216 EARTHWORK 



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 Ai and Az are readily obtained as areas of 

 triangles. For rinding 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 e\ and e\ 

 Fig. 10, wiiere the central stake lies in the cut, are 



ei = gu = J (x c + $b nc) 

 and '-g'u' = J(*/+J& + nc) 



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



and ei' = g f u 



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 exca- 

 vation. In the third column is given the number of cubic 

 yards of excavation required for each 1,000 cu. yd. of embank- 

 ment, 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 



