RESULTS 



Representative failure curves obtained from equations 27 and 30 are shown in 

 figure 5., For the particular slope and soil properties chosen for illustrative pur- 

 poses in figure 5, the critical depth for the case of no seepage is 11.85 ft. The 

 curves for two of the cases, z = 5 ft . and z > 11.85 ft., coincide to a depth of 

 5 ft. WW' 



The critical depths z^, z^, and Z3 are found from the expressions 



c 



~ cos-^ e {y, (tan 6 - tan 4)) + y tan 9} '■^^•^ 



D W 



c - z^ cos^ 6 (tan 6 - tan (|)) 



z, = z + ^ ; ; (33) 



^ w cos-^ 9 {yu (tan 9 - tan (}>) + y tan 9} 

 b 'w 



z. = Y 5 (34) 



^ cos^ e (tan 9 - tan (})) 



The values of 1^^^^, l^p* -'■2A' ^2^' "'"3A' ^""^ "'"3P found by dividing the appropriate 



horizontal lengths, x, by cos 9. 



The ratios l^^^/zg, and I3P/Z3 are plotted in figures 6a and 6b to illustrate their 

 dependency upon cj) and 9. For cases of no seepage, the length-to-depth ratios are in- 

 dependent of the soil properties, c and Yt • Auxiliary curves have been plotted in 

 figures 6a and 6b to illustrate the dependence of length-to-depth ratios on the values 

 of (6 - (})) . As (9 - ({1) approaches zero, the length-to-depth ratios increase toward 

 infinity . 



The length-to-depth ratios depend upon the buoyant unit weight of the soil, 

 Y^, as well as upon <}) and 9 for cases where seepage occurs throughout the soil profile 

 and flow is parallel to ground slope. The relationships of Ija/^i and lip/zj to (}> and 

 6 for buoyant unit weights of 30, 60, and 90 p.c.f. are shown in figures 7, 8, and 9, 

 respectively. As in the case of no seepage, these length-to-depth ratios are independ- 

 ent of soil cohesive strength, c. 



Although not illustrated in figures 7, 8, and 9, the length-to-depth ratios in- 



crease rapidly toward infinity as the values of tan 9 - tan (jj approach zero. 



'sat 



Finally, it is of interest to examine the variations of length-to-depth ratios as 

 varies between and Z3. Figure 10 shows the relationships of ^2k^^2' ^2?^ ^2' 

 ^^2k -'■2P^/^2 ^° ^'^^ particular slope and soil conditions assumed in figure 5. 

 The actual variations of lengths l2^, ^2?' ^""^ '■''■2A ^ ''^2?^ with z^ are also shown in 

 figure 10. 



12 



