NRCEST

Equilibrium beach

Chang Hsien Kuo

國立交通大學土木工程學系中華民國 102年 4月 11日

2

Definition of beach morphology

淺化帶 (shoaling zone); 碎波帶 (surf zone); 沖刷帶 (swash zone) ;灘線 (shore line); 海灘 (shore , beach); 海岸 (coast); 平台 (berm);內灘 (inshore); 外灘 (offshore); 沙洲 (bar); 灘面 (beach face); 灘崖 (beach scarp); 台梯 (step) ; 沙谷 (trough)

3

Type of beach profile

Definition:平衡海灘斷面 (equilibrium beach profile): 在同一波浪條件長期作用下，海灘斷面將呈現平衡之狀態。

Type of beach:Type A: 暴風海灘 (storm beach) 或冬季海灘 (winter beach) Type B: 中間型海灘 (transition beach)Type C: 正常海灘 (normal beach) 或夏季海灘 (summer beach)

Sunamura and Horikawa , 1974

4

Slope of beachface

Sunamura (1984)4/12 50

12.0tan

bbf H

d

H

gT

TdgHb

5.05.0 50/

tan

f

5

Classification of beach profile

Sunamura and Horikawa (1974)

67.0

0

27.0

0

0

67.0

0

27.0 50tan8

50tan4

L

d

L

H

L

d

Experiment: 4-8Field:9-18

6

Equilibrium beach: theory

Dean (1977)

hDECxt

Eeqg

hDghgH

dx

deq

/

212

8

1

hH hDdx

dhhg eq 2

5

8

1 2/322/3

3/2xh 32

2235

24/

/

eq

g

D

7

Brunn-Dean profile:Equilibrium beach:

Moore (1982) 64.05027.0 d

,

44.0 067.0 fWDean(1991)

Disadvantages:1. Infinity slope at shoreline2. Monotonic function: infinity depth

Kriebel et al. (1998)

8

Other forms of beach profile

Bodge (1992)

mxf em

h

1tan

5

05

4

04

3

03

2

02

01

0

L

xa

L

xa

L

xa

L

xa

L

xa

L

h

Hsu e al. (1998)

Simple form?Theoretical approach?Bar shape profile?

9

Advanced reference

mAxh

10

A and m coefficients of Bruun/Dean profile

11

A and m coefficients of Bruun/Dean profile

12

A and m coefficients of Bruun/Dean profile

Artcic beach

13

A and m coefficients of Bruun/Dean profile

14

Shape parameter

15

Shape parameter

16

Shape parameter

17

Best fitting for a1

a1=03285

18

Shape parameter

19

Extended equilibrium beach

Larson (1991)

20

Three-parameter equilibrium profile

21

Three-parameter equilibrium profile

22

Three-parameter equilibrium profile

23

Three-parameter equilibrium profile

24

Three-parameter equilibrium profile

Goodness of fit: overall errors

25

Validity of equilibrium beach

26

Validity of equilibrium beach

27

Reflective natural beaches

28

Surf profile

29

Shoaling profile

30

Comparison with field data

31

Parameter

32

Discussion

1. Does an equilibrium beach exist in real beach?2. What is the application of equilibrium to coast

engineering?3. Theoretical approach ?