Figure 10. — Mohr diagram for active and passive stress conditions. 



The strength characteristics of a soil material may be defined by Coulomb's 

 equat. on: 



s = c + atan<j>. (13) 



Where: s = the shear strength of the soil material; 



c = the unit cohesion; 



a - the normal effective stress; and 



<f> = the angle of internal friction. 



Equation 13 is shown graphically in figure 10, and this graphic illustration of equa- 

 tion 13 is known as the Mohr rupture envelope. The leaves of the Mohr rupture envelope, 

 MN and M'N', shown in figure 10, represent the strength of the soil based on Coulomb's 

 equation. A state of stress above MN or below M'N 1 will cause failure of the slope, 

 whereas a state of stress that lies within the envelope may exist in a stable slope. 

 The leaves of the envelope define impending failure conditions. 



The main objective of this development is to find equations for two limiting 

 values of stresses, commonly called the active and passive states of stress. When the 

 soil is on verge of failure it will be in a state of plastic equilibrium. 



in 



