long, the volume is

X2,025=1,215 cu. yd., and this number

is written in column 4 (b) opposite Sta. 129.

The computation for the other stations is made in a similar way. It will be observed that the sections at Sta. 126 and Sta 127 are three-level sections, and that in this case there are no minus areas.

The sum of the numbers in column 4 (b) is 4,927 cu. yd.; the prismoidal correction, which is figured according to the formula for C under the heading Three-Level Section, is -54 cu. yd.; the final volume between Sta. 126 and Sta. 129, is, therefore, 4,927-54-4,873 cu. yd.

Side-Hill Work.-When both the cut and the fill occur in the same section, as in Fig. 9, the areas, volumes, and their corrections are determined for the fill and the cut separately. For

the purpose of calculating the prismoidal and curvature corrections, each part of the section, cut or fill, is considered as a triangle and the formulas previously given are used.

For calculating the areas, it is also frequently sufficient to consider that the section in either fill or cut is triangular. This is, however, not exact enough when the ground is very irregular. In Fig. 9, the area of the fill would be taken as that of the triangle mnp, while for determining the area of the cut the method of irregular sections would be used.

Suppose that the shoulder m, Fig. 9, of the slope is 8 ft. from the center; that the fill begins at 2 ft. from the center, and is a rock fill with a slope of 1:1, and that the slope stake n is 16.8 ft. from the center. Then, mk=ck-cm=16.8-8.0 =8.8 ft.; and, since the slope km÷nk is 1:1, the vertical distance nk of n below subgrade will also be 8.8 ft. The area

In determining the area of the cut, it will be observed that

0

the fraction for the point is -; that for t is

2'

for vis

C8.2
18.2

The center depth is 1.3 ft., and the distance

cq=b 10 ft. The notes for the entire section shown in Fig. 9, will therefore be as given in the following table:

The series of fractions will therefore be, considering only the section of cut,

The desired area for cut is, therefore, X (207.3-62.3)

=72.5 sq. ft.

Eccentricity in Side-Hill Work.-As stated before, in making the correction for curvature in side-hill work the sections of fill or cut are considered as triangles and the following formula is used:

The values of A1 and A2 are readily obtained as areas of triangles. For finding the eccentricities, two cases are to be distinguished in either cut or fill. Using the notation of Figs. 10 and 11, in which g and g' are the centers of gravity at the cuts and fills considered as triangles, the formulas for ei and ei' Fig. 10, where the central stake lies in the cut, are

and

ei=gu=}(xc+b-nc)

er' = g'u' = }(xƒ+}b+nc)

When the central stake lies in the fill, as in Fig. 11,

and

e1=gu= }}(x+b+nc)

e'=g'u' = {}(xf+}b−nc)

As will be noted, the value of b to be substituted in the formulas is not the same for cut as for fill.

CHANGE IN VOLUME OF EARTHWORK Shrinkage of Earthwork.-When earth is excavated and formed into an embankment the volume of earth is at first larger than the original excavation, but, after some time, it shrinks to a volume less than that of the original excavation. The accompanying table contains for various kinds of soils, in the second column, the approximate number of cubic yards of embankment that can be formed from 1,000 cu. yd. of excavation. In the third column is given the number of cubic yards of excavation required for each 1,000 cu. yd. of embankment, and in the fourth column is shown the per cent. of shrinkage.

Growth of Rock.-The material from a rock excavation has a larger volume than the original volume in the cut, and there is practically no subsequent shrinkage. The following table shows the approximate number of cubic yards of embankment that can be formed from 1,000 cu. yd. of excavation, the

number of cubic yards of excavation required for 1,000 cu. yd. of embankment, and the per cent. of growth for the various sizes of hard rock.

Limit of Free Haul.-Specifications for earthwork usually allow the contractor extra compensation for transporting material beyond a certain distance, say 800, or, perhaps, 1,000 ft., which distance is called the limit of free-haul. No deduction is made for hauls that are less than the specified limit; but in cases of long hauls, he receives compensation for overhaul only; that is, only for the distance exceeding the