FOUNDATIONS AND RETAINING WALLS 211 



stability of abutments, namely, that the wall must be secure against 

 sliding on its base and against overturning. 



Let P 2 denote the weight of the wall, P 1 the resultant earth pres- 

 sure, and R the resultant of P 2 and P' (Fig. 143). Then, if R is resolved 

 into two components R F and R N , respectively parallel and perpen- 

 dicular to the base of the wall, the condition for stability against 

 sliding is that R F shall be less than the friction on the base, or, 

 symbolically, R r <kR y . 



Let g denote the factor of safety. Then this condition may be written 

 (108) R, = **. 



t7 



To find the values of R F and R v , let P' and P 2 be resolved into com- 

 ponents parallel to R F and R v respectively. Then, in the notation of 

 the preceding article, 



R F = P' sin (a + + f) - P 2 sin 0, 

 7.'. v = P 2 cos e - P' cos (a + d + ?) 



Substituting these values of R F and R v in equation (108) and solving 

 the resulting expression for y, 



_ k[P t cos - P' cosfo + + ?)] 

 fa a (a + e + f)-P t a^e 



If the base of the wall is horizontal, 6 = and equation (109) becomes 



^-P'cosKfiO]. 

 P'sin(a + r) 



For security against sliding the factor of safety should not be less 

 than 3 ; consequently, the criterion for stability against sliding may 

 be stated as 



where the value of g is calculated from equation (109) or (110). 



In applying this criterion it should be noted that the value of f 

 must first be assumed (Article 163 ; < < o>). 



The following table gives average values of the angle of repose 

 and coefficient of friction of masonry on various substances.* 



* See references at the foot of p. 198. 



