From equilibrium considerations. 



3 T 9 a 



ns s 



= Y sin 9 - — (38a) 



da 9 T 



, eos e - (38b) 



T =T (38c) 



ns sn 



9 a 9 T 

 s sn 



Under the assumptions of the infinite slope theory, ^ ^ = — = 0, 



and the stresses within the slope are given simply as ^ 



T = T = y n sin 6 (39a) 



ns sn ' ^ 



0^ = Y n cos 6 (39b) 



a^ (1 + 2 tan^ <i>) + 2 c tan 4) 



- {(a tan (j) + c)^-T ^} ^ < a 



cos (J) n ns - s 



< a (1+2 tan^ A) + 2 c tan * 



— n ■ 



+ r {(a tan ()) + c)2 - T 2}^ (•39c) 



cos c}) ^ n ns 



where a^ remains constant at all locations in the slope at a given depth. 



However, if it is assumed that a^ increases uniformly from the active to the 

 passive condition in length of slope, L, then 



s_ _ passive - active = 



9 s ~ L 



= — - {(a tan * + c)2 - T 2}^ (40) 



L cos (}) n ns 



whereby from equation 38a, 



9 T A - h 



-— ^ = Y sin 6 - — - {(a tan (}> + c)2 - t 2} (41) 



3 n L cos <f) n ns ^ 



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