EJEMPLO 6.1 A co!(i!u$cio! s# +$! los -#sul($+os +# u!$ ,-u#$ +# co!soli+$cio! #! l$o-$(o-io so-# u! #s,#cim#! o(#!i+o #! c$m,o: m$s$ s#c$ +#l #s,#cim#! = 116.74 g' $l(u-$ +#l #s,#cim#! $l i!icio +# l$ ,-u#$ = 25.40 mm' Gs =2.72 +i$m#(-o +#l #s,#cim#! =63.50 mm. u-$ !$ # #s,#c m#! $ DATOS: *-#sio! ' i!$l +# l$ co!soli+$cio co!soli+$cio ! %/cm& %mm& 0 25.40 Ws = 116.74 50 25.19 H = 25.40 100 25.00 Gs = 2.72 200 24.29 ø = 6.35 400 23.22 800 22.06 #c(u# #c(u# los c$ c$ lculos !#c#s$-ios +iu;# u!$ cu-$ elog
g mm g/cm3 mm
Solucio Solucio !: D# l$ #cu$cio #cu$cio ! %6.2&' (#!#mos: =
116.74
[
) 4
% 6.35 &
2
g
] % 2.72
& % g/cm3 &
= 1.36 cm = 13.552 mm
*o+#mos ,-#,$-$- l$ sigui#!(# ($l$ *-#sio! ' Al(u-$ i!$l +#l #s,# #s,# cim#! cim#! $l H = H Hs %/cm& i!$l +# l$ co!soli+$cio co!soli+$cio ! %mm& %mm& 0 25.40 11.85 50 25.19 11.64 100 25.00 11.45 200 24.29 10.74 400 23.22 9.67 800 22.06 8.51 $ g-$ic$ #log s# mu#s(-$ #! l$ igu-$ 6.6
FIGURA 6.6 1
& s " c a v e % n ó i c a l e $
0.9
0.8
0.859
0.845 0.792 0.713
0.7
0.628 0.6
30
300
Pres Pr es ió n Ef Efectv ectva a (u n/m2)(es cal a l !ar"#mic !ar"#mica) a)
# = H / Hs 0. 874 0. 8 5 9 0. 8 4 5 0. 7 9 2 0. 7 1 3 0. 6 2 8
EJEMPLO 6.2 <#i# -$s# $ l$ cu-$ #log o(#!i+$ +#l #;#m,lo 6.1 $.D#(#-mi!# l$ ,-#sio ! +# ,-# co!soli+$cio ! c .!cu#!(-# #l !+ic# +# com,-#sio ! >c? T$l$ 6.1 >om,-#sio! #@,$!sio ! +# su#los !$(u-$l#s
Limite Liquido 41.00 A-cill$ $ul +# Bos(o! 60.00 A-cill$ +# >Cic$go A-cill$ +# u#-(# Go-+o!' G#o-gi$ 51.00 80.00 A-cill$ +# u#$ O-l#$!s 60.00 A-cill$ +# Eo!($!$
Limite ndice de ndice de Plástico com!"esión # $c e%!&nsión# $s 20.00 0.35 0.07 20.00 0.40 0.07 26.00 0.12 25.00 0.30 0.05 28.00 0.21 0.05 Solución $. $ g-$ic$ #log mos(-$+$ #! l$ igu-$ 6.6 s# ,-#s#!($ !u#$m#!(# #! l$ igu-$ 6.13.Fs$!+o #l ,-oc#+imi#!(o #! l$ igu-$ 6.8' +#(#-mi!$mos l$ ,-#sio ! +# ,-# co!soli+$cio ! . D# l$ g-$ic$ c = 160 . D# l$ g-$ic$mos(-$+o #log ' #!co!(-$mos Suelo
' (1 ' (2
=
400
/cm
=
800
/cm
#1 #2
=
0.713
=
0.628
*o- ($!(o' =
0.713 log % 800 /
0.628 400 &
=
0.284
EJEMPLO 6.3 <#i# -$s# $ los #;#m,los 6.1 6.2'*$-$ l$ $-cill$' cu$l s#-$ l$ -#l$cio ! +# $cos ,$-$ u!$ ,-#sio ! +# 1000 I/m ² %Nota: c = 160 I/m.& Solucio ! : D#l #;#m,lo 6.1 ' #!co!(-$mos los sigui#!(#s $lo-#s
' (1 ' (2
=
400
/cm
=
800
/cm
#1 #2
=
0.713
=
0.628
>c = ' (3 =
0.284 1000 /cm
A+#m$ s ' +#l #;#m,lo 6.2' >c = 0.284 co! -##-#!ci$ $ l$ igu-$ 6.14' (#!#mos
0.713
0.284
% 1000 400 &
log
=
0.60
EJEMPLO 6.4 ! l$ igu-$ 6.15 s# mu#s(-$ #l ,#-il +# u! su#lo. S s# $,lic$ u!$ c$-g$ Δσ u!io-m#m#!(# +is(-iui+$ #! l$ su,#-ici# +#l su#lo ' J cu$l s#-$ #l $s#!($mi#!(o +#l #s(-$(o +# $-cill$ c$us$+o ,o- l$ co!soli+$cio! ,-im$-i$K *$-$ l$ $-cill$' c = 125 I/m >s = 1/6 >c DATOS
16.50
105.325 I/m²
%
7.00
2.50
&[
18.81
16.50
I/m³
C = 2.50 m
=
18.81
I/m³
C = 7.00 m
=
19.24
I/m³
C = 5.00 m
'
9.81
I/m³
= 50.00
#
= 0.90 = 125.00 I/m²
c
2.50 @
=
9.81
5 ] % 2 & [ 19.2
9.81
]
' (c
= 125.00 I/m²
>
105.325
105.325 I/m
50.00
= 155.33 I/m²
>
' (c
%o($: Δσ=Δσ´ $l i!$l +# l$ co!soli+$cio !.&#c#si($mos #!(o!c#s us$- l$ #cu$cio !%6.17&: '
T#!#mos H= 5m #0 =0.9.D#l$ #cu$cio ! %6.18&. 0.009 %
1 @ 6
10 & =
0.36
=
0.009 %
0.36 6
50.00
10 &
=
0.36
= 0.06
!(o!c#s' 5.00 1 0.9 0.1011
125.00 & [ 0.06 log % 105.325 m
0.36 log
% 105.33
50.00
125.00
&
]
=
101.111 mm
EJEMPLO 6.5 ! l$ igu-$ 6.16$ s# mu#s(-$ #l ,#-il +# u! su#lo .*-u#$s +# co!soli+$cio! #! l$o-$(o-io u#-o! ll#$+os $ c$o so-# u! #s,#cim#! (om$+o +# l$ -#gio! i!(#-m#+i$ +#l #s(-$(o +# l$ $-cill$ .$ cu-$ +# co!soli+$cio! #! c$m,o i!(#-,ol$+$ +# los -#sul($+os +# l$ ,-u#$ +# l$o-$(o-io%como mu#s(-$ l$ igu-$ 6.10& s# os#-$ #! l$ igu-$ 6.16. >$lcul# #l $s#!($mi#!(o #! #l c$m,o c$us$+o ,o- co!soli+$cio! ,-im$-i$ ,$-$ u!$ so-#c$-g$ +# 48 I/m² $,lic$+$ #! l$ su,#-ici# +#l (#--#!o.
Solución
5 % 18.00 9.81 &
40.95
#0 =
I/m²
1.1
Δσ = 48.00 I/m²
ig.6.16 $&*#-il +#l su#lo L & >u-$ +# co!soli+$cio ! +# c$m,o
EJEMPLO 6.6 <#i#-$c# $l #;#m,lo 6.4. Su,o!g$ Mu# l$ co!soli+$cio! ,-im$-i$ s# (#-mi!$-$ #! 3.5 $!Nos.s(im# l$ co!soli+$cio ! s#cu!+$-i$ Mu# ocu--i-$ +# 3.5 $ 10 $!N os +#s,u#s +# l$ $,lic$cio ! +# l$ c$-g$.Si >α = 0.022' J>u$l #s #l $s#!($mi#!(o (o($l ,o- co!soli+$cio ! +#s,u#s +# 10 $!N osK
Solución
>?α
D#l$ #cu$cio! %6.26&' (#!#mos >
=
#,
1
l $lo- +#
#, s# c$lcul$ como
#,
#0
=
Δ# ,-im$-i$
>omi!$!+o l$s #cu$cio!#s %6.12& %6.17&' o-(#!#mos =
= 0.06 log
S# +$
#,
=
% 125.00 & 105.325
0.9
0.36 log
% 155.33 & 125.00
#,
=
0.9
0.01182 @ 5.00 log
%
10 3.5
&
' ,o- lo Mu#
= 0.038
0.038 =
0.862
!(o!c#s
1
0.022 0.862
= 0.0118
= 0.02) m
As#!($mi#!(o ,o- co!soli+$cio!= $s#!($mi#!(o%S& ,o- co!soli+$cio! ,-im$-i$ $s#!($mi#!(o %Ss& ,o- l$ co!soli+$cio! s#cu!+$-i$:D#l #;#m,lo 6.4' S = 101 mm ,o- lo Mu# #l $s#!($mi#!(o (o($l ,oco!soli+$cio! = 101 27 = 128 mm EJEMPLO 6.) ! l$ igu-$ 6.22 s# mu#s(-$ #l ,#-il +# u! su#lo.S# $,lic$ u!$ so-#c$-g$ +# 120 I/m ² = Δσ so-# l$ su,#-ici# +#l (#--#!o $. J>u$ !(o s# #l#$-$ #l $gu$ #! #l ,i#om#(-o i!m#+i$($m#!(# +#s,u#s +# l$ $,lic$cio ! +# l$ c$-g$K . J>u$ l #s #l g-$+o +# co!soli+$cio! #! #l ,u!(o A cu$!+o C= 6.5 mK c. !cu#!(-# C cu$!+o #l g-$+o +# co!soli+$cio! #! A #s +# 60P DATOS 120 I/m² = Q C = FAP
6.5 m '
60P
Solución Su,o!i#!+o u! i!c-#m#!(o u!io-m# #! #l #@c#so i!ici$l +# l$ ,-#sio! +# ,o-o +#l $gu$ $ (-$#s +# los 4 m +# &. ,-ou!+i+$+ +#l #s(-$(o +# $-cill$' -(#!#mos
u0 = Δσ =
C
=
120.00 I/m²
120.00 = 12.23 m 9.81
uA u0
*. U A% = % 1 c. U A
U A
=
1
6.50 @ 12.23 @
%
1
uA u0
&
oR 0.6 =
0.6
& %
120
&=
48.0 I/m²
= 0.6 =
% 1
& 100 = %
%
9.81 9.81
1
& 100
uA
=
46.86+
&
120
Entonces h=
48.0 9.81
=
4.8,
m
EJEMPLO 6.8 l (i#m,o -#Mu#-i+o ,$-$ 50P +# co!soli+$cio! +# u! #s(-$(o +# $-cill$ +# 25 mm +# #s,#so- %+-#!$+$ $--i$ $$;o& #! #l l$o-$(o-io #s +# 2 mi!u(os 20 s#gu!+os. Ju# (i#m,o l# (om$-$ %#! +i$s& $ u! #s(-$(o +# $-cill$ +# 3 m +# #s,#so- +# l$ mism$ $-cill$' #! #l c$m,o $;o #l mismo i!c-#m#!(o +# ,-#sio!'$lc$!$- 50P +# co!soli+$cio!K ! #l c$m,o s# (i#!# u! #s(-$(o +# -oc$ #! #l o!+o +# l$ $-cill$.
Solución
o =
140 0.025 s
s 2
=
t campo 2
= 8064000
s = ,3.33 +i$s
2
EJEMPLO 6., <#i#-$s$ $l #;#m,lo 6.8. J>u$!(o (i#m,o %#! +i$s& (i#!# Mu# ,$s$- ,$-$ Mu# ocu--$ u! 30P +# co!soli+$cio! ,-im$-i$ #! #l c$m,o KFs# l$ #cu$cio! %6.39&. D#l$ #cu$cio! %6.39&' (#!#mos
Solución
Entonces#
93.33
oR
+i$s
t 2
=
50² 30
t 2 =
33.6 +i$s
^
EJEMPLO 6.10 *$-$ u!$ $-cill$ !o-m$lm#!(# co!soli+$+$
#
σR0 = 200.00 I/m σR0 =
=
#0 #
ΔσR = 400.00 I/m
=
=
1.22 0.98
$ ,#-m#$ili+$+ k +# l$ $-cill$ ,$-$ #l -$!go +# c$-g$ #s +# 0.61@10 ¯4 m/+i$ J>u$ !(o (i#m,o %#! +i$s& l# (om$-$ $ u! #s(-$(o +# $-cill$ +# 4 m +# #s,#so- %+-#!$+$ ,o- u! solo l$+o& #! #l &. c$m,o $lc$!$- 60P +# co!soli+$cio!K
*. J>u$ l #s #l $s#!($mi#!(o #! #s# (i#m,o' #s +#ci- ' $;o 60P +# co!soli+$cio! Solución &. l co#ici#!(# +# com,-#siili+$+ #s
Δ#
=
1.22
0.98
=
Δσ' = 400.00 200.00 =
=
1.22
2
0.98
0.24
200 m/I
= 1.1
!(o!c#s' 0.24 / 200.00 = 5.)14E-04 I/m 1 1.1
%
6.1005 m/+i$ 5.71404 m/I & % 9.81
=
0.010,
log
400 200
I/m² &
m²/+i$
+#s,#;$mos D#l$ ($l$ 6.2' ,$-$ U= 60P' #l $lo- +# T60 #s +# 0.286' ,o- lo Mu# %
0.286 & % 4 &² = 41,.8 +i$s 0.0109 1.22 0.98 = 0.),) l! % 400 / 200 &
D# l$ #cu$cio! %6.14&' (#!#mos %
S $ 60P
% 0.60 & % 0.432 & =
=
0.797 1
& % 4 & 1.22
%
&=
0.432 m
0.25, m
EJEMPLO 6.11 F!$s ,u#$ +# co!soli+$cio! #! l$o-$(o-io so-# u! #s,#cim#! +# su#lo %+-#!$;# ,o- $mos l$+os& +io los -#sul($+os sigui#!(#s: #s,# so- +#l #s,#siom#! +# $-cill$ = 25 mm
σR1 =
50
I/m²
#1
=
0.92
σR2 =
120
I/m²
#2
=
0.78
(i#m,o ,$-$ 50P +# co!soli+$cio! =2.5 mi! D#(#-mi!# l$ ,#-m#$ili+$+ k +# l$ $-cill$ ,$-$ #l -$!go +# c$-g$.
Solución
H =
25
mm =
( = 2.5
0.025 m
mi!
0.92 0.78 120 50 0.92 0.78 1 2
0.14 70 1.7 2
= 1
0.14 70 3.7 2
=
=
0.00108 m/I
D# l$ ($l$ 6.2' ,$-$ U =50 ' #l $lo- +# T = 0.197' ,o- lo Mu#
% 0.197 & % 0.0252 2.5
m
&²
= 1.231E-05 m²/mi!
mi!
= % 1.23105 & %
0.00108
& %
& = 1.306E-0) m/mi!
9.81
EJEMPLO 6.12 >$lcul# #l $s#!($mi#!(o ,o- co!soli+$cio! ,-im$-i$ +#l #s(-$(o +# $-cill$ +# 3m +# #s,#so- %igu-$ 6.23& Mu# -#sul($-$ +# l$ c$-g$ (om$+$ ,o- u!$ $,$($ cu$+-$+$ +# 1.5 m . $ $-cill$ #s($ !o-m$lm#!(# co!soli+$+$.
Solución
+o!+#
'
*$-$ u!$ $-cill$ !o-m$lm#!(# co!soli+$+$' +# l$ #cu$cio! %6.14& (#!#mos
>c
=
0.009
%
H
=
3000
mm
#0
=
1.0
4.5 @
1.5
= 4.5 @ 15.7 1.5 %
10
& =
[
18.9 9.81 &
0.009
%
40
9.81
] 3 2
10
& =
0.27
1.5 %
17.3 9.81 & =
B
9.81
U
,5.52 I/m
*$-$ c$lcul$- QR ' ,-#,$-$mos l$ sigui#!(# ($l$: m1
4.5 6.0 7.5
B
1 1 1 M
=
!1
1.5 1.5 1.5 890 2.25
%B/2&
Vc %T$l$ 6.3&
QR = M/c
6 8 10
0.051 0.029 0.019
20.17 11.47 7.52
= 3,5.6 I/m
I/m
>$lcul$mos 20.17
% 4 & %
11.47
&
7.52
6
= 12.26 I/m
Al sus(i(ui- #s(os $Ilo-#s #! l$ #cu$cio! +#l $s#!($mi#!(o' o(#!#mos % 0.27 & % 3000 1 1.0
&
log
%
95.52
12.26 95.52
&=
21.24 mm
EJEMPLO 6.13 <#i#-$s# $ l$ igu-$ 6.24. Du-$!(# l$ co!s(-uccio! +# u! ,u#!(# c$--#(#-o' l$ c$-g$ ,-om#+io ,#-m$!#!(# so-# #l #s(-$(o +# $-cill$ s# #s,#-$ Mu# c-#c$ $,-o@im$+$m#!(# 115 I/m2. $ ,-#sio! +# so-#c$-g$ ##c(i$ ,-om#+io' #! m#+io +#l #s(-$(o +# $-cill$' #s +# 210 I/m2' AMui ' H = 6 m ' Cc= 0.28 ' #0 = 0.9 ' c = 0.36 m²/m#s. $$-cill$ #s($ !o-m$lm#!(# co!soli+$+$.
&. D#(#-mi!# #l $s#!($mi#!(o (o($l ,o- co!soli+$cio! ,-im$-i$ +#l ,u#!(# si! ,-#com,-#sio!. *. J>u$l #s l$ so-# c$-g$ Δσ%& !#c#s$-i$ ,$-$ #limi!$- ,o- ,-#com,-#sio! #l $s#!($mi#!(o (o($l ,oco!soli+$cio! ,-im$-i$ #! 9 m#s#s. Solución P&"te a l $s#!($mi#!(o (o($l ,o- co!soli+$cio! ,-im$-i$ s# c$lcul$ co! l$ #cu$cio! %6.48& :
% 0.28 & % 6 1 0.9
&
log
% 210
115.00 210
&=
0.16))
m
16).) mm
P&"te b
cv
= 0.36 m²/m#s
( 2
= 9.0
m#s
Hdr
= 3.0
%+-#!$;# #! +os +i-#ccio!#s&
*o- co!sigui#!(#' =
% 0.36 & % 9.0 3.0 ²
&
0.36
=
D# $cu#-+o co! l$ igu-$ 6.27' ,$-$ T v = 0.36' #l $lo- +# U #s +# 47P
Q(p)
=
115
I/m
=
210
I/m
ACo-$
Q(p)
115 210
=
= 0.548
D# $cu#-+o co! l$ igu-$ 6.25 ' ,$-$ U = 47P Q%,& /σR0= 0.548' X%&&/ X%,& Y1.8 *o- ($!(o' %
1.8
& %
115
& =
20) I/m
EJEMPLO 6.13 <#su#l$ #l #;#m,lo 6.13 co! l$ $+icio! +# $lgu!os +-#!#s +# $-#!$ . Su,o!g$ Mu# r w =0.1 m L d e= 3 m c = c-
Solución P&"te a l $s#!($mi#!(o (o($l ,o- co!soli+$cio! ,-im$-i$ s#-$ igu$l Mu# $!(#s +# 166.) mm D#l #;#m,lo 6.13' T v = 0.36 . l $lo- +# U v +# l$ ($l$ 6.2 #s $,-o@im$+$m#!(# +# 67P. D# l$ P&"te b #cu$cio! %6.57& ' (#!#mos 3 = 15.00 @ 0.1
2 D# !u#o ' %
0.36
& % 9.0 3 ²
&
0.36
=
D# l$ ($l$ 6.4 ,$-$ ! =15 T- = 36 ' #l $lo- +# F- #s $,-o@im$+$m#!(# +# 77P. *o- co!sigui#!(#' 1
0.,24 =
%
1
0.67 & %
1
0.77 & =
,2.4+
ACo-$ ' +# l$ igu-$ 6.24 ,$-$ Q%,& /R0= 0.548 U vr = 92.4P ' #l $lo- +# X%&&/ X%,& Y0.12 . *o- co!sigui#!(# ' (#!#mos
%
115
& % 0.12 & =
13.8 I/m
*rase a la !ura 6.24. +uran#e la cns#rucción %e un ,uen#e carre#er& la car!a ,rme%i ,erma
nen#e s-re el es#ra# %e arcilla se es,era ue creca a,rima
<#$i#-$c# $ l$ cu-$ #log o(#!i+$ +#l #;#m,lo 6.1 $.D#(#-mi!# l$ ,-#sio ! +# ,-# co!soli+$cio ! c .!cu#!(-# #l !+ic# +# com,-#sio ! >c? T$l$ 6.1 >om,-#sio! #@,$!sio! +# su#los !$(u-$l#s
Limite Liquido 41.00 A-cill$ $ul +# Bos(o! 60.00 A-cill$ +# >Cic$go A-cill$ +# u#-(# Go-+o!'G#o-gi$ 51.00 80.00 A-cill$ +# u#$ O-l#$!s 60.00 A-cill$ +# Eo!($!$
Limite ndice de ndice de Pl&stico com!"esión # $c e%!&nsión# $s 20.00 0.35 0.07 20.00 0.40 0.07 26.00 0.12 25.00 0.30 0.05 28.00 0.21 0.05 Solución $. $ g-$ic$ #log mos(-$+$ #! l$ igu-$ 6.6 s# ,-#s#!($ !u#$m#!(# #! l$ igu-$ 6.13.Fs$!+o #l ,-oc#+imi#!(o mos(-$+o #! l$ igu-$ 6.8' +#(#-mi!$mos l$ ,-#sio ! +# ,-# co!soli+$cio ! . D# l$ g-$ic$ c = 160 I/m². . D# l$ g-$ic$ #log ' #!co!(-$mos Suelo
' (1 ' (2
=
#1
=
=
#2
=
UNIVERSIDAD TECNICA DE MACHALA UAIC-CARRERA DE INGENIERIA CIVIL
JAIME GOMEZ ROMERO
MECANICA DE SUELOS II
PLAN REMEDIAL
DOCENTE: ING.YUDI MEDINA SANCHEZ
6to AÑO "C"
UNIVERSIDAD TECNICA DE MACHALA UAIC-CARRERA DE INGENIERIA CIVIL
JAIME GOMEZ ROMERO
MECANICA DE SUELOS II
PLAN REMEDIAL
DOCENTE: ING.YUDI MEDINA SANCHEZ
6to AÑO "C"