OCE421 Marine Structure Designs Lecture

1
OCE421 Marine Structure DesignsLecture 5
(breaking wave and design breaker)

• Fall, 2003

2
Design Criteria

• A number of sometimes conflicting criteria
• Structural stability (survivability under extreme
  conditions)
• Functional performance (intended function and
  desired effect)
• Environmental impact (ecosystem etc.)
• Life-cycle cost (annual maintenance vs. first
  cost)
• Others

3
Design Wave Conditions

• Breaking Waves
• Non-breaking Waves
• Broken Waves

4
Breaking Wave critical design condition

• The largest breaking wave to which a coastal
  structure might be exposed often represents the
  critical design condition for that structure.

5
General wave breaking

• Two criteria
• In relative deep water, wave stability depends
  critically on the wave steepness
• In shallow water, wave stability becomes
  dependant upon the wave height to water depth
  ratio
• It is not as yet possible to adequately describe
  a breaking wave in mathematical form hence an
  essentially empirical approach is usually adopted.

6
Breaking Point
The breaking point is an intermediate point in
the breaking process between the first stages
of instability and the area of complete breaking
7
Early Breaking Wave Formulas
8
Breaker Height and Depth SPM Approach
9
Godas Empirical Curves
for m 1/10, 1/20, 1/30 and 1/50
breaker height index depends on beach slope
and incident wave steepness
10
SPM Figure 7-3 (also 2-72)
11
Weggels Empirical Formula
SPMs Figure 2-73
12
SPM Figure 2-73 (Weggel)
13
Breaker Plunge Distance
breaking point
14
Design Breaker Illustration
breaking point
15
SPM Design Breaker Estimate
water depth at structure toe, near shore slope
Given quantities
(specify T )
16
Factors to determine the maximum breaker height

• The depth of water in which the structure is
  sited
• The beach slope and bathymetry in front of the
  structure
• The variables which describe the incident waves
  in deep water.

17
SPM Figure 7-4
m
18
Design Breaker Matlab Development
for various nearshore slope m
(design breaker)
Matlab function development
19
MATLAB function dbreaker

• Develop a MATLAB function dbreaker (the
  calculation for must directly or indirectly
  apply Fig. 7-5 of SPM, i.e. it is not allowed to
  use the shoaling coefficient calculated based on
  the linear wave theory) with the heading

function Hb,Hop,db dbreaker(m,T,ds) Hb
design breaker height Hop unrefracted
deepwater wave height db breaking depth T
wave period ds water depth at structural
toe m beach slope
20
dbreaker matlab code
function Hb,Hop,db dbreaker(m,T,ds) g9.8 tau
p 4.0 - 9.25 m am 43.75(1-exp(-19m)) bm
1.56 / (1exp(-19.5m)) tol 0.001 diff
1 Hbi ds initial guess
on Hb while (diff gt tol) kappa bm - am Hbi
/(gT2) beta 1/ kappa Hb ds / (beta -
m taup) SPM's eq.7-5 diff abs (Hb/Hbi
-1) Hbi (HbHbi)/2 end db beta Hb
determine Ho based on Goda's data Hop
fig7_5(Hb,T,m) SPM Fig. 7-5 Ks
shoal(db,T) Hop Hb / Ks (if using linear
wave theory)
21
SPM Figure 7-5 (vs. 7-3)
SPMs Figure 7-5
SPMs Figure 2-72 (Figure 7-3)
for m 1/10, 1/20, 1/30 and 1/50
22
SPM Figure 7-5
23
Matlab code Fig.7-5 (I)
function Hop fig7_5(Hb,T,m) -----------------
---------------------------------------
function Hop fig7_5(Hb,T,m) This function
interpolates from the data of SPM Figure 7-5
to find unrefracted deepwater wave height from
breaker height. Hop unrefracted deepwater
wave height Hb breaker height T wave
period m beach slope
24
Matlab code Fig.7-5 (II)
g 9.81 gravity m/s2 Initial
data entry for bottom slope, steepness, and
breaker index if (mlt0.02) disp('WARNING beach
slope is less than 0.02, SET m0.02') m
0.02 end if (mgt0.1) disp('WARNING beach
slope is greater than 0.1, SET m0.1') m
0.1 end
25
Matlab code Fig.7-5 (III)
data from Fig 7-5 M 0.1 .05 .033
.02 ST log10(.0007 .0008 .0009 .001 .0015
.002 .0025 .003 .004 .005 .006 .007 ...
.008 .01 .012 .015 .02) BI
2.85 2.8 2.7 2.6 2.2 1.96 1.8 1.68
1.52 1.43 1.35 1.28 ... 1.23
1.16 1.1 1.08 1.04 2.7 2.6 2.5
2.4 2.02 1.8 1.67 1.56 1.43 1.32 1.25 1.2
... 1.16 1.08 1.04 1 1
2.55 2.4 2.3 2.2 1.87 1.67 1.53 1.44
1.31 1.23 1.16 1.12 ... 1.08
1.04 1.01 0.99 0.98 2.24 2.14
2.04 1.96 1.68 1.51 1.4 1.32 1.2 1.12 1.08
1.04 ... 1.03 1. 0.97 0.96
0.96
26
Matlab code Fig.7-5 (IV)
xHb/(gT2) steepness for
this case to enter x-axis if (xlt0.0003)
disp('WARNING Hb/(gT2) is less than .0007, SET
it .0007') x 0.0003 end if (xgt0.02)
disp('WARNING Hb/(gT2) is greater than .02,
SET it .02') x 0.02 end yinterp2(ST,M,BI,l
og10(x),m) breaker index from interpolating
table HopHb/y resulting
unrefracted deepwater wave height
27
Incipient breaking vs. design breaker
parameters to be determined
given parameters
Incipient breaking
Design breaker
(check dose it exist in deep water location?)
28
Numerical Example
T110 wave period m 0.05
beach slope ds 2.5 water depth at
structure toe Kr 0.85 refraction
coefficient Hb1,Hop1,db1
dbreaker(m,T1,ds) Ho1 Hop1 / Kr
(all in meters)
29
(linear wave)