342 RETAINING WALLS 



and the line of maximum pressure bk. The general method 

 of procedure is the same as previously described, except that 

 in this case, be is no longer equal to J be, and the point of appli- 

 cation e of the pressure P is located by determining the center 

 of gravity gi of the area zukbcz and drawing the line gie par- 

 allel to the line of maximum pressure. The intersection e of this 

 line with the back of the wall is the required point of application 

 of P. Fig. 3 shows all the remaining steps that should be taken 

 in the analysis of the retaining wall, which are the same as 

 those already described. 



SUPERIMPOSED LOADS 



In case of loads resting on the top of the back filling, they 

 must be added to the weight of the prism of maximum pressure, 

 or of the body of earth causing the maximum pressure. The 

 method of procedure is the same as the one already given for a 

 surcharged wall, the modification being only in the manner of 

 locating the center of gravity gi, which, in this case, is the center 

 of gravity of the system of bodies consisting of the earth filling 

 and of the loads. 



EMPIRICAL RULES 



All the theories of the equilibrium and stability of retaining 

 walls are based on assumptions that have not been conclusively 

 proved. For this reason, empirical rules based on observation 

 and experience are extensively employed in practice. Of these 

 rules, those by John C. Trautwine are most widely used. They 

 are given with slight modification in the following paragraph. 



Rules for Vertical Walls. For a vertical wall resting on a 

 foundation of masonry suitably enlarged for a proper distribu- 

 tion of the load on the soil, with the top of the fill leveled off at 

 the top of the wall, the ratio of the thickness to the height of 

 the wall should be .35 for a wall of cut stone, or of first-class 

 large-ranged rubble, in mortar, or of concrete; .4 for a wall of 

 good common rubble or brick, in mortar; and .5 for a wall of 

 dry rubble. 



For a wall with a battered or stepped back, Trautwine 

 recommends using the same average thickness as for a vertical 



