of Turns AEA does not consider where along the section the material is located. This can result in errors if you have non- parallel lines and have material along the inside or outside of the turn

31. For Example: 50m wide strip of material on outside of turn50m wide strip of material on middle of turn50m wide strip of material on inside of turn

32. Volume Summary AEA MethodTIN MODEL Material on Outside of Turn 18,962m 3 (60%) 31,621m 3 Material on Center of Turn 19,127m 3 (99%) 19,237m 3 Material on Inside of Turn 19,723m 3 (330%) 5,977m 3 CONCLUSION:If you are going around a turn, use a TIN MODEL. CONCLUSION: If you are going around a turn, use a TIN MODEL.

33. Single Beam Data in TIN MODEL If you have single beam data…. If your planned lines are of unequal length and/or direction…. If the planned lines are not perpendicular to the bottom contour…. If you are doing volumes in TIN MODEL…. BEWARE of Scallops!!!

34. Our Example I have a ‘flat’ bottom of 10m across most of the channel. When I get to about 20m of the western side, the bottom slopes up to 0m at the end-of-line.

35. Sections North Segment: 316.2m long. Note the bottom travels directly along the template in the center channel and up the right slope. South Segment: 200m long. Note the bottom travels directly along the template in the center channel and up the right slope. AEA Volume = 0m 3 above design template. This is correct!

36. TIN MODEL – Delaunay Triangles When you create ‘Delaunay’ triangles, one sounding at the end of a line can be used as a vertex in many triangles. If this ‘one sounding’ is shallow, it can create a ‘scalloping’ effect on the surface model. TIN MODEL Volume = 8,976 m 3

37. TIN MODEL – Proportional Triangles If we remove the ‘Delaunay’ triangle requirement and create triangles that are ‘proportional’ based on the distance along line, the TIN MODEL can give a more appropriate result. TIN MODEL Volume = 0.00 m 3

38. USACE Buffalo Data Set (Stapleton) This is where we discovered the problem. The lines are non- parallel and the material is concentrated at the ‘outside’ of the turn.

39. Stapleton Data – Standard HYPACK Method The ‘Standard HYPACK’ [SH] method provides a more accurate volume when you have non-parallel lines and material is concentrated at the outside [or inside] of the turn. SH cuts the area between survey lines into proportional ‘slices’. It computes a depth at each corner of the slice, compares it to the design template and computes the volume for each slice. It then ‘sums’ the volume for all of the slices to get the volume for the section. “I can see why the SH might be more accurate than the AEA for this example, but why is the TIN coming up with so much material?”

40. Stapleton Data Set - TIN The graphic shows the contours generated from the TIN of the Stapleton data. Along the edge, you can see a “scalloping” effect, where the contours ‘bulge’ into the channel. This is caused by the survey lines being non- parallel to the upslope and by the way the TIN MODEL connects data points.

41. Stapleton Data Summary MethodCenter Vol AEA26,664 yd³ St. HYPACK34,217 TIN MODEL45,261 All of these values came from the same data set. All of these values came from methods that are accepted and widely used in industry. Does this mean that one method is better than another? No. Each method has its strengths and weaknesses, based on the underlying assumptions. [I would use the Standard HYPACK method or the TIN MODEL with ‘Align TIN’ in this case if it was my money.]

42. Data Thinning You can influence the volume quantity by ‘thinning your data’. –True with Single Beam Data in AEA. –True with Multibeam Data in TIN MODEL.

43. Single Beam Data: Original Data at 0.5’/sounding; Thinned Data at 10’/sounding Data Thinning: Single Beam Data Dredge Vol.Over-Dredge Vol. 0.5’ Spacing (Black)28,938 yd³30,928 yd³ 10.0’ Spacing (Green)28,009 yd³30,663 yd³ Delta = 929 yd 3 (-3.2%) This is what 929 yd 3 of contaminated material looks like:

44. Same SB Data, Different Thinning In general: –The total volume quantity will vary as you change the spacing between your data points. –It may not always look like the graph shown, but there is usually a maximum and minimum point. Note: Surveying at a faster speed is the same as ‘thinning’ your data.

45. Multibeam Volumes Volume vs. BIN Size – Three Examples Design VolumeOver-Dredge Volume Example #1 Example #2 Example #3 The same rule applies to Multibeam and Multiple Transducer survey data. Volume quantity changes as you change the BIN size used to reduce the data. It’s impossible to predict if increasing the BIN size will result in an increase or decrease in volume quantity.

46. Data Spacing In the last couple of years, the USACE guidelines now recommend that maximum spacing between soundings and maximum BIN sizes be included as a part of the project specification. For single beam data in HYPACK, we recommend that the user take the edited data file directly into CS&V without performing any sounding selection.

47. Contour Dredging (Only Affects Overdepth Volume Quantity) Non-Contour: –Includes all available overdepth material (top). Contour: –Includes only overdepth material where the bottom is above the design template. Problems arise when computing the Contour material removed between a Pre-Dredge and a Post-Dredge survey.

48. Example: Contour versus Non-Contour Method Pre-Dredge Depth = 9.9’ Post-Dredge Depth = 10.1’ Non-Contour Overdepth: Pre-Dredge = 200 ft 2 Post-Dredge = 180 ft 2 Delta = 20ft 2 Contour Overdepth: Pre-Dredge = 200 ft 2 Post-Dredge = 0 ft 2 Delta = 200ft 2

49. Shifting versus Digging Up top is my Pre- Dredge section. Available Design Mat. = 40 x.5 = 20ft 2 Available Overdepth (Contour) = 40 x.5 = 20ft 2 Below is my Pre- Dredge section. I haven’t dug anything, I’ve just shifted the material to the right. Available Design Mat. = 40 x.5 = 20ft 2 Available Overdepth = 40 x.5 = 20ft 2 Pre-Dredge Survey Post-Dredge Survey

50. Pre vs. Post – Philadelphia Method If we don’t consider the ADDBACK (Y1) material, we will get credit for removing the 20ft 2 of design material and 20ft 2 of overdepth material on the Left of Center.

51. Pre vs. Post – Philadelphia Method If we consider the ADDBACK (Y1) material, the ‘material removed’ will equal the ‘material added’, and we will get no credit for any material.

52. AEA3 Method Reported Materials Single Surveys: AEA 1:V1L V1 V1R V2L V2 V2R V3L V3 V3R AEA 2:V1L V1 V1R V2P V2NP V3 Pre-Dredge vs. Post-Dredge: AEA 3:V1L V1 V1R V2 V2P V2NP V2R V3L V3 V3R X1 X2 Y1

53. AEA3 – Other Materials X1:Side slope overdredge material available after dredging. X2:Material removed beneath the overdredge template within a user-defined distance of the toe. Y1:Material added during the dredging operation.

54. Pre-Dredge SectionPost-Dredge Section Our ‘Shifting’ Example in AEA3

55. Design Material (V1) – Pre-Dredge This shows the area of available material (based on the Pre-Dredge survey) to be 20ft 2. V2P material (for both Pre-Dredge and Post-Dredge surveys will only be computed underneath this V1-Pre material. Outside this area will be V2NP.

56. Design Material (V1) – Post-Dredge This shows the area of available material (based on the Post-Dredge survey) to be 20ft 2. Note: The computation of the V1-post material is not limited by the location of the V1-Pre material.

57. Design Material (Y1) – Add Back Everywhere the Post-Dredge survey is above the Pre-Dredge survey will be computed as Add Back (Y1) material. Everywhere the Post-Dredge survey is above the Pre-Dredge survey will be computed as Add Back (Y1) material. It will be assigned V1, V2, V2NP based on the location of the added material. It will be assigned V1, V2, V2NP based on the location of the added material.

58. V1 Info Delta = Pre – Post = 0.0ft 2 This represents the material difference between the Pre- Dredge and Post-Dredge surveys. This represents the material difference between the Pre- Dredge and Post-Dredge surveys. You get no credit for moving stuff sideways. (Our example!) You get no credit for moving stuff sideways. (Our example!) This can be a negative number if more material is found in the Post-Dredge survey than was available based on the Pre- Dredge survey. This can be a negative number if more material is found in the Post-Dredge survey than was available based on the Pre- Dredge survey. TotPay = Pre – Post + Y1 = 20.0ft 2 This is the ‘Delta’ value (left) plus the Add Back material. In our example, they are credited for removing (or moving) the V1 material found in the Pre-Dredge Survey.

59. Overdepth (V2P) – Pre-Dredge V2P = Overdepth material where the Pre-Dredge bottom is above the design. V2P material (for both Pre-Dredge and Post-Dredge surveys) will only be computed underneath this V1-Pre material. Outside this area will be V2NP. This is the basis for both the Pre-Dredge and Post-Dredge!

60. Overdepth (V2P) – Post-Dredge V2P = Overdepth material where the Pre-Dredge bottom is above the design depth.

61. V2P Info Delta = Pre – Post = 20.0ft 2 This represents the material difference between the Pre- Dredge and Post-Dredge surveys. This represents the material difference between the Pre- Dredge and Post-Dredge surveys. TotPay = Pre – Post + Y1 = 20.0ft 2 Since there isn’t any material that has been ‘Added Back’ in the V2P area, the Delta = TotPay. Pre-Dredge SectionPost-Dredge Section

62. Overdepth (V2NP) – Pre-Dredge V2NP = Overdepth material computed only where the Pre-Dredge survey bottom is beneath the design.

63. Overdepth (V2NP) – Post-Dredge V2NP = Overdepth material computed only where the Pre-Dredge survey bottom is beneath the design.

64. Overdepth (V2NP-Y1) – Add Back Everywhere the Post-Dredge survey is above the Pre-Dredge survey will be computed as Add Back (Y1) material. Everywhere the Post-Dredge survey is above the Pre-Dredge survey will be computed as Add Back (Y1) material. It will be assigned V1, V2, V2NP based on the location of the added material. It will be assigned V1, V2, V2NP based on the location of the added material.

65. V2NP Info Delta = Pre – Post = -20.0ft 2 This is negative, as there is more V2NP material in the Post- Dredge survey than in the Pre- Dredge survey. This is negative, as there is more V2NP material in the Post- Dredge survey than in the Pre- Dredge survey. TotPay = Pre – Post + Y1 = 0.0ft 2 Pre-Dredge SectionPost-Dredge Section

66. What’s it all mean? The Delta number shows me that they didn’t actually remove anything. They shifted some overdepth material so that it’s classification changed from V2P (+20) to V2NP (-20). The TotPay number shows me that if I only perform the computation in the area of available material (based on the Pre-Dredge Survey), they have eliminated the V1 and V2P material that existed. Pre-Dredge SectionPost-Dredge Section

67. Differing Side Slope Treatments 1.It’s not easy to dig accurately on the side slopes. 2.If the bottom material is ‘soft’, the contractor might be allowed to dig a hole at the bottom of the side slope. 3.The idea is that the material on the side slope will ‘fall’ into the hole over time. 4.Different USACE methods use different parameters to compute the available material and the size of the hole.

68. HYPACK AEA3 Method X1:Side slope overdepth material available after dredging. No Design Material is included! X2:Material removed beneath the overdepth template within a user- defined distance inward from the toe. Idea:If X2>X1 then contractor gets credit for X1. If X1>X2 then contractor gets credit for X2.

69. Jacksonville Post-Dredge Method A = Side slope material available in both the overdepth prism and above the design template. B = Void in direction outward from the toe line. C = Void in direction inward from toe line to a user-specified distance. (Bottom must be beneath overdepth template at toe line for either B or credit.) If A > (B+C), then Credit = B+C If A < (B+C), then Credit = A

70. GLDD Method AreaAvailable Material Void AppliedRules Design MaterialAD + E + FUse A – (D + E + F) If A < (D + E + F) then use 0.0 Overdepth MaterialA + BE + FUse (A + B) - (E + F) If (A + B) < (E + F) then use 0.0 Superdepth MaterialA + B + CFUse (A + B + C) - F If (A + B + C) < F then use 0.0

71. The End Pat Sanders, Pres. HYPACK, Inc. pat@hypack.com www.hypack.com