- Email: [email protected]
Experimental Investigation of Strength Anisotropy of Varved Clay
Available online at www.sciencedirect.com
ScienceDirect Procedia Earth and Planetary Science 15 (2015) 732 – 737
:RUOG0XOWLGLVFLSOLQDU\(DUWK6FLHQFHV6\PSRVLXP:0(66
([SHULPHQWDO,QYHVWLJDWLRQRI6WUHQJWK$QLVRWURS\RI9DUYHG&OD\ 0DW\OGD7DQNLHZLF]D a
Wrocáaw University of Technology, Wrocáaw, Poland
$EVWUDFW 9DUYHGFOD\LVDVHGLPHQWDU\VRLOIRUPHGLQJODFLHUODNHV,WFRQVLVWVRIWZRDOWHUQDWLQJWKLQOD\HUVZLWKGLIIHUHQWJUDQXORPHWULF FRPSRVLWLRQDQGPHFKDQLFDOSURSHUWLHV7KHUHVXOWRIOD\HUHGVWUXFWXUHLVVWUHQJWKDQLVRWURS\RIWKHPDWHULDO6XFKVRLOUHTXLUHV VSHFLDO DWWHQWLRQ DQG GHVLJQ DSSURDFK LQ JHRWHFKQLFDO HQJLQHHULQJ ,Q WKLV SDSHU WKH ILQGLQJV RI ODERUDWRU\ H[DPLQDWLRQV DUH SUHVHQWHG7KHLQYHVWLJDWLRQVDUHIRFXVHGRQYDUYHGFOD\IRXQGLQ3RODQGQHDUFLW\%HáFKDWy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© 2015 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license 7KH$XWKRUV3XEOLVKHGE\(OVHYLHU%9 (http://creativecommons.org/licenses/by-nc-nd/4.0/). 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKHRUJDQL]LQJFRPPLWWHHRI:0(66 Peer-review under responsibilty of the Organizing Commitee of WMESS 2015. Keywords:VWUHQJWKDQLVRWURS\YDUYHGFOD\WULD[LDOWHVW3DULHVDXFULWHULRQ
,QWURGXFWLRQ /D\HUHGVWUXFWXUHFRPPRQO\RFFXUULQJLQVRLOVDQGURFNVDIIHFWVVWURQJO\WRDQLVRWURS\EHKDYLRURIVXFKPDWHULDO ,W UHTXLUHV VSHFLDO DWWHQWLRQ DQG GHVLJQ DSSURDFK LQ JHRWHFKQLFDO HQJLQHHULQJ 1RZDGD\V DQLVRWURSLF FULWHULRQ LV XVXDOO\ XVHG LQ GHVLJQLQJ RI VWUXFWXUHV ORFDWHG LQ VXFK PDWHULDOV ZKHUH LGHQWLILFDWLRQ RI DQ DGHTXDWH DQLVRWURSLF
&RUUHVSRQGLQJDXWKRU7HO E-mail address:PDW\OGDWDQNLHZLF]#SZUHGXSO
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.2015.08.116
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
733
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áFKDWy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à\GĪEDDQG7DQNLHZLF]
)LJXUH,QYHVWLJDWHGPDWHULDO±YDUYHGFOD\
$VHULHVRIFRQYHQWLRQDOWULD[LDOFRPSUHVVLRQWHVWVKDYHEHHQFRQGXFWHGIRUHYDOXDWLRQRIPHFKDQLFDOEHKDYLRURI WKHPDWHULDO7KHLQYHVWLJDWLRQVKDYHEHHQPDGHDFFRUGLQJWRWKHSURFHGXUH7;&,87HVWSURFHGXUHVLQJHQHUDOKDYH IROORZHGWHFKQLTXHVSURYLGHGE\+HDG KRZHYHUWKHVDPSOHVKDYHQRWEHHQVDWXUDWHGEHIRUHWKHWHVW,QWDFW F\OLQGULFDOVSHFLPHQVZLWKPPLQGLDPHWHUDQGPPLQOHQJWKKDYHEHHQXVHG7KHFRUHVKDYHEHHQFXWRXWDW YDULRXVRULHQWDWLRQVRIODPLQDWLRQVĮUHODWLYHWRWUDQVYHUVHD[LVRIWKHVSHFLPHQLH 7KH LQYHVWLJDWLRQVKDYH EHHQ SHUIRUPHG XQGHUILYHGLIIHUHQW FRQILQLQJ SUHVVXUHV LHN3DN3DN3D N3DDQGN3D,QILUVWWZRFDVHVWKHYDOXHRILPSRVHGSUHVVXUHLVORZHUWKDQHVWLPDWHGYHUWLFDOLQVLWXVWUHVV DQGWKHVDPSOHVKDYHEHHQWHVWHGLQRYHUFRQVROLGDWLRQVWDWHRIVWUHVV7KHWRWDODPRXQWRIWHVWHGVSHFLPHQVLV 6SHFLPHQVKDYHEHHQVXEMHFWHGWRLVRWURSLFFRQVROLGDWLRQXQGHUIL[HGFRQILQHPHQWı3XQWLOWKHUHZDVQRFKDQJHLQ
734
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
YROXPH$IWHUZDUGVWKH\KDYHEHHQFRPSUHVVHGZLWKFRQVWDQWVSHHGRIPPPLQZLWKRXWDOORZLQJIRUGUDLQDJH 'XHWRWKHWHVWSURFHGXUHGLIIHUHQWGLVWULEXWLRQRISRUHZDWHUSUHVVXUHLQOD\HUVDQGYDULDEOHDUUDQJHPHQWRIYDUYHV LQHDFKVSHFLPHQWKHPHDVXUHPHQWRISRUHSUHVVXUHLVXQUHOLDEOHDQGLWKDVEHHQRPLWWHG7KHPDLQRXWFRPHVRIWKH H[DPLQDWLRQVDUHWKHGLUHFWLRQDOIDLOXUHFKDUDFWHULVWLFVSUHVHQWHGLQ)LJXUH7KH\DUHSORWWHGE\PDUNLQJWKHYDOXH RISHDNGHYLDWRULFVWUHVV(ı1- ı3)IURPHDFKWHVWLQGHSHQGHQFHWRYDOXHRIRULHQWDWLRQDQJOHĮ7KHUDQJHRIYDOXHVLV N3D IRU FRQILQHPHQW RI N3D N3D IRU N3D N3D IRU N3D N3D IRU N3D DQG N3D IRU N3D 7KH ORZHVW YDOXHV RI VWUHVVHV DUH REWDLQHG IRU RULHQWDWLRQDQJOH H[FHSWIRUFRQILQHPHQWRIN3D 7KHKLJKHVWYDOXHVDUHDFKLHYHGIRURULHQWDWLRQDQJOHV H[FHSWIRUFRQILQHPHQWRIN3D
)LJXUH5HVXOWVRIODERUDWRU\WULD[LDOWHVWVIRUYDUYHGFOD\
0DWKHPDWLFDOPRGHOOLQJ 0DQ\ UHVHDUFKHUV GHDO ZLWK PRGHOLQJ RI VWUHQJWK DQLVRWURS\ IRU YDULRXV JHRPDWHULDOV 7KH YDULRXV FULWHULD ZHUH SURSRVHGLQWHUDOLDE\+LOO 3DULVHDX 7VDLDQG:X &D]DFX 'XYHDXDQG+HQU\ 3LHWUXV]F]DNDQG0Uy] à\GĪEDDQG.DZD 7KHFULWHULRQVHOHFWHGIRUHYDOXDWLRQLQWKHSDSHULVWKH RQH SURSRVHG E\ 3DULVHDX ,W LV DQ H[WHQVLRQ RI DQLVRWURSLF +LOO¶V FULWHULRQ IRU FRKHVLRQ IULFWLRQDO PDWHULDOV ,Q JHQHUDOIRUPWKHFULWHULRQFDQEHH[SUHVVHGDVIROORZV n
AijV ij AijklV ijV kl d
ZKHUH Aij DQG Aijkl DUH DQLVRWURSLF PDWHULDO WHQVRUV ıij DQG ıkl DUH FRPSRQHQWV RI WKH VWUHVV WHQVRUV DQG n LV WKH DGGLWLRQDO PDWHULDO FRQVWDQW +RZHYHU IRU PRVW JHRPDWHULDOV WKH EHVW ILWWLQJ LV REWDLQHG IRU n ZKLFK LV DOVR DVVXPHG LQ WKH LQYHVWLJDWLRQV )RU WKH WUDQVYHUVHO\ LVRWURSLF PDWHULDO WKH PDWHULDO WHQVRUV FDQ EH SURYLGHG DV IROORZV
735
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
Aij
Aijkl
º ª U « V »» « «¬ sym V »¼ G G ª G « F G F « « F G « « « « « « « sym « « « « « « « « « «¬
M
M
M
M
F G
M
M
º » » » » » » » » » F G » » » » » » » » » F G » »¼
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Į DQG YHUWLFDO Į ODPLQDWLRQ ZLWK FRQILQLQJ SUHVVXUH ı3 WKH 3DULVHDX FULWHULRQ FDQ EH VLPSOLILHGWRWZRHTXDWLRQV G V VV V UV VV ° ® °¯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
736
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
7KHZRUNIRULGHQWLILFDWLRQRIDGHTXDWHFULWHULRQIRUWKHWHVWHGVRLOZLOOEHFRQWLQXHGLQWKHIXWXUH
)LJXUH&RPSDULVRQRIWKHWHVWUHVXOWVDQGWKHRUHWLFDOPRGHO
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
737
)LJXUH&RPSDULVRQRIWKHWHVWUHVXOWVDQGWKHRUHWLFDOPRGHOIRUFRQILQHPHQW D N3DE N3DF N3DG N3DH N3D
5HIHUHQFHV
&D]DFX2&ULVWHVFX1'6KDR-)+HQU\-3 $1HZ$QLVRWURSLF)DLOXUH&ULWHULRQIRU7UDQVYHUVDO\,VRWURSLF6ROLGV 0HFKDQLFVRI&RKHVLYH)ULFWLRQDO0DWHULDOV 'XYHDX*6KDR-)+HQU\-3 $VVHVVPHQWRI6RPH)DLOXUH&ULWHULDIRU6WURQJO\$QLVRWURSLF*HRPDWHULDOV0HFKDQLFVRI &RKHVLYH)ULFWLRQDO0DWHULDOV 'H*URRW'-/XWHQHJJHU$-&KDUDFWHUL]DWLRQE\6DPSOLQJDQG,Q6LWX7HVWLQJ±&RQQHFWLFXW9DOOH\9DUYHG&OD\6WXGLD *HRWHFKQLFDHW0HFKDQLFD 'H-RQJ-7
ScienceDirect Procedia Earth and Planetary Science 15 (2015) 732 – 737
:RUOG0XOWLGLVFLSOLQDU\(DUWK6FLHQFHV6\PSRVLXP:0(66
([SHULPHQWDO,QYHVWLJDWLRQRI6WUHQJWK$QLVRWURS\RI9DUYHG&OD\ 0DW\OGD7DQNLHZLF]D a
Wrocáaw University of Technology, Wrocáaw, Poland
$EVWUDFW 9DUYHGFOD\LVDVHGLPHQWDU\VRLOIRUPHGLQJODFLHUODNHV,WFRQVLVWVRIWZRDOWHUQDWLQJWKLQOD\HUVZLWKGLIIHUHQWJUDQXORPHWULF FRPSRVLWLRQDQGPHFKDQLFDOSURSHUWLHV7KHUHVXOWRIOD\HUHGVWUXFWXUHLVVWUHQJWKDQLVRWURS\RIWKHPDWHULDO6XFKVRLOUHTXLUHV VSHFLDO DWWHQWLRQ DQG GHVLJQ DSSURDFK LQ JHRWHFKQLFDO HQJLQHHULQJ ,Q WKLV SDSHU WKH ILQGLQJV RI ODERUDWRU\ H[DPLQDWLRQV DUH SUHVHQWHG7KHLQYHVWLJDWLRQVDUHIRFXVHGRQYDUYHGFOD\IRXQGLQ3RODQGQHDUFLW\%HáFKDWy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© 2015 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license 7KH$XWKRUV3XEOLVKHGE\(OVHYLHU%9 (http://creativecommons.org/licenses/by-nc-nd/4.0/). 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKHRUJDQL]LQJFRPPLWWHHRI:0(66 Peer-review under responsibilty of the Organizing Commitee of WMESS 2015. Keywords:VWUHQJWKDQLVRWURS\YDUYHGFOD\WULD[LDOWHVW3DULHVDXFULWHULRQ
,QWURGXFWLRQ /D\HUHGVWUXFWXUHFRPPRQO\RFFXUULQJLQVRLOVDQGURFNVDIIHFWVVWURQJO\WRDQLVRWURS\EHKDYLRURIVXFKPDWHULDO ,W UHTXLUHV VSHFLDO DWWHQWLRQ DQG GHVLJQ DSSURDFK LQ JHRWHFKQLFDO HQJLQHHULQJ 1RZDGD\V DQLVRWURSLF FULWHULRQ LV XVXDOO\ XVHG LQ GHVLJQLQJ RI VWUXFWXUHV ORFDWHG LQ VXFK PDWHULDOV ZKHUH LGHQWLILFDWLRQ RI DQ DGHTXDWH DQLVRWURSLF
&RUUHVSRQGLQJDXWKRU7HO E-mail address:PDW\OGDWDQNLHZLF]#SZUHGXSO
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.2015.08.116
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
733
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áFKDWy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à\GĪEDDQG7DQNLHZLF]
)LJXUH,QYHVWLJDWHGPDWHULDO±YDUYHGFOD\
$VHULHVRIFRQYHQWLRQDOWULD[LDOFRPSUHVVLRQWHVWVKDYHEHHQFRQGXFWHGIRUHYDOXDWLRQRIPHFKDQLFDOEHKDYLRURI WKHPDWHULDO7KHLQYHVWLJDWLRQVKDYHEHHQPDGHDFFRUGLQJWRWKHSURFHGXUH7;&,87HVWSURFHGXUHVLQJHQHUDOKDYH IROORZHGWHFKQLTXHVSURYLGHGE\+HDG KRZHYHUWKHVDPSOHVKDYHQRWEHHQVDWXUDWHGEHIRUHWKHWHVW,QWDFW F\OLQGULFDOVSHFLPHQVZLWKPPLQGLDPHWHUDQGPPLQOHQJWKKDYHEHHQXVHG7KHFRUHVKDYHEHHQFXWRXWDW YDULRXVRULHQWDWLRQVRIODPLQDWLRQVĮUHODWLYHWRWUDQVYHUVHD[LVRIWKHVSHFLPHQLH 7KH LQYHVWLJDWLRQVKDYH EHHQ SHUIRUPHG XQGHUILYHGLIIHUHQW FRQILQLQJ SUHVVXUHV LHN3DN3DN3D N3DDQGN3D,QILUVWWZRFDVHVWKHYDOXHRILPSRVHGSUHVVXUHLVORZHUWKDQHVWLPDWHGYHUWLFDOLQVLWXVWUHVV DQGWKHVDPSOHVKDYHEHHQWHVWHGLQRYHUFRQVROLGDWLRQVWDWHRIVWUHVV7KHWRWDODPRXQWRIWHVWHGVSHFLPHQVLV 6SHFLPHQVKDYHEHHQVXEMHFWHGWRLVRWURSLFFRQVROLGDWLRQXQGHUIL[HGFRQILQHPHQWı3XQWLOWKHUHZDVQRFKDQJHLQ
734
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
YROXPH$IWHUZDUGVWKH\KDYHEHHQFRPSUHVVHGZLWKFRQVWDQWVSHHGRIPPPLQZLWKRXWDOORZLQJIRUGUDLQDJH 'XHWRWKHWHVWSURFHGXUHGLIIHUHQWGLVWULEXWLRQRISRUHZDWHUSUHVVXUHLQOD\HUVDQGYDULDEOHDUUDQJHPHQWRIYDUYHV LQHDFKVSHFLPHQWKHPHDVXUHPHQWRISRUHSUHVVXUHLVXQUHOLDEOHDQGLWKDVEHHQRPLWWHG7KHPDLQRXWFRPHVRIWKH H[DPLQDWLRQVDUHWKHGLUHFWLRQDOIDLOXUHFKDUDFWHULVWLFVSUHVHQWHGLQ)LJXUH7KH\DUHSORWWHGE\PDUNLQJWKHYDOXH RISHDNGHYLDWRULFVWUHVV(ı1- ı3)IURPHDFKWHVWLQGHSHQGHQFHWRYDOXHRIRULHQWDWLRQDQJOHĮ7KHUDQJHRIYDOXHVLV N3D IRU FRQILQHPHQW RI N3D N3D IRU N3D N3D IRU N3D N3D IRU N3D DQG N3D IRU N3D 7KH ORZHVW YDOXHV RI VWUHVVHV DUH REWDLQHG IRU RULHQWDWLRQDQJOH H[FHSWIRUFRQILQHPHQWRIN3D 7KHKLJKHVWYDOXHVDUHDFKLHYHGIRURULHQWDWLRQDQJOHV H[FHSWIRUFRQILQHPHQWRIN3D
)LJXUH5HVXOWVRIODERUDWRU\WULD[LDOWHVWVIRUYDUYHGFOD\
0DWKHPDWLFDOPRGHOOLQJ 0DQ\ UHVHDUFKHUV GHDO ZLWK PRGHOLQJ RI VWUHQJWK DQLVRWURS\ IRU YDULRXV JHRPDWHULDOV 7KH YDULRXV FULWHULD ZHUH SURSRVHGLQWHUDOLDE\+LOO 3DULVHDX 7VDLDQG:X &D]DFX 'XYHDXDQG+HQU\ 3LHWUXV]F]DNDQG0Uy] à\GĪEDDQG.DZD 7KHFULWHULRQVHOHFWHGIRUHYDOXDWLRQLQWKHSDSHULVWKH RQH SURSRVHG E\ 3DULVHDX ,W LV DQ H[WHQVLRQ RI DQLVRWURSLF +LOO¶V FULWHULRQ IRU FRKHVLRQ IULFWLRQDO PDWHULDOV ,Q JHQHUDOIRUPWKHFULWHULRQFDQEHH[SUHVVHGDVIROORZV n
AijV ij AijklV ijV kl d
ZKHUH Aij DQG Aijkl DUH DQLVRWURSLF PDWHULDO WHQVRUV ıij DQG ıkl DUH FRPSRQHQWV RI WKH VWUHVV WHQVRUV DQG n LV WKH DGGLWLRQDO PDWHULDO FRQVWDQW +RZHYHU IRU PRVW JHRPDWHULDOV WKH EHVW ILWWLQJ LV REWDLQHG IRU n ZKLFK LV DOVR DVVXPHG LQ WKH LQYHVWLJDWLRQV )RU WKH WUDQVYHUVHO\ LVRWURSLF PDWHULDO WKH PDWHULDO WHQVRUV FDQ EH SURYLGHG DV IROORZV
735
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
Aij
Aijkl
º ª U « V »» « «¬ sym V »¼ G G ª G « F G F « « F G « « « « « « « sym « « « « « « « « « «¬
M
M
M
M
F G
M
M
º » » » » » » » » » F G » » » » » » » » » F G » »¼
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Į DQG YHUWLFDO Į ODPLQDWLRQ ZLWK FRQILQLQJ SUHVVXUH ı3 WKH 3DULVHDX FULWHULRQ FDQ EH VLPSOLILHGWRWZRHTXDWLRQV G V VV V UV VV ° ® °¯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
736
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
7KHZRUNIRULGHQWLILFDWLRQRIDGHTXDWHFULWHULRQIRUWKHWHVWHGVRLOZLOOEHFRQWLQXHGLQWKHIXWXUH
)LJXUH&RPSDULVRQRIWKHWHVWUHVXOWVDQGWKHRUHWLFDOPRGHO
Matylda Tankiewicz / Procedia Earth and Planetary Science 15 (2015) 732 – 737
737
)LJXUH&RPSDULVRQRIWKHWHVWUHVXOWVDQGWKHRUHWLFDOPRGHOIRUFRQILQHPHQW D N3DE N3DF N3DG N3DH N3D
5HIHUHQFHV
&D]DFX2&ULVWHVFX1'6KDR-)+HQU\-3 $1HZ$QLVRWURSLF)DLOXUH&ULWHULRQIRU7UDQVYHUVDO\,VRWURSLF6ROLGV 0HFKDQLFVRI&RKHVLYH)ULFWLRQDO0DWHULDOV 'XYHDX*6KDR-)+HQU\-3 $VVHVVPHQWRI6RPH)DLOXUH&ULWHULDIRU6WURQJO\$QLVRWURSLF*HRPDWHULDOV0HFKDQLFVRI &RKHVLYH)ULFWLRQDO0DWHULDOV 'H*URRW'-/XWHQHJJHU$-&KDUDFWHUL]DWLRQE\6DPSOLQJDQG,Q6LWX7HVWLQJ±&RQQHFWLFXW9DOOH\9DUYHG&OD\6WXGLD *HRWHFKQLFDHW0HFKDQLFD 'H-RQJ-7