Note: The methods of measuring the amounts of bed material removed during commercial projects were obtained from, "State of Wisconsin, Department of Transportation, Division of Highways, Standard Specifications for Road and Bridge Construction, Edition of 1975, Section 208.4 Method of Measurement", page 103.
The following excerpt from, "Elementary Surveying, 5th Ed.", by Russell C. Brinker, pages 477 & 478, presents formulas for the methods of calculation specified by the Wisconsin department of transportation and incorporated in NR 346.
End-areas formulas. The volume between 2 vertical cross sections A1 and A2 is equal to the average of the end areas multiplied by the horizontal distance L between them. Thus:
Ve =L(A1) A2) cu. yd.
2 x 27
This formula is approximate and gives answers which generally are slightly larger than the true prismoidal volumes. It is used in practice because of its simplicity. Increased accuracy is obtained by decreasing the distance L between the 2 sections. When the ground is irregular, cross-sections must be taken closer together.
Prismoidal formula. The prismoidal formula applies to the volumes of all geometric solids which can be considered prismoids. Most earthwork volumes fit this classification but relatively few of them warrant the precision of the prismoidal formula, which is:
Vp =L(A1) 4Am) A2)
6
where Vp = volume;
A1 and A2 = areas of successive cross-sections taken in the field;
Am = area of a section midway between A1 and A2;
L = horizontal distance between A1 and A2.
Wis. Admin. Code Department of Natural Resources NR 346.07