• Nie Znaleziono Wyników

Dune erosion

N/A
N/A
Protected

Academic year: 2021

Share "Dune erosion"

Copied!
30
0
0

Pełen tekst

(1)

m i n i s t e r i e van v e r k e e r en w a t e r s t a a t r i j k s w a t e r s t a a t

d i e n s t weg- en waterbouwkunde a f d e l i n g a d v i s e r i n g waterbouw

Comett course on c o a s t a l morphology D e l f t , a p r i l 1990

D u n e e r o s i o n

K.J. Verhagen, r i j k s w a t e r s t a a t , c i v i l e n g i n e e r i n g d i v i s i o n , D e l f t

1 . I n t r o d u c t i o n

1.1 The d i f f e r e n c e between a c u t e e r o s i o n and c h r o a i c e r o s i o n

I n t h e N e t h e r l a n d s t h e dune c o a s t i s a f l e x i b l e sea-defence a g a i n s t t h e N o r t h Sea, C h a r a c t e r i s t i c i s t h e c o n t i n u o u s movement of sand i n t h e c o a s t a l Eone, There i s an exchange of sand between t h e s u b a e r i a l and s u b a q u a t i c p a r t of t h e beach. C u r r e n t s and waves move t h e sand on t h e shore i n c r o s s s h o r e and l o n g -shore d i r e c t i o n . T h i s p r o c e s s may course a l o s s of sand from t h e sea-defence zone t o a d j a c e n t c o a s t a l s e c t i o n s or t o n e i g h b o r i n g i n l e t s . Because of t h e s e p r o c e s s e s t h e r e i s a c o n t i n u o u s movement of t h e b o r d e r l i n e between l a n d and w a t e r . E r o s i o n and a c c r e t i o n a l t e r n a t e each o t h e r . E r o s i o n n e a r l y always causes p r o b l e m s .

There are two t y p e s of c o a s t a l e r o s i o n :

* A f a s t , b i g e r o s i o n caused by q u i c k e r o s i o n of dunes d u r i n g s t o r m surges * A s l o w l y , c h r o n i c e r o s i o n , which i s n o t so s t r i k i n g , caused by s e a - l e v e l

r i s e and o t h e r m o r p h o l o g i c a l phenomena. The c h r o n i c e r o s i o n moves sand o u t o f t h e c o a s t a l defence zone. An i n c r e a s e s e a l e v e l r i s e may cause an i n -c r e a s e d -c h r o n i -c e r o s i o n . I n t h a t -case a l s o t h e -c o a s t a l p r o f i l e w i l l adapt t o t h e new w a t e r l e v e l by moving i n a landward d i r e c t i o n .

I n t h e p a s t c h r o n i c e r o s i o n was o f t e n not p r e v e n t e d . On l o n g e r terms c h r o n i c e r o s i o n weakened t h e dunes, so t h a t one had t o f e a r t h a t d u r i n g a s t o r m t h e s t o r m surge e r o s i o n c o u l d wipe away t h e r e m a i n i n g dune. T h i s would cause f l o o d -i n g o f t h e p o l d e r s . T h e r e f o r e t h e P o l d e r Boards, r e s p o n s -i b l e f o r s e a - d e f e n c e , improved t h e dunes by p l a c i n g more sand b e h i n d t h e dunes on t h e l a n d w a r d s i d e . T h i s caused c o n s i d e r a b l e damage t o n a t u r e ,

1.2 cause and e f f e c t

I t i s assumed t h a t f o r a g i v e n w a t e r l e v e l and a g i v e n wave c o n d i t i o n t h e r e i s an e q u i l i b r i u m p r o f i l e . U n f o r t u n a t e l y t h i s c o n d i t i o n o c c u r s o n l y i n l a b o r a t o -r i e s , and c o n s e q u e n t l y we d o n ' t f i n d e q u i l i b -r i u m p -r o f i l e s a l o n g t h e c o a s t . C o n s t a n t l y t h e w a t e r l e v e l and t h e wave changes, and t h u s t h e p r o f i l e changes. E s p e c i a l l y d u r i n g s t o r m surges (much h i g h e r w a t e r , much h i g h e r waves) t h e p r o f i l e has t o a d a p t . T h i s causes dune e r o s i o n . Sand i s moved f r o m t h e dune t o -wards t h e beach. On s t a b l e c o a s t s , one may expect t h a t t h e dune r e c o v e r s com-p l e t e l y a f t e r t h e s t o r m . F i g u r e 1 shows t h e l o c a t i o n of t h e d u n e - f o o t as a

(2)

s h o a l s o r t r e n c h e s a r e p r e s e n t near t h e c o a s t . These problems w i l l n o t be d i s -cussed h e r e , some of t h e problems and t h e suggested s o l u t i o n s a r e g i v e n i n t h e " g u i d e " [TAW 1 9 8 9 ] . I t i s c l e a r t h a t t h e shape o f t h e p r o f i l e b e f o r e t h e s t o r m i n f l u e n c e s t h e p o s i t i o n of t h e r e s u l t i n g X - c o o r d i n a t e Xe.

T h i s model i s c a l l e d t h e Duros-model (DUne eROSion) o r V e l l i n g a - m o d e l , The wave h e i g h t (H) t o be a p p l i e d i n t h e e q u a t i o n i s t h e s i g n i f i c a n t wave h e i g h t , on "deep" w a t e r . The o t h e r parameter i s t h e s e t t l i n g v e l o c i t y o f t h e s e d i m e n t . T h i s parameter can be computed f o r seawater and f o r a t e m p e r a t u r e o f 5 as f o l l o w s : ^ " l o g (1/w) = 0.476 ( ^ " l o g D )2 + 2.180 ^ " l o g D + 3.226 i n w h i c h D i s t h e median g r a i n s i z e o f t h e e r o d i n g dune m a t e r i a l . The c a l c u l a t i o n i t s e l f i s an i t e r a t i v e p r o c e s s , because o f t h e f a c t t h a t t h e e r o d i n g q u a n t i t y has t o be e q u a l t o t h e a c c r e t i n g q u a n t i t y . V a r i o u s computer programs a r e a v a i l a b l e t o c a r r y o u t t h e c o m p u t a t i o n . 3.2 p r o b a b i l i s m

A c c o r d i n g t o t h e p r e s e n t Dutch r e g u l a t i o n a sea defence has s u r v i v e w i t h o u t problems a s t o r m surge w i t h a p r o b a b i l i t y o f o c c u r r e n c e of 1/10,000 per y e a r . For a d i k e t h i s g e n e r a l l y means t h a t i t has t o w i t h s t a n d a w a t e r l e v e l w i t h a p r o b a b i l i t y o f 1/10,000 per y e a r . Dune e r o s i o n i s a more c o m p l i c a t e d p r o c e s s , and n o t o n l y t h e w a t e r l e v e l i s o f i m p o r t a n c e . A l s o t h e wave h e i g h t and t h e d u r a t i o n o f t h e s t o r m surge a r e i m p o r t a n t . T h e r e f o r e i t i s b e t t e r t o d e s i g n a dune i n such a way t h a t i t has a g i v e n p r o b a b i l i t y of f a i l u r e .

T h i s p r o b a b i l i t y of f a i l u r e has t o be l e s s t h a n 1/10,000 per y e a r . A good d e s i g n e d d i k e which can s u r v i v e a 1/10,000 s t o r m w i l l n o t f a i l . Research has i n d i c a t e d t h a t t h e p r o b a b i l i t y o f f a i l u r e of a good d e s i g n e d d i k e i s approx. 1/100,000. The d i f f e r e n c e between s u r v i v a l and f a i l u r e i s t h e r e f o r e a f a c t o r 10.

A p r o p e r dune-design t h e r e f o r e r e q u i r e s 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 . I n t h i s course t h e t h e o r y o f p r o b a b i l i s t i c c o m p u t a t i o n w i l l n o t be d i s c u s s e d . For back-ground i n f o r m a t i o n can be r e f e r r e d t o Ang & Tang [ 1 9 8 4 ] . For a s i m p l e case ( f o r example t h e s t r e n g t h of a t h r e a d ) on can say t h a t t h e t h e p r o b a b i l i t y o f

( s t r e n g t h l o a d ) i s n e g a t i v e , s h o u l d be s m a l l e r t h a n a g i v e n v a l u e . I n p r o b a b i l i s t i c c a l c u l a t i o n s i t i s customary t o d e f i n e a s o c a l l e d r e l i a b i l i t y f u n c t i o n Z. T h i s f u n c t i o n s h o u l d be such t h a t Z ) 0 r e p r e s e n t s f a i l u r e o f t h e s y s -tem. I n t h i s case, as an example:

P r { Z < 0 1 = 1/100,000.

I n case o f t h e s t r e n g t h o f a t h r e a d Z = S - F, i n w h i c h S= s t r e n g t h of t h e t h r e a d and F i s t h e l o a d on t h e t h r e a d .

For dunes one s h o u l d ask t h e f o l l o w i n g q u e s t i o n : "given a certain

x-coordi-nate Xg, what is the probability that an erosion profile occurs such that the erosion point Xe is situated more landward than Xg ?" o r :

(3)

figure 3: definition of Xe and Xg

So t h e Z " f u n c t i o n s h o u l d meet t h e f o l l o w i n g r e q u i r e m e n t : Z = Xg - Xe.

Xg i s a p r e s c r i b e d v a l u e f o r t h e X - c o o r d i n a t e . However Xe depends on t h e parameters c a u s i n g t h e e r o s i o n p r o f i l e . So t h e problem i s t o c a l c u l a t e Pr {Z<0!. where Z i s a f u n c t i o n o f t h e parameters i n v o l v e d . S t a n d a r d methods a r e a v a i l a b l e f o r c a l c u l a t i o n of Pr iZ<0!, p r o v i d e d t h a t t h e i n v o l v e d parameters are known and moreover: t h e s t a t i s t i c a l d i s t r i b u t i o n of t h e v a r i a b l e s must be known, as w e l l as t h e s t a t i s t i c a l d e p e n d e n c i e s .

The main p a r a m e t e r s i n f l u e n c i n g t h e shape of t h e e r o s i o n p r o f i l e a f t e r a s t o r m a r e :

- t h e w a t e r l e v e l d u r i n g t h e s t o r m surge - t h e wave h e i g h t d u r i n g t h e s t o r m surge - t h e s t o r m d u r a t i o n

- t h e g r a i n - s i z e of t h e dune sand.

The shape of t h e e r o s i o n p r o f i l e can be c a l c u l a t e d w i t h t h e above mentioned Duros-model f o r a g i v e n s e t of p a r a m e t e r s .

A r e a l e r o s i o n p r o f i l e a f t e r a s t o r m surge w i l l c e r t a i n l y d i f f e r f o r m t h e c a l c u l a t e d e x p e c t e d e r o s i o n p r o f i l e . The r e a s o n f o r t h i s d i s c r e p a n c y might be:

- The a c c u r a c y of t h e model f o r t h e e x p e c t e d p r o f i l e . - The v a r i a n c e of t h e sediment d i a m e t e r D50.

The i n i t i a l p r o f i l e j u s t b e f o r e t h e s t o r m i s never known, u s u a l l y a p r o -f i l e i s used t h a t i s measured some t i m e b e -f o r e t h e s t o r m o c c u r s .

- The r e a l v a l u e s f o r t h e p a r a m e t e r s t h a t c h a r a c t e r i z e t h e s t o r m d i f f e r f r o m the v a l u e s assumed f o r d e t e r m i n a t i o n of t h e t h e o r e t i c a l e r o s i o n p r o f i l e a f t e r a s t o r m s u r g e . These a r e : t h e w a t e r l e v e l , t h e w a v e - h e i g h t , t h e s t o r m d u r a t i o n and a l s o t h e p o s s i b l e o c c u r r e n c e of g u s t bumps d u r i n g maximum w a t e r l e v e l .

Van de G r a a f f [1983, 1986] g i v e s f u l l d e t a i l s on how p r o b a b i l i s t i c c a l c u l a -t i o n s can be made f o r -t h e e r o s i o n of dunes.

I n a g e n e r a l purpose p r o b a b i l i s t i c program t h e z - f u n c t i o n (= t h e Duros model) can be b u i l d i n , as w e l l as mean v a l u e s , s t a n d a r d d e v i a t i o n s and s t a t i s t i c a l d i s t r i b u t i o n of t h e f o l l o w i n g 7 s t o c h a s t i c v a r i a b l e s :

1 hmax t h e maximum w a t e r l e v e l d u r i n g a s t o r m surge

2 Hs t h e s i g n i f i c a n t wave h e i g h t d u r i n g t h e s t o r m surge 3 T s t t h e t o t a l s t o r m d u r a t i o n

4 D50 t h e median g r a i n s i z e of t h e dune sand 5 Bpr f l u c t u a t i o n s of t h e beach p r o f i l e

(4)

L e t A be t h e c a l c u l a t e d e r o s i o n (m /ra) above t h e s t o r m surge l e v e l a c c o r d i n g t o t h e Duros model f o r a g i v e n c o m b i n a t i o n o f hmax, Hs, D50 and Bpr. The e f f e c t of t h e o t h e r t h r e e s t o c h a s t i c v a r i a b l e s T s t , Bump and Mod can be s c h e m a t i z e d t o an a d d i t i o n a l e r o s i o n above s t o r m surge l e v e l : A e x t r a , h a v i n g a normal d i s t r i -b u t i o n and t h e f o l l o w i n g c h a r a c t e r i z i n g p a r a m e t e r s :

mean o f A - e x t r a = A/20

v a r i a n c e of A - e x t r a = 0.02 * sqr (A) + 4*A + 400

figure 4: A-extra

The p r o b a b i l i t y d e n s i t y f u n c t i o n s f o r hmax and Hs must be known. For example: the maximum w a t e r l e v e l d u r i n g s t o r m surge can have an e x p o n e n t i a l d i s t r i b u t i o n :

Pr {hmax>h! = exp [ - { h - a ) / b ] ,

where a and b a r e parameters c h a r a c t e r i z i n g t h e d i s t r i b u t i o n .

3.0 4.0 5.0 6.0 7.0

~ storm surge level Im.NAP)

figure 4: Expected value of the significant wave height as a function of the storm surge level at a number of locations along the Dutch coast.

(5)

Up u n t i l now a l l c o n c 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 s t o c h a s t i c i n d e pendent (however t h i s i s a r g u a b l e ) , An e x c e p t i o n must be made f o r t h e s i g n i f i -cant wave h e i g h t d u r i n g s t o r m c o n d i t i o n s and t h e maximum w a t e r l e v e l : t h e h i g h e r the w a t e r l e v e l , t h e h i g h e r t h e waves w i l l be ( b o t h a r e s t r o n g l y i n f l u e n c e d by the wind) . A l s o two storms h a v i n g t h e same maximum w a t e r l e v e l , w i l l n o t have the same s i g n i f i c a n t wave h e i g h t s . For t h e Dutch c o a s t t h e s t a t i s t i c a l depen-dency o f Hs as f u n c t i o n o f hmax has been p r o v e n t o be as i n f i g u r e 5.

I n t h e model t h e f o l l o w i n g s c h e m a t i z a t i o n was made f o r t h e s t a t i s t i c a l d i s -t r i b u -t i o n o f -t h e wave h e i g h -t as f u n c -t i o n o f -t h e maximum w a -t e r l e v e l d u r i n g s -t o r m s u r g e :

For a c e r t a i n v a l u e o f hmax, t h e wave h e i g h t i s normal d i s t r i b u t e d w i t h a mean o f Hs = c * hmax" ( w i t h a p r e s c r i b e d maximum Hmax) s t a n d a r d dev. of Hs = 0.60 m

and where c and d a r e l o c a t i o n dependent c o e f f i c i e n t s , as does t h e maximum v a l u e o f Hs: Hmax.

3.3 example 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

P r o b a b i l i s t i c c a l c u l a t i o n s can be made w i t h v a r i o u s t y p e s o f p r o b a b i l i s t i c models. As an example a c a l c u l a t i o n f o r a Dutch dune i s made w i t h a L e v e l I I method, implemented on a p e r s o n a l computer. See example 1 i n t h e a p p e n d i x . 3.4 t h e Dutch g u i d e t o t h e assessment o f t h e s a f e t y o f dunes as a sea defence

A few y e a r s ago no g e n e r a l purpose p r o b a b i l i s t i c programs were a v a i l a b l e which c o u l d be used e a s i l y . T h e r e f o r e i t was d e c i d e d n o t t o p r e s c r i b e t h e f u l l p r o b a b i l i s t i c c o m p u t a t i o n i n t h e Guide, b u t an a p p r o x i m a t i o n o n l y . For normal dunes a l o n g t h e Dutch c o a s t t h e r e s u l t s o f t h e a p p r o x i m a t i o n a r e n e a r l y e q u a l t o those o f a complete c o m p u t a t i o n . For d e t a i l s can be r e f e r r e d t o Van de G r a a f f , 1 9 8 3 , 1 9 8 6 . As i n d i c a t e d above, now such programs a r e a v a i l a b l e . I t i s expected t h e r e f o r e t h a t i n a n e x t e d i t i o n of t h e G u i d e l i n e s a p r o b a b i l i s t i c c o m p u t a t i o n w i l l be p r e s c r i b e d .

The r e s u l t o f t h e suggested a p p r o x i m a t i o n i s as f o l l o w s :

C a l c u l a t i o n s s h o u l d be be made, n o t u s i n g t h e s t o r m surge l e v e l and t h e g r a i n s i z e o f t h e dune sand, b u t u s i n g a c o m p u t a t i o n a l l e v e l and a c o m p u t a t i o n a l g r a i n s i z e . The c o m p u t a t i o n a l l e v e l i s t h e d e s i g n l e v e l + 2 / 3 d e c i m a t i o n h e i g h t . The d e c i m a t i o n h e i g h t i s t h e d i f f e r e n c e i n h e i g h t between t h e w a t e r l e v e l w i t h a p r o b a b i l i t y o f exceedance 1 0 t i m e s s m a l l e r t h a n t h a t o f t h e d e s i g n l e v e l , and t h e d e s i g n l e v e l . I n t h e N e t h e r l a n d s t h e d e c i m a t i o n h e i g h t i s ap-p r o x . 7 0 cm. The c o m ap-p u t a t i o n a l g r a i n s i z e i s c a l c u l a t e d as f o l l o w s " ^comp = MD5 0 - 5 I (C 7 D5 0 ) ' / MD5 0 '

i n which Mn^o t h e e x p e c t e d v a l u e o f t h e median g r a i n s i z e and Oncn i s t h e s t a n d a r d d e v i a t i o n .

With t h e s e v a l u e s an e r o s i o n a n a l y s i s i s made f o r each y e a r , u s i n g t h e Duros-model. A s u r c h a r g e i s added t o t a k e account o f t h e i n f l u e n c e s o f t h e i n a c c u r a c y of t h e c o m p u t a t i o n a l model, t h e g u s t o s c i l l a t i o n s and t h e g u s t surges and t h e u n c e r t a i n t y about t h e t i m e d u r i n g which t h e w a t e r l e v e l remains a t about m a x i -mum l e v e l . The e f f e c t o f t h i s s u r c h a r g e i s expressed i n an a d d i t i o n a l r e c e s s i o n of t h e s t e e p dune f r o n t . The s u r c h a r g e T i s computed as f o l l o w s :

T = 0 . 2 5 A + 2 0

(6)

P o i n t F i s t h e i n t e r s e c t i o n o f t h i s s h i f t e d dune f r o n t w i t h t h e c o m p u t a t i o n a l l e v e l . See f i g . 6. The changes i n t h e p o s i t i o n o f P a r e a measure f o r t h e c h r o -n i c c o a s t a l e r o s i o -n from t h e f o l l o w i -n g p o i -n t s o f v i e w :

- s a f e t y f o r t h e p o l d e r s b e h i n d t h e dunes - o n l y f o r a r e l a t i v e l y s h o r t p e r i o d .

figure 6: Definition sketch

The above c a l c u l a t i o n s y i e l d a t i m e s e r i e s f o r t h e p o s i t i o n o f p o i n t P. These p o s i t i o n s can be p l o t t e d i n a d i a g r a m as a f u n c t i o n o f t i m e (see f i g . 7) . I t can be e a s i l y i n d u c e d from t h e p o s i t i o n whether t h e r e i s q u e s t i o n o f a s t a b l e , e r o d i n g o r e a c c r e t i n g c o a s t . The t r e n d of t h e p o s i t i o n of p o i n t P as a f u n c t i o n of t i m e can be e s t i m a t e d by means of r e g r e s s i o n a n a l y s i s . A l i n e a r a p p r o x i m a -t i o n w i l l u s u a l l y do ( u s i n g approx. 10 y e a r s o f d a -t a ) . The p r o f i l e f l u c -t u a -t i o n s are e x p r e s s e d i n t h e s c a t t e r e d p o s i t i o n o f t h e p o i n t s P around t h i s r e g r e s s i o n l i n e . time (yearl 1960 SEASIDE 1970 1980 d*g= distance over which the regression line is

shifted landwards so as to include : - the processing of profile fluctuations (d)

- the influence of the gradient in longshore transport ig)

extrapolation

critical position

expected point in time when the| safety standard

LIMIT PROFILE

(7)

The found r e g r e s s i o n l i n e has t o be moved landward over a d i s t a n c e d+g. The v a l u e d i s t o t a k e i n t o account t h e p r o f i l e v a r i a t i o n s d u r i n g t h e y e a r , and i s d e f i n e d as: _

d = z / 275

i n w h i c h a 2 i s t h e s t a n d a r d d e v i a t i o n o f p o i n t P around t h e r e g r e s s i o n l i n e and z i s t h e average h e i g h t of t h e p r o f i l e . The v a l u e g i s f o r t a k i n g i n t o account t h e c u r v a t u r e of t h e c o a s t l i n e : g = G / z G = A*/300 (H/7.6)^-''2 („/o.0268) ^•'^^ G A = A + T G^= f ( c o a s t a l c u r v a t u r e ) A dune i s r e g a r d e d as s a f e as l o n g as l a n d w a r d of p o i n t P t h e r e i s a t l e a s t a so c a l l e d " l i m i t p r o f i l e " i s p r e s e n t . T h i s l i m i t p r o f i l e (see f i g . 8) has a c r e s t h e i g h t of a t l e a s t 2.5 m above c o m p u t a t i o n a l l e v e l . I n case of h i g h and l o n g d e s i g n waves the c r e s t of t h e l i m i t p r o f i l e may be h i g h e r .

figure 8: The limit profile

The method o u t l i n e d i n t h e above p a r a g r a p h i s d e s c r i b e d i n d e t a i l i n t h e " G u i d e l i n e s " [TAW, 1989] .

3.5 p r a c t i c a l a p p l i c a t i o n i n t h e N e t h e r l a n d s

The Dutch v e r s i o n of these g u i d e was p u b l i s h e d i n 1984. I n t h e f o l l o w i n g y e a r s t h e whole Dutch c o a s t was t e s t e d upon s a f e t y .

The r e s u l t of t h e c o m p u t a t i o n s i s p r e s e n t e d i n f i g u r e 9. As can be seen most of t h e dunes were s a f e enough. At some p l a c e s o n l y t h e seadunes d i d n o t f u l f i l l t h e r e q u i r e m e n t s , b u t t h e dune as a whole were s t r o n g enough. I f t h e s a f e -t y was n o -t s a -t i s f a c -t o r y , dune improvemen-t works were e x e c u -t e d . G e n e r a l l y -t h e s e improvement works were c a r r i e d o u t by p l a c i n g sand l a n d w a r d of t h e weak dunes. C h r o n i c e r o s i o n was t a k e n i n t o c o n s i d e r a t i o n . G e n e r a l l y t h e amount of sand was s u f f i c i e n t t o g u a r a n t e e s a f e sea-defences u n t i l t h e y e a r 2000. Of c o u r s e t h i s g i v e s s e r i o u s problems i n t h e year 2001.

(8)

figure 9: Safety of the Dutch dunes in 1984

V l Q G n d e r e n

• »•• heoyy erosie»

(9)

I t i s c l e a r t h a t i t i s n o t s u f f i c i e n t t o t e s t t h e dunes o n l y once. T h i s s h o u l d be done c o n t i n u o u s l y . At t h i s moment l e g i s l a t i o n i s b e i n g p r e p a r e d f o r a g e n e r a l t e s t i n g of a l l t h e s e a - d e f e n c e s , r i v e r - and l a k e d i k e s . The new B i l l on Waterdefences w i l l p r o b a b l y be a c c e p t e d by p a r l i a m e n t i n 1990. A f t e r p a s s i n g the B i l l , e v e r y w a t e r d e f e n c e system i n t h e N e t h e r l a n d s has t o be t e s t e d a t l e a s t once i n f i v e y e a r s . A r e p o r t has t o be made by t h e manager of t h e seade-fence system, and p r e s e n t e d t o t h e n a t i o n a l government [Verhagen and V o l k e r , 1989] .

For t e s t i n g t h e dunes t h e manager i s o b l i g e d t o use t h e method d e s c r i b e d i n the " g u i d e " .

3.6 examples

As an example a p r o f i l e a l o n g t h e Dutch coast i s t e s t e d upon s a f e t y a c c o r d i n g t o t h e " g u i d e " . The chosen p r o f i l e i s a s t r o n g l y e r o d i n g s e c t i o n of t h e Dutch c o a s t , where t h e s a f e t y i s r a t h e r m a r g i n a l . I s i s n e c e s s a r y t o improve t h e coast h e r e r e g u l a r l y . See example 2 i n t h e appendix.

4. T h e D u r o s t a m o d e l

4.1 f o r m u l a t i o n o f t h e n o d e l

general

The f a c t t h a t Duros i s not t i m e - d e p e n d e n t , but o n l y g i v e s t h e f i n a l p r o f i l e a f t e r t h e s t o r m surge i s n o t a problem. T h e r e f o r e i t i s p r i n c i p a l l y n o t neces-s a r y t o d e v e l o p a time-dependent dune e r o neces-s i o n model.

However, t h e r e are a few s i t u a t i o n s w h i c h cannot be s o l v e d u s i n g t h e Duros-model . These s i t u a t i o n s a r e :

* e r o s i o n on v e r y c u r v e d c o a s t l i n e s ; d u r i n g e r o s i o n t h e d e p o s i t e d sand d i -r e c t l y -removed f-rom t h e beach by a g -r a d i e n t i n t h e l o n g s h o -r e c u -r -r e n t ; t h i s w i l l cause e x t r a dune e r o s i o n . Duros i s n o t a b l e t o p r e d i c t t h e e x t r a e r o s i o n .

* I f t h e r e i s a d u n e f o o t p r o t e c t i o n , Duros cannot c a l c u l a t e t h e f i n a l p r o -f i l e .

* On p l a c e s were dunes t r a n s f o r m t o d i k e s , t h r e e - d i m e n s i o n a l a s p e c t s a r e i m p o r t a n t . Duros cannot cope w i t h them.

* I f t h e r e i s a v e r y s t e e p f o r e s h o r e , sand w i l l n o t o n l y be d e p o s i t e d on t h e beach, b u t a l s o d i s a p p e a r i n t o t h e t i d a l c h a n n e l . I t i s q u i t e d i f f i c u l t t o f i n d an e q u i l i b r i u m - p r o f i l e i n these s i t u a t i o n s .

A time-dependent dune e r o s i o n model i s a b l e t o s o l v e t h e above m e n t i o n e d p r o b l e m s . T h e r e f o r e i t was d e c i d e d by t h e T e c h n i c a l A d v i s o r y committee on Wa-t e r d e f e n c e s (TAW) Wa-t o have Wa-t h e D u r o s Wa-t a model d e v e l o p e d . The b a s i s of Wa-t h e model i s v e r y s i m p l e :

1 C a l c u l a t e t h e t i m e - a v e r a g e d w a t e r movement i n t h e b r e a k e r z o n e . 2 C a l c u l a t e t h e t i m e - a v e r a g e d c o n c e n t r a t i o n .

3 M u l t i p l y w a t e r movement and c o n c e n t r a t i o n i n o r d e r t o f i n d t h e sediment t r a n s p o r t

4 C a l c u l a t e t h e e r o s i o n and s e d i m e n t a t i o n from t h e d i f f e r e n c e s i n sediment t r a n s p o r t

D u r i n g de e l a b o r a t i o n of t h e model, i t proved a l i t t l e b i t more c o m p l i c a t e d t h a n s c h e t c h e d above.

(10)

The b a s i c f o r m u l a f o r t i m e averaged sediment t r a n s p o r t i s : S = U.C + u ' ( t ) . C ' ( t )

I n D u r o s t a i t i s assumed t h a t u ' ( t ) . C ' ( t ) << u.C

Data a n a l y s i s has i n d i c a t e d t h a t t h i s a s s u m p t i o n i s c o r r e c t . I n t h i s c o u r s e t h i s w i l l n o t be worked o u t . For d e t a i l s see S t e e t z e l [ 1 9 9 0 ] . I t i s c o n c l u d e d i n t h a t r e p o r t t h a t under c i r c u m s t a n c e s where much sediment i s p r e s e n t i n t h e v e r t i c a l p r o f i l e , t r a n s p o r t i s m a i n l y d e t e r m i n e d by t h e average v e l o c i t y . The c o n t r i b u t i o n of f l u c t u a t i n g v e l o c i t i e s t o t h e t r a n s p o r t , t h e s o c a l l e d c o r r e l a -t i o n c o n -t r i b u -t i o n , i s r e l a -t i v e l y s m a l l ( o r d e r 5 % ) .

waves and water movement

The b a s i s f o r t h e d e s c r i p t i o n o f t h e v e l o c i t y p r o f i l e i s t h e v e l o c i t y near t h e b o t t o m . Based upon s t u d i e s from S t i v e and Wind and o t h e r s t h e shape o f t h e p r o f i l e i s g i v e n as:

u ( z ) = u j ^ + P/ E Q + a / s^ . z 2

I n t h i s f o r m u l a a,p a r e f u n c t i o n s o f t h e shear s t r e s s , t i s a m i x i n g c o e f f i c i -e n t .

I m p o r t a n t i s t h a t c o a s t w a r d sediment t r a n s p o r t i s n o t t a k e n i n t o r e g a r d , Coastward sediment t r a n s p o r t , caused by wave asym.m.etry can be n e g l e c t e d d u r i n g s t o r m surge c o n d i t i o n s . T h i s makes i n d e e d t h e D u r o s t a model o n l y v a l i d f o r s t o r m c o n d i t i o n s .

concentrations

The average c o n c e n t r a t i o n v e r t i c a l can be d e s c r i b e d by C(x) = CQ.f^(z) i s t h e c o n c e n t r a t i o n near t h e b o t t o m , f ( z ) i s a d i s t r i b u t i o n - f u n c t i o n over the v e r t i c a l . From a n a l y s i s f o l l o w s t h a t z f (z) = exp [-W . dz ] c S oJ £(Z)

i n w h i c h Wg i s t h e s e t t l i n g v e l o c i t y o f t h e sediment and t i s a m i x i n g parame-t e r .

A l l t h e d e r i v a t i o n s i n o r d e r t o a c h i e v e t h e s e r e s u l t s w i l l n o t be p r e s e n t e d h e r e . Reference i s g i v e n t o S t e e t z e l [1990] .

sediment transport and sand balances

When a d e s c r i p t i o n i s a v a i l a b l e f o r t h e v e l o c i t y and f o r t h e c o n c e n t r a t i o n , t h e r e s t o f t h e model i s q u i t e s i m p l e . Sediment t r a n s p o r t i s found by m u l t i p l i -c a t i o n o f -c o n -c e n t r a t i o n and v e l o -c i t y . S e d i m e n t a t i o n and e r o s i o n i s -c a l -c u l a t e d from t h e d i f f e r e n c e s i n sediment t r a n s p o r t . T h i s i s a l l b u i l t i n a a m a t h e m a t i -c a l t r a n s p o r t . Changes i n t h e p r o f i l e d u r i n g a s t o r m -can be p l o t t e d on t h e computer s c r e e n , and t h e r e s u l t s l o o k v e r y r e a l i s t i c .

The model has been c a l i b r a t e d upon t e s t r e s u l t s f r o m dune e r o s i o n t e s t s on a v e r y l a r g e s c a l e i n t h e D e l t a f l u m e o f D e l f t H y d r a u l i c s (De V o o r s t ) . F i g u r e 10a and 10b shows a comparison o f model r e s u l t s and computed r e s u l t s .

examples

D u r o s t a w i l l be used f o r t h e d e s i g n and t e s t i n g o f v a r i o u s p r o b l e m s . At t h i s moment t h e use f o r t e s t i n g e x i s t i n g dune f o o t p r o t e c t i o n s i s most u r g e n t . As an example a c a l c u l a t i o n i s p r e s e n t e d f o r t h e d u n e - f o o t p r o t e c t i o n n e a r Den H e l d e r . See example 3 i n t h e a p p e n d i x .

(11)

figure 10a: comparison measured and calculated erosion for a fixe waterlevel

(12)

figure 10b: comparison of measured and calculated erosion for a varying waterlevel

(13)

5. C o c i s t a l d a t a base^s a n d t h e i r u s e 5.1 o l d databases

Because a sandy coast i s a v e r y dynamic c o a s t l i n e , and because s t a b i l i t y o f t h e c o a s t l i n e i s v i t a l f o r t h e s a f e t y of t h e N e t h e r l a n d s a g a i n s t i n u n d a t i o n by s t o r m surges (dunes p r o t e c t t h e p o l d e r a r e a , which i s s i t u a t e d below sea l e -v e l ) , a l r e a d y i n f o r m e r c e n t u r i e s i t was n e c e s s a r y t o g e t some knowledge about t h e movements of t h e c o a s t l i n e . I n t h e m i d d l e of t h e 1 9 t h c e n t u r y s y s t e m a t i c c o a s t a l measurements s t a r t e d . On f i x e d i n t e r v a l s ( a p p r o x . 250 m) t h e p o s i t i o n of t h e d u n e - f o o t , t h e h i g h w a t e r l i n e and the low w a t e r l i n e was measured e v e r y y e a r . I n o r d e r t o have a f i x e d r e f e r e n c e , monuments were p l a c e d on t h e beach.

A l l t h e g a t h e r e d data a r e now s t o r e d i n a c o m p u t e r i z e d database and a r e a v a i -l a b -l e f o r v a r i o u s types of c o a s t a -l r e s e a r c h . Because t h e database c o v e r s a -l o n g p e r i o d and a l o n g c o a s t l i n e , i t i s v e r y u s e f u l f o r t h e s t u d y of l o n g p e r i o d i c phenomena l i k e moving c o a s t a l sand waves.

From t h i s database i t became c l e a r t h a t the L W - l i n e , and a l s o t h e HW-line shows b i g f l u c t u a t i o n s . F i l t e r i n g of d a t a i s n e c e s s a r y . That makes t h a t t h e d a t a cannot be used f o r d e t e r m i n i n g s h o r t term c o a s t a l movement (< 10 y e a r s ) . Besides t h e above mentioned sandwaves, a l s o c l i m a t i c changes have a b i g i n f l u -ence on t h e c h r o n i c e r o s i o n [Verhagen, 1989] .

5.2 J a r k u s

Around 1960 i t became c l e a r t h a t more d e t a i l e d i n f o r m a t i o n was n e c e s s a r y . T h e r e f o r e t h e system of monuments and base l i n e s was somewhat u p d a t e d , and a d e t a i l e d program f o r c o a s t a l measurements was s e t up.

A l o n g t h e whole N o r t h Sea c o a s t l i n e f r o m Cadzand i n t h e s o u t h t o Rottumeroog a f i x e d s e t of measuring l i n e s was d e f i n e d (see f i g . 1 1 ) . I n t o t a l approx. 3000 l i n e s a r e d e f i n e d t h i s way. The l i n e s have a i n t e r m e d i a t e d i s t a n c e of 200 m and are p e r p e n d i c u l a r t o t h e base l i n e . The base l i n e i s p a r a l l e l t o t h e c o a s t -l i n e , and i s p o s i t i o n e d a p p r o x . near t h e h i g h w a t e r -l i n e . On c o a s t a -l s e c t i o n s w i t h g r o i n s , t h e measuring l i n e s are p l a c e d i n t h e m i d d l e between t h e g r o i n s . P r o f i l e s are measured e v e r y y e a r from 200 m l a n d w a r d o f t h e base l i n e t o 800 m seaward of t h e base l i n e ( t h a t means t o an average d e p t h o f 8 m below mean sea l e v e l ) . Every f i v e y e a r s e v e r y k i l o m e t e r a l i n e i s measured u n t i l 2500 m f r o m t h e base l i n e . A l l measurements are made i n t h e p e r i o d between a p r i l and sep-tember.

The measurements are p e r f o r m e d i n two p a r t s (see f i g . 12) : * l e v e l i n g above t h e low w a t e r l i n e

* s o u n d i n g below approx. mean sea l e v e l l i n e

leveling

The l e v e l i n g s a r e done by t h e s u r v e y department o f R i j k s w a t e r s t a a t , u s i n g a e r i a l p h o t o g r a p h y (see f i g . 1 3 ) . I n t h e f i e l d o n l y some c a l i b r a t i o n p o i n t s a r e measured u s i n g c o n v e n t i o n a l equipment. I n f l i g h t d i r e c t i o n 60 % o v e r l a p i s used i n o r d e r t o g e t a good s t e r e o s c o p i c e f f e c t . I n more t h a n one s t r i p i s r e q u i r e d , an o v e r l a p of 20 - 30 % between t h e s t r i p s i s used. W i t h t h e use o f an a n a l y t i c p l o t t e r t h e h e i g h t i s measured i n t h e measuring l i n e s . I n t h i s p l o t t e r t h e o v e r l a p p i n g p h o t o g r a p h s are p r e s e n t e d a a t h r e e d i m e n s i o n a l image. The p o s i t i o n of t h e bends i n t h e p r o f i l e a r e read as d i g i t a l v a l u e s . The program i n t e r p o -l a t e d t h e d a t a , and e v e r y 5 m a h e i g h t - p o i n t of t h e p r o f i -l e i s s t o r e d i n memo¬ r y .

(14)
(15)
(16)
(17)

soundings

The soundings a r e done by s u r v e y v e s s e l s o f v a r i o u s R i j k s w a t e r s t a a t d e p a r t -ments and by s u r v e y v e s s e l s o f t h e w a t e r b o a r d s . P r o f i l e d a t a a r e a u t o m a t i c a l l y s t o r e d on board as x - y - z - v a l u e s . P o s t p r o c e s s i n g equipment c a l c u l a t e s t h e depths i n t h e p r o f i l e w i t h i n t e r m e d i a t e d i s t a n c e s o f 10 m.

L e v e l i n g d a t a and s o u n d i n g d a t a are c o u p l e d and s t o r e d on a mainframe compu-t e r o f R i j k s w a compu-t e r s compu-t a a compu-t . The d a compu-t a a r e a v a i l a b l e compu-t o c o a s compu-t a l managers, r e s e a r c h e r s and everyone e l s e who i s i n t e r e s t e d . A l l d a t a a r e o n - l i n e a v a i l a b l e s i n c e 1963 . T h i s data-base i s c a l l e d J a r k u s ( a b b r e v i a t i o n from J A a R l i j k s e KUStmetingen, y e a r l y c o a s t a l measurements).

Post p r o c e s s i n g s o f t w a r e i s a v a i l a b l e t o r e a d t h e d a t a , and t o p e r f o r m a d d i -t i o n a l c o m p u -t a -t i o n s . S-tandard P o s -t p r o c e s s i n g i s p l o -t -t i n g p r o f i l e s and making t h r e e d i m e n s i o n a l p l o t s ( f i g . 14) . A l s o v o l u m e t r i c c a l c u l a t i o n s can be made. T h i s can be done i n h o r i z o n t a l and i n v e r t i c a l s l i c e s ( f i g . 1 5 ) . The v e r t i c a l s e c t i o n s a r e used f o r g e n t l e c o a s t l i n e s , w h i l e t h e h o r i z o n t a l s e c t i o n s a r e used f o r c o a s t l i n e s f a c i n g r e l a t i v e l y s t e e p t i d a l c h a n n e l s .

figure 15: horizontal and vertical volumetric calculations

5.3 A p p l i c a t i o n o f c o a s t a l d a t a bases

The J a r k u s database i s used f o r v a r i o u s p u r p o s e s . I t i s used f o r s a f e t y a s -sessment o f dunes, as d e s c r i b e d above, b u t a l s o f o r o t h e r purposes r e l a t e d t o c o a s t a l movement. C h r o n i c c o a s t a l e r o s i o n can be d e t e r m i n e d q u i t e a c c u r a t e l y w i t h t h e database by s i m p l e v o l u m e t r i c i n t e g r a t i o n . V o l u m e t r i c i n t e g r a t i o n g i v e s t h e t o t a l volume o f sand i n a c o a s t a l s e c t i o n . Changes i n t h e volume i n d i c a t e e r o s i o n o r a c c r e t i o n o f t h e c o a s t l i n e . Recent a n a l y s i s o f changes i n t h e sand volume a l o n g t h e Dutch c o a s t i n d i c a t e e r o s i o n zones and a c c r e t i o n zones. These zones do n o t c o i n c i d e w i t h t h e e r o s i o n were a t t h i s moment f o r example t h e d u n e - f o o t i s e r o d i n g . V o l u m e t r i c a n a l y s i s shows t h e r e a l p r o b l e m , and n o t t h e s h o r t t e r m problem (Verhagen, 1989) .

F i g u r e 16 g i v e s t h e r e s u l t o f t h a t a n a l y s i s .

(18)
(19)

I n f a c t c o a s t a l e r o s i o n s h o u l d always be i n d i c a t e d as a l o s s o f sand ( i n m /year p e r m c o a s t l i n e ) . R e c e n t l y O e r t e l e t a l . [1989] suggested a s c a l e f o r q u a n t i f y i n g t h e e r o s i o n r a t e . A l t h o u g h i n t h e paper t h e i n t e g r a t i o n range n o t e x p l i c i t l y i s i n d i c a t e d , t h e y suggested a t t h e i r p r e s e n t a t i o n t o i n t e g r a t e o n l y between t h e low-water l i n e and t h e storm surge l e v e l . E x p e r i e n c e f r o m t h e N e t h e r l a n d s show t h a t e s p e c i a l l y below low w a t e r a l s o b i g v a r i a t i o n s may o c c u r . S t e e p e n i n g of t h e u n d e r w a t e r s h o r e l i n e i s i n f a c t a l s o c o a s t a l e r o s i o n . The proposed s c a l e i s a l o g a r i t h m i c one, u s i n g n - u n i t s .

n = 0.72 I n 5V - 1.8

i n which 5V i s t h e y e a r l y change i n beach volume ( m ^ / y e a r ) . T h i s g i v e s t h e f o l l o w i n g n o m e n c l a t u r e : volume change r a t e n - r a t e n o m e n c l a t u r e ( d u t c h d e s c r i p t i o n ) m V y e a r 768 3.0 192 — 2.0 96 ^^^-^^^^^^^^ 1.5 48 — - 1,0 24 0.5 12 •^•^^-^-^--^•^•^--^ 0.0 .„12 -^^^^^^ 0.0 „24 ^0.5 -48 -1.0 ^96 ^^^^^^^ „i_5 ^192 ..^-^^ ^2.0 ^76g ^3_o

P e r s o n a l l y I t h i n k t h e suggested e r o s i o n s c a l e can be used, b u t a v o l u m e t r i c a n a l y s i s s h o u l d be made f o r t h e whole a c t i v e p r o f i l e , i . e . from approx. 2 t i m e s t h e b r e a k e r d e p t h (under low w a t e r ) u n t i l t h e t o p o f t h e dune. When t h i s s c a l e i s a p p l i e d t o t h e N e t h e r l a n d s , we s u f f e r m a i n l y f r o m m i l d and moderate e r o s i o n . Only on few s p o t s we have s t r o n g e r o s i o n . Severe e r o s i o n does n o t o c c u r i n t h e N e t h e r l a n d s , i f one uses a y e a r l y b a s i s . F i g u r e 17 shows t h e d a t a o f t h e Dutch c o a s t (used e r o s i o n d a t a f r o m i n t e r n a l r i j k s w a t e r s t a a t r e p o r t GWAO-88-007; used p e r i o d 1965/1985) .

v e r y severe a c c r e t i o n (zeer s t e r k e aanzanding) severe a c c r e t i o n ( s t e r k e aanzanding)

s t r o n g a c c r e t i o n ( a a n z i e n l i j k e aanzanding) moderate a c c r e t i o n (gematigde aanzanding) m i l d a c c r e t i o n ( e n i g e aanzanding) s t a b l e ( s t a b i e l ) m i l d e r o s i o n ( e n i g e e r o s i e ) moderate a c c r e t i o n (gematigde e r o s i e ) s t r o n g e r o s i o n ( a a n z i e n l i j k e e r o s i e ) severe e r o s i o n ( s t e r k e e r o s i e ) v e r y severe e r o s i o n (zeer s t e r k e e r o s i e )

(20)
(21)

P o l i c y makers have b i a problems w i t h t h e above s k e t c h e d d e f i n i t i o n of c o a s t a l e r o s i o n . The l o s s of m cannot be seen on t h e beach. I t i s a l s o i m p o s s i b l e t o draw a l i n e on a map, i n d i c a t i n g t h e c o a s t l i n e r e g r e s s i o n , i f one c a l c u l a t e s o n l y t h e l o s s i n ra^^. I n t h e N e t h e r l a n d s i s t h e a d d i t i o n a l problem t h a t t h e B i l l on Waterdefence says t h a t t h e low w a t e r l i n e i s an i n d i c a t o r f o r t h e c o a s t l i n e .

To overcome t h i s p r o b l e m i n t h e N e t h e r l a n d s t h e f o l l o w i n g d e f i n i t i o n o f " C o a s t l i n e " i s g i v e n : A v o l u m e t r i c i n t e g r a t i o n i s made f o r t h e c o a s t a l p r o f i l e f r o m t h e d u n e - f o o t ( a p p r o x . t h e h e i g h t o f a once-a-year s t o r m s u r g e ) u n t i l a d e p t h h under mean low w a t e r l i n e . The v a l u e h i s t h e h e i g h t d i f f e r e n c e between the d u n e - f o o t and t h e low w a t e r l i n e . The r e s u l t o f t h e v o l u m e t r i c a n a l y s i s i s d i v i d e d by 2 h. So t h e r e s u l t i s a d i s t a n c e , which i s g e n e r a l l y i n t h e n e i g h -borhood o f t h e low water l i n e . F i g u r e 18 shows t h e d e f i n i t i o n .

flSP-lijn

figure 18: Definition of coastline

The dune i t s e l f i s n o t p a r t o f t h e i n t e g r a t i o n , because t h e dune i s under j u r i s d i c t i o n of t h e Waterboard, w h i l e beach maintenance i s t h e r e s p o n s i b i l i t y of t h e n a t i o n a l government. A l a n d w a r d movement of t h e " c o a s t l i n e " i s e r o s i o n . The n a t i o n a l p o l i c y i s t o m a i n t a i n t h e c o a s t l i n e on i t s 1990 p o s i t i o n . So e v e r y y e a r t h e p o s i t i o n o f t h e c o a s t l i n e i s c a l c u l a t e d w i t h t h e above d e s c r i b e d me-t h o d , and a r e g r e s s i o n l i n e i s c a l c u l a me-t e d . I f me-t h e r e g r e s s i o n l i n e i n me-t e r c e d e s the 1990 p o s i t i o n , t h e c o a s t l i n e has t o be r e s t o r e d . G e n e r a l l y t h i s w i l l mean t h a t a beach n o u r i s h m e n t has t o be p e r f o r m e d . T h i s beach n o u r i s h m e n t moves t h e c o a s t l i n e t o a more seaward p o s i t i o n . E r o s i o n c o n t i n u e s , t h e c o a s t l i n e moves a g a i n i n a l a n d w a r d d i r e c t i o n u n t i l i t i n t e r c e d e s t h e 1990 p o s i t i o n , and t h e n e x t n o u r i s h m e n t i s due. See f i g u r e 19.

(22)

•J—I—I I 4—1—I—I—I—j—I—I—I—t—l—I—I—I—^-j—I—I—I—I—I—t—l—I—I—j—I—1—4.

1990 y e c i r i

figure .1.9: Determination of the required moment of beach nourishment

The a c t i v e h e i g h t i n t h e N e t h e r l a n d s i s g e n e r a l l y 2 0 m ( f r o m t h e t o p o f t h e dune u n t i l t h e d e p t h u n t i l one observes e r o s i o n d u r i n g s t o r m s ) . So g e n e r a l l y a c o a s t l i n e r e t r e a t o f 1 0 m/year causes a volume l o s s o f 200 m'Vyear ( n = 2 ; t h u s m i l d / m o d e r a t e e r o s i o n ) . I n a d e n s e l y p o p u l a t e d c o u n t r y t h i s e r o s i o n i s g e n e r a l -l y seen as a severe p r o b -l e m . So, i n t h e N e t h e r -l a n d s m i -l d e r o s i o n causes a se-v e r e p r o b l e m .

7. r e f e r e n c e s

Ang, A.H.S and Tang, W.N., 1984; P r o b a b i l i t y concepts i n e n g i n e e r i n g p l a n n i n g and d e s i g n , v o l 2. John W i l e y & Sons, New York.

G r a a f f , J . v . d . , 1983; p r o b a b i l i s t i c d e s i g n o f dunes, Proc. C o a s t a l S t r u c t u r e s ASCE, 1983.

G r a a f f , J. v . d . , 1986; p r o b a b i l i s t i c d e s i g n o f dunes; an example from t h e Ne-t h e r l a n d s . C o a s Ne-t a l e n g i n e e r i n g , v o l 9, 1986.

Kaufman, W. and P i l k e y , O.H., 1983; The beaches a r e moving, t h e d r o w n i n g o f America's s h o r e l i n e . Duke U n i v e r s i t y P r e s s , Durham, N.C., 336 pp.

O e r t e l , G.F., Ludwick, J.C. and O e r t e l , D.L.S., 1989; Sand a c c o u n t i n g methodo-l o g y f o r B a r r i e r i s methodo-l a n d sediment budget a n a methodo-l y s i s . Proc. C o a s t a methodo-l Zone '89 C h a r l e s t o n , ASCE, pp 43-61.

S t e e t z e l , H.J. [ 1 9 9 0 ] ; D u r o s t a , a time-dependent c r o s s - s h o r e model f o r extreme c o n d i t i o n s ; D e l f t H y d r a u l i c s , r e p o r t H298; T A W - p u b l i c a t i o n n r . CC90.xx ( i n Dutch)

TAW ( T e c h n i c a l A d v i s o r y committee on W a t e r d e f e n c e s ) . Guide t o t h e assessment o f the s a f e t y o f dunes as a sea d e f e n c e . Report 140. R i j k s w a t e r s t a a t / C U R p u b l i s h i n g f o u n d a t i o n , Gouda, The N e t h e r l a n d s , 1989.

(23)

V e i i i n g a , P. Beach and dune e r o s i o n d u r i n g s t o r m s u r g e s , C o a s t a l e n a i n e e r i n a v o l 6 , 1982

V e i i i n g a , P. Beach and dune e r o s i o n d u r i n g s t o r m s u r g e s . D e l f t H y d r a u l i c s Com-m u n i c a t i o n s n r . 372, 1986 ( P h . D . - t h e s i s D e l f t U n i v e r s i t y ) .

Verhagen, H.J. Sand waves a l o n g t h e Dutch c o a s t . C o a s t a l E n g i n e e r i n g , 1989 (13) pp 129-147.

Verhagen, H.J. and V o l k e r , W. S a f e t y a g a i n s t i n u n d a t i o n , t h e Dutch a p p r o a c h . C o a s t a l zone '89, C h a r l e s t o n , ASCE 1989.

(24)

AMELAND PGM NR d. n u m b e r o f v a r i a b l e s : 7 •""^ Name T y p T r A B C G E M „ H W D e t N 0.0 0.0 0, 0 Z E E S P D e t N 0.0 0.0 0. 0 D50 Nor N 1 6 4 E - 6 1 5 . 0 E ~ 6 0. 0 Hs_ONZEK Nor N 0. 0 0. 6 0 0. 0 Hh_WATERS E x p N 2 . 6 5 0 9 0 . 3 1 1 7 0. 0 Hh_ONZEK D e t N 0.0 0.0 0. 0 T O E S L A G F A Nor N 0.0 1.0 0. 0 n u m b e r o f c a l c u l a t i o n s : 13 AF-COORDINAAT : 2 8 0 3 0 0 3 2 0 3 4 0 3 6 0 3 3 0 -Fmmp)e. -4. D Mu S i X m i n Xmax 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 0. 0 0. 0 0.0 0. 0 0. 0 1 6 4 E - 6 1 5 . O E - 6 l O ü E -6 5 0 0 E - 6 0,0 0. 0 0. 6 0 0.0 2. 0 0 0.0 4.0 0 . 3 1 1 7 3. 0 6.0 0.0 0. 0 0. 0 0.0 0.0 0. 0 0. 0 1, 0 0. 0 5.0 lO. --420 - 4 4 0 - 4 6 0 - 4 8 0 - 5 0 0 - 5 2 0 R E S U L T PROCEDURE P R O B A B I L , K o s t e r E n g . S o f t w a r e J o b I d e n t i f i c a t i o n = AMELAND PGM NR 4 R e s u l t s o f t h e M e a n - V a l u e a p p r o a c h f o r AF-COORDINAAT : = - 4 . 4 E + 0 0 0 2 P r o b a b i l i t y o f f a i l u r e = 1 . 6 E - 0 0 1 1 T h e Mean V a l u e o f Z i s . . . . = 2 . 1 E + 0 0 0 2 T h e S t a n a r d D e v i a t i o n o f t h e f u n c t i o n Z i s = 3. l E + 0 0 0 1 T h e v a l u e o f B e t a i s = 6 . 6 E + 0 0 0 0 D50 A l p h a ~ 2 [ 1 ] = 0 . 0 5 Hs_ONZEK A l p h a ~ 2 [ 2 ] = 0 . 0 0 Hh_WATERS A l p h a ' 2 C 3 ] = 0 . 8 2 T O E S L A G F A Alpha'"2 C 4 ] = 0 . 1 3 R e s u l t s o f t h e AFDA a p p r o a c h f o r AF-COORDINAAT : = - 4 . 4 E + 0 0 0 2 T h e n u m b e r o f i t e r a t i o n s w a s = T h e v a l u e o f t h e R e l i a b i l i t y -f u n c t i o n i n t h e c a l c u l a t e d d e s i g n p o i n t i s = T h e v a l u e o f B e t a i s = T h e P r o b a b i l i t y o f f a i l u r e i n d e c i m a l s i s T h e a c c u r a c y a c c o r d i n g t o t h e AFDA a p p r o a c h o f t h e P r o b a b i l i t y o f f a i l u r e i s ... = T h e J o i n t P r o b a b i l i t y F u n c t i o n i n t h e c o m p u t e d d e s i g n p o i n t = = 6 . 0 E - 0 0 0 5 = 5 . 1 E - 0 0 0 6 1 . 4 E + 0 0 0 0 T h e v a l u e s o f t h e d e t e r m i n i s t i c v a r i a b l e s G E M _ H U ) = O . O E + 0 0 0 0 Z E E S P = O . O E + O O O O Hh O N Z E K = O . O E+ 0 0 0 0 V a r i a b l e D 5 0 , T y p e N O R D e s g n P o i n t 1 .6 E - 0 0 0 4 A l p h a 0 . 0 1 Mu 1. 6 E - 0 0 0 4 S i g m a 1 . 5 E - 0 0 0 5

(25)

s i O ' " - 1 L i l j * N H P i . 5 i f - - O . i i i O - CrlJ S I G H . G O L F H O O G T E I H Ï n 3 G G L F P E K I Ü D E I H Ï S J K Ü K R E L D l H f l E T E R I H C l O ' - G H J - i .T •i . i O 1 2 . 0 0 i S 7 . 0 0 - 2 , 1 . 0 - 3 . 5 - ^ . 2 . D U I H P R D F Ï E L H F S L i i G P R Q F I E L 2 0 H D E K I Q E Ï L H G K O S T U S K H i i f i n J f t f i f t R i i H l ï ¥ P E D H T H D H T L H H E L H H D i S S S i ^ O O 0 i ^ O * i O s

(26)

imi 0.7 -0.0 - i - 2 , 1 5 I G N , GDLFHDÖGTE I N E n ] GOLFPEKIODE I N C S J K a R R E L D T H f l E T E R I N L i O " - F N J 3 , 10 1 2 . 0 0 1 5 5 , 0 0

K U S T U H K H H H H .TftiiR K H i i l TïPE DftTH DiiTL

HHELiiHD iSU 1^20 0 H O ^ 103 ¥ 1 0 - 1 Efl^TNfipj i.i - 1,1 h 0.^ DUINPRÖFIEL HFSLiiGPRöFÏEL 2DNDEK ? Q E5L H G nFïLHGPRDFIEL NET T Ü E S L H G G K E N S P R D F I E L 0,6 A F S L A G H O E V E E L H E D E N A a n z a n d i n g ( e x c l , i n v l o e d l a n g s t r a n s p o r t ) A f s l a g ( e x c l , i n v l o e d l a n g s t r a n s p o r t ) A f s l a g b o v e n r e k e n p e i l ( e x c l . i n v l o e d l a n g s t r , ) T o e s l a g op a f s l a g b o v e n r e k e n p e i l AFSTANDEN A a n z a n d a f s t a n d (X [ A ] - X C B ] ) A f s l a g a f s t a n d ( X C B ] - X C E ] ) E x t r a v e r s c h u i f a f s t a n d t g v l a n g s t r a n s p o r t ( i n B C ) V e r s c h u i f a f s t a n d i n c l . l a n g s t r a n s p o r t (X C B ] - X [ C ] ) V e r s c h u i f a f s t a n d v o o r d e t o e s l a g ( X[ C] - X [ D ] ) V e r s c h u i f a f s t a n d i n c l . l a n g s t r a n s p o r t + t o e s l a g ( X C B] - X[ D 3 ) X c o o r d . v a n a f s l a g p r o f i e l op r e k e n p e i l ( X C C ] ) X c o o r d . a f s l a g + t o e s l a g p r o f i e l op r e k e n p e i l ( X [ D ] )

34-5.19 (m3)

-345.13 (m3)

-192,09 (m3)

-68,02 (m3)

334.48

( m )

106.12

( m )

0.00

( m )

104.48

( m )

21.45

( m )

125,93

( m )

-351.64

( m )

-373.09

( m )

D u i n a f s l a g AMELAND RWS-DWW DUINAFSLAGPGM D U I N A F - P C O O l

(27)

CL.

1

UJ "1 n

;::ld" d ! 3 I

l.,l..l 1:5 I J O T O i D " ' f O ' f 0 0 " E''|J:::' Ü 0 " ' £ 2 : i i ; : ; i D O " ï''£;'P O O " St';::: 0 0 " 9 9 : 9 O i D " . i S z i Ciij"S..;;:iÖ 0 0 " 6 9 i ; : : i 0 0 " O i i !• I-llll[lll1II!llll]lli!lllllinlilII[llliaQ!IIINIIIIllllllllll|lIllllllillll[li(illliljlllllllllII11llllllllll[lll!]llllll!lli^^^

(28)
(29)

- -t- h

--250.00 -210.00 -170.00 -130

R f s t

.00

and

-90 .00

o .

V

-50.00 -10.00 30.00

o o r s r o n g [ i y i ]

70.00

I f I

•f-I

f I

+

I f

I

+

I

I

t

I 4 4 -I

110.00 150.00

(30)

RökQnröostsr

1 T J , . 4 . + 4 . + - H - 4 "h'i' I 4 " ! I I M 1 I I I i| 11 I I H I I f I I M ' M I M ' I ! I ' I ! ' I ' ! ' ' ' • ' ' ' ' ' ' ' ' ' ' • • ' ' ' ' ' ' ' • ' ' '

-250.00 -210.00 -170.00 -130.00 -90.00 -50.00 -10.00 30.00 70.00 110.00 150.00

A f s t a n d

t . o

. v . o o r s p r o n g

[ m ]

FLLe: 'DEMO.dat

TnW/WL

DUR03rn-i.o

Cytaty

Powiązane dokumenty

Steadystate results for wave elevation, horizontal force and pitch moment are experimentally validated except when heavy roof impact occurs The analysis of small depth requires

The cross-shore profile just before the storm surge, the grain size of the sediment, the maximum storm surge level and the wave characteristics at the MSL – 20 m depth contour

Effects of the wave period on the transition of the dune erosion profile to the initial profiles have been considered on the basis of the small-scale test results of research

Tail behavior of sationary solutions of random difference equations: the case of regular matrices.. Iterated function systems and multiplicative ergodic theory, in Diffusion Theory

Since the effect of the wave period is included in the formulation of the shape of the erosion profile, the relative effect on both the erosion volume A* and the retreat distance

Keeping the type of option constant, in-the-money options experience the largest absolute change in value and out-of-the-money options the smallest absolute change in

Syftet med denna studie är att analysera vågor och vattenstånd, utifrån befintlig klimatdata, för att kunna dra slutsatser om hur stranden, speciellt klitterna, i Ystads Sandskog

Based on the measurements with the levelling rod (see Figure B.20 to Figure B.22) the difference between the average of the measured heights in the transects where the profile