230 RETAINING WALLS. CHAP. V. 



diameter AD describe arc A CD. Draw M C normal to AD and with A as a center and a radius 

 AC describe arc CN. Then A N = y, AM = b and y = Vo^>. Draw EN parallel to BM. 

 With N as a center and radius E N, describe arc ES. Then A E is the trace of the plane of 

 rupture, and P = area SEN-w. 



Cain's Formulas.* Professor William Cain assumes that the angle z is equal to <', the 

 angle of friction of the filling on the back of the wall. By substituting in (5) we have for a 



Vertical Wall With Level Surface, 5 = o. 



where 



Vsin (<f> + <t>') sin <f> 

 cos</>' 

 If $ = </>', then n = V 2 sin <f>, and 



, -M 



(i + sm ^> i/2) a 

 If <' = o, then 



P = ^-A 2 -tan 2 (45 - (IS) 



Fer/icoJ Wctf Witt Surcharge = 5. 



. 



n + i / cos </>' 

 where 



Vsin (<f> -|- ft') sin (</> 5) 

 cos 0' cos 5 

 If 5 = 4, 



P = ? w - hZ ^j-T' ( J 7) 



If <f>' = o, and 5 = <f>, 



p = ^wffi'cos* <i> (18) 



Inclined Wall With Horizontal Surface. 



P = \wh*( sin(g ~.^ \*-. L (I9) 



where 



Vsin (<ft + </>Q-sin <t> 

 sin (<' + (?)-sin<? 



Inclined Wall With Surcharge = d. 



where 



Vsin (<^> + (/>Q-sin (<^> 

 sin (' + ) sin (9 - 



5) 

 8) 



Wall With Loaded Filling. In Fig. 6, the filling is loaded with a uniformly distributed load. 

 Calculate hi by dividing the loading per sq. ft. by w. Let h + hi = H. Then the resultant 

 pressure for a wall with height H, will be 



P z = %w-H*-K (21) 



and the resultant pressure for a wall with height hi, will be 



Pi = i> *!. (22) 



* Professor Rebhann makes the same assumptions and uses the graphic method of Fig. 5. 



