DISCUSSION 



The results presented in figures 6a and 6b indicate that the combined active and 

 passive length-to-critical depth ratios for cases of no seepage are less than 25 when 

 6 - cf) > 1° and <p < 45°. Figures 7, 8, and 9 illustrate that seepage reduces the length- 

 to-depth ratios. Figures 5 and 10 illustrate that seepage reduces both the lengths of 

 the failure surfaces and the critical depths. However, the minimum length-to-depth 



ratios can occur at intermediate seepage conditions (i.e., when < z < z 1. 



^ w cr 



Although the shapes of the derived failure surfaces appear similar to those 

 observed in real circumstances (e.g., see fig. 5), these active and passive failure 

 surfaces cannot simply be combined, as was correctly pointed out by Terzaghi . If, as 

 stated by Taylor, the active and passive states must exist simultaneously at the upper 

 and lower ends, respectively, of a real failure, then the infinite slope theory remains 

 an unsatisfactory means for predicting the state of stress within any real slopes in 

 which failure is impending. 



Consider the stresses on planes normal to the slope. Figure 11 illustrates these 

 stresses for both the active and passive conditions, for the soil and slope conditions 

 assumed in figure 5, without seepage. Note that the active and passive stress states 

 are identical at the critical depth. This represents the depth where and are on 

 the strength envelope (see fig. 2) ; hence, only one circle of stress is possible on the 

 Mohr diagram. Note also that these stress distributions are not linear, as was assumed 

 by Terzaghi. 



Because of moment equilibrium, the shear stresses on planes normal to the slope 

 are identical for both the active and passive conditions as well as for all intermediate 

 stress conditions; only the normal stresses differ (except at the critical depth). Let- 

 ting n and s represent the coordinates normal and parallel to the slope, respectively, 

 (fig. 11) then from equation 11, 



2 tan^ <t>) + 2 c tan <^ 



+ 



2 



{a 2 (tan^ ij) - tan^ e) 



cos (}> 



+ 2 (c tan (() - S tan 9) + (c^ - S^) } ^ . . . . (35) 



where the (+) and ( 

 respectively. 



) signs are associated with the passive and active states. 



23 



