Figure 11 . --Active state of stress. 



Figure 12. — Passive state of stress. 



In the active case the lateral pressure is relieved and elongation occurs parallel 

 to the direction of pressure release, as shown in figure 11. The lateral pressure, P a , 

 shown in figure 11, is the minimum which will maintain stability. This state of stress 

 is shown by the active stress circle in figure 10. 



In the passive case the lateral pressure is increased and compression occurs 

 parallel to the direction of pressure increase, as shown in figure 12. The lateral 

 pressure, Pp, shown in figure 12, is the maximum that will maintain stability. This 

 state of stress is shown by the passive stress circle in figure 10. 



Figure 10 shows that three conditions must be met for a soil to be in an active or 

 passive state of stress: (1) The stress circle must be tangent to the Mohr failure 

 envelope, (2) the center of the stress circle must lie on the a axis, and (3) the stress 

 circle must pass through the point of known stress (o a ,T a ). 



A modification of the Mohr's circle of stresses will be used herein. This modifica- 

 tion, the origin of planes, allows a better visualization of the stresses and the orien- 

 tation of planes on which the stresses act than the conventional Mohr's circle method. 

 The origin of planes, OP, is shown in figure 10 and is obtained as follows: 



1. Through the point of known stress condition, draw a line oriented identically 

 to the plane on which the known stress acts. 



2. The intersection of this line and the circle of stresses locate the origin of 

 planes (a b ,x b ). 



3. The stress condition on any plane can be found by constructing a line oriented 

 identically to the plane on which the stresses are to be found. 



4. The point where this line again intersects the circle of stresses yields the 

 desired stress condition (5 c ,t c ). 



The stresses for the active case ( a c > T c ) ac t anc * the passive case (5 c ,T c )p ass are 

 shown for planes oriented 45° clockwise from the horizontal. 



11 



