206 



STRENGTH OF MATERIALS 



the second assumes that the earth pressure against the wall is the 

 same as if the earth was a liquid. However, the uncertainty attend- 

 ing the exact degree of homogeneity of the materials under consid- 

 eration probably does not warrant any greater precision in these first 

 two assumptions. 



The third assumption relates to the direction of the maximum 

 pressure, and is the point on which the various theories differ. Thus 

 Coulomb and Weyrauch assume that the pressure is normal to the 



FIG. 142 



back of the wall ; Rankine assumes that it makes an angle with the 

 back of the wall equal to the angle of repose of the material : while 

 other authorities assume values intermediate between these two. 



In the present discussion the first two conditions mentioned above 

 will be retained, and the third condition will be replaced by the 

 assumption that the resultant earth pressure makes an unknown 

 angle f with a normal to the back of the wall. The assumptions 

 are, then : 



1. The surface of rupture is a plane. 



2. The point of application of the resultant pressure is one third 

 of the height of the wall from the bottom. 



