CADOB, Computer Aided Breakwater Design

Ministry of Public Works and Water Management

Civil Engmeering Division, Hydraulic Engineering Branch

C O M P U T E R A I D E D D E S I G N I N G O F B R E A K W A T E R S

CONTENTS

1.0 SUMMARY 1 2 . 0 INTRODUCTION 2 3 . 0 CADOB, THE PROGRAM 3

3 . 1 Introduction

3 . 2 Program restriction 3

3.3 The input 4 3 . 4 The output 4

3.5 Determination of Crest elevation and D„5OA 6

3 . 6 Determination Secondary Armour layer and Core 7

3 . 7 Design Armour Lee-side of Breakwater 8 3.8 Rules of thumb and Choice for the toe construction 1 0

3 . 9 Design Toe construction 1 1

3 . 1 0 The designs 1 2 3 . 1 1 Requirements per running meter breakwater 1 2

3 . 1 1 Printing calculated values • 1 3

3 . 1 2 Repeat 1 3 4 . 0 METHODOLOGY 1 4

4 . 1 Introduction 1 4 4 . 2 Crest elevation and Primary armour layer 1 4

4 . 3 The secondary armour layer and the core 1 6

4 . 4 The lee-side of the breakwater 1 7 4 . 5 Determination toe construction 1 8

4 . 6 The designs 1 9 4 . 7 Breakwater requirements and the Rosin-Rammler 2 0

5 . 0 E X A M P L E 2 3 5 . 1 Design Criteria 2 3

5 . 2 The computation 2 4 5.3 Conclusion 2 6 6 . 0 RECOMMENDATIONS 2 8

APPENDIX A Results Example Computations APPENDIX B List of Symbols

APPENDIX C Definition Sketch APPENDIX D References

SUMMARY

The following is the manual for CADOB (Computer Aided Designing Of Breakwaters). CADOB is a program designed by the Ministry of Public Works and Water Management, Civil Engineering Division, Hydraulic Engineering Branch in Utrecht. The program is based on a manual for the use of rock in coastal and shoreline engineering, prepared by the CIRIA (Construction Industry Research and Information Associates, UK) and the CUR (Centre for Civil Engineering Research, Codes and Specifications, The Netherlands).

CADOB designs four different cross sections for a conventional breakwater, by making use of the formulas and considerations presented in the above mentioned manual.

After determining all the required dimensions CADOB schematizes a chosen design.

The volumes of required stone are then determined and subsequently compared to a cumulative distribution cure for the quarry product (Rosin-Rambler: Waybill distribution curve).

The objective of the program is to let the user adapt the design (by altering construction criteria) in order to gain an optimum use of the quarry product.

This manual is provided with an example computation described in section 4 .

The program is still in it's development stage. The user is kindly requested to contact the Ministry of Public Works and Water Management for comments.

2.0 INTRODUCTION

In February 1990 the CiRIA (Construction Industry Research and Information Associates, U K ) and the CUR (Centre for Civil Engineering Research, Codes and Specifications, The Netherlands) prepared a manual on the use of rock in coastal and shoreline engineering [ref 1]. The manual provides with a scala of design formulas and considerations.

CADOB (Computer Aided Designing Of Breakwaters) is a program developed by the Ministry of Public Works and Water Management, Civil Engineering

Division, Hydraulic Engineering Branch, Utrecht The Netherlands. (Rijkswaterstaat Bouwdienst, Utrecht).

The objective of CADOB is to give designers of rubble mound breakwaters a first impression of the proportions of required construction material. CADOB is based on the formulas provided by the CIRIA/CUR manual.

CADOB generates a schematisation of chosen brealcwater cross sections, after which it calculates the required tonnage per running meter breakwater for the different gradings in rubble mound. These amounts are subsequently compared to the cumulative distribution curve for the quarry production. In this way the designer may consider to alternate construction criteria in order to achieve a better fitting curve of required rubble mound versus available rubble mound.

CADOB is in a way an optimisation program. It is possible to repeat CADOB a number of times until a satisfactory result (to the user) is generated by altering construction criteria. The designer must bear in mind that CADOB does not discern inappropriate designs, although in some stages of the computations it notifies the user i f values or construction types are unacceptable. The final design is thus a result of the designers own interpretation of the calculated values. The program is not designed as an expert system. Each breakwater is an unique structure, subject to it's own characteristic design conditions at the project site. It is therefore of utmost importance that the user interprets the resulting values with caution.

3.0 CADOB, T H E PROGRAM

3.1 Introduction

CADOB is written in TURBO PASCAL version 5 . 5 . It uses the graphic units provided by Borland International Inc.

Figure 3.1 shows the program structure diagram. In this section the diagram will be discussed.

3.2 Program restrictions

Concerning Hardware/Software

- The program may result in run-time errors i f the computer on which CADOB is run is not supported by a graphics adaptor.

- Plots may show imperfections i f the resolution of the used graphics card is less than 640x480 pixels.

- During the input make sure that <Caps L o c k > is switched off.

- I f a printout of the values is required make sure the printer is turned on and is 'on line'.

- Printing of the design plots and cumulative curve are standardized to the dimensions of A4-paper (21cm.x29.7cm.). Printers equiped with a sheetfeeder should not be a problem,

- When printing the calculated results, set the printer to a small font (smaller than lOcpi) to get all results on one single page.

Concerning design and input values

- CADOB can only design cross sections of rubble mound breakwaters with conventional filter layers (coarse gravel). It is possible to insinuate a fascine mattress (geotextile) as filter construction as described in section 3.8 and 4 . 5 .

- CADOB designs alternative breakwaters on a horizontal sea bed (bottom) and consequently also calculates the required volumes with a horizontal bottom. - The program does not perceive i f the design parameters used are indeed

pai-ameters that can occur at the site (e.g.: the significant wave height is not checked on depth limitation etc.).

- CADOB gives the best performance i f realistic design conditions are used. I f not, results should be interpreted with care.

- Submerged breakwaters with a crest height lower than the calculated toe height can not be plotted in CADOB. It is therefore advised not to use

CADOB i f the breakwater is to be constructed with a crest height lower than 5 meter above the bottom. It is not possible to design the crest below mean sea level as the used formulas (Van der Meer) are not valid in such case.

- When designing the lee-side of the breakwater dissimilar to the sea-side, the design wave height at the lee-side should be less than the design wave height at the sea-side. Else, the resulting plot will just as the computation be

illogical.

3.3 Tlie input

CADOB is equipped with standard default values as design parameters. I f the default value suits a design parameter press < enter > to continue.

I f the value has to be changed, type the new value at the cursor position and press < enter > .

I f the input is provided with a help option, this will be indicated under the active window. Press < F 1 > for 'help' or < enter > to continue. The input can only be executed i f the cursor reappears at the input parameter.

It is not possible to move the cursor back to a previous input. If, an error is made during the input of the parameters continue the rest of the input in the active window, and use the option repeat (press < R > ) which occurs after all values are entered.

3.4 The output

The output occurs immediately after the first value is entered in the calculation. The computation is executed with the still remaining default values, and changes with the input of the remaining values.

It is possible to print all plots (designs and cumulative distribution curve) on either an Epson compatible matrix printer or an Hewlett Packard compatible laser printer.

H y d r a u l i c C r i t e r i a : W a t e r l e v e l s , H s , T , N I C o n s t r u c t i o n C r i t e r i a ; P . S , C r e s t e l e v a t i o n , p , s l o p e , l a y e r t h i c k n e s s . T r a n s m i t t e d W a v e h e i g h t T o p l a y e r o f s l o p e R e p e a t -> H y d r a u l i c C r i t . Norm. W e a t h e r Cond. T r a n s m i t t e d Waveh. T C o n s t r u c t . C r i t . P , S , S l o p e S e c o n d a r y L a y e r C o r e m a t e r i a l R e p e a t -> D e s i g n B o t h s i d e s i d e n t i c a l ? Dn50AL=Dn5OA DnSOAL f o r Ht DnSOAL Norm.W.Cond. DnSOAL d e s i g n wave l e e R e p e a t -> C h o o s e T o e - t y p e S t a n d a r d t o e B o t h s i d e D r e d g e d T o e b o t h s i d e s r S e a - s i d e s t a n d a r d t o e L e e - s i d e L i g h t e r d e s i g n 1 S e a - s i d e d r e d g e d t o e L e e - s i d e l i g h t e r d e s i g n R e p e a t D e s i g n t o e c o n s t r u c t i o n Dn50TA,Dn50TS D e s i g n f i l t e r l a y e r s t o e F i l t e r / H y d r a u l i c C r i t e r i a R e p e a t - > D e s i g n B r e a k w a t e r C r o s s - s e c t i o n D e t e r m i n a t i o n o f r e q u i r e d v o l u m e s D e t e r m i n a t i o n o f R o s i n - R a m m l e r . c u m u l a t i v e d i s t r i b u t i o n c u r v e f o r t h e q u a r r y - p r o d u c t i o n . D e t e r m i n a t i o n o f a v a i l a b l e g r a d i n g s i n q u a r r y - p r o d u c t i o n . P l o t R o s i n - R a m m l e r C u r v e P l o t B a r s a v a i l a b l e a n d r e q u i r e d P r i n t i n g o f r e s u l t s END

Figure 3.1 Program Structure Diagram.

3.5 Determination of Crest elevation and D

The required design criteria are divided into two parts, the Hydraulic Criteria and the Construction Criteria.

Tlie required Hydraulic criteria are:

- The water levels:

Mean Sea Level (MSL). The bottom is the zero elevation.

High High Water Level (HHL) including the setup and tide. MSL is the zero elevation.

Low Water Level (LWL). The input is a positive value although MSL is the zero eleyation. L W L is the lowest water level possible during design

conditions.

- The significant wave height H^ is the design wave height at the project site. Assumed is that the wave height has already experienced shoaling, refraction and energy dissipation due to the current and the bottom friction.

- The significant wave period T^ is the wave period corresponding to the significant wave height.

- The number of waves during one storm period (N). This value is restricted to a value higher than 1000 waves and less than 7000 waves. CADOB uses the formula generated by Van Der Meer [ref. 2 ] , in which a value N < 1000 and N > 7 0 0 0 give unrealistic results for the dimensions of the armour layer [ref.3].

Tlie required Construction criteria are:

- The proposed breakwater crest elevation. This is the height of the breakwater above the bottom (Bottom is zero elevation).

- The permeability (P) of the armour layer. Advised is to use a value in the vicinity of 0.4 as CADOB generates design alternatives with an average P-value of 0.4 (see figure 3.2).

- The slope angle as function of cotan(Q!) (l:cotan(Q:)).

- The number of armour units per layer thickness (mj). The layer thickness is determined Kj^'mj^DnSOA. For rubble mound the value of K j is assumed 1. - The mass density of the armour units ( p j in kg/m^

- The mass density of water ( p j in kg/m^.

With the above given design parameters the nominal diameter D„5OA for the primary armour at the sea-side is determined with the formulas introduced by Van Der Meer [ref 2]. Secondly a check is made on wave overtopping and the

possibility of reduction of the D^QA in case of overtopping. The methodology is discussed in section 3.

This section of the program can be repeated until either the D^OA is in the range of an available BOSOA or ^ designer's own criterion for overtopping is reached by altering the construction criteria. This can be interpreted as a form of

optimisation.

Dj,5QiV " n o m i n a l d i a m e t e r o f armour a t o n e D„5oF » n o m i n a l d i a m e t e r o f f i l t e r m a t e r i a l

DJJ5OC " n o m i n a l d i a m e t e r o f c o r e

Figure 3.2 Permeability coefficient assumptions for various structures [ref 2]

Determination Secondary A r m o u r layer and Core

The secondary armour layer should be designed in such a way that it remains stable during construction and that during severe weather conditions the loss of material through the primary armour is negligible. The first criterion is a stability criterion with respect to the hydraulic design parameters and the second criterion is considered a construction criterion ('Filter criterion').

The hydraulic criteria are:

- The significant wave height for normal weather conditions (Hs„J. This does not necessaiily have to be the wave height for normal conditions. Any wave height, which ever is decisive during construction can be used.

- The corresponding wave period T^, for the given

B.,ao-- And the number of waves the breakwater experiences characterised by these design parameters. The value of N should still be between 1000 and 7000. During normal weather conditions the number of waves is much larger than 7000 (long period of normal weather, compared to a storm period). It is advised to use a value of 5000, which is an average value to be used in the method developed by Van der Meer [ref.3].

Tlie construction criteria are:

- The Permeability, which can diverge from the permeability of the primary armour.

- The slope which during construction can differ from the final slope.

- The mass densities p,, which may be different i f not one single quarry is used. - The ratio DnjoA/Dnjos which is the ratio between the nominal diameters in the

primary layer and the secondary layer (recommended: use value 2 to 3). - The ratio Dn5os/D„5oc which is the ratio between the nominal diameter in the

secondary armor and the core material. CADOB calculates with no filter construction between the core and the secondary armour. As a filter rule the ratio in the order of 4 to 6 is recommended,

- The number of armour units per layer thickness (mj). The layer thickness is determined K(,'''mi*Dn50S. For rubble mound the value of K j is assumed 1.

CADOB now determines the required D„5os based on the hydraulic criteria and the filter criterion. There is also an option to use a D„5os which is available but not calculated by CADOB. I f the available T>„^QS is larger than the required D^QS

this diameter can be entered into the program and will be used in further computations. I f not, the largest calculated D„5os will be used ih further computations (see also section 4.5).

Design A r m o u r Lee-side of Breakwater

CADOB has the option to either design both sides of the breakwater as identical, or to design the brealcwater lee-side separately. It may occur that the breakwater is positioned perpendicular to a coastline, or in such a position that both sides of the breakwater experience the same design conditions (figure 3.3.1). I f the latter

occurs CADOB automatically determines the D^JOAL (Nominal diameter of the primary armour (A) at the lee-side (L)) and the D^QSL identical to respectively the Dn50A and the D^QS at the sea-side. I f not, the D^QAL is determined based on the transmitted wave height ( H J , the significant wave height for normal weather conditions E.,„^ and the design wave height at the lee-side (HsJ (and the construction criteria for the lee-side).

The design wave height at the lee-side is introduced in case decisive hydraulic design parameters, higher than (H„^„T„„J,(H„Ts) may occur.

The largest required diameter is decisive and w i l l be used in further

computations. The procedure in the determination of the layer thickness etc. are identically to the procedures used at the sea-side.

The secondary armour at the sea-side is extended from the crest to the filter layer at the lee-side. From the level lower than the depth of the primary armour, the secondary armour becomes the primary armour of the lee-side. (The primary armour at the lee-side extends to a depth of l*Ht or 1*11^^^ or 1*H3L below the low water level (LWL), which ever is decisive). From here on down a lighter stone is allowed. An extension of the secondary armour is chosen as the alternative (figure 3.3.2).

DnSOA -:-T,,IN, DnSOAL

£ig. 3.3.1 I Bi:eaktrate£ ld«nt:lcal on botli aittea

Dn50A

DnSOS

DnSOTF

£!Lg. 3.3.2 i Bzeskirater not Ideutlcal on both sides

Figure 3.3 Design of cross-sections

Rules of thumb and Choice for the toe construction

In this stage of the program the crest width is determined as Kj^mj^D^oA- ^3 Is the number of primary ai'mour units placed horizontally on the crest. This value should be at least larger than 2.

The depth to which the primary armour must extend is l.S^H, below the low water level. The value given is the height above the bottom (bottom is zero elevation).

Next the choice for the toe-construction type is required. Two types of toe constructions are possible.

- A standard toe construction. This is a toe construction build above the bottom. Consisting (from the bottom up) of a coarse gravel filter construction, a secondary toe layer and a primary toe-layer (see figure 3.4.1). This type of toe construction is only allowed i f the water depth (from bottom to MSL) is higher than 8 meters. I f the depth is less than 8 meters the top layer of the 'standard' toe can be subject to the same design conditions as the slope requiring a heavy toe construction.

- A toe-construction in a dredged trench. This type of toe construction is more expensive than the standard toe construction. A dredged trench is required i f the depth is less than 8 meters (see figure 3.4.2).

The choice is made to use only these two types of toe constructions for the

uniformity of the program. The designer may consider to still construct the toe as a standard toe, i f the depth is less than 8 meter, but not with C A D O B . C A D O B

can not and does not allow the design of a standard toe i f the depth is less than 8 meters. The required D^QTA should then be much larger and the layout of the toe will diverge from standard toe designs. I t was not the objective to create a program that can account for such a variety of toe types.

DnBOTA

DnSOTA

F i g u r e 3.4.2 : D r e d g e d t o e d e s i g n

Figure 3.4 Toe construction types

3.9 Design Toe construction

In this computation CADOB determines the nominal diameter for the toe layers. The toe is build up of a top layer (primary armour toe) a secondary layer and a gravel filter construction (no geotextile). The methodology is described in section 4.5.

3.9 The designs

After the determination of the dimensions of the breaiwater, the chosen type of brealcwater cross section is schematised.

The program rounds o f f real values during the schematisation. Layer thicknesses may appear to be identical. The real values are shown in the plot.

After designing the breakwater cross section on screen, the plot can be send to a laser printer (HP-compatible) or a matrix printer (Epson-compatible). Make sure the printer is turned on and is on line.

3.10 Requirements per running meter breakwater CADOB determines the volumes per layer.

Next CADOB determines the required tonnage of rubble mound per layer by multiplying the volumes with the mass density used for the rubble mound.

CADOB then distinguishes the different required gradings of rubble mound as shown in table 3.1. according to the class limits (range) produced by the Dutch standard NEN5180 (W5o,„^ and Wscnax).

With the estimated required tonnage CADOB computes the total tonnage per running meter breakwater and determines the percentage of each required grading per total tonnage (also per running meter).

The distribution of the armour size gained by blasting is most conveniently described by the Rosin-Rammler equation (section 4.7). The Rosin-Rammler equation is a cumulative WeibuU distribution for the nominal weight of the quarry stone (Wjo) set out on a logarithmic x-axis (weights) and a linear y-axis (percentage of non-exceedence as shown in figure 4.2. The range of the available grading classes are determined by the Lower Class Limit (LCL) and the Upper Class Limit (UCL) as shown in table 2.1 (Dutch standard NEN5180). By using the ranges Wsomü, and the y^so^mx ^ determine the required class and the L C L respectively the U C L for the available class, the designer is assured that the calculated required armour unit (W50) is located within the range of the class for the quarry product.

The boundaiies of the gradings are represented by the vertical dashed lines. The boundaries are divided in two, to display two bars per grading class.

The red (dotted) bars in figure 3.2 represent the available percentile of each ^ stone class. The required percentile is represented by the blue (hatched) bars.

Gradings Wjcnin kg Wjon,,;, kg L C L kg UCL kg 1/10 kg. 1,0 10,0 1 10 10/60 kg. 10,0 45,0 10 60 60/300 kg. 45,0 220,0 60 300 300/1000 kg. 220,0 760,0 300 1000 1/3 ton 760,0 2200,0 1000 3000 3/6 ton 2200,0 5050,0 3000 6000 6/10 ton 5050,0 8900,0 6000 10000

> 10 ton 8900,0 higher 10000 higher

Table 3.1: Rubble mound gradings for required W50 and class limits for quarry product.

In most cases the required percentage of large armour units is higher than the percentage of availability. In this case the designer may consider to alter the slope (more gradual) or the crest height (lower) in order to reduce the required D„5o's.

The user can also print this plot on a laser or matrix printer.

3.11 Printing calculated values

It is possible to print the results. Make sure the printer is turned on and is on line before inserting < y > for 'yes' at the prompt.

3.12 Repeat

The program can be repeated until a more fitting distribution is achieved between the required percentage and the available percentage of armour units.

The used design parameters are now the default parameters. The user can run through the program by just pressing < enter > i f the values passed should remain the same and adjust the required design parameters i f necessary.

4.0 M E T H O D O L O G Y

4.1 Introduction

This section describes the formulas used in CADOB, The formulas used are not always the same as presented in the CIRIA/CUR manual [ r e f . l ] . In some cases it was more practical to use the following formulas instead. The design procedure is however consistent with the manual.

4.2 Crest elevation and Primary armour layer

The primary armour layer is designed based on the formulas generated by van der Meer for hydraulic stability of armour units on a slope [ref. 2].

for plunging waves i^<^J:

4.1 for surging waves {^>^J:

In which:

H , = Significant design wave height A = (Ps-Pw)/Pw relative mass density Dnso = Nominal diameter (Wjo/ps)"-'

W50 = 50% value of the mass distribution curve ^2 = surf similarity parameter

P = permeability coefficient S = damage level (A/AD^„5o)

N = number of waves (storm duration) a = slope angle

The surf similarity parameter is determined by:

^^=tana/y/27r/fygr/

CADOB

The stability of the armour units on a slope increases for overtopping breakwaters. The extent of overtopping is approximated by the run-up. The run-up is given by [ref. 4]:

where: s^=HJig/2u)T; In which:

R = run-up parameter

Sp = fictitious wave steepness with Tp Tp = wave peek period (T/0,9)

F = Freeboard (Crest height above MSL)

fo is the reduction factor for D^^Q^, -^n50A(overtoppe<i/-l-^n50A(non-ovcrlopped)

The value for f,, is given by [ref 4]:

1/(0.25-4.8 *i?) for 0<i2<0.052

for /?^0.052

4.3

4.4

4.5

The wave transmission factor Ki is approached as follows [ref.4]:

K=HJH^=0.478*(1.16-F/R;) 4.6

Where:

Hi = Transmitted wave height R, = Significant run-up

Rj is approximated by [ref 4]:

i?^=0.72*^^ for 1^^1.5

R=QM*'i^-^^ for 1.5^^^<2.Z R^=135 for 1>2.Z

A.l

With the repeat option < r > , the user can thus reiterate the computation until either a D^OA is reached that is sufficiently available in the quarry product, or the criterion on wave transmission is reached.

The secondary armour layer and the core

The secondary armour layer is determined by the hydraulic criteria and the filter criteria.

The secondary armour layer is initially determined with formula 4,1 in which the wave conditions for normal weather conditions can be used or any other value decisive during construction of this layer. The reduction in case of overtopping is not used in this computation. The crest height modifies during construction, A real (constant) value for 'K^ and 4 can therefore not be calculated. The reduction (if allowed) during construction is therefore assumed a 'safety factor'.

The nominal diameter for the secondary armour layer is also calculated

dependent on the ratio D„5OA/D„5OS. This ratio determines porosity and the stability of the structure. I f the ratio is high, loss of secondary armour through the

primary armour is possible. The user may therefore set his/her own criterion for the ratio.

The final Dnjos is the largest required D„5os resulting from the hydraulic criterion or the construction (filter) criterion.

It is further possible to insert an available D^sos irito the computation. This value however, must be larger than the previous determined D„5os,

The inserted value for D„5os can either be a value known beforehand by the user or the user can use a Dnsos which is hardly used in the design during a previous run with CADOB concluded from Distribution curve (see section 3,10 and section 4.7) and thus gain a more optimum use of the total quarry product.

The nominal diameter for the core material is determined solely by the ratio

I^n50s/Dn50C-This computation can also be repeated until an acceptable result is obtained (based on the users own interpretation).

The lee-side of the breakwater

I f the breakwater can experience the same design conditions at the lee-side as at the sea-side, C A D O B has the option to dimension the lee-side identical to the sea-side.

I f not, the lee side is determined with the same formulas as in section 4 . 1 . The nominal diameter DnjoAL for the primary armour at the lee-side is calculated by using the transmitted wave height (HJ, or the significant wave height for normal weather conditions (H,nJ, or the design wave height for the lee-side H^L- The largest resulting DnjoAL is used in further computations. It may occur that a small wave height results in a larger D^^OAL- This is the result of a larger wave period. The wave period used together with H j is T3 (design wave period), for H,„e a wave period T^^ (wave period for normal weather conditions) is used and for H , L the design wave period is T , L . Which indicates the influence of the wave period in the formulas presented in section 4 . 1 .

The reduction in case of overtopping is also included in these computations.

C A D O B only schemadses the primary armour at the lee-side i f the D^QAL >

(DnSOS=Dn5osL)- Thc tcxt lu the plot indicates i f the W50AL is smaller than W50S. In some cases i f D„5OAL is just a little larger than D„5OSL the designer may consider to exclude the primary armour at the lea-side.

I f a large D„5os is inserted in the computation, this may result in a larger armour unit than the required primary armour layer at the lee-side. In such case the primary armour at the lee-side is not schemadsed.

When determining the required volumes and WJQAL < W50S, the volume of

required W50AL is added to volume of the exteded secondary armour layer. In this

way C A D O B designs the primary armour lee-side identical to the secondary

armour.

In the print out of the calculated values the value W50AL and D„5OAL are given as calculated but in the mean time C A D O B has already set the unit identical to the

secondary armour for the determination of the required volumes.

Determination toe construction

For tlie thickness of the primary armor layer of the toe-construction (top-layer) the number of armour units (m4) is required.

The weight (WJQTA) (W=weight, T=toe, A=primary armour unit) is determined as WsOTA^WsoA, i f the height to which the primary armour on the slope should extend is less than the thickness of the primary armour plus 2m., with the bottom as zero elevation. I f the opposite occurs, W5OTA=0-5*W5OA. From the W S ^ A the DnSOTA can be calculated.

The secondary toe layer is determined based on either the hydraulic criteria or the filter criteria. Filter criterion signifies no transport of Dn^^s through the top layer D^QTA- The criterion is determined by the ratio of DJOTA over D^ors- I f the ratio lays between a factor 4 and 6 the layer may be regarded as geometrically closed. A factor 6 to 10 yields in a hydraulically closed layer. In this case only the flow velocity is important. C A D O B does not check the stability against occurring flow velocities in the structure.

The layer thickness follows from the factor

m6'^Kd*Dn50Ts-The bottom soil conditions determine the filter construction. C A D O B designs a number of filter layers, each described by D„50TF(i). based on the used hydraulic or filter criterion which ever is preferred. The number of layers is dependent of the ratio D„50Ts/D„5OTF(top) and the ratio D„5OTFI/D„5OB in which D^QB is the nominal diameter for the bottom soil grain size. Each layer is determined with the same ratio D„50TF(i)/Dn50TF(i.i)- In which i is the layer and i-1 is the previous layer (from the bottom up).

I f D„50TF(i) is larger than 0,1m. the layer thickness is determined as 2*D„5OTF(Ö- I f the filter grain size is less than 0,1m. the layer thickness is set to 0,3 meters. The value of 0,3m. is chosen because of the dispersion of the filter material during placing. A larger volume of material is required during construction to achieve an adequate layer thickness. The value of 0.3 should account for this.

For very small bottom grain sizes, a thick filter will be designed. In this case facsine matresses (geotextiles) are recommended. C A D O B does not account for geotextiles. I f the user wants to exclude the filter layers from the total amount of material required, the user can increase the bottom soil nominal diameter to a size of for instance gravel in which case C A D O B designs less layers to satisfy ' both ratios.

The designs

By now all the measurements for the breakwater cross section ajre determined. CADOB generates plots for the different types of breakwater cross sections: - A breakwater with a dredged toe construction on both sides.

- A breakwater with a standard toe construction on both sides.

- A breakwater with a dredged toe construction at the sea-side and a lighter construction at the lee-side.

- A breakwater with a standard toe construction at the sea-side and a lighter construction at the lee-side.

The design of the toe construction is a follows:

- I f the depth to which the primary armour must a least extent at the sea-side (depth primary armour=LWL-1.5 *Hs) is higher (bottom is zero elevation) than - in case of a standard design - the toe height plus 4 meter, the toe layers are extended to this primary armour depth (height) as shown in figure 4.1. I f not the slope is designed as in figure 3.4

- I f the height to which the primary armour should extend is more than 4 meter (from the bottom up) - in case of a dredged trench - the toe layers are

extended to this height.

For large depths and relatively low waves this will result in a transition area on the slope at the sea-side. This area on the slope is vulnerable to damage. In such case a berm-structure should be considered at this height (which automatically is LWL-l.S^^H^).

CADOB does not account for the construction of a berm in the breakwater. This is done for various reasons:

Rubble mound breakwaters are mostiy not constructed at large depths because of the cost factor. The costs increase with the square of the depth. In which case a monolithic breakwater is preferred.

A berm would be necessary at large depths with low waves. CADOB mainly designs breakwaters based on in meanwhile depth limited significant (design¬ )wave heights (relatively shallow water). In such case the bottom w i l l mostly not be located at a depth deeper than LWL-1.5*H3-4 meters.

L W L 1 . 5 x H s D n S O A D n 6 0 S D n S O T A D n S O T S L W L 1 . S x H s D n S O A D n S O S D n S O T A D n S O T S

Figure 4.1 Toe construction for sufficient deptli

Breakwater requirements and the Rosin-Rammler distribution

As now the design has been made, the required volumes and tonnage of stone can be determined. CADOB calculates these volumes and weights per layer per running meter breakwater length. Subsequently CADOB classifies the required weights to required tonnage of standard gradings as shown in table 3 . 1 .

CADOB uses as starting point that the armour stone (units) are acquired from a quarry by blasting.

Prediction of blasted results is subject to continual research study but accuracy in detail is limited because the geological conditions can not easily be mapped for every blast and there are limitations arising from the difference between the blast plan design and its practical implementation.

A most convenient theoretical equation for the distribution for stone gradations and fragmentation curves is the log-linear Rosin-Rammler distribution curve [ r e f l ] :

- ( • _4.8

R=l-e

- Wy = the weight for which the fraction R is lighter on the distribution curve.

- W63.2 is a location factor for the Weibull distribution at the 63.2 percentile.

- n, is the index of uniformity for the Rosin-Rammler distribution. An example is given in figure 4.2

The value of can be estimated by the modified algorithm (Cunningham 1987

where:

B = Burden d = hole diameter S = Spacing (m)

BCL = bottom charge length CCL = column charge length

W = standard deviation of drilling accuracy H = bench height

The determination of n^ requires a number of parameters. This has been avoided in CADOB. Most quarry exploiters provide with the value for n,.

From the distribution curve CADOB generates 2 bars per grading (as in table 3.1). The boundaries of the gradings are represented by the vertical dashed lines. The boundaries are divided in two, to display the two bars per grading class. The red (dotted) bars represent the available percentile of each stone class. The

required percentile is represented by the blue (hatched) bars. [ r e f l ] ) :

«,=(2-2

4.9

Figure 4.2: Rosin-Rammler distribution curve, Bars for availability and required stone.

Some of the quarry product may appear not to be required in the breakwater. I f large enough and sufficienüy available, such stone can be inserted in the

secondary armour layer in a re-run of the program.

I f to little primary armour is available the user can consider to lower the crest height (overtopping is reduction, but not lower than MSL) or the construct a more gradual slope.

5.0 E X A M P L E

5.1 Design Criteria

For illustrative purposes the following design is generated. The results are shown in appendix A . - Hydraulic criteria: H , = 4,50 m. T, = 8,00 s. Depth = 10,00 m. H H L = 2,50 m. L W L = 1,50 m.

Normal weather conditions (or decisive during construction) : H,„e = 2,0 m.

T„e = 5,0 m.

I f decisive the lee-side of the breakwater should be designed with: H 3 L = 1,5 m.

T3L

The transmitted wave height (HJ must be less than 1,0 meter.

The hydraulic criteria at the lee-side are not identical to the hydraulic criteria at the sea-side.

- Construction criteria:

The slope at the sea side must be more gradual than 1:2,50. The permeability is approximately 0.4 (40%).

Little damage is allowed (S=2).

The lee-side of the breakwater has the same slope, porosity and damage-level as the sea-side. Ratios: Dn50A/Dn5os = 2 D„5os/D„5oc = 4 Dn50TA/Dn50TS ~ 2 D„50Ts/Dn50TFiop " 4

Dn50F(i)/Dn50B = 4 (ratio filter layer 1 over bottom)

Material

The maximum to be used stone (primary armour W^OA) must be less than 10 tons.

A fascine mattress will be used.

According to the cumulative distribution curve ^^3.2 = 1000 kg. (1 ton) and the index for uniformity for the Rosin-Rammler (n,) equation is 1.

The computation

The crest elevation is set to 17,0 meters above the bottom and the slope is taken as 1:2,50. This results in an Hi of 0,61 m. which is below the criterion. The required WJQA is 9388 kg., which suffices the weight criterion. The crest height is now reduced (reduction of volume breakwater is reduction of costs), until one of the two above criteria is exceeded. With a crest height of 16,1 meter above the bottom the transmitted wave height reaches its criterion (Hi=0,98 m.). The required weight for the primary armour (WSOA) remains 9388 kg., D ^ O A = 1,52m. (no reduction due to non-overtopping).

The results are shown in table A . l .

The secondary armour layer is dimensioned with an H , for normal weather conditions of 2,0 meters, a corresponding wave period of 5,0 seconds and a filter criterion of D^oA/Dn5os=2. The filter criterion is decisive. Resulting in a D^os of 0,76 m. and a corresponding

W50S

dimensioned on a rado D„5os/D„5oc=4, resulting in an D„5oc of 0,19 m. yielding a W5oc=18,34 kg..

Both primary and secondary are twice the nominal diameter thick, resulting in respectively a layer of 3,05 m. and a layer of 1,52 meter.

The design conditions at the lee of the breakwater are not identical. The construction criteria are identical to the criteria at the sea-side. C A D O B

calculates that the design conditions for normal weather conditions are decisive for the dimensions of the primary armour at the lee of the breakwater. Based on these conditions the D„5OAL=0,66 m. and the W5OAL=748,13 kg. This is the minimum required primary armour at the lee-side.

The D^oAL is smaller than the

D„5os.

becomes zero. The volume in case D^JOAL is larger than D n j o s is added to the total

volume of required D^QS- In this way C A D O B determines that for construction

purposes the D^SQAL is replaced by the larger

D„5os.

A choice is made for a standard toe design.

Due to the relatively Low Water Level and the high design wave, the depth (height) to which the primary armour must extend is 1,75 above the bottom. This height is less than the thickness of the primary armour. As a result CADOB determines the

W50TA

W50A

CADOB

(primary armour slope). With the ratio 'D^ffj-JD^sms-'^ the weight and diameter of the secondary armour is determined.

In the previous was stated that a geotexdle will be used. To prevent CADOB from designing a layered gravel filter construction the bottom grain size is set to the size gravel (5cm. < B^o^ < 30 cm. ) . A diameter of 50.000jum = 5 cm. is used. This diameter suffices both the Dn50TF(iop)/Dn5os ratio and the D„50F(top)/D„50B ratio.

The required D,^OTF(IOP) (first layer under the secondary armour in the toe construction) is 0,19m. (W5oxF(iop) = 18,34).

In this hypothetical design the diameters required for the toe layers are identical to the diameters required on the slope as a result of the decisive filter criteria.

This yields the following design as shown in appendix A , figure A . l .

Figure A.2 shows the plot for the required weights and the available weights. The bar heights are also plotted in round values on the y-axis. The print output for the calculated values (at the end of the program) produces the real values. These values are shown in table A . l at the end of the appendix.

Class 10/60 kg. represents the core. Class 1/3 ton represents the secondary armour layer. Class > 10 ton represents the primary armour layer.

Figure A.2 indicates that the quarry does not produce the required WJQA (9388 kg. class > 10 ton). Further more this design does not make use of the most available classes of the quarry product, and all required percentile exceed the available percendle.

Figure A.2 also shows that the percendle of required WJQAL is zero as the layer is replaced by units of W50S.

The next step is to re-run the program with altered construction criteria. The previous criteria are now set to the default values. By just pressing < enter > the user can quickly run through the input and change criteria where necessary. Note that the toe-length, W^j 2 and n^ will not return as the user appointed value.

The slope is now set to cotan(a)=3 (1:3). Iterative the crest height is reduced unül once again one of the design criteria is exceeded. Hi is exceeded when the crest height becomes more than 15,85 meter. A l l further design criteria are kept constant. This yields the design in figure A.3. The required class for the primary armour is now reduced to the 6/10 ton class (7141,61 kg.). The quarry however

does not produce this class. The required class for secondary armour ( 8 9 3 kg.) and the core ( 1 3 , 9 5 kg.) remain the same (figure A . 4 ) .

The total width has increased with 1 1 meters and the total required tonnage per meter with approximately 1 1 ton/m'.

This design is a slight improvement to the preliminary design. I f this quarry is the only available quarry in the neighbourhood of the project site, the purchase of the class 6 / 1 0 ton stone is probably cheeper than the class > 1 0 ton.

The construction criteria are altered again. The slope is set to cotan(a)=4

resulting in a minimum crest height of 15,6 meter, (figure A . 5 ) . Figure A . 6 now shows a slight reduction of the required percentile of class 1 0 / 6 0 kg. The

required secondary armour (Wsos) is now 7 0 8 kg.(class 3 0 0 / 1 0 0 0 kg.). The required percentile is now only 2 % more than the available percentile. The increase of the total tonnage is now approximately 9 ton/m'.

Because the last design makes better use of the quarry product, an extra

computation is carried out with a dredged toe design and the same construction criteria. Figure A . 7 shows the result. The required weights for the units on the slope remain the same. As now the toe is constructed in a dredged trench with sufficient water depth the required top-layer (W^QTA) is now 0,5*W5OA yielding a

W5OTA=2833 kg. (class 3/6 ton stone). This class is also sufficiently available. In

this case the required percentile of class 6 / 1 0 (previous design figure A . 5 ) is reduced with the required percentile 3 / 6 ton for the lighter toe construction in this design (figure A . 7 ) .

It is now important for the designer to determine i f the costs for purchasing the extra volume 6 / 1 0 stone in design A . 5 are less than dredging a trench for the last design. Which probably will be the case. Under water dredging and constructing is a considerable cost factor.

Conclusion

The fourth design (figure A . 7 ) is up until now the "best fitting design" with respect to the quarry curve.

With respect to the cost factor design 3 (figure A . 5 ) is preferred when not looldng further than the previous computation with CADOB.

The previous comparisons have been made on the fitting of the 'bars' in the figure A . 2 , A . 4 and A . 6 . The cost factor is however of much more importance to the designer/constructor. With the previous computations CADOB has only produced a starting point for the further design and optimisation of the design of the proposed breakwater. From here on the design must be optimised based on

the construction costs versus damage costs. CADOB does not account for probabilistic optimisation.

A more appropriate conclusion is that the quarry is not suitable for the construction of the breakwater i f the constructor wants to construct the breakwater by using just this single quarry.

R E C O M M E N D A T I O N S

CADOB version 2.0 is the first release (Version 1.0 was without printing options).

The following items are recommended for the expansion of the program:

- The program presented is now in a 'draft state' with respect to listing of the program. As a result many units are programmed and collected in an overlay file. Many of these units can be shortened and joined as one unit. In this way CADOB w i l l require less space on disk.

- CADOB does not design a filter layer between the secondary layer and the core (on the slopes). This requires larger stones in the core. It is thus recommended to add the design of an extra filter layer on the slope to the program.

- For a realistic design with CADOB a permeability of 0,3 to 0,5 (30% to 50%) should be used. Lower or higher permeability values are more for respectively dikes and berm breakwaters. Designing of different types of coastal structure could also be added to CADOB.

- Only two types of toe constructions can be designed by CADOB, with a restriction on designing a standard toe type i f the depth is less than 8 meter. In some cases a standard toe design may be preferred, even i f the depth is less than 8 meter. This will require larger armour units for the toe layers. The option of designing such toes can also be included in the program.

- CADOB designs the breakwaters in a graphic mode requiring round values for the dimensions. This can give an unrealistic impression of the dimensions of the plots. An expansion of CADOB by sending the results to a Computer Aided Designing (CAD) station without this restriction will produce a better result.

- A t this moment the available quarry product is determined by the theoretical Rosin-Rammler Distribution curve. An option for CADOB is to also include that the user can insert available volumes (percentiles etc.) per grading class, resulting in a more realistic comparison of required classes versus available classes.

- The user gains an optimum breakwater alternative with CADOB based on just the comparison of the available classes versus the required classes. The cost

factor is hot included in the opdmisadon. Costs usually play a dominant role in the design of coastal structures. It is therefore recommended to also include the cost aspects and subsequently the expected damage costs in CADOB. This can then result in combined probabilistic-feasibility opdmum design.

A P P E N D I X A

A P P E N D I X A

B r e a k u a t e r Design (Standard toe d e s i g n ) I 5 0 a - : I B s - ; •toa-; 3 5 i r f 30a-L » e - ï i d » - > W80AL 1 7 1 8 . 1 3 k g . MSOSL : U 7 3 . - ) 9 k<j. T h e s e c o n d . VBOur at t h 9 Mn-sido isi « x t « n d « d u p r i B . i T H . at t t w ! • » -3 i d 9 . C a u t i o n s c t > a M t i s a t i o n r t s u l t s i n r o u n d v a l o » » . C h s c k l a 4 « r t h l d ! r > M « On s l o p * t P I 0.W tHOft I 3 3 8 7 . 8 9 k g . UBOS I 1173.-43 k i ) . USOC I i a . 3- f ktf. S l o p * l a v t r t h l c k n * » t p r i i u r i 3 . 0 9 •>. t z f d I 1 . S 2 B . T o * F U t * r I Dn80Tr<top>i a i 3 a. MBOTS 1 1 1 7 3 . 4 9 k g . l«OTrt I 3 3 8 7 . 8 9 k g . T o * l a i ^ t h i d e r w s a t t | » - i a I 3 . C » 0. t t s c d I 1 . 5 2 B. t t f i l t I ass B . Oa.

"To't'if Hrd"thi"iö>:a"i" - - \ ,

m d t h - > I I j i i i i i III111 i i i i i i i i j i i i j i i i i i j i i i i i i i i i j i i i i I I I I i { i I i i i i i i i | i i i i i I i i i j i II m i l l I I I I I n i l I j l i i i i i i i i { i j i i I I I !

l O a . 2 0 a . 3 0 B . 1 0 B . 5 » » . « O » . 7 0 B . 8 0 a . 3 0 « u 100a. ilOm. CflDOB UERSIOH 2 . Q RWS UTRECHT T I C ( C T > E R U * C I S

F i g u r e A . l E x a m p l e D e s i g n ( p r e l i m i n a r y d e s i g n )

B r e a k u a t e r Design (Standard Toe) Required Uolumes Y - a x l s i P « r c » n t « < } » R 9 q u i r « < i / i ^ a i l « ö l e / H C I « - » x c » « l w i c *

S t - K ü n q « i Iz-lO k 9 , t 0 / < 0 « 0 / 3 0 0 , 3 0 0 / - 1 0 0 0 , l y 3 t e n , 3^6 >10 t o n

Q u i s j - r y - c u r v » H a i g h t C k g l - > A v a i l a b l *

Require ro^^M

CADOB UERSICN 2 . 0 RUS UTPECHT THE H E T H E R L / W S |

D e s i g n f i g u r e A . l W e i g h t k g . C l a s s * P r i m . Arm. Wgg^ 9 3 8 8 8 S e c . Arm. Wggg 1 1 7 4 5 C o r e Wjoc 1 8 2 P r i m . L e e WJQ^L 7 4 8 4 S e c . L e e Wgog^ 1 1 7 4 5 P r i m . T o e WgQ^^ 9 3 8 8 8 S e c . T o e Wgg^g 1 1 7 4 5 E x t r a Wso.p,,,^, 1 8 2 t o t a l = 1 1 5 3 , 7 8 ton/m^ = 4 3 5 , 4 mVm^ * C l a s s % r e q i u r e d / m ^ % a v a i l a b l e 1 = 1 / 1 0 k g 0 , 0 0 2 , 0 0 2 = 1 0 / 6 0 k g 2 8 , 0 7 4 , 0 0 3 = 6 0 / 3 0 0 k g 0 , 0 0 2 0 , 0 0 4 = 3 0 0 0 / 1 0 0 0 k g 0 , 0 0 3 8 , 0 0 5 = 1 / 3 t o n 3 7 , 3 0 3 2 , 0 0 6 = 3 / 6 t o n 0 , 0 0 4 , 0 0 7 = 6 / 1 0 t o n 0 , 0 0 0 , 0 0 8 = > 1 0 t o n 3 1 , 6 7 0 , 0 0 T a b l e A . l R e s u l t s P r i l i m i n a r y d e s i g n ( f i g u r e A . l )

B r e a k u a t e r Design (Standard toe d e s i g n ) « ^ 3 TOa-j tfOa-j 5SH-Ê 80a-i 2 5 a - ; 20»-; 1 5 » - ; 10a4 0» leom. ie<s.t2 k q . USOSL 1 8 3 2 . 7 0 k g . T l w ««cond. «-BOUT at th» »»»-«ide i s •xt<md»d a z prlB. are. at th« les-l i d » . ' C a u t l o r a s c h s e a t i u t i o n r e z u l t s i n r o u i d v a l u a s . Chacic l a i ( « - t h i c k n « i « On « l o p o I p I a - w HBOft I 7t1l.<$l k g . U S 0 3 I 8 8 2 . 7 0 k g . USX I 1 3 . % k g . S l o p s l a v w t h i c k n M W t p r i m a r i 2 . 7 8 B . t s a c l I 1 . 3 3 B. T o * • r i l t w I O n 6 0 T F ( t o p ) i 0 . 1 7 B. MS0T3 I 8 3 2 . 7 0 k g . UBOTA I 7 1 1 1 . ^ k g . T o * l a ^ a r t h i c k n a s n t t p r i a I 2 . 7 8 a . t t M d I 1 . 3 3 B . t t < i l t I 0 . 3 S B . Msu laoo-B LQE^CSÖ a. U i d t h 100B. U O Ü . 120B. ISOit. IWa. Om. 1 0 a . 2 0 « . 3 ( t e . ' » O a . 5 0 a . < O l « . 7 0 a . 8 0 « > . 9 0 B .

CAD08 MERSIOM 2 . 0 RWS UTRECHT THE fCTHERUVMOS

F i g u r e A.3 E x a m p l e D e s i g n , a d j u s t e d s l o p e a n d c r e s t e l e v a t i o n

B r e a k u a t e r Design (Standard Toe) Required Uolumes Y - a x i a P e r o m t s g * R » c i u i r e d / r t v a i l a b l e / t W N - » x c e « l « n c *

. G r a d i n q s j 1/10 k * iCUéO , « 0 / 3 0 0 , 3 0 0 / 1 0 0 0 ,1/ 3 t o n , 3 / « ,«/19 >10

loaoonf ^ 1 ' ' — -

D e s i g n f i g u r e A.3 W e i g h t k g . C l a s s * P r i m . Arm. WJQ^^ 7 1 4 1 7 S e c . Arm. Wggg 8 9 3 5 C o r e 1 4 2 P r i m . L e e Wjo^^^ 5 7 0 4 S e c . L e e VI^Q^I 8 9 3 5 P r i m . T o e WJQ^^ 7 1 4 1 7 S e c . T o e Wg^^g 8 9 3 5 E x t r a V!^or,(,oo) 1 4 2 t o t a l = 1 1 6 5 , 1 0 ton/m^ = 4 3 9 , 7 mVm^ * C l a s s % r e q i u r e d / m i % a v a i l a b l e 1 = 1 / 1 0 k g 0 , 0 0 2 , 0 0 2 = 1 0 / 6 0 k g 2 6 , 7 9 4 , 0 0 3 = 6 0 / 3 0 0 kg 0 , 0 0 2 0 , 0 0 4 = 3 0 0 0 / 1 0 0 0 kg 0 , 0 0 3 8 , 0 0 5 = 1 / 3 t o n 3 8 , 8 2 3 2 , 0 0 6 = 3 / 6 t o n 0 , 0 0 4 , 0 0 7 = 6 / 1 0 t o n 0 , 0 0 0 , 0 0 8 = > 1 0 t o n 3 1 , 7 6 0 , 0 0 T a b l e A . 2 R e s u l t s C A D O B ( f i g u r e A . 3 )

B r e a k u a t e r Design ( S t a n d a r d toe d e s i g n ) BBmi 70B-j « 6 « - : <50a-j 3 0 » ; L « - » l ö » - > m)H. i - t B l . « 3 k * H80S». i70e.1l kg. T h 9 s e c o n d . V B O u -a t t h » » e » - « i c i » 1» e x t e n d a d a s p r i e . a r e . at t h * s i d * . C a u t i o n s c h e m a t i s a t i o n r e s u l t s i n r o u n d v a l u e s . C h e c k l a < ; « r t h l c k n » s s On s l o p e I p I 0 . « USOft I S < S 7 . » ) k g . uses I 7<».-M kg. UeOC I 11.07 kg. S l o p * l a v e r t h l d c n v s s i t p r l B a r i 2 . B 8 » . t s e d I 1 . 2 3 B . T o * + F i l « * r I DnCOTFCtop)! 0,16 b users I 7 0 e . 1 1 k g . USOTA I S M 7 . 3 0 k g . T o * l a g a r t h i c k n e s s t t t p r i a I 2 . B 8 a . t t s m d I 1 . 2 3 a . t t f U t • 0 . 3 2 a . O a . 1(^ 2 0 a . 3 0 s . T o l a l " I i r d t l ï t ~ r 3 l . ' Ö Ö " £ ii|iiiiiiiii|iiiiimiiiiiiiiiii|iiiiiiiii|iiniiiii|iiiiiiiii|iiiiiii

1 0 a . eOss. «Cte. T O B , SOst 9 0 » . l O f t t

J l d t h - >

IMIHIIIIII l|IIIIIIUI|lllllllll|lllll

nOm, 1 2 0 » . 1 3 0 a . I I O B .

CftOOB UERSIDN 2 . 0 RWS UTRECHT T f C ^ C T ^ C R L A M ) S

F i g u r e A.5 E x a m p l e D e s i g n , a d j u s t e d s l o p e and c r e s t e l e v a t i o n

[ B r e a k u a t e r Design ( S t a n d a r d Toe) R e q u i r e d Uolumes Y - a x i s « P e r c e n t a g e R w j u i r e d / r t y a l l a b l e / N W - e x c e e d e n c » S r a d l n g a 1/10 k g , lOySO «0/300 300/1000 1/3 t o n 1 3/6 , < / l ( 1 >10 t o n 10a00-:T ' !—' / i i 8aoo4j

\

D e s i g n f i g u r e A. 5 W e i g h t k g . C l a s s * P r i m . Arm. WJQ^ 5 6 6 7 7 S e c . Arm. Wjgg 7 0 8 4 C o r e W50C 1 1 2 P r i m . L e e WJQ^^ 4 5 1 4 S e c . L e e ^^Q^L 7 0 8 4 P r i m . Toe Wjg^^ 5 6 6 7 7 S e c . Toe WjQ^g 7 0 8 4 E x t r a Vl^onnoo) 1 1 2 t o t a l = 1 1 7 4 , 9 0 ton/m^ = 4 4 3 , 3 mVm^ * C l a s s % r e q i u r e d / m ^ % a v a i l a b l e 1 = 1 / 1 0 k g 0 , 0 0 2 , 0 0 2 = 1 0 / 6 0 k g 2 5 , 4 0 4 , 0 0 3 = 6 0 / 3 0 0 k g 0 , 0 0 2 0 , 0 0 4 = 3 0 0 0 / 1 0 0 0 kg 4 0 , 2 6 3 8 , 0 0 5 = 1 / 3 t o n 0 , 0 0 3 2 , 0 0 6 = 3 / 6 t o n 0 , 0 0 4 , 0 0 7 = 6 / 1 0 t o n 3 1 , 9 7 0 , 0 0 8 = > 1 0 t o n 0 , 0 0 0 , 0 0 T a b l e A.3 R e s u l t s CADOB ( f i g u r e A. 5 )

i R r o a k i m t P r Oesion (Dredged trenchj_ 7 0^ 1 5SB-i 10<H 35B-i L e « - « l d » - > HBOftL k i j . l ^ S ( ^ 1 7 0 8 . 1 1 k * T h » s e c o n d , a - t o u r S t t h » M B - S l d 9 i * • x t c n d r d u p r i n . a r s . a t t h » l e t -s i d a . C a u t i o n s e h e s a t i s a t i o n r e s u l t s i n r o u n d v a l u e s . C h e d c l a y e r t h i c k n e s s On s l o p a S » a - s i < t e « p 1 a - w USOh I B * S 7 . 3 0 k * USDS I 7 0 8 . 1 1 k<J. HBOC I 1 1 . 0 7 k g . S l o p » l a < * » r t h l d < n e s s i t p r i s a - i 2 . B S R . t s e d 1 1 . 2 3 B . T o e / f l l t t i - S e a r ^ d e » DnBOTr<top>l a i 3 B . MBOTS I 3 « S 1 . 2 1 k g . UBOTA I 2 8 3 3 . « 8 k g . T o » l a y e r t M e k n e s s i t t p r i a I 2 . 0 S a . t t s e d I 1 . 0 2 a . t t « i l t I 0 . 2 « a . ïïTrmii|iiiiiiiii|iiiiir Ï3a. l O a . 2 0 B .

CAOOB U E R S I O N 2 . 0 RUS UTRECHT T>C t C T t g R L A N O S

F i g u r e A.7 E x a m p l e D e s i g n , d i f f e r e n t t o e c o n s t r u c t i o n f o r t h e ' b e s t f i t t i n g ' d e s i g n .

B r e a k u a t e r Design (Dredged t r e n c h ) R e q u i r e d Uolumes y - a x l « P e r c e n t a < j » R « < i u i r * d / ( W a i l a i j l e / ^ W N - e x c e e < l « n c »

(SO/300 , 3 0 0 / 1 0 0 0 , 1 / 3 t o n . 3/<S , * / l O >10 t o n l o a o o - n ^

D e s i g n f i g u r e A.7 W e i g h t k g . C l a s s * P r i m . Arm. Wj^^ 5 6 6 7 7 S e c . Arm. WgQg 7 0 8 4 C o r e W50C 1 1 2 P r i m . L e e Wjo^^' 4 5 1 4 S e c . L e e WggjL 7 0 8 4 P r i m . T o e WJQ^^ 2 8 3 4 6 S e c . Toe Wjo^s 3 5 4 4 E x t r a Vl,,„,^^^, 1 1 2 t o t a l = 1 1 7 4 , 9 0 ton/m^ = 4 4 3 , 3 mVm^ C l a s s % r e q i u r e d / m ^ % a v a i l a b l e 1 = 1 / 1 0 k g 0 , 0 0 2 , 0 0 2 = 1 0 / 6 0 kg 2 5, 4 0 4 , 0 0 3 = 6 0 / 3 0 0 kg 0 , 0 0 2 0 , 0 0 4 = 3 0 0 0 / 1 0 0 0 kg 4 0 , 2 6 3 8 , 0 0 5 = 1 / 3 t o n 0 , 0 0 3 2 , 0 0 6 = 3 / 6 t o n 0 , 0 0 4 , 0 0 7 = 6 / 1 0 t o n 0 , 0 0 0 , 0 0 8 = > 1 0 t o n 3 1 , 9 7 0 , 0 0 T a b l e A.4 R e s u l t s CADOB Dredged t r e n c h ( f i g u r e A .7 )

L I S T O F S Y M B O L S a Dn50(index) index A index S index C index TA index TS index TFtop index TFi index B f o F Hsnc H H L K, L L C L L W L m; N P R R Rs S Tp UCL W50(index) - slope angle

- nominal diameter (Wjodn^j/p,)"^ - primary armour slope

- secondary armour - core

- top layer toe construction - secondary armour toe - top fdter layer just under TS

- fdter layer i , where 1 = first layer above bottom (B) - bottom grain size

- reduction factor for D„5OA. in case of overtopping - freeboard (Crest height above MSL)

- significant design wave height

- significant wave height at the lee-side

- significant wave height normal weather conditions - transmitted wave height

- high high water level (highest design water level, including set-up and tide)

- layer coefficient ('packing' of units) - transmission coefficient

- wave length (at location)

- lower class timit quarry product

- low Water Level (minimum design water level) - number of units to determin layer thickness - number of waves (storm duration)

- index of uniformity (Rosin-Rammler) - permeability coefficient

- run-up parameter

- percentile lighter than W50

- significant run-up parameter - damage level (A/AD^^^ - fictitious wave steepness with Tp - significant design wave period - wave peek period ( = Ty0,9)

- wave period normal weather conditions - design wave period lee-side

- upper class limit quarry product

- nominal weight (for index see D„50(i„jex))

- nominal minimum weight for determination lower class limit required W50

Wson.ax - nominal maximum weight for determination upper class limit required W50

W 6 3 . 2 - location factor for the Weibull distribution at the 63.2 percentile.

Wy - the weight for which the fraction R is lighter on the distribution curve.

A - (prPw)/Pw relative mass density Ps - mass density stone

Pw - mass density water - surf similarity parameter

Crest Elevation High Water Level (HHL)

Mean S e a Level (MSL)

trtnary armmir sea-ski^

U » f Water Lev®! (LWL)

secondaiy armour to

D e f i n i t i o n S k e t c i i

tpriml+tsed

LWL-1 .SxHs £» LWL-1.5xHt prfrnary armour te«-s!d®

lprhv4ee LWL: U w Water L e v e L Dn: nomha! d l a m e t ^ LOKATIONS O F A R M O U R : W: primary-or top-layer 'S-: seondary layer 'C: Gore material 'P: Flter-layer T : t£»-Iay©r

Toes with sufficient depth

L W L I.SxHs 1 p r u ^ l y armour >4v0 1 LWL I.SxHs XjOm.

REFERENCES

1. Manual on the use of rock in Coastal and Shoreline Engineering. Second draft by CUR and CIRIA, February 1990.

2. Stability of breakwater armour layers. Deterministic and probabilistic design. J.W. van der Meer and K . W . Pilarczyk

Delft Hydraulics Laboratory, February 1987. 3. Rekenregels voor waterbouwkundig Ontwerpen.

Ministerie van Verkeer en Waterstaat,

Rijkswaterstaat bouwdienst, Utrecht, mei 1990.

4. Computer Aided Optimum Design of Rubble-Mound Breakwater Cross-sections.

Manula for the Rumba Computer Package, Release 1. Wiebe de Haan.

T U Delft, Faculty of Civil Engineering.

Hydraulic and geotechnical Engineering Division, Hydraulic Engineering Group.

5. Coastal Structures and Breakwaters,

Wave transmission at low crested structures, J.W. van der Meer, K. d'Angremond, The institution of Civil Engineers, London. November 1991.

6. Coastal Engineering

Volume 3 Breakwater Design Edited by W . W . Massie, P.E.

T U Delft, Faculty of Civil Engineering.

Hydraulic and geotechnical Engineering Division, Hydraulic Engineering Group.

7. Turbo Pascal

Reference guide Version 5.0 Borland international.

M A T H C A D H E L P F I L E

T A B L E O F C O N T E N T S

MATHCAD DOCUMENTS ,. „ , , „ „ - 1 UNITS DOCUMENTS „,.„..„....,... , „ , , . . . 1

PROBRAM NOTES ( p r i n t e r and g r a p h i c B - a d a p t o r ) ..„.,,,. ,,,.„„„.. :-i HOW TO USE MATHCAD ... 4

FUNCTION KEYS 4 CTRL-FUNCTION KEYS ,.,„,,„..,,„...'.. = ...•..••.. 4

CONTROL KEYS ,„,,..., , „ , . . , , . . . 4 SPECIAL KEYS . . „ . , . . „ . . . , . . , . . . • . . " " • • " " " -GREfEK LETTERS „ . „..„..,„. ,„„,„,... »... 4 KEYS TO MOVE THE CURSOR , , . . „ , , , . . „ , . . . . , . . , . . . 5 KEYS TiJ MOVE AROUND I N TEXT . . „ ..,„„„.,.... . - -. 5

KEYS TO CUT AND PASTE TEEXT 5 MATHCAD EQUATIONS , ..„,,.,„... 5

MATHCAD OPERATORS 6 VECTOR AND MATRIX OPERATORS . , 6

USER-DEFINED FUNCTIONS „....,..,... . . 7 B U I L T - I N FUNCTIONS ,, . . . ."„ » 7

B U I L T - I N VECTOR AND MATRIX FUNCTIONS . , . „ , . . , . . , . , , . . . B

DATA FIl-ES „ „ „ 8 HOW TO READ AND WRITE DATA , B

HOW TO USE COMMANDS . . » » ? L I S T OF COMMANDS . .»

SYSTEM COMMANDS • • •« - •9"

F I L E COMMANDS > 10

COMPUTATION COMMANDS 10 EDITING AND MOVING COMMANDS ... 11

IN-REGION AND TEXT COMMANDS 11 WINDOW AND PAGE COMMANDS = 12

STEPS I N PRINTING A DOCUMENT . . . . „ . , , . . . 12 RANGE VARIABLES . . . . , . . . „ . . , . , . . . , . . . » . . . - . " . • . 13

VECTORS,, E5UBSCRIPTS, AND ITERATION . . . „ . , . „ . 13

HOW TO CREATE A VECTOR OR MATRIX 13 COMPUTING WITH VECTORS AND MATRICES ,.„.„. .. 13

SOLVE BLOCKS i 4 CREATING A PLOT - « - 14

CHANGING PLOT S I Z E AND CHARACTERISTICS ... 15 UNITS AND DIMENSIONS . . . . „ . . „ . . „ . . . 15 FORMATTING NUMERIC RESULTS . . . , . . . , . , . = . . - . . . - . . . 16

KEYS TO USE WITH TEXT , - » . 16 TYPICAL TEXT REGION ,,,...,....,.. = ... 16