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J.P.F.M. J a n s s e n and R.E. J o r i s s e n , M i n i s t r y o f T r a n s p o r t and P u b l i c Works,

P.O. Box 5044, 2600 GA D e l f t , The N e t h e r l a n d s

A b s t r a c t

I n 1989 t h e D u t c h government d e c i d e d t o b u i l d a s t o r m surge b a r r i e r i n t h e New Waterway n e a r R o t t e r d a m b e i n g a good and cheap a l t e r n a t i v e f o r t h e n e c e s s a r y s t r e n g t h e n i n g o f d i k e s a l o n g t h e l o w e r r e g i o n s o f t h e D u t c h r i v e r s R h i n e and Meuse. To be f e a s i b l e t h e b a r r i e r had t o meet

s e v e r a l g o a l s . The most i m p o r t a n t ones b e i n g :

* c l o s i n g f r e q u e n c y l e s s t h e n once e v e r y 10 y e a r s now and once e v e r y 5 y e a r s a f t e r 50 y e a r s f r o m now ( i n c l u d i n g 25 cm s e a - l e v e l r i s e ) * p r e s c r i b e d r e d u c t i o n o f d e s i g n w a t e r - l e v e l s a t t w o r e p r e s e n t a t i v e

l o c a t i o n s , b e i n g R o t t e r d a m and D o r d r e c h t .

These and o t h e r p a r a m e t e r s a r e c a l c u l a t e d by means o f a p r o b a b i l i s t i c c a l c u l a t i o n method. T h i s method i n v o l v e s a m a t h e m a t i c a l o p e n - c h a n n e l n e t w o r k model o f w h i c h t h e r e s u l t s a r e combined w i t h t h e s t a t i s t i c a l p r o p e r t i e s o f i n p u t p a r a m e t e r s . A r i s k - a n a l y s i s o f t h e p e r f o r m a n c e o f t h e b a r r i e r i s i n c l u d e d . F i n a l l y t h e model i s a d a p t e d t o s t u d y o p e r a t i o n a l a s p e c t s . 1 . I n t r o d u c t i o n The p r o j e c t a r e a i s s i t u a t e d i n t h e s o u t h w e s t o f t h e N e t h e r l a n d s as shown i n f i g u r e s 1 and 2. I n f i g u r e 2 t h e d i k e s a r e shown, w h i c h were t o be r e i n f o r c e d as a consequence o f t h e D e l t a p l a n . T h i s p l a n was

d e v e l o p e d a f t e r t h e f l o o d o f 1953. I t i n c l u d e d s h o r t e n i n g o f t h e c o a s t l i n e by c l o s i n g a number o f t i d a l i n l e t s and t o s t r e n g t h e n r e m a i n i n g d i k e s . By t h e t i m e o f 1985 most o f t h i s p l a n has been com-p l e t e d : s t i l l a b o u t 200 km o f d i k e s had t o be s t r e n g t h e n e d . A r e - e x a m i n a t i o n o f d e s i g n w a t e r - l e v e l s (DWL) l e d t o h i g h e r v a l u e s t h a n t h o s e o r i g i n a l l y c a l c u l a t e d . T h i s i m p l i e d v e r y c o s t l y c o n s t r u c t i o n w o r k s i n d e n s e l y p o p u l a t e d o r o t h e r w i s e c o m p l i c a t e d a r e a s . T h e r e f o r e , i n 1987 t h e D u t c h government i n i t i a t e d a s t u d y t o c o n s i d e r a s t o r m surge b a r r i e r n e a r R o t t e r d a m . T h i s b a r r i e r s h o u l d meet two m a i n g o a l s . F i r s t l y t h e DWL s h o u l d be r e d u c e d s i g n i f i c a n t l y t o a v o i d p r o b l e m s r e l a t e d t o d i k e r e c o n s t r u c t i o n w o r k s . The p r e s c r i b e d r e d u c t i o n s o f DWL a r e based on t h e s i t u a t i o n i n t h e a r e a s , w h i c h w o u l d be most a f f e c t e d by t h e r e c o n s t r u c t i o n w o r k s . These a r e a s a r e t h e c i t i e s o f R o t t e r d a m and D o r d r e c h t . S e c o n d l y t h e p r e s e n c e o f R o t t e r d a m h a r b o u r d o e s n ' t a l l o w t h e b a r r i e r t o be c l o s e d t o o o f t e n . The c l o s i n g f r e q u e n c y o f t h e

b a r r i e r s h o u l d ( o n a v e r a g e ) be l e s s t h a n once e v e r y 10 y e a r s now and l e s s t h a n once e v e r y 5 y e a r s a f t e r 50 y e a r s f r o m now. The l a t t e r

s i t u a t i o n i n c l u d e s a s e a - l e v e l r i s e o f 25 c e n t i m e t r e s . From s e v e r a l p r e d e s i g n s a f i n a l c h o i c e was made a t t h e end o f 1989. The s e l e c t e d b a r r i e r d e s i g n f e a t u r e s two s e m i - c i r c u l a r d o o r s . The b a r r i e r i s c l o s e d by r o t a t i n g t h e f l o a t i n g d o o r s i n t o t h e r i v e r ( f i g u r e 3) and l o w e r i n g t h e e n t i r e c o n s t r u c t i o n t o t h e r i v e r b o t t o m by f i l l i n g b a l l a s t t a n k s w i t h w a t e r . T h i s paper d e a l s w i t h h y d r a u l i c a s p e c t s o f t h i s b a r r i e r and t h e i n f l u e n c e o f r e l i a b i l i t y o f t h e b a r r i e r on DWL and o p e r a t i o n a l a s p e c t s . Fig. 1

2. H y d r a u l i c a s p e c t s 2.1 The h y d r a u l i c s y s t e m p r o j e c t e d r i v e r / b a r r i e r d i s c h a r g e o r i v e r d i k e s e a d i k e \ \ \ \ n p o l d e r

Fig. 4 The system

I n f i g u r e 4 t h e h y d r a u l i c s y s t e m i s shown i n a s c h e m a t i c f o r m . B a s i c a l l y t h e r e a r e two r i v e r b r a n c h e s w i t h s e v e r a l c o n n e c t i o n s . The s o u t h e r n b r a n c h r u n s i n t o the l a r g e H a r i n g v l i e t e s t u a r y . T h i s e s t u a r y i s s e p a r a t e d f r o m t h e sea by a b a r r a g e w i t h l a r g e d i s c h a r g e s l u i c e s . The n o r t h e r n b r a n c h r u n s f r e e l y i n t o t h e sea v i a t h e c i t y o f R o t t e r d a m and t h e New Waterway. T i d a l movement and t h e r e f o r e s t o r m s u r g e s e n t e r t h e system t h r o u g h t h i s n o r t h e r n b r a n c h . C l o s e t o t h e r i v e r m o u t h t h e w a t e r -l e v e -l i s d e t e r m i n e d c o m p -l e t e -l y by t i d a l movement combined w i t h s t o r m surge e f f e c t s . F i g u r e 5 shows t h a t the w a t e r - l e v e l a t t h e r i v e r - m o u t h can be c o n s t r u c t e d as a c o m b i n a t i o n of a s t r o n o m i c a l t i d e and a s t o r m s u r g e . The maximum sea w a t e r - l e v e l (MSWL) i s i n f l u e n c e d by f i v e p a r a -m e t e r s : a s t r o n o -m i c a l t i d e , d u r a t i o n ,

shape and h e i g h t o f t h e s t o r m surge and phase d i f f e r e n c e between s t o r m surge and a s t r o n o m i c a l t i d e . T h i s number o f v a r i a b l e s can be r e d u c e d . The v a r i a t i o n o f t h e a s t r o n o m i c a l t i d e a t Hoek v a n H o l l a n d i s so s m a l l , t h a t a mean t i d a l c u r v e w i l l 5 12 U Tim (diysl • A . M . 0 . 0 0 . o» .a.oo. + 1 . 0 4 ? 0.0O. -1.00. : I • : 7 m / : ~ r \ : - i 3 «-a 12 i s S 12 U 5010» « ^ W Tint tdtysl 5 12 U « 12 11 S 12 U Tim (dêysl F i g u r e 5

be u s e d . S e c o n d l y t h e shape o f t h e s t o r m surge i s c o n s i d e r e d t o be con-s t a n t acon-s con-shown i n f i g u r e 5.

The i n c o m i n g t i d a l wave i s damped t r a v e l l i n g u p s t r e a m and phase d i f -f e r e n c e s o c c u r , as shown i n -f i g u r e 6. I n t h i s i n t e r m e d i a t e r e g i o n t h e w a t e r - l e v e l s a r e d e t e r m i n e d by b o t h t i d a l movement and r i v e r d i s c h a r g e ,

i ; 760104 12 780107 12 780108 12 Tim (days) «-L o c a t i o n H o e k v o n Ho 1 1 a n d 760108 l2 7 M 1 0 7 l 2 760108 12 780109 780108 & 780107 & 760108 T1M4 (days) 1 Tim* (days) »-L o c a t i o n R o t t e n d a m L o c a t i o n D o r d r a c n t : _r + 4 . 0 0 • 3 . 0 0 +*.00 • t.oc Q.QQ - 1 . 0 0 r : - 0 . 0 7 ;

Tim (dsyi) _{rit (<un) Tlmt Usysl}

F i g u r e 6

The r e l a t i o n between MSWL, r i v e r d i s c h a r g e and maximum r i v e r w a t e r -l e v e -l (MRWL) i s shown i n f i g u r e 7. T h i s f i g u r e shows -l i n e s o f e q u a -l MRWL a t R o t t e r d a m and D o r d r e c h t as a f u n c t i o n o f r i v e r d i s c h a r g e and MSWL. I n t h e s e g r a p h s t h e v a l u e s o f d u r a t i o n and phase d i f f e r e n c e o f t h e s t o r m s u r g e a r e k e p t c o n s t a n t a t 29 and 4.5 h o u r s . L o c a t i o n R o t t e r d a m I 1 ' ' I L o c a t i o n D o r d r e c h t i 2 1 7 1 1 | 1 1 1 | 1 1 1K I I i ' . , r | i i I j . i i -— 1 r I i I I I t i ' ' i i ' i i i t i i i i i 8 12 River Discharge (103 m3/s) 0 4 8 12 River Discharge (103 m3/s) 16 F i g u r e 7 The h y d r a u l i c c o n d i t i o n s i n t h e p r o j e c t a r e a a r e g o v e r n e d by f o u r v a r i a b l e s . Three v a r i a b l e s d e t e r m i n e t h e boundary c o n d i t i o n a t t h e r i v e r - m o u t h (MSWL). These v a r i a b l e s a r e d u r a t i o n ( s ) , h e i g h t (m) and phase d i f f e r e n c e ( p ) o f t h e s t o r m s u r g e . The f o u r t h v a r i a b l e i s t h e r i v e r d i s c h a r g e ( q ) , w h i c h i n c o m b i n a t i o n w i t h t h e MSWL, d e t e r m i n e s t h e MRWL. The r i v e r d i s c h a r g e v a r i e s on a much l a r g e r t i m e s c a l e t h a n s t o r m

surges do. T h e r e f o r e t h i s v a r i a b l e c a n be t r e a t e d as a c o n s t a n t d u r i n g a s t o r m s u r g e . The f o u r g o v e r n i n g v a r i a b l e s a r e c o n s i d e r e d t o be i n d e p e n d e n t . T h i s method o f d e t e r m i n i n g w a t e r - l e v e l s i s an e x t e n s i o n o f t h e u s u a l a p p r o a c h , w h i c h i s based on o n l y two g o v e r n i n g v a r i a b l e s : s t o r m surge h e i g h t and r i v e r d i s c h a r g e . The p a r a m e t e r s s t o r m surge d u r a t i o n and phase d i f f e r e n c e a r e assumed t o be c o n s t a n t ( 2 9 and 4.5 h o u r s ) . F o r t h e s i t u a t i o n w i t h o u t a b a r r i e r t h e r e s u l t s o f b o t h c a l c u l a t i o n methods d o n ' t d i f f e r v e r y much.

2.2 The e f f e c t o f t h e b a r r i e r

The e f f e c t s o f t h e b a r r i e r on w a t e r - l e v e l s i n t h e h y d r a u l i c s y s t e m a r e t w o f o l d . One e f f e c t i s t h e r e d u c t i o n o f w a t e r - l e v e l s because t h e s t o r m s u r g e s c a n ' t e n t e r t h e system any more. On t h e o t h e r hand t h e r e i s an i n c r e a s e o f w a t e r - l e v e l s i n t h e system because o f t h e a c c u m u l a t i o n o f r i v e r d i s c h a r g e . To c a l c u l a t e t h e t o t a l b a l a n c e o f e f f e c t s t h e h y d r a u -l i c s y s t e m has been m o d e -l -l e d by a m a t h e m a t i c a -l o p e n - c h a n n e -l n e t w o r k m o d e l . The s c h e m a t i z a t i o n o f t h e system i s c o n f o r m f i g u r e 2 and con-s i con-s t con-s o f a b o u t 200 b r a n c h e con-s and nodecon-s. T h i con-s model hacon-s been i n ucon-se f o r a l o n g t i m e t o p r e d i c t w a t e r - l e v e l s on a d a i l y b a s i s . The b a r r i e r s h o u l d r e d u c e t h e DWL a t R o t t e r d a m and D o r d r e c h t . The p r e s c r i b e d DWL a r e 3.60 m e t e r above NAP f o r R o t t e r d a m and 3.00 m e t e r above NAP f o r D o r d r e c h t .

I n o r d e r t o r e a c h t h i s g o a l t h e b a r r i e r has t o be c l o s e d whenever t h e p r e d i c t e d maximum sea w a t e r l e v e l (PMSL), g i v e n t h e a c t u a l r i v e r d i s c h a r g e , w o u l d r e s u l t i n a exceedance o f t h e DWL a t one o f t h e l o c a t i o n s . I n o r d e r t o have some f r e e b o a r d r e g a r d i n g t h e e f f e c t s o f i n -a c c u r -a c y o f t h e PMSL (see p -a r -a g r -a p h 3) -a c r i t i c -a l w -a t e r - l e v e l (CL) i s i n t r o d u c e d . T h i s l e v e l i s somewhat l o w e r t h a n t h e DWL. The m a r g i n between DWL and CL i s 40 cm f o r t h e l o c a t i o n o f R o t t e r d a m and 10 cm f o r t h e l o c a t i o n o f D o r d r e c h t . The r e a s o n f o r t h e s e d i f f e r e n t m a r g i n s i s t h e f a c t , t h a t D o r d r e c h t i s about t w i c e as f a r f r o m t h e N o r t h Sea as R o t t e r d a m and t h e r e f o r e l e s s s e n s i t i v e t o s e a - l e v e l v a r i a t i o n . T h i s means, t h a t t h e m a r g i n , w h i c h i s s t r o n g l y i n f l u e n c e d by t h e a c c u r a c y o f t h e PMSL, c a n be somewhat s m a l l e r a t D o r d r e c h t . I t s h o u l d be k e p t i n m i n d , t h a t b o t h DWL and CL a r e f i x e d w a t e r l e v e l s a t t h e l o c a t i o n s R o t -t e r d a m and D o r d r e c h -t . F i g u r e 6 can be used -t o -t r a n s f o r m -t h e CL i n -t o a

r i v e r d i s c h a r g e d e p e n d e n t c r i t e r i o n C L ( q ) f o r t h e l o c a t i o n Hoek v a n H o l l a n d f o r w h i c h a l s o t h e PMSL i s g i v e n . I n f i g u r e 8 t h e e f f e c t o f t h e b a r r i e r i s shown f o r t h e l o c a t i o n s o f R o t t e r d a m and D o r d r e c h t f o r a s p e c i f i c s t o r m surge and r i v e r d i s c h a r g e . I n f i g u r e 9 t h e e f f e c t o f t h e b a r r i e r on t h e r e l a t i o n between MSWL, r i v e r d i s c h a r g e and MRWL i s shown. I n f i g u r e 9 t h e t h i c k l i n e r e p r e s e n t s t h e c l o s i n g c r i t e r i o n C L ( q ) . Below t h i s l i n e f i g u r e 9 i s e x a c t l y t h e same as f i g u r e 7. Above t h i s l i n e t h e b a r r i e r i s c l o s e d and t h i s r e d u c e s t h e MRWL s i g n i f i c a n t l y compared w i t h f i g u r e 7. Only f o r v e r y h i g h r i v e r d i s c h a r g e s t h e e f f e c t o f t h e b a r r i e r i s l e s s s i g n i f i c a n t . " 150107 « U ! » 750101 S " H 76010J Tlae (days) w . L o c a t i o n R o t t e r d a m + 2 . 5 0

1

• 2 . 0 0 • 1.50 • 1.00 +0.5Q "C 0 . 0 0 3 - 0 . 5 0 closura ^ l OF birr léf* • f 1 \ 1 _r f-*-0 39 ^ — ' • 2 . 5 0 + 2 . 0 0 ^5 + 1 . 5 0 + 1 . 0 0 è + 0 . 5 0 5 - 0 . 5 0 13 18 760107 a 12 t l 7 M 1 M 8 Tiag (days) L.ocaTi i o n D o r a r a c h t i<w\/.V s> / " ^ V of óérrj'tr i<w\/.V r ; - 0 . 0 7 : U 750107 < U 117M101 l u 11 tlmê (days) m-F i g u r e 8 L o c a t i o n R o t t e r a a m _{L o c a t i o n C j o r a n e c n t} 0 . C 0 + O . 5 0 + 1 . 0 0 * 1 . 5 0 River Discharge (103 r/s) 1 0 . 0 0 « 3 . 5 0 + 1 . 0 0 . l . J O River Discharge lid3 t V s / —

F i g u r e 9

2.3 C a l c u l a t i o n o f s t a t i s t i c a l a s p e c t s

So f a r o n l y h y d r a u l i c s have been d i s c u s s e d . The l i n k w i t h s t a t i s t i c s however has t o be made because o f t h e p r o b a b i l i s t i c d e s i g n p r o c e d u r e o f t h e b a r r i e r and t h e d e f i n i t i o n o f DWL. A DWL i s a w a t e r - l e v e l w h i c h has a p r e s c r i b e d f r e q u e n c y o f exceedance. The DWL i s t h e most i m p o r t a n t f a c t o r i n d e s i g n i n g a d i k e . The p r e s c r i b e d f r e q u e n c y v a r i e s a l o n g t h e

c o u n t r y d e p e n d i n g on t h e t y p e o f t h r e a t ( s e a / r i v e r / l a k e ) , p o p u l a t i o n d e n s i t y and e c o n o m i c a l a c t i v i t i e s . For R o t t e r d a m t h i s f r e q u e n c y i s 1/10000 p e r y e a r w h i l s t f o r D o r d r e c h t t h i s f r e q u e n c y i s 1/4000 p e r y e a r f o r t h e s i t u a t i o n w i t h o u t a b a r r i e r and 1/2000 p e r y e a r f o r t h e s i t u a t i o n w i t h a b a r r i e r . T h i s i n c r e a s e d d e s i g n f r e q u e n c y i s based on t h e r e d u c t i o n o f t h e t h r e a t by s t o r m s u r g e s . By means o f t h e h y d r a u l i c n e t w o r k - m o d e l , m e n t i o n e d i n t h e p r e v i o u s p a r a g r a p h , t h e p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n s o f t h e b o u n d a r y con-d i t i o n s a r e t r a n s f o r m e con-d i n t o p r o b a b i l i t y con-d i s t r i b u t i o n f u n c t i o n s o f t h e w a t e r - l e v e l s i n t h e h y d r a u l i c system. From t h e s e f u n c t i o n s t h e DWL can

be c a l c u l a t e d e a s i l y . T h i s method can a l s o be a p p l i e d t o c a l c u l a t e d e s i g n d i s c h a r g e s , v e l o c i t i e s and h y d r a u l i c head o f t h e b a r r i e r . The t r a n s f o r m a t i o n o f p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n s can be d e t e r m i n e d by a n u m e r i c a l s o l u t i o n o f t h e f o l l o w i n g e q u a t i o n : P(MRWL>X) = f f f f ~~f {m, s , p , g) dmdsdpdq J J J JMRWL=X I n t h i s e q u a t i o n f ( m , s , p , q ) i s t h e combined p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n o f t h e s t o c h a s t i c v a r i a b l e s m, s, p and q. The p r o b a b i l i t y d i s t r i b u t i o n s o f r i v e r d i s c h a r g e and s t o r m surge d u r a t i o n a r e d i r e c t l y d e r i v e d f r o m r e c o r d i n g s d u r i n g t h e l a s t c e n t u r y . The p r o b a b i l i t y o f

s t o r m surge h e i g h t and t h e phase d i f f e r e n c e a r e d e t e r m i n e d i n such a way, t h a t t h e c a l c u l a t e d p r o b a b i l i t y d i s t r i b u t i o n o f t h e MSWL shows a good agreement w i t h t h e h i s t o r i c a l d a t a and i t s e x t r a p o l a t i o n .

3 . R e l i a b i l i t y a s p e c t s PSHL y e s b a r r i e r y e s b a r r i e r y e s HHHL PSHL s u s t a i n s ? <DHL? above C L ? c l o s e d ? s u s t a i n s ? <DHL? no f ( 0 l _no HRHL <DHL? no

I

no I P b H R H L < D H L ?

ho

HRHL <0HL? v e s y e s n o , n o , P . y * p, no 2 ' 3 ' 4

Fig. JO Basic event tree

P (MRHDDHL) The b e n e f i c i a l e f f e c t o f t h e b a r r i e r on MRWL i s s t r o n g l y i n f l u e n c e d by f u n c t i o n a l and s t r u c t u r a l r e l i a b i l i t y o f t h e b a r -r i e -r . To i n v e s t i g a t e t h e s e i n f l u e n c e s a r i s k -a n -a l y s i s h-as been c -a r r i e d

o u t . I n f i g u r e 10 an e v e n t t r e e i s shown w i t h a l l p o s s i b l e b r a n c h e s l e a d i n g t o a MRWL e x c e e d i n g t h e DWL. A t t h e t o p o f t h e f i g u r e t h e

' n o r m a l ' sequence o f e v e n t s i s shown. That i s a good p r e d i c t i o n , a c o r r e c t d e c i s i o n , a p r o p e r l y f u n c t i o n i n g b a r r i e r , w h i c h i s s t r o n g

enough t o w i t h s t a n d t h e f o r c e s , m o s t l y g e n e r a t e d by t h e h y d r a u l i c head. T h i s l e a v e s f o u r p o i n t s where something can go w r o n g :

* a PMSL l o w e r t h a n t h e C L ( q ) , so t h e b a r r i e r i s n o t c l o s e d , b u t an a c t u a l MRWL h i g h e r t h a n t h e DWL a t e i t h e r R o t t e r d a m o r D o r d r e c h t . * a PMSL h i g h e r t h a n t h e C L ( q ) , b u t t h e b a r r i e r i s n o t c l o s e d and as

a consequence MRWL c a n be h i g h e r t h a n DWL.

* a PMSL h i g h e r t h a n t h e C L ( q ) , t h e b a r r i e r i s c l o s e d , b u t c o l l a p s e s due t o t h e enormous ( h y d r a u l i c ) l o a d . As a consequence t h e MRWL can be h i g h e r t h a n DWL. * even i f e v e r y t h i n g f u n c t i o n s w e l l , t h e r e i s s t i l l a p o s s i b i l i t y t h a t t h e MRWL i s h i g h e r t h a n DWL. 4. D e s i g n c o n d i t i o n s / c a l c u l a t i o n s 4.1 C a l c u l a t i o n method For a n u m e r i c a l i n t e g r a t i o n t h e p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n s o f the b o u n d a r y c o n d i t i o n s have t o be sampled. C o m b i n i n g t h e f o u r sampled p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n s , y i e l d s a t o t a l number o f h y d r a u l i c c a l c u l a t i o n s t o be made. The t o t a l number o f c a l c u l a t i o n s i s s e t a t 6900, w h i c h i s s u f f i c i e n t f o r a c c u r a t e r e s u l t s . The r e s u l t s o f t h e s e c a l c u l a t i o n s a r e s t o r e d i n a d a t a b a s e . T h i s d a t a b a s e c o n t a i n s t h e f o l l o w i n g i n f o r m a t i o n : t h e boundary c o n d i t i o n and i t s p r o b a b i l i t y d e n s i t y , t h e MSWL, t h e MRWL a t each node o f t h e n e t w o r k m o d e l , t h e h y d r a u l i c head and maximum d i s c h a r g e s i n s p e c i f i c b r a n c h e s o f t h e n e t w o r k m o d e l . Two o f t h e s e d a t a b a s e s a r e made. One d a t a b a s e c o n t a i n s i n f o r m a t i o n f o r t h e s i t u a t i o n w i t h o u t a b a r r i e r . The o t h e r d a t a b a s e c o n t a i n s i n f o r m a t i o n f o r t h e s i t u a t i o n w i t h a b a r r i e r , w h i c h i s b e i n g c l o s e d f o r e v e r y s t o r m s u r g e . By r e a d i n g b o t h d a t a b a s e s and d e t e r m i n i n g i f t h e b a r r i e r s h o u l d have been c l o s e d [ b y c o m p a r i n g t h e MSWL and t h e C L ( q ) ] a c h o i c e f o r t h e 'open' o r ' c l o s e d ' d a t a can be made. A f t e r r e a d i n g b o t h d a t a b a s e s t h e p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n s o f a l l

d a t a c a n be c o n s t r u c t e d . Because o f t h i s s e p a r a t i o n between c a l c u l a t i o n and s e l e c t i o n , s e v e r a l v a l u e s f o r CL(q) and o t h e r r e l i a b i l i t y p a r a

-m e t e r s (see n e x t p a r a g r a p h ) can be used w i t h o u t h a v i n g t o -make a n e x t e n s i v e c a l c u l a t i o n . T h i s i s v e r y c o n v e n i e n t f o r a s e n s i t i v i t y a n a l y s i s .

4.2 I n t e g r a t i o n o f r e l i a b i l i t y a s p e c t s

The s e p a r a t i o n between c a l c u l a t i o n and s e l e c t i o n a l s o o f f e r s t h e p o s s i -b i l i t y o f i n t e g r a t i o n o f t h e r e l i a -b i l i t y a s p e c t s . By i n t e g r a t i n g t h e e v e n t t r e e o f f i g u r e 10 i n t o t h e s e l e c t i o n p r o g r a m , a p r o b a b i l i t y f o r each s i t u a t i o n ('open' o r ' c l o s e d ' ) can be c a l c u l a t e d . T h i s p r o b a b i l i t y i s d e t e r m i n e d by t h e C L ( q ) , t h e a c c u r a c y o f t h e PMSL, t h e u n r e l i a b i l i t y o f t h e b a r r i e r (C) and t h e p r o b a b i l i t y o f c o l l a p s e o f t h e b a r r i e r ( P b ) . I f t h e b a r r i e r c o l l a p s e s , t h e d a t a f o r t h e 'open' s i t u a t i o n i s assumed t o be v a l i d . The u n r e l i a b i l i t y C i s t h e p r o b a b i l i t y o f n o t c l o s i n g t h e b a r r i e r g i v e n t h e f a c t t h a t t h e PMSL exceeds t h e CL(q) . I t i s c l e a r t h a t t h e p a r a m e t e r s C L ( q ) , t h e a c c u r a c y o f t h e PMSL, t h e u n r e l i a b i l i t y C and t h e p r o b a b i l i t y o f c o l l a p s e Pb p l a y a c e n t r a l r o l e i n d e t e r m i n i n g t h e e f f e c t o f t h e b a r r i e r i n terms o f DWL and c l o s i n g f r e q u e n c y . The p r e s e n t e d c a l c u l a t i o n method a l s o p r o v i d e s t h e pos-s i b i l i t y o f pos-s e t t i n g t a r g e t pos-s c o n pos-s i d e r i n g c l o pos-s i n g c r i t e r i o n , a c c u r a c y o f PMSL, u n r e l i a b i l i t y and s t r u c t u r a l s t r e n g t h .

4.3 S e n s i t i v i t y a n a l y s i s

A l r e a d y i n an e a r l y s t a g e o f t h e p r o j e c t t h e p e r m i s s i b l e p r o b a b i l i t y o f c o l l a p s e was f i x e d a t I 0 "6 i n any one y e a r . C o n s i d e r i n g t h e f r e q u e n c y o f DWL f o r R o t t e r d a m ( 1 0 "A p e r y e a r ) t h e e f f e c t o f Pb can be n e g l e c t e d . The c l o s i n g c r i t e r i o n CL(q) i s s e t t o such a l e v e l t h a t t h e c l o s i n g

f r e q u e n c y i s t o l e r a b l e . T h i s l e a v e s t h e a c c u r a c y and t h e u n r e l i a b i l i t y as v a r i a b l e s . A s e n s i t i v i t y a n a l y s i s has been c a r r i e d o u t c o n s i d e r i n g t h e s e two p a r a m e t e r s . I n i t i a l l y , the a c c u r a c y was s e t t o t h e p r o p e r t i e s d e t e r m i n e d by an a n a l y s i s o f p r e d i c t e d MSWL d u r i n g t h e l a s t decades . T h i s a n a l y s i s showed t h a t t h e d i f f e r e n c e between p r e d i c t e d and measured

MSWL c o u l d be assumed t o have a n o r m a l p r o b a b i l i t y d i s t r i b u t i o n w i t h an average ( j j l ) o f -20 cm a n d a s t a n d a r d d e v i a t i o n (or) o f 25 cm. T h i s means t h a t t h e p r e -d i c t i o n s were on a v e r a g e on t h e s a f e s i d e . I n f i g u r e 1 1 t h e s e n s i t i v i t y o f t h e DWL a t R o t t e r d a m f o r t h e a i s shown. T h i s l i n e shows a v e r y l a r g e s e n s i t i v i t y t o cr. By u s i n g v o n Kalman f i l t e r i n g , based on o n - l i n e measurements d u r i n g t h e passage o f t h e n 1 1 r 5 10 15 Sigma PMSL fern) F i g u r e 1 1 Unraliaoiiity C !-) F i g u r e 12 s t o r m a t t h e B r i t i s h e a s t c o a s t and p l a t f o r m s i n t h e N o r t h Sea, one b e l i e v e s t h a t cr can be r e d u c e d t o 15 cm. T h i s v a l u e i s used f o r d e s i g n c a l c u l a t i o n s o f t h e s t o r m surge b a r r i e r . The s e n s i t i v i t y o f t h e DWL a t R o t t e r d a m f o r t h e u n r e l i a -b i l i t y i s shown i n f i g u r e 12. T h i s f i g u r e shows a s h a r p i n c r e a s e o f s e n s i t i v i t y f o r v a l u e s o f C l a r g e r t h a n 10"3. T h e r e f o r e t h e maximum v a l u e o f C was s e t t o 10"3. 4.4 R e s u l t s I n t h e f i g u r e 13 t h e r e s u l t s o f a com-p l e t e c a l c u l a t i o n f o r t h e s i t u a t i o n w i t h o u t a b a r r i e r a r e shown. I n t h i s f i g u r e t h e p r o b a b i l i t y o f e x c e e d i n g c e r t a i n w a t e r - l e v e l s a t t h e l o c a t i o n s Hoek v a n H o l l a n d , R o t t e r d a m and D o r d r e c h t i s shown. The DWL f o r t h e s e l o c a t i o n s a r e 5.15, 4.80, 3.78 m e t e r s . I n f i g u r e 14 t h e same l i n e s a r e shown f o r t h e s i t u a t i o n w i t h a s t o r m s u r g e b a r r i e r . The DWL f o r R o t t e r d a m and D o r d r e c h t a r e reduced t o 3.52 and 3.15 m e t e r s . •7,(104. O Hoe* i « i ftllind • aotterdal * 6 . 0 0 4 . i A Oordrtctit * .5 M.QO-L, * 1 A -1 -i 10 10 10 10 10 10 10 10 Frequency of exceedance (1/year)

O Hoik ra Holland • Rottsrdai A öordrecnt 'SS -A öordrecnt or These r e s u l t s show t h a t t h e p r e s c r i b e d r e d u c t i o n o f DWL f o r t h e l o c a t i o n D o r d r e c h t i s n o t a c h i e v e d , a c c o r d i n g t o t h e c a l c u l a t i o n method w i t h f o u r v a r i a b l e s . However, f o r t h e c a l c u l a t i o n o f DWL t h e method w i t h two v a r i a b l e s has been a p p l i e d f o r a l l d i k e r e c o n s t r u c t i o n works up t i l l now. F o r reasons o f

c o n t i n u i t y t h i s method w i l l be a p p l i e d f o r t h e f i n a l s t a g e o f t h e d i k e r e c o n s t r u c t i o n w o r k s as w e l l . A n o t h e r c a l c u l a t i o n w i t h o n l y t h e v a r i a b l e s s t o r m s u r g e h e i g h t and r i v e r d i s -c h a r g e r e d u -c e s t h e DWL f o r t h e l o -c a t i o n D o r d r e -c h t t o 2.90 m e t e r above NAP. F o r t h e l o c a t i o n R o t t e r d a m t h e DWL i s r e d u c e d t o 3.46 m e t e r above NAP. F o r t h e s i t u a t i o n w i t h a b a r r i e r t h e d i f f e r e n c e between t h e r e s u l t s o f b o t h c a l c u l a t i o n methods a r e i n c r e a s e d . E s p e c i a l l y f o r

l o c a t i o n s , w h i c h a r e r e l a t i v e l y f a r away f r o m t h e sea. These l o c a t i o n s s u f f e r t h e most f r o m t h e n e g a t i v e e f f e c t o f t h e b a r r i e r .

10" 10" 10s 10"' 10"1 10"J 10"* 10"* 10"* !0*] Frequency of exceeaancs (1/yearl

F i g u r e 14

5. O p e r a t i o n a l a s p e c t s

5.1 S p e c i f i c p r o b l e m s r e l a t e d t o o p e r a t i o n a l use o f t h e b a r r i e r

D u r i n g o p e r a t i o n d e c i s i o n s have t o be made a b o u t t h e c l o s i n g and o p e n i n g o f t h e b a r r i e r . For b o t h d e c i s i o n s c r i t e r i a have been s e t . To c l o s e t h e b a r r i e r Lhe PMSL must be h i g h e r t h a n t h e C L ( q ) and a c l o s i n g c o n d i t i o n (CC) must be a c t u a l l y r e a c h e d . I n t h e c u r r e n t d e s i g n t h e CC depends on t h e r i v e r d i s c h a r g e . For l o w d i s c h a r g e s t h e CC i s a w a t e r -l e v e -l o f 2.00 m e t e r above NAP and f o r h i g h d i s c h a r g e s t h e CC i s t h e l o c a l z e r o i n f l o w c o n d i t i o n . I t i s o b v i o u s t h a t t h e s e c o n d i t i o n s can be met s e v e r a l t i m e s d u r i n g a s t o r m . To p r e v e n t h i g h w a t e r - l e v e l s by

u n n e c e s s a r y l o n g c l o s u r e s o f t h e b a r r i e r ( a c c u m u l a t i o n o f d i s c h a r g e ) t h e c l o s u r e s t a r t s a t t h e l a s t CC b e f o r e t h e sea w a t e r - l e v e l exceeds C L ( q ) .

To open t h e b a r r i e r a o p e n i n g c o n d i t i o n (OC) must be r e a c h e d and t h e PMSL may n o t exceed t h e DWL any more. The OC i s d e f i n e d t o be t h e

moment when t h e w a t e r - l e v e l s on b o t h s i d e s o f t h e b a r r i e r a r e e q u a l . Non-exceedance o f t h e DWL i s g u a r a n t e e d i f t h e PMSL does n o t exceed t h e CL(q) any more.

The i n v o l v e m e n t o f p r e d i c t e d w a t e r - l e v e l s causes some p r o b l e m s . I f

p r e d i c t i o n s were p r e c i s e i t w o u l d be v e r y easy t o p i c k t h e r i g h t moment t o c l o s e and open t h e b a r r i e r . I n p r a c t i c e however p r e d i c t i o n s a r e i n -a c c u r -a t e ( i n c r e -a s i n g w i t h t i m e ) -and -a l s o o n l y -a v -a i l -a b l e f o r -a l i m i t e d t i m e ahead ( a t t h e most 18 h o u r s ) . T h i s i m p l i e s t h a t e v e r y o c c u r r e n c e o f CC o r OC i n a s p e c i f i c s t o r m i s a p o t e n t i a l c l o s i n g o r o p e n i n g moment. Which moment i s chosen depends on t h e outcome o f t h e p r e d i c t e d w a t e r - l e v e l s . The use o f p r e d i c t e d w a t e r - l e v e l s may even cause t h e b a r r i e r n o t t o be c l o s e d a t a l l a t t h e l a s t CC; f o r example i f t h e p r e d i c t e d ( l a s t ) CC does n o t o c c u r i n r e a l i t y . S i n c e t h i s i s t h o u g h t t o be u n a c c e p t a b l e an e x t r a p o s s i b i l i t y f o r c l o s i n g t h e b a r r i e r i s i n t r o d u c e d a t Hoek v a n H o l l a n d b e h i n d b a r r i e r 5,00 I M O I 3.00 £ 2.00 Ü W 0 ~ 0.00 CLIol

\ '

• - 3 0 - 2 0 -10 0 ii time ( h o u r s ) -\ OC CLIo) f - 2 0 -10 0 firn* ( h o u r s ) - 3 0 - 2 0 -10 0 d) Mme ( h o u r s ) F i g u r e 15 t h e l o w e s t w a t e r - l e v e l a f t e r t h e l a s t CC. F i g u r e 15 i l l u s t r a t e s f o u r p o s s i b i l i t i e s f o r a s i n g l e s t o r m : so-c a l l e d r e a l i z a t i o n s . I n t h i s case t h e r e a r e two CC t h a t can be combined w i t h two OC. C o m b i n a t i o n c ) i l l u s t r a t e s t h e optimum c h o i c e . The model d e s c r i b e d i n t h e p r e v i o u s p a r a g r a p h s o n l y i n c l u d e s t h e optimum c l o s u r e and o p e n i n g o f t h e b a r r i e r [ c o m b i n a t i o n c]

i n f i g u r e 1 5 ] . S i n c e o t h e r c l o s u r e o r o p e n i n g moments may g e n e r a t e d i f -f e r e n t MRWL and l o a d s on t h e b a r r i e r a model i s d e v e l o p e d t o i n c l u d e t h e e f f e c t o f a l l p o s s i b l e r e a l i z a t i o n s . The c a l c u l a t i o n scheme i s d e s c r i b e d i n t h e n e x t p a r a g r a p h .

5.2 A d a p t i o n o f t h e c a l c u l a t i o n method

The c a l c u l a t i o n method t o d e t e r m i n e DWL and l o a d s

w a t e r - l e v e l s . F o r e v e r y s t o r m a l l r e a l i z a t i o n s a r e i n c l u d e d . The p r o c e d u r e t o g e n e r a t e a l l r e a l i z a t i o n s f o r a s t o r m i s shown i n f i g u r e 16. For e v e r y r e a l i z a t i o n t h e r e s u l t i n g MRWL and

i s r o u g h l y t h e same as d e s c r i b e d i n p a r a g r a p h 4.1. The h y d r a u l i c model i s used t o c a l c u l a t e t h e

c l o s e a g r a t i o n o f a l l p o s s i b l e c o m b i n a t i o n s . However t h e i m p o r t a n t d i f f e r e n c e w i t h t h e method d e s c r i b e d i n d e s i g n l o a d s i s based a g a i n on n u m e r i c a l i n t e -The s t a t i s t i c a l c a l c u l a t i o n t o d e r i v e DWL and l o a d s a r e d e t e r m i n e d and s t o r e d i n a d a t a b a s e . p a r a g r a p h 4.1 i s t h a t f o r a s i n g l e s t o r m more r e a l i z a t i o n s a r e p o s s i b l e and t h i s r e q u i r e s an e x t r a i n t e g r a t i o n o v e r r e a l i z a t i o n s . The o o e n e n d F i g u r e 16 c o n d i t i o n a l p r o b a b i l i t y o f t h e r e a l i z a t i o n ( f o r a g i v e n s t o r m ) i s c a l c u l a t e d . A t t h e c u r r e n t CC t h e p r o b a b i l i t y o f sa-t i s f y i n g sa-t h e c r i sa-t e r i a f o r c l o s i n g i s c a l c u l a sa-t e d and sa-t h e same p r o c e d u r e i s f o l l o w e d f o r t h e OC w i t h r e s p e c t t o t h e c r i t e r i a f o r o p e n i n g . I n p r i n c i p l e more t h a n one p r e d i c t e d h i g h w a t e r i s c o n s i d e r e d i n c a l c u l a t i n g t h i s p r o b a b i l i t y . An a n a l y s i s o f p r e d i c t i o n s d u r i n g t h e l a s t decades showed t h a t t h e s e p r e d i c t i o n s were i n d e p e n d e n t . The c o n d i t i o n a l p r o b a b i l i t y o f a r e a l i z a t i o n w i l l depend on t h e C L ( q ) l e v e l , t h e h e i g h t o f i n d i v i d u a l h i g h w a t e r s and t h e a c c u r a c y o f t h e p r e d i c t e d w a t e r - l e v e l s . The p r o b a b i l i t y o f a r e a l i z a t i o n i s c a l c u l a t e d by m u l t i p l y i n g t h e c o n d i t i o n a l p r o b a b i l i t y w i t h t h e p r o b a b i l i t y o f t h e b o u n d a r y c o n d i t i o n s . I n i t i a l l y a v e r y f a s t and s i m p l i f i e d open c h a n n e l n e t w o r k model was used -because o f c a l c u l a t i o n t i m e . I t a p p e a r e d t h a t by t a k i n g i n t o a c c o u n t r e a l i z a t i o n s t h e number o f c a l c u l a t i o n s i n c r e a s e d w i t h a f a c t o r 3.5. I n t h e f u t u r e t h e more complex model d e s c r i b e d i n

s e c t i o n 2.2 w i l l be used. The p r e l i m i n a r y r e s u l t s i n t h e n e x t p a r a g r a p h a r e based on c a l c u l a t i o n s w i t h t h e s i m p l i f i e d m o d e l .

5.3 P r e l i m i n a r y r e s u l t s

The a n a l y s i s w i t h t h e model d e s c r i b e d i n s e c t i o n 5.2 was f o c u s e d on t h e i n f l u e n c e o f t h e o p e r a t i o n a l d e c i s i o n s on DWL and d e s i g n l o a d s . When a cr o f 0.25 meter was used f o r t h e a c c u r a c y o f w a t e r - l e v e l p r e d i c t i o n s t h e f o l l o w i n g r e s u l t s were f o u n d . * an 30Z i n c r e a s e i n c l o s i n g f r e q u e n c y r e s u l t i n g f r o m more p o t e n t i a l c l o s u r e s f o r e v e r y s t o r m * no i n f l u e n c e on DWL a t t h e r e p r e s e n t a t i v e l o c a t i o n s compared t o t h e p r e v i o u s a n a l y s i s ( a l s o i n c l u d i n g cr = 0.25 m e t e r ) * no i n f l u e n c e on t h e p o s i t i v e d e s i g n head o v e r t h e b a r r i e r * an i n c r e a s e d n e g a t i v e d e s i g n head o v e r t h e b a r r i e r (202) r e s u l t i n g f r o m c l o s u r e s a t an e a r l i e r moment and/or o p e n i n g a t a l a t e r moment. I n f l u e n c e s a t o t h e r l o c a t i o n s and f o r o t h e r p a r a m e t e r s c o u l d n o t be d e t e r m i n e d w i t h t h e s i m p l i f i e d model. T h i s w i l l be a n a l y z e d w i t h t h e complex model. 6. C o n c l u s i o n s

* The use o f l a r g e n u m e r i c a l models does n o t n e c e s s a r i l y r u l e o u t t h e use o f p r o b a b i l i s t i c d e s i g n methods.

* The a c c u r a c y o f t h e p r e d i c t i o n s o f w a t e r - l e v e l s i s o f v i t a l i m p o r t a n c e f o r t h e p e r f o r m a n c e o f t h e s t o r m surge b a r r i e r . * The c a l c u l a t i o n method o f DWL s h o u l d be based on a l l g o v e r n i n g

v a r i a b l e s . Reducing t h e number o f v a r i a b l e s i s o n l y t o l e r a b l e a f t e r a s e n s i t i v i t y a n a l y s i s . Based on such an a n a l y s i s t h e s i g n i f i c a n t v a l u e o f t h e v a r i a b l e can be used i n t h e c a l c u l a t i o n o f DWL. * The e f f e c t o f a c t u a l l y o p e r a t i n g t h e s t o r m surge b a r r i e r s h o u l d be i n c l u d e d i n t h e d e s i g n p r o c e s s , a l s o i n t h e phase o f d e t e r m i n i n g t h e boundary c o n d i t i o n s .

7. Acknowledgements

I t i s o b v i o u s t h a t t h e s t u d y p r e s e n t e d i n t h i s p a p e r i n v o l v e s an enormous number o f c o m p u t a t i o n s . Most o f t h i s w o r k i s done by mr. Henk de Deugd a l s o f r o m R i j k s w a t e r s t a a t . The a u t h o r s a r e d u l y g r a t e f u l f o r t h i s .

A b b r e v i a t i o n s and symbols used i n t h i s paper

C = u n r e l i a b i l i t y CC = c l o s i n g c o n d i t i o n CL = c r i t i c a l w a t e r - l e v e l a t R o t t e r d a m and D o r d r e c h t CL(q) = c r i t i c a l w a t e r - l e v e l a t Hoek v a n H o l l a n d . DWL = d e s i g n w a t e r - l e v e l MRWL = maximum r i v e r w a t e r -l e v e -l MSWL = maximum sea w a t e r - l e v e l m = s t o r m s u r g e h e i g h t [i = a v e r a g e o f e r r o r i n PMSL NAP = r e f e r e n c e w a t e r - l e v e l OC = o p e n i n g c o n d i t i o n p = phase d i f f e r e n c e Pb = p r o b a b i l i t y o f c o l l a p s e PMSL = p r e d i c t e d maximum sea w a t e r - l e v e l cr = s t a n d a r d d e v i a t i o n o f e r r o r i n PMSL q = r i v e r d i s c h a r g e s = d u r a t i o n o f t h e s t o r m s u r g e