Mecánica de Suelos II
I.
PROPIEDADES HIDRÁULICAS DE LOS SUELOS
1.1 1.1 Defin Definic ició ión n de de Per Perme meab abili ilida dad: d: La permeabilidad es la propiedad que tienen los suelos de dejar pasar el agua a través de él. Se dice que un material es permeable cuando este contiene vacíos en su estructura, tales vacíos existen en todos los suelos y rocas, solamente es una diferencia de magnitud de la permeabilidad entre materiales, por ejemplo ejemplo entre una grava gruesa y una roca roca sana. La permeabilidad tiene un efecto decisivo sobre las dificultades a encontrar en las obras, por ejemplo en las excavaciones a cielo abierto, cuando la cantidad de agua que escurre a través del material están pequeña como el caso de superficies expuestas al aire, esta se evapora totalmente.
1.2 Ley de de Darcy: Los cálculos de la permeabilidad gravitacional se basan en la ley de arcy !"#$%&. Seg'n la cual la velocidad del flujo es directamente proporcional al gradiente (idráulico, tal como se muestra en la figura )* ".
V = K i … … … … … … … … … … … … … … … … … … … … … … … … … … … . … … . ( 1.1 ) Donde : K : : Coeficiente de permeabilidad permeabilidad
h i= L h + iferencia de los niveles del agua libre a ambos lados de una capa de suelo, es decir, es la pérdida de agua en la distancia -L. L + /spesor de la capa de suelo medida en la direcci0n de la corriente. i + radiente (idráulico+
Seg'n el dispositivo mostrado, arcy encontr0 que para velocidades pequeñas+ pequeñas+
( ) ( )
cm3 = K cm x Q x A ( cm2) x i= K x A x i … … … … … … … … … … … … . ( 1.2) seg seg
Ecación de C!n"inidad: Q=V x A … … … … … … … … … … … … … … … … … … … … … … … … … … … … .. ( 1.3 )
#a$"! en fnción del "iem%! f &"': /l gasto total que pasa por una secci0n transversal de suelo durante un tiempo t es+ Q= K x A x i x t … … … … … … … … … … … … … … … … … … … … … … … … … .. ( 1.4 ) 1
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Mecánica de Suelos II
onde+ ond e+ t es el tiem tiempo po de escur escurrim rimie ient nto, o, Q es el gasto en cm 12seg 2seg33 K es el coeficien coeficiente te de permeabilidad permeabilidad del suelo suelo !cm2seg.& !cm2seg.& o !min2seg&, !min2seg&, A es el 4rea total de la 5 secci0n transversal del suelo !cm & /n la naturale6a los suelos muestran un amplio campo de variabilidad de los coeficientes de permeabilidad !7&, para distintos tipos de suelos, seg'n se muestra en la figura )* 5, 8asagrande y 9adum !":";&.
1.( )el!cidad )el!cidad de: )e )el!cidad l!cidad del del fl*! &De$car+a &De$car+a', ', -il"raci -il"ración ón y Real. Real. )el!cidad de De$car+a &)': Llamada velocidad superficial del flujo, se determina mediante las siguientes ecuaciones+ Si sabem sabemos os que : Q= A x V … … … Ecuaci Ecuaci n de cotinuidad
Q= K x A x i … . Ecuaci Ecuaci n del gasto seg! seg ! n Darc" #gualandoestas ecuaciones ecuaciones obtenemos : V = K x i
cm … … … … … … … . ( 1.5 ) seg
)el!cidad de -il"ración &) f ': ':
A x V = A $ x V f V f =
A V x V = A $ A $ A
Sabemos Sabemos que : e =
V $ V s
y
n=
V $ e = V m 1 + e
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Mecánica de Suelos II
( )
V ( 1 + e ) cm V f = = x V … … … … … … … … … … … … … … … … … … … … . ( 1.6 ) n e seg
)el!cidad Real &)R ': ': 8onsiderando la misma figura )* 1, obtenemos+ V % Lm = V f f L V % =V f
Lm L
=1
+ e Lm e
x
L
x V
cm … … … … … … … … … … … … … … … … …( 1.7 ) seg
Sel!$ ani$ó"r!%!$: Los suelos anis0tropos que se representan en la naturale6a suelen tener tres planos ortogonales de simetría que se cortan seg'n tres ejes principales x, y, 6. Las ecuaciones equivalentes a las anteriores serán+ V & =− K &
'h 'h 'h ( V ) =− K ) ( V * =− K * , ' & ' ) ' *
Inflencia de la ani$!"r!%a en la %ermeabilidad: e los resultados de diversos ensayos se deduce que la relaci0n entre las permeabilidades (ori6ontal y vertical de una arcilla aumenta con+ a& La máxima tensi0n efectiva vertical que (a sufrido la arcilla en el pasado. b& 8ada nuevo ciclo ciclo de carga. carga. c& /l porcentaje de fricci0n de arcilla. 1./ 0"!d!$ 0"!d!$ %ara medir el c!eficien c!eficien"e "e de %ermeabil %ermeabilidad idad &Ob"enid! &Ob"enid! en el lab!ra"!ri lab!ra"!ri!! ! InSi"' /l cono conoci cimi mien ento to de la perm permea eabi bili lida dadd de los los suel suelos os,, tien tienee gran gran impo importa rtanc ncia ia,, como como el conocimiento de la permeabilidad en presas de tierra, la capacidad de las bombas para rebajar el nivel freático durante las excavaciones y la velocidad de asentamiento de los edificios. Los métodos son los siguientes+
1./ 1./.1 0"! 0"!d d! Dir Direc"!: c"!: a. Perme3 Perme3me" me"r! r! de Car+ Car+aa )a )ariable riable:: Se utili6a generalmente para suelos relativamente impermeables en los que el desag>e es muy pequeño, así así tenemos las arcillas. arcillas. /l procedimiento para determinar el coeficiente de permeabilidad de un suelo es el siguiente+ ". La muestra muestra de suelo suelo se coloca coloca entre entre dos dos placas placas porosas porosas que que sirven sirven de filtros. filtros. 5. /l desag>e desag>e se mide mide en un tubo delga delgado do de vidrio vidrio de secci0n secci0n -a -a 1. 8álculo 8álculo del coeficie coeficiente nte de permeabili permeabilidad dad -7+ -7+ urante el tiempo tiempo elemental elemental dt la altura altura del agua en el tubo disminuye un d(, por lo tanto el volumen de agua despla6ado, medido en el tubo es a x d h + que es igual al volumen dQ que pasa a través de la
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Mecánica de Suelos II
Si tenemos en cuenta la ecuaci0n !".?&+ h dQ=−a x d h= K . . A .dt L
()
h L
−a x d h = K . . A . d t #ntegrandoesta #ntegrando esta ecuci ecuci n + si h 1 " h2 son son las las altu altura rass del del aguaen aguaen eltubo eltubo enlos instantest 1 " t 2 , respectivamente tenemos+ dQ=−a x d h= K .
()
h . A .dt L
( )
−dh = K . hA . dt h L . a e donde+ h2
−log∫ h1
, =
t 2
( )∫
A h= K . L. L . a
t
t 1
h1 l.a log … … … … … … … … … … … … … … … … … … … … (1.8 ) h2 A ( t 2−t 1 )
, =2.3
h1 l.a log … … … … … … … … … … … … … … … … … … . ( 1.8 - ) h2 A ( t 2−t 1 )
4. Per Perme3m me3mee"r! "r! de de Car Car+a +a C! C!n$ n$"a "an" n"e: e: Son utili6ados utili6ados generalmente generalmente para suelos suelos granulares granulares !suelos muy permeable permeables&, s&, como las arenas, en los que el desag>e es rápido. /l procedimiento para determinar el coeficiente de permeabilidad de un suelo es el siguiente+
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Mecánica de Suelos II
1. /l agua agua se filtra a través través del suelo suelo y pasa pasa al dep0s dep0sito ito inferi inferior or como se obser observa va en la figura )* $, el cual tiene un aliviadero dispuesto de tal manera que la diferencia de altura -( y por lo tanto el gradiente (idráulico -i permanecen constantes. ?. /l gasto gasto o volumen volumen de agua en en un tiempo -t -t dado se se mide directam directamente ente en el dep0sit dep0sitoo inferior tal como se muestra en la figura. $. 8álculo 8álculo del coeficient coeficientee de permeabil permeabilidad idad++
Q Q.L V . L = = , = … … … … … … … … … … … … … … … … … … … … .. ( 1.9 ) A . i A . h A . h .t
C. En$ay!$ In Si":
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Mecánica de Suelos II
1./.2 0"!d!$ 0"!d!$ Indir Indirec"! ec"!$: $: A. C3lcl! C3lcl! a %ar"ir del An3li$ An3li$i$ i$ #ranl!m #ranl!m"ric! "ric! /n la permeabilidad del suelo intervienen factores como+ tamaño de las partículas, forma de las partículas, vacios, plasticidad, etc. Ber6ag(i, etermin0 la conductividad (idráulica para suelos arenosos mediante la siguiente expresi0n+ , =C 1 D10 ( 0.7 + 0.03 ) … … … … … … … … … … … … … … … … … … . ( 1.10 ) 0
C 1 =C 0
( n −0.13 )2 −2
… … … … … … … … … … … … … … … … … … … … … ( 1.10 - )
( 1−n ) 3 onde+ n : /orosidad /orosidad 0 : emperatura C 0 : Coefi Coefici cien ente te ( D0 : Diametro efecti$o
0a"erial @rena de granos redondeados
C!eficien"e C5 #;;
@rena de granos angulosos
?%;
@renas con limos
C ?;;
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Mecánica de Suelos II
de con consol solida idaci0 ci0n, n, lo que permit permitee calcu calcular lar el coefic coeficien iente te de permea permeabil bilida idadd median mediante te la siguiente expresi0n+ 2
C c 2 C $ 0 1 K =C $ m $ 0 1= 1+ e Donde : K es el coeficiente de permeabilidad, D es la máxima trayectoria del agua, 0 1 es el peso específico del agua, C $ es el coeficiente de consolidaci0n, m $ es el
coeficiente de compresibilidad, e la relaci0n de vacíos. ".$
2 … … … … … … … … … … … … … … … … … … … (1.12 ) 2 1 2 2 2 3 2 n + + +…+ K 1 K 2 K 3 K n
K p= √ K V x K 2 … … … … … … … … … … … … … … … … … … … … … . ( 1.13 ) B@GL@ )* "+
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Mecánica de Suelos II
estrato saturado cuando no existe filtraci0n o el agua de los poros esta en reposo !figura :.a& y cuando existe filtraci0n o el agua contenida en los poros esta en movimiento !figura :.b&+
FIGURA 9: Presión Total, Total, efeti!a " #resión $e #oros
a' El a+a c!n"en c!n"enida ida en l!$ %!r!$ %!r!$ e$"a en re%! re%!$! $! &n! e9i$"e e9i$"e fil"ración fil"ración'' -i+. .a: 3 =h1 0 + h2 0 sat … … … … … … … … … … … … … … … … … . ( 1.14 )
onde+ 3 es el esfuer6o total en el fondo f ondo en el punto -@, del estrato (", 0 sat es el peso espesífico del estrato ( 5.
0 es el peso espesífico
/l esfuer6o total soportado parcialmente por el agua de poro en los espacios vacíos y otra parte por los s0lidos s0lidos en sus puntos puntos de contacto entonces+ entonces+ 3 =3 e + 4 … … … … … … … … … … … … … … … … … … … … … ( 1.15 )
onde+
3 e es el esfuer6o efectivo o intergranular, 4= 0 1 h es la presi0n de poros
(h
h
)
h
h
h (
)
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Mecánica de Suelos II
3 =3 e + 4 6 3 e = 3 − 4 … … … … … … … … . … … … … … … … … … … … … … ( 1.16 )
3 =( h1 0 1+ h2 0 sat ) 4=( h1+ h2 +h ) 0 1
Jeempla6ando Jeempla6ando estos valores en !"."?& 3 e =( h1 0 1 + h 2 0 sat ) −( h1 + h2 + h ) 0 1 0 ( ¿ ¿ sat −0 1)− h 0 1 3 e =h2 ¿ 0
( ¿ ¿ - −
onde+
h 0 ) … … … … … … … … … … … … … … … … … .. (1.17 ) h2 1 3 e =h2 ¿
h =i ( gradiente gradiente hidr7ulico hidr7ulico) h2
La causa de la filtraci0n de agua a través de la muestra es el gradiente (idráulico. Si el agua circula (acia arriba, la fricci0n entre el agua y las paredes de los vacíos tiende a levantar los granos de suelo. /n este mismo instante cuando empiecen levantándose las partículas, la presi0n efectiva se (ace igual a cero en todo punto de la masa de arena !a cualquier profundidad& o sea el gradiente (idráulico alcan6a su valor crítico+
(
3 e = o= h2 0 - −
)
h 0 =0 - −i 0 1 h2 1 1.18
0 -
( S −1 )
&
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Mecánica de Suelos II
2 S /2= / A − cos 8 … … … … … … … … … … … … … … … … .. … ( 1.19 ) % . 0 1
/l agua posee cierta B s P Q$ dinas2cm P !;.;Q%? g2cm&
1.;.2 A$cen$ió A$cen$ión n Ca%ilar Ca%ilar 8uando introducimos un tubo de vidrio, de diámetro pequeño en un dep0sito lleno de agua, observamos que el agua, por ascensi0n capilar sube en el tubo (asta una determinada altura. La altura capilar que alcan6a el agua en un suelo, se determina considerando una masa de tierra como si fuera un enjambre de tubitos capilares formados por varios existentes en su masa.
∑ 9 $=0 ( : . %2 ) 2 . 0 1 =2 : . % . s cos8 espejando se obtiene+ 2 =
2 s cos8
% . 0 1 Si 8 =0 2 m7 x =
… … … … … … … … … …(1.20 )
0.1528
% . 0 1
=
0.306
D
I.;. I.;.(( An+ An+l! l! De De C! C!n"ac n"ac"! "! /ste fen0meno tiene su origen en la tensi0n superficial del agua y de la atracci0n molecular de las paredes del tubo.
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Mecánica de Suelos II
I.;.> I.;.> De"er De"ermina minació ción n de la Al" Al"ra ra de A$ce A$cen$i n$ión ón Ca%il Ca%ilar: ar: a. Se+? Se+?n n
C … … … … … … … … … … … … … … … … … … … … … … (1.21 ) e D10
onde+ 8 es una 8onstante empírica que depende de los granos, e es la Jelaci0n de vacíos. ;."; cm 5 ≤ C ≤ ;.$; cm 5 C = ;.5$cm 5 para suelos suelos finos
b. Se+?n e+?n Pe Pel"ie l"ierr ; . x2 2 = … … … … … … … … … … … … … . … … … … … … … … … (1.22 ) 2 ,t
onde+ R es la
1. 1. Efec fec"!$ "!$ Ca%i Ca%ila larre$ /ntre los fen0menos causados por la tensi0n superficial, uno de los más característicos y de mayor importancia práctica es, el de ascensi0n capilar. capilar.
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Mecánica de Suelos II
1. 1. C! C!n" n"ra racc cció ión n de de Se Sel! l!$$ -in -in!$ !$ @ la fuer6a que tira el agua en un tubo capilar corresponde una reacci0n que comprime las paredes del tubo, si el agua se evapora, los meniscos se retraerán (acia el interior del tubo, conservando su curvatura y manteniéndose invariable la tensi0n del agua. Se ve que en un tubo capilar (ori6ontal, el esfuer6o de tensi0n del agua es el mismo en toda la longitud, a diferencia del tubo vertical, en donde las fuer6as siguen una ley de variaci0n triangular. 9uer6a de tensi0n que genera la tensi0n superficial 9B P 9uer6as de tensi0n desarrolladas por el agua en toda la superficie del menisco 9J P P 9uer6as de reacci0n !de igual valor de 9 B& desarrollados por el tubo capilar en toda su superficie
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Mecánica de Suelos II
S!lción: e la ecuaci0n !".5& obtenemos+ Q= ,. A.i =, .
h 1− h2 .A L
e los datos del problema+ , =
0.063 cm
=
0.00063 m
seg seg h1− h2=188−181 =7 m 2 A =1.5 x 1 ,m =1500 m m 7 m3 2 Q=0.00063 x x 1500 m =0.145 / ,m seg 45 seg
5. /n un permeáme permeámetro tro de carga carga variable variable de $ cm. cm. de diámetro diámetro se prob0 prob0 una muestra muestra de # cm. cm. de longitud, /l tubo tenía un ∅ de 5 mm. /n % minutos la carga paso de ";; cm a $; cm. 8alcule el coeficiente de permeabilidad !K& del suelo en cm2sg.
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Mecánica de Suelos II
J e emplazando+ d 5 L x h" L x d 5 h ? K = 5.1 x log x log " = 5 .1 5 5 π D h5 D x t h5 x t ? L x ;.;? cm 5 K = 5.1 x lo g 5 = 5.?% x "; − $ cm 2 seg 5 5$ cm x 1%; seg . π
1. /n un terreno terreno formado por tres tres estratos estratos de diferentes diferentes materiale materialess y de diferentes diferentes espesores espesores se determinaron los coeficientes de permeabilidad vertical K N y (ori6ontal K D, para cada estrato, como se muestra en la figura. 8ual será el coeficiente de permeabilidad del conjuntoT
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Mecánica de Suelos II
eterminar la permeabilidad 7 G del bra6o G sabiendo que 5# cm 1 de agua atraviesa las dos muestras de suelo en :$ minutos.
S!lción: e la ecuaci0n de continuidad+ = @ P =G P =
2 1− 2 m ) ( 2 L A
A … … … … … … … … … … … … ( a )
2 m− 2 2 ) ( 2 L<
A … … … … … … … … … … … .. ( b )
e la ecuaci0n !b& obtenemos: Q L< K < = … … … … … … … … … … … … … … … … … … … ( c) A ( 2 2 m− 2 2 ) e la ecuaci0n !a& obtenemos+
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Mecánica de Suelos II
promedio de % metros. Se desea calcular el flujo perpendicular a su secci0n transversal en cm1.2minuto2metro de anc(o del acuífero !cm 1.2min.2m&.
S!lción: e la ecuaci0n !".5& obtenemos+ h − h Q= K . i . A = K 1 2 A L
e los datos del problema+ K =
0.06 cm 60 cm . =0.06 x . seg min
h1− h2=30 −28=2 m=200 cm S= A 6
1
600 100 (
2
)
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Mecánica de Suelos II
2 c =
C e D10
8álculo de la relaci0n de vacíos que tendrá el terraplén ya construido+ γ d
=
S S γ o "+ e
⇒
e=
S S γ S ! L&
−
"=
5.Q
(".Q%) ( ;.:$)
La altura que ascendera el agua +
−
"=
5.Q ".%Q5
−
" = ;.%"
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Mecánica de Suelos II
dinas gr 4.2 x 10−4 lbs =0.0764 = S=75 ( parael parael casodel casodel agua. agua. cm cm plg D=2 %= 0.1 mm =0.01 cm6%= 0.005 cm o 8 =12
Jeempla6ando+ 2
(
0.0764 gr
)
cm gr gr =1003 −30.56 =972.44 2 /2=1003 2 − ( 0.005 cm) cm cm
#. 8omo resulta resultado do de una explora exploraci0n ci0n de suelos suelos se cuenta cuenta con con el perfil perfil del suelo seg'n seg'n la figura figura adjunta, determine el esfuer6o vertical total, la presi0n de poro y el esfuer6o vertical efectivo, a la profundidad V P "Q m.
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Mecánica de Suelos II
:. /n la figura figura se muestra muestra un recipien recipiente te de vidrio vidrio totalme totalmente nte lleno lleno de agua. agua. /n su superfic superficie ie superior (ay un orificio de " P ;.;" cm., y el menisco está totalmente desarrollado, en su superficie inferior (ay otro orificio de diámetro 5. a& 8ual es el máximo valor que puede tener 5 si el menisco en ese orificio está totalmente desarrolladoT b& Si " P 5 P ;.;" cm. /ncuentre el ángulo de contacto, µ 5, en el orificio inferior cuando en el superior el menisco está totalmente desarrollado.
S!lción: a' B8ual es el máx. valor que puede tener 5 si el menisco en ese orificio está totalmente desarrolladoT D 1=0.01 cm 8 1=00 ( por estar totalmente desarrollado desarrollado ) D 2=> > 8 2=00 La tensi0n en el menisco del orificio superior será+
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Mecánica de Suelos II
b' Si " P 5 P ;.;" cm. /ncuentre el ángulo de contacto, µ 5, en el orificio orifi cio inferior, cuando en el superior el menisco está totalmente desarrollado. 8on la formula y el equilibrio del sistema+ − 4 s+ 20 − 4 s cos 8 2 = D1 D2 Sabemos Sabemos que : hc =
0.3
D
( ? =
4 s cos8
D
D1= D2= 0.01 cm 8 2=> > " 8 1=00
e donde −0.3cos 8 2 −0.3 + 20 = 0.01
0.01
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Mecánica de Suelos II
/n el proceso de consolida consolidaci0n ci0n el movimiento movimiento de las partículas partículas de un suelo, sucede sucede en el sentido vertical, guardando la misma posici0n relativa particular, en consecuencia consecuencia el volumen disminuye3 pero el despla6amiento de la partículas s0lidas son nulas.
La consolidaci0n que experimentará un estrato de arcilla saturado !sumergido& doblemente drenado, cuando el esfuer6o se incrementa, por la construcci0n de una cimentaci0n !Wp&, la presi0n de poro del agua se incrementará, esto se debe a que la permeabilidad (idráulica de las arcillas es muy pequeña, se requerirá alg'n tiempo para que el exceso de presi0n de poro del agua se disipe y el incremento del esfuer6o se transfiera gradualmente a la estructura del suelo. e acuerdo con la figura )* 5.1, si el incremento !Wp& es una sobre carga o presi0n de
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Mecánica de Suelos II
/ntonces, el incremento del esfuer6o efectivo en la capa de arcilla es+ @ 3 e = @ 3 −@ 4 = @ p−0 = @ p … … … … … . … … … … … … … … … ( 2.2)
/n este incremento gradual ocasionará asentamientos durante cierto tiempo y se conoce como consolidaci0n.
2./ 2./ Pre Preba ba$$ de lab! lab!ra ra"! "!ri ri!! $!br $!bree me me$"ra $"ra$$ de arci arcill lla$ a$ $a" $a"ra rada da$$ e inal inal"e "era rada da$$ &de$i+nación de %reba D2/(> del AS<0'. Se lleva a cabo para determinar el asentamiento por consolidaci0n causado por varios
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Mecánica de Suelos II
3 2 Seccin
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Mecánica de Suelos II
h5 2=
1 + e n c m … … … … … … … … … … … ….. ( 2.4 ) A
/n una muestra completamente saturada se observa lo siguiente+ 2 =h + h + @ h
(2.5 )
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Mecánica de Suelos II
8on los resultados de los ensayos de laboratorio, se tra6a una gráfica que muestre la variaci0n de la relaci0n de vacíos -e sobre el eje \ en escala natural, versus el esfuer6o vertical correspondiente p, sobre el eje en escala logarítmica. La variaci0n de la curva de compresibilidad, para un tipo de arcilla, después que se alcan6a la presi0n de consolidaci0n deseada, el espécimen puede descargarse gradualmente !periodo de descarga& descarga& lo que resultará el tramo de curva correspondiente a la expansibilidad de la muestra.
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Mecánica de Suelos II
#L=
1 + L/ … … … … … … … … … … … … … … … … … … … … … … … . ( 2.9) #/
onde+ 1 + 8ontenido de (umedad natural, LL+ Límite líquido, L<+ Límite
( )
1.22−
p =¿
e0
e L
− 0.0463 0.0463 log p0 ( En
KB
(2.10 )
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Mecánica de Suelos II
Babla Babla 5."+ Nalores Nalores del coeficiente c oeficiente de compresibilidad
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Mecánica de Suelos II
ond o nde, e, S P ∆D, es igual igual al asenta asentamie miento nto ∆e es el cambio total de la relaci0n de vacíos
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Mecánica de Suelos II
S=
C S 2 c 1+ e
log
p0 + @ p p
… … … … … … … … … … … … … … … … ( 2.20)
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Mecánica de Suelos II
/n todos los puntos de la capa de arcilla se cumple que el esfuer6o efectivo es la diferencia
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considera consid erable ble rigidi rigidi6ac 6aci0n i0n que pod podrá rá alivia aliviarr el proble problema ma de la (etero (eterogen geneid eidad ad del terren terrenoo impidiendo grandes asientos diferenciales.
/.2. /.2.// L!$a$ !$a$ de cime cimen" n"ac ació ión n Se podrán emplear en casos en que el área cubierta por eventuales cimentaciones aisladas o por emparrillados cubra un porcentaje elevado de la superficie del solar. /n edificaci0n podrán utili6arse los siguientes tipos de losas de cimentaci0n
-a/
-/
9igura ?.$+ !a& Losa continua y uniforme y !b& 8on refuer6os bajo los pilares
-/ -$/ 9igura ?.%+ !c& Losa con pedestales y !d& 8on secci0n en caj0n
-e/
-f/
9igura ?.Q+ !e& Losa nervada y !f& losa aligerada.
/.2. /.2.>> P!7 P!7!$ de cime cimen" n"ac ació ión n 8uando el terreno apto para cimentar se encuentre a una profundidad comprendida entre 1m y $m, se podrá considerar la posibilidad de recurrir a la ejecuci0n de po6os de cimentaci0n .
Los po6os más (abituales en edificaci0n son de dos tipos !9igura ?.%&. /l primero consiste en
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9igura ?.#+
/.( /.( ".
5.
1.
?.
/./
Pr!c Pr!ced edim imie ien" n"!! %ara %ara el %r!y %r!yec ec"! "! de cime cimen" n"ac aci! i!ne ne$$ $%e $%erf rfic icia iale le$$ de e$"r e$"rc c" "ra ra$$ de edificación ato a toss de la sup super eres estr truc uctu tura ra • La tipología estructural. • Su configuraci0n geométrica • La situaci0n de los pilares, muros y demás elementos estructurales que transmitan cargas a la cimentaci0n. • Las cargas muertas y vivas deben ser diferenciadas dimensionado correspondiente a las condiciones sísmicas sísmicas de la 6ona, • La situaci0n de dimensionado etc. ato a toss del del terr terren enoo • La informaci0n geotécnica Los datos datos relativos relativos a la resistencia resistencia y deformabili deformabilidad dad de las unidades unidades geotécnicas geotécnicas • implicadas. • )ivel freático. eterminar eterminar la profund profundidad idad requerida requerida para la cimentac cimentaci0n i0n • /sta puede ser la mínima
/./.1 /./.1 Pre$i Pre$ión ón ! e$f e$fer7 er7!! "!"al "!"al de $!bre $!bre car+a car+a &, ! %' /s la intensidad de la presi0n total debida a los pesos del suelo como del agua contenida en el suelo, sobre cualquier plano (ori6ontal, en o bajo el nivel de la cimentaci0n antes que se inicien las actividades de la construcci0n. /./. /./.22
Pre$ Pre$ió ión n efec efec"i "i8a 8a de de $!br $!bree car+ car+aa &e, ! %e' /s la presi0n intergranular sobre cualquier plano (ori6ontal en o bajo el nivel de la cimentaci0n antes que se inicie las actividades de la construcci0n
/./. /./.((
Pr ión ión "!"a "!"all de la la ci
n" ión ión &%
'
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/s el incremento neto en la presi0n sobre el suelo que se encuentra bajo el nivel de cimentaci0n, debida a la carga muerta y viva aplicada por la estructura, se utili6a para determinar la distribuci0n del esfuer6o a cualquier profundidad bajo el nivel de la cimentaci0n.
q n= pc − p /./.> /./.> Pre$i Pre$ión ón efec"i8 efec"i8aa de de la la cime cimen"a n"ació ción&= n&=e' /s el incremento efectivo en presi0n sobre el suelo que se encuentra bajo el nivel de la cimentaci0n, debidas a las cargas muertas y vivas aplicadas por la estructura.
q e= p c − p0 /./.6 /./.6 Ca%aci Ca%acidad dad de car car+a +a de de @ndi @ndimie mien"! n"! ! ?l"im ?l"imaa &=' /s el valor de la presi0n o esfuer6o con la cual el suelo falla por cortante. /./. /./.;; Ca Ca%a %aci cida dad d de de car+ car+aa ne"a ne"a ?l" ?l"im imaa &=n'
q nu =qu − p /./. /./.
Ca%aci Ca%a cida dad d de de car+ car+aa admi admi$i $ibl blee &=adm' /s la intensidad neta de carga considerada apropiada para el caso particular de suelo seg'n los prop0sitos de diseño preliminar. /l valor particular esta basado, ya sea en la experiencia local, o en le cálculo resultante de las pruebas de fuer6a o de garaga del suelo utili6ando un factor de seguridad contra la ruptura al cortante.
/./. /./.
Pre$ Pre$ió ión n de de car car+a +a admi admi$i $ibl blee & Madm' /s la intensidad de carga impuesta por la cimentaci0n
9igura ?.:+
/.> /.>
E$"i E$"ima maci ción ón de la car+ car+aa %er %ermi mi$i $ibl blee
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Segundo+ @ partir dela determinaci0n de los asentamientos.
/.6 /.6 Ca Ca%a %aci cida dad d de de Car Car+a +a Nl"i Nl"ima ma /l asentamiento se incrementa bajo una carga aplicada gradualmente. 8uando la carga toma un valor de q u se produce una falla s'bita del suelo que lo soporta a la cimentaci0n. /sta carga se denomina -capacidad de carga 'ltima de la cimentaci0n. Se presentan 1 tipos de fallas por corte+
/.6.1 -alla #enera #enerall %!r C!r"e. C!r"e. /s un tipo de falla s'bita del suelo, que va acompañada por una falla en la superficie del terreno, se presenta en arenas densas o arcillas dur as.
9igura ?.";+ 9alla general por corte
/.6.2 /.6.2 -alla -alla L!cal L!cal %!r C!r"e C!r"e. .
9igura ?.""+ 9alla local por corte
/.6.( -alla de
C!r"e %!r Pn7!namien"!. /n arenas sueltas o arcillas blandas, la superficie de falla no se extenderá a la superficie del terreno, para valores de carga más grandes que q u, la grafica de de carga vs asentamiento asentamiento tendrá una fuerte pendiente y será prácticamente lineal.
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Nesic !":%1&, reali60 varias pruebas de laboratorio de capacidad de carga sobre placas circulares y rectangulares soportadas por una arena con diversas densidades relativas o compacidades compacidades relativas !8 r U&. U&. Las variaciones de+ q u( 1) 1 0 < 2
"
anc(o de
qu Ibtenidas se muestran en la figura ?."1, &4 P diámetro de la placa circular o 1 0< 2 la placa rectangular y, : eso esec;0ico de la arena)
#;
:$ :; 1
Nesic !":Q1&, con rectangulares sobre la superficie de una arena, Nesic Nesic resultados experimentales, relaci0n para el modo capacidad de carga cimentaciones que descansan descansan en arenas, la figura ?."?, muestra la relaci0n+ r elaci0n+ f 2G 2G 8$ 8ompacidad relativa !8rU&, Sí+ 2< L < ¿= < + L Donde + < es el anc(o anc(o de la 6apata y L Longitud de la 6apata
base
en
propuso una de falla por de
Nesic !":%1&, propuso la variaci0n del 9igura ?."?+ Eodos de falla en cimentaciones sobre arena, Nesic asentamiento !S&, de placas circulares !":Q1& y rectangulares sobre superficie de una arena bajo carga 'ltima como se describe en la l a figura ?."$. @llí se muestra el rango general de S2G con la compacidad relativa !8rU& de la arena. /ntonces
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de la falla local o de corte por pun6onamiento, la carga 'ltima puede presentarse para asentamientos de "$U al 5$U del anc(o de la cimentaci0n !G&.
9igura ?."$+ Jango del asentamiento de placas circulares y rectangulares bajo carga 'ltima ! f 2G 2G P ;& en arena, Nesic,
/.;
de la Ca%ac Ca%acida idad d de Se+?n
Car+a
Ber6ag r6ag(i (i !":? !":?1& 1&,, pres presen ento to su teor teoría ía para para eval evalua uarr la capa capaci cida dadd de carg cargaa 'ltim 'ltimaa de cimentaciones superficiales. 8ondiciones, para que se considere una cimentaci0n superficial es que+ f O G, Itros investigadores f P P 1 0 ? veces el anc(o de la cimentaci0n onde.M f + profundidad de desplante y G+ anc(o de la cimentaci0n < 6 0 + La superficie de falla se considera Ber6ag(i Ber6ag(i sugiri0 para una cimentaci0n corrida L seg'n la mostrada en la figura ?."%. /l efecto del suelo arriba del fondo de la cimentaci0n puede también suponerse suponerse reempla6ado reempla6ado por una sobre carga equivalente efectiva. efectiva.
(
)
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Ca$! de la falla +eneral: 1. Para Para cimen cimen"ac "ación ión c!rrid c!rrida: a: 1 2
qu =c B c + q B q + 0 < B 0 … … … … … … … … … … . … … … … … … … ( 4.1 )
onde+ c es la co(esi0n del suelo, 0 es el peso específico del suelo, q = D f x 0 es la sobre carga, B c + B q + B 0 !ver tabla )* ?."& son los factores de correcci0n por capacidad de carga que están en f ! ∅ &. Los factores de capacidad de carga, B c + B q + B 0 se determinan mediante las siguientes expresiones+ B c =cot ∅
[
2
e
B q=
2
4−
e
( ) 4−
(
∅
tg ∅
2
( )
]
−1 =cot ∅ ( B q −1 ) …………………… ( 4.2)
tg ∅
2
0
2cos 45
(
∅
: ∅ + 2cos 2 2 2
3 :
2
B 0 =
( ) 3 :
+
∅
2
)
… … … … … … … … … … … … … … … … … … … .. ( 4.3 )
)
1 K p 0 −1 tg ∅ … … … . … … … … … … .. … … … … … … … .. (4.4 ) 2 2cos2 ∅
Coeficientede empue empue pasi$ode pasi$ode latierra latierra . onde+ K p 0 esel Coeficientede
2. Para Para cime cimen"a n"ació ción n cad cadrad rada: a: qu =1.3 c B c + q B q+ 0.4 0 < B 0 … … … … … … … . … … … … … … . … ( 4.5 )
(. Para Para cime cimen"a n"ació ción n circ circla lar: r: q =1.3 c B + q B + 0.3 0 < B
( 4.6 )
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qu =0.867 c B - c + q B - q + 0.4 0 < B - 0 … … … … … … … … … … … … . ( 4.8 )
(. Para Para cime cimen"a n"ació ción n circ circla lar: r: qu =0.867 c B - c + q B - q + 0.3 0 < B - 0 … … … … … . … … … … … … . … ( 4.9 ) esla Cohe hesi sin n del del suel sueloo + 0 es el peso específico del suelo, q es la sobre carga, onde+ c eslaCo B - c + B - q + B - 0 son factores de capacidad de carga modificada que están en funci0n de ∅ calculán calculándose dose a partir partir de las ecuacion ecuaciones es !?.5&, !?.1& y !?.?&, !?.?&, reempla6a reempla6ando ndo ∅ por ∅
- =tg−1
( ) 2 tg ∅ 3
2 3
, c - = c
la variaci0n variaci0n de B - c + B - q + B - 0 , con el
∅
se presentan
en la tabla &F /.2'. Las ecuaciones de capacidad de carga de Ber6ag(i se modifican para tomar en cuenta los efectos de la forma de la cimentaci0n !G2L&, profundidad de empotramiento ! f &, &, e inclinaci0n de la carga.
/./.1 0!dificaci 0!dificación ón de la$ ecaci!ne ecaci!ne$$ de la ca%acidad ca%acidad de car+a %!r %re$enci %re$enciaa del i8el -re3"ic!: Las ecuaciones anteriores se desarrollaron para determinar la capacidad de carga 'ltima con base en la (ip0tesis de que el nivel freático esté locali6ado muy por debajo de la cimentaci0n, sin embargo, si el nivel freático está cerca de la cimentaci0n será necesario modificar las ecuaciones de capacidad de carga, dependiendo dependiendo de la locali6aci0n del nivel freático. CASO I: Si el nivel freático se locali6a de manera que ; O " O f , el factor q en las ecuaciones de la capacidad de carga toma la forma+ q = D1 + D2 ( 0 sat −0 1 ) … … … … … … … … … … … … … … … … … … … … … (4.10 ) t −la BN 4.2 cidadd
onde+ γ sat es el el
es el
@demás, el valor de : en el 'ltimo término t érmino de las ecuaciones tiene que ser reempla6ado por+
0 - = 0 sat −0 1
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CASO III
9igura ?."Q+ /squema para la modificaci0n de las ecuaciones de Ber6ag(i, Ber6ag(i, con presencia del nivel freático
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/./.2 Ca%acidad Ca%acidad de Car+a Car+a Admi$ible Admi$ible /l cálculo de la capacidad de carga bruta admisible de cimentaciones superficiales superficiales requiere de aplicar un factor de seguridad !9S& a la capacidad de carga 'ltima bruta+ q q adm= u … … … … … … … … … … … … … … … … … … … … … … … … (4.13 ) 9S Sin embargo, algunos ingenieros prefieren usar un factor de seguridad de+
#ncremento #ncrementoneto neto=
Capac Capacid id ad de carga!lti carga!ltima ma neta neta … … … … ( 4.14 ) 9S
La capacidad de carga 'ltima neta se define como la presi0n ultima por unidad de área de la cimentaci0n que es soportada soportada por el suelo en exceso de la presi0n causada por el suelo que la rodea en el nivel de la cimentaci0n. Sí la diferencia entre el peso específico del concreto usado para la cimentaci0n y el peso específico del suelo que la rodea se supone insignificante+ q neta (u ) =q u−q … … … … … … … … … … … … … … … … … … … … … ( 4.15 )
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q : Df x 0 ( esfuer esfuero o efecti$oa efecti$oa ni$el ni$el del fondo fondo dela de la ciment cimentaci acin n) G+ @nc(o de la cimentaci0n !diámetro para una cimentaci0n circular& 9 cs 9 cs 9 cs : 9actoresde 9actores de forma 9 qd 9 qd 9 qd : 9actores 9actores de profundidad 9 ci 9 qi 9 0i : 9actores 9actores por inclinacin de la carga B c + B q + B 0 : Sonfactor Sonfactores de capaci capacidad dadde decar carga ga
-ac"!re$ de ca%acidad de car+a: Nesic !":Q1&, de los estudios de 8ampo y laboratorio, sobre capacidad de carga, la naturale6a básica de la superficie de falla en suelos seg'n la teoría de Ber6ag(i Ber6ag(i parece afirmarse lo correcto. 0 J Sin embargo, el ángulo α como se observa en la figura )*?.#, es más cercano a 45 + , que 2
a J , si se acepta esta afirmaci0n, los valores de B c + B q + B 0 para un ángulo de fricci0n del suelo cambiará también respecto a los proporcionados en la tabla !)*?."&. 0 -ac"!re$ de ca%acidad de car+a: 8on % P 45 +
J 2
Jeissner !":5?&, presento la siguiente ecuaci0n+ 2
(
0
B q= tan 45 +
)
J :tanJ e … … … … … … … … … … … … … … … … … … ( 4.18 ) 2
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Dansen !":Q;&, propuso los siguientes factores de profundidad+ 8ondici0n !a&+ 9 cd =1 + 0.4
D f <
O1
D f … . … … .. … … … … … … … … … … … … … . … … … … … . ( 4.24 ) <
9 qd =1 + 2tan J ( 1− senJ )
2
D f <
… . … .. … … … … … … … … … … . … . ( 4.25 )
9 0d=1 … … … … .... …. … .. … … … … … … … … … … … … … . … … … … … ( 4.26 )
8ondici0n !b&+ 9 cd =1 + 0.4tan −1
D f >1 <
( )
Df … . … … . … … … … … . … … … … … . … … … … ( 4.27 ) <
9 qd =1 + 2tan J ( 1− senJ ) tan−1 2
( )
Df … . … … … … … … … … … . ( 4.28 ) <
9 0d=1 … … … … .... …. … .. … … . … … … … … … … … … … … . … … … … . ( 4.29 )
-ac"!re$ de inclinación:
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S7empton !":$"&, propuso una ecuaci0n para la capacidad de carga 'ltima neta para suelos arcillosos !condici0n J =0 &, que es similar a la ecuaci0n !?.15&.
(
q neta (u )=5 c 1 +0.2
D f <
)( + ) 1 0.2
< … … . … … … … … … … … … … … . ( 4.33 ) L
/..( /..(
qu =c B c 9 cs 9 cd 9 cc +q B q 9 qs 9 qd 9 qc + 0 < B 0 9 0s 9 0d 9 0c … … … … … … … ( 4.34 ) 9 cc + 9 qc " 9 0c + 9actores de compresibilidad del suelo.
Nesic !":Q1&, los factores de compresibilidad del suelo, para ser determinados se parte de la analogía de expansi0n de cavidades, se sigue el siguiente procedimiento+ ". 8alcul 8alcular ar el índic índicee de rigide rigide66 del del suelo suelo !Hr& a una una profund profundida idadd aproxi aproximad madaa de debajo del fondo de la cimentaci0n+
< 2
, por
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6 9 cc + 9 qc " 9 0c=1
?. Sí+ # r < # r (cr )
{( 9 = 9 =e
)
−4.4 + 0.6 < tan J +
0c
L
[
l og2 # r ) (3.07 senJ ) (log2 1+ senJ
qc
]}… … … … … … . … .. (4.37 )
/n la figura ?."; se muestra la variaci0n de 9 0c= 9 qc con Hr y /ara ∅ =0 6 9 cc =0.32 + 0.12
/ara ∅ > 0 6 9 cc= 9 qc−
< + 0.60 logL L
1 − 9qc
B q tan ∅
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/. Ca%acidad de car+a car+a de cimen"aci!ne$ car+ada$ car+ada$ e9cn"ricamen"e e9cn"ricamen"e /n ocasiones las cimentaciones, como por ejemplo las que están en la base de un muro, son sometidas a momentos además de la carga vertical, en tales casos, la distribuci0n de presi0n de contacto sobre el suelo no es uniforme. La distribuci0n de la presi0n nominal es+
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9i ura ?.":+ 8imentaci 8imentaciones ones car adas excéntrica excéntricamente mente
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< - : Anchoefecti Ancho efecti$o $o= <− 2 e L- L - : Longitud efectiva P L 5e
Si la excentricidad es en la direcci0n de la longitud de la cimentaci0n, el valor de L será de L−2 e . /l valor de G es entonces igual a G, la menor de de las dos dimensiones ya sea L
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/.15 /.15 Ca Ca%a %aci cida dad d de car+ car+aa de cime cimen" n"ac aci! i!ne ne$$ car+ car+ad ada$ a$ e9c e9cn" n"ri rica came men" n"ee en d!$ d!$ direcci!ne$. Si consideramos el caso en el cual una cimentaci0n esta sometida a carga vertical 'ltima !<'lt.&, y un momento !E&, como observamos en la figura )* ?.5;. 8onsiderando este caso, las componentes del momento !E& respecto a los ejes vs \ se determinan como Ex y Ey respectivamente. /n este caso la carga de (undimiento !< 'lt.&, colocada excéntricamente sobre la cimentaci0n con x P e G, y P eL, onde+ G G e <= x ( e L = " … … … … … … … … … … … … … … … .. ( 4.48) /!lt. /!lt.
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La capacidad 'ltima de carga !q u&, para suelos estratificados se expresa mediante la ecuaci0n+ qu =q est. ( i)+
2 ( C a + / p senR )
<
−0 1 2 … … … … … … … … … … … … .. … . ( 4.62 )
Anchode la apata apata onde+ < : Anchode C a : 9ueraadhesi$a 9uera adhesi$a / p : 9uera pasi$a por und . de long . de las carasaa - " bb - q est.( i) : Capacida Capacidad d de carga carga del estrato estratoinfe inferior rior R : ngulodeinclinacindela/ p +conrespectoalahoriontal.
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Para el Ca$!: Si la altura D es relativamente grande, entonces la superficie de falla en el suelo estará completamente locali6ada en el estrato superior de suelo más fuerte.
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1 2
q t = 0 1 ( D D f ) B q ( 1) 9 qs( 1) + 0 1 < B 0 ( 1) 9 0s (1)
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qu = 0< B 0q … … … … … … … … … … … … … … … … … … … … … … … … … .. ( 4.84 )
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/.1( C3lcl! de %re$i!ne$ %re$i!ne$ de car+a de $er8ici! $er8ici! &%ermi$ible$' en $el!$ $el!$ n!c!@e$i8!$ %!r medi! de %reba$ In Si".
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9igura %.5+ Eartillo de aire o vapor de acci0n doble
9igura %.1+ Eartillo de aire o vapor de acci0n simple
9igura %.?+ Eartillo disel
%.$ Pila$ y %il!"e$ e9ca8ad!$ Son cimentaciones profundas, de gran capacidad de carga, que se diferencian de los pilotes por sus dimensione dimensiones. s. Las pilas tienen secci0n transversal transversal circular o oblonga oblonga !elíptica&, !elíptica&, por lo general general llevan
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u= ¿ / p + / f … … … … … … … … … … … … … … … … … … … … … … … … … … … . ( 6.1) /¿ onde+
6.6. 6.6.11 Ca Ca%a %acid cidad ad de car+ car+aa %!r %!r %n" %n"aa &P &P%' La ecuaci0n desarrollada considera para un área unitaria desarrollada en la punta+ Seg'n, Ber6ag(i Ber6ag(i y
u= ¿ / p =C B c¿ + q B q¿ + D0 B 0 ¿ … … … … … … … … … … … … … … … . … … . … .( 6.2) /¿ u= ¿ / p =C B c¿ + q B q¿ … … … … … … … … … … … … … … … … … … … . … … . … . ( 6.3 ) /¿ ¿
D0 B 0 .. Secancela por ser tan pequeHo sin introducirerror
Jeempla6ando q por q, se obtiene+
u= ¿ / p =C B c¿ + q - B q¿ … … … … … … … … … … … … … … … … … … … . … … . … . ( 6.4 ) /¿ onde+ < p es la Jesistencia unitaria de la punta, 8 es la 8o(esi0n del suelo, qes la presi0n efectiva a ¿ ¿ nivel de la punta del pilote, B c + B q son los 9actores de carga. %.%.5 Ca%acidad de car+a %!r fricción &M$' La resistencia por fricci0n o superficial de un pilote se expresa mediante la ecuaci0n+ Qfs =
∑ p @ L f … … … … … … … … … … … … … … … … … … … . … … . … … …... (6.5 )
onde+ p+ es el perímetro del pilote, @Lesla Longitud del pilote sobre el cual p y f se consideran constantes, f es la Jesistencia unitaria por fricci0n fricci0n a la profundidad V a. Eétodo de Eeyer(of+
a.1
Sel! Aren!$! &M%' ¿
Q p= A p x q p = A p x q - B q … … … … … … … . … … … … … … . … . … . … … … .. ( 6.6 )
8onsiderando que la carga total != p& soportada por el pilote no debe exceder el valor límite !
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La resistencia de punta límite es+
( )
q t
( )
,g lb ¿ ¿ = B … … … … … … … … .. … ( 6.8 ) 50 tan ∅= 1000 B q tan ∅ q 2 2 m pie
9igura %.$+ Nariaci0n Nariaci0n de la resistencia unitaria de punta en una arena (omogénea
9igura %.%+ Nariaci0n de !L b2&cri, con el ángulo de fricci0n del suelo, Eeyer(of !":Q%&
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¿
¿
9igura %.Q+ Nariaci0n de los valores máximos de B q " B c , con el ángulo de fricci0n interna del suelo Eeyer(of !":Q%&
a.2 a.2
Sel Sel!! arc arcil ill! l!$! $! &W 5F' 5F' &M &M%'
b. 0"!d! de )e$ic )e$ic &E$"imación &E$"imac ión de M%' Nesic !":QQ&, propuso+
cB A p ( q p )= A p ( ¿ ¿ c + 3 - B ) … … … . … … … … … … . … . … . … … … . … .. (6.10 ) Q p=¿ ¿
¿ 3
onde+ X es el esfuer6o efectivo normal medio del terreno a nivel de la punta del
( )q - … … . … … … … … … … … … … … … … …
3 - =
1 + , 0
... … . … . … … … . … .. ( 6.11 )
3
¿ ¿ onde+ , 0 =1+ sen ∅ , es el coeficiente pasivo de la tierra, B c + B 3 , son los factores de carga. ¿
¿ 3 3
B =
3 B q 1+ 2 , 0
¿
¿
B q−1 ) cot ∅ , B c =( B
,
¿
B 3 = f ( # rr )
onde+ Hrr , es el ]ndice de rigide6 reducido por el suelo.
# rr =
# r 1 # @
,
# r =
Es 2(1
)(
-
∅
)
+ Ps =
Es 2 (1
)
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: ¿ 4 B c = ( ln #rr + 1 ) + + 1 6 para ara ∅= 0 ( condicinnodrenada ) 3 2
c. Eétodo de ambu !/stimaci0n de = p& ambu !":Q%&, propuso la siguiente expresi0n+
cB A p ( q p )= A p ( ¿ ¿ c + q - B ) … … … . … … … … … … . … . … . … … … . … ..( 6.12 ) Q p= ¿ ¿
¿ q
B q¿ =( tan ∅ + √ 1 + tan2 ∅ ) ( e 2 ;- tan ) 2
d.
∅
,
B c¿ =( B B ¿q+ 1 ) cot ∅
9igura %.#.+ 9actores de capacidad de carga ambu Eétodo Eétodo de de 8oyle 8oyle y 8aste 8astello llo !/st !/stima imaci0 ci0n n de!":Q%& = p&
8oyle y 8astello !":#"&, (icieron ensayos en arena y (an propuesto+
Q p= A p ( q p ) = A p ( q - B q¿ ) … … … . … … … … … … … … … … … ... … . … … … .... ( 6.13) ¿ onde+ q - : es la presi0n vertical en la punta del pilote. B q + es el factor de capacidad de carga
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9igura %.";+ Nariaci0n K con L2 ¿ 8oyle y 8astello !":#"& 9igura %.:+ Nariaci0n Nariaci0n B q , con L2
%.%.1 Re$i$"encia %!r fricción &M$' La resistencia por fricci0n o superficial de un pilote se expresa mediante la ecuaci0n+
Qs=∑ p @ L f … … … … … … … … … … … … … … … … … … … . … … . … … … ... ( 6.14 ) /n las figuras se observa que+ L es la Longitud crítica, Ana estimaci0n sería L P "$
9igura %.""+ 8ompactaci0n y resistencia por fricci0n unitaria para pilotes en arena
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onde+ q - =0 x L + /sfuer6o efectivo a la profundidad considerada. K+ 8oeficiente efectivo de la tierra R + 4ngulo de fricci0n entre suelo y pilote. K varía con la profundidad, es aproximadamente igual a K p y C K ; !presi0n de reposo& Nariaci0n Nariaci0n de K, con la profundidad
6.6./ 6.6./ Re$i$" Re$i$"enc encia ia %!r %!r fricci fricción ón $%e $%erfi rficia ciall a& /n @rci rcilla a."& Eétodo Nijayvergiya Nijayvergiya y 9oc(t !":Q5&, propusieron el método, el que se basa en la (ip0tisis de que el despla6amiento del suelo causado por el (incado del pilote conduce a una presi0n lateral pasiva a cualquier profundidad y que la resistencia unitaria superficial promedio es+ f prom= T ( 3 - $ =2 c u ) … … … … … … … … … … … … … … … … … … … … … ( 6.11 ) onde+ 3 - $ + es el esfuer6o vertical efectivo promedio para toda la longitud de empotramiento. 8u, es la resistencia cortante media no drenada ! P ;*&. /l valor de cambia con la profundidad de la penetraci0n del pilote !figura %."1&. Jesistencia total por fricci0n se obtiene+ Q s= p L f promedio … … … … … … … … … … … … … … … … … … … … … … .. ( 6.12 )
ebe tener especial cuidado al obtener 3 - $ " c u en suelos estratificados !figura %."$&. e acuerdo con la figura %."$. b, el valor medio de 8 u es+ C u 1 L1+ C u 2 L2 + … + ¿
¿ C u= ¿
e acuerdo con la figura %."$. b, el valor medio de
3 - $ es+
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Qs=∑ f p @ L=∑ C u p @ L … … … … … … … … … … … … … … … … . ( 6.13 ) ∝
9igura %."5+ Nariaci0n Nariaci0n de con la profundidad de empotramiento de un pilote Ec 8lelland, !":Q?&
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9igura %."?+ Nariaci0n Nariaci0n de con la co(esi0n no drenada de una arcilla.
a.5& Eétodo 8uando los pilotes se (incan en arcillas saturadas, presi0n de poro en le suelo alrededor de los pilotes aumenta3 este este exceso de presi0n de poro en arcillas normalmente normalmente consolidadas consolidadas es de ? a % veces 8u. Sin embargo, en aproximadamente aproximadamente un mes, esta presi0n se disipa gradualmente+ por consiguiente, la resistencia unitaria por fricci0n en el pilote se determina con base en los parámetros de esfuer6o esfuer6o efectivo de la arcilla en un estado estado remoldeado !c P ;&, entonces entonces a cualquier profundidad+ f =3 - $ M … … … … … … … … … … … … … … … … … … … … … … … … … … .. (6.14 )
onde+ 3 - $ es el esfuer6o vertical efectivo, M = Ktan ∅ % , ∅ % + ángulo de fricci0n drenada de la arcilla remoldeada, r emoldeada, K es el coeficiente de presi0n de la tierra. K =1 + sen ∅ % , para arcillas normalmente consolidadas y K =( 1 + sen ∅ % ) √ C% C% , para arcillas preconsolidadas
one+ I8J es la tasa de preconsolidaci0n
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q p =q u ( B B + 1 ) … … … … … … . … … … … … … … … … … … … … … … … . ( 6.18 ) ∅
(
2 0 onde+ B = tan 45 + ∅
∅
2
)
,
el ángulo de fricci0n drenado. q laboratorio qu = u
qu + resistencia a compresi0n no confinada de la roca. es
q qu ( admisible )= u 9S 5 Pr!blema F 1: An pilote tiene "$ m de longitud y de secci0n transversal ;.? x ;.?; m. /l pilote esta totalmente empotrado en arena de "Q?#.;# P 7g2m1 y P 1;*. 8alcule la carga 'ltima por punta = p mediante los métodos+
z
a& Eéto Eétodo do de de Eey Eeyer(o er(of f b& Eétodo de Ne Nesic, usando Hr P Hrr P $; c& Eétodo Eétodo de amb ambu, u, Asan Asando do RP RP :;* :;*
S!lción: Pr!blema F 1: An pilote de tubo (incado en arcilla, con un exterior de ?;.% cm y un espesor de pared de %.1$ mm, tal como se muestra en la figura. 5m 5m
3
n / m
n / m
2
n / m3 3
n / m 20
)II. ES
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An talud en arena o grava limpia es estable, cualquiera sea su altura, siempre que el ángulo β entre el talud y la (ori6ontal sea igual o menor que el ángulo de fricci0n interna ∅ del suelo friccionante en estado suelto. /l factor de seguridad !9s& en este caso puede expresarse por simple relaci0n+
9igura Q."+ Balud natural de un suelo granular
;.1. ;.1.(( E$"a E$"abi bilid lidad ad de
onde+ Dcr es la @ltur @lturaa crític críticaa para para un valor valor dado, dado, ) s es el coeficiente de estabilidad que depende depende del ángulo de fricci0n ∅ y del ángulo entre el talud y la (ori6ontal ! β&, 8 es la 8o(esi0n, γ es el el
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9igura Q.1+ @baco de Baylor Baylor
5+ Se busca la altura crítica comien6a a desli6arse el !con ∅ P "$` y β P ?$`&
)s P "5
B . C 12 x 1.00 =6.0 m 2 cr = s = 0 2.0
;.1./ E$"abilida E$"abilidad d de
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9igura Q.?+ /squema de círculos tentativos de una masa desli6ante
/l peso Q de la faja tiende a provocar el desli6amiento, en el equilibrio la suma de las fuer6as verticales debe ser nula, la fricci0n en el límite de equilibrio está completamente desarrollada+
∑ 9 ($ertical)=0 onde+
P 7= x sen 8 1 + B x cos 8 1 " con B = x cot ∅ P 7= x sen 8 1 + x cos 8 1 espejando se obtiene+ =
P7 sen8 1+ cot ∅ xcos 8 1
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EP x r Sen !M&
8on+
=
EP B x
P sen8 + cos8cot ∅
−¿ ¿ ¿ ¿ +¿ ¿ Pder x sen8 sen8 ¿ P iq x sen8 ¿ P −∑ ¿ sen8 + cos8cot ∅
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( ¿¿ 9 +C ) sen8 + Bcos8 P =¿
8on+
B = 9 cot ∅
C =c x
P= 9 sen8 + 9 cot ∅ cos8 + c x
b cos8
b cos8
La fuer6a de corte !B& esta compuesta de una parte debida a la fricci0n y de otra parte debida a la co(esi0n !9igura Q.$&. 9 =
P −cbtan8 sen8 + cot ∅ cos8
9 S=
∑ x r+ ∑ C x r −∑ P ∑ P x r sen8 9
x r sen8
iq.
der
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8uadro Q.5+ Babla para determinar el 9actor de Seguridad !9S&
1
2
Faa
n&'lo $e la faa ; -<,=/
4
#
An>o G ? .en $e la -Tn/ faa -/ -Tn+2/ ;
$
"
1!
11
12
?os ?ot 4 @ 5 @ 6<7< 2<9 -1%/-11/ ; ; 8 8
9 S=
Sumat Sumatori oriaa dela de la column columnaa 12 −Sumato Sumatoria ria dela de la column columnaa 13 Sumatoriade Sumatoriade la columna columna 14
9 S=
∑ Col .12−∑ SumatoriaCol .13 1.5 ∑ Col .14
1
14
G$er Gi* @ @ .en ; .en ;
/n general los círculos tentativos !circunferencias desli6antes& dependen de ciertas condiciones+ a& /n materiales materiales (omogéneo (omogéneoss la superficie superficie desli6a desli6ante nte siempre siempre pasa por por el pie del talud talud
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9igura Q.#+ /squema de una masa desli6ante en materiales (omogéneos
d& Si se emplean emplean muros muros de contenci0n contenci0n en desnivel desniveles es la superficie superficie desli6ant desli6antee pasa por el pie de tal tal construcci0n
9igura Q.:+ /squema de una masa desli6ante con la presencia de muros
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;.2.2 E$=ema$ de de$li7amien"!: de$li7amien"!: 0!8imien"! de la %ared, Em%*e Em%*e ac"i8!. ac"i8!. Em%*e %a$i8!. Em%*e en el e$"ad! de re%!$!. a' Em% Em%*e *e Ac"i8 c"i8!: !: &Ea' &Ea' 8onsideremos un Euro de 8ontenci0n sin rugosidad& La pared !muro de contenci0n& tiende a alejarse del terraplén y en el equilibrio plástico aparece una cuña de desli6amiento que forma el ángulo con la (ori6ontal.
9igura Q.""+ /squema de una masa desli6ante en el empuje activo
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9igura Q."1+ /squema de empuje en el estado de reposo
;.2.( Pre$ión la"eral la"eral de la "ierra: Un mr! =e =e $e de$li7a de$li7a $!bre el %lan!
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9igura Q."%+ /squema de la influencia de la rugosidad del muro en el estado activo
b& /stado pasivo+
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/l suelo detrás del muro se encuentra en el estado de equilibrio plástico 3 * P γ x 6 es una tensi0n principal y la presi0n 3 h , normal a la cara vertical, también es una tensi0n principal.
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9igura Q.":+ /squema del circulo de Eo(r en suelos friccionantes
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N
N
90 − ∅ =180 −2 ∅ N 90 + ∅=2 ∅
= 45N + ∅
∅
2
Línea de acci0n del empuje activo !/a&
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9igura Q.51+ /squema del plano de falla y líneas de acci0n de los empujes
/n este caso los coeficientes de empuje de tierras se calculan como+ Sen ( 8 + ∅ ) 2
K
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Son suelos no saturados que sufren un gran cambio de volumen al saturarse. /ste cambio
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