RETAINING WALLS 339 



is supposed to be perfectly dry and to possess no cohesive 

 power, which is practically true of pure sand. 



It is generally assumed that the maximum pressure on a 

 retaining wall is caused by a wedge-shaped prism of earth bsc 

 included between the wall and the line bs, which bisects the 

 angle cbi. This line is called the line of maximum pressure, 

 and the prism whose cross-section is cbs is called the prism of 

 maximum pressure. 



The earth pressure P on the wall is the resultant of two forces 

 X and F, Fig. 1. The pressure X is obtained by determining 

 the weight of the prism of maximum pressure and resolving it 

 into two components, one perpendicular to cb and one parallel 

 to bs. The former is the force X. For a wall with a vertical 

 back; X = $wAtan*(45 iZ) 



in which w is the weight per cubic foot of back filling; h, the 

 height of the wall; and Z, the angle of repose of the back filling, 

 which for 1 horizontal to 1 vertical is 33 41'. 



The force F is the friction between the wall and the filling, 

 due to the pressure X; and if /denotes the coefficient of friction 

 between the material of the wall and that of the filling, 

 Y=fX 



As is well known, / is the tangent of the angle of friction 

 between the material of the wall and that of the back filling. 

 This angle is shown as Zi in the illustration. For dry earth, 

 it is generally taken as equal to Z. In this case, P would be 

 parallel to bi and / would be .67. 



The point of application e of P is assumed to be such that 

 be =i bc = i hf 



Pressure on Base of Wall. When X, Y, and the position of 

 e have been determined, the magnitude and exact position of 

 P are most conveniently determined graphically. The total 

 pressure R, Fig. 1, acting on the base of the wall is then the 

 resultant of the pressure P and the weight W of the wall. Its 

 magnitude and line of action are determined by the parallelo- 

 gram oeirv, in which oei = P and ov=W, the point o being the 

 intersection of the line of action of P with a vertical through the 

 center of gravity g of the wall. 



If both the wall and the foundation were absolutely incom- 

 pressible and incapable of fracture or crushing, the wall would 



