GeotecniaFrancisco Callejas MEjercicio 3. Determinar el factor de seguridad del talud mostado en la fguraDovela bi hi hwi i i Li# (m) (m) (m) () (rad) (m)1 1.296 2.72 ! 73.3 1.279 ".12 1.296 .!6 ! #.9# 1.!29 2.13 1.296 7.297 ! "#.7# !.#1 2.!!7" 1.296 7.217 ! "2.1 !.736 1.7"# 1.296 6.!1 ! 3.36 !.617 1.#96 1.296 ".#1 ! 29.12 !.!# 1."#37 1.296 2.972 !."3 23.2" !."!6 1."1# 1."#3 1.!77 !.6#3 17.21 !.3!! 1.2$ % 1.#&'m3C(% 1.9&'m2) % 2* !."36rad$+ % 1&'m3Do,elas-lano de falla .rograma slo.e'+Factor de seguridad mas critico calculado .or el .rograma %1.!"2Ejercicio " . Determinar la inclinacion necesaria .ara /ue el talud tenga un factor de seguridad entre 1.2 0 1.MTODO DE BISHOPTL!D DEL LDO I"#!IE$DOPla%o de &alla ma' (ri)i(o (al(*lado (o% el +ro,ramaE1&23&4 1Do5ela ,i 6i 6+i 7i 7i 89i :s.seco%;,i< ;m= ;m= ;m= ;*= ;rad= ;m= ;&'m=1 1.!71 1.79 ! 6#.#1 1.2!1 2.963 2.79!2 1.!71 3.732 ! 9.22 1.!3" 2.!93 6.93 1.!71 .2# ! 1.96 !.9!7 1.73# 9.339" 1.!71 ".17# ! ".76 !.799 1.3 7.3#3 1.!71 2.377 ! "!.19 !.7!1 1."!2 ".2!16 1.!71 !.7 ! 3.!6 !.612 1.3!# 1.!167 1.!71 ! ! 3!.23 !.2# 1.2" !.!!!# 1.!71 ! ! 2.63 !.""7 1.1## !.!!!E1&32&4 2Do5ela ,i 6i 6+i 7i 7i 89i :s.seco%;,i< ;m= ;m= ;m= ;*= ;rad= ;m= ;&'m=1 1.!71 ! ! 6#.#1 1.2!1 2.963 !2 1.!71 ! ! 9.22 1.!3" 2.!93 !3 1.!71 ! ! 1.96 !.9!7 1.73# !" 1.!71 !.#3 ! ".76 !.799 1.3 1.736 1.!71 1.79 ! "!.19 !.7!1 1."!2 3.636 1.!71 2.66 ! 3.!6 !.612 1.3!# .2227 1.!71 1.971 ! 3!.23 !.2# 1.2" ".!11# 1.!71 !.6#3 ! 2.63 !.""7 1.1## 1.39!F1 seg>n el .rograma 194-E':Do,elas del .rimer estratoDo,elas estrato 2&39?D DE9 93D4 DE2EC@4MA&4D4 DE BC1@4-E1&23&4 1Do5ela ,i 6i 6+i 7i 7i 89i :s.seco%;,i< ;m= ;m= ;m= ;*= ;rad= ;m= ;&'m=1 1.339 1."71 ! 63.2" 1.1!" 2.97" 3.2!2 1.339 3.6 ! ".3 !.9"9 2.297 #.!73 1.339 .2#6 ! "7.16 !.#23 1.969 11.679" 1.339 6.7 ! "!.# !.713 1.77 1".26 1.339 .2# ! 3.11 !.613 1.637 12.2136 1.339 3.1"2 ! 29.7 !.19 1."2 6.9"27 1.339 !.76 ! 2".67 !."31 1."7" 1.67!# 1.3" ! ! 19.79 !.3" 1."2 !.!!!E1&32&4 2Do5ela ,i 6i 6+i 7i 7i 89i :s.seco%;,i< ;m= ;m= ;m= ;*= ;rad= ;m= ;&'m=1 1.339 ! ! 63.2" 1.1!" 2.97" !2 1.339 ! ! ".3 !.9"9 2.297 !3 1.339 ! ! "7.16 !.#23 1.969 !" 1.339 ! ! "!.# !.713 1.77 ! 1.339 !.2#2 ! 3.11 !.613 1.637 !.7176 1.339 1.199 ! 29.7 !.19 1."2 3.!!7 1.339 1.93 ! 2".67 !."31 1."7" ".969# 1.3" !.92 ! 19.79 !.3" 1."2 2.3"2Do,elas estrato 1Do,elas estrato 2 -'.'e(o/(bi 0 hi 0 1)2-a,*a/(bi 0 hwi 0 1)2w-)o)al(T3m) (T3m) (T3m)6.9# ! 6.9#13.2!1 ! 13.2!117."9 ! 17."917.3!3 ! 17.3!31"."1! ! 1"."1!1!.9#3 ! 1!.9#37.126 !.#7 7.7132.9 1.!13 3.96#%;DE %1= ( ^FG; (H ) ( ) =;1' ;7===I =';DE %1= F ( ( ^ = ( =Factor de seguridad mas critico calculado .or el .rograma %1.!"2Ejercicio " . Determinar la inclinacion necesaria .ara /ue el talud tenga un factor de seguridad entre 1.2 0 1.TL!D DEL LDO I"#!IE$DOPla%o de &alla ma' (ri)i(o (al(*lado (o% el +ro,rama:agua%;,i J 6+i J 1=$+:total ui J 89i % $+ ;&'m= ;&'m= ;&'m=! 2.79! !! 6.9 !! 9.339 !! 7.3#3 !! ".2!1 !! 1.!16 !! ! !! ! !:agua%;,i J 6+i J 1=$+:total ui J 89i % $+ ;&'m= ;&'m= ;&'m=! ! !! ! !! ! !! 1.736 !! 3.63 !! .222 !! ".!11 !! 1.39! !:agua%;,i J 6+i J 1=$+:total ui J 89i % $+ ;&'m= ;&'m= ;&'m=! 3.2! !! #.!7 !! 11.679 !! 1".26 !! 12.213 !! 6.9"2 !! 1.67! !! ! !:agua%;,i J 6+i J 1=$+:total ui J 89i % $+ ;&'m= ;&'m= ;&'m=! ! !! ! !! ! !! ! !! !.717 !! 3.!! !! ".969 !! 2.3"2 !*i 0 Li / 2w 0 hw 0 Li (4 Li 5o'i (-i6 *i Li 5o'i) Ta% 7 -i Se%i(T3m) (T3m) (T3m) (T3m)! 2."62 3.!77 6.32!! 2."63 6.16 11.313! 2.13 #.1# 13.16!! 2."62 #.!69 11.612! 2."62 6.719 #.339! 2."62 .122 .3"!.639 2."62 3.323 3.!"31.!6! 2.#17 1.37# 1.17"89.:98;.S. / %;DE %1= ( ^FG; (H ) ( ) =;1' ;7===I =';DE %1= F ( ( ^ = ( =c( 89i Cos7i ;:iK ui 89i Cos :i 1en7i &an;)= &an;7i=;&'m= ;&'m= ;&'m=2.67# !.9!7 2.6!2 !.#3#2.67# 2.1"3 .666 !."2.677 3.!3 7.36 !."12.677 2.399 .2#9 !.33"2.677 1.36 2.711 !.27"2.677 !.33! !.#" !.22#! ! ! !! ! ! !2".2!7c( 89i Cos7i ;:iK ui 89i Cos :i 1en7i &an;)= &an;7i=;&'m= ;&'m= ;&'m=! ! ! !! ! ! !! ! ! !1.2# 1.21 1.2"" !.7191.2# 2.# 2.37 !.921.2# 3.66 2.999 !."911.2#6 2.#!# 2.!19 !."!#1.2# !.973 !.6!1 !.3369.2211umatoria 33."2#F1 %1L"6c( 89i Cos7i ;:iK ui 89i Cos :i 1en7i &an;)= &an;7i=;&'m= ;&'m= ;&'m=3.3"# 1.!6 2.9!2 !.6""3.3"7 2.62" 6.62 !."33.3"7 3.79 #.63 !.3!3.3"7 ".72! 9.!1 !.2#13.3"# 3.96# 7.!2" !.22#3.3"7 2.26 3."" !.1#63.3"9 !."3 !.697 !.1"9! ! ! !3#.69c( 89i Cos7i ;:iK ui 89i Cos :i 1en7i &an;)= &an;7i=;&'m= ;&'m= ;&'m=! ! ! !! ! ! !! ! ! !! ! ! !1.6!7 !.!2 !."13 !."921.6!7 2.136 1.1" !."!!1.6!7 3."79 2.!7" !.3221.6!9 1.6"! !.793 !.22".7931umatoria "3."##F1 %Ta%(7) Ta%(i) ;S Mi() ((4 Li 5o'i < (-i6 *i Li 5o'i) Ta% 7)3(13Mi())(T3m)1." 1.9=> !.716 7.736!.77 1.9=> !.#99 9.##!.32 1.9=> !.996 1!.719!."22 1.9=> 1.!"2 1!.1!9!.331 1.9=> 1.!7 #."!.26! 1.9=> 1.!91 6.9"#!.2!! 1.9=> 1.!9 .2#!!.1"" 1.9=> 1.!## 3.#78>.?@:1.9=%;DE %1= ( ^FG; (H ) ( ) =;1' ;7===I =';DE %1= F ( ( ^ = ( =F1 Mi;7= ;c( 89i Cos7i H ;:iK ui 89i Cos7i= &an )=';1'Mi;7;&'m=1.311 !.93 6.!"91.311 !.72 6.621.311 !.#11 7.!"!1.311 !.#7 .#!!1.311 !.92" ".3761.311 !.961 3.1291.311 !.#6" !1.311 !.9!2 !33.!"F1 Mi;7= ;c( 89i Cos7i H ;:iK ui 89i Cos7i= &an )=';1'Mi;7==;&'m=1.311 !.361 !1.311 !.12 !1.311 !.616 !1.311 1.!#! 2.311.311 1.1!9 3."661.311 1.12 ".3911.311 1.133 3.61"1.!"2 1.192 1.#9"1.6#!1umatoria"#.72F1 Mi;7= ;c( 89i Cos7i H ;:iK ui 89i Cos7i= &an )=';1'Mi;7==;&'m=1.29" !.67" 6.291.29" !.7#7 7.##1.29" !.#6" #.261.29" !.921 #.7621.29" !.962 7.6!21.29" !.993 .6"31.29" 1.!1" 3.#391.29" !.9"1 !"#.22#F1 Mi;7= ;c( 89i Cos7i H ;:iK ui 89i Cos7i= &an )=';1'Mi;7==;&'m=1.29" !."! !1.29" !.#3 !1.29" !.6#! !1.29" !.76 !1.29" 1.129 1.#6#1.29" 1.137 3.2921.29" 1.13 "."#31.29" 1.12" 2.#9!12.3"1umatoria 6!.7621."!((4 Li 5o'i < (-i6 *i Li 5o'i) Ta% 7)3(13Mi());c( 89i Cos7i H ;:iK ui 89i Cos7i= &an )=';1'Mi;7==;c( 89i Cos7i H ;:iK ui 89i Cos7i= &an )=';1'Mi;7==;c( 89i Cos7i H ;:iK ui 89i Cos7i= &an )=';1'Mi;7==