H = 1/2 wh^ tsi? 1/2 (90 



^) 



(50) 



where 11 = the horizontal coiiponent of the lateral force 

 w = the unit weight of fill 

 = the internal aiigle of friction of the material!.. 



230. Equation (50) is used orHrj for vertical walls ifith substantially 

 horizontal backfill,. The structure is assumed to be non-rigid to the 

 extent that an extremely small rotational movement, necessary to produce 

 the internal friction of the bacIcCill, can occur* Table 11 gives values 

 for tan2 1/2 (90 ■= 0) for various values of /, 



Table 11 - Values of tan^ 1/2 (90 - ^) . 







tan ^ 



taji^ 1/2 (90 - 



- /) 



/ 



taxi 



tan^ 1/2 (90 - i2f 











1.00 





1;5 



1*000 



0.17 



10 



0.176 



0.70 





50 



1,192 



0.13 



20 



O.36U 



0.k9 





60 



1*732 



0.07 



25 



0.1.66 



oaa 





70 



2wii8 



0.03 



30 



0.577 



0.33 





80 



5.671 



0*01 



35 



0.700 



0.27 





90 



CO 







ho 



0.839 



0»22 











231 i If the wall is vertical but the fill slopes at an angle p to the 



horizontal, the coirplete equation is 



P = 



wh 



cos p 



-•I 



COS p- 



^ 



, 2 



'COS £- 



, 2 T 



'COS p- COS 



(51) 



232. For structures having a uniform back batter and fills irf-th 

 uniform slope, the general xredge theory, equation (52) may be used 

 to evaluate the ma.gnitude and direction of earth force. This fori:iula 

 takes into account the friction along the surface of the wall» (See 

 Figure 83 ) » 



P - 1/2 



sin (-9-- <^) 

 (1 + iOsin 9 



wh 



(52) 



in which 



I'Jhere 



^^ ^ ii5rr^— P^) sin (© - p) 



^. = 



total force in pounds 



vertical height of fill in feet 



unit weight of fill material 



internal friction ajigle of fill material 



friction angle betxjeen backfill and face of wall 



angle between surface of backfill and horizontal plane 



angle between back of retaining wall and a horizontal 



plane. 



118 



