STABILITY OF RETAINING WALLS. 231 



The pressure on the wall AD will be 



P = P t - P, = \w(H* - hS)K (23) 



and the point of application is through the center of gravity of ADGE, which makes 



t 



yi ~ * ~ 



A L oading per sq. ft+Hr 

 DA 



)* 

 I H*+ Hh,-2h? 



FIG. 6. 



Walls With Negative Surcharge. For the calculation of the pressures on retaining walls with 

 negative surcharge, 5 negative, see the author's " The Design of Walls, Bins and Grain Elevators," 

 second edition. 



STABILITY OF RETAINING WALLS. A retaining wall must be stable (i) against 

 overturning, (2) against sliding, and (3) against crushing the masonry or the foundation. 



The factor of safety of a retaining wall is the ratio of the weight of a filling having the same 

 angle of internal friction that will just cause failure to the actual weight of the filling. For a 

 factor of safety of 2 the wall would just be on the point of failure with a filling weighing twice 

 that for which the wall is built. 



1. Overturning. In Fig. 7, let P, represented by OP', be the resultant pressure of the earth, 

 and \V, represented by OW, be the weight of the wall acting through its center of gravity. Then 

 E, represented by OR, will be the resultant pressure tending to overturn the wall. 



Draw 05 through the point A. For this condition the wall will be just on the point of 

 overturning, and the factor of safety against overturning will be unity. The factor of safety 

 for E = OR will be 



/o = SWIRW (25) 



2. Sliding. In Fig. 7 construct the angle Hi G equal to <f>', the angle of friction of the masonry 

 on the foundation. Now if E passes through I, and takes the direction OQ, the wall will be on 

 the point of sliding, and the factor of safety against sliding, /, will be unity. For E = OR, the 

 factor of safety against sliding will be 



/. = QM'/RM (26) 



Retaining walls seldom fail by sliding. 



The factor of safety against sliding is sometimes given as 



/? 

 /. = jj tan *'. (27) 



where H is the horizontal component of P. Equations (26) and (27) give the same values only 

 where the resultant P is horizontal. 



3. Crushing. In Fig. 7 the load on the foundation will be due to a vertical force F, which 

 produces a uniform stress, p\ = Fid, over the area of the base, and a bending moment = F-b, 

 which produces compression, fa, on the front and tension, fa, on the back of the foundation. 



