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Debido a la capacidad de representar situaciones lmites, el modelo establece un puente entre algunas de las diferentes formulaciones aparecidas en los ltimos aos y permite ser usada para los citados fines. Finalmente, mediante la utilizacin del mtodo de los elementos finitos se resuelve el problema de una fundacin superficial y se comparan los resultados con los obtenidos a partir de formulaciones simplificadas presentadas en trabajos previos.PMODELO CONCEPTUAL"$$Se puede describir la formulacin presentada como un conjunto de tres elementos, un modelo de deformacin, un modelo de flujo de agua y otro de flujo de aire. Las ecuaciones constitutivas mecnicas se expresan en trminos de tensin efectiva, teniendo esto la ventaja de manejar una sola variable adems de facilitar el pasaje de un sistema bifsico a uno trifsico pues mantiene el mismo conjunto de variables. El modelo de flujo est basado en la interaccin de las dos fases de fluido: agua y gas. El acoplamiento entre el flujo y el campo de deformaciones se realiza mediante la introduccin de parmetros que relacionan las presiones de las fases agua y aire con un cambio en la configuracin de la matriz de deformaciones.xZ$ECUACIONES QUE GOBIERNAN EL PROBLEMA%%$ Para describir la relacin tensin-deformacin en un suelo no saturado, se considera un volumen representativo de suelo sujeto a una tensin externa total sij . El estado de tensiones en este volumen de suelo debe satisfacer las siguientes ecuaciones de equilibrio.F xZ l$ECUACIONES QUE GOBIERNAN EL PROBLEMA%%                   !   &  2  3  4  5RESULTADOS NUMRICOS$ 7RESULTADOS NUMRICOS$ 9  <  : CONCLUSIONES $ ; REFERENCIAS $ %7  0` b!+fl` ii_EEfL u` f;v3ff` XVΟ` _V?" dd@,?n<d@ " d n<@" d`n< n?" dd@   @@``PR    @ ` `6p>> 22@++1(  -T   "  c TBCDE`Fjd @ Hes>9Na }  ZaI9HH24@`"B *  c ByC DE,F6d @  y%f  ryyy@`"   c BTCfDE F*d @ ff0<TT*6ff@`"0vb    # "    c BHCDEF"d @ <H @`" -   c BCDEFd @   *H`xT ~ l N* 6Zx N lT6BD@`"    c BOCDEFd @ $$I=%N Bx1=C =0 1[   x  % =[ I0 O IIJL@`" o   c BCDEFd @ $$mI Z T =a  m I 7~7U y   JL@`"\   c B,CDEFd @ $$,=~ r1   H s   7frC  s H , ,,JL@`"j   c BCDEFd @ $$&z>% 2n&@ Z hs ,  sr~ 8 ty ` @ &&JL@`"Hj   c ,B]CDEFd @ 33WP?*(u[ba UVa{ "3*EKPQK| ? 3 1  W  J O[V  ]  (7 ? K W| ]WPWPhl@`" 2  c BCDEFd @ ,,^*3;MS_-kqV}HHwqeV_S-GA03^* g  $ ;Y}eG0 $ g 0 Z\@`"_   c B+CDEFd @ $$6T~+rN0F r  6 ` l B * x F JL@`"  c BCDEFd @ $$<kAJd ~ / Y  Zf e ; #~ d J)GwHJL@`"  c B>CDEFd @ $$ b66`O>2CT* <b  B x s N *  b bJL@`"h  c BCDEFd @ $$ 2G<D87};2d  M < ,H Y ) d 2 2JL@`"J  c BECDEFd @ //0`mE92aT$ 0 r c 17m(P\(y=7 c ~ <  `d@`" hr  c 4B\CDEPFZd @ 6*`@1=J\17"fn066*,@`"U d  c BCDE$F.d @  lJr@`"2  c dBCDEhFrd @ MuQa2%> >! aiQS68@`"  BCMDE0F:  M5>]8oMM@`"M  BCDE$F.   lf@`"r  c 4BWCDEPFZd @ Q6~;7,8WE&,7u#<QQ*,@`"`  BJCWDE0F:  J8x?WxJJ@`"RW  B CDE$F.  xr<~x  @`"nB  0D> "  nB  0D> "4 4 nB  0D> "F F b  # "nB   0D> "nB ! 0D> "nB " 0D> """nB # 0D> "nB $ 0D> "nB % 0D> "XXnB & 0D> "   ' <4Ĩ " `}  _+Haga clic para cambiar el estilo de ttulo , , ( 0Ȩ "] `}  B*  ) 0Ψ "`   D*  * 0Ө "] `}  D* = + 0Dר " `  kHaga clic para modificar el estilo de texto del patrn Segundo nivel Tercer nivel Cuarto nivel Quinto nivel7    lh  Bdd޽h @ ?"` f;v3ff___PPT10i. |7+D=' = @B +  Globo.3 | 0 E2=2P++1(  -T   "  c TBCDE`Fjd @ Hes>9Na }  ZaI9HH24@`"B *  c ByC DE,F6d @  y%f  ryyy@`"   c BTCfDE F*d @ ff0<TT*6ff@`"0vb    # "    c BHCDEF"d @ <H @`" -   c BCDEFd @   *H`xT ~ l N* 6Zx N lT6BD@`"    c BOCDEFd @ $$I=%N Bx1=C =0 1[   x  % =[ I0 O IIJL@`" o   c BCDEFd @ $$mI Z T =a  m I 7~7U y   JL@`"\   c B,CDEFd @ $$,=~ r1   H s   7frC  s H , ,,JL@`"j   c BCDEFd @ $$&z>% 2n&@ Z hs ,  sr~ 8 ty ` @ &&JL@`"Hj   c ,B]CDEFd @ 33WP?*(u[ba UVa{ "3*EKPQK| ? 3 1  W  J O[V  ]  (7 ? K W| ]WPWPhl@`" 2  c BCDEFd @ ,,^*3;MS_-kqV}HHwqeV_S-GA03^* g  $ ;Y}eG0 $ g 0 Z\@`"_   c B+CDEFd @ $$6T~+rN0F r  6 ` l B * x F JL@`"  c BCDEFd @ $$<kAJd ~ / Y  Zf e ; #~ d J)GwHJL@`"  c B>CDEFd @ $$ b66`O>2CT* <b  B x s N *  b bJL@`"h  c BCDEFd @ $$ 2G<D87};2d  M < ,H Y ) d 2 2JL@`"J  c BECDEFd @ //0`mE92aT$ 0 r c 17m(P\(y=7 c ~ <  `d@`" hr  c 4B\CDEPFZd @ 6*`@1=J\17"fn066*,@`"U d  c BCDE$F.d @  lJr@`"2  c dBCDEhFrd @ MuQa2%> >! aiQS68@`"  BCMDE0F:  M5>]8oMM@`"M  BCDE$F.   lf@`"r  c 4BWCDEPFZd @ Q6~;7,8WE&,7u#<QQ*,@`"`  BJCWDE0F:  J8x?WxJJ@`"RW  B CDE$F.  xr<~x  @`"nB  0D> "  nB  0D> "4 4 nB  0D> "F F b  # "nB   0D> "nB ! 0D> "nB " 0D> """nB # 0D> "nB $ 0D> "nB % 0D> "XXnB & 0D> "   ' <04 "*p 4 _+Haga clic para cambiar el estilo de ttulo , , ( 0,4 " `   4 n:Haga clic para modificar el estilo de subttulo del patrn; ; ) 0В4 "] `} 4 B*  * 04 "`  4 D*  + 0؜4 "] `} 4 D* h  Bdd޽h @ ?"` f;v3ff___PPT10i. |7+D=' = @B +} 0  (    c $Ԩ4''3<$ 0 4    <4@~@~("` <$ 0 4   c :AUNNE-color,$@ 0  B4 ,$ 0 :UNNEb  0p4 $  ,$ 0 J* Departamento de Mecnica Aplicada Universidad Nacional del Nordeste Centro de Mecnica Aplicada y Computacional (CEMACOM) Universidad Federal do Rio Grande do Sul"P>FG H  0޽h ? 33y___PPT10Y.]I+6-DM' 4= @B D' = @BA?%,( < +O%,( < +D ' =%(%(D ' =%(D' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D. ' =%(D ' =%(DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =-u6Bwipe(right)*<3<*XDF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-u6Bwipe(right)*<3<*$DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$F%(D' =-u6Bwipe(right)*<3<*$FDF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*F}%(D' =-u6Bwipe(right)*<3<*F}DF' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*}%(D' =-u6Bwipe(right)*<3<*}++0+0 ++0+0 ++0+0 ++0+0 + } 0 H@`(    s *3C']<$ 0 C    B4C@~@~("`i<$ 0 C b  c :AUNNE-color  Bl6C  :UNNEH  0޽h ? 33<4___PPT10.]I+?8Dx' = @B D3' = @BA?%,( < +O%,( < +Dj' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*+p+0+0 ++0+0 +} 0 H@p(    s *OC'<$ 0 C    BPC@~@~("`mY<$ 0 C b  c :AUNNE-color  BRC  :UNNEH  0޽h ? 33  ___PPT10 .]I+csD. ' = @B D ' = @BA?%,( < +O%,( < +D ' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+p+0+0 ++0+0 +} 0  Y(      s *pkC'<$ 0 C     BplC@~@~("`" <$  0 C ^   6   >AL Y ??#" `?S ` 8 $D 0N   <nC@~@~ "` ,$  0 Extendiendo el concepto de tensiones efectivas de Terzaghi y considerando los efectos de las presiones de agua y aire en los poros, la tensin total sij y la tensin efectiva sij pueden relacionarse en forma incremental segn la siguiente expresin:nxZ  I2b   c :AUNNE-color   BtzC  :UNNE   B(}C@~@~ "`/O,$ 0 GEquilibrio Mecnico$H   0޽h ? 33___PPT10.]I+t3D' C= @B Dx' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*  %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*  D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*  D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D' =-g6B fade*<3<* D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* ++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 +D} 0 |t( (  ( (  H|C '"` <$ 0 C ^ ( 6 ( 6d,@~ "`*,$ 0 ASiendo:xZb ( c :AUNNE-color ( BC  :UNNE  ( BC@~@~ "`z,$ 0 GEquilibrio Mecnico$  ( >AL Y  ??#" `?:]8  $D 0  ( 0 C %  ,$   0 k1: parmetro de tensin efectiva para la fase agua2xZ2 ( 0(C   ,$  0 k1: parmetro de tensin efectiva para la fase aire2xZ2^ ( 6++ ( >AL Y ??#" `?7 8 $@ 0^ ( 6++ ( >AL Y ??#" `? 7 8 $@  0 ( 0įC V 8 ,$   0 [!: tasa de presin de poro de agua"xZ" ( 0C  ,$  0 [!: tasa de presin de poro de aire"xZ" ( VAL Y ??#" `? 7.8 $@ 0 ( P-u oAL Y ??#" `?) 79 8 $@  0 ( <̷C  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%%$H ( 0޽h ? 3365___PPT105.]I+jD3' C= @B D3' = @BA?%,( < +O%,( < +D2' =%(%(DJ ' =%(D<' =A@BB@BB0B%()?)?)Ds' =.;7 BBBBBMM -0.0059 0.08009 L -0.0059 -0.11551 *3>*B ppt_xB ppt_y=@0BBAApBBBȽ<*(%DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*(%D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*(%D' =-g6B fade*<3<*(%D' =1:Bhidden*o3>+B#style.visibility<*(%%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D'  =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*(D'  =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*(D'  =-g6B fade*<3<*(D' =%( D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =-o6Bdissolve*<3<* (DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* (D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* (D' =-g6B fade*<3<* (D' =%( D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =%( D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* (D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* (Dn' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-6B#slide(fromRight)*<3<*(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(++0+(0 ++0+(0 ++0+ (0 ++0+(0 ++0+(0 ++0+(0 ++0+(0 ++0+(0 +0} 0 " ,(  ,^ , 6 , <D@~@~ "`% ,$  0 'El flujo de agua en suelos saturados y no saturados puede describirse mediante una combinacin de la Ley de Darcy y de la de conservacin de la masa de fluido, dando como resultado la siguiente ecuacin:xZl[b , c :AUNNE-color , B   :UNNE^  , 6++^  , 6++ , B ?"6@ NNN?N , >AL Y ??#" `?6 t 8 $D 0 , <HC "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%% , B8@~@~ "`z,$ 0 OModelo de Flujo. Fase Agua.$H , 0޽h ? 33  ___PPT10 .]I+2&D ' = @B D ' = @BA?%,( < +O%,( < +D ' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-o6Bdissolve*<3<*,D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*,D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*,D' =-g6B fade*<3<*,+p+0+,0 ++0+,0 +>} 0 0 (  0 (  0 0 B@~@~ "`z,$ 0 Q Fase Aire.  $ ^ 0 6S 0 <!@~@~ "`F ,$  0 IEl flujo de aire a travs de un suelo no saturado puede ser modelado usando la Ley de Fick. Para condiciones isotrmicas, y teniendo en cuenta la concentracin de aire con respecto a una unidad de volumen de suelo, se puede obtener una forma modificada de dicha ley satisfaciendo la conservacin de la masa de aire, as se tiene:JxZJVb 0 c :AUNNE-color 0 B8)  :UNNE^ 0 6++^  0 6++  0 B ?"6@ NNN?N  0 B ?"6@ NNN?N  0 >AL Y "??#" `? >o8 "$D 0 0 <@- "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%% 0 Bh0@~@~ "`z VModelo de Flujo.$ G H 0 0޽h ? 33  ___PPT10 .]I+U$D ' 1= @B D ' = @BA?%,( < +O%,( < +D ' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-o6Bdissolve*<3<*0D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*0D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*0D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* 0%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* 0D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* 0D' =-g6B fade*<3<* 0+p+0+00 ++0+00 +R} 0    4 (  4^ 4 6  4 <d>@~@~ "`% ,$  0 [Para establecer las relaciones dVw/dt y las variables primarias de fluido (Khalili 1995) se considera un volumen representativo de medio poroso no saturado sujeto a las siguientes condiciones: 8xZ! >&pb 4 c :AUNNE-color 4 B0D  :UNNE^ 4 6++^ 4 6++  4 B ?"6@ NNN?N  4 B ?"6@ NNN?N  4 <H "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%%  4 BK@~@~ "`z,$ 0 [Deformacin del poro.$ G  4 VA L Y?fig21tesispablo"`% ,$D 0 4 <`Q@~@~ "` C,$ 0 ;1) Correspondiente a una presin isotrpica externa de ds, una presin interna de agua dpw, y una presin interna de aire dpg. lxZ8  " ,!  GH 4 0޽h ? 33___PPT10.]I+D' ^= @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* 4%(D' =-o6Bdissolve*<3<* 4DS' =%(D' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4Dt' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*4D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*4DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*4D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*4D' =-g6B fade*<3<*4++0+40 ++0+ 40 ++0+40 +} 0    < (  <^ < 6 < <h@~@~ "`%  [Para establecer las relaciones dVw/dt y las variables primarias de fluido (Khalili 1995) se considera un volumen representativo de medio poroso no saturado sujeto a las siguientes condiciones: 8xZ! >&pb < c :AUNNE-color < BK4  :UNNE^ < 6++^ < 6++ < B ?"6@ NNN?N  < B ?"6@ NNN?N  < <p "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%%  < B@t@~@~ "`z [Deformacin del poro.$ G ?  < <y@~@~ "` C,$ 0 =2) Se refiere a presiones externas e internas iguales a dpw. 8>xZ:  < VA  L Y?fig22tesispablo"` &,$D 0H < 0޽h ? 33 ~ ___PPT10^ .]I+kn/D ' = @B D ' = @BA?%,( < +O%,( < +D' =%(%(Dt' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* <%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* <D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* <DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*<D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*<D' =-g6B fade*<3<*<+8+0+ <0 +} 0 '   @ (  @^ @ 6 @ <C@~@~ "`%  [Para establecer las relaciones dVw/dt y las variables primarias de fluido (Khalili 1995) se considera un volumen representativo de medio poroso no saturado sujeto a las siguientes condiciones: 8xZ! >&pb @ c :AUNNE-color @ BC  :UNNE^ @ 6++^ @ 6++ @ B ?"6@ NNN?N  @ B ?"6@ NNN?N  @ <` "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%%  @ Bĥ@~@~ "`z [Deformacin del poro.$ G o  @ <@~@~ "` &,$ 0 m3) Correspondiente a una presin externa y del poro de aire iguales a dpw, y presin del agua igual a cero. 8nxZH % @ VA  L Y?fig23tesispablo"` &,$D 0H @ 0޽h ? 33 ~ ___PPT10^ .]I+!,bD ' = @B D ' = @BA?%,( < +O%,( < +D' =%(%(Dt' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* @%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* @D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* @DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*@D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*@D' =-g6B fade*<3<*@+8+0+ @0 +#} 0   H! (  H^ H 67 H <$@~@~ "`,$  0 OPara extender este razonamiento a la fase aire, se agregan dos nuevos estados: PxZPb H c :AUNNE-color H Bȼ  :UNNE^ H 6++^ H 6++ H B ?"6@ NNN?N  H B ?"6@ NNN?N  H <P4 "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%%  H B@~@~ "`z [Deformacin del poro.$ G >  H <Ɓ@~@~ "`& ,$ 0 <4) Se refiere a presiones externas e internas iguales a dpg.8=xZ:  H VA  L Y?fig24tesispablo"` dq ,$D 0i H <xЁ@~@~ "`) &,$ 0 g5) Corresponde a una presin externa y del poro de agua iguales a dpg, y presin del aire igual a cero.8hxZD # H VA  L Y?fig25tesispablo"`V 9,$D 0H H 0޽h ? 33___PPT10u.]I+HD' Ձ= @B D\' = @BA?%,( < +O%,( < +D' =%(%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*HD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*HDt' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* H%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* HD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* HDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =-g6B fade*<3<*HDt' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*HD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*HDI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*HD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*HD' =-g6B fade*<3<*H++0+H0 ++0+ H0 ++0+H0 +} 0    DR (  D^ D 6% D <߁@~@~ "`X ,$  0 w A partir de este anlisis, y luego de aplicar el teorema de reciprocidad a los casos [(1) - (2)], [(1) - (3)], y [(2) - (3)], (Khalili y Khabbaz, 1995), primero y luego entre los casos [(1) - (4)], [(1) - (5)], y [(4) - (5)] , se obtienen las siguientes relaciones: xZ ,zb D c :AUNNE-color D B  :UNNE^ D 6++^ D 6++ D B ?"6@ NNN?N  D B ?"6@ NNN?N  D <  "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%%  D B@~@~ "`z [Deformacin del poro.$ G  D B ?"6@ NNN?NPP D B ?"6@ NNN?Nbb D >A L Y )??#" `?0 l8 )$D 0 D < @~@~ "`,$  0 @Donde xZ D B ?"6@ NNN?N.. D >AL Y ,??#" `?=8 ,$D 0H D 0޽h ? 33___PPT10b.]I+367D' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*DD' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*DD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DD' =-g6B fade*<3<*DDl' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-}6B!slide(fromLeft)*<3<*DD' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*DD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D+p+0+D0 ++0+D0 +0} 0 0 L (  L^ L 6u L <]@~@~ "`@,$  0 Trabajando algebraicamente y ordenando las ecuaciones que gobiernan la consolidacin no saturada, resulta el siguiente sistema de ecuaciones:xZb L c :AUNNE-color L B`  :UNNE^ L 6++^ L 6++ L B ?"6@ NNN?N  L B ?"6@ NNN?N  L B ?"6@ NNN?NPP  L B ?"6@ NNN?Nbb L B ?"6@ NNN?N.. L B ?"6@ NNN?N L 8AL Y 3??#" `?p7 8 3$D 0 L B ?"6@ NNN?N L 8AL Y 5??#" `?c 7i 8 5$D 0 L B ?"6@ NNN?N L 8AL Y 7??#" `? 7V8 7$D 0 L <h "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%% L BHl@~@~ "`j,$ 0 j$Consolidacin de suelos no saturados%%$ G H L 0޽h ? 33___PPT10.]I+³D ' n= @B D ' = @BA?%,( < +O%,( < +D ' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bdissolve*<3<*LD#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*LD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*LD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =%( D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*L%(+p+0+L0 ++0+L0 +"} 0 ph@ &P(  P^ P 6b P c :AUNNE-color P B|  :UNNE^ P 6++^ P 6++ P B ?"6@ NNN?N  P B ?"6@ NNN?N  P B ?"6@ NNN?NPP  P B ?"6@ NNN?Nbb  P B ?"6@ NNN?N.. P B ?"6@ NNN?N P B ?"6@ NNN?N P B ?"6@ NNN?N P <@~@~ "`/l,$  0 @Donde xZ P B ?"6@ NNN?N(( P >AL Y C??#" `?G8 C$D 0 P >AL Y A??#" `?PGQ8 A$D 0 P B ?"6@ NNN?N P 8AL Y E??#" `?G# 8 E$D 0 P B ?"6@ NNN?N P 8AL Y G??#" `? G5- 8 G$D 0  P B ?"6@ NNN?N P >AL Y J??#" `?V G{8 J$D 0 !P >AL Y M??#" `?G8 M$D 0 %P < "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%% &P B(@~@~ "`j j$Consolidacin de suelos no saturados%%$ G H P 0޽h ? 33___PPT10.]I+ޖ<:D' = @B D?' = @BA?%,( < +O%,( < +Dv' =%(%(D' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-}6B!slide(fromLeft)*<3<*PD' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =%( D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =%( D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*!P%(+8+0+P0 +9} 0 P ##Tl(  T^ T 6b T c :AUNNE-color T B8  :UNNE^ T 6++^ T 6++ T B ?"6@ NNN?N T B ?"6@ NNN?N  T B ?"6@ NNN?NPP  T B ?"6@ NNN?Nbb  T B ?"6@ NNN?N..  T B ?"6@ NNN?N  T B ?"6@ NNN?N T B ?"6@ NNN?N T <@~@~ "`/l @Donde xZ T B ?"6@ NNN?N(( T >AL Y O??#" `?G O T >AL Y P??#" `?PGQ P T B ?"6@ NNN?N T B ?"6@ NNN?N T B ?"6@ NNN?N8 G# TG# T 8AL Y Q??#" `?G#  Q T 8AL Y R??#" `?G 5-  R T >AL Y S??#" `?GV { S T >AL Y T??#" `?G T T < "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%% T B|@~@~ "`j/ j$Consolidacin de suelos no saturados%%$ G  T <t@~@~ "` ,$ 0 @Donde xZ T B ?"6@ NNN?N T 8AL Y Y??#" `? Gy8 Y$D 0 !T B ?"6@ NNN?N  T 8AL Y [??#" `? 8 [$D  0 #T B ?"6@ NNN?N "T >AL Y ]??#" `? 8 ]$D  0H T 0޽h ? 33""___PPT10b".]I+ED!' = @B D!' = @BA?%,( < +O%,( < +D ' =%(%(D' =%(D' =A@BBBB0B%(D' =+4 8?`CB ppt_xBCB0-ppt_w/2B*Y3>B ppt_x<*TD ' =+4 8?XCB ppt_yBCB ppt_yB*Y3>B ppt_y<*TD' =1:Bhidden*o3>+B#style.visibility<*T%(D ' =%(D' =4@BBBB%(D' =+4 8?`CB ppt_xBCB0-ppt_w/2B*Y3>B ppt_x<*TD ' =+4 8?XCB ppt_yBCB ppt_yB*Y3>B ppt_y<*TD' =1:Bhidden*o3>+B#style.visibility<*T%(D ' =%(D' =4@BBBB%(D' =+4 8?`CB ppt_xBCB0-ppt_w/2B*Y3>B ppt_x<*TD ' =+4 8?XCB ppt_yBCB ppt_yB*Y3>B ppt_y<*TD' =1:Bhidden*o3>+B#style.visibility<*T%(D' =%(DP' =4@BBBB%())D' =0l9 BBBB*<3<*TD7' =4@BB@BB%())D' =.S7 BBBBBeM -2.77778E-7 -1.50289E-6 L -2.77778E-7 -0.26081 *3>*B ppt_xB ppt_y=@0BBAApBBBʈ<*TD#' =%( D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*TD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*TD' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*TD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*TD' =-g6B fade*<3<*TD' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* TD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* TD' =-g6B fade*<3<* TD' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*"T%(D' =-o6Bdissolve*<3<*"T+p+0+T0 ++0+T0 +(} 0 80` Y(  X^ X 6b X c :AUNNE-color X Bŝ  :UNNE^ X 6++^ X 6++ X B ?"6@ NNN?N X B ?"6@ NNN?N  X B ?"6@ NNN?NPP  X B ?"6@ NNN?Nbb  X B ?"6@ NNN?N..  X B ?"6@ NNN?N  X B ?"6@ NNN?N X B ?"6@ NNN?N X <_4@~@~ "`/},$  0 De esta manera se obtiene un sistema de ecuaciones acoplado no simtrico que permite modelar el comportamiento del suelo no saturado ante el fenmeno de consolidacin.xZ X B ?"6@ NNN?N X B ?"6@ NNN?N X B ?"6@ NNN?N X <\Н "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%% X Bӝ@~@~ "`j/ j$Consolidacin de suelos no saturados%%$ G O Y <ٝ@~@~ "`},$  0 Sin embargo, en ciertos casos la variacin de la saturacin con la succin, dSw/dpc, pierde importancia, con lo que el sistema de ecuaciones anterior se torna simtrico (haciendo dSw/dpc = 0)xZN  b  8! ,+d H X 0޽h ? 33  ___PPT10p .]I+$ƼD ' = @B D ' = @BA?%,( < +O%,( < +D' =%(%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*XD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*XD#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Y%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*YD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*Y+p+0+X0 ++0+Y0 +n%} 0 p !"\(  \^ \ 6b \ c :AUNNE-color \ B,b4  :UNNE^ \ 6++^ \ 6++ \ B ?"6@ NNN?N \ B ?"6@ NNN?N  \ B ?"6@ NNN?NPP  \ B ?"6@ NNN?Nbb  \ B ?"6@ NNN?N..  \ B ?"6@ NNN?N  \ B ?"6@ NNN?N \ B ?"6@ NNN?N \ B ?"6@ NNN?N \ B ?"6@ NNN?N \ B ?"6@ NNN?N \ <| "`  V$ECUACIONES QUE GOBIERNAN EL PROBLEMA%% \ B@~@~ "`j/ j$Consolidacin de suelos no saturados%%$ G z .$= \ }q(,$@ 0HB \ C Dy#0y#E9b b,$; \ #" .$=HB \ C D-$--$I/HB \ C Dy#-$-HB \ C Dy#I/$I/HB \ C Dy#7$7HB \ C Dy#9$9HB \ C D-$7-$9 \ s x AN ),0""}*vW W-AATWT06J8;}>W?CWHH!L*M(O(P(4Q/4Q/O-YN*MT!LRHpRO?*55E10"`b,"; \ <@~@~ "`} Sin embargo, en ciertos casos la variacin de la saturacin con la succin, dSw/dpc, pierde importancia, con lo que el sistema de ecuaciones anterior se torna simtrico (haciendo dSw/dpc = 0)xZN  b  8! ,+d    \ H "`2,$ 0 PFormulacin SimtricaxZ  !\ H, "`,$ 0 PFormulacin SimtricaxZ  "\ H< "`6 9 ,$ 0 RFormulacin No SimtricaxZH \ 0޽h ? 33___PPT10_.]I+Z8DS ' = @B D ' = @BA?%,( < +O%,( < +DE ' =%(%(D ' =%(D' =A@BB@BB0B%()?)?Da' =.)7 BBBBB;M 0 -4.33526E-6 L 0 -0.1415 *3>*B ppt_xB ppt_y=@0BBAApBBB"搽<*\DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-6B%slide(fromBottom)*<3<*\DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* \%(D' =-6B%slide(fromBottom)*<3<* \DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"\%(D' =-6B%slide(fromBottom)*<3<*"\DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!\%(D' =-6B%slide(fromBottom)*<3<*!\++0+\0 ++0+ \0 ++0+!\0 ++0+"\0 +!} 0 F> %`(  `^ ` 6b ` c :AUNNE-color ` B'  :UNNE^ ` 6++^ ` 6++ ` B ?"6@ NNN?N ` B ?"6@ NNN?N  ` B ?"6@ NNN?NPP  ` B ?"6@ NNN?Nbb  ` B ?"6@ NNN?N..  ` B ?"6@ NNN?N  ` B ?"6@ NNN?N ` B ?"6@ NNN?N ` B ?"6@ NNN?N ` B ?"6@ NNN?N ` B ?"6@ NNN?N ` </@~@~ "`},$  0 El ejemplo consiste modelar, mediante las formulaciones simtrica y no simtrica, una masa de suelo de 10m x 10m sometida a las cargas de una fundacin superficial. xZ "` N1 'Z1<$ 0   $` C $A! 1fig1} W,$D 0 %` <3@~@~ "`P ,$ 0 La discretizacin se realiz mediante elementos fintos serendiptos de 8 nodos, haciendo una mayor concentracin de elementos en la cercana de las cargas.xZ> YH ` 0޽h ? 33___PPT10.]I+>D' == @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"`%(D' =-o6Bdissolve*<3<*"`D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*`D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*`D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%`%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*%`D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*%`D' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*$`%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*$`D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*$`D' =-g6B fade*<3<*$`++0+`0 ++0+"`0 ++0+%`0 +'4} 0  dI(  d^ d 6b d c :AUNNE-color d BI  :UNNE^ d 6++^ d 6++ d B ?"6@ NNN?N d B ?"6@ NNN?N  d B ?"6@ NNN?NPP  d B ?"6@ NNN?N..  d B ?"6@ NNN?N  d B ?"6@ NNN?N d B ?"6@ NNN?N d B ?"6@ NNN?N d B ?"6@ NNN?N d B ?"6@ NNN?N d N i4 ' 4  d HA h??"6@`NNN?NM 8 h$ 0O d <TP@~@~ "` ,$ 0 gA continuacin se presentan los resultados de presin de poro de agua y descenso correspondientes al nodo 330 para las formulaciones simtricas y no simtricas, pudiendo observarse que para valores extremos de saturacin la diferencia entre ambas formulaciones se minimiza, lo cual justifica la utilizacin del modelo simtrico simplificado para dichos casos.hxZh d <TR "`7,$ 0 FRESULTADOS NUMRICOS d HA i??"6@`NNN?NM8 i$  0H d 0޽h ? 33$$___PPT10#.]I+FA>D"' _= @B D!' = @BA?%,( < +O%,( < +D@' =%(%(D( ' =%(D' =A@BB@BB0B%()?)?Da' =.)7 BBBBB;M 0 -4.9711E-6 L 0 -0.17618 *3>*B ppt_xB ppt_y=@0BBAApBBBi<*dDV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*dD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*dD' =-g6B fade*<3<*dDP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*dD' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*dD' =-g6B fade*<3<*dD' =1:Bhidden*o3>+B#style.visibility<*d%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-o6Bdissolve*<3<*dD^ ' =%(D ' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*dD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*dD' =-g6B fade*<3<*dDP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*dD' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*dD' =-g6B fade*<3<*dD' =1:Bhidden*o3>+B#style.visibility<*d%(D^ ' =%(D ' =%(DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*dD' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*dD' =-g6B fade*<3<*dD' =1:Bhidden*o3>+B#style.visibility<*d%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*dD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*dD' =-g6B fade*<3<*d++0+d0 ++0+d0 ++(+d 0+a+(+d 0+b+0+d0 ++0+d0 ++0+d0 ++(+d 0+dM} 0   h (  h^ h 6b h c :AUNNE-color h Bo  :UNNE^ h 6++^ h 6++ h B ?"6@ NNN?N h B ?"6@ NNN?N  h B ?"6@ NNN?NPP  h B ?"6@ NNN?N..  h B ?"6@ NNN?N  h B ?"6@ NNN?N  h B ?"6@ NNN?N h B ?"6@ NNN?N h B ?"6@ NNN?NW h <Lv@~@~ "`M@,$  0 oA continuacin, se muestra la evolucin de la disipacin de presiones de poro en la masa del suelo no saturado.pxZp h <z "`7 FRESULTADOS NUMRICOS h 3 A"qx $ 0 0 0H h 0޽h ? 33  ___PPT10 .]I+GD` ' ~= @B D ' = @BA?%,( < +O%,( < +DD ' =%(%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*hD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*hD' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*h%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*hD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*hD' =-g6B fade*<3<*hD'  = B`B?<*h%(/%,( < +/%,( < +)?+8+0+h0 +b} 0   t (  t^ t 6b t c :AUNNE-color t B  :UNNE^ t 6++^ t 6++ t B ?"6@ NNN?N t B ?"6@ NNN?N  t B ?"6@ NNN?N..  t B ?"6@ NNN?N  t B ?"6@ NNN?N  t B ?"6@ NNN?N t B ?"6@ NNN?N t B ?"6@ NNN?N t <@~@~ "`M@,$  0 n4Desplazamiento vertical de la fase slida del suelo.5xZ5 t <o4 "`7 FRESULTADOS NUMRICOS t 3 A"x $ 0 0 0H t 0޽h ? 33  ___PPT10 .]I+aD` ' = @B D ' = @BA?%,( < +O%,( < +DD ' =%(%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*tD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*tD' =%(DI' =4@BB5BB%(D' =1:Bvisible*o3>+B#style.visibility<*t%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*tD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*tD' =-g6B fade*<3<*tD'  = B`B?<*t%(/%,( < +/%,( < +)?+8+0+t0 +} 0  l(  l^ l 6b l c :AUNNE-color l BԖ  :UNNE^ l 6++^ l 6++ l B ?"6@ NNN?N l B ?"6@ NNN?N  l B ?"6@ NNN?NPP  l B ?"6@ NNN?Nbb  l B ?"6@ NNN?N..  l B ?"6@ NNN?N  l B ?"6@ NNN?N l B ?"6@ NNN?N l B ?"6@ NNN?N l B ?"6@ NNN?N l B ?"6@ NNN?N l <H@~@~ "`p$ 0<4___PPT9  Se ha presentado un modelo matemtico para la simulacin del proceso de consolidacin de suelos no saturados basado en el comportamiento bsico del suelo no saturado. Se amplan trabajos anteriores,3,4 mediante el agregado de su interaccin con otros mtodos y la consideracin de la variacin de la saturacin con relacin a la succin. Se han establecido puntos de contacto entre el modelo aqu presentado y las formulaciones basadas en ecuaciones de conservacin,1,2,5 de amplia aplicacin a problemas ms complejos. Mediante la formulacin desarrollada es posible recomendar lmites de aplicabilidad de los modelos con matrices simtricas3 y condiciones en las que formulaciones ms complejas y generales con matrices no simtricas, deben ser usadas. x " ZxZ    q0T , , l N 'Z1<$ 0  H l 0޽h ? 332*___PPT10 .]I+sjDn' = @B D)' = @BA?%,( < +O%,( < +D` ' =%(%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-o6Bdissolve*<3<*lDH ' =%(Dv' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*l%(D' =-u6Bwipe(right)*<3<*lDv' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*lT%(D' =-u6Bwipe(right)*<3<*lTDv' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*lT %(D' =-u6Bwipe(right)*<3<*lT Dv' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*l %(D' =-u6Bwipe(right)*<3<*l +p+0+l0 ++0+l0 +Y} 0 44 p64(  p^ p 6b p c :AUNNE-color p B,u4  :UNNE^ p 6++^ p 6++ p B ?"6@ NNN?N p B ?"6@ NNN?N  p B ?"6@ NNN?NPP  p B ?"6@ NNN?Nbb  p B ?"6@ NNN?N..  p B ?"6@ NNN?N  p B ?"6@ NNN?N p B ?"6@ NNN?N p B ?"6@ NNN?N p B ?"6@ NNN?N p B ?"6@ NNN?N p N 'Z1<$ 0   p <@~@~ "`p$  0<4___PPT9  [1] R.W. Lewis and B.A. Schrefler. The Finite Element Method in the Deformation and Consolidation of Porous Media. John Wiley and Sons, (1987). [2] D. Gawin, P. Baggio, and B.A. Schrefler. Coupled heat, water and gas flow in deformable porous media. Int. Journal for numerical methods in fluids. John Wiley and Sons, 20, 969 987 (1995). [3] N. Khalili and M.H. Khabbaz. On the theory of three-dimensional consolidation in unsaturated soils. Unsaturated soils. Alonso and Delage (eds), pages 745 750 (1995). [4] N. Khalili and B. Loret. An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation. International Journal of solid and structures. Pergamon., (2001). [5] E.E. Alonso, A. Lloret, J. Delahaye, A. Gens, and G. Volckaert. Coupled analysis of backfill hydration test. International Journal for numerical and analytical methods in Geomechanics, 22, 1 27 (1998). [6] H.A. Di Rado, A.M. Awruch, and P.A. Beneyto. Consolidation in saturated porous media. implementation and numerical problems. Computational Mechanics. New Trends and Applications. International Center for Numerical Methods in Engineering (CIMNE) and Fourth World Congress on Computational Mechanics. Buenos Aires. Argentina., (1998). [7] P.A. Beneyto, H.A. Di Rado, A.M. Awruch, and J.E. Manzolillo. Anlisis de fundaciones directas usando el mtodo de los elementos finitos. Centro de Informacin Tecnolgica (CIT), (1999). [8] O.C. Zienkiewicz and R.L. Taylor. The finite element method, volume II. McGraw Hill, (1991).$x " Zp                                    (    p <H@~@~ "`xD<4___PPT9 8$x " Zr p <8@~@~ "`r$  0>6___PPT9 ~J[9] J.H. Atkinson and P.L. Bransby. The mechanics of soils. An introduction to critical state soil mechanics. University Series in Civil Engineering. McGraw Hill, (1978). [10] D.G. Fredlund and Rahardjo H. Soils Mechanics for unsaturated soils. Wiley and Sons Inc., (1993). [11] T.W. Lambe and R.V. Whitman. Soil Mechanics. John Wiley and Sons, (1979). [12] S. Idelsohn and E. Onate. Finite element and finite volumes. two good friends. Int. J. Num. Meth. Engng., 37, 3323 3341 (1994). [13] S.L. Barbour. The soil-water characteristic curve: a historical perspective. Canadian Geotechnical Journal, 35, 873 894 (1998). [14] M. A. Biot. General theory of three - dimensional consolidation. Journal of Applied Physics, (1941). [15] D.G. Fredlund and A. Xing. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, 31, 521 532 (1994). [16] H.A. Di Rado, P.A. Beneyto, J.L. Mroginski, J.E. Manzolillo, and A.M. Awruch. Anlisis tridimensional de la consolidacin de suelos saturados utilizando el mef. Mecnica Computacional, 23 (2004).$&x " Z&           !      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MroginskiJavier L. MroginskiRoot EntrydO) _lPicturesCurrent UserbSummaryInformation(2TU      !"#$%&'()*+,-./013456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\^_`abcdw._Facultad de IngenieriaFacultad de Ingenieria  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./013456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\^_`abcdfghijklwRoot EntrydO)PicturesCurrent UsereSummaryInformation(2TUPowerPoint Document(T+DocumentSummaryInformation8]