DETERMINACION DEL CONTENIDO DE HUMEDAD, ANALISIS GRANULOMETRICO Y LIMITES DE ATTERBERG ATTERBERG
ALBA LISET PABON PABON CASTILLO LENDY FABIOLA PARRA PARRA BASTO JENIFER ALEXANDRA PUCHANA
UNIVERSIDAD DE PAMPLONA DEPARTAMENTO DE INGENIERIA AMBIENTAL, CIVIL Y QUIMICA PROGRAMA DE INGENIERIA CIVIL PAMPLONA 2016 DETERMINACION DEL CONTENIDO DE HUMEDAD, ANALISIS GRANULOMETRICO Y LIMITES DE ATTERBERG ATTERBERG
ALBA LISET PABON PABON CASTILLO COD: 10242!" LENDY FABIOLA PARRA PARRA BASTO COD: JENIFER ALEXANDRA PUCHANA COD:
ING# OLIVER NOGUERA
UNIVERSIDAD DE PAMPLONA DEPARTAMENTO DE INGENIERIA AMBIENTAL, CIVIL Y QUIMICA PROGRAMA DE INGENIERIA CIVIL PAMPLONA 2016
2
TABLA DE CONTENIDO
PAG LISTA LISTA DE FIGURA................ FIGURA.................................... ........................................ ........................................ ................................. .................... ....... 5 1. INTRODUC INTRODUCCION. CION...... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... ........... ........ ..8 8 2. OBJETIVO OBJETIVOS... S........ ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ................ ..................... ....................10 ..........10 2.1
OBJETIVOS OBJETIVOS GENERA GENERALES. LES..... ......... .......... .......... .......... .......... .......... ........... ................ .................... .....................10 ...........10
2.2
OBJETIVOS OBJETIVOS ESPECIFI ESPECIFICOS.. COS....... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... .............. ........... 10
3. JUSTIFICA JUSTIFICACIÓN CIÓN..... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... ........... ................ ..................... ................. ......11 11 4. EXTRA EXTRACCION CCION DE LA MUESTR MUESTRA.... A......... ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ...........12 ......12 4.1
Mu!"#$ Mu!"#$ %$#$ %$#$ $'u( $'u()*" )*"#+$ #+$ , (-*-" (-*-"!... !........ .......... .......... .......... .......... .......... .......... .......... .......... ........12 ...12
4.2
Mu!"#$ Mu!"#$ %$#$ )'"'-/ )'"'-/) ) / / u*/$ u*/$/..... /.......... .......... .......... .......... .......... .......... .......... .............. ...........13 ..13
4.3
M$"#-$( M$"#-$(! ! %$#$ ()! '!$,)!.. '!$,)!....... .......... .......... .......... .......... ......... ......... ........... ................. ..................... ............ ..14 14
5. ENSA ENSAO DE CONTENIDO CONTENIDO DE UMEDAD.... UMEDAD......... ......... ......... .......... .......... .......... .......... .......... .......... ............1 .......1 5.1
P#-'-% P#-'-%-) -) /( *")/).. *")/)...... ......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... ............... ............ ..1 1
5.2
P#)/ P#)/-*-' -*-'").. ")....... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ....... 1
5.3
A'6(-!-! A'6(-!-! / /$")!.... /$")!......... ......... ......... .......... .......... .......... .......... .......... .......... ............... .................... .................... .............. ....17 17
. ENSA ENSAO DE LMITES DE ATTERB ATTERBERG.. ERG....... .......... .......... .......... .......... .......... ............. ................... ...................22 ........22 .1
L-*-" L-*-" (+9u-/). (+9u-/)...... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... ............ ............. ......22 22
.2
L-*-" L-*-" %(6!"%(6!"-).. )....... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... ............ .................. ..................23 .......23
.3
'/- '/- / %($!"--/$/. %($!"--/$/...... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... .......... ............23 .......23
.4
E'!$,) E'!$,) (-*-" (-*-" (+9u-/).. (+9u-/)...... ......... .......... .......... .......... .......... .......... .......... .......... ............... ..................... ....................23 .........23
.4.1
P#-'-% P#-'-%-) -) /( *")/)... *")/)........ .......... .......... .......... .......... .......... .............. .................... ..................... .................23 .......23
.4.2
P#)/ P#)/-*-' -*-'").. ")....... .......... .......... .......... .......... .......... .......... .......... .......... .......... ............. .................. ....................24 ..........24
.4.3
A'6(-!-! A'6(-!-! / /$")!... /$")!........ .......... .......... .......... .......... .......... .......... .......... .......... .......... ............... ..................... ............. ..2 2
.5
E'!$,) E'!$,) (-*-" (-*-" %(6!"-)... %(6!"-)........ ......... ......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... ............ ......... ..30 30
.5.1
P#)/ P#)/-*-' -*-'").. ")....... .......... .......... .......... .......... .......... .......... .......... .......... .......... ............. .................. ....................30 ..........30
.5.2
A'6(-!-! A'6(-!-! / /$")!... /$")!........ .......... .......... .......... .......... .......... .......... .......... .......... .......... ............... ..................... ............. ..32 32
. ENSA ENSAO DE GRANUL GRANULOMET OMETRA.. RA....... .......... .......... .......... .......... .......... .......... ......... ......... ............... .................... ............. ...34 34 .1
P#-'-% P#-'-%-) -) /( *")/).. *")/)...... ......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... ............... ............ ..34 34
3
.2
P#)/ P#)/-*-' -*-'").. ")....... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ....... 34
.3
A'6(-!-! A'6(-!-! / /$")!.... /$")!......... ......... ......... .......... .......... .......... .......... .......... .......... ............... .................... .................... .............. ....3 3
.3.1
C):-'" C):-'" / u'-;)#* u'-;)#*-/$/. -/$/...... .......... .......... .......... .......... .......... .......... .............. ................... ...............38 .....38
.3.2
C):-'" C):-'" u#<$"u# u#<$"u#$.... $........ ......... .......... .......... .......... .......... .......... .......... .......... .......... ......... .............. ............ ..38 38
.3.3
Cu#<$ Cu#<$ $'u()* $'u()*"#"#-$... $....... ......... .......... .......... .......... .......... ............ .................. ..................... ..................38 ........38
.4
C($!-:$ C($! -:$-=' -=' %)# !-! !-!"*$ "*$ AASTO.... AASTO......... .......... .......... .......... .......... .......... .......... ......... .......... .............37 .......37
.4.1 .5
P#)/ P#)/-*-' -*-'").. ")....... .......... .......... .......... .......... .......... .......... .......... .......... .......... ............. .................. ....................37 ..........37
C($!-:$ C($! -:$-=' -=' %)# %)# SUCS...... SUCS........... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .............37 ........37
.5.1
P#)/ P#)/-*-' -*-'").. ")....... .......... .......... .......... .......... .......... .......... .......... .......... .......... ............. .................. ....................37 ..........37
8. ENSA ENSAO DE GRANUL GRANULOMET OMETRA.. RA....... .......... .......... .......... .......... .......... .......... ......... ......... ............... .................... ............. ...41 41 >SUELO >SUELO GRANULAR?................ GRANULAR?................................... ....................................... ......................................... ................................... .............. 41 8.1
P#-'-% P#-'-%-) -) /( *")/).. *")/)...... ......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... ............... ............ ..41 41
8.2
P#)/ P#)/-*-' -*-'").. ")....... .......... .......... ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ....... 41
8.3
A'6(-!-! A'6(-!-! / /$")!.... /$")!......... ......... ......... .......... .......... .......... .......... .......... .......... ............... .................... .................... .............. ....43 43
8.4
CLASIFICA CLASIFICACION CION POR SUCS..... SUCS.......... .......... .......... .......... .......... .......... .......... .......... .......... ............. ..................44 ..........44
8.4.1
P#)/ P#)/-*-' -*-'").. ")....... .......... .......... .......... .......... .......... .......... .......... .......... .......... ............. .................. ....................44 ..........44
7. CONCLUSION CONCLUSIONES.. ES....... ......... ......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... .......... .......... .......... .......... ....... 45 10.
.BIBLIOGR .BIBLIOGRAFIA AFIA..... .......... .......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ............ ................... ..................... ............ 4
11.
ANEXOS... ANEXOS....... ......... .......... .......... .......... .......... .......... .......... .......... .......... ......... ......... .......... ........... ................ ..................... ................. ......4 4
LISTA DE FIGURA
5
LISTA DE GRAFICAS
LISTA DE TABLAS
1# INTRODUCCION
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
E- %9-*/ )% &(%$+& $/ )%'%.*-/*8- )% +-'%-*)+ )% <(%)/) %& (- .+%&+ 5(% .%5(*%.% %-'.% 12 24 <+./ E$ +-'%-*)+ )% <(%)/) %- %$ &(%$+ %& )% /$'/ .%$%7/-*/ '/-'+ %- /+ ++ %$ $/+./'+.*+ / 5(% '*%-% %$*/*8- ;&*/ )%*-% $+& +.+& %- %$ &(%$+# L/ +'%-*/$ (%.=/ '%-&*8- )% /(/ )%$ &(%$+, %& .+)('+ )% $/ /)<%&*8- + /'./*8- %-'.% $/ &(%.**% )% $/& /.';($/& )% &(%$+ %$ /(/3 $/ +<%&*8-, + $/ /'./*8- %-'.% $/& +$($/& )% /(/#
L/ ./-($+%'.;/, (%)% )%*-*.&% ++ $/ )*7*&*8- )%$ *&+ %- )*%.%-'%& ./*+-%& $/&**/)/& &%@- %$ '//+ )% &(& /.';($/ E$ /-9$*&*& )% $/ )*&'.*(*8- )% $/& /.';($/& )%$ &(%$+ %& *-)*&%-&/$% &* &% )%&%/ /./'%.*=/. &(& +-)**+-%& +- %$ *- )% )%'%.*-/. &* ($% +- $/& %&%**/*+-%& )% ./)/)+ /'/& /./ )/. &++.'% / (-/ %&'.('(./#
2# OBJETIVOS
2#1 OBJETIVOS GENERALES
A)5(*.*. +-+**%-'+& )%$ '+)+ )% /-9$*&*& ./-($+'.*+ %9-*+ /./ +)%. )%'%.*-/. )% /-%./ /)%(/)/ $/ )*&'.*(*8- )% $/& /.';($/ D%'%.*-/. %$ +-'%-*)+ )% <(%)/) .%&%-'% %- (- &(%$+# I-'.+)(*. /$ %&'()*/-'% /$ .+%)**%-'+ )% )%'%.*-/*8- )% $+& $;*'%& $;5(*)+ $9&'*+ )% (- &(%$+
2#2 OBJETIVOS ESPECIFICOS
A$*/. %$ '+)+ )% /-9$*&*& ./-($+'.*+ %9-*+ /./ (-/ (%&'./ )% &(%$+# G./*/. $/ (.7/ ./-($+'.*/, %)*/-'% $+& )/'+& .%+*)+& %- %$ $/+./'+.*+ +- %$ *- )% /-/$*=/. %$ ++.'/*%-'+ /./'%.;&'*/& )%$ &(%$+# D%'%.*-/. $+& +%**%-'%& )% (.7/'(./ (-*+.*)/), /./ )%'%.*-/. +-)**+-%& )% ./)/*8- )%$ &(%$+#
$/&
D%'%.*-/. $/ <(%)/) )% (- &(%$+, '%-*%-)+ %- (%-'/ $/ /-'*)/) /(/ .%&%-'% %- (-/ (%&'./ )% &(%$+ %- '.*-+& )% &( %&+ %- &%+# D%'%.*-/. %)*/-'% %$ $/+./'+.*+, %$ $;*'% $;5(*)+ $9&'*+ )% (- &(%$+#
7
# JUSTIFICACIN
4# EXTRACCION DE LA MUESTRA
4#1 M(%&'./ /./ ./-($+%'.;/ $**'%&
S% .%/$*=/ (- /*5(% / (-/ .+(-)*)/) )+-)% &% (%)/ )%'%.*-/. $+& %&'./'+& )%$ &(%$+ %&' $*.% )% /'%.*/$ +.9-*+#
1.0
F*(./ 1# E/7/*8-
P/./ +)%. ./&/. )% $/& /.%)%& &//. (-/ (%&'./ )% 12 /.+*/)/%-'%, $(%+ $$%7/.$/ / (- &%/)+ /$ /*.% $*.%#
11
F*(./ 2# S%/)+ /$ /*.%
4#2 M(%&'./ /./ +-'%-*)+ )% <(%)/)
D%$ $(/. )+-)% &% '+8 $/ (%&'./ )% 12 , /)**+-/$ / %&'/ %//+& %- +'./ +$&/ )*%.%-'% +- &%$$+ <%.'*+ (-/ (%&'./ )% /./ +)%. )%'%.*-/. $/ <(%)/) )% %&'% '*+ )% &(%$+#
F*(./ # M(%&'./ /./ <(%)/)
4# M/'%.*/$%& /./ $+& %-&/+&
F-&u#$ 4. Ju&) / "$*-!
F*(./ # B/$/-=/ )**'/$
F*(./ 6# H+.-+
13
F*(./ "# R%**%-'%& )% /$(*-*+
F*(./ !# M/&+ )% +/
F*(./ # P/$(&'.%
F*(./ 10# C/=(%$/ )% C/&/./-)%
# ENSAYO DE CONTENIDO DE HUMEDAD
P/./ (<+& '*+& )% &(%$+, %$ +-'%-*)+ )% /(/ %& (-/ )% $/& .+*%)/)%& ;-)*%& 9& &*-**/'*7/&, 5(% &% %$%/ /./ %&'/$%%. (-/ +..%$/*8- %-'.% %$ ++.'/*%-'+ )% )*<+ &(%$+ +'./& .+*%)/)%& ;-)*% E$ +-'%-*)+ )% /(/ )% (- &(%$+ &% (&/ %- /&* '+)/& $/& %(/*+-%& 5(% %.%&/- $/& .%$/*+-%& )% /&% %-'.% /*.%, /(/ &8$*)+&, %- (- 7+$(%- )/)+ )% /'%.*/$#
E- &(%$+& )% ./-+ *-+ >+<%&*7+&?, $/ +-&*&'%-*/ )%%-)% )% &( +-'%-*)+ )% /(/# E$ +-'%-*)+ )% /(/ )% (- &(%$+, (-'+ +- &(& $;*'%& $;5(*)+& $9&'*+, &+- (&/)+& /./ %.%&/. &( +-&*&'%-*/ .%$/'*7/, + ;-)*% )% $*5(*)%=# E$ '.*-+ /(/ ++ &% (&/ %- I-%-*%.;/ G%+'-*/, &% /&(% ';*/%-'% ++ %$ /(/ )% +.+& + /(/ $*.% -+ /5($ 5(% %&'9 <*)./'/-)+ $/& &(%.**%& *-%./$%& >/(/ )% +-&'*'(*8-?# P+. $+ '/-'+, %$ +-'%-*)+ )% /(/ )% /'%.*/$%& 5(% '*%-%- /-'*)/)%& &*-**/'*7/& )% /(/ <*)./'/)/, >/(/ )% +-&'*'(*8-?, / '%%./'(./ /*%-'% + %-+. )% 110C >20F? (%)% &%. %-/+&+#
E$ '.*-+ )% /.';($/& &8$*)/& ++ &% (&/ %- I-%-*%.;/ G%+'-*/, &% /&(% ';*/%-'% ++ $/& /.';($/& *-%./$%& 5(% &% %-(%-'.%- %- &( %&'/)+ -/'(./$ 5(% -+ &+- 9*$%-'% &+$($%& %- /(/# P+. $+ '/-'+, %$ +-'%-*)+ )% /(/ )% $+& /'%.*/$%& 5(% +-'*%-%- /'%.*/& %'.//& >++ %%-'+?, /'%.*/$%& &+$($%& %- /(/ >++ &/$? /'%.*/ /$'/%-'% +.9-*/, -+./$%-'% .%5(*%.%)% (- './'/*%-'+ %&%*/$, + )% (-/ )%*-**8- /$**/)/ )%$ +-'%-*)+ )% /(/#
#1 P.*-**+ )%$ '+)+
15
S% )%'%.*-/ %$ %&+ )% /(/ %$**-/)/, &%/-)+ %$ &(%$+ <@%)+ &'/ (- %&+ +-&'/-'% %- (- <+.-+ +-'.+$/)+ / 110 K C# E$ %&+ )%$ &(%$+ 5(% %./-%% )%$ &%/)+ %- <+.-+ %& (&/)+ ++ %$ %&+ )% $/& /.';($/& &8$*)/ L/ .)*)/ )% %&+ )%*)+ /$ &%/)+ %& +-&*)%./)+ ++ %$ %&+ )%$ /(/# E$ '+)+ './)**+-/$ )% )%'%.*-/*8- )% $/ <(%)/) )%$ &(%$+ %- $/+./'+.*+, %& +. %)*+ )%$ &%/)+ / <+.-+, )+-)% $/ <(%)/) )% (- &(%$+ %& $/ .%$/*8%.%&/)/ %- +.%-'/% %-'.% %$ %&+ )%$ /(/ %*&'%-'% %- (-/ )%'%.*-/)/ /&/ )% &(%$+ %$ %&+ )% $/& /.';($/& &8$*)/
S% /$($/ %$ +-'%-*)+ )% <(%)/) )% $/ (%&'./, %)*/-'% $/ &*(*%-'% 8.($/
w=
W 1 −W 2 Ww ∗100= ∗100 W 2 −Wt Ws
D8-)%: E& %$ +-'%-*)+ )% <(%)/), >? P%&+ )%$ /(/ & P%&+ &%+ )%$ /'%.*/$ 1 E& %$ %&+ )% '/./ 9& %$ &(%$+ <@%)+, %- ./+& 2 E& %$ %&+ )% '/./ 9& %$ &(%$+ &%/)+ %- <++, %- ./+&: ' E& %$ %&+ )% '/./, %- ./+&
#2 P.+%)**%-'+
D%'%.*-/. .%*&'./. $/ /&/ )% (- +-'%-%)+. $**+ &%+ > &( '// &* %& (&/)/?#
C+$+/. $/ (%&'./ <@%)/ %- %$ +-'%-%)+. &* &% (&/, +$+/. $/ '// /&%(./)/ %- &( +&**8-# D%'%.*-/. %$ %&+ )%$ +-'%-%)+. /'%.*/$ <@%)+ (&/-)+ (-/ /$/-=/# R%*&'./. %&'% 7/$+. >7%. '/$/ -1?#
F*(./ 11# P%&+ <@%)+
R%+7%. $/ '// >&* &% (&8? +$+/. %$ +-'%-%)+. +- /'%.*/$ <@%)+ %- %$ <+.-+# S%/. %$ /'%.*/$ &'/ /$/-=/. (-/ /&/ +-&'/-'%# M/-'%-%. %$ &%/)+ %- %$ <+.-+ / 110 K C / %-+& 5(% &% %&%**5(% +'./ '%%./'(./# E$ '*%+ .%5(%.*)+ /./ +'%-%. %&+ +-&'/-'% 7/.*/.9 )%%-)*%-)+ )%$ '*+ )% /'%.*/$, '*+ )% <+.-+ //*)/), +'.+& /'+.%& L/ *-$(%-*/ )% %&'+& /'+.%& %-%./$%-'% (%)% &%. %&'/$%*)/ +. (- (%- (**+, %%.*%-*/ +- $+& /'%.*/$%& 5(% &%/- %-&//)+& $+& //./'+& 5(% &%/- %$%/)+
T./-&(..*)/& 24 <+./& &% &//.+- $/& (%&'./& )%$ <+.-+ %&/-)+ -(%7/%-'% %- $/ *&/ /$/-=/ )+-)% &% %&8 $/ (%&'./ /-'%.*+.%-'%, /./ %7*'/. 7/.*/*8- %- %$ %&+# R%*&'./+& %&+& )%$ &(%$+ &%+ >7%. '/$/ -1?#
1
F*(./ 12# R%'*.+ (%&'./& )%$ <+.-+
# A-9$*&*& )% )/'+&
CONTENIDO DE HUMEDAD .%**%-'% - %&+ )%$ .%**%-'% &(%$+ <@%)+ >? %&+ )%$ .%**%-'% &(%$+ &%+ >? %&+ )%$ .%**%-'% >? %&+ )% &(%$+ &%+ >? %&+ )% /(/ >? +-'%-*)+ )% <(%)/) +-'%-*)+ )% <(%)/) )%$ &(%$+
1 4,!! 2,1
2 ,!0 2,
4,12 !,0!
",0 22,06 ," 2,"
6,"" 2,1! ,! 2,24 2,0
!,6! 2,40 ",04 2,
T/$/ 1# C+-'%-*)+ )% <(%)/)
P/./ $$/. %$ %&+ )%$ &(%$+ &%+ >&? )% /)/ (-/ )% $/& (%&'./& &% <*=+ $+ &*(*%-'%:
Ws=( peso del recipiente + suelo seco )− peso del recipiente
M(%&'./ 1
Ws =29.15 g−7.09 g= 22.06 g
M(%&'./ 2 Ws=29.95 g−6.77 g=23.18 g
M(%&'./ Ws=38.08 g−8.68 g =29.40 g
D%'%.*-/+& %$ %&+ )%$ /(/ /./ /)/ (-/ )% $/& (%&'./&
Ww =( peso del recipiente + suelo humedo)− peso delrecipiente ¿− peso del suelos seco
M(%&'./ 1 Ww =( 34.88 g −7.09 g )−22.06 g =5.73 g
M(%&'./ 2 Ww =( 35.80 g −6.77 g ) −23.18 g =5.85 g
M(%&'./ Ww =( 45.12 g−8.68 g ) −29.40 g =7.04 g
C/$($/+& %$ +-'%-*)+ )% <(%)/) .%&%-'% %- $/& (%&'./&
17
w=
Ww ∗100 Ws
+-'%-*)+ )% <(%)/) %&+ )%$ /(/ & %&+ )% $/ (%&'./ &%/
M(%&'./ 1 w=
5.73 ∗100=25.97 22.06
M(%&'./ 2 w=
5.85 ∗100=25.24 23.18
M(%&'./ w=
7.04 ∗100=23.95 29.40
C+- $+& )/'+& +'%-*)+& /$($/+& (- .+%)*+ )% $/& '.%& (%&'./& /./ O'%-%. .%&($'/)+& '+'/$%&
prom=
25.97 + 25.24 + 23.95 3
w =25.05
6# ENSAYO DE LMITES DE ATTERBERG L/ +-)**8- ;&*/ )% $/ %=$/ )% &(%$+ /(/ %&'9 )%-+'/)/ +. $/ C+-&*&'%-*/# L/ C+-&*&'%-*/ &% )%*-% ++ $/ .%&*&'%-*/ /$ $(+, 5(% %&'9 .%$/*+-/)+ +- $/ (%.=/ )% /'./*8- %-'.% /.';($/& %& 9& 9*$ )% &%-'*. ;&*/%-'% 5(% )% )%&.**. (/-'*'/'*7/%-'% >Y+- /.%'*-, 16? >%- S+*$ M%-*& B/&* C+-%'& /-) E-*-%%.*- A$*/'*+-# A&%-, A# 2002?
21
T/$/ -1# L;*'%& )% /''%.%.
6#1 L**'% $;5(*)+ >L + LL?: +-'%-*)+ )% <(%)/) )%$ &(%$+ %- %$ $;*'% %-'.% %$ %&'/)+ &%* $;5(*)+ $9&'*+#
6#2 L**'% $9&'*+ > + LP?: %& %$ +-'%-*)+ )% <(%)/) )%$ &(%$+ %- %$ $;*'% %-'.% $+& %&'/)+& &%*&8$*)+ $9&'*+#
6# -)*% )% $/&'**)/) >IP?: %& $/ )*%.%-*/ %-'.% $+& $;*'%& $;5(*)+ $9&'*+, %& )%*., %$ ./-+ )% <(%)/) )%-'.+ )%$ (/$ %$ &(%$+ &% /-'*%-% $9&'*+:
PI =¿− LP
6#4 E-&/+ $**'% $;5(*)+
6#4#1 P.*-**+ )%$ '+)+
L+& $;*'%& )% A''%.%. &+- %-&/+& )% $/+./'+.*+ -+./$*=/)+& 5(% %.*'%+'%-%. $+& $;*'%& )%$ ./-+ )% <(%)/) )%-'.+ )%$ (/$ %$ &(%$+ &% /-'*%-% %%&'/)+ $;5(*)+ $9&'*+#
P/./ +'%-%. %&'+& $;*'%& &% .%5(*%.% .%+$)%/. >/-*($/.? $/ (%&'./ )% &(%$+ )%&'.(%-)+ &( %&'.('(./ +.**-/$ +. %$$+ %& 5(% (-/ )%&.**8- )%$ &(%$+ %&(& +-)**+-%& -/'(./$%& %& /&+$('/%-'% -%%&/.*/ +$%%-'/.*/#
P/./ .%/$*=/. $+& $;*'%& )% A''%.%. &% './// +- '+)+ %$ /'%.*/$ %-+. 5(% $/ /$$/ 40 >0#42 )% )*9%'.+?# E&'+ 5(*%.% )%*. 5(% -+ &+$+ &% './// +- $/ /.'% *-/ )%$ &(%$+ >W /$$/ 200?, &*-+ 5(% &% *-$(% *(/$%-'% $/ ./*8- )% /.%-/ *-/# 6#4#2 P.+%)**%-'+
T+/+& 20 ./+& )% $/ (%&'./ *-**/$ /&/)/& +. %$ '/*= 40, /./ )%'%.*-/. $+& $;*'%& $;5(*)+& $;*'% $9&'*+#
23
F*(./ -14 (%&'./ /&/)/ +. '/*= -40
S% +-% $/ (%&'./ %- %$ .%**%-'% /.%9-)+$% &(**%-'% /-'*)/) )% /(/ )%&'*$/)/, %=$/-)+ +- $/ %&9'($/ &'/ $+./. (-/ /&'/ <++-%/# E&'/ (%&'./ )%% (./.&% )(./-'% %$ '*%+ 5(% &%/ -%%&/.*+ /./ $+./. (-/ /)%(/)/ )*&'.*(*8- )% $/ <(%)/)#
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
F*(./ -1# D%8&*'+ )% $/ (%&'./
C(/-)+ &% '*%-% %$ &(.+, &% *./ $/ /-*7%$/ )%$ //./'+ +- (-/ .%(%-*/ )% 2 +$%& +. &%(-)+, +-'/-)+ %$ -@%.+ )% +$%& -%%&/.*+& /./ 5(% $/ ./-(./ *%..% %- 12#" )% $+-*'() %- %$ +-)+ )% %$$/#
F*(./ -16# S%$$/)+ )% $/ (%&'./
F*-/$%-'%, &% '+/- /.+*/)/%-'% 10 )%$ /'%.*/$ 5(% &% (-'/ %- +-)+ )%$ &(.+ /./ )%'%.*-/. $/ <(%)/)
25
. F*(./ -1"# T+/ )% (%&'./
E$ /'%.*/$ &+./-'% &% './&$/)/ /$ $/'+ )% %7/+./*8- /./ %=$/.$+ -(%7/%-'% +- /(/ )%&'*$/)/ .%%'*. %$ .+%)**%-'+ +. $+ %-+& 2 7%%& 9&, )% +)+ )% +'%-%. '.%& (-'+& 5(% 7/.;%- %- (- ./-+ )% 1 / 20 +$%&, 202 +$%&, 20 040 >&% '+8 (%&'./& )% /)/ ./-+ ?#
C+- $/& (%&'./& +'%-*)/& &% .+'($/, %&/ +&'%.*+.%-'% &% $$%7/ /$ <+.-+ / 110K >C?, )(./-'% 24 <+./&
F*(./ -1!# M(%&'./ <@%)/
P+. @$'*+ &//+& $/& (%&'./& )%$ <+.-+, %&/+& .+%)%+& /$ /-9$*&*& )% )/'+&
F*(./ -1# M(%&'./ &%/
6#4# A-9$*&*& )% )/'+&
DETERMINACION DEL LIMITE LI@UIDO #-%-'" %!) / !u() */) #-%-'" >&? %!) / !u() !) #-%-'" >&? %!) / #-%-'" >&? %!) / !u() !) >&? %!) / $&u$ )'"'-/) / u*/$/ 'u*#) / &)(%!
Rango 1520
Rango 2025
1
2
3
1
18
17 87
23 1
1 2
18 1 22 5 7 03
24 220 17 42 3 5
24 204 4
12
18 02
17 7
15 54
1 155 18 12 74
20 173 1 85 3 88
21 14 51 7
5
11 47
8 3
83
82 7 2
8 3 772 1 1
11 3 4
5 3 18 25 28 28 4 4 1 18
11 7 33 8 28 2 20
1 20 8 27 01 23
83 8 10 5 2 24 30 222 4 7 27 285 28 22 3 82 21 21 28
12 741 75 24 35 2 2 7 27 28 28 1 7 11 2 2 34
10 101 11 2 28 278 7 28 274 57 5 38 32
8
2
3
25-30 1
2
30-40 3
1
T$($ '2. L-*-" (+9u-/)
E$ +-'%-*)+ )% <(%)/) $+ +)%+& /$($/. +- $/ &*(*%-'% +.($/
2
2
3
w=
Ww ∗100 Ws
C/$($/+& %$ $;*'% $;5(*)+ %)*/-'% $/ 8.($/:
TANG ( 0.121)
( )
N ¿= w 25
D='/ H)'"'-/) / u*/$/ N '*#) / &)(%!
TANG ( 0.121 )
¿1=28.74
( )
¿2=28.64
( )
¿3=28.26
( )
16 25
18 25
20
TANG ( 0.121 )
=28.62
TANG ( 0.121)
25
=28.24
TANG ( 0.121 )
( )
23 ¿4 =29.01 25
=28.71
=29.00
TANG ( 0.121)
( )
21 ¿5=29.33 25
¿6= 28.53
=29.32
TANG ( 0.121)
( ) 21
= 28.52
25
TANG ( 0.121)
( )
28 ¿7= 28.82 25
¿8= 29.17
=28.83
TANG ( 0.121 )
( ) 26
=29.17
25
TANG ( 0.121 )
( )
27 ¿9= 28.69 25
=29.69
TANG ( 0.121)
¿10 =28.11
( )
¿11=28.59
( )
¿12 =29.45
( )
34
25
38 25
32 25
=28.13
TANG ( 0.121 )
=28.61
TANG ( 0.121)
= 29.46
27
LL 34.3
L(%+ .+%)*/+& %$ $;*'% $;5(*)+ )% $/& (%&'./& +'%-*)/&
(
346.3 ¿ PROMEDIO= 12
❑
)=
28.9 ≅ 29
Limite Líquido ;>K? 1K R 1 C)'"'-/) / u*/$/
15 1 17 21 23 25 2 27 31 33 35 N*#) / &)(%!
G#$:$ '1. L-*-" (+9u-/)
6# E-&/+ $**'% $9&'*+
6##1 P.+%)**%-'+
S% '+/ (-/ ./*8- )% $/ (%&'./ )% <++-%/ &% .%/$*=/- (-+& .+$$*'+&
F*(./ -20# M(%&'./ )% .+$$*'+&
S %!$' , *"' $( )#') $(#//)# / 24 )#$! %)!"#-)#*'" ! ")*$ 'u<$*'" ( %!) , ! #$(-$ ( $'6(-!-! / /$")!
F*(./ -21# M(%&'./ &%/
31
6##2 A-9$*&*& )% )/'+&
N LATA LATA >G?
LATA HUMEDO >G?
LIMITE PLASTICO LATA SECO /(/ SECO >G? >G? HUMEDO >?
CONTENIDO DE HUMEDAD
1
871
1023
10
107
132
023
2110
2
842
782
7
118
14
022
184
3
47
818
8
051
07
018
3527
T$($ '3. L-*-" %(6!"-)
E$ +-'%-*)+ )% <(%)/) $+ +)%+& /$($/. +- $/ &*(*%-'% +.($/
w=
Ww ∗100 Ws
L(%+ .+%)*/+& /./ $$/. %$ $;*'% $9&'*+ )%$ &(%$+
lp =
w 1 + w 2+ w 3 3
=
21.10 + 18.64 + 35.29 3
lp =25
P/./ )%'%.*-/. %$ ;-)*% )% $/&'**)/) )%$ &(%$+ .%/$*=/+& $/ &*(*%-'% +%./*8 PI =¿− LP
PI =29−25 =4
G./*/ - 2 #/.'/ )% $/&'**)/) )% C/&/./-)%
33
1 ENSAYO DE GRANULOMETRA >SUELO NATURAL?
S( *-/$*)/) %& +'%-%. $/ )*&'.*(*8- +. '//+ )% $/& /.';($/& .%&%-'%& %(-/ (%&'./ )% &(%$+# A&; %& +&*$% '/*- &( $/&**/*8- %)*/-'% &*&'%/& ++ AASHTO + SUCS# E$ %-&/+ %& *+.'/-'% / 5(% ./- /.'% )% $+& .*'%.*+& )% /%'/*8- )% &(%$+& /./ &%. ('*$*=/)+& %- /&%& + &(/&%& )% /..%'%./&, .%&/& )% '*%../ + )*5(%&, ).%-/%&, %'# D%%-)%- )% %&'% /-9$*&* P/./ +'%-%. $/ )*&'.*(*8- )% '//+&, &% %$%/- '/*%& -+./$*=/)+& -(%./)+&, )*&(%&'+& %- +.)%- )%.%*%-'%# U'*$*=/-)+ %$ (%+ )% '/*% L/ ./-($+%'.;/ %& $/ %)**8- )% $+& ./-+& )% (-/ +./*8- &%)*%-'/.*/ %$ 9$($+ )% $/ /(-)/-*/ )% $+& +..%&+-)*%-'%& / /)/ (-+ )% $+& '//+& .%7*&'+& +. (-/ %&/$/ ./-($+'.*/ +- *-%& )% /-9$*&*& '/-'+ )% &( +.*%++ )% &(& .+*%)/)%& %9-*/&
6#6 P.*-**+ )%$ '+)+
L/ ./-($+%'.;/ %$ '//+ 9*+ )% /.%/)+ /%'/- $/& .++.*+-%& .%$/'*7/& )% $+& /.%/)+& /&; ++ $+& .%5(*&*'+& )% /(/ %%-'+, $/ './//*$*)/), //*)/) )% +%+, %+-+;/, +.+&*)/), +-'./*8- )(./*$*)/) )%$ +-.%'+# E$ '+)+ )% )%'%.*-/*8- ./-($+'.*+ 9& &%-*$$+ %& +'%-%. $/& /.';($/& +. (-/ &%.*% )% /$$/& )% )*&'*-'+& /-<+& )% %-'.//)+, 5(% /'@%- ++ *$'.+& )% $+& ./-+& 5(% &% $$// +@-%-'% +$(-/ )% '/*%
6#" P.+%)**%-'+
T*./-)+ $+& 12 %- %$ &(%$+ &% .+%)*8 %. %$ (/.'%+ 5(% +-&*&'*8 %- )*7*)*. %&'/ %- 4 /.'%& *(/$%& +- /()/ )%$ /$(&'.% +- %$ *- )% &*($/. $/& +-)**+-%& -/'(./$%& )% '%..%-+, &% ('*$*=8 %$ /=+ )% +/ /./ )%&.%-)%. $/& /.';($/
F*(./ 22# C(/.'%+ )% $/ (%&'./
L(%+ .+%)%+& / '+/. (-/ (%&'./ /&% + *)%/$, %- %&'% /&+ '%-*%-)+ %(%-'/ %$ )*9%'.+ )% $/ /.';($/ '+/+& (-/ (%&'./ .%.%&%-'/'*7/ )% !00., /./ %%=/. / .%/$*=/. %$ '/*=/)+# L+& '/*%& ('*$*=/)+& (%.+- '+/)+& )% /(%.)+ / $/ -+./ I#N#V#E121#
F*(./ 2# T/*=/)+ )% $/ (%&'./
35
S%(*)+ .%/$*=/+& %$ %&/% /./ &/%. -(%&'.+ +.%-'/% .%'%-*)+ %- /)/ '/*=, .%*&'./+& $+& 7/$+.%& %- $/ .%&%'*7/ '/$/ >7%. '/$/ -4?
6#! A-9$*&*& )% )/'+&
- T/*= D*9%'.+ ! , 4 4," ! 2,6 16 1,1! 20 0,! 0 0,6 40 0,42 0 0, 60 0,2 !0 0,1! 100 0,1 140 0,106 200 0,0" +-)+
(
error = 1 −
ANALISIS GRANULOMETRICO '/*= .%'%-*)+ '/*= (%&'./ .%'%-*)+ /(&'% .%'%-*)+ /(($/)+ /&/ "10," 662,16 4!,4 4!, 6,12 6,12 ,!! 64!,6! "0,4 101,!1 102,6! 12,! 1!, !1,0 4,!4 6!0,22 14,! 1,2 16,4 ,! 64,11 4,2 61,16 14",!" 14,1 1!,64 4,4 4,46 26,2 4,!! 2!,6! 2!,2 ,62 !,1 41,! 21,! "2, 0,"6 1,1 6,40 64, ,4 1!, 4!,46 2,!4 ,12 4,14 6!,6 1,1 02,2 22,2 20 20,1" 2,2 "1,21 2!," 00," 2,01 24,64 24,! ,11 "4,2 2,6! 4",01 4!,! 2!,!2 2,0" ,6 "", 22,0 4,1 00,4 41, 41,6 ,21 !,16 16,!4 44,2 4,0 ,"" 100,62 12,! ," 4,2" 4",42 4"1, 14, 14,6 1,! "," 2,4 !"," 6!, 1,1 1,4" 2,4 100,00 0,00 ",2 !00,00 100,00 T/$/ -4# A-9$*&*& ./-($+'.*+
793.25 g 800 g
)∗
100= 0.84
C++ '%-%+& (- %..+. %-+. /$ 2 .%/$*=/+& (- /(&'% %)*/-'% $/ &*(*%-'% +.($/:
Rajuste=WR +
WR ( W Inicial −WTR ) WTR
R %&+ .%'%-*)+ %- /)/ '/*= RT%&+ '+'/$ .%'%-*)+ *-**/$ P%&+ *-**/$ )% $/ (%&'./ >!00?
E$ +.%-'/% 5(% /&/ %- /)/ '/*= $+ +)%+& $$/. +- $/ &*(*%-'% +.($/
(
pasa =
M − M A!"M"LADO M
)∗
100
P/./ )%'%.*-/. %$ +%**%-'% )% (-*+.*)/) %$ +%**%-'% )% (.7/'(./, -%%&*'/+& $$/. %$ )*9%'.+: 10,0 60 +- $/ &*(*%-'% 8.($/:
log (#$ )−log ( 1 ) D2 − D1 ∗¿+ D1 log ( 2)− log ( 1) D & =¿
3
log ( 60 )− log ( 64.11 ) 1.18−2.36 ∗¿+ 2.36 log ( 45.46 )−log ( 64.11 ) D60 =¿
D60=2.13
D 30=
[
]
0.3−0.425 ∗(log ( 30 )− log ( 31.31 ) ) + 0.425 log ( 28.79 )− log ( 31.31 )
D30=0.361
log ( 10 )− log ( 16.84 ) 0.106 −0.150 ∗¿+ 0.150 log ( 4.27 )−log ( 16.84 ) D10=¿
D10=0.133
6#!#1 C+%**%-'% )% (-*+.*)/)
D 60 2.13 c= = =16.01 D 10 0.133
6#!#2 C+%**%-'% (.7/'(./
D 60∗¿ D
10
=
D ( 0.361 )2
(2.13∗0.133 ) (¿¿ 30 )2 ¿ !c =¿
=0.460
6#!# C(.7/ ./-($+'.*/
G#$:$ ' 3. Cu#<$ $'u()*"#-$
6# C$/&**/*8- +. &*&'%/ AASHTO 6##1
P.+%)**%-'+
37
•
M%-+& )%$ /&/ $/ /$$/ -200 >2#4W? L+ 5(% $+ $/&**/ %- (- &(%$+ .(%&+#
•
COMO: LL2 W 40 G.(+ A24 >0? PI4W 10
E$ '*+ )% &(%$+ %&: A24 >0?
6#10 C$/&**/*8- +. SUCS
6#10#1 P.+%)**%-'+
•
M9& )% $/ *'/) )% $/ (%&'./ .%'%-*)/ %- %$ '/*= 200 100!1#01!# >./7/? !1#02#4"!#62 >/.%-/? 2#4 *-+&
•
•
•
M9& )% $/ *'/) ./*8- .(%&/ /&/ %$ %- %$ '/*= -4,$+ (/$ *-)*/ 5(% %& (-/ /.%-/# E$ +.%-'/% )% *-+& %& %-+. /$ >2#4W?, $+ 5(% *-)*/ 5(% %& (-/ /.%-/ $**/ T%-*%-)+ %- (%-'/ $+& +%**%-'%& )% (-*+.*)/) +&%.7/+& 5(%:
C(6 >/.%-/?
1W C
C 0#460 W1 SP >/.%-/ /$ ./)/)/?#
•
C++ $ +.%-'/% )% ./7/ %& /+. /$ 1 >1!#1? E$ '*+ )% &(%$+ %& : Arena mal gradada con grava
"# ENSAYO DE GRANULOMETRA >SUELO GRANULAR? "#1 P.*-**+ )%$ '+)+
L/ ./-($+%'.;/ %$ '//+ 9*+ )% /.%/)+ /%'/- $/& .++.*+-%& .%$/'*7/& )% $+& /.%/)+& /&; ++ $+& .%5(*&*'+& )% /(/ %%-'+, $/
41
'.///*$*)/), //*)/) )% +%+, %+-+;/, +.+&*)/), +-'./*8- )(./*$*)/) )%$ +-.%'+# E$ '+)+ )% )%'%.*-/*8- ./-($+'.*+ 9& &%-*$$+ %& +'%-%. $/& /.';($/& +. (-/ &%.*% )% /$$/& )% )*&'*-'+& /-<+& )% %-'.//)+, 5(% /'@%- ++ *$'.+& )% $+& ./-+& 5(% &% $$// +@-%-'% +$(-/ )% '/*%
"#2 P.+%)**%-'+
T%-*%-)+ %- (%-'/ %$ )*9%'.+ '+/+& (-/ (%&'./ .%.%&%-'/'*7/ )% 1000 )% &(%$+ .(%&+ ($*%-)+ $+ %&'/$%*)+ %- $/ -+./ .%/$*=/+& %$ $/7/)+ %%$ '/*= -200 .+%)%+& / %'%.$/ /$ <+.-+ /./ &( &%/)+ +. 24 <+./&
F*(./ -24# L/7/)+ )% $/ (%&'./
S//+& $/ (%&'./ )%$ <+.-+, %&/+& '+/+& )/'+& >7%. '/$/ - ? P.+%)%+& / .%/$*=/. %$ '/*=/)+ )% $/ (%&'./ &%/ ('*$*=/-)+ $+& '/*%& )% /(%.)+ / $/ -+./ I#N#V#E 60
F*(./ -2# T/*=/)+
S%(*)+ .%/$*=/+& %$ %&/% /./ &/%. -(%&'.+ +.%-'/% .%'%-*)+ %- /)/ '/*=, .%*&'./+& $+& 7/$+.%& %- $/ .%&%'*7/ '/$/ >7%. '/$/ -?
F*(./ -26# P%&/% )% $/ (%&'./
"# A-9$*&*& )% )/'+& Mu!"#$ -'--$( 1000& Mu!"#$ /!%u! /( ($<$/) , !$/)74.1 & P!) 9u ! ( !u*$ $( ;)'/) 35.84 & >:')!?
43
ANALISIS GRANULOMETRICO '/*= '/*= (%&'./ .%'%-*)+ 662,2" 10!!," 426,46 64!," !60,14 211,44
T/*= - D*9%'.+ ! , 4
4,"
!
2,6
16
/(&'%
.%'%-*)+ .%'%-*)+ /(($/
/&/
42",0!
42,"1
42,"1
",2
211,"
21,1"
6,!!
6,12
"!,! 6,!0
",0 6,!
"1,"! 2!,22 "!,"6 21,24
624,"
1,1!
4,!6 4,
61
"!,!" 6,"
0
0,6
21,!
"",64
,"
,!"
,
!4,
1,6
0
0,
02,2"
4!,4
46,1!
46,2
4,62
!!,"
11,0
100
0,1
4,22
0,!
44,"6
44,!2
4,4!
,46
6,4
6!,4
",1
6,
6,44
6,4
100,00
0,00
!, 1000,00
100,00
+-)+
Z
T$($ ' 5. A'6(-!-! $'u()*"#-) !u() $'u($#
(
error = 1 −
962.71 g 964.165 g
)∗
100 =0.15
C++ '%-%+& (- %..+. %-+. /$ 2 .%/$*=/+& (- /(&'% %)*/-'% $/ &*(*%-'% +.($/: Rajuste=WR +
WR ( W Inicial −WTR ) WTR
"#4 CLASIFICACION POR SUCS "#4#1 P.+%)**%-'+
•
•
•
•
M9& )% $/ *'/) )% $/ (%&'./ %& .%'%-*)/ %$ '/*= 200 M9& )% $/ *'/) ./*8- .(%&/ %& .%'%-*)/ %- %$ '/*= -4, $+ (/$ *-)*/ 5(% %& (-/ ./7/ E$ +.%-'/% )% *-+& %& %-+. /$ $+ 5(% *-)*/ 5(% %& (-/ ./7/ $**/ C++ -+ ($% $/& +-)**+-%& )% +%**%-'%& )% (-*+.*)/) +%**%-'% )% (.7/'(./ %$ '*+ )% &(%$+ %&: GP (grava mal gradada).
"# CLASIFICACIN POR LA AASHTO "##1 P.+%)**%-'+ •
•
M%-+& )%$ /&/ $/ /$$/ -200, *-)*/ 5(% %& (- /'%.*/$ ./-($/. O&%.7/-)+ 5(% %-+& )%$ 1 /&/ $/ /$$/ -200 %$ &(%$+& %.'%-%% /$ .(+ A1
45
!# CONCLUSIONES
# #BIBLIOGRAFIA
4