Note: hydraulic gradient i = sinO 



Figure 5. — Flout net within an infinite slope. 



The effective stress, a & , is found by subtracting the neutral stress from the 

 total stress: 



a = y 1 cos^e + y „(Z-Z )cos z 6 - y (Z-Z )cos' 

 a t w sat w J » w J 



(7) 



Because the buoyant unit weight, y^, is equal to Cy ^ - Y w ) > equation 7 can be 

 written as: 



a = y^Z cos 2 6 + Y K (Z-Z )cos 2 6. 

 a t w 'b w y 



(8) 



Because water cannot resist shear stress at negligible velocities, the shear stress, 

 x a , is not affected by the neutral stress. Equations 5 and 8 are the basic relation- 

 ships for the effective stresses at a given depth and on a given plane of investigation, 



With this information, the stress condition (a , t ) may be adapted to a Mohr diagram. 



a a 



Stresses cannot be added vectorial ly because they are not vector quantities, but 

 because they are acting on the unit area of plane A-A', the normal and tangential 

 stresses can be used interchangeably with normal and tangential forces. The subsequent 

 development makes use of this resolving of stresses in order to define obliquity angles 

 (the angle between the resultant and the normal effective stress) . 



6 



