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Understood Volume ComputationsUnderstood Volume Computations
Did Not Understand Did Not Understand Volume ComputationsVolume Computations
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
TerminologyLeft Top Left Top of Bankof Bank
Left Left ToeToe
CenterlineCenterline Right Top Right Top of Bankof Bank
Center ChannelCenter Channel
Right ToeRight Toe
Design Design TemplateTemplate
Overdepth Overdepth TemplateTemplate
Supergrade Supergrade TemplateTemplate
Left Side SlopeLeft Side Slope Right Side SlopeRight Side SlopeLeft of CenterLeft of Center Right of CenterRight of Center
Design TemplateDesign Template
Overdepth TemplateOverdepth Template
Supergrade TemplateSupergrade Template
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 (3rd level) material and Norfolk reports a 4th level.
Reported Materials
• Sometimes, overdepth material is sometimes classified as Pay (V2P) vs Non-Pay (V2NP).
• Some folks call this ‘Contour’ material.
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
V2PV2NP
X2L
Y1
Average End Area (AEA)
What AEA Computes
Volume = L * (Area 1 + Area 2) / Volume = L * (Area 1 + Area 2) / 22
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.
AEA Treatment of Soundings Below Design0+
00
1+00
2+00
3+00
4+00
5+00
6+00
Bottom Alternating Above and Below Design
0+00
1+00
2+00
3+00
4+00
5+00
6+00
What AEA ‘Sees’
If the channel is 200m wide:
AEA Volume = 50,000m3 TIN Volume = 25,000m3
9m10m11m
10m9m
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 ft2
• 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 ft2. There is no ‘credit’ for the bottom being beneath the template.
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.
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.
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 Line 1: Area = 22.55 ft2ft2
Line 2: Area = 36.59 Line 2: Area = 36.59 ft2ft2
It’s a small difference It’s a small difference in this example, but in this example, but can be a significant can be a significant amount of material in amount of material in cases where the lines cases where the lines are almost parallel to are almost parallel to the side slopes.the side slopes.
Gaps In Survey Data
• Exterior Gaps
• Interior Gaps
• Pre-Dredge versus Post-Dredge Coverage
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.)
Incomplete Survey Data: Exterior
• Line 3 has incomplete survey data.
• AEA doesn’t care.– V23 = 100*(A2+A3)/2– V34 = 100*(A3+A4)/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.– V24 = 200*(A2+A4)/2
– Better overall result if the sectional profiles are similar.
Incomplete Data: Interior GapsInterior 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 No Data Between Between ArrowsArrows
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.
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.
Average End AreaDistance Between Lines
L
Line 1
Line 2 Line 2
Line 1
VOLUMEAEA = L * (A1 + A2)
Parallel Lines of Parallel Lines of Equal Length:Equal Length:
Generally Good Agreement on L
Non-Parallel Lines of Non-Parallel Lines of Unequal Length:Unequal Length:
Hoo-boy.
L???L?
Line 1
Line 2
Parallel Lines of Parallel Lines of Unequal Length:Unequal Length:
Trouble starts.
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)
Mathematical Truth
50m
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 = 2,500m3
Volume 2 = 5,000m3
Volume 3 = 5,000m3
Volume Total = 12,500m3
Area 1 = .5 x 50 x 100
Area 1 = 2,500 m2
Area 2 = 50 x 100
Area 2 = 5,000 m2
Area 3 = .5 x 100 x 100
Area 3 = 5,000 m2
Midpoint to Midpoint
50m
100m
200m
111.80m
141.42m
Line 1
Line 2
50m
50m
25m
L
L = sqr(752 + 502) = 90.14mA1 = 111.80m2
A2 = 200.00m2
AEA = L * (A1 + A2) / 2
AEA = 90.14 * (111.80 + 200.00) / 2
AEA = 14,053m3 (+12%)
Average Distance Between Endpoints
50m
100m
200m
111.80m
141.42m
Line 1
Line 2
50m
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 = 14,921m3 (+19%)
If anybody tries to pull this one on you, just send them to jail.
HYPACK® MethodIn Theory
50m
100m
200m
111.80m
141.42m
Line 1
Line 2
50m
50m
25m
L2
L = (L1 + L2) / 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 = 12,818m3 (+2%)
L1
50m
HYPACK® MethodIn Practice
50m
100m
200m
111.80m
141.42m
Line 1
Line 2
50m
50m
25m
L2
A1 = 111.80m2
A2 = 200.00m2
AEA = L * (A1 + A2) / 2
AEA = 82.22 * (111.80 + 200.00) / 2
AEA = 12,818m3 (+2%)
L1
HYPACK® TIN MODELTIN MODEL Volume = TIN MODEL Volume = 12,499.77 m12,499.77 m33 (0%) (0%)
With a ‘uniform’ With a ‘uniform’ surface, the TIN surface, the TIN MODEL gives the best MODEL gives the best answer when lines are answer when lines are non-parallel and of non-parallel and of unequal length.unequal length.
Comparisons
Method Volume (m3) Error
Mathematical Truth 12,500 None
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%
CONCLUSIONCONCLUSION: If you have lines that are non-parallel and/or of If you have lines that are non-parallel and/or of different lengths, the TIN MODEL method will give the most accurate different lengths, the TIN MODEL method will give the most accurate result.result.
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
For Example:
50m wide strip of material on outside of turn
50m wide strip of material on middle of turn
50m wide strip of material on inside of turn
Volume Summary
AEA Method TIN MODEL
Material on Outside of Turn
18,962m3
(60%)31,621m3
Material on Center of Turn
19,127m3
(99%)19,237m3
Material on Inside of Turn
19,723m3
(330%)5,977m3
CONCLUSION:CONCLUSION: If you are going around a turn, use a TIN If you are going around a turn, use a TIN MODEL.MODEL.
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!!!
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.
SectionsNorth 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 = 0mAEA Volume = 0m33 above design template. above design template. This is correct!This is correct!
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 m3
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 m3
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.
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?”
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.
Stapleton Data Summary
Method Center Vol
AEA 26,664 yd³
St. HYPACK 34,217
TIN MODEL 45,261
•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.]
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.
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 yd³ 30,928 yd³
10.0’ Spacing (Green) 28,009 yd³ 30,663 yd³
Delta = 929 yd3 (-3.2%)
This is what 929 yd3 of contaminated material looks like:
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.
Multibeam Volumes Volume vs. BIN Size – Three Examples
Design Volume Over-Dredge Volume
Exam
ple
#1E
xamp
le #2
Exam
ple
#3
The same rule The same rule applies to applies to Multibeam and Multibeam and Multiple Transducer Multiple Transducer survey data.survey data.
Volume quantity Volume quantity changes as you changes as you change the BIN size change the BIN size used to reduce the used to reduce the data.data.
It’s impossible to It’s impossible to predict if increasing predict if increasing the BIN size will the BIN size will result in an increase result in an increase or decrease in or decrease in volume quantity.volume quantity.
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.
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 Problems arise when computing the Contour material removed between a Contour material removed between a Pre-Dredge and a Post-Dredge survey.Pre-Dredge and a Post-Dredge survey.
Example: Contour versus Non-Contour Method
Pre-Dredge Depth = 9.9’Pre-Dredge Depth = 9.9’ Post-Dredge Depth = 10.1’Post-Dredge Depth = 10.1’
Non-Contour Overdepth:Non-Contour Overdepth:
Pre-Dredge = 200 ftPre-Dredge = 200 ft22
Post-Dredge = 180 ftPost-Dredge = 180 ft22
Delta = 20ftDelta = 20ft22
Contour Overdepth:Contour Overdepth:
Pre-Dredge = 200 ftPre-Dredge = 200 ft22
Post-Dredge = 0 ftPost-Dredge = 0 ft22
Delta = 200ftDelta = 200ft22
Shifting versus DiggingUp top is my Pre-Up top is my Pre-Dredge section.Dredge section.
Available Design Mat. = Available Design Mat. = 40 x .5 = 20ft40 x .5 = 20ft22
Available Overdepth Available Overdepth (Contour) = 40 x .5 = (Contour) = 40 x .5 = 20ft20ft22
Below is my Pre-Below is my Pre-Dredge section. I Dredge section. I haven’t dug anything, haven’t dug anything, I’ve just shifted the I’ve just shifted the material to the right.material to the right.
Available Design Mat. = Available Design Mat. = 40 x .5 = 20ft40 x .5 = 20ft22
Available Overdepth = Available Overdepth = 40 x .5 = 20ft40 x .5 = 20ft22
Pre-Dredge Survey
Post-Dredge Survey
Pre vs. Post – Philadelphia Method
If we don’t consider the ADDBACK (Y1) material, we will get credit for removing If we don’t consider the ADDBACK (Y1) material, we will get credit for removing the 20ftthe 20ft22 of design material and 20ft of design material and 20ft22 of overdepth material on the Left of Center. of overdepth material on the Left of Center.
Pre vs. Post – Philadelphia Method
If we consider the ADDBACK (Y1) material, the ‘material removed’ will equal the If we consider the ADDBACK (Y1) material, the ‘material removed’ will equal the ‘material added’, and we will get no credit for any material.‘material added’, and we will get no credit for any material.
AEA3 Method Reported Materials
Single Surveys:Single Surveys:
AEA 1:AEA 1: V1L V1 V1R V2L V2 V2R V3L V3 V3RV1L V1 V1R V2L V2 V2R V3L V3 V3R
AEA 2:AEA 2: V1L V1 V1R V2P V2NP V3V1L V1 V1R V2P V2NP V3
Pre-Dredge vs. Post-Dredge:Pre-Dredge vs. Post-Dredge:
AEA 3:AEA 3: V1L V1 V1R V2 V2P V2NP V2R V3L V3 V3R X1 X2 Y1V1L V1 V1R V2 V2P V2NP V2R V3L V3 V3R X1 X2 Y1
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.
Pre-Dredge Section
Post-Dredge Section
Our ‘Shifting’ Example in AEA3
Design Material (V1) – Pre-Dredge
This shows the area of available material (based on the Pre-This shows the area of available material (based on the Pre-Dredge survey) to be 20ftDredge survey) to be 20ft22..
V2P material (for both Pre-Dredge and Post-Dredge surveys V2P material (for both Pre-Dredge and Post-Dredge surveys will only be computed underneath this V1-Pre material. will only be computed underneath this V1-Pre material. Outside this area will be V2NP.Outside this area will be V2NP.
Design Material (V1) – Post-Dredge
This shows the area of available material (based on the Post-This shows the area of available material (based on the Post-Dredge survey) to be 20ftDredge survey) to be 20ft22..
Note: The computation of the V1-post material is not limited Note: The computation of the V1-post material is not limited by the location of the V1-Pre material.by the location of the V1-Pre material.
Design Material (Y1) – Add Back
• Everywhere the Post-Dredge survey is above the Pre-Dredge Everywhere the Post-Dredge survey is above the Pre-Dredge survey will be computed as Add Back (Y1) material.survey will be computed as Add Back (Y1) material.
• It will be assigned V1, V2, V2NP based on the location of the It will be assigned V1, V2, V2NP based on the location of the added material.added material.
V1 Info
Delta = Pre – PostDelta = Pre – Post = 0.0ft = 0.0ft22
• This represents the material This represents the material difference between the Pre-difference between the Pre-Dredge and Post-Dredge Dredge and Post-Dredge surveys.surveys.
• You get no credit for moving You get no credit for moving stuff sideways. (Our example!)stuff sideways. (Our example!)
• This can be a negative number This can be a negative number if more material is found in the if more material is found in the Post-Dredge survey than was Post-Dredge survey than was available based on the Pre-available based on the Pre-Dredge survey.Dredge survey.
TotPay = Pre – Post + Y1TotPay = Pre – Post + Y1 = 20.0ft = 20.0ft22
This is the ‘Delta’ value (left) plus This is the ‘Delta’ value (left) plus the Add Back material.the Add Back material.
In our example, they are credited In our example, they are credited for removing (or moving) the V1 for removing (or moving) the V1 material found in the Pre-Dredge material found in the Pre-Dredge Survey.Survey.
Overdepth (V2P) – Pre-Dredge
V2P = Overdepth material where the Pre-Dredge bottom is V2P = Overdepth material where the Pre-Dredge bottom is above the design.above the design.
V2P material (for both Pre-Dredge and Post-Dredge surveys) V2P material (for both Pre-Dredge and Post-Dredge surveys) will only be computed underneath this V1-Pre material. will only be computed underneath this V1-Pre material. Outside this area will be V2NP. This is the basis for both the Outside this area will be V2NP. This is the basis for both the Pre-Dredge and Post-Dredge!Pre-Dredge and Post-Dredge!
Overdepth (V2P) – Post-Dredge
V2P = Overdepth material where the Pre-Dredge bottom is V2P = Overdepth material where the Pre-Dredge bottom is above the design depth.above the design depth.
V2P Info
Delta = Pre – PostDelta = Pre – Post = 20.0ft = 20.0ft22
• This represents the material This represents the material difference between the Pre-difference between the Pre-Dredge and Post-Dredge Dredge and Post-Dredge surveys.surveys.
•
TotPay = Pre – Post + Y1TotPay = Pre – Post + Y1 = 20.0ft = 20.0ft22
Since there isn’t any material that Since there isn’t any material that has been ‘Added Back’ in the V2P has been ‘Added Back’ in the V2P area, the Delta = TotPay.area, the Delta = TotPay.
Pre-Dredge Section
Post-Dredge Section
Overdepth (V2NP) – Pre-Dredge
V2NP = Overdepth material computed only where the Pre-V2NP = Overdepth material computed only where the Pre-Dredge survey bottom is beneath the design.Dredge survey bottom is beneath the design.
Overdepth (V2NP) – Post-Dredge
V2NP = Overdepth material computed only where the Pre-V2NP = Overdepth material computed only where the Pre-Dredge survey bottom is beneath the design.Dredge survey bottom is beneath the design.
Overdepth (V2NP-Y1) – Add Back
• Everywhere the Post-Dredge survey is above the Pre-Dredge Everywhere the Post-Dredge survey is above the Pre-Dredge survey will be computed as Add Back (Y1) material.survey will be computed as Add Back (Y1) material.
• It will be assigned V1, V2, V2NP based on the location of the It will be assigned V1, V2, V2NP based on the location of the added material.added material.
V2NP Info
Delta = Pre – PostDelta = Pre – Post = -20.0ft = -20.0ft22
• This is negative, as there is This is negative, as there is more V2NP material in the Post-more V2NP material in the Post-Dredge survey than in the Pre-Dredge survey than in the Pre-Dredge survey.Dredge survey.
TotPay = Pre – Post + Y1TotPay = Pre – Post + Y1 = 0.0ft = 0.0ft22
Pre-Dredge Section
Post-Dredge Section
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
Differing Side Slope Treatments1.1. It’s not easy to dig It’s not easy to dig
accurately on the side accurately on the side slopes.slopes.
2.2. If the bottom material is If the bottom material is ‘soft’, the contractor might ‘soft’, the contractor might be allowed to dig a hole at be allowed to dig a hole at the bottom of the side the bottom of the side slope.slope.
3.3. The idea is that the The idea is that the material on the side slope material on the side slope will ‘fall’ into the hole over will ‘fall’ into the hole over time.time.
4.4. Different USACE methods Different USACE methods use different parameters use different parameters to compute the available to compute the available material and the size of material and the size of the hole.the hole.
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.
Jacksonville Post-Dredge Method
A = Side slope material available A = Side slope material available in both the overdepth prism and in both the overdepth prism and above the design template.above the design template.
B = Void in direction outward B = Void in direction outward from the toe line. from the toe line.
C = Void in direction inward from C = Void in direction inward from toe line to a user-specified toe line to a user-specified distance. (Bottom must be distance. (Bottom must be beneath overdepth template at beneath overdepth template at toe line for either B or credit.)toe line for either B or credit.)
If A > (B+C), then Credit = B+CIf A > (B+C), then Credit = B+C
If A < (B+C), then Credit = AIf A < (B+C), then Credit = A
GLDD Method
Area Available Material
Void Applied Rules
Design Material A D + E + F Use A – (D + E + F)If A < (D + E + F) then use 0.0
Overdepth Material A + B E + F Use (A + B) - (E + F)If (A + B) < (E + F) then use 0.0
Superdepth Material A + B + C F Use (A + B + C) - FIf (A + B + C) < F then use 0.0
