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|x]@=Qu}vJty w l =N l =m]Y= |x} w=R � `tW|@v=H |Q@ Q=@C}iQ_ |x]@=Q "2"OvDUy |]N ,=@} QkD 'l =N XwYNt uRw � `tW |@v=H |Q@ Q=@ C}iQ_

jta� XNWt OL l} R= V}@ `tW pw] V}=Ri= 'u}W}B C=ar=]t =@ j@=]D QO "3"OQ=Ov `tW |@v=H |Q@ Q=@ C}iQ_ u=R}t QO |Q}F-=D '�|Q=OQ}o

|}x_Lqt p@=k|DNU 'l =N|v=UWm pwOtV}=Ri= '`tW |q=@|DNU p}rOx@ "4C}iQ_ 'l =N |@Uv Ctw=kt R}J=v uDiQq=@ =@ xH}Dv QO 'CU= xOQmv O=H}=

"Ci=} Oy=wNv V}=Ri= u=OvJ `tW |@v=H |Q@ Q=@3 |x]@=Q CQwYx@ '`tW |@v=H |Q@ Q=@ C}iQ_ |twta |x]@=Q 'C}=yv QO

%CU= xOW O=yvW}BPu = (62 66kp D2)� Lf Q=OQ}oQU `tW (3)

Q]k D 'xU=t XwYNt uRw '|@v=H |Q@ Q=@ C}iQ_ |wQ}v Pu 'u; QO xmw CU= xOW xDiQo Q_vQO |Q=OQ}o jta Q@=Q@ xm `tW QF-wt pw] Lf w '`tW

"kp = tan2(45 + '2 )

"l =N sw=kt Q=Wi ?} Q[ � |@v=H Q=@ Q=Owtv R= \N u} QDy@ Qw@a "19 pmW

|=yp}rLD R= xOt;CUOx@ Q=OQ}oQU `tW|@v=H |Q@ Q=@C}iQ_ |xU}=kt "20 pmW"�hrDNt l =m]Y= |=}=wR <=R= x@� |O=yvW}B|x]@=Q w |OOa

|=yp}rLD R= xOt;CUOx@ Q=OQ}oQU `tW|@v=H |Q@ Q=@C}iQ_ |xU}=kt "21 pmW"�hrDNt XwYNt uRw <=R= x@� |O=yvW}B |x]@=Q w |OOa

=yCWwv=B1. classical plasticity- based models

2. bounding surface models3. nested surface models4. generalized plasticity models

58

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=tW'32

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tR�h}

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yt

�References� `@=vt1. Rahmani, A. \Dynamic analysis of pile in liquefaction",

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