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INTEROFFICE CORRESPONDENCE |
To: File Project Number 0284-319 Date: March 7, 2006
Non-Public
Properties Study Area,
This memo provides a description of how fill volumes were calculated for contiguous fill and isolated fill. The contiguous fill volumes were calculated differently than the isolated fill volume and are discussed separately. Note that the calculations are for in-situ volumes. It is assumed that the fill will be excavated, transported and placed at the Middle School with the existing fill materials and compacted with the result that one cubic yard of fill excavated equals one cubic yard placed. Although the recommended remedy does not require the excavation of roadways, no attempt was made deduct these quantities from the overall calculation.
Contiguous Fill
Volumes in the contiguous fill areas were calculated using the contour lines of the fill because borings in the contiguous fill area were not evenly distributed. Contour lines of these fill areas were drawn in CAD and later imported to ArcGIS where areas (ft2) were calculated using the “Field Calculator” function. Figure F-1 depicts an example of a contiguous fill area. Table F-1 shows the components used in calculating fill volumes in each contiguous fill area.
In the example illustrated in Figure F-1, there are three contours; 10 feet below grade (fbg), 4 fgb, and 0 fbg (edge of fill). The area calculated by subtracting the area of circle A from the area of circle B represent a “doughnut” of fill and the area of circle C is the column of the deepest fill. Because the sides of the fill areas are sloped, the depths used in the calculations are averages of depths between contours except at the bottom where 0.5 ft was added to the lowest contour. This 0.5 feet was necessary because the bottom of fill line is not flat at 10 feet but rounds just below the 10 foot contour. This rounding was represented as a square and has a built in overestimation factor. This method incorporates the changing slope between contours. The following average depths were used between contours:
Depth A-B (ft) = (4-0) / 2 = 2 ft
Depth B-C (ft) = (10-4) / 2 + 4 =7 ft
Depth C (ft)= 10 + 0.5 = 10.5 ft (this is the bottom)
For the Southwest Satellite Area, which has fill contours of 10, 15 and 20 fbg, the fill thicknesses were calculated in a similar manner using the corresponding average depths of 12.5, 17.5, and 20.5 fbg.
The areas between the contours (inter-contour area) were calculated in the following way:
Area A-B = Area of Circle A –Area of Circle B
Area B-C (ft2) = Area of Circle B – Area of Circle C
Area C (ft2) = Area Circle C
Applying the average depths to these areas, the inter-contour volumes (“doughnuts”) were calculated in the following way:
Volume A-B (yd3) = Area A-B
x Depth A-B / 27 ft3/yd3
Volume B-C (yd3) = Area B-C x Depth B-C) / 27 ft3/yd3
Volume C
(yd3) = Area C x Depth C
/ 27 ft3/yd3
The total fill volume is the sum
of the three inter-contour volume components.
The results for all contiguous fill areas within the Study Area are
presented in Table F-1.
Figure F-1 illustrates the described method of calculating fill in the contiguous fill areas. The bold line in the cross section view represents the bottom of the fill and the boxes are the geometric representation of how the fill volume was calculated. Illustrated in the cross section view as shaded boxes are triangles 1 to 4. Shaded triangle 1, which is outside of the fill, and shaded triangle 2, which is inside the fill, have equal volumes. Corresponding triangles 3 and 4 follow the same logic. As illustrated, the unaccounted fill areas in the volume calculations, triangles 2 and 4, are accounted for in the volume estimation by triangles 1 and 3. Thus the volumes are considered accurate.
Using the example shown, if we
assume the area of circle C is 30 ft2, B is 300
ft2, and C is 1300 ft2, the inter-contour areas will be:
Area A-B = 1300 ft2- 300 ft2 = 1000 ft2
Area B-C = 300 ft2 - 30 ft2 = 270 ft2
Area C = 30 ft2
and the inter-contour volumes (“doughnuts”) will be:
Volume A-B = 1000 ft2 x 2 ft / 27 ft3/yd3 = 74 yd3
Volume B-C = 270 ft2 x 7 ft / 27 ft3/yd3 = 70 yd3
Volume C = 30 ft2 x 10.5 ft / 27 ft3/yd3 = 12 yd3
The total fill volume for the example is the
sum of the three inter-contour volume components: 74 + 70 + 12 = 156 yd3.
Special case, fill volume <4 feet deep only
Table F-2 shows the volume of fill in the
contiguous fill areas less than four feet deep.
These calculations were done in a similar way. In the example in Figure F-1, only circles A
and B were used in the calculations, as shown below:
Volume (yd3) = [(Area B x 4) + ((Area A – Area B) x 2)]/ 27 ft3/yd3 =
[(300 ft2
x 4 ft) + ((1300 ft2
- 300 ft2) x 2 ft)] / 27 ft3/yd3 =
120 yards3
Isolated
Fill
Borings in the isolated fill locations are typically evenly distributed within a given isolated fill area and all borings fully penetrate the fill. These areas are generally very thin, but may be irregular shaped. Outlines of these fill areas based on the boring information were drawn in CAD and later imported to ArcGIS where areas (ft2) were calculated using the “Field Calculator” function. Figure F-2 illustrates a typical example of a delineated fill area and Table F-3 shows the average depth, internal area, and calculated volumes of each isolated fill area identified in the NPP Study Area.
Isolated fill volume estimates were calculated
by multiplying the internal area calculated from borings within the fill and
that fully penetrated the fill by the average depth. This approach was used because, unlike the
contiguous fill, the isolated fill borings are generally evenly distributed
within a particular isolated fill area. The
average depth was calculated by summing the total fill depths of all the borings
inside a particular isolated fill area and dividing by the total number of
borings inside that isolated fill area.
Volume
(yd3) = (Area x average depth) / 27 ft3/yd3
Isolated fill volume calculations are different than that for contiguous fill. Figure F-2, is an illustration of a typical isolated fill area. The dashed line in the cross section view represents the average boring depth within the isolated fill area. The cross section view shows fill between grade and the bottom of fill sloping. To calculate volume, the slope is ignored and the isolated fill area is modeled as a box. The shaded area in the cross section view represents volume that is overestimated using this method. Volumes of isolated fill that are defined by one boring are usually poorly constrained by surrounding borings. The total calculated volume of isolated fill is less than 3% of the total calculated volume of fill for the whole NPP Study Area.