In 1936, Terzaghi (1936) presented a discussion of Frontard's solution in connec- 

 tion with the analysis of simple slopes. He implied that Frontard had combined the 

 vertical projections of the active and passive failure surfaces to obtain the critical 

 height of simple slopes. However, Frontard made no statements in his 1922 paper with 

 regard to the application of his work to simple slopes; nor, indeed, did he mention the 

 active failure surface or present the solution for same. 



Terzaghi correctly criticized attempts to combine the active and passive curves 

 obtained by this procedure for, by the assumptions of the infinite slope theory, the 

 active and passive states of stress cannot exist simultaneously in a slope. However, 

 he was incorrect in attributing any statements to Frontard regarding the applicability 

 of this theory to real slopes. 



Hartsog and Martin (1974) presented general solutions for the active and passive 

 earth pressures in an infinite slope for cases with and without seepage forces. They 

 used the Mohr stress coordinates as a basis for their work, and derived expressions for 

 the state of stress on a plane oriented at any angle under conditions of either active 

 or passive failure. Their paper formed the basis for the following development. 



The active and passive stress circles for the general case of a point located 

 beneath the phreatic surface when ground water flows parallel to the ground slope are 

 shown in figure 2. Note that and are the effective normal and shear stresses, 

 respectively, acting on a plane parallel to ground surface at the point or depth being 

 considered. For a depth less than that to ground water, the coordinates (o^, r^) 

 would simply lie along the line extending from the origin of stresses at an angle, 9, 

 to the a, or normal stress, axis. 



Passive Circle 



Figure 2. — Active and passive stress airoles and their relationship to Mohr's rupture 

 envelope. {After Hartsog and Martin (2)}. 



5 



