�1395

R}}=B�'h

}QWu=Qt

a|UOvyt

�| :viC

W=OO=}�

'116�1

07"X

'3/1|

xQ=tW'

32�2

|xQwO

Res

earc

hN

ote|=Q@ |]NQ}e |m}D=DU= p}rLD VwQ |HvUQ=@Da=

Q=w}O |=yxR=U |}xRQr |=yu=mtQ}}eD |x@U=LtxOW|@wmM}t u=@yov

�Q=}Wv=O� �x=vBltm |ra�|QDmO� u=}O}Ht =v}U

TQOt C}@ QD x=oWv=O 'u=Qta |UOvyt |xOmWv=O

pOt |]NQ}e |m}D=DU= p}rLD ?}mQD =@ xm CU= xOW x�=Q= |O}OH VwQ 'VywSB u}= QO|=yQ=w}O |=yu=mtQ}}eD CU= QO=k |O=R; xHQO wO |xR=U l} |m}t=v}O p}rLD w pt=m

C}iQ_ |vLvt wO "Ovm x@U=Lt xRQru}tR C=m} QLD ZQat QO =Q xOW|@ wmM}t|O=R; xHQO wO sDU}U p}rLD |xt=vQ@ QO |]NQ}e |m}D=DU= |=yp}rLD R= xOt;CUOx@

Q=@ |wor= l} p=ta= =@ |]NQ}e |m}D=DU= |=yp}rLD w xO=iDU= |OwQw C=aq]= u=wvax@"CU= xOW s=Hv= |O=R; xHQO OvJ pOt O=R; K]U |wQ w KrUt lwr@ CWB QO |Owta

sR}v=mt =@ w x�=Q= |Q}tN \=kv C}a[w CQwYx@ |]NQ}e |m}D=DU= |=yp}rLD G}=Dv|x@U=Lt |=Q@ |O=yvW}B VwQ G}=Dv u}@ |rw@k p@=k j@=]D w xU}=kt |}xRQr |oDN}UoVwQ xm |r=L QO 'CU= xOW xOy=Wt pt=m |m}t=v}O p}rLD VwQ w |}xRQr u=mtQ}}eD

O}OH Q=R@= l} 'pY=L G}=Dv x@ xHwD =@ u}vJty "OyO|t Vy=m =Q p}rLD u=tR |O=yvW}Bu=@yov Q=w}O |=yxR=U QO xrRrR Q=F; |@=} RQ= |=Q@ |y=oW}=tR; w |OOa |@}mQD

"CU= xOW O=yvW}B xOW|@ wmM}t

a-panah@modares.ac.irsina majidian@modares.ac.ir "|m}t=v}O p}rLD '|]NQ}e |m}D=DU= p}rLD '|@ wmM}t %|O}rm u=oS=w

xtOkt "1|xv}W}@ u=wD|t "CU= 1�SDOF� |O=R; xHQO l} |=ysDU}U MU=B |xv}W}@|m}t=v}O |=yp}rLD w |m}D=DU= Qw)=VwB |vLvt u}@ |x]@=Q R= xO=iDU= =@ =Q Q}O=ktx@U=Lt 'OvQ}o|t Q=mx@ =Q xrRrR MU=B h}] xm |}=yVwQ =} |O=R; xHQO l} |xR=U

"OQmxO=iDU= u}tR |wQ |=yxR=U |=yp}rLD |=Q@ ,qwtat SDOF sDU}U MU=Bw[wt u}= p}rO "CU}v O}it �|m =N� |m}vmDw�S |=yxR=U |=Q@ ,=twta w OwW|t

|=ypmWQ}}eD C=QF= w xR=U w l =N VvmQOv= sDU}U MU=B |oO}J}B R= |W=vl =N p�=L |=yQ=w}O w |v}tRQ} R |=yxR=U |}xRQr Q=DiQ QO u}tR |m}D=DU=x@W

"CU=xDN=U Qw@Ht =Q u=QoWywSB 'OwOLt p[=iD w OwOLt <=RH= |=yxw}W |oO}J}Bpt=wa xm &OvwQ@ |OQ@ Q=m w j}kO =t= 'QD`} QU w QDxO=U |=yVwQ p=@vO xm CU=w l =N VvmQOv= p�=Ut |x@U=Lt |=Q@ =Q RmQtDt |=ysQH w =yQvi Q}_v |}xO=U=@ =Q Qvi � Qo =Q}t � sQH |=ypOt [4�2]'u=QoWywSB |NQ@ "Ovvm|t xO=iDU= xR=UQ=DiQ |R=Ux}@W |=Q@ |O=R; xHQO OvJ |=ysDU}U pOt R= QDtm |O=R; C=HQOl} QLD 'QwmPt |=yVwQ QO "Ov=xOQm xO=iDU= |m =N |xOvQ=Oyov |=yQ=w}O |}xRQrMU=B |]N w u=UWm Cr=L QO u; CWB l =N w Q=w}O OwW ZQi xmv}= |=Q@ u}tRC=YNWt Qw@ Rt |=yVwQ 'p=L Qy x@ "CU= COW sm |i=m |xR=Ov= x@ 'OvyO|t

|r=mU}v w '�1995� x@ wm '�1989� =D} QB=twr� =yxrRrR |NQ@ wkw R= TB C=Oy=Wt'l =N |=HQO K}rUD u=wvax@ xOW|@ wmM}t |=yQ=w}O xmCU= xO=O u=Wv ��2001�p}rO x@ QDW}@ w[wt u}= "Ov=xO=O u=Wv OwN R= =Q |WN@C}=[Q ,=D=P |}xRQr MU=B|=yptar=QwDUO QO OwHwt |Q=mx_i=Lt w xOW|@ wmM}t |=yxR=U |Q}PBh=]av=xOW|@ wmM}t |=yxR=U |xv}y@ |L=Q] |=Q@ =Pr [1]"CU= xOW xO=O C@Uv |L=Q]OQmrta xmCU= syt Q=}U@ u}vJty "OwW xar=]t =yv; |}xRQr OQmrtaCU= |QwQ[=yv; Qta pw] QO u}tR l} QLD hrDNt Kw]U QO QwmPt |=yxR=U lU} Q w |}xRQrQou=Wv u=wvax@ 'wQ}v |=H x@ |}=Hx@=H Q@ RmQtD =@ |}xRQr |L=Q] "OW=@ XNWt

"CU= O}it h=Oy= u}= x@ uO}UQ QO OQmrta =} ?}U; s}kDUt|Q=}U@ xHwD OQwt �Qw)=VwB� |]NQ}e |m}D=DU= |=yp}rLD 'Q}N= |=yp=U QOx@ OQmrta T=U=Q@ |}xRQr |L=Q] |=Q@ Ov=wD|t xm =QJ 'CU= xOw@ u=QoWywSB R="OQ}o Q=Qk xO=iDU= OQwt pt=m |]NQ}e |v=tR |xJN} Q=D p}rLD R= xO=iDU= |=HQO OwHwt |v=tR |=yC}OwOLt R= ?re= w CU= Q+@u=tR '|v=tR |xJN} Q=D p}rLD|@=} RQ= T=U=Q@ '|]NQ}e |m}D=DU= |=yp}rLD OQm} wQ "Ovm|t Rw=HD |L=Q] QD=iO

pw�Ut xOvU} wv �"1393 10 20 VQ}PB '1393 9 25 x}LqY= '1393 4 3 Ci=} QO %M} Q=D

"""|=Q@|

]NQ}e

|m}D=DU

=p}rLD

VwQ|

HvUQ=@Da

=xrRrR ZQat QO �xOW|@ wmM}t� KrUt l =N |=yxR=U MU=B w [11w7]'Ow@ Oy=wN"OW Oy=wN u}at x} wQ |@v=H |}=Hx@=H w VNQJ \UwD

|@wmM}t |=yxR=U |Oa)@wO pOt "3sDU}U pm |}=Hx@=H '|vD@ |x} wQ =@ xOW|@ wmM}t |xQ=w}O pmWQ}}eD x@ xHwD =@"OwW u}}aD �x} wQ \=kv u} QDu}}=B w u} QDq=@� |@=NDv= |O=R; xHQO wO \UwD Ov=wD|t'|O=R; xHQO wO Qo =Q}t � Qvi � sQH l}t=v}O pOt R= xO=iDU= =@ sDU}U u}=Q@=v@

"CU= xOW xO=O u=Wv 2 pmW j@=]t|O=R; xHQO Qy QO KrUt lwr@ R= RmQtDt sQH <=RH= m2 w m1 '2 pmW QO|WQ@ RQt |DNU k2 'KrUt lwr@ |WQ@ w |WtN |DNU k1 'OvDUy xOWh} QaDCWB |y=vDt=v |m =N |xOwD |DNU ks w 'M}t u} QDu}}=B |Q=yt QF= w |ki=O=H}= =Q KrUt lwr@ CWB l =N QF-wt w sw=kt |=yQ=Wi xm 'CU= KrUt lwr@lwr@ |xOQDUo sQH |=Q@ |m}D=DU= pO=aD |Q=QkQ@ =@ m2 w m1 |=ysQH "Ovm|tx@U=Lt p}=t \N CQwYx@ |v}}=B |oDN}Uo K]U |R=UxO=U w �1 pmW� KrUt

"OvwW|t|=Q@ |m}t=v}O |=yp}rLD |=Q@ xDiQQ=mx@ |Oa)@ wO |=ypOt x}@W pOt a VN@V}B |xr�Ut QO "CU= [12]'V=aDQ= Qo =OH =@ =yxR=U w [2]'?rY |m =N |=yQ=w}Oxm '|O=R; xHQO OvJ pOt |m}D=DU= p}rLD R= xO=iDU= =@ a VN@ C=YNWt 'wQQ_v QO =Q =HQO |=yVvD C=QF= w 'R=U w CN=U pL=Qt 'xR=U w l =N VvmQOv=p}rLD QO |rY= O}rm ?U=vt Q=@ p}iwQB uOQmOQ=w "CU= xOW |@=} RQ= 'OQ}o|t|m}v=mt C=YNWt "CU= xOW xO=O KQW xt=O= QO w xOw@ |]NQ}e |m}D=DU=KrUt lwr@ u}@ |m}t=v}O VvmQOv= w |m =N |xOwD u=UWm C=YNWt R= b VN@

"CU= xOW x@U=Lt u; CWB l =N w

|]NQ}e |m}D=DU= p}rLD "1"3l} 'VywSB u}= QO "CU= syt xR=U Q@ p=ta= |=Q@ ?U=vt |Q=PoQ=@ |wor= ?=NDv=xOW p=ta= pt=m pOt |}q=@ RQt QO KrUt lwr@ CWB QO |Owta |Q=PoQ=@ |wor='s�=O |x} wQ |=QH= w |Q=iL R= Oa@ xDi=}pmWQ}}eD pOt R= wQW =@ "�3 pmW� CU=xOW OQ=w pOt |RQt \=kv QO C@=F CaQU p=ta= =@ w |H} QOD CQwYx@ |}=Hx@=HKrUt lwr@ CWB QO Q=Wi xi=[= l} 'xOWQmP |}=Hx@=H |wor= p=ta= =@ "CU=

"CU= xOW O=H}='RmQtDt |=yQ=@ u=wvax@ |O=R; xHQO wO sDU}U Q@ xOWOQ=w |}x]kv |=ywQ}v'�3 pmW� Ov=xOw@ KrUt lwr@ CWB |xOQDUo |Q=PoQ=@ pO=at |m}D=DU= Q_v R= xmQO s=o Qy QO xDi=}s}taD |=yQ=@ '|]NQ}e |m}D=DU= p}rLD s=Hv= =@ "Ov=xOW h} QaDxO=iDU= =@ "Ov=xOW s}UQD C=YDNt |xLiY QO xDi=}s}taD \=kv |}=Hx@=H p@=kt

"CU= xOt; CUOx@ xOW|@ wmM}t |xR=U |=Q@ C}iQ_ |vLvt wO 'Ov}=Qi u}= R=|=y|vLvtu}tND |=Q@ |Oa)@ wO 2�FDM� OwOLtp[=iDVwQVywSBu}= QO

"xOW|@wmM}t |xR=U R= |Oa)@wO pOt "2 pmW

w VRer |v}@V}B |=Q@ u}=Q@=v@ "OvQ}o|tv Q_v QO =Q Q=w}O w l =N u=UWmQ}e|r=L QO "OvQ=Ov OQ@ Q=m |}xRQr O=O} wQ l} R= Oa@ Q=w}O l} Ov=tUB |=ypmWQ}}eD|=ypmWQ}}eD 'u}tR h}a[ C=m} QLD QO |DL 'l =N u=@yov Q=w}O |=yxR=U xm

"OvyO|t u=Wv OwN R= Ov=tUB=@ xm 'CU= xOW xO=O xaUwD |]NQ}e |m}D=DU= VwQ l} 'VywSB u}= QOQO =Q xOW|@ wmM}t p�=L |=yQ=w}O |]NQ}e |m}t=v}O MU=B u=wD|t u; ltmC@Uv QDtm Q=}U@ |D=@U=Lt VqD =@ w pw@k p@=k |DkO =@ u}tR |ki= |=yVRQr

"OQm x@U=Lt |O=R; xHQO OvJ pOt |m}t=v}O p}rLD x@|oDN}Uo w s}rUD |UQQ@ u=mt= 'xOWx�=Q= |]NQ}e |m}D=DU= p}rLD VwQsDU}U l} |m}t=v}O |=yp}rLD "OQw;|t sy=Qi =Q xR=U pm w =yu=tr= |xOvwQV}B\=@DQ= |]NQ}e |m}D=DU= p}rLD u}= x@ pt=m pOt x@ C@Uv QDtm |O=R; C=HQO =@

"OR=U|t umtt =Q j}kO w `} QU C=@U=Lt w OwW|t xO=O|@ wmM}t |=yQ=w}O R= pt=m|m}t=v}O |=yp}rLD R= xOt;CUO x@ |=ypmWQ}}eDxOW xU}=kt |]NQ}e |m}D=DU= p}rLD G}=Dv =@ `HQt pL x=Q l} u=wvax@ 'xOW"OwW pY=L u=v}t]= |O=yvW}B VwQ \UwD xOt;CUOx@ G}=Dv CkO R= =D 'CU=

xOW|@wmM}t |=yxR=U |}xRQr Q=DiQ "2|wor= xmCU= u}= Qou=}@ Sw}i} QDv=U |=yV}=tR; R= xO=iDU= =@ u}W}B C=ar=]t G}=DvpY=L |oDN}Uo K]U 3 w |WRer lwr@ 2 R= xOW|@ wmM}t |=yxR=U |oDN}Uou}vJty w [9]'xRQrR}t |=yV}=tR; s=Hv= R= R}v x@=Wt|oDN}Uo Kw]U [8�5]"OwW|tR= l}D=tW KQ] l} '1 pmW "CU= xOt; CUOx@ [11w10]'|OOa |=y|R=Ux}@W=Q [11]'�2013� u=}O}Ht w x=vBltm VywSB QO xOWxO=O u=Wv |oDN}Uo Kw]U

"OyO|t u=Wv |OOa |R=Ux}@W QOs}rUD K]U 3 =@ KrUtQ}e w KrUt |WRer lwr@ 2 'OwW|t xOy=Wt xm u=vJOwOLt u; CWB Owta |Q}tN K]U |x]U=w x@ KrUt l =N lwr@ "Ov=xOW p}mWDh}OQ u=}=B pLt CtU x@ xvW=B R= pmW|vLvt w |ki= ,=D@Uv VRer K]U l} wl =N sQH xm |FrFt KrUtQ}e |xwo l} "CU= xOW sDN hm R= =yM}t swO =} pw=pw] V}=Ri= "CU= xOW p}mWD VRer ?Qwt K]U \UwD 'OyO|t p )y =Q KrUt"OvwW pt=m |QDq=@ |=y?=DW QO |mDN}Uo Kw]U =D CU= xOW Ea=@ =yM}tl =N |=yQDt=Q=B x@ xDU@=w KrUt lwr@ CWB p}=t |oDN}Uo K]U |x} w=R xwqax@l =N w |DWB l =N u}@ Q=yt u=wvax@ |v}}=B |=yM}t '|tR}v=mt u}vJ QO "CU=pmW|vLvt |Q}tN K]U pLt QO xOW`tH |WQ@ Ctw=kt "Ovvm|t pta KrUtxm |t=ovy 'KrUt lwr@ VRer w |Q=O}=B=v p@=kt QO |v}}=B |=yM}t |Q=yt QF= w|DNU =@ x} wQ ?Yv swRr Crax@ "Ovm|t Ctw=kt 'OwW|t OQ=w u; x@ |UQv}= |wQ}v|]N CQwYx@ x} wQ pmWQ}}eD 's�=O |@ wmM}t |=yxR=U QO q=@ |WtN Ctw=kt w

[11]"|Q}tN Kw]U l}D=tW "1 pmW

108

3 1|xQ

=tW'32

�2|xQ

wO-�13

95R}}=B

�'h}QW

u=Qta|

UOvyt %OwW |U} wvR=@ 2 |x]@=Q pmW x@ Ov=wD|t"

m1 00 m2

#(�u1�u2

)+

"k1 + ks �k1 � ks�k1 � ks k1 + ks + k2

#(

u1u2

)+

"c11 c12c21 c22

#(_u1_u2

)=

( 0k2ug + cg _ug

)(2)

l =N |xR=U |x}=B QO �u}tR� x=ox}mD |O=R; xHQO Qou=}@ g T}Ov= 'u; QO xm"CU= xOW|@ wmM}t

|r}=Q RwmU} w |}=Q}t u}=Q@=v@ 'OwW ^=Lr |m}t=v}O R}r=v; QO O}=@ xR=U |}=Q}tT} QD=t w sQH R= |]N ?}mQD pmW x@ Ov=wD|t |}=Q}t T} QD=t "CU= xOW xO=iDU=

%�4 w 3 \@=wQ� OwW xDiQo Q_v QO xR=U |x}rw= |DNU[c] = � [m] + � [k] (3)

cg = �m2 + � (4)

%Ov};|t CUOx@ 6 w 5 \@=wQ R= xm 'OvDUy C@=F ?}=Q[ � w � '=yu; QO xm� = 2�!1!2

!1 + !2(5)

� = 2�!1 + !2

(6)

xm 'OvDUy 2 w 1 |=ypOt |x}rw= |}x} w=R Ot=U@ ?}DQD x@ !2 w !1 '=yu; QO xm0 05 Q@=Q@ xm 'CU= |v=QL@ |}=Q}t � 'Ov=xOt; CUO x@ p=Owt p}rLD R= xO=iDU= =@

[4�2]"CU= xOW xDiQoQ_v QOCmQL |}xmD CqO=at x@ 1 |xrO=at 'CU= |]NQ}e Qvi |DNU xmv}= p}rO x@xOw@ sRq MU=B pwYL |=Q@ |v=tR |=ys=o |Q}op=QoDv= 'xH}Dv QO "OwW|t p}O@DQO [14]"OvDUy OwHwt CmQL CqO=at |}xmD pL |=Q@ |v=w=Qi |=yVwQ "CU=

[15]"CU= xOW ?=NDv= lQ=tw}v VwQ R= |]N ?=DW |Ov@pwtQi 'VywSB u}=s=o Qy R=e; QO |U=tt |DNU |=yT} QD=t ks w k2 'k1 xm OwW xHwD O}=@'|]NQ}e |m}D=DU= p}rLD "CU= xDN=vW=v |QDw |DNU xm |r=L QO 'OvDUy |v=tR|Q=PoQ=@ |vLvt C=YNWt u}}aD |=Q@ 'CU= xOW xO=O KQW u}= R= V}B xmuDiQoQ_vQO |=Q@ "Ov=xOW xO=iDU= �C}iQ_ |=y|vLvt� k2 w k1 (backbone)

Q@=Q@ |Q=OQ@ Q=@ w |Q=PoQ=@ |DNU '|}xRQr |=yQ=@ �|}xNQJ� l}rm}U Ca}@]l =N sQH |=Q@ h]avt x=ox}mD l} u=wvax@ ks w xO=iDU= x}rw= u=UWm |DNUlwr@ '|}xRQr V=aDQ= QF= QO "CU= xOW xDiQo Q=mx@ |@v=H |=ypmWQ}}eD QO KrUtx@ w Ovm|t u=Uwv CWB l =N CtU hqNQO w CtU x@ ?ka w wrH x@ KrUt|@v=H Q=Wi Ov=wD|tv KrUt lwr@ CWB l =N "OyO|t MU=B |ki= Qvi l} pmW�backbone� VwB |vLvt '5 pmW "Ovm O=H}= �p=ai Q=Wi� VQF-wt Q=Wi R= QDtmQO =Q KrUt lwr@ CWB l =N |@v=H pmWQ}}eD � |ki= Q=Wi |x]@=Q x@ \w@ Qt|xOwD |m}t=v}O Q=DiQ |R=UpOt |=Q@ |Q=DiQ u}vJ "OyO|t u=Wv |m}D=DU=Cr=L

[16]"CU= xO=iDU= p@=k p�=L |=yQ=w}O CWB QO l =N6 pmW QO xm Qw]u=ty 'KrUt lwr@ |=Q@ |]N pmWQ}}eD uDiQoQ_vQO =@xHQO wO pOt |=Q@ QU CWB l =N |xOv}=tv u=UWm |DNU 'CU= xOW xO=O u=Wv

%CU= xOt; CUOx@ 7 |x]@=Q R= |O=R;

K = 0 65E(1� �2) (7)

"|O=R; xHQO wO sDU}U C}iQ_ |=y|vLvt u}tND |=Q@ PDA "3 pmW

"xOWQ=yt |xR=U C}iQ_ |=y|vLvt "4 pmW

|OOa |R=Ux}@W "CU= xOW xO=iDU= xOW|@ wmM}t l =N |xR=U |}xRQr C}iQ_T=U=Q@ |Q=PoQ=@ |wor= l} "CU= xDiQo CQwY [13]'FLAC3 Q=Ri=sQv =@MQv "CU= xOW p=ta= K]U Q@ Cw=iDt pw] w Cw=iDt COW =@ |}=Hx@=Hpw] w p=ta= KrUt lwr@ CWB QO K]U |x]kv u}rw= x@ |Owta |}=Hx@=HxHQO wO pOt QO "CU= xDi=} V}=Ri= p}rLD |=ys=o V}=Ri= =@ |}=Hx@=H p=ta=w u1 |r[=iD |}=Hx@=H Q@=Q@ QO f1 w k2 'u2 Q@=Q@ QO f2 w f1 `tH '|O=R;u=Wv =Q u2 w u1 'f2 'f1 '3 pmW "CU= xOQm u}}aD =Q k1 '(u1 � u2) u2

"OyO|t=Q CN=U pL=Qt =D 'CU= xOW s=Hv= |m}D=DU= \}=QW QO =yp}rLD =OD@= QO'CU= xOW s=Hv= |L]U Q=@ =@ |]NQ}e |m}D=DU= p}rLD 'xt=O= QO "Ovm |R=Ux}@WCUOx@ '4 pmW j@=]t C}iQ_ |=y|vLvt R= xO=iDU= =@ sDU}U |}xRQr Q=DiQ =D

"O};

|O=R; xHQO wO sDU}U |m}t=v}O p}rLD "2"3x@ =Q |rY= CqO=at u=wD|t '2 pmW R= =ysQH |m}t=v}O |xrO=at uDiQoQ_vQO =@

%�1 |x]@=Q� CWwv |U} QD=t pmW

[m]

(�u1�u2

)+ [k]

(u1u2

)+ [c]

(_u1_u2

)=

(p1p2

)(1)

|wQ}v p w |DNU T} QD=t k '|}=Q}t T} QD=t c 'sQH T} QD=t m 'u; QO xm'CaQU 'jr]t ?=DW |=yMU=B ?}DQD x@ u w _u '�u u}vJty w CU= ptar=Tma|x} wQ MU=B |xOv}=tv |O=R; xHQO Qou=}@ '2 w 1 |=yT}Ov= "OvDUy |}=Hx@=H wCmQL |xrO=at '1 |xrO=at QO T} QD=t \U@ =@ "OvDUy xOW|@ wmM}t |xR=U

109

"""|=Q@|

]NQ}e

|m}D=DU

=p}rLD

VwQ|

HvUQ=@Da

=CWB l =N |xwo 'Ovm|t x@ QHD =Q |]NQ}e MU=B QU CWB l =N xm u}=tRlwr@ pmWQ}}eD x@ xDU@=w xwo u}= p}mWD "OQ=O p}mWD u=mt= KrUt l =N lwr@|wU R= "OyO|tv Q}}eD =Q |O=R; xHQO wO pOt |xOvvmu=Uwv sQH w CU= KrUt"Ovm|t =Q}t '|UOvy |}=Q}t ltm x@ =Q xrRrR |SQv= 'KrUt lwr@ CWB l =N 'Qo}OQDW}@ QF= u}= p=L Qy x@ 'OQ=Po@ Q}F-=D xR=U |}xRQr MU=B QO Ov=wD|t xi=[= |}=Q}t u}=|m =N |=yQ=w}O Ovv=t 'sQv |=yxR=U |=Q@ [16]"CU= syt q=@ |DNU =@ xR=U |=Q@u}=Q@=v@ "OwW xDiQo xO}O=v Ov=wD|t w CU= R}J=v |UOvy |}=Q}t QF= 'xOW|@ wmM}t|UOvy |}=Q}t w KrUt lwr@ CWB |oDN}Uo |xwo sQH C=QF= 'xar=]t u}= QO

"Ov=xOW xDiQo xO}O=v|m}t=v}O p}rLD |xt=vQ@ 'p@k VN@ QO xOWxO=O KQW sD} Qwor= R= xO=iDU= =@R= xO=iDU= =@ Q=DWwv u}= u=oOvU} wv \UwD |]NQ}e |O=R; xHQO wO |=ysDU}U|=yxR=U |}xRQr |=ypmWQ}}eD CU= QO=k xm xOW xDWwv 4l}U}@ p;wS} w |xt=vQ@|m}D=DU= |=yp}rLD R= xOt;CUOx@C}iQ_|vLvt wO "Ovm x@U=Lt =Q KrUt|m =N|O=R; xHQO wO p}rLD |xt=vQ@ QO xR=U pm |m}v=mt C=YNWt u=wvax@ |]NQ}eOv=wD|t u}vJty xOWQmP VwQ xm OQm xHwD O}=@ "Ov=xOW xO=iDU= |OwQw u=wvax@|=yxR=U QO xrRrR C=QF= |@=} RQ= |=Q@ |y=oW}=tR; w |OOa |@}mQD Q=R@= l} u=wvax@|=Q@ xO=U |m}D=DU= |Q=PoQ=@ ?}mQD R= VwQ u}= "OwW xO=iDU= l =N u=@yov Q=w}OxO=iDU= |O=R; xHQO wO sDU}U |m}t=v}O p}rLD w T=}ktlJwm |m} R}i |=ypOt'CU= |R=Ov=x=Q p=L QO TQOt C}@ QD x=oWv=O QO Qw_vt u}O@ |tDU}U "Ovm|t

"OW Oy=wN x�=Q= xOv}; QO u; G}=Dv xm

|OQwt C=ar=]t "4Q_v QO |OQwt C=ar=]t u=wvax@ '7 pmW j@=]t xOW|@ wmM}t |m =N |xR=U wO|xOv}=tv '1 pOt "OvQ=O `=iDQ= QDt 19 5 w 8?}DQD x@ 2 w 1 |=ypOt "Ov=xOW xDiQo|R=Ux}@W QO pL=Qt "CU= x=Dwm |xR=U l} |xOv}=tv '2 pOt w Ovr@ |xR=U l}=yM}t |=yp=J "CU= |W=BuD@ w '=yM}t ?Yv '|}xrLQt |Q=iL %pt=W CN=U�|}=yv� |t�=O |x} wQ "CU= xOW s=Hv= Q=Wi CLD j} QRD w QiL |WNQJ p} QO =@xOW ?Yv '�xOWVwH Vt |xm@W =@ C} QmD=W� Ckwt |x} wQ |=QH= R= Oa@

"CU= xOW x�=Q= 1 pwOH QO =ypOt C=YNWt "CU=

|R=UpOt w |OOa Q=R@= "1"4|xJN} Q=D w|]NQ}e|m}D=DU=|=yp}rLDTBUw|}xrLQtCN=U|=yp}rLD =OD@=|Oa)@ wO |}xLiY VvQm |=ypOt "CU= xOW s=Hv= pt=m pOt |m}t=v}O |v=tRhqDN= |=ypOt OQwt QO "Ov=xOW xO=iDU= 'MDOF sDU}U p}rLD |=Q@ FLAC

w ZQa QDt 40 '2 pOt w &`=iDQ= QDt 33 w ZQa QDt 65 '1 pOt 'OwOLt

"xOW?=NDv= |=ypOt C=YNWt "1 pwOH2 pOt 1 pOt

8 19 5 �QDt� jta10 15 �QDt|Dv=U� Ckwt VWwB25 40 �QDt|Dv=U� |t�=O VWwB

1 88 3 49 �`@ QtQDt Q@ QDt� |@ wmM}t sm =QD15 15 �QDt|Dv=U� |Q=iL |xr=J Q]k

"KrUtQ}e l =N |=Q@ |@v=H pmWQ}}eD � |@v=H |wQ}v u}@ |x]@=Q "5 pmW

"KrUt lwr@ QO QU CWB l =N C=QF= |R=UxO=U "6 pmW

uwU=wB ?} Q[ w u=UWm pwOt ?}DQD x@ � w E w Qrmv} w Qvi |DNU k 'u; QO xmx]@=Q '|Qovr pO=aD |x]@=Q |Q=QkQ@ w |]N pmWQ}}eD uDiQoQ_vQO =@ "OvDUy l =N

%O};|t CUO x@ 8ks � (u1 � u2)� h = 1

2K � (u1 � u2)� h� 23 (8)

%O};|t CUOx@ 9 |x]@=Q '8 w 7 |=yx]@=Q ?}mQD =@ "CU= Q=w}O `=iDQ= h 'u; QO xmks = 0 65E � h

3(1� �2) (9)

'xOW|@ wmM}t |m =N |=yxR=U |=Q@ xHwD p@=k |m}D=DU= pmWQ}}eD 'u}= Q@ xwqaV}B lQLt Q=Wi |xR=Ov= =D |@v=H Q=Wi Vy=m Ea=@ 'CN=U pL=Qt R= |W=v"OwW|t xrRrR pw] QO (u1 � u2) |mJwm pmWQ}}eD R= Oa@ =} w CN=U u=}=B R=CWB l =N Qvi s}rUD \}=QW (k1) 1 Qvi C}iQ_ |vLvt CU= xOW ZQi u}=Q@=v@R= QDtm Q}O=kt x@ \w@ Qt k1 xm |t=ovy '|m}t=v}O Cr=L QO %CU= xOw@ (ks) QU� |@v=H |wQ}v |vLvt R= u=UWm Q=Okt pO=at ks &CU= xOw@ V=C}iQ_ |vLvtQ}O=kt xm |t=ovy w �|Q=OQ@ Q=@ � |Q=PoQ=@ Q}Ut� CU= �5 pmW� |@v=H pmWQ}}eDxOQm =O}B pRvD QiY x@ ks 'CU= xOQm p=@vO =Q VwB |vLvt |xt=O= 1 Qvi |DNU'xar=]t OQwt p�=L Q=w}O |Q}PBh=]av= w wv x@ xHwD =@ xm CU= sRq QmPD u}= "CU=|OL x@ Q=w}O CWoQ@ QO l =N |xOwD x@ KrUt lwr@ R= OQ=w Q=Wi CU= xOW ZQil =N Qvi |=Q@ |t}rUD Q=}at w OwW O=H}= sw=kt Q=Wi |oDN}Uo |=yxwo xm CU}v

"CU= xOWv xDiQo Q_v QO sw=kt Cr=L QO KrUt lwr@ CWB

110

3 1|xQ

=tW'32

�2|xQ

wO-�13

95R}}=B

�'h}QW

u=Qta|

UOvyt |xrY=i |xR=Ov= x@ �Ctw=kt w |DNU� =yM}t w l =N lQDWt K]U w =yM}t

'|}xLiY VvQm |R=UxO=U QO |Oa)@xU QF= =D 'CU= xOW s}UkD =yQ=yt u}@ |ki=wv u}= xOWxQ=W= `H=Qt G}=Dv Q@=v@ [18w17'10]"OwW ^=Lr =yM}t u}@ |xrY=i QO=@ =Q |}xRQr w |m}D=DU= |=yQ=@ CLD xOW|@ wmM}t |=yxR=U Q=DiQ '|R=UpOtCw=iD Vy=m x@ xHwD =@ s�=O |=yxR=U QO u}vJty "Ovm|t |v}@V}B |}q=@ CkO|QDq=@ CkO |R=UxO=U u}= 's�=O |x} wQ OwHw Crax@ x} wQ |ki= u=mtQ}}eD

"OQ=OR= Oa@ "CU= xOW xDiQo xO}O=v Ckwt |x} wQ QF= '|t�=O VWwB ?Yv R= Oa@|m}t=v}O p}rLD w |]NQ}e |m}D=DU= p}rLD R= V}B w |}xrLQt CN=U p}rLD|x} wQ |=yQDt=Q=B uO=OQ}}eD =@ q=@ |WtN Ctw=kt =@ |t�=O |x} wQ ?Yv 'pt=m|WtN Ctw=kt '=yM}t w l =N |x} wQ VvmQOv= C=QF= "CU= xOW s=Hv= CkwtxDiQo Q_v QO MDOF p}rLD QO CN=U pL=Qt w '=yM}t |QwLt Ctw=kt 'x} wQ

"Ov=xOW\=kv QO |ki= ?=DW |v=tR |xJN} Q=D p=ta= =@ pt=m pOt |m}t=v}O p}rLDQO pOt |Q=vm |=yRQt QO O=R; u=O}t |RQt\}=QW "CU= xOW s=Hv= pOt u}}=B |RQt'FLAC QO |m}t=v}O p}rLD "OwW xv}tm Gwt ?=DR=@ C=QF= =D 'CU= xOW xDiQo Q_v

"OyO|t =Q |Oa)@ wO |]NQ}e |m}t=v}O p}rLD |xR=H='K}rUD 'l =N C=QF= uDiQoQ_vQO =@ |rta |WwQ |x�=Q= QO VywSB u}= RmQtD|L=Q] |=Q@ |}xRQr pmWQ}}eD |v}@V}B |=Q@ xrRrR |=yQDt=Q=B w 'CN=U pL=QtC=YNWt C=QF= Q@ VywSB u}= "CU= |}=Hx@=H T=U=Q@ xOW|@ wmM}t |=yxR=U=Q} R 'CU= xOQmv RmQtD hrDNt |=yVvQm QO |DNU Ovv=t |m =N Kr=Yt |xS} wO=H}= G}=Dv u}@ QO Kr=Yt pOt uO=OQ}}eD =@ |DL=Q x@ Ov=wD|t TwULt |=yCw=iD?trwm � Qwt pOt '|R=Ux}@W |R=Uu=U; |=Q@ w hOy u}= uDiQoQ_vQO =@ "OwWOwHw |m =N |=yxR=U |m}t=v}O p}rLD |=Q@ |Q=}U@ |=ypOt "CU= xOW xO=iDU='QwyWt |}xv=}=Q |=yOm QO uOw@OwHwt w |oO=U Cra x@ ?trwm � Qwt pOt "OQ=O|=yxR=U |}xRQr p}rLD |=Q@ u=vJty V}=yC}OwOLt seQ|ra w OQ=O OQ@ Q=m Q=}U@|=Q@ �2 l =N w 1 l =N� w} Q=vU wO 'VywSB u}= QO "OwW|t xO=iDU= |m}vmDw�S"OyO|t u=Wv =Q l =N wO u}= C=YNWt '2 pwOH "CU= xOW xO=iDU= l =N |xOwDR=}v |]NQ]e |m}D=DU= p}rLD R= xOt;CUOx@ |=y|vLvt x@ |O=R; xHQO wO pOt

"OQ=O

|OwQw C=m} QLD "2"4'�1989� =D} QB=twr w �1940� wQDvUr= |=yxrRrR 'pt=m |v=tR |xJN} Q=D p}rLD QOp=ta= R= p@k xOWxO=iDU= |=yCW=ov?=DW w xO=iDU= |OwQw |xrRrR u=wvax@

"2 w 1 |=ypOt l =N C=YNWt "2 pwOHswO l =N pw= l =N

800 500 pOt36 34 �`@ Qt QDt|Dv=U Q@ sQowr}m � nv=} pwOt5 20 �`@ QtQDt Q@ uDw}vwr}m � |oOv@UJ0 5 �xHQO� `=UD= |x} w=R

0 29 0 39 uwU=wB ?} Q[16 19 �?amtQDt Q@ uDw}vwr}m � OL=w uRw

"=yQ=yt ?Yv |wor= w xUOvy %xOWQ=yt |m =N |=yxR=U "7 pmW

"OwOLt hqDN= |=ypOt |xUOvy "8 pmWQDt 0 4 Q@=Q@ '1 pOt |=Q@ OwOLt hqDN= Vt O=a@= "Ov=xDW=O `=iDQ= QDt 15 6|Ov@Vt w =ypOt |xUOvy '8 pmW "CU= xOw@ QDt 0 2 Q@=Q@ '2 pOt |=Q@ ws�=k CyH wO QO u}}=B RQt |]NQ}e |m}D=DU= |=yp}rLD QO "OyO|t u=Wv =Q|xJN} Q=D |=yp}rLD QO "Ov=xOW xDU@ |ki= CyH QO |Q=vm |=yRQt w |ki= w\}=QW w xDU@ s�=k w |ki= CyH wO QO |v}}=B RQt 'MDOF sDU}U |v=tRuOQm^=Lr |=Q@ "CU= xOW xO=O X=YDN= |Q=vm |=yRQt x@ O=R; u=O}t |RQtC=YNWt '?w=vDt |ki= pY=wi QO =yM}t =@ xOW|@ wmM}t |xR=U |Oa)@xU C=QF=

111

"""|=Q@|

]NQ}e

|m}D=DU

=p}rLD

VwQ|

HvUQ=@Da

=[7]"Sw}i} QDv=U pOt C=YNWt "4 pwOHQ=Okt QDt=Q=B50 g Sw}i} QDv=U ?=DW

152 mm pOt jta7 6 m |rY= |xvwtv jta360 l =N |rN=O l =m]Y= |x} w=R

7 2 kPa l =N |oOv@UJ20 MPa l =N |v=UWm pwOt

15 05 kN/m3 l =N XwYNt uRw3 M}t |=yh}OQ O=OaD

50 mm =yM}t |Owta w |ki= |xrY=i102 mm =yM}t pw]0 28 g |rm}U Q=@ ?=DW

|m}t=v}O p}rLD w Sw}i} QDv=UV}=tR; QO M}t u} QDq=@|v=tR |xJN} Q=D "10 pmW"pt=m pOt

pt=m pOt |m}t=v}O p}rLD |HvUCLY "3"4G}=Dv w xO=iDU= `HQt pL x=Q u=wvax@ pt=m |m}t=v}O p}rLD 'VywSB u}= QO"CU= xOW xU}=kt pt=m |m}t=v}O p}rLD G}=Dv =@ |O=yvW}B VwQ R= xOWx@U=Lt|HvUCLY CyH [7]'Sw}i} QDv=U pOt R= G}=Dv x@ uDN=OQB R= p@k CyH u}O@xOW xO=iDU= FLAC Q=Ri=sQv QO xOW|@ wmM}t |=yxR=U |m}t=v}O |R=UpOtQO x} wQ |ki= |}=Hx@=H "OyO|t u=Wv =Q Q_vOQwt pOt C=YNWt '4 pwOH "CU="CU= xOW xO=iDU= pt=m |m}t=v}O p}rLD |HvUCLY |=Q@ M}t u} QDq=@ u=mt|OOa |R=Ux}@W w V}=tR; QO Q_vOQwt |x]kv |ki= u=mtQ}}eD |v=tR |xJN} Q=D

"OwW|t xOy=Wt 10 pmW QO

Q}UiD w G}=Dv "5FLAC |O=R; xHQO OvJ pOt |m}t=v}O p}rLD R= xOt;CUOx@ G}=Dv 'VN@ u}= QO

"CU= xOW xU}=kt =yp}rLD G}=Dv w x�=Q= |O=yvW}B VwQ w

|O=R; xHQO OvJ |=ypOt |]NQ}e |m}D=DU= p}rLD G}=Dv "1"5|Q=PoQ=@ CLD FLAC Q=Ri=sQv QO xOWxDN=U |=ypOt G}=Dv CtUk u}= QOxOW x�=Q= �11 pmW� xv}W}@ |WQ@ |=yVvQm QwDvm CQwYx@ |Owta |m}D=DU=

"VywSB u}= QO xOWxDiQo Q_v QO C=m} QLD C=YNWt "3 pwOH=D} QB=twr wQDvUr= xrRrR

Gilroy Array #1 Imperial Valley x=oDU}=LOMAP/G01000 IMPVALL/I-ELC180 xir-wt

0 41 0 31 (g) u}tR ?=DW |xv}W}@0 31 0 29 u}tR CaQU |xv}W}@

�x}v=F Q@ QDt�

"|OwQw C=m} QLD |v=tR |xJN} Q=D "9 pmW

|}=yCW=ov?=DW QF= CLD MDOF OwOLt p[=iD |=ypOt "Ov=xOW K}LYD3 pwOH QO =yxrRrR |OwQw C=YNWt "Ov=xDiQo Q=Qk 0 5 w 1 |=yT=}kt =@xOW xO=O u=Wv 8 pmW QO \w@ Qt |=y?=DW MU=B |=yh}] R}v w [19]'x�=Q=

"CU=R= xO=iDU= 'xOW|@ wmM}t |xR=U MU=B |oO}J}B Cra x@ xm OwW O}m -=D O}=@QHvt CW=ov?=DW uOQmT=}kt |=Q@ xR=U |rY= ?w=vD |xQwO w MU=B h}]Q=DiQ pt=W Q_vOQwt sDU}U MU=B "OwW|t MU=B |@=} RQ= QO |DUQO=v G}=Dv x@KrUtQ}e w KrUt l =N |xOwD w x} wQ Q}_v hrDNt |=yVN@ ?}mQD w |]NQ}e"Ovm|t pQDvm =Q sDU}U MU=B Q}eDt |=yxvt=O =@ Owt wO '|O=yvW}B VwQ QO "CU=|m}t=v}O p}rLD |OwQw l} QLD u=wva x@ 9 pmW QO xOWxO=O u=Wv |=yxrRrRCaQU |v=tR |xJN} Q=D '|O=R; xHQO wO pOt QO "CU= xOW xO=iDU= pt=m pOtwO pOt |OwQw |=yOQwmQ u=wva x@ MDOF |xOW|@ wmM}t |=ypOt |x}=B QO|O=R; xHQO wO |=ypOt u}@ MU=B Cw=iD OQwt u}= "CU= xOW xO=iDU= |O=R; xHQO"OR=U|t xv}tm =Q Q=w}O |x}=B R=QD Q} R l =N |x}q C=QF= R= |W=v pt=m |m}t=v}O wx@ p=ta= |=Q@ Ov=wD|t |Oa)@ l} |m =N uwDU l} C}=U MU=B p}rLD 'pta QO

"OwW xO=iDU= |O=R; xHQO wO |xR=U

112

3 1|xQ

=tW'32

�2|xQ

wO-�13

95R}}=B

�'h}QW

u=Qta|

UOvyt "OvyO|t x�=Q= =Q 2 w 1 |=ypOt |=Q@ pt=m |m}t=v}O p}rLD w |O=yvW}B VwQ R=

|m}t=v}Op}rLD pOtG}=Dv w |O=yvW}BVwQG}=Dv |xU}=kt QO|rw@kp@=k|v=wNtyG}=Dv u}@ Cw=iD '|}=yv pmWQ}}eD V}=Ri= =@ 'xJQo = "CU= xOt; CUOx@ pt=m pOt'CU= xOW xO=O u=Wv 12 pmW QO xmv=vJ 'p=Ft |=Q@ "CU= xDi=} V}=Ri= sy?} Q[ =@ =D} QB=twr |xrRrR QF= CLD 1 pOt |=Q@ VwQ wO Qy u}@ |k}kO j}@]Dx@ |O=R; xHQO wO pOt |}=yv |}=Hx@=H xm |r=LQO 'CU= xOt; CUOx@ 1 T=}kt

"CU= xOW x@U=Lt u}}=B QO QDt|Dv=U 1 2 w q=@ QO QDt|Dv=U 5 3 |xR=Ov=|q=@ Q}O=kt x@ xHwD =@ '1 T=}kt ?} Q[ =@ wQDvUr= |xrRrR QO Qo}O hQ] R="CU= QDt|Dv=U 15 OwOL QO VwQ wO G}=Dv u}@ |}=Hx@=H Cw=iD 'pmWQ}}eDwO G}=Dv u}@ Cw=iD xrRrR T=}kt ?} Q[ Vy=m =@ xm OwW|t xOy=Wt u}vJty|q=@ Q}O=kt QO VwQ wO G}=Dv u}@ |}=Hx@=H Cw=iDV}=Ri= "CU= xDi=}Vy=m VwQp}rLD QO QDq=@ |=yOwt C=QF= "1 %OwW ?wYvt =yxO}OB u}= x@ Ov=wD|t pmWQ}}eDQ=DiQ u}@ Cw=iD "2 'OwW|t |]NQ}e |xR=@ OQ=w xR=U xm |Dkw 'pt=m |m}t=v}O|m}D=DU= p}rLD QO KrUt lwr@ CWB l =N |@v=H |=ywQ}v QF= CLD KrUt lwr@p}rLD QO VRQr u}L KrUt lwr@ QO |ki= `} RwD =@ |UQv}= |=ywQ}v w |]NQ}euDiQoxO}O=v "4 'KrUt lwr@ CWB l =N C=QF= |R=UxO=U "3 'pt=m |m}t=v}Op[=iD |=yVt QO G=Hwa= "5 'KrUt lwr@ CWB l =N QO sw=kt |xwo p}mWD|=yMQv QO l =N |DNU QO Vy=m R= |W=v |WQ@ Gwt u}}=B |=yCaQU QO OwOLtCU= pwtat "CU= Ot=U@ u} QDnQR@ x@ xDU@=w u=tr= |xR=Ov= u} QDnQR@ "q=@ VvQmu} QDx=Dwm sDWy l} x@ u=tr= |xR=Ov= u} QDnQR@ 'u=tr= G=Hwa= R= |Q}owrH |=Q@ xm|DNU xm |v=tR Ov=wD|tv \}=QW u}= 'p=L Qy x@ [20]"OwW OwOLt (�s) Gwt pw]"OwW <=[Q= OwOLt hqDN= VwQ QO 'O@=}|t Vy=m |Q}tN |WQ@ VvQm QF= QO=Q |QDy@ |=yMU=B CU= umtt |O=yvW}B VwQ xm CU= u}= Qou=Wv OQwt u}tHvB|=ypmWQ}}eD Cr=L QO XwYN x@� OyO x�=Q= pt=m |m}t=v}O p}rLD |=yMU=B R=

"�nQR@ Q=}U@C=YDNt sDU}U QO |O=R; xHQO wO pOt |m}t=v}O CmQL CqO=at xm =Hv; R=w OQ=O OwHw MU=B |v=tR |xJN} Q=D QO |OwQw |}=Hx@=H 'Ov=xOW xDWwv jr]tx@ "CU}v xR=U |xv}W}@ |}=Hx@=H Qou=Wv 15 |r= 12 |=ypmW QO xv}W}@ MU=B|xR=U |L=Q] |=Q@ OQmrta Q=}at =@ Ov=wD|t xrRrR |=yDv= QO |}=yv Q}O=kt 'p=L Qy

"|]NQ}e |m}D=DU= p}rLDQO |Q}tN \=kv C}a[w "11 pmWp}rLD G}=Dv R= C}iQ_ |=y|vLvt 'CU= xOW u=}@ QDW}B xm Qw]u=ty "CU=|D; |=yVN@ QO 2 w 1 |=ypOt C}iQ_ |=y|vLvt "OvwW|t OQw;Q@ |m}D=DU=x@=Wt |oDN}Uo Kw]U 'OwW|t xOy=Wt 11 pmW QO xmv=vJ "CU= xOW x�=Q=K]U u}OvJ xJQo = "OwW|t xOy=Wt pOt wO Qy QO �1 pmW� |}xRQr VRer Kw]UxOy=Wt |]NQ}e |m}D=DU= |=yp}rLD QO KrUt lwr@ CWB QO Qo}O |oDN}Uo'|]NQ}e |m}D=DU= p}rLD hOy xm =Q} R &OvDU}v QF-wt G}=Dv QO um}rw 'OwW|tl =N |xOwD QO VvD C}a[w w CU= KrUt lwr@ |m}v=mt C=}YwYN OQw;Q@

"OQ=Ov xOWx�=Q= VwQ G}=Dv QO |Q}F-=D |L]U Q=@ CLD KrUt lwr@ CWB

|m}t=v}O p}rLD R= xOt;CUOx@ u}}=B w q=@ |=ypmWQ}}eD "2"5|O=R; xHQO wO pOt w pt=m

pmW x@ |]NQ}e |m}D=DU= p}rLD w |O=R; xHQO wO pOt R= xOt;CUOx@ G}=Dvpt=m |m}t=v}O p}rLD G}=Dv =@ w u=}@ xOW|@ wmM}t |=yx} wQ u}}=B w q=@ |}=Hx@=HxOt;CUOx@ |=ypmWQ}}eD ?}DQD x@ 15 |r= 12 |=ypmW "CU= xOW xU}=kt

"1 T=}kt ?} Q[ =@ |OwQw l} QLD =@ 1 pOt u}}=B w q=@ |=ypmWQ}}eD |v=tR |xJN} Q=D "12 pmW

113

"""|=Q@|

]NQ}e

|m}D=DU

=p}rLD

VwQ|

HvUQ=@Da

=

"0 5 T=}kt ?} Q[ =@ |OwQw l} QLD =@ 1 pOt u}}=B w q=@ |=ypmWQ}}eD |v=tR |xJN} Q=D "13 pmW

"1 T=}kt ?} Q[ =@ |OwQw l} QLD =@ 2 pOt u}}=B w q=@ |=ypmWQ}}eD |v=tR |xJN} Q=D "14 pmW

"0 5 T=}kt ?} Q[ =@ |OwQw l} QLD =@ 2 pOt u}}=B w q=@ |=ypmWQ}}eD |v=tR |xJN} Q=D "15 pmW

114

3 1|xQ

=tW'32

�2|xQ

wO-�13

95R}}=B

�'h}QW

u=Qta|

UOvyt p}rLD |D=@U=Lt u=tR xm |r=L QO 'Ovm x@U=Lt |rw@k p@=kCkO =@ =Q xrRrR QF=CLD

|=Q@ xDiQoCQwY |R=UxO=U 'xwqa x@ "OyO|t Vy=m =Q |rta |xr�Ut l} |=Q@� KrUt l =N VvmQOv= w xR=U |]NQ}e Q=DiQ Ovv=t '=yC}a]k sOa uDiQoQ_vQO|xQwO Q}_v� |m}t=v}O C=YNWt R= |QDj}ta lQO 'KrUt lwr@ CWB l =N

"Ovm|t O=H}= 'OvQ=O Q}F-=D |}xRQr MU=B QO xm �|rY= |=y?w=vDxHQO wO |=yu=tr= T} RQDU}y Q=DiQ w C}iQ_ |=y|vLvt "3"5

|O=R;|m}t=v}OQ=DiQ C=YNWt |xar=]t |=Q@ x=Ql} u=wvax@?re=T} RQDU}y |xNQJ|=ypOt |=yp}rLD R=T} RQDU}y |=yxkrL "OwW|t xDiQo Q_v QO =yu=tr= w =yxR=Up}rLD Ov}=Qi '�16 pmW� =yu; x@ \w@ Qt C}iQ_ |=y|vLvt w |O=R; xHQO wOQ=DiQ l} pOt 'QwmPt pmW j@=]t "OyO|t KQW =Q |O=R; xHQO wO |xt=vQ@l =N s}rUD pw] QO `=UD= |x]U=w x@CU= umtt xm 'Ovm|t x@ QHD =Q |}xOvwWsQvw xOvwQV}B |oDN}Uo Cra x@ Ov=wD|t |oOvwWsQv "OW=@ 50 `=UD= |x} w=R QO 1xOWxDWwv |xt=vQ@ "OW=@ l =N |xOvvm QwYLt Q=Wi QO Vy=m l} |x]U=w x@ =}xO=iDU= =@ =Q xOvwWsQv |=yl =N QO xOW|@ wmM}t |xR=U l} |}xRQr MU=B Ov=wD|txOy=Wt 1 pOt QO xJv; Ovv=t Ov=tUB w xv}W}@ Ctw=kt =@ C}iQ_ |=y|vLvt R=

"Ovm x@U=Lt '�16 pmW� OwW|t

|Q}oxH}Dv "6Ov=wD|t xm 'CU= xOW x�=Q= |]NQ}e |O=R; xHQO wO pOt l} 'VywSB u}= QOu}tR C=m} QLD QF= CLD |m =N p�=L |=yQ=w}O |m}t=v}O |=ypmWQ}}eD u}}aD |=Q@'|O=yvW}B |O=R; xHQO wO pOt QO =yQvi |]NQ}e Q=DiQ u}tND |=Q@ "OwW xO=iDU=lwr@ CWB QO |Owta |Q=PoQ=@ |wor= l} w xO=iDU= |]NQ}e |m}D=DU= p}rLD

"CU= xOW p=ta= |]NQ}e |m}D=DU= p}rLD QO pt=m pOt RQt |q=@ QO KrUtp}rLD R= xO=iDU= =@ |O=yvW}B VwQ |xar=]t |=Q@ |OQwt |xar=]t wOG}=Dv "Ov=xOW `k=w hrDNt |}xRQr l} QLD wO QF= CLD w ?=NDv= pt=m |m}t=v}O|xR=U |=ypmWQ}}eD |WN@C}=[Q pmW x@ |O=yvW}B VwQ xm CU= xO=O u=Wvp�=Ut |=Q@ =Q C=@U=Lt u=tR w Ovm|t |v}@V}B =Q xrRrR QF= CLD xOW|@ wmM}tu}@ hqDN= 'O@=}|t V}=Ri= =ypmWQ}}eD K]U xm u=vJty "OyO|t Vy=m |rta

"O@=}|t V}=Ri= R}v pt=m pOt |m}t=v}O p}rLD w |O=R; xHQO wO pOt G}=Dv"CU= xOQm ltm |rta pmW x@ xr�Ut |m} R}i Q=DiQ syi QO |O=yvW}B VwQ"Ov=xDiQo Q=Qk V}=tR; OQwt xR=U |rY= Ot=U@ w xrRrR |Ot=U@ |wDLt QF= u}vJty?r=e ?w=vD |xQwO x@ xHwD =@ R}v xR=U u=UWm |rY= ?w=vD |xQwO lQDWt QF=

"Ovm|t pQDvm =Q pmWQ}}eD K]U 'l} QLD K]U w MU=B h}]

|OQwt C=ar=]t x@ \w@ Qt C}iQ_ |=y|vLvt w T} RQDU}y |=yxkrL "16 pmW"�1 T=}kt ?} Q[ =@ wQDvUr= |xrRrR |=Q@�

|=Q@ 2001 uB=S |}xRQr |L=Q] |=tvy=Q 'PIANC "OwW xU}=kt KrUt l =N'um}rw "CU= xOQm x�=Q= p�=L |=yQ=w}O |=Q@ |}=Hx@=H Q=}at [21]'|QOv@ |=yxR=U

"CU= Q=DWwv u}= |xOwOLt R= QD=Qi R=Ht |=ypmWQ}}eD =@ G}=Dv |xU}=ktQ}}eD |xv}tm 'OwW|t xOy=Wt 15 |r= 12 |=ypmW QO xm Qw]u=ty|xR=Ov= x@ ?=DW |xv}W}@ seQ|ra '=D} QB=twr |xrRrR QF= CLD |=ypOt R= =ypmW'1989 p=U QO =D} QB=twr |xrRrR R= Oa@ "CU= xOt; CUOx@ 0 205 g w 0 41 g

seQ|ra xm OyO|t u=Wv xOW|@ wmM}t p�=L Q=w}O 9 QO xrRrR R= TB C=Oy=Wt[6]"Ov=xO=Ov RwQ@ O}OW |=ypmWQ}}eD R= |}xv=Wv I}y =yxR=U u}= 'q=@ |ki= ?=DW|=yQ=w}O |}xRQr OQmrta QO xrRrR |Ot=U@ |=wDLt QF= p}rO x@ Ov=wD|t Qt= u}=u}tR l} QLD QDt=Q=B =yvD u}tR |xv}W}@ ?=DW xm |r=L QO 'OW=@ xOW|@ wmM}t

[1]"OwW|t xO=iDU= xOW|@ wmM}t l =N |=yQ=w}O |rta |L=Q] |=Q@ xm 'CU=|=wDLt x@ MU=B Vy=m =} V}=Ri= xm Ovvm|t u=}@ |vt[ Qw] x@ =yxU}=kt u}=xR=U xm '|}=Hx@=H K]U w xR=U |m}v=mt C=YNWt w |OwQw l} QLD |Ot=U@u}= pY=L |xH}Dv u} QDsyt 'p=L Qy x@ "CU= xDU@=w xOQm x@ QHD l} QLD pw] QOxOW|@ wmM}t |xR=U |m}t=v}O pmWQ}}eD Ov=wD|t |O=yvW}B VwQ xm CU= xOw@

=yCWwv=B1. single-degree of freedom systems2. �nite di�erence method

3. Fast Lagrangian Analysis of Continue4. Visual Basic

115

"""|=Q@|

]NQ}e

|m}D=DU

=p}rLD

VwQ|

HvUQ=@Da

=

�References� `@=vt1. Lazarte, C., Elias, V., Espinoza, R. and Sabatini, P.,

Geotechnical Engineering Circular No. 7 Soil Nail Walls,United States Federal Highway Administration, No.FHWA0-IF-03-017 (1999).

2. Veletsos, A.S. and Younan, A.H. \Dynamic soil pressureson rigid retaining walls", Earthq. Engng. Struct. Dyn.,23(3), pp. 275-301 (1994).

3. Veletsos, A.S. and Younan, A.H. \Dynamic response ofcantilever retaining walls", J. Geotech. Geoevviron. En-gng., ASCE, 123(2), pp. 161-172 (1997).

4. Cakir, T. and Livaoglu, R. \Fast practical analyticalmodel for analysis of back�ll- rectangular tank- uid in-teraction system", Soil Dyn. Earthq. Engng., 37, pp. 24-37 (2012).

5. Vucetic, M., Tufenkjian, M.R. and Doroudian, M.\Dynamic centrifuge testing of soil-nailed excavation",Geotech. Testing J., 16(2), pp. 172-187 (1993).

6. Vucetic, M., Iskandar, V.E., Doroudian, M. and Luc-cioni, L. \Dynamic failure of soil-nailed excavationsin centrifuge", In: Proceeding of International Sym onEarth Reinforc, Fukuoka, Japan, pp. 829-834 (1993).

7. Tufenkjian, M.R. and Vucetic, M. \Dynamic fail-ure mechanism of soil-nailed excavation models incentrifuge", J. Geotech. Geoenviron. Engng., ASCE,126(3), pp. 227-235 (2000).

8. Kocijan, J. \Analysis of forces and displacements leadingto failure of di�erent con�gurations of soil-nailed excava-tion centrifuge models under cyclic loads", Ph.D Thesis,University of Los Angeles (2005).

9. Hong, Y., Chen, R., Wu, C. and Chen, J. \Shaking tabletest and stability analysis of steep nailed slopes", Can,Geotech,, J., 42(5), pp. 1264-1279 (2005).

10. Komak Panah, A. and Majidian, S. \Assessment of soil-nailed excavations seismic failure under cyclic loadingand pseudo-static forces", In: Proceeding of the 5th Int.Con. on Rec. Adv. in Geotech. Earthq. Engng. and SoilDyn., San Diego, California (2010).

11. Komak Panah, A. and Majidian, S. \2D numerical mod-eling of soil-nailed structures for seismic improvement",Geomech. Engng., 5, pp. 37-55 (2013).

12. Webe, L. and Christopoulos, C. \Characterizing accel-eration spikes due to sti�ness changes in nonlinear sys-tems", Earthq. Engng. Struct. Dyn., 39(14), pp. 1653-1670 (2010).

13. FLAC, Fast Lagrangian Analysis of Continua, ItascaConsulting Group, Mineapolis, MN, USA (1998).

14. Bathe, K.J. and Wilson, E.L. \Stability and accuracyanalysis of direct integration methods", Earthq. Engng.Struct. Dyn., 1(3), pp. 283-291 (1993).

15. Chopra, A.K. and Goel, R.K. \A modal pushover anal-ysis procedure for estimating seismic demands for build-ings", Earthq. Engng. Struct. Dyn., 31(3), pp. 561-582(2002).

16. EI Ganainy, H. and EI Naggar, M.H. \Seismic perfor-mance of three-dimensional frame structures with un-derground stories", Soil Dyn. Earthq. Engng., 29(9), pp.1249-1261 (2009).

17. Cheuk, C.Y., Ng, C.W.W. and Sun, H.W. \Numericalexperiments of soil nails in loose �ll slopes subjectedto rainfall in�ltration e�ects", Comput. Geotech., 32(4),pp. 290-303 (2005).

18. Singh, V.P. and Babu, G.L.S. \2D numerical simulationsof soil nail walls", Geotech. Geol. Eng., 28(4), pp. 299-309 (2010).

19. PEER, PEER NGA Database, Paci�c Earthquake Engi-neering Research Center, University of California, Berke-ley, California, http://peer.berkeley.edu/nga/.

20. Lysmer, J. and Kuhlmeyer, R.L. \Finite dynamic modelfor in�nite media", J. Engng. Mech., ASCE, 4, pp. 859-878 (1996).

21. PIANC, Seismic design quidlines for port structures,International Navigation Association, Balkema, Tokyo(2001).

116