Technical note for sediment transport rate: Analysis of delta flume data and calculations

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Technical Note for Sediment Transport Rate

A n a l y s i s o f D e l t a Flume Data and C a l c u l a t i o n s

Zhang Changkuan

F a c u l t y o f C i v i l E n g i n e e r i n g D e l f t U n i v e r s i t y o f T e c h l o g y

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Technical Note for Sediment Transport Rate

Data A n a l y s i s o f D e l t a Flume and C a l c u l a t i o n s Zhang Changkuan

F a c u l t y o f C i v i l E n g i n e e r i n g , D e l f t U n i v e r s i t y o f T e c h n o l o g y ( R e s e a r c h f e l l o w from H o h a i U n i v e r s i t y , N a n j i n g , P . R . C h i n a )

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

To a c h i e v e h i g h q u a l i t y and h i g h r e s o l u t i o n d a t a on h y d r o d y n a m i c s and s e d i m e n t t r a n s p o r t dynamics on a n a t u r a l 2DV beach, a programme o f d e t a i l e d measurements o f h y d r o d y n a m i c s and s e d i m e n t t r a n s p o r t i n t h e s u r f zone has been c a r r i e d o u t i n DELFT HYDRAULICS' D e l t a Flume i n 1993. The e x p e r i m e n t c o n s i s t s o f 7 s e p a r a t e t e s t s (DELFT HYDRAULICS 1994).

The o b j e c t i v e o f t h e p r e s e n t s t u d y i s t o a n a l y s e t h e measurement d a t a o f p r o f i l e s and v e l o c i t y moments, t o d e r i v e t h e measured c r o s s - s h o r e s e d i m e n t t r a n s p o r t r a t e s f r o m t h e p r o f i l e r e c o r d s and t o compare t h e o b s e r v e d t r a n s p o r t r a t e s w i t h t h e r e s u l t s f r o m s e v e r a l e x i s t i n g p r e d i c t i o n models o f c r o s s - s h o r e s e d i m e n t t r a n s p o r t . T h i s r e p o r t i s a summary o f p r e l i m i n a r y a n a l y s i s and c a l c u l a t i o n s o f 2 t e s t s w i t h t e s t number 2A and 2B. The r e p o r t i n c l u d e s p r o f i l e a n a l y s i s , t h e d e r i v a t i o n o f measured t r a n s p o r t r a t e s , t h e c o m p u t a t i o n s o f c r o s s - s h o r e t r a n s p o r t r a t e by B a i l a r d ' s f o r m u l a and t h e c o m p a r i s o n between t h e measured and t h e computed r e s u l t s .

2. P r o f i l e measurement a n a l y s i s

2.1 T e s t c o n d i t i o n s and measurement p a r a m e t e r s

P r o f i l e measurements used i n t h i s s t u d y come f r o m 2 o f 7 t e s t s w i t h t e s t number 2A and 2B.

The i n i t i a l beach geometry o f t e s t 2A was a Dean-type p r o f i l e i n t h e p r e s e n c e o f a l o w dune showing i n F i g . l . The i n i t i a l beach geometry o f t e s t 2B i s t h e r e s u l t o f t e s t 2A. The bed sand p r o p e r t i e s and h y d r a u l i c c o n d i t i o n s o f t h e t w o t e s t s a r e summarized i n T a b l e 1 .

D u r i n g t h e t e s t s t h r e e p r o f i l e s were measured each t i m e : one i n t h e m i d d l e o f t h e f l u m e and t w o a t t h e d i s t a n c e o f 0.85 m f r o m t h e f l u m e w a l l s . Three p r o f i l e s r e p r e s e n t a same w i d t h o f t h e f l u m e . The p r o f i l e d a t a were s t o r e d a t 0.01 m i n t e r v a l s . F o r t e s t 2A, p r o f i l e measurements were c a r r i e d o u t a t 1 h o u r i n t e r v a l s , t h a t i s , 13 p r o f i l e s a r e a v a i l a b l e ( a t 0, 1 , 2, 3, 4, 5, 6, 7,

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8, 9, 10, 11 and 12 h o u r s a f t e r s t a r t o f t h e t e s t ) . For t e s t 2B, 10 p r o f i l e s a r e a v a i l a b l e ( a t 0, 1 , 2, 3, 4, 5, 6, 7, 8 and 12 h o u r s a f t e r s t a r t o f t h e t e s t ) .

V e l o c i t y measurements a t some c r o s s - s e c t i o n s a l o n g t h e wave f l u m e were c a r r i e d o u t t o o , b u t f o r a c e r t a i n s e c t i o n , say t h e s e c t i o n x=65 m, t h e f l o w v e l o c i t y was measured o n l y once. T a k i n g t e s t 2A as an example, t h e v e l o c i t y measurement a t x=65 m was c o n d u c t e d 1 h o u r a f t e r s t a r t o f t h e t e s t w h i l e i t was c a r r i e d o u t 2 h o u r s a f t e r s t a r t o f t h e t e s t a t x=100 m, e t c . A number o f v e l o c i t y p a r a m e t e r s such as t h e second o r d e r v e l o c i t y moments, t h e t h i r d o r d e r v e l o c i t y moments and t h e f i f t h o r d e r v e l o c i t y moments, a r e a v a i l a b l e f r o m DELFT HYDRAULICS' d a t a b a s e . T a b l e 1 T e s t c o n d i t i o n s T e s t D1 0 D5 0 D9 0 Hm 0 W.L. D u r a t i o n # (mm) (mm) (mm) (Ml) (s) (m) (h) 2A 0. 164 0.200 0.247 0.9 5 4 . 1 12 2B 0. 164 0.200 0.247 1.4 5 4 . 1 12 2.2 Data a n a l y s i s

The f o l l o w i n g p r o c e d u r e s have been t a k e n when t h e a n a l y s e s were p r o c e e d i n g : . e r r o r c h e c k i n g B e f o r e t h e d a t a a n a l y s i s , i t i s n e c e s s a r y t o do some e l a b o r a t i o n on t h e d a t a , c h e c k i n g t h e p o s s i b l e e r r o r s . To check t h e p o s s i b l e e r r o r s i n measured p r o f i l e s , t h e p r o f i l e d a t a were p l o t t e d . F i g . l shows t h e p r o f i l e development o f t e s t 2A i n c l u d i n g i n i t i a l p r o f i l e , 3-hour p r o f i l e , 6-hour p r o f i l e , 9-hour p r o f i l e and 12-h o u r p r o f i l e . More s p e c i f i c a l l y F i g . 2 t 12-h r o u g 12-h F i g . 4 s12-how some l o c a l p r o f i l e s a t d i f f e r e n t l o c a t i o n s . By e x a m i n i n g t h e p r o f i l e s some measurement e r r o r s can be c l e a r l y f o u n d . For example, i n t h e case o f 4.1 m w a t e r l e v e l and 0.9 m wave h e i g h t , t h e p r o f i l e above 5.5 m e l e v a t i o n ( f r o m t h e bed) can n o t change v e r y much. However, f r o m t h e F i g s . 3 and 4 i t can be seen t h a t t h e 3-hour p r o f i l e f r o m s e c t i o n x=178.0 m t o s e c t i o n x=200.0 m i s 5-10 cm h i g h e r t h a n t h e i n i t i a l p r o f i l e . T h a t can n o t be t r u e . The same s i t u a t i o n happens f o r t h e 1-hour p r o f i l e . So i t i s n e c e s s a r y t o c o r r e c t some e r r o r s i n t h e measured p r o f i l e r e c o r d s . The p r o f i l e c o r r e c t i o n was c a r r i e d o u t by a v e r a g i n g t h e i n i t i a l p r o f i l e and 2-hour p r o f i l e t o g e t a c o r r e c t 1-hour p r o f i l e f o r x>=178.0 m.

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The same was done f o r t h e 3-hour p r o f i l e .

F i g . 5 d e m o n s t r a t e s t h e p r o f i l e development o f t e s t 2B showing t h a t no e r r o r was f o u n d i n t h e measured p r o f i l e d a t a o f t e s t 2B.

. p r o f i l e a v e r a g i n g

As m e n t i o n e d above, t h r e e p r o f i l e s were measured a t t h e same t i m e a c r o s s t h e f l u m e s e c t i o n . One i s i n t h e m i d d l e o f t h e wave f l u m e and t w o a r e a t t h e d i s t a n c e o f 0.85 m f r o m t h e wave f l u m e w a l l s . For t h e p r e s e n t u t i l i z a t i o n t h e y have been a v e r a g e d w i t h t h e same w e i g h t t o o b t a i n a r e p r e s e n t i n g mean p r o f i l e ( t h e f o l l o w i n g p r o f i l e r e f e r s t o t h i s mean p r o f i l e ) .

. sand g a i n / l o s s c o n s i d e r a t i o n

A c c o r d i n g t o t h e measured p r o f i l e s , t h e t o t a l sand volume i n t h e f l u m e a t a m e a s u r i n g moment was c a l c u l a t e d . I f t h e measurement and t h e p r e s e n t a t i o n a r e p e r f e c t , t h e t o t a l sand volumes a t each m e a s u r i n g t i m e s h o u l d be e q u a l . A c t u a l l y , t h e r e a l w a y s a r e d i f f e r e n c e s o f t h e t o t a l volumes among d i f f e r e n t measurements, namely sand g a i n s o r sand l o s s e s .

The p o s s i b l e r e a s o n s o f t h e s e d i f f e r e n c e s c o u l d be sand p o r e d i f f e r e n c e s i n t h e volume o r m e a s u r i n g e r r o r s o r o t h e r s . I f i t

i s due t o t h e p o r e volume r e d u c t i o n , t h e t o t a l sand volume i n t h e f l u m e s h o u l d be g r a d u a l l y r e d u c e w i t h t i m e . However, f r o m F i g . 6 i t can be seen t h a t t h e m a g n i t u d e o f t o t a l sand volume f l u c t u a t e s a r o u n d a mean v a l u e i n s t e a d o f j u s t d e c l i n i n g w i t h t i m e . T h e r e f o r e i n a u t h o r ' s o p i n i o n t h e p o r e volume d e c r e a s e i s n o t an o b v i o u s r e a s o n o f t h e t o t a l volume d i f f e r e n c e s . A f t e r t h e e r r o r c h e c k i n g , t h e m e a s u r i n g e r r o r s can n o t be c o n s i d e r e d as a r e a s o n o f t h e d i f f e r e n c e s t o o . As measured s e d i m e n t t r a n s p o r t r a t e s a r e v e r y s e n s i t i v e t o ' a r t i f i c i a l ' sand l o s s e s and g a i n s , t h e a p p a r e n t f l u c t u a t i o n s i n sand volume i n t h e f l u m e must be c a r e f u l l y c o n s i d e r e d and t r e a t e d . F i g . 7 shows t h e e f f e c t s o f sand g a i n on t h e r e s u l t s o f s e d i m e n t t r a n s p o r t r a t e . I t can be seen t h a t w i t h o u t sand g a i n / l o s s c o r r e c t i o n t h e m a g n i t u d e o f t r a n s p o r t a t a c e r t a i n f l u m e s e c t i o n c o u l d be v e r y d i f f e r e n t d e p e n d i n g on w h i c h c a l c u l a t i o n approache i s used. Moreover, a s i g n i f i c a n t sand t r a n s p o r t , w i t h a m a g n i t u d e o f 10*10"6 m3/m/s, e x i s t s c r o s s - t h o u g h t h e l o w e r end o f t h e f l u m e (x=19 m) o r c r o s s - t h r o u g h t h e u p p e r end o f t h e f l u m e (x=203 m) . B u t , i n r e a l i t y , b o t h cases above w i l l n e v e r o c c u r s i n c e i t i s supposed t h a t no sand pass t h r o u g h

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t h e s e c t i o n s x=19 m and x=203 m a t a l l . Thus t h e appearance o f s e d i m e n t t r a n s p o r t a t t h e s e t w o s e c t i o n s w h o l l y a t t r i b u t e t o sand g a i n s / l o s s e s .

The p r e s e n t c o n s i d e r a t i o n i s a v e r a g i n g t h e t o t a l volumes o v e r a l l p r o f i l e measurements and t a k i n g t h e mean v a l u e as a " t r u e " volume, t h e n a d d i n g o r e x t r a c t i n g sand o v e r t h e w h o l e bed s u r f a c e

( m o d i f y i n g t h e bed e l e v a t i o n z) t o e n s u r e t h a t t h e e x a c t same t o t a l sand volume a t each measurement i s a c h i e v e d . I t i s o u r c h o i c e , and o f c o u r s e b e s i d e s t h e p r e s e n t method t h e r e a r e o t h e r p o s s i b i l i t i e s w h i c h one can choose. For example, r e l a t i n g t h e c o r r e c t i o n t o t h e d i f f e r e n c e s i n p r o f i l e , t h a t i s , u n e v e n l y s p r e a d i n g o f t h e r e q u i r e d volume o v e r t h e p r o f i l e . However, i t i s h a r d t o d e c i d e t h e w e i g h t f o r d i f f e r e n t p a r t s o f t h e p r o f i l e . T h e r e f o r e , f o r t h e t i m e b e i n g , i t m i g h t be w i s e t o t a k e t h e d i f f e r e n c e as a s y s t e m a t i c e r r o r and e v e n l y s p r e a d o v e r t h e w h o l e s u r f a c e o f t h e bed. T a b l e 2 g i v e s t h e t o t a l sand volumes and g a i n s / l o s s e s a t d i f f e r e n t t i m e s o f t e s t s 2A and 2B.

T a b l e 2 Sand g a i n s and sand l o s s e s ( p e r r u n n i n g m e t e r )

T e s t # 2A 2A 2B 2B Time (h) T o t a l Volume (m3/m) Gain/Loss (m3/m) T o t a l Volume (m3/m) Gain/Loss (m3/m) 0 497.248 -0.393 497.939 -0.327 1 497.250 -0.392 498.275 0. 009 2 497.962 0.321 497.759 -0.507 3 498.086 0 . 444 497.757 -0.509 4 497.664 0. 022 498.252 -0.014 5 497.629 -0.013 498.315 0 . 049 6 497.609 -0.033 498.299 0. 033 7 497.709 0. 067 499.075 0 .809 8 497.151 -0.490 498.585 0. 319 9 497.221 -0.421 10 497.989 0. 347 11 497.885 0 .243 12 497.939 0. 297 498.404 0 . 138 mean 497.642 0 . 000 498.266 0 . 000

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.measured sediment t r a n s p o r t r a t e

For each p r o f i l e , a c c u m u l a t i v e sand volumes a t d i f f e r e n t s e c t i o n s w i t h 0.01 m i n t e r v a l s were worked o u t . A t a c e r t a i n s e c t i o n t h e volumes o f sand f o r two p r o f i l e s , say i n i t i a l p r o f i l e and 12-hour p r o f i l e , a r e d i f f e r e n t . T h i s d i f f e r e n c e was caused by t h e sediment t r a n s p o r t . So sediment t r a n s p o r t r a t e c r o s s t h i s s e c t i o n e q u a l s t h e volume d i f f e r e n c e between t h e two p r o f i l e s d i v i d e d by t i m e i n t e r v a l s . Based on t h e computed r e s u l t s o f a c c u m u l a t i v e volumes, measured sediment t r a n s p o r t r a t e s a t any s p e c i f i c s e c t i o n can be o b t a i n e d .

There a r e t w o c h o i c e s o f s t a r t i n g t h e a c c u m u l a t i v e volume c a l c u l a t i o n t h a t i s e i t h e r s t a r t i n g f r o m t h e l o w e r end p a r t o f t h e p r o f i l e o r s t a r t i n g f r o m t h e upper end p a r t o f t h e p r o f i l e . S i n c e sand g a i n s / l o s s e s have been t a k e n i n t o a c c o u n t and t h e volumes o f sand i n t h e f l u m e a r e e x a c t l y t h e same f o r d i f f e r e n t p r o f i l e measurements, t h e s e two methods have no e f f e c t s on t h e r e s u l t s o f measured sediment t r a n s p o r t r a t e and b o t h can be chosen. O t h e r w i s e , as m e n t i o n e d above, w i t h o u t sand g a i n / l o s s s m o o t h i n g two c h o i c e s w i l l d e f i n i t e l y g i v e two d i f f e r e n t r e s u l t s

(see F i g . 7 )

T a b l e 3 summarizes t h e r e s u l t s o f sediment t r a n s p o r t r a t e s d e r i v e d f r o m p r o f i l e measurements a t v e l o c i t y measurement p o s i t i o n s a l o n g t h e f l u m e over d i f f e r e n t t i m e spans. The m a g n i t u d e o f t r a n s p o r t g i v e n i n t h e t a b l e i n c l u d e s p o r e s . An o v e r v i e w o f averaged t r a n s p o r t r a t e o v e r d i f f e r e n t d u r a t i o n s (0-6 h o u r s , 6-12 h o u r s and 0-12 h o u r s ) a l o n g t h e f l u m e i s shown i n F i g . 8 and F i g . 9 f o r t e s t 2A and t e s t 2B r e s p e c t i v e l y . The v a r i a t i o n s o f t r a n s p o r t r a t e w i t h t i m e i n some s e c t i o n s a r e p l o t t e d i n Fig.10 t h r o u g h Fig.19 f o r t e s t 2A, and F i g . 2 0 t h r o u g h Fig.28 f o r t e s t 2B. The f i g u r e s g e n e r a l l y show l a r g e v a r i a t i o n b u t no s y s t e m a t i c t r e n d s .

2.3 D i s c u s s i o n on t h e r e s u l t s o f measured t r a n s p o r t r a t e s

As m e n t i o n e d above, d u r i n g t h e t e s t d u r a t i o n , f o r a c e r t a i n s e c t i o n t h e v e l o c i t y measurement was c a r r i e d o u t o n l y once, t h e v e l o c i t y moments a t d i f f e r e n t f l u m e - c r o s s s e c t i o n s were o b s e r v e d a t d i f f e r e n t t i m e i n t e r v a l s , t h u s t h e p r e d i c t i o n o f t h e t r a n s p o r t r a t e by a m a t h e m a t i c a l model i s based on t h e one-hour t i m e averaged v e l o c i t y moments. For t h e comparison between measured and computed r e s u l t s t h e d e t e r m i n a t i o n o f a c c u r a t e v a l u e s o f measured t r a n s p o r t r a t e s i s t h e f i r s t s t e p . However, t h e r e e x i s t s a l i t t l e b i t o f u n s u r e o f t h e measured sediment t r a n s p o r t r a t e .

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T a b l e 3.1 Summary o f sediment t r a n s p o r t r a t e s o f t e s t 2A ( U n i t o f t r a n s p o r t r a t e i s 10"6(m3/m)/s ) X(m) Time(h) 65 100 115 125 130 138 145 152 160 170 0-1 38.9 43.8 41.1 34.4 30.9 9.1 -5.4 -7.1 -15.4 -35.8 1-2 -27.6 -9.8 -1.7 1.3 3.6 -5.8 -5.2 8.7 11.2 9.7 2-3 -3.5 3.0 2.7 2.2 0.2 -17.5 -21.6 -12.2 -17.6 -26.7 3-4 12.8 18.5 20.4 20.5 20.5 8.1 5.0 11.5 5.4 -10.3 4-5 1.3 3.5 1.6 -3.4 -5.5 -22.2 -22.9 -11.0 -14.5 -19.5 5-6 1.9 5.6 5.7 4.0 1.8 -15.2 -15.8 -4.6 -8.2 -12.2 6-7 10.5 16.1 16.5 14.3 12.9 -6.2 -4.7 3.8 -5.4 -6.3 7-8 12.6 11.3 11.5 10.1 6.7 -16.0 -11.0 -3.6 -16.8 -15.0 8-9 -4.6 -1.3 -0.7 -3.5 -6.3 -25.0 -19.9 -8.2 -18.4 -11.9 9-10 8.6 6.8 5.9 3.8 2.1 -18.2 -17.0 -5.7 -18.1 -13.9 10-11 -2.6 3.0 2.2 -0.2 -2.9 -22.0 -14.3 -6.5 -18.6 -12.7 11-12 4.0 8.3 7.6 7.3 4.1 -15.5 -6.3 5.8 -6.6 -4.4 0-6 4.0 10.8 11.7 9.8 8.6 -7.2 -11.0 -2.4 -6.5 -15.8 6-12 4.7 7.4 7.2 5.3 2.8 -17.2 -12.2 -2.4 -14.0 -10.7 0-12 4.3 9.1 9.4 7.6 5.7 -12.2 -11.6 -2.4 -10.2 -13.2 T a b l e 3.2 Summary o f sediment t r a n s p o r t r a t e s o f t e s t 2B ( U n i t o f t r a n s p o r t r a t e i s 10"6(m3/m)/s ) x(m) Time(h) 65 100 115 130 138 145 152 160 170 0-1 -2.1 0.7 -7.7 -23.8 -54.5 -41.3 -23.3 -36.1 -24.3 1-2 1.9 13.6 11.0 -1.5 -27.1 -14.9 -6.7 -18.1 -19.0 2-3 -10.0 3.8 4.6 -3.8 -28.6 -6.6 1.0 -11.0 -6.4 3-4 2.6 4.6 2.0 -15.8 -38.4 -19.1 -18.9 -33.2 -29.3 4-5 -2.1 9.5 8.4 -9.0 -27.5 -9.7 -4.8 -18.9 -19.6 5-6 -3.0 20.5 20.4 -0.4 -12.5 2.0 7.5 -4.8 -1.3 6-7 -11.9 3.0 4.7 -10.4 -21.5 1.1 7.6 -3.0 2.1 7-8 -15.0 -7.5 -8.7 -33.0 -46.3 -28.5 -22.4 -35.5 -36.3 8-12 -14.0 33.5 34.7 -90.6 -70.2 -16.3 10.0 -35.4 -21.9 0-6 -2.1 8.8 6.5 -9.1 -31.4 -14.9 -7.5 -20.4 -16.6 6-12 -6.8 4.8 5.1 -22.3 -23.0 -7.3 -0.8 -12.3 -9.4 0-12 -4.5 6.8 5.8 -15.7 -27.2 -11.1 -4.2 -16.3 -13.0

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T a b l e 4 Measured s e d i m e n t t r a n s p o r t r a t e o v e r 3 t i m e spans ( U n i t o f t r a n s p o r t r a t e i s 10"6(m3/m)/s ) T e s t # Wave Hour (h) X (m) Smed1 Sm e d 3 Sm e d 1 2 2A 1 65 38 . 9 5.7 4 . 3 2A 2 100 -9 . 8 12 . 3 9.1 2A 3 115 2.7 7 . 1 9 . 4 2A 4 130 20.5 5 . 1 5 . 7 2A 5 138 -22 . 2 -9 . 8 -12 . 2 2A 6 145 -15 . 8 -14 . 5 - 1 1 . 6 2A 7 152 3 . 8 -1.5 -2.4 2A 8 160 -16.8 -13 . 5 -10. 2 2A 9 170 - 1 1 . 9 -13 . 6 -13 . 2 2A 10 102 5.9 2 . 7 9 . 4 2A 11 125 -0 . 2 3 . 6 7 . 6 2A 12 130 4 . 1 0 . 6 5 . 7 2B 1 65 -2 . 1 -0.1 -4 . 5 2B 2 100 13 . 6 6 . 0 6 . 8 2B 3 115 1.0 1.5 5.8 2B 4 130 -15.8 -9 . 5 -15 . 7 2B 5 138 -27 . 5 -26.1 -27 . 2 2B 6 145 2 . 0 -2 . 2 - 1 1 . 1 2B 7 152 7 . 6 -2.4 -4.2 2B 8 160 -35 . 5 -24 . 6 -16 . 3 2B 12 170 -21.9 -29 . 1 -13 . 0

Note: Sm e d l denotes t h e t r a n s p o r t r a t e a t v e l o c i t y measuring time Sm e d 3 denotes t h e averaged t r a n s p o r t r a t e over 3 hours smedi2 denotes t h e averaged t r a n s p o r t r a t e over 12 hours

As t o t h e v a r i a t i o n o f t r a n s p o r t r a t e w i t h t h e t e s t t i m e a o b v i o u s f l u c t u a t i o n can be n o t i c e d and i t i s h a r d t o j u d g e w h i c h t r a n s p o r t i s t h e t r u e one. F i g . 1 0 t h r o u g h F i g . 1 4 s u g g e s t t h a t a

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s i g n i f i c a n t onshore s e d i m e n t t r a n s p o r t t o o k p l a c e d u r i n g t h e f i r s t t e s t hour f o l l o w i n g by a s i g n i f i c a n t o f f s h o r e t r a n s p o r t o r a s m a l l onshore t r a n s p o r t d u r i n g t h e n e x t h o u r . Then, t w o h o u r s l a t e r a r e m a r k a b l e onshore t r a n s p o r t r e a p p e a r e d a g a i n . A t o t h e r t i m e t h e d i f f e r e n c e s among t h e t r a n s p o r t r a t e s d u r i n g d i f f e r e n t t i m e i n t e r v a l s a r e a l s o n o t i c e a b l e . A t l e a s t t h r e e v a l u e s can be chosen t o r e p r e s e n t t h e " t r u e " measured s e d i m e n t t r a n s p o r t r a t e : t r a n s p o r t r a t e a t v e l o c i t y m e a s u r i n g moment, averaged t r a n s p o r t r a t e o v e r t h r e e h o u r s ( t h e f o r m e r h o u r , t h e v e l o c i t y m e a s u r i n g h o u r and t h e l a t e r h o u r ) , and a v e r a g e d t r a n s p o r t r a t e o v e r 12 h o u r s ( t e s t d u r a t i o n ) . T a b l e 4 summaries t h e r e s u l t s . A g a i n f r o m t h e t a b l e i t i s d i f f i c u l t y t o make a judgement w h i c h v a l u e c o u l d be t h e " t r u e " t r a n s p o r t r a t e . B e f o r e a f i n a l d e c i s i o n more c o n s i d e r a t i o n s s h o u l d be t a k e n i n t o a c c o u n t and more t e s t d a t a need t o be a n a l y s e d .

3. S e d i m e n t t r a n s p o r t r a t e c a l c u l a t i o n

3.1 Sediment t r a n s p o r t model

A number o f s e d i m e n t t r a n s p o r t models have been p r o p o s e d by r e s e a r c h e r s . For t h e t i m e b e i n g , B a i l a r d ' s c r o s s - s h o r e t r a n s p o r t model i s a d o p t e d ( 1 9 8 1 a , 1 9 8 1 b ) . B a i l a r d ' s model i s based on an a d a p t a t i o n o f Bagnold's e n e r g e t i c approach w i t h s e p a r a t e b e d l o a d and suspended l o a d e f f i c i e n c y f a c t o r s . The model i s g e n e r a l i z e d f o r t i m e - v a r y i n g f l o w o v e r an a r b i t r a r y s l o p i n g b o t t o m , r e s u l t i n g i n : S(t) -Sb(t) +Sg(t) (1) sb=- .p c 'e V [ l u ( t ) l2 u ( t ) - - ^ lu<t)l»] (2) * (p s-p) g(l-p) tan(p tan(p ss=~, PC\ftï* w7[ \u(t)\3 u ( t ) - 4 f t a n p l u ( f c ) l5 ] (3) (p s-p) ff(i-p) w w where S(t) : t o t a l i n s t a n t a n e o u s v o l u m e t r i c s e d i m e n t t r a n s p o r t r a t e (m3/m/s) Sb(t) : b e d l o a d i n s t a n t a n e o u s v o l u m e t r i c s e d i m e n t t r a n s p o r t r a t e (m3/m/s) Ss(t) : suspended i n s t a n t a n e o u s v o l u m e t r i c s e d i m e n t t r a n s p o r t r a t e (m3/m/s) p : mass d e n s i t y o f w a t e r (kg/m3) p : mass d e n s i t y o f s e d i m e n t (kg/m3)

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p : p o r o s i t y o f bed cf : d r a g c o e f f i c i e n t o f t h e bed eb : t h e bed l o a d e f f i c i e n c y f a c t o r <p : i n t e r n a l a n g l e o f f r i c t i o n o f t h e s e d i m e n t (degree) tan/3 : t h e bed s l o p e es W : suspended l o a d e f f i c i e n c y f a c t o r es W : t h e f a l l v e l o c i t y o f t h e s e d i m e n t (m/s) u(t) : i n s t a n t a n e o u s near b o t t o m f l u i d v e l o c i t y (m/s) < > : t i m e - a v e r a g e I t s h o u l d be n o t e d t h a t i n B a i l a r d ' s o r i g i n a l e q u a t i o n a v a l u e

o f Cf=0.005 was recommended w h i l e i n some o t h e r p a p e r s l / 2 * fw i s

used t o r e p l a c e Cf, i n w h i c h f w i s wave f r i c t i o n f a c t o r .

I n p r e s e n t s t u d y t h e f o l l o w i n g p a r a m e t e r s a r e s p e c i f i e d : tan</?=0.625 ( f r i c t i o n a n g l e e q u a l s 32 d e g r e e ) , eb= 0 . 1 , es=0.02, p=1000.0 kg/m3, jOs=2650.0 kg/m3, W=0.023 m/s ( a c c o r d i n g t o

D50= 0 . 0 0 0 2 m) , p=0.4. For t h e wave f r i c t i o n f a c t o r Jonsson's

f o r m u l a t i o n i s a p p l i e d r e s u l t i n g i n : f„=exp[5.21(-^)-°-194-5.9 8] f o r - ^ 1 . 5 9 (4) f =0 .3 f o r - ^ - < l .59 (5) r where a0 : s e m i - e x c u r s i o n l e n g t h o f w a t e r p a r t i c l e s due t o t h e h o r i z o n t a l o s c i l l a t o r y f l o w (m) r : roughness h e i g h t o f t h e bed (m) 3.2 P r e d i c t e d r e s u l t s o f t r a n s p o r t r a t e by B a i l a r d ' s f o r m u l a For t h e u t i l i z a t i o n o f t h e B a i l a r d ' s model t h e v a l u e s o f t h e s e m i - e x c u r s i o n l e n g t h and t h e roughness h e i g h t o f t h e bed s h o u l d be s p e c i f i e d . A c c o r d i n g t o Al-Salem's r e s e a r c h ( 1 9 9 3 ) , t h e f o l l o w i n g f o r m u l a t i o n can be employed:

3 = 0 . 8 6 - ^ ^ (6)

where ur m s : r o o t mean square v e l o c i t y (m/s)

T : wave p e r i o d ( s )

Much u n c e r t a i n t y e x i s t s w i t h r e s p e c t t o t h e f o r m u l a t i o n o f t h e r o u g h n e s s . As a f i r s t c h o i c e a bed roughness h e i g h t r=D5 0=0.2 mm i s assumed.

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T a b l e 5 i s t h e summary o f t h e main r e s u l t s o f computed s e d i m e n t t r a n s p o r t r a t e s . For c o m p a r i s o n measured s e d i m e n t t r a n s p o r t r a t e s a r e a l s o l i s t e d i n t h e t a b l e . The v a l u e s i n t h e s e v e n t h column o f t h e t a b l e , S ., a r e p r e d i c t e d r e s u l t s f r o m B a i l a r d s1 model. The r e s u l t s i n d i c a t e t h a t f o r t h o s e p r o f i l e measurement p o i n t s where measured t r a n s p o r t r a t e i s h i g h e r t h a n 10*10"6 m2/s t h e B a i l a r d f o r m u l a g i v e s a q u i t e good agreement w i t h t h e measurements ( w i t h a f a c t o r 2 - 3 ) , and f o r t h o s e p o i n t s where measured t r a n s p o r t r a t e i s l e s s t h a n 10*10"6 m2/s t h e B a i l a r d f o r m u l a does n o t g i v e b e l i e v a b l e r e s u l t s . T a b l e 5 Summary o f main r e s u l t s T e s t # T e s t Hour ( h ) X (m) _(m/s) a0 (m) ( 1 03) (10 W s ) Smed12 (10"em2/s) ^medl d o V / s ) Smed3 (10"em2/s) 2A 1 65 0.349 0.478 8.0 0.37 4.30 38.9 5.7 2A 2 100 0.413 0.565 7.7 2.02 9.10 -9.8 12.3 2A 3 115 0.419 0.573 7.7 1.62 9.40 2.7 7.1 2A 4 130 0.468 0.641 7.5 -4.29 5.70 20.5 5.1 2A 5 138 0.509 0.697 7.4 -21.31 -12.20 -22.2 -9.8 2A 6 145 0.468 0.641 7.5 -32.35 -11.60 -15.8 -14.5 2A 7 152 0.397 0.543 7.8 -11.76 -2.40 3.8 -1.5 2A 8 160 0.466 0.638 7.5 -21.79 -10.20 -16.8 -13.5 2A 9 170 0.448 0.613 7.6 -17.01 -13.20 -11.9 -13.6 2A 10 102 0.411 0.563 7.7 0.70 9.40 5.9 2.7 2A 11 125 0.433 0.593 7.6 -1.31 7.60 -0.2 3.6 2A 12 130 0.468 0.641 7.5 4.96 5.70 4.1 0.6 2B 1 65 0.516 0.706 7.4 -14.35 -4.47 -2.1 -0.1 2B 2 100 0.482 0.660 7.5 -7.76 6.81 13.6 6.0 2B 3 115 0.479 0.656 7.5 -10.27 5.79 1.0 1.5 2B 4 130 0.532 0.728 7.3 -16.89 -15.68 -15.8 -9.5 2B 5 138 0.545 0.746 7.3 -53.11 -27.21 -27.5 -26.1 2B 6 145 0.460 0.630 7.5 -34.10 -11.11 2.0 -2.2 2B 7 152 0.440 0.602 7.6 -21.16 -4.16 7.6 -2.4 2B 8 160 0.522 0.714 7.3 -32.91 -16.34 -35.5 -24.6 2B 12 170 0.474 0.649 7.5 -20.25 -13.00 -21.9 -21.9

F i g . 2 9 and F i g . 3 0 a l s o show t h e c o m p a r i s o n between t h e measured ( a v e r a g e d o v e r 0-12 h o u r s ) and t h e computed n e t t r a n s p o r t r a t e s a l o n g t h e wave f l u m e f o r t e s t 2A and t e s t 2B r e s p e c t i v e l y i n d i c a t i n g a p o o r agreement between them. I t s h o u l d be n o t i c e d

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t h a t c a l c u l a t i o n p o i n t s i n t h e f i g u r e s a r e f r o m v e l o c i t y moments measured i n d i f f e r e n t t i m e i n t e r v a l s .

F i g u r e s 3 1 , 32 and 3 3 a r e f u r t h e r c o m p a r i s o n s between computed and measured t r a n s p o r t r a t e s . Three d i f f e r e n t measured v a l u e s , t h a t i s , Sm e d 1 2 ( a v e r a g e d o v e r 12 h o u r s ) and Sm e d 1 ( a t v e l o c i t y m e a s u r i n g t i m e ) as w e l l as Sm e d 3 ( a v e r a g e d o v e r 3 h o u r s ) a r e used r e s p e c t i v e l y . I n t h e f i g u r e s , dashed l i n e s w i t h a s l o p e 1:1 i n d i c a t e t h e p e r f e c t r e l a t i o n s h i p between computed and measured t r a n s p o r t r a t e s and t h e r e f o r e t h e b e s t agreement between them s h o u l d be a l l p o i n t s f i t t i n g i n t h e l i n e s . However, f r o m t h e f i g u r e s i t can be seen t h a t a l m o s t a l l p r e d i c t i o n p o i n t s a r e p o s i t i o n e d below t h e dashed l i n e s i m p l y i n g t h a t B a i l a r d ' s f o r m u l a o v e r p r e d i c t s t h e o f f s h o r e s e d i m e n t t r a n s p o r t r a t e s ( w i t h a f a c t o r 2-3) w h i l e i t u n d e r p r e d i c t s t h e onshore s e d i m e n t t r a n s p o r t r a t e s , and t h a t t h e f o r m u l a p r e d i c t s o p p o s i t e d i r e c t i o n t r a n s p o r t i n some cases, e s p e c i a l l y , i n t h e low t r a n s p o r t r a t e r e g i m e . T h i s s y s t e m a t i c a l t r e n d e x i s t s no m a t t e r Sm e d l 2 o r Sm e d 3 o r Sm e d l i s s e l e c t e d .

F i g s . 3 4 and 3 5 show t h e comparisons between Sm e d 1 2 and Sm e d l as

w e l l as between Sm e d 1 2 and Sm e d 3. I t can be seen t h a t t h e r e l a t i o n between Sm e d l 2 and Sm e d 3 i s b e t t e r t h a n t h e r e l a t i o n between Sm e d l 2 and Sm e d 1. C a r e f u l l y l o o k i n g i n t o F i g . 31 t h o u g h F i g . 3 5 i t seems t h a t Sm e d 1 i s n o t a good r e p r e s e n t a t i o n f o r t h e measured s e d i m e n t t r a n s p o r t r a t e w h i l e e i t h e r Sm e d 1 2 o r Sm e d 3 c o u l d be a c h o i c e . 3.3 E f f e c t o f wave f r i c t i o n f a c t o r

As m e n t i o n e d above, much u n c e r t a i n t y e x i s t s w i t h r e s p e c t t o t h e f o r m u l a t i o n o f t h e roughness h e i g h t o f t h e bed. S i n c e wave f r i c t i o n f a c t o r i s a f u n c t i o n o f t h e r o u g h n e s s h e i g h t , t h e wave f r i c t i o n f a c t o r w i l l a l s o show some u n c e r t a i n t y . I n t h e above

c a l c u l a t i o n r=D50=O.2OO mm has been assumed. As a c o m p a r i s o n t w o

a l t e r n a t i v e s , r=D1 0=O.l64 mm and r=D9 0=0.247 mm, were used. T a b l e

6 shows t h e r e s u l t s o f wave f r i c t i o n f a c t o r w i t h d i f f e r e n t roughness h e i g h t s . I t can be seen t h a t compared w i t h t h e v a l u e s o f f w t a k i n g r = D5 0, t h e v a l u e s o f f w w i t h r = D? 0 a r e 5% i n c r e a s i n g w h i c h w i l l r e s u l t i n a same p e r c e n t a g e i n c r e a s e o f s e d i m e n t t r a n s p o r t r a t e because t h e wave f r i c t i o n f a c t o r i n B a i l a r d f o r m u l a i s a l i n e a r f a c t o r . The v a l u e s o f f w w i t h r = D1 0 a r e 4% d e c r e a s i n g , and s i m i l a r l y t h e same d e c r e a s e o f s e d i m e n t t r a n s p o r t w i l l r e s u l t e . S i n c e 5% d i s c r e p a n c y o f s e d i m e n t t r a n s p o r t can n o t be c o n s i d e r e d as a s i g n i f i c a n t d i f f e r e n c e , i n t h e p r e s e n t s t u d y r = D5 0 i s i m p l i e d .

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T a b l e 6 Wave f r i c t i o n f a c t o r T e s t # X f w(1 0"3) (m) r =D1 0 r=D 5 0 r= D9 0 2A 65 7.7 8.0 8 . 4 2A 100 7.4 7.7 8 .1 2A 115 7.4 7 . 7 8 .1 2A 125 7.3 7 . 6 8 . 0 2A 130 7 . 2 7 . 5 7 . 9 2A 138 7 . 1 7.4 7 . 7 2A 145 7 . 2 7.5 7 . 9 2A 152 7.5 7.8 8 . 2 2A 160 7 . 2 7.5 7 . 9 2A 170 7 . 3 7 . 6 7 . 9 3.4 E f f e c t o f h e i g h t o f v e l o c i t y measurements I n B a i l a r d ' s c r o s s - s h o r e s e d i m e n t t r a n s p o r t model, u ( t ) d e n o t e s i n s t a n t a n e o u s near b o t t o m f l u i d v e l o c i t y . I t i s n o t c l e a r l y p r e s c i b e d t h a t t h e v e l o c i t y measurement s h o u l d be c a r r i e d o u t a t w h i c h h e i g h t . Fig.32 and Fig.33 show how t h e c a l c u l a t e d s e d i m e n t t r a n s p o r t r a t e s change d e p e n d i n g on measured v e l o c i t y moments a t d i f f e r e n t h e i g h t s . I t can be seen t h a t a l t h o u g h t h e s e d i m e n t t r a n s p o r t r a t e s g e n e r a l l y d e c r e a s e w i t h t h e h e i g h t f r o m t h e bed, t h e r e s u l t s o f u s i n g 10 cm (above t h e bed) v e l o c i t y moments and t h e r e s u l t s o f u s i n g 2 0 cm v e l o c i t y moments have n o t shown much d i f f e r e n c e b u t r a t h e r u n i f o r m . F i g . 3 4 a l s o g i v e s t h e same i d e a t h a t s e d i m e n t t r a n s p o r t r a t e s d e r i v e d f r o m 10 cm v e l o c i t y

moments, S and t h e r a t e s f r o m 2 0 cm v e l o c i t y moments, Sc a l 2 0,

a r e a l m o s t t h e same. However, a l t h o u g h t h i s u n i f o r m i t y e x i s t s , y e t t h e q u e s t i o n o f t h e i m p a c t o f t h e boundary l a y e r on c r o s s -s h o r e -s e d i m e n t t r a n -s p o r t i -s open. 3.5 C o n t r i b u t i o n s o f d i f f e r e n t components i n B a i l a r d ' s f o r m u l a B a i l a r d ' s f o r m u l a o f c r o s s - s h o r e s e d i m e n t t r a n s p o r t r a t e s u g g e s t s t h a t t h e t o t a l r a t e c o n s i s t s o f t h e b e d l o a d t r a n s p o r t r a t e and t h e suspended l o a d t r a n s p o r t r a t e . The b e d l o a d t r a n s p o r t r a t e i s composed o f two components, one due t o t h e i n s t a n t a n e o u s v e l o c i t y

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and t h e o t h e r t o t h e beach s l o p e . S i m i l a r a s s u m p t i o n h o l d s t o t h e suspended t r a n s p o r t r a t e .

T a b l e 7 shows t h e c o n t r i b u t i o n s o f d i f f e r e n t components i n B a i l a r d ' s f o r m u l a . I t can be seen t h a t suspended l o a d sediment r a t e h o l d s 70-80% o f t o t a l t r a n s p o r t r a t e w h i l e b e d l o a d t r a n s p o r t r a t e t a k e s 2 0-3 0% o f t h e t o t a l t r a n s p o r t r a t e . The sediment t r a n s p o r t caused by t h e beach s l o p e a r e n e g l i g i b l e . T a b l e 7 P e r c e n t a g e o f t r a n s p o r t r a t e o f d i f f e r e n t components i n B a i l a r d model T e s t # X (m) Component R a t e / T o t a l R a t e ( % ) T e s t # X (m) Sb 2A 130 33 7 46 14 39 61 2A 138 20 2 74 4 21 79 2A 145 19 1 78 2 20 80 2A 152 22 2 73 4 24 76 2A 160 16 2 76 5 18 82 2A 170 18 3 74 5 20 80 2B 65 20 2 73 5 22 78 2B 100 28 3 63 6 31 69 2B 115 24 2 69 5 27 73 2B 130 21 2 71 6 23 77 2B 138 18 1 79 2 18 82 2B 145 19 1 78 1 20 80 2B 152 17 1 78 3 19 81 2B 160 16 2 77 5 18 82 2B 170 17 3 74 7 20 80

Note: S, p r e s e n t s |u|2 u component 52 p r e s e n t s | u ]3 component 53 p r e s e n t s j u ]3 u component 54 p r e s e n t s | u ]6 component

Sb = S, + S2 i s bed load sediment t r a n s p o r t r a t e Ss = S3 + S4 i s suspended load sediment t r a n s p o r t r a t e T o t a l sediment t r a n s p o r t r a t e = Sb + S8

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4. Remarks

As i n d i c a t e d a t t h e b e g i n n i n g , t h i s r e p o r t d e s c r i b e s j u s t a summary o f t h e p r e l i m i n a r y a n a l y s i s . A number o f q u e s t i o n s r e m a i n t o answer and more e l a b o r a t e r e s e a r c h e s a r e t o be c a r r i e d o u t , e.g. cause a n a l y s i s o f d i s c r e p a n c y between measured and computed s e d i m e n t t r a n s p o r t r a t e s , p r e d i c t i o n s by d i f f e r e n t models o f c r o s s - s h o r e s e d i m e n t t r a n s p o r t and e f f e c t s o f wave f r i c t i o n f a c t o r on p r e d i c t e d t r a n s p o r t r a t e s .

R e f e r e n c e s

Al-Salem, A.A.(1993) , Sediment t r a n s p o r t i n c s c i l l a t o r y boundary l a y e r s under s h e e t - f l o w c o n d i t i o n s , Ph.D. T h e s i s , D e l f t U n i v e r s i t y o f T e c h n o l o g y , 1993.

B a i l a r d , J.A. and D.L. I n m a n ( 1 9 8 1 a ) , An e n e r g e t i c s b e d l o a d model f o r a p l a n e s l o p i n g beach: l o c a l t r a n s p o r t , J . o f G e o p h y s i c a l Reach, v o l . 8 6 , No. C3, pp2035-2043, March 20,1981.

B a i l a r d , J . A . ( 1 9 8 1 b ) , An e n e r g e t i c s t o t a l l o a d s e d i m e n t t r a n s p o r t model f o r a p l a n e s l o p i n g beach, J . o f G e o p h y s i c a l Reach, v o l . 8 6 , No. C l l , ppl0938-10954, November 20,1981.

DELFT HYDRAULICS, L I P 11D D e l t a Flume E x p e r i m e n t s - d a t a r e p o r t , 1994 .

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f

1 0 3 0 5 0 7 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0

D i s t a n c e f r o m w a v e b o a r d x ( m )

Figure 1 Profile development of test 2A

1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9

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1 8 0 1 8 4 1 8 8 1 9 2 1 9 6 2 0 0

Figure 3 Upper end part of profile of test 2A

1 7 0 1 7 2 1 7 4 1 7 8 1 7 8 1 8 0 1 8 2 1 6 4 1 8 6 1 8 8 1 9 0

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E, 1 0 1 2 - h o u r p r o f i l e 6-hour p r o f i l e I i n i t i a l p r o f i l e 9 0 1 1 0 1 3 0 1 5 0 D i s t a n c e f r o m w a v e b o a r d x ( m ) 2 1 0

Figure 5 Profile development of test 2B

4 9 8 . 5

( T e s t 2 A )

T i m e ( h )

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( T e s t 2 B )

1 0 3 0 5 0 7 0 8 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0

D i s t a n c e f r o m w a v e b o a r d ( m )

Figure 7 Comparison of transport rates (transport rates between t = 0 and t=12h)

1 0 3 0 5 0 7 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0

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1 0

1 0 3 0 5 0 7 0 8 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0

Figure 9 Sediment transport rate along the flume of test 2B

cn S CO e CD b 4-> m M -p u O ft w c rö U +J +J C (U B -o 0) w 5 0 4 0 3 0 2 0 1 0 - 1 0 - 2 0 - 3 0 - 4 0 ( A t s e c t i o n x - 6 5 m ) v e l o c i t y m e a s u r e m e n t s a v a i l a b l e t r a n s p o r t f r o m t = l h t o t = 2 h 1 6 T i m e ( h ) 1 0 1 2

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eft g CO & ID a -p id U •p u o ft tft c nl U •P - P c I T3 cl) W 5 0 4 0 3 0 2 0 1 0 - 1 0 - 2 0 ( A t s e c t i o n x - 1 0 0 m ) 6 T i m e ( h ) 1 0 1 2

Figure 11 Transport rate of test 2A at section x = 100 m

Cfl S e b Q) • P cd U + J Vh O ft w C cfl U +J •P c CD £ <]j w 5 0 4 0 3 0 2 0 1 0 - 1 0 - 2 0 ( A t s e c t i o n x = 1 1 5 m ) 6 T i m e ( h ) 1 0 1 2

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w CO B CO b -p M +J u o ft to a rü M +J - P a d) e •H w 4 0 3 0 2 0 1 0 - 1 0 ( A t s e c t i o n x - 1 2 5 m ) v e l o c i t y m e a s u r e m e n t s a v a i l a b l e 1 6 T i m e ( h ) 1 0 1 2

T i m e ( h )

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( A t s e c t i o n x - 1 3 8 m )

0 2 4 6 8 1 0 1 2

T i m e ( h )

CO B CD b w 4-1 rd U +J u 0 ft m c rd U 4-> 4J C CD E •r4 T3 CD W 2 0 1 0 - 1 0 H - 2 0 - 3 0 ( A t s e c t i o n x = 1 4 5 m ) I 6 T i m e ( h ) 1 0 1 2

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2 0 1 5 1 0 1 " 5 oo - 1 0 - 1 5 - 2 0 ( A t s e c t i o n x - 1 5 2 m ) 2 4 T i m e ( h ) 1 0 1 2

OJ +J crj l-l 4-> M 0 ft 01 C rd U +J 4-) G Q) Ë •H T) m 2 0 1 5 1 0 - 1 0 - 1 5 - 2 0 ( A t s e c t i o n x = 1 6 0 m ) 4 T i m s ( h ) 1 0 1 2

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tl) e QJ -p id u +j u O ft ui c n) H -P - P C 0) e •rH T S OJ w 2 0 1 0 - 1 0 - 2 0 - 3 0 - 4 0 ( A t s e c t i o n x - 1 7 0 m ) 1 0 1 2 T i m e ( h )

Figure 19 Transport rate of tset 2A at section x = 170 m

0) -p id U -p u 0 ft in c SH -P G (1) a • H T i 0) w 1 0 8 6 4 2 O - 2 - 4 - 6 -e - 1 0 - 1 2 - 1 4 - 1 6 - 1 8 - 2 0 ( A t s e c t i o n x - 6 5 m ) t i 1 r 1 0 1 2 T i m e ( h )

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4 0 ( A t s e c t i o n x - 1 0 0 m ) 3 0 1 0 cn CO £ CO b c—i 2 0 CD 4-> cfl rH •P U O ft W a Cfl rH + J + J a CD i •rH T l CD W - 1 0 - 2 0 T i m e ( h )

Figure 21 Transport rate of test 2B at section x = 100 m

cn £~ e CO b CD 4-> cfl U -P O ft in c cfl u 4-1 4-) C CD £ •rH •a CD CO 4 0 3 0 2 0 - \ 1 0 - 1 0 - 2 0 ( A t s e c t i o n x - 1 1 5 m ) 1 0 1 2 T i m e ( h )

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1 0 0 - 1 0 J , - 2 0 CD -P id U 4J U 0 ft U) c cti n 4 J 4-1 a a) £ - H -a 0) CO - 9 0 - 1 0 0 - 3 0 - 4 0 - \ - 5 0 - 6 0 - 7 0 - 8 0 ( A t s e c t i o n x - 1 3 0 m ) 1 6 T i m e ( h ) 1 0 1 2

cn ~ £ CO £ CD b CD 4-> cti U 4J U O ft cn fi CÖ U 4-1 +J c CD £ •rH •o CD CO 1 0 O - 1 0 - 2 0 3 0 -- 4 0 - 5 0 - 1 0 0 - 6 0 - 7 0 - 8 0 - 9 0 - \ ( A t s e c t i o n x - 1 3 8 m ) 1 6 T i m e ( h ) 1 0 1 2

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in o 6 CD b 01 - p id u 4-1 c d) e •H T3 (1) W 1 0 - 1 0 - 2 0 - P O ft in C Id - 3 0 S-l 4-> - 4 0 - 5 0 ( A t s e c t i o n x - 1 4 5 m ) 1 0 1 2 T i m e ( h )

in CO e CD b 0) 4-> (I) rH 4-) U 0 ft w c id U 4J 4-> e OJ e •o 2 0 1 0 • 1 0 - 2 0 - 3 0 ( A t s e c t i o n x = 1 5 2 m ) 1 0 1 2 T i m e ( h )

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-p c O) a • H T3 CD CO 1 0 cn "s" s CD b 3 i o -cd 14 - P M O ft - 2 0 cn G cd U - P - 3 0 - 4 0 ( A t s e c t i o n x - 1 6 0 m ) I 6 T i m e ( h ) 1 0 1 2

cn e CD b CD -p cd U - P H O ft cn c cd J4 - P +J c CD B • H TJ CD CO 1 0 - 1 0 - 2 0 - 3 0 - 4 0 ( A t s e c t i o n x - 1 7 0 m ) 1 0 1 2 T i m e ( h )

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e co e b 01 fd n 2 0 1 0 ( T E S T 2 A ) - 1 0 4 J U O ft cn c fd - 2 0 n 4-> 4-1 C m e •H T ) 01 CO - 3 0 - 4 0 m e a s u r e d computed 1 0 3 0 5 0 I I I I I I I 1 1 1 1 1 7 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 D i s t a n c e from wave b o a r d (m)

Figure 29 Comparison between measured and computed transport rates of test 2A ( Remark: the computed transport rates refer to different time intervals)

in e CO e CD b CD 4-1 rd U 4-) U O ft cn c cd u 4-1 c CD s •r4 T> CD W 2 0 1 0 ( T E S T 2 B ) - 1 0 - 2 0 - 3 0 - 4 0 - 5 0 - 6 0 O n s h o r e s e d i m e n t t r a n s p o r t computed O f f s h o r e s e d i m e n t t r a n s p o r t 1 0 3 0 5 0 7 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0 D i s t a n c e from wave b o a r d (m)

Figure 30 Comparison between measured and computed transport rates of test 2B ( Remark: the computed transport rates refer to different time intervals)

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O H 0) 4-> rd U •P M O ft ui C id M +J •a ai •p 3 ft e o o 2 0 1 0 - 1 0 - 2 0 - 3 0 H - 4 0 - 5 0 - 6 0 o n s h o r e s e d i m e n t t r a n s p o r t • • • o f f s h o r e s e d i m e n t t r a n s p o r t _• • • • • • • - 6 0 - 4 0 - 2 0 0 M e a s u r e d t r a n s p o r t r a t e Sm e d l 2 (10-6m3/m/s) 2 0

Figure 31 Comparison between computed and measured transport rates (2A & 2B)

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Figure 33 Comparison between computed and measured transport rates (2A & 2B)

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Figure 35 Comparison between two measured transport rates (2A & 2B) ( T E S T 2 A ) to S

Ï

CO b 01 4-> ft! U + J U O ft w c rd U - P T3 (U +J 3 ft S O U 4 0 3 5 3 0 2 5 2 0 1 5 1 0 H e i g h t from bed (cm) x=160 m x=130 m x=152 m

Figure 36 Transport as function of 'determining' height of velocity measurements (Remark: two measurements were carried out at section x = 130 m)

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( T E S T 2B ) 80 -in - - . 70 -e CO s o 60 -O H Q) 50 --P rd M x=138 m x — _ _ _ _ _ _ _ _ _ Compute d transpor t III ! x=145 m v x=130 m * „— x= 65 m o ^ ____ x - 1 1 5 m o. — -:====== = = & x=100 m + h 0 -c T7C- _ ^ *w m 1 1 i 1 20 4o H e i g h t f r o m b e d (cm)

Figure 37 Transport as function of 'determining' height of velocity measurements

20 10 -10 w S to -20 O o -30 CN c/T -40 -50 -60 -60 -40 ( T e s t s 2A & 2B) • • ^6 • / n / • 20 "6 m3 , Sc a l l 0 ( 1 0-bm 7 m / s ) 20