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"�5 pmW� CUOq=@ QO |QBU Q=w}O xqm =} |vD@ Ov@?; Q=w}O QO |R} QuD@xOW ZQi QDt 1 |vD@ Ov@?; Q=w}O ZQa� d1 � 3 m |=Q@ SKBUP

%O};|t CUOx@ 24 |x]@=Q R= �CU=SKBUP = d1� tmin (24)

xR=U CUOq=@ QO Ov@?; xQ=w}O |=QH= hrDNt |=yVwQ "5 pmW

"TEMP3 � 0 w TEMP2 � 0 "4 pmW

(G � 1)tmin =@ Q@=Q@ xm TTMIN =@ 'OwW|t |FvN (tmin) hm |R} QuD@2 42 Q@=Q@ w uD@ XwYNt |r=oJ 'G u; QO xm &CU= xOW xO=O u=Wv 'CU=u=Wv 4 =D 2 |=ypmW QO 'hrDNt \=kv |=Q@ xOWvpO=aDt HGL Q=Okt "CU=TEMP5 w TEMP4 'TEMP3 'TEMP2 =yu; QO xm &CU= xOW xO=O

%Ov};|t CUOx@ 15 |r= 12 \@=wQ R=

TEMP2 = H�02 � Y2 � TTMIN (12)

TEMP3 = H�03 � Y3 � TTMIN (13)

TEMP4 = H�04 � Y4 � TTMIN (14)

TEMP5 = H�0E � Y5 � TTMIN (15)

"OvDUy 4 w 3 '2 \=kv QO xOW|@=}uwQO Q}O=kt ?}DQD x@ �04 w �03 '�02hm |R} QuD@ Ct=N[ |x@U=Lt |=Q@ A2 Q=Okt R= '3 w 2 |=ypmW QOxO=iDU= 3 w 2 \=kv u}@ 'CU= R=}v OQwt |R} QuD@ Ct=N[ |xv}tm Q@ xi=[= xmK]U R= QDq=@ QO TEMP5 w TEMP4 'TEMP3 'TEMP2 "OwW|tQ}O=kt "OvwW|t xDiQo Q_v QO |ivt u; R= QDu}}=B QO w C@Ft TTMIN p}iwQBw 3 '3 w 2 \=kv u}@ HGL \N Q} R QO pO=aDt=v Kw]U ?}DQD x@ A4 w A3 'A2u}= j@] TEMP5 =D TEMP2 x@ xHwD =@ Q}O=kt u}= xm &OvDUy 5 w 4 w '4

%OvwW|t x@U=Lt \@=wQx@U=Lt 16 |x]@=Q R= A2 Q=Okt 'TEMP3 � 0 w TEMP2 > 0 Qo = ��

%�2 pmW� OwW|t

A2 = 0 5X1 TEMP2 (16)

%O};|t CUOx@ 17 |x]@=Q R= X1 'u; QO xm

X1 = TEMP2TEMP2 +ABS(TEMP3) l2 (17)

"CU= TEMP3 jr]tQOk Q@=Q@ ABS(TEMP3) Q=Okt|x]@=Q R= A2 Q=Okt '�3 pmW� TEMP3 > 0 w TEMP2 > 0 Qo = ��

%OwW|t x@U=Lt 18

A2 = 0 5 (TEMP2 + TEMP3) l2 (18)

Ow@ Oy=wN A2 = 0 Q=Okt 'TEMP3 � 0 w TEMP2 � 0 Qo = ��"�4 pmW�

%s} Q=O x@=Wt CQwYx@

16

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�+ [l2 + (l2 � x)] tmin

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x = Y1l3Y3

j@] '6 pmW x@ xHwD =@ (ASFILL) ZQa OL=w QO |R} Qm =N sHL Q=Okt%O};|t CUOx@ 28 |x]@=Q

ASFILL =

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g(")@" = (l2� l6) (Y3 + y1) + 12 l5 (Y3� y1)

+ 12�l3 +

�Y1 l3Y3

��(Y3� y1) (28)

|L=Q] |=yQ}eDt w hOy `@=D |iQat "5"3x�=Q= 29 |x]@=Q CQwYx@ |i=QLv= OU E=OL= |=yxv} Ry x@ \w@ Qt hOy `@=D

%OwW|tMinimize COST =(TV CON)(COST1)

+ (SKBX1)(COST2)

+ (SKBX2)(COST3)

+ (ASCUT )(COST4)

+ (ASFILL)(COST5) (29)

Q=Okt TV CON 'ZQa OL=w QO|i=QLv= OU E=OL= |xv} Ry pmCost 'u; QO xm|QBU Q=w}O jta SKBX1 'hm |R} QuD@ |xv} Ry COST1 'hm QO |R} QuD@'uO}@ wm pt=W CUOq=@ |QBU Q=w}O |xv} Ry COST2 '|vD@ hm Q} R CUOq=@Q=w}O |xv} Ry COST3 '|vD@ hm Q} R CUOu}}=B |QBU Q=w}O jta SKBX2COST4 '|Q=OQ@l =N s=HL= Q=OktASCUT 'uO}@ wm pt=WCUOu}}=B |QBU|xv} Ry COST5 '|R} Qm =N s=HL= Q=Okt ASFILL '|Q=OQ@l =N |xv} Ry

"|R} Qm =N

xr�Ut |=yO}k |iQat "6"3pw] =@ |HwQN |m}rwQO}y u=}O=Qo j} Q] R= '(d2) CUOu}}=B |QBU Q=w}O jtaO}=@ 'hm pw] (L) w 'CUOu}}=B |QBU Q=w}O jta (d2) "Ovm|t =O}B \=@DQ= hmu=}O=Qo Q=Okt R= |HwQN |m}rwQO}y u=}O=Qo =D OvW=@ xDW=O \=@DQ= sy =@ |}xvwox@

"OW=@ QDtm (PGE) R=Ht |m}rwQO}y(GE) |HwQN u=}O=Qo 'CU= CUOu}}=B |=yDv= QO |QBU Q=w}O xm |Dr=L |=Q@

%O};|t CUO x@ 30 |x]@=Q R=GE = H

d21

�p�

(30)

%O};|t CUOx@ 31 |x]@=Q R= � Q=Okt u; QO xm� = 1 +

p1 + �2

2 (31)

w 0 5 ?}DQD x@ |QBU Q=w}O xqm ZQa w jta� d1 > 3 m |=Q@ SKBUP w"CU= 0 5 |w=Ut '�CU= xOW ZQi QDt 1

CUO u}}=B |QBU Q=w}O w |vD@ Ov@?; Q=w}O |=Q@ x@=Wt CQwYx@ u}vJty|QBU Q=w}O xqm =} |vD@ Ov@?; Q=w}O QO |R} QuD@ sHL Q=Okt 'SKBDN %s} Q=O

"CUOu}}=B QO%O};|t CUOx@ 25 |x]@=Q R= 'd2 � 3 m |=Q@ SKBDN

SKBUP = d2� t2 (25)

"CU= 0 5 |w=Ut 'd2 > 3 m |=Q@ SKBDN wQ=w}O |=Q@ R=}v OQwt |R} QuD@ Q=Okt x@ xHwD =@u}vJty w 23 w 10\@=wQ?}mQD R='(TV CON) ZQa OL=w QO |R} QuD@ pm sHL Q=Okt '|QBU Q=w}O =} |vD@ Ov@?;

%OwW|t x�=Q= 26 |x]@=Q CQwYx@ xOWxO=O |i=QLv= OU p}iwQB |=Q@

TV CON=Ltmin +�A2+A3 +A4

G� 1�

+ SKBUP + SKBDN

(26)

|R} Qm =N w |Q=OQ@l =N sHL u}}aD "4"3'(ASCUT ) ZQa OL=w QO R=}vOQwt |Q=OQ@l =N sHL Q=Okt '6 pmW x@ xHwD =@w hm K]U |q=@ QO OwHwt l =N sHL pt=W 'hm |R} QuD@ |=QH= |=Q@|QBUQ=w}O =} Ov@?; Q=w}O w hm |R} QuD@ sHL =@ Q@=Q@ xm 'CU= |m =N sHL

"CU=p@=k 27 |x]@=Q j@] |Q=OQ@l =N sHL Q=Okt '6 w 1 |=ypmW x@ xHwD =@

%CU= x@U=Lt

ASCUT =Y1l4 + 0 5�Y1Y1l3Y3

�+ Ltmin +

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g(")@"

35+SKBUP+SHBDN

(27)

"hm |R} QuD@ s=Hv= |=Q@ |R} Qm =N w |Q=OQ@l =N sHL "6 pmW

17

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=yQ}eDt OwOL u}}aD "8"3x@ \w@ Qt |=yQ=}at T=U=Q@ CUOu}}=B w CUOq=@ |QBU |=yQ=w}O jta |xv}tmCU= xOW u}}aD |rta C=_Lqt uDiQoQ_vQO =@ =yu; jta |xv}W}@ w |oDUW?;|xJ[wL pw] w =y?}W pw] 'R} QQU pw] x@ xHwD =@ 'hm pw] |xv}tm u}vJty w|R=Uxv}y@ OvwQ QO xDiQQ=mx@ |vOW |=[i '1 pwOH "CU= xOt; CUO x@ Vt=Q;

"OyO|t u=Wv =Q

EL@ w G}=Dv "4(PGE) R=Ht |HwQN |m}rwQO}y u=}O=Qo Q}F-=D "1"4

"OQ=O |oDU@ |i=QLv= OU Q} R l =N wv x@ R=Ht |HwQN |m}rwQO}y u=}O=Qo Q=Oktu}@ l =N |=yxv=O |xR=Ov= x@ xHwD =@ w Cr}U R= QDW}@ |xU=t |=Q@ PGE Q=OktG}=Dv "CU= |UQ Cr}U w Cr}U |=Q@ 0 2 R= QDtm Q}O=kt "CU= 0 25 =D 0 2xOW xOQw; 3 w 2 |=ypwOH QO PGE hrDNt Q}O=kt |=Q@ l}DvS sD} Qwor= |=QH=

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"CU= xOW xO=O u=Wv 2 p}iwQB |=Q@ 'R=Ht |HwQNV}=Ri= =@ 'CU=XNWt 2 w 1 p}iwQB |=Q@ 16 w 9 |=ypmW QO xm Qw]u=typw] w CUOu}}=B |QBU Q=w}O jta Q=Okt R=Ht |HwQN |m}rwQO}y u=}O=Qo Q=OktOU E=OL= |xv} Ry Q=Okt Vy=m Ea=@ xH}Dv QO w CU= xOQm =O}B Vy=m hmQ=OktV}=Ri= "CU= xOW R=Ht |HwQN |m}rwQO}y u=}O=Qo Q=OktV}=Ri= =@ '|i=QLv=CU= xDW=Ov |Q}F-=D CUOq=@ |QBU Q=w}O jta QO R=Ht |HwQN |m}rwQO}y u=}O=Qo

%O};|t CUOx@ 32 |x]@=Q R= � Q=Okt u; QO xm� = L

d2(32)

%O};|t CUOx@ 33 |x]@=Q R= PGE u}=Q@=v@PGE � H

d2 �p�

(33)

|]NQ}e O}k '|R=UxO=U s=Hv= w 33 |x]@=Q QO 31 |x]@=Q R= � Q=Okt|v} Ro}=H =@%CU= xOW x�=Q= 34 |x]@=Q QO xm O};|t CUO x@ xr�Ut

L� d2

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%�35 |x]@=Q�

Lmin � L � Lmax; d1 min � d1 � d1 max;

d2 min � d2 � d2 max (35)

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"|vD@ hm

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18

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"�1 p}iwQB� PGE Q}}eD =@ xv} Ry Q}}eD "12 pmW

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19

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20

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21

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=yCWwv=B1. barrage2. uplift3. exit hydraulic gradient

4. sheet-piles5. �lling6. excavation7. genetic algorithm8. Visual Basic.NET

23

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�References� `@=vt1. Shamsai, A., Design of Diversion Dams, Sharif Univer-

sity Press Iran, ISBN: 978-964-7982-14-6 (2007) (In Per-sian).

2. Da Silva, J.F. \Optimization of concrete gravity damsfoundation systems", 22nd International Congress onLarge Dams-ICOLD, Barcelona, Spain (2006).

3. Sedghi-Asl, M., Rahimi, H. and Khaleghi, H., Labo-ratory Investigation of the Seepage Control Measuresunder Coastal Dikes, Experimental Techniques, doi:10.1111/j.1747-1567.2010.00692, 36, pp.61-71 (2011).

4. Garg, N.K., Bhaghat, S.K. and Asthana, B.N. \Opti-mal barrage design based on subsurface ow considera-tions", Journal Of Irrigation And Drainage Engineering,128(4), pp. 253-263 (2002).

5. Goldberg, D.E., Genetic Algorithms in Search, Opti-mization and Machine Learning, Kluwer Academic Pub-lishers, Boston (1989).

6. Khosla, A.N., Bose, N.K. and Taylor, M.T., Design ofWeirs on Permeable Foundation, India, Central Boardof Irrigation and Power, Technology & Engineering, 178pages (1936).

7. Tomlinson, S.S. and Vaid, Y.P. \Seepage forces andcon�ning pressure e�ects on piping erosion", CanadianGeotechnical Journal, 37(1), pp. 1-13 (2000).

8. Garg, N. K. \Barrage Design Consideration Based onSubsurface Flow", (2004). Available on line at http://www.actapress.com/Abstract.aspx?paperId=18641.

9. Turan, K.H. \Software program for optimum design ofdiversion structures", Unpublished M.Sc thesis, Depart-ment of Civil Engineering, Middle East Technical Uni-versity (2004).

10. Ijam, A.Z. \Conformal analysis of seepage below a hy-draulic structure with an inclined cuto�", InternationalJournal of Numerical and Analytical Methods in Ge-omechaneics, 18(5), pp. 345-353 (2005).

11. Ahmed, A.A. \Design of hydraulic structures consideringdi�erent sheet pile con�gurations and ow through canalbanks", Computer and Geotechnics, 38(4), pp. 559-565(2011).

12. Amiri Tokaldany, E. and Khalili Shayan, H. \Upliftforce, seepage, and exit gradient under diversion dams",Proceedings of the ICE - Water Management, ISSN:1741-7589, E-ISSN: 1751-7729. 10.1680/wama.11.00084(2012).

13. Sedghi-Asl, M., Rahimi, H. and Khaleghi, H. \The ef-fect of optimum location of the sheet pile in decreasingseepage ow under hydraulic structures using numericalmodel", 5th Iranian Hydraulic Conference, Iran (2005)(In Persian).

14. Lashte-Nashaei, M., Khoda-Bakhshi, M., Saber, M. andNik-Ghalb-Pour, M. \E�ect of cuto� wall depth anddrains on uplift pressure and exit hydraulic gradientin diversion dams", 7th International Seminar of RiverEngineering, Shahid Chamran University, Ahvaz, Iran(2006) (In Persian).

15. Ahmadi, H., Ghahreman-nezhad, M. and Verdi-nezhad,V. \Investigation on the e�ects of drainage systems andcuto� walls to control the uplift force under diversiondams", 3rd Irrigation and Drainage Network Manage-ment National Conference, Iran (2011) (In Persian).

16. Khalili Shayan, H., Amiri Tokaldany, E. and Yeganeh, A.\Evaluation of di�erent methods to estimate the upliftforce under diversion dams by experimental and numer-ical data", 3rd Irrigation and Drainage Network Man-agement National Conference, Iran (2011) (In Persian).

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