Numerical Modelling of Deformation of Soil Foundations - Science Direct

Available online at www.sciencedirect.com

ScienceDirect Procedia Earth and Planetary Science 15 (2015) 119 – 124

:RUOG0XOWLGLVFLSOLQDU\(DUWK6FLHQFHV6\PSRVLXP:0(66

1XPHULFDO0RGHOOLQJRI'HIRUPDWLRQRI6RLO)RXQGDWLRQV a

6XOWDQRY/8D 

Kazan Federal University, 18 Kremlevskaya Str., Kazan, building #06, Kazan

$EVWUDFW 7KHDOJRULWKPIRULQYHVWLJDWLRQRIVRLOIRXQGDWLRQVXQGHULWVRZQZHLJKWDQGVXUIDFHORDGLQJLVFRQVLGHUHG$VRLOLVSUHVHQWHG DVDFRQWLQXRXVPHGLXPZKLFKKDVVSHFLILFSK\VLFDODQGPHFKDQLFDOSURSHUWLHV6WUXFWXUDOO\WKHUHDUHWKUHHJURXSVRIVRLOVWKH ILUVW±VDQGWKHVHFRQG±FOD\DQGWKHWKLUG±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‹7KH$XWKRUV3XEOLVKHGE\(OVHYLHU%9 © 2015 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKHRUJDQL]LQJFRPPLWWHHRI:0(66 (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibilty of the Organizing Commitee of WMESS 2015. Keywords:IRXQGDWLRQSODVWLFGHIRUPDWLRQILQLWHHOHPHQWPHWKRG

,QWURGXFWLRQ ,Q WKLV SDSHU WKH SUREOHP RI ODUJH HODVWLFSODVWLF GHIRUPDWLRQV RI VRLO IRXQGDWLRQ LV VROYHG QXPHULFDOO\ ,QYHVWLJDWLRQRIQRQOLQHDUGHIRUPDWLRQVDQGWKHGHYHORSPHQWRIYDULRXVPHWKRGVRIFDOFXODWLQJUHDOVWUXFWXUHVDUH IUHTXHQWO\ SUHVHQWHG LQ OLWHUDWXUH %DGULHY DQG %DQGHURY D E %DGULHY  %DGULHY HW DO  



&RUUHVSRQGLQJDXWKRU7HOID[ E-mail address:/HQDU6XOWDQRY#NSIXUX

1878-5220 © 2015 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibilty of the Organizing Commitee of WMESS 2015. doi:10.1016/j.proeps.2015.08.029

120

L.U. Sultanov et al. / Procedia Earth and Planetary Science 15 (2015) 119 – 124

%HUH]KQRL DQG 3DLPXVKLQ  %HUH]KQRL HW DO   $ VRLO IRXQGDWLRQ LV SUHVHQWHG DV FRQWLQXRXV PHGLXP %RQHWDQG:RRG7D\ORUDQG%HFNHU .LQHPDWLFVRIDPHGLXPLVGHVFULEHGE\WKHGHIRUPDWLRQUDWH WHQVRUWKHVWUHVVVWDWHLVGHWHUPLQHGE\WKH&DXFK\VWUHVVWHQVRU%RQHWDQG:RRG 6FKU|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± XQLW YHFWRU RI JOREDO &DUWHVLDQ FRRUGLQDWH V\VWHP GHVFULELQJ ZKLFK SURFHVV RI GHIRUPDWLRQ LV LQYHVWLJDWHG ILJ 

[

j

U [

 ± PDWHULDO/DJUDQJLDQ FRRUGLQDWHV

5 [ j

j

x i [

j

H  ± SRVLWLRQYHFWRURIDPDWHULDOSRLQWLQUHIHUHQFHVWDWH y [ H  ± SRVLWLRQYHFWRURIDPDWHULDOSRLQWLQFXUUHQWVWDWH i

j

i

i

i

w y  ± FKDQJLQJRIYROXPH w xj   ± YHORFLW\YHFWRU Y vi Hi y iHi 5 J

GHW



3URFHVV RI GHIRUPDWLRQ LV UHSUHVHQWHG DV D IORZ RI FRQWLQXD ZLWK HODVWRSODVWLF SURSHUWLHV 7KHUHIRUH IROORZLQJ WHQVRUVKDYHWREHFRQVLGHUHG'DY\GRY6XOWDQRYDE 

K

wvi Hi H j wy j

G

 ªK  KT ¼º ¬ 

Ȧ

hij Hi H j  ± VSDWLDOJUDGLHQWRIUDWHWHQVRU

 § wv i wv j ·  ¨ ¸ Hi H j d ij Hi H j  ± GHIRUPDWLRQUDWHWHQVRU  © wy j wy i ¹   § wv i wv j · ª¬K  KT º¼  ¨ ¸ Hi H j Zij Hi H j  ± UDWHRIURWDWLRQWHQVRU   © wy j wy i ¹



ɏl

ɏ0 ʇ

ʇ

ʇ1

ʇ

M0

ʇ1 M

X

U

H 

H 

ʇ

5

H 

)LJ5HIHUHQFHDQGFXUUHQWVWDWHV



121

L.U. Sultanov et al. / Procedia Earth and Planetary Science 15 (2015) 119 – 124

 6WUHVV6WUDLQ5HODWLRQVKLS  7KHVWDWHRIDVWUHVVLQDERG\LVGHILQHGE\&DXFK\VWUHVVWHQVRU Ȉ

V Hi H j 6XOWDQRY6XOWDQRYDQG ij

J

'DY\GRY $OVRZHXVHREMHFWLYH-DXPDQQUDWHRI&DXFK\VWUHVV Ȉ *RORYDQRYDQG6XOWDQRY  

ȈJ



  Ȧ ˜ Ȉ  Ȉ ˜ Ȧ Ȉ 













 

 LVWKHUDWHRI&DXFK\VWUHVV ZKHUH Ȉ &RQVLGHU LVRWURSLF PDWHULDO DQG GHQRWH *RORYDQRY DQG 6XOWDQRY  *RORYDQRY DQG 6XOWDQRY  

d

dii   V J

V iiJ   dijc

dij  G ij d  V ijcJ

V ijJ  G ijV J ZKHUH Gij LV.URQHFNHUGHOWD

:HDGRSWDQDGGLWLYHVSOLWRIWKHGHIRUPDWLRQRIUDWHLQWRHODVWLFGHIRUPDWLRQRIUDWHDQGSODVWLFGHIRUPDWLRQRIUDWH *RORYDQRYDQG6XOWDQRY*RORYDQRYDQG6XOWDQRY  G 6WUHVVVWUDLQUHODWLRQVKLSIRUHODVWLFGHIRUPDWLRQLVZULWWHQDV

ȈcJ



E K    P

ZKHUH G

GGcH  ȈJ

KG 





GH  GS 











 

E  E ± l Ȉ  G l G  l 4 ˜ G l Y@d :  ³³ l 3 ˜ G l YdS ¾ 't   ³³³ l Ȉ wm ˜G l Gd :  :l SlV ¯° :l ¿° 

 m  w

l

Ȉc

m 



 

 cm mLVWKHQXPEHURILWHUDWLRQlLVWKHQXPEHURIVWHS Ȉ

7KHQXPHULFDOLPSOHPHQWDWLRQLVEDVHGRQWKHILQLWHHOHPHQWPHWKRG$QQRGHEULFNHOHPHQWLVXVHG*RORYDQRY DQG6XOWDQRYD   1XPHULFDOUHVXOWV  7KHSUREOHPRISODQHGHIRUPDWLRQRIVRLOIRXQGDWLRQVXQGHULWVRZQZHLJKWDQGVXUIDFHORDGLQJLVFRQVLGHUHG7KH ERWWRP IDFH KDV QR YHUWLFDO GLVSODFHPHQW DQG ODWHUDO ± KRUL]RQWDO )LJ   ȿ= MPa P= ɋ  KPa M q GHQVLW\ U  NJ/m3 DQG ORDGLQJ q   MPa )LJ GLVSOD\V WKH YHUWLFDO GLVSODFHPHQW RI VRLO IRXQGDWLRQVXQGHULWVRZQZHLJKWDQGORDGLQJ)LJ±HTXLYDOHQWVWUHVV)LJ±HTXLYDOHQWSODVWLFGHIRUPDWXLRQ

)LJ9HUWLFDOGLVSODFHPHQWRIVRLOIRXQGDWLRQV



123

L.U. Sultanov et al. / Procedia Earth and Planetary Science 15 (2015) 119 – 124

)LJ9HUWLFDOGLVSODFHPHQWRIVRLOIRXQGDWLRQV

 )LJ(TXLYDOHQWVWUHVV

)LJ(TXLYDOHQWSODVWLFGHIRUPDWLRQ







&RQFOXVLRQV  ȺPHWKRGRIQXPHULFDOLQYHVWLJDWLRQRIHODVWLFSODVWLFVRLOZLWKILQLWHGHIRUPDWLRQVLVFRQVLGHUHG)RUSODVWLFLW\WKH 'UXFNHU3UDJHUFULWHULRQLVDSSOLHG,QFUHPHQWDOORDGLQJSURFHGXUHLVXVHGZKHUHDOORZLQJWKHYDULDWLRQHTXDWLRQ LVGHULYHGIURPWKHSULQFLSOHRIYLUWXDOZRUNLQWKHFXUUHQWFRQILJXUDWLRQ)RUWKHVLPXODWLRQRISODVWLFGHIRUPDWLRQ WKHUDGLDOUHWXUQPHWKRGZLWKLWHUDWLYHUHILQHPHQWRIWKHFXUUHQWVWUHVVVWUDLQVWDWHLVDSSOLHG  $FNQRZOHGJHPHQW  7KHUHSRUWHGVWXG\ZDVVXSSRUWHGE\5)%5UHVHDUFKSURMHFW1R  

124

L.U. Sultanov et al. / Procedia Earth and Planetary Science 15 (2015) 119 – 124

5HIHUHQFHV                    

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|GHU-*UXWWPDQQ)/|EOHLQ-&RPSXWDWLRQDO0HFKDQLFV 6XOWDQRY / 'DY\GRY 5  7KH DOJRULWKP RI VROYLQJ WKH SUREOHP RI ODUJH HODVWLFSODVWLF GHIRUPDWLRQ E\ )(0 $SSOLHG 0HFKDQLFVDQG0DWHULDOV 6XOWDQRY/80DWKHPDWLFDOPRGHOLQJRIGHIRUPDWLRQVRIK\SHUHODVWLFVROLGV$SSOLHG0DWKHPDWLFDO6FLHQFHV   6XOWDQRY/8'DY\GRY5/0DWKHPDWLFDOPRGHOOLQJRIODUJHHODVWLFSODVWLFGHIRUPDWLRQV$SSOLHG0DWKHPDWLFDO6FLHQFHV   7D\ORU /0 %HFNHU (%  6RPH FRPSXWDWLRQDO DVSHFW RI ODUJH GHIRUPDWLRQ UDWHGHSHQGHQW SODVWLFLW\ SUREOHPV &RPSXW 0HWK$SSO0HFK(QJ 33