where, 



P^ = active force per unit length (lbs. /linear ft. of wall) 



w = unit weight of soil (lbs. /ft?) 



h = height of wall or height of fill at wall if lower than 

 wall (feet) 



6 = angle between horizontal and back slope of wall (degrees) 



i = angle of backfill surface from horizontal (degrees) 



(j) = internal angle of friction of the material (degrees) 



6 = wall friction angle (degrees) 



These symbols are further defined in Figure 7-101. Equation 7-116 may be 

 reduced to that given by Rankine for the special Rankine conditions where 

 6 is considered equal to i, and 9 equal to 90° (vertical wall face). 

 When, additionally, the backfill surface is level (i = 0°), the reduced 

 equation is 



wh^ , , 

 P, - — tan^ (45° -tl- (7-117) 



Figure 7-102 shows that P from Equation 7-117 is applied horizontally. 



Unit weights and internal friction angles for various soils are 

 given in Table 7-13. 



The resultant force for Equation 7-116 is inclined from a line per- 

 pendicular to the back of the wall by the angle of wall friction 6. 

 (See Figure 7-101.) Values for 6 can be obtained from Table 7-14, but 

 should not exceed the internal friction angle of the backfill material (fi. 

 and for conservatism, should not exceed (3/4) 4>. (U.S. Army, Corps of 

 Engineers, 1961.) 



7.72 PASSIVE FORCES 



If the wall resists forces that tend to compress the soil or fill 

 behind it, then the earth must have enough internal resistance to trans- 

 mit these forces. Failure to do this, will result in rupture; a part of 

 the earth will move sideways and upward away from the wall. This resis- 

 tance of the earth against outside forces is called passive earth foraes. 



Tlie general equation for the passive force is 



CSC 6 sin (6 + 0) 



wh2 



'-^^ 



Vsm(0 + 5) - / sin (0-5) sin ((^ + i)' 

 sin (6 - i) 



(7-118) 



7-209 



