½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¾»¾
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1 ÓÖ ÁÒ ØØÙØ Ó ÌÒÓÐÓÝ ¹ ÇØÓÖ Ø ¾¼½¾ ÓÒ ØØÙØÚ ÑÓÐ ÓÙÔÐÒ Ñ Ò ÔÐ ØØÝ ÓÖ ÙÒ ØÙÖØ ÓÑØÖÐ ËÓÐÒÒ Ä ÈÆË È ËÙÔÖÚ ÓÖ Ñ ÈÇÍ ÖÓÙÞ ÌÅÁÊÁ
2 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¾»¾
3 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¾»¾
4 ÅÝ Ò ØØÙØÓÒ ÓÐ ÆØÓÒÐ ÈÓÒØ Ø Ù ÇÐ Ø ÓÓÐ Ó ÚÐ ÒÒÖÒ Øº ½µ ¼¼ ØÙÒØ ÁÒÒÙÖ ÔÐÓÑ ÕÙÚº ØÓ Å ØÖ Öµµ ÄÓÖØÓÖ ÆÚÖ ÆÈ» ÁËÌÌÊ» ÆÊ˵ ½¼ ÔÓÔÐ ¼ Ö ÖÖ ¼ È ½½»¾ Ò ÊÅ˵ ÑÒ Ò ÔÝ Ó ÑØÖÐ ØÖÙØÙÖ Ò ÓÑØÖÐ ÔÔÐØÓÒ Ó¹ÓÒÔØÓÒ ÙÖÐØÝ Ò ÒÒÖÒ Ó ÑØÖÐ Ò ØÖÙØÙÖ ÓØÒ ÓÐÓÐ ØÓÖ ÒÙÐÖ Û Ø ¼ ¾ µ ÔØÖÓÐÙÑ ÒÒÖÒº Ö Ö ØÑ ÝÒÑ ÓØÒ ÊÅ˵ ÑÙÐØ Ð ÔÓÖÓÙ Ñ ÖÓÔÝ ØÖÓÒÓÙ ØÖÙØÙÖ º ÍÒÚÖ Ø ÈÖ ¹ Ø ÊÖÓÙÔ ÚÖÐ ÓÓÐ Ò ÙÒÚÖ Ø ¾»¾
5 ÄÖ ÕÙÔÑÒØ Ø ÄÓÖØÓÖ ÆÚÖ ÖÙÐÖ ÑÔÐ Ö Ú ² ÅÊÁ ÅÙÐØ Ð ¹ÖÝ ØÓÑÓÖÔ Ö Óк < ½µÑ ½¼¼µ ÄÖ ØÖܺ ÕÙÔº ÓÖ ÝÐ ÐÓÒ»¾
6 ÓØÒ ØÑ ¹ Ê Ö ÒØÖ Ø ÓÑÒ Ò ÒÖÝ ÆÙÐÖ Û Ø ÔÓ Ð ÈØÖÓÐÙÑ ÓÑÒ ÅÖÒ ÓØÒ Ç¾ ÓÐÓÐ ØÓÖ ÓØÒÐ ØÖÙØÙÖ ÓÙÒØÓÒ ËÓÐ ÑÔÖÓÚÑÒØ ÊÐÛÝ ÓØÒ»¾
7 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ»¾
8 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒØÜØ ÇØÚ Ó Ø Ø ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ»¾
9 ÆÙÐÖ Û Ø ÔÓ Ð Æʳ ØÓÖ ÓÐÙØÓÒ ÜÚØÓÒ = ÓÑÔÖ ÓÒ ËØÖ Ö ØÖÙØÓÒ ÖÓÙÒ Ø ÓÔÒÒ ÖØÓÒ Ó Ò ÜÚØÓÒ Ñ ÞÓÒ µ ÁÒÖ Ó ÔÖÑÐØÝ ØÙÖØÓÒ Ù ØÓ ÚÒØÐØÓÒ»¾
10 ÆÙÐÖ Û Ø ÔÓ Ð Æʳ ØÓÖ ÓÐÙØÓÒ ÖÐÝ ÐÓ ÙÖ Ø Ê ØÙÖØÓÒ Ù ØÓ ÐÓ ÙÖ ÀØ ÖÐ ÖÓÑ Û Ø ÔÖ ÙÖ Ù ØÓ ÐÐ ÛÐÐÒ»¾
11 ÆÙÐÖ Û Ø ÔÓ Ð Æʳ ØÓÖ ÓÐÙØÓÒ ÄØ ÐÓ ÙÖ Ø Ëй ÐÒ ÑÐ Ò ÓÐÓÐ Ø ÖØÓÒ Ó ÑØÖл¾
12 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒØÜØ ÇØÚ Ó Ø Ø ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ»¾
13 ÇØÚ ÌÓ ÚÐÓÔ ÑÒÐ ÓÒ ØØÙØÚ ÑÓÐ ÓÙÔÐÒ Ñ Ò ÔÐ ØØÝ ÓÖ ÙÒ ØÙÖØ ÓÑØÖл¾
14 ÇØÚ ÌÓ ÚÐÓÔ ÑÒÐ ÓÒ ØØÙØÚ ÑÓÐ ÓÙÔÐÒ Ñ Ò ÔÐ ØØÝ ÓÖ ÙÒ ØÙÖØ ÓÑØÖÐ ÌÓ Ø ÒØÓ ÓÙÒØ ÓÙÔÐÒ ØÛÒ Ø ÑÒÐ ÑÓÐ Ò ØÖÒ Ö ÐÛ ØÑÔÖØÙÖ Ò Ù ÓÛ µ»¾
15 ÇØÚ ÌÓ ÚÐÓÔ ÑÒÐ ÓÒ ØØÙØÚ ÑÓÐ ÓÙÔÐÒ Ñ Ò ÔÐ ØØÝ ÓÖ ÙÒ ØÙÖØ ÓÑØÖÐ ÌÓ Ø ÒØÓ ÓÙÒØ ÓÙÔÐÒ ØÛÒ Ø ÑÒÐ ÑÓÐ Ò ØÖÒ Ö ÐÛ ØÑÔÖØÙÖ Ò Ù ÓÛ µ ÌÓ ÑÔÐÑÒØ Ø ÑÓÐ ÒØÓ Å Ó θ ËØÓ ÚÐÓÔ Ý ØÑÖ Ò ÓÛÓÖÖ µ»¾
16 ÇØÚ ÌÓ ÚÐÓÔ ÑÒÐ ÓÒ ØØÙØÚ ÑÓÐ ÓÙÔÐÒ Ñ Ò ÔÐ ØØÝ ÓÖ ÙÒ ØÙÖØ ÓÑØÖÐ ÌÓ Ø ÒØÓ ÓÙÒØ ÓÙÔÐÒ ØÛÒ Ø ÑÒÐ ÑÓÐ Ò ØÖÒ Ö ÐÛ ØÑÔÖØÙÖ Ò Ù ÓÛ µ ÌÓ ÑÔÐÑÒØ Ø ÑÓÐ ÒØÓ Å Ó θ ËØÓ ÚÐÓÔ Ý ØÑÖ Ò ÓÛÓÖÖ µ ÌÓ ÚÐØ Ø Å Ó Ý ÖÔÖÓÙÒ Ü ØÒ ÜÔÖÑÒØÐ ØÙ»¾
17 ÇØÚ ÌÓ ÚÐÓÔ ÑÒÐ ÓÒ ØØÙØÚ ÑÓÐ ÓÙÔÐÒ Ñ Ò ÔÐ ØØÝ ÓÖ ÙÒ ØÙÖØ ÓÑØÖÐ ÌÓ Ø ÒØÓ ÓÙÒØ ÓÙÔÐÒ ØÛÒ Ø ÑÒÐ ÑÓÐ Ò ØÖÒ Ö ÐÛ ØÑÔÖØÙÖ Ò Ù ÓÛ µ ÌÓ ÑÔÐÑÒØ Ø ÑÓÐ ÒØÓ Å Ó θ ËØÓ ÚÐÓÔ Ý ØÑÖ Ò ÓÛÓÖÖ µ ÌÓ ÚÐØ Ø Å Ó Ý ÖÔÖÓÙÒ Ü ØÒ ÜÔÖÑÒØÐ ØÙ ÌÓ ÔÔÐÝ Ø Ó ØÓ ÑÙÐØ ÓÑÔÐÜ ÔÖÓÐÑ»¾
18 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ»¾
19 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ Ñ ÍÒ ØÙÖØ ÓÐ ÀÝÔÖÐ ØØÝ ÈÐ ØØÝ ËÙÑÑÖÝ Ó Ø ÕÙØÓÒ Ò ÒÖÑÒØÐ ØÖ ¹ ØÖÒ ÖÐØÓÒ Ô ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ»¾
20 ÁÖÖÚÖ Ð ÑÖÓ ÓÔ ÑÒÐ ÚÓÙÖ Ñ Ò ÔÐ ØØÝ ÈÐ ØØÝ ÁÖÖÚÖ Ð ØÖÒ Ñ ÖØÓÒ Ó ÑÖÓÖ ÖØÓÒ Ó Ð Ø ÔÖÓÔÖØ ÅÓØÓÒ Ó Ù ØÖÒ Ö ÔÖÓÔÖØ σ σ σ E 0 E 0 E 0 E(Ω) E 0 E 0 E(Ω) E 0 ε ε p ε e ε e ε ε ε p ε e ÈÐ Ø ÚÓÙÖ ÖØØÐ ÚÓÙÖ ÓÙÔÐÒ Ó Ñ Ò ÔÐ ØØÝ ½¼»¾
21 ÈÖÒÔÐ Ó ØÚ ØÖ ÃÒÓÚ ½µ Ê ØÒ ØÓÒ Ö ÛØ Ñ = Ë Ë = σë = σë σ > σ Ë σ = σ Ë Ë σ = σ = ½ ½½»¾
22 ÅÒ ÝÔÓØ ËÐÖ ÓØÖÓÔ Ñ ÓÖÑ Ó ÀÐÑÓÐØÞ Ö ÒÖÝ ÂÙ ½µ ψ (ε, ) = ψ ¼ (ε )(½ ) σ = ψ ε = ψ ¼ ε (½ ) Í Ó ØÚ ØÖ ÓÒÔØ ÃÒÓÚ ½µ σ = σ ½ = ψ ¼ ε ÈÖÒÔÐ Ó ØÖÒ ÕÙÚÐÒ ÄÑØÖ ½µ ÒÝ ØÖÒ ÓÒ ØØÙØÚ ÕÙØÓÒ ÓÖ Ñ¹ ÑØÖÐ ÑÝ ÖÚ Ò Ø Ñ ÛÝ ÓÖ ÚÖÒ ÑØÖÐ ÜÔØ ØØ Ø Ù ÙÐ ØÖ ÖÔÐ Ý Ø ØÚ ØÖ º ½¾»¾
23 Ñ ÒØØÓÒ Ò Ñ ÚÓÐÙØÓÒ ÕÙÚÐÒØ ÓÖ ÓÒØÖÓÐÐÒ Ñ =  ¾ ¾ Á ½ = Õ ¾ Ô Ñ ÖØÖÓÒ (, ) = ¼ ½ Ñ ÚÓÐÙØÓÒ ÐÛ ÓØÚ ÓÛ ÖÙе = Λ ÖÙÖ ÈÖÖ ÝÐ ÖØÖ ½»¾
24 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ Ñ ÍÒ ØÙÖØ ÓÐ ÀÝÔÖÐ ØØÝ ÈÐ ØØÝ ËÙÑÑÖÝ Ó Ø ÕÙØÓÒ Ò ÒÖÑÒØÐ ØÖ ¹ ØÖÒ ÖÐØÓÒ Ô ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ½»¾
25 ÍÒ ØÙÖØ ÓÐ Air Water meniscus ÌÖ Ô ËÓÐ ÓÐ ÐØÓÒ ÄÕÙ ÛØÖ ÓÐÚ Ö Ö Ò ÛØÖ ÚÔÓÙÖ ÁÑÔÓÖØÒØ ÚÖÐ ËØÖ σ ËÙØÓÒ = Ô Ô Ð Ö Ó ØÙÖØÓÒ Ë Ð = Î Ð Î Ú ½»¾
26 ÀÝÖÙÐ ÚÓÙÖ ÊÐ ÛØÖ ÖØÒØÓÒ ÙÖÚ = ÀÝ ØÖ Volumetric water content s s Air entry value Residual air content 20 Adsorption Desorption curve curve 10 Residual water content, 0 r Soil suction (kpa) ÌÝÔÐ ÓÖÔØÓÒ Ò ÓÖÔØÓÒ ÙÖÚ ÓÖ ÐØÝ ÓÐ ÖÐÙÒ Ò ² ÀÙÒ ½µ ËÑÔÐ ÙÖÚ ÒÐØÒ Ý ØÖ µ S l s (kpa) ÎÒ ÒÙØÒ ÑÓÐ ½¼µ ½ Ë Ð = (½ Ë Ö) (½ +(α ) Ò )) + Ñ ËÖ ½»¾
27 ËÔ ØÙÖ Ó ÙÒ ØÙÖØ ÓÐ ÑÒÐ ÚÓÙÖ ËÙØÓÒ ր = ÓÐ ØÒÒ ÓÐÐÔ ÔÒÓÑÒÓÒ v=1+e ln p Swelling s 1 s 2 >s 1 Collapse ÓÑÔÖ ÓÒ ÙÖÚ º ÐÓÒ Ó Ò ² ÂÓ ½¼µ ½»¾
28 ËØØ ÚÖÐ ÓÖ ÙÒ ØÙÖØ ÓÐ ÊØ Ó ÛÓÖ ÒÔÙØ ØÓ Ò ÙÒ ØÙÖØ ÖÒÙÐÖ ÑØÖÐ ÀÓÙÐ Ý ½µ Û = [σ (Ô Ð Ë Ð +(½ Ë Ð )Ô )Á ]: ε (Ô Ô Ð )φ Ë Ð = σ : ε ËÐ ÓÒ ØØÙØÚ ØÖ σ = σ [Ô Ð Ë Ð +(½ Ë Ð )Ô ]Á = σ ÒØ + Ë Ð Á ËØØ ÚÖÐ { σ ε Ë Ð ½»¾
29 ÓÒ ØØÙØÚ ÕÙØÓÒ ÐÙ Ù ¹ÙÑ ÒÕÙÐØÝ ψ ÀÐÑÓÐØÞ Ö ÒÖݵ ( σ ψ ) ( : ε ε + ψ ) Ë Ð +σ : ε Ô ψ ψ χ Ë Ð χ Ô ψ χ Ô χ ¼ ËØÖҹРÚÖÐ ÏÓÖ ÓÒÙØ ÚÖÐ ε Ð Ø ØÖÒ ØÒ ÓÖ σ ÓÒ ØØÙØÚ ØÖ ØÒ ÓÖ Ë Ð Ö Ó ØÙÖØÓÒ ÅÓ ÙØÓÒ Ñ χ ÀÖÒÒ ÚÖÐ ξ σ = ψ ε = ψ Ë Ð = ψ ξ = ψ χ ½»¾
30 ÓÖÑ Ó ÀÐÑÓÐØÞ Ö ÒÖÝ ÀÐÑÓÐØÞ Ö ÒÖÝ ψ = ψ(ε, Ë Ð,,χ Ô,χ ) = ψ (ε, )+ψ Ð (Ë Ð )+ψ Ô (χ Ô,χ ) ¾¼»¾
31 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ Ñ ÍÒ ØÙÖØ ÓÐ ÀÝÔÖÐ ØØÝ ÈÐ ØØÝ ËÙÑÑÖÝ Ó Ø ÕÙØÓÒ Ò ÒÖÑÒØÐ ØÖ ¹ ØÖÒ ÖÐØÓÒ Ô ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¾½»¾
32 ÀÝÔÖÐ ØØÝ ÀÝÔÖÐ ØØÝ ÀÓÙÐ Ý Ò ÈÙÞÖÒ ¾¼¼µ ËØÖ Ö ÖÚ ÖÓÑ ØÖÒ ÒÖÝ ÔÓØÒØÐ Ð Ø ÀÐÑÓÐØÞ Ö ÒÖÝ ψ ¼ = ψ ¼ (ε Ú,ε ) Ô = ψ ¼ ε Ú σ = ψ ¼ ε ¾¾»¾
33 ÀÝÔÖÐ Ø ÔÓØÒØÐ ÛØ ÙÐ ÑÓÙÐÙ ÔÒÒ ÓÒ ÓÒÒÒ ØÖ Ò ÓÒ ØÒØ Ö ÑÓÙÐÙ ÀÓÙÐ Ý Ø Ðº ¾¼¼µ ψ ¼ = Ô Ö (¾ Ò) [(½ Ò)](¾ Ò)/(½ Ò) [ ( ε Ú + ) ¾ ½ + ¾ε : ε (½ Ò) (½ Ò) ] (¾ Ò)/(¾ ¾Ò) Ò½ ψ ¼ = Ô Ö κ ÜÔ ( ε Ú κ + ε : ) ε κ { Ô } [ } à  ]{ ε Ú = σ  ¾ ε à = Ô κ  = σ κ ¾ = ¾ Ô + σ : σ κô ¾»¾
34 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ Ñ ÍÒ ØÙÖØ ÓÐ ÀÝÔÖÐ ØØÝ ÈÐ ØØÝ ËÙÑÑÖÝ Ó Ø ÕÙØÓÒ Ò ÒÖÑÒØÐ ØÖ ¹ ØÖÒ ÖÐØÓÒ Ô ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¾»¾
35 Ð ØÓ¹ÔÐ Ø ÑÓÐ ÖÐÓÒ ÅÓÐ ÐÓÒ Ó Ø Ðº ½¼µ ØÖ Ö ÖÔÐ Ý Ñ ÓÒ ØØÙØÚ ØÖ σ = σ ÒØ + Ë Ð Á ½ q~ s ~* p c (p ~* 0,s) ~* p 1 c (p~* 0,s) ~* p 2 c (p~* 0,s) 3 M s s=0 p~* 0 p~* c (s) p~* ~* p ~* 01 p 0 ~* p ~* p ¾»¾
36 Ð ØÓ¹ÔÐ Ø ÑÓÐ Ð ÙÖ Ô ( σ, Ô ¼, ) = Õ ¾ Å ¾ Ô ( Ô ( Ô ¼, ) Ô ) ÐÓÛ ÖÙÐ ÓØ Ô = Ô µ ÀÖÒÒ ÐÛ Ô ¼ ε Ô = Λ Ô Ô σ = Ô ¼ λ ¼ κ εô Ú ÚÓÐÙØÓÒ Ó ÔÖÓÒ ÓÐØÓÒ ÔÖ ÙÖ Ò ÆÄ ÐÓÔ ÛØ ÙØÓÒ ËÒ Ø Ðº ¾¼¼µ ( ) λ ¼ κ Ô = λ( ) κ Ô Ô¼ Ö + ËÐ Ô Ö λ( ) = λ ¼ [(½ Ö) ÜÔ( β )+Ö] ¾»¾
37 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ Ñ ÍÒ ØÙÖØ ÓÐ ÀÝÔÖÐ ØØÝ ÈÐ ØØÝ ËÙÑÑÖÝ Ó Ø ÕÙØÓÒ Ò ÒÖÑÒØÐ ØÖ ¹ ØÖÒ ÖÐØÓÒ Ô ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¾»¾
38 ËÙÑÑÖÝ Ñ ÓÒ ØØÙØÚ ØÖ Ð ØØÝ σ = σ Ô I+Ë Ð I (½ ) σ = (σ ) ε ÈÐ ØØÝ Ô ( σ, Ô ¼, ) = Õ ¾ Å ¾ Ô ( Ô ( Ô ¼, ) Ô ) Ô < ¼ ÓÖ Ô < ¼ Ô = ¼ Ò Ô = ¼ ε Ô = ¼ ε Ô Ô = Λ Ô σ Ô ¼ = Ô¼ λ ¼ κ Λ Ô Ô Ô ¾»¾
39 ËÙÑÑÖÝ Ñ (, ) = (ε ) ¼ ½ < ¼ ÓÖ < ¼ = ¼ = ¼ Ò = ¼ ÁÒÖÑÒØÐ ØÖ ¹ ØÖÒ ÖÐØÓÒ Ô = Λ σ = Ô ( σ, ) ε+ ( σ, ) Ô Ð +(I ( σ, )) Ô ¾»¾
40 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¼»¾
41 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ËØÖ ÔÓÒØ ÐÓÖØÑ ÌÖÜÐ Ø Ø ÑÙÐØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ¼»¾
42 ËØÖ ÔÓÒØ ÐÓÖØÑ ÁÒØÐ ØØ ËØÖ ØØ σ ¼ ËØÖÒ ε ¼ ε ¼ ÐÙ ÔÖ ÙÖ Ô ¼ Ô Ð ¼ ÈÖÓÒ ÓÐØÓÒ ÔÖ ÙÖ Ô ¼ ÁÒØÐ Ñ ¼ ÄÓÒ ε Ô Ô Ð ½»¾
43 ÌÖÐ Ð Ø ØØ Ñ ÓÒ ØØÙØÚ ØÖ σ ¼ = σ ¼ Ô ¼I+Ë Ð ( ¼ ) ¼ I (½ ¼ ) ÌÖÐ Ð Ø ØØ ε ½ = ε ¼ + ε Ô ½ = Ô ¼ + Ô Ô Ð ½ = Ô Ð ¼ + Ô Ð σ ½ ØÖ = σ + ¼ ( σ ¼) ε ε ½ ØÖ = ε ¼ + ε ½ = ¼ ¾»¾
44 ÈÐ ØØÝ ¹ Ì Ø ÔÐ ØØÝ Ò Ñ ÓÒ ØØÙØÚ ØÖ Ô Á Ô ( σ ½ ØÖ, Ô ¼¼, ½) ¼ ÌÒ σ = σ ½ ½ ØÖ ε ½Ô = ε Ô ¼ Ñ Ð ÓÖÖØ Ø ØÖ ØØ Ô ¼½ = Ô ¼¼»¾
45 ÈÐ ØØÝ ¹ ÓÖÖØÓÒ Ó Ø ØÖ ØØ ½ Ò Ø ÔÖØ Ó Ø ØÖ Û Ð Ø Ù Ô ( σ Ò +α ε, Ô ¼ Ò, Ò +α ) = ¼ ¾ ËØÖ ÒØÖØÓÒ ÛØ ÔØØÚ Ù ØÔÔÒ Ð ÖØ ÓÖÖØÓÒ σ ½ = ε ½ Ô ½»¾
46 Ñ Ñ ÛØ Ð Ø ØÖÒ ÚÒ Ý Ø ÔÐ Ø ÐÓÓÔ Á ( ½, ½ ) = (ε ) ½ ¼ ½ ½ < ¼ ÌÒ ½ = ¼ Ð ½ = ¼ +»¾
47 ÒÐ ØØ ¹ ØÓ ØÓØÐ ØÖ Ô σ ½ = σ ½ (½ ½)+Ô ½I Ë Ð ( ½ ) ½ I»¾
48 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ËØÖ ÔÓÒØ ÐÓÖØÑ ÌÖÜÐ Ø Ø ÑÙÐØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ»¾
49 ÖÒ ØÖÜÐ Ø Ø ÛØ ÒÓÒ ÐÒÖ Ð ØØÝ ÓÓÑ ÐÝ ÔÖÑØÖ ¹ Ò = ¼. ¹ = ¼¼ È Stress Path Critical State Line Stress Path Critical State Line Initial yield surface Initial damage surface Initial yield surface Initial damage surface q (MPa) ~ q (MPa) p (MPa) ~* p (MPa) ËØÖ ÔØ Ò ØÓØÐ ØÖ Ô ËØÖ ÔØ Ò ØÚ ØÖ Ô q (MPa) d ε a 0.05 ε r ε (%) ÚÓÐÙØÓÒ Ó ØÖÒ q (MPa) ÚÓÐÙØÓÒ Ó Ñ»¾
50 Ø Ó ÙØÓÒ ÓÒ ÖØØл ÔÐ Ø ÚÓÙÖ Stress Path Critical State Line 4 Stress Path Critical State Line 1 Initial yield surface Initial damage surface Initial yield surface Initial damage surface ~ q (MPa) ~ q (MPa) ~* p (MPa) ~* p (MPa) = ¼ È = ¼¼ È q (MPa) s=500 kpa s=200 kpa s=100 kpa d s=500 kpa s=200 kpa s=100 kpa 0.4 s=50 kpa 0.1 s=50 kpa s=10 kpa s=0 kpa s=10 kpa s=0 kpa ε a (%) q (MPa) ÚÓÐÙØÓÒ Ó ØÖÒ ÚÓÐÙØÓÒ Ó Ñ»¾
51 ÅÒ ØÙÖ Ó Ø ÑÓÐ ÓÒÒÒ ÔÖ ÙÖ ր = Ñ ց ÇÚÖÓÒ ÓÐØÓÒ ր = Ñ ր ËÙØÓÒ ր = Ñ ր ¼»¾
52 ½ ÅÝ Ò ØØÙØÓÒ ¾ ÁÒØÖÓÙØÓÒ ÓÒ ØØÙØÚ ÑÓÐÐÒ ÆÙÑÖÐ ÑÔÐÑÒØØÓÒ ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ½»¾
53 ÓÒÐÙ ÓÒ Ò ÔÖ ÔØÚ ÚÑÒØ ÚÐÓÔÑÒØ Ó ØÓÖØÐ ÑÒÐ ÑÓÐ ÓÙÔÐÒ Ñ Ò ÔÐ ØØÝ ÁÑÔÐÑÒØØÓÒ Ó Ø ØÖ ÔÓÒØ ÐÓÖØÑ Ò ÇØÚ ÇÒ ØÖÜÐ Ø Ø Ø ÑÓÐ Ö ÔØ ÑÔÓÖØÒØ ØÒÒ Ó ÙÒ ØÙÖØ ÓÐ ÚÓÙÖ ÈÖ ÔØÚ ÁÑÔÐÑÒØØÓÒ Ó Ø ÑÓÐ Ò θ ËØÓ ÚÐØÓÒ Ò ØÙ ÁÑÔÖÓÚÑÒØ Ó Ø ØÓÖØÐ ÑÓÐ Ø Ó Ñ ÓÒ ØÖÒ Ö ÐÛ ÀÐÒ Ø Ò ÐÝ ½»¾
54 ÌÒ ÝÓÙ ÓÖ ÝÓÙÖ ØØÒØÓÒ ÒÝ ÕÙ ØÓÒ ¾»¾
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