ECONOMIC OPTIMIZATION OF BREAKWATERS

Transcription

1 Delft University of Technology Additional Graduation Work (CIE ) ECONOMIC OPTIMIZATION OF BREAKWATERS Case study: Maintenance of Port of Constantza s Northern Breakwater CAROLINA PICCOLI Supervision: Ir. Henk Jan Verhagen February 2014

2 Title: Case Study: Document: Economic Optimization of Breakwaters Maintenance of Port of Constantza s Northern Breakwater Additional Master Thesis Report Author: C. Piccoli Place and date: Delft, February 2014 Supervisor: ir. H.J. Verhagen University: Faculty: Department: Delft University of Technology Faculty of Civil Engineering and Geosciences Hydraulic Engineering In cooperation with: Van Oord List of trademarks used in this report Core-Loc TM is a registered trademark of the US Army Corps of Engineers The use of trademarks in any publication of Delft University of Technology does not imply any endorsement of this product by the University

3 PREFACE This report presents the work performed during my Additional MSc Thesis as part of the Master Programme of Hydraulic Engineering from the Delft University of Technology Civil Engineering and Geosciences Faculty. The objective of this additional graduation work was to provide a better insight on economical optimization of breakwaters. Information about the processes of optimizing a breakwater is gathered in this report. A description of the design and optimization methods of new breakwater structures is provided and the method is adapted and applied on a maintenance optimization case study for an existent breakwater. I would like to thank ir Henk-Jan Verhagen who has supervised me, without his collaboration this work wouldn t have been achieved. I would also like to thank Van Oord, especially Cuno Langeveld and Johan Roos, that made the study case possible and Boyan Savov who transmitted me his enthusiasm for the Constantza s breakwater project. Additionally, I would like to thank Pieter van Gelder for his valuable contribution. Last but not least, I would like to thank João Dobrochinski for the many hours we spent together discussing this subject and for your more than helpful comments. Moments like these make me feel confident that I made the right decision when coming to Delft and you know better than anyone else the reason that brought me here. Carolina Piccoli 28/02/2014 Additional Master Thesis i

4 ABSTRACT The design process is complex and a cluster of considerations has to be taken into account not only at the moment of conception but for the whole life cycle of the project. Technical aspects should be integrated together with social, environmental, economic and other factors. The outcome of a successful integrated design should be a structure that delivers the required performance and which is robust, easy to build and maintain, socially and aesthetically acceptable, cost-effective and produces the fewest negative impacts on its environment (CIRIA/CUR/CETMEF, 2007). Nearly always there are conflicts in between those factors and optimization is needed. Optimization of a breakwater is a very challenging task since the optimum is subjective and can be different depending on the point of view. Part I of this report covers the design process and optimization methods. A breakwater could be optimized with respect to amongst others, construction costs, construction time, material reduction, environmental impacts and total cost. In this report the economic optimization is considered and the definition of optimum design by (Van de Kreeke & Paape, 1964) is used: A breakwater design is optimum when it results in a structure that meets the requirements at minimum total cost. The total cost is defined as the cost of construction plus the anticipated damage and economic loss due to failure of the structure. The functionalities of the breakwater have to be guaranteed by the layout of the breakwater, the breakwater type and the structural design of its cross section. With respect to the selection of the breakwater type, usually few alternatives are selected by eliminating clearly unfeasible options. The most promising alternatives should be economically optimized and the results should be compared in order to assess the best solution. A method for economic optimization is here described. When designing a structure, the return period has to be established and the respective design wave should be determined. Given that the design wave is a stochastic value, there is always a probability of this value to be exceeded. An increase of the design wave value leads to a raise on the costs of construction. Nevertheless, by selecting a higher design wave, the probability of exceedance of this new value is reduced hence the capitalized anticipated damage and economical losses become smaller. The sum of these values (cost of construction plus capitalized anticipated damage and economic losses) is calculated in order to identify the optimum design wave at which the total costs are minimized. In the second part of the report, optimization is applied to the maintenance of the Port of Constantza s Northern Offshore Breakwater in Romania. The Port of Constantza is the Romania s largest sea port. It is located at the crossroads of the trade routes linking the markets of the landlocked European countries to Transcaucasus region, Central Asia and the Far East. The present length of the North breakwater is 8,344 m and the South breakwater is 5,560 m. This case study focuses on the Northern breakwater, particularly the so called offshore breakwater which was built between 1976 and In the original design the offshore breakwater should be 5,900m long. However, due to budget restrictions the project was stopped in 1990 with only 4,800m of its extension being completed. The armour layer consists of 25 tons stabilopodes at the sea side slope and 4.5 tons at the port side. In 2001, the offshore breakwater was repaired by a local company as part of the Constantza Port Rehabilitation Project. The repair was done by replacing the removed units with new or reused stabilopodes of the same dimensions as the initial ones. Additionally, 15 tons Antifer cubes were placed at the toe of the sea side slope at highly damaged locations. The goal of this case study is to perform an optimization of the maintenance costs, identifying the less costly maintenance strategy. Economic Optimization of Breakwaters ii

5 First of all, the hydraulic boundary conditions were verified by analyzing the design wave conditions. Then, the section of the offshore breakwater to which this boundary condition is applicable was selected based on As-built elevations. The damage which was repaired in 2001 during a Rehabilitation Project was checked at the entire breakwater extension in order to validate the selection of the breakwater section. After having selected the breakwater section for which the given hydraulic boundary conditions are applicable, the origin of the damage repaired in 2001 was investigated. The first hypothesis is that one storm has caused the massive damage at the offshore breakwater. The significant wave height needed to cause such a damage was calculated as well as its probability of occurrence (in terms of return period). This result gave a quite unlikely event and no records of such a significant wave height exist for the area in the recent period. Therefore, the second hypothesis was analyzed: the damage was accumulated for many years starting at the end of its construction (1990). The probability of the actual damage repaired in 2001 to occur in 11 years of damage accumulation was checked. The result was again a low probability of occurrence, however much more plausible than the first hypothesis. Other hypotheses for the damage were also raised. In order to optimize the maintenance strategy, it was assumed that the method for damage accumulation that was used to assess the damage that occurred until 2001 is valid after the Rehabilitation Project was held. In other words, the hypothesis two for damage evolution is considered a good representation of the reality from 2001 onwards and the other raised hypotheses were neglected. Simulations of the damage accumulation were carried on. The following repair strategy was applied. For minor (0.5 N od <2.5) and major (2.5 N od <5) damage, the repair is simulated to be done in the traditional way as it was performed in 2001, replacing the damaged stabilopodes with new ones. When failure occurs (N od 5), repair is simulated to be done by removing all the stabilopodes and replacing them with a new Core-Loc single layer armouring. N od is the number of units displaced out of the armour layer within a strip equal to the nominal diameter. Additionally to this repair strategy a threshold for repair was incorporated above which repairs are executed. This threshold, represented by the N od, was set up to different values between 1 and 5. The costs related to the simulated damage and respective applied maintenance strategy were estimated, discounted and added over a period of 100 years (total costs). Because of the spread in the simulation results (due to the stochastic behavior of the wave climate), median and expected values are not so representative. Therefore, probability distributions of expected total costs were assessed for every maintenance strategy and used to draw the conclusion. There is not a sharp optimum threshold of repair. The selection of the optimum threshold is highly dependent on the accepted probability of exceedance. Based on the analysis of all acceptable probabilities of exceedance it can be concluded that the threshold that meets the optimum requirements for ranges below 20% and between 20 and 40% is a N od equal to 4. However, if a probability of having the expected costs exceeded of 50% is tolerated the threshold goes up to a N od of 4.5. Nevertheless, the increase in expected total lifetime costs for probabilities of exceedance of 5 and 15% from a threshold of 4 to 4.5 is in the order of 2 million Euros (which corresponds to less than 2% of the failure costs). Therefore, it can be concluded that a threshold for repair of 4.5 fulfills the requirements of all accepted probabilities of exceedance equal or smaller than 50%. Hence, the optimum threshold for repair is a N od of 4.5. This damage corresponds to the major damage level and for this situation the repair is done in the traditional way, by replacing the removed stabilopodes with new ones. Nevertheless, when letting the repair threshold getting too close to the failure (N od = 5) it is recommended to Additional Master Thesis iii

6 reconsider the repair solution. In reality no sharp transition between major damage and failure exists and since a damage of 4.5 N od corresponds to the displacement of 28% of the armour units, the possibility of performing the reconstruction with Core-Locs already for this value is recommended. It is recommended to monitor the damage of the breakwater and as soon as the structure either reaches the threshold of 4.5 N od or starts losing its functionality the reconstruction of the affected segment with Core-Locs should start. A N od of 4.5 corresponds to on average 220 stabilopodes removed in 100m of breakwater length. The time needed to design, to raise funds and to initiate the reconstruction should also be taken into account when deciding to start the actions. This conclusion is based on the judgment that the difference between 4.5 and 5 is relatively small (about 25 units in 100m). The interest rate was raised to 3 and 4 % and the same pattern could be noticed. Beyond the fact that the total lifetime costs have an overall decrease due to the increased interest rate, a shift of the optimum threshold to the higher values can be observed. It can be concluded that the choice for a threshold of 4.5 is not very sensitive to changes in the interest rate. Recommendations for improving the reliability of the results and remarks about the made assumptions are given. Other parameters should be varied in order to test the robustness of the results and to identify which variables have more influence. For example, the number of storms was assumed to be deterministic and equal to the average number of storms per year. However it is known that there is a lot of variability in this variable and the influence of this variability should be better explored. It is very difficult to make costs predictions for a 100-year time horizon. It is not only inflation that plays a role in the costs rising. Some causes are difficult to predict like for example, economic crisis, market crashes and others. Also, material prices variation and changes in labor costs could change significantly the results. A sensitivity analysis for the costs variables should also be performed. Furthermore, the inclusion of the blocks breakage in the damage accumulation could increase the predictability of the model since it was observed at the verification of the 2001 damage that only the damage accumulation could not reproduce the witnessed conditions. It is very likely that the breakage of concrete units plays an important role for the breakwater degradation. Economic Optimization of Breakwaters iv

7 TABLE OF CONTENTS PREFACE... i ABSTRACT...ii TABLE OF CONTENTS... v LIST OF FIGURES... vi LIST OF TABLES... viii 1. INTRODUCTION... 1 PART I GENERAL DESIGN AND OPTIMIZATION PROCESS Breakwater Types Aspects related to breakwater type Technical aspects Economic aspects Economic Optimization of Breakwaters Construction costs Capitalized anticipated damage and economic losses Full Probabilistic Economic Optimization of Breakwaters PART II CASE STUDY DESCRIPTION METHOD APPLIED ON THE CASE STUDY Introduction Design wave height return period Selection of the section to be analyzed Causes of the observed damage in Cumulative damage Other possible damage contributors Maintenance strategy Costs Optimization of the threshold for repair CONCLUSION AND RECOMMENDATIONS BIBLIOGRAPHY Additional Master Thesis v

8 LIST OF FIGURES Figure 2-1 Total costs as a function of the design wave height Figure 3-1 Location of the study area Figure 3-2 View from the crown wall of the offshore breakwater Figure 4-1 Weibull fit applied for directional sector 45 N~75 N on wave height Figure 4-2 Return period of the design wave height (m). Nearshore values presented between brackets Figure 4-3 Example of available As-built drawing Figure View from the Crown Wall of the offshore breakwater around km Stabilopodes 25 tons Figure 4-5 As-built elevations of the existing Offshore Breakwater Figure 4-6 Number of replaced stabilopodes within a strip of one nominal diameter (D n ). 21 Figure 4-7 Original design of the offshore breakwater cross-section Figure 4-8 Significant wave heights, return periods and associated damage Figure 4-9 Calculation flow for one lifetime cycle Figure 4-10 Cumulative damage in 100 years (10000 runs) Figure 4-11 Probability of damage occurrence in time Figure 4-12 Snapshot of visual inspection video Figure tons Stabilopodes at the sea side of the offshore breakwater Figure 4-14 Number of stabilopodes replaced at the sea side slope and antifers placed at the toe of the sea side slope Figure 4-15 Stabilopodes and filter layer to be removed Figure 4-16 Cross-section used for the breakwater reconstruction Figure 4-17 Probability of damage occurrence in time Figure 4-18 Probability of damage level occurrence in time Figure 4-19 Probability of occurrence of damage between 0 and Figure 4-20 Example of lifetime simulation results - repair threshold equal to Figure 4-21 Maintenance costs given the previous cumulative damage Figure 4-22 Example of lifetime simulation results - repair threshold equal to Figure 4-23 Maintenance costs given the previous cumulative damage Figure 4-24 Example of lifetime simulation results - repair threshold equal to Figure 4-25 Maintenance costs given the previous cumulative damage Figure 4-26 Example of lifetime simulation results - repair threshold equal to Figure 4-27 Maintenance costs given the previous cumulative damage Figure 4-28 Example of lifetime simulation results - repair threshold equal to Figure 4-29 Maintenance costs given the previous cumulative damage Figure 4-30 Cumulative damage for repair threshold equal to Figure 4-31 Probability of exceedance of total lifetime costs for an interest rate of 2% Economic Optimization of Breakwaters vi

9 Figure 4-32 Probability of exceedance of total lifetime costs for an interest rate of 3% Figure 4-33 Probability of exceedance of total lifetime costs for an interest rate of 4% Additional Master Thesis vii

10 LIST OF TABLES Table 2-1 Examples of different scale levels... 2 Table Structural types of breakwaters Table 2-3 Aspects to be taken into account when selecting a breakwater type Table Limit state damages and respective repair strategies (Burcharth, 2009) Table 4-1 Offshore and nearshore design wave characteristics for different return periods (adapted from ARCADIS, 2013) Table 4-2 Values of significant wave height in meters (m) for different damages N od Table 4-3 Limit state damages and respective repair strategies (adapted from Burcharth, 2009) Table 4-4 Repair costs estimate Table 4-5 Calculation of reconstruction costs Economic Optimization of Breakwaters viii

11 1. INTRODUCTION This Additional MSc. thesis report is part of the master program in Civil Engineering (track Hydraulic Engineering) of Delft University of Technology. The additional MSc thesis consists of 10 European Credits (ECs), which is equivalent to approximately hours. As part of the learning activities of the Master Course, the main purpose of this research is providing a better insight of breakwaters economic optimization. The quantitative results presented in this report are indicative only and should be considered within the context of the additional graduation work, i.e. including important assumptions and limitations. The work was supervised by ir. Henk Jan Verhagen in cooperation with Van Oord. The report is divided in two parts: Part I presents general information on the design process followed by the selection of location and layout of the breakwater. The optimum design concepts are introduced including descriptions of the breakwater types and factors that influence the choice for each of them. A section is dedicated to economic optimization of breakwaters. The full probabilistic economic method is briefly introduced. Part II starts with the presentation of the case study. Subsequently, the method applied for the optimization of the maintenance of Port of Constantza s northern breakwater is presented. All the steps needed to obtain information to apply the method and the prevailing assumptions are described. A maintenance strategy is defined and the optimization of the threshold for repair is done by means of Monte Carlo simulations. The results of the simulations are presented and discussed. Conclusions and recommendations are referred in the last chapter. Additional Master Thesis 1

12 PART I (General study on breakwater optimization)

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14 2. GENERAL DESIGN AND OPTIMIZATION PROCESS The design process is complex and a cluster of considerations has to be taken into account not only at the moment of conception but for the whole life cycle of the project. Technical aspects should be integrated together with social, environmental, economic and other factors (CIRIA/CUR/CETMEF, 2007). The Rock Manual (CIRIA/CUR/CETMEF, 2007) defines these categories as follows: Technical considerations: physical conditions, engineering, construction, maintenance. Economic considerations: capital and maintenance costs, benefits, whole-life costs. Environmental considerations: impacts on the natural environment. Social considerations: impacts on the human environment comprising the workforce, stakeholders, general public etc. At every design phase the relative importance of each of these factors changes. The functional performance is more important in the earlier stages. Construction (hence costs) is imperative in the later stages. The required performance is evaluated based on the functional requirements of the breakwater. A non-exhaustive list of the breakwater functions is given below: shelter vessels from waves and currents; protect the shore against waves and currents; prevent siltation of navigation channel (shoaling); provide dock or quay facilities; prevent thermal mixing. The outcome of a successful integrated design should be a structure that delivers the required performance and which is robust, easy to build and maintain, socially and aesthetically acceptable, cost-effective and produces the fewest negative impacts on its environment (CIRIA/CUR/CETMEF, 2007). In The Rock Manual (CIRIA/CUR/CETMEF, 2007) three abstraction levels of the design process are presented. The designer has to be involved in all the three following levels: Macro level: the system Meso level: a component of the system Micro level: an element of one of the components In order to exemplify the application of the three abstraction levels to breakwater design, part of a table from Verhagen, D Angremond and van Roode (2012) is reproduced in Table 2-1 showing examples of different scale levels relating ports and their breakwaters. Table 2-1 Examples of different scale levels General terms Macro level Meso level Micro level System Component Element Example 1a Harbour in the global and regional Harbour layout Breakwater transport chain Example 1b Harbour layout Breakwater Crest block In this study the scale levels are taken as follows: The choice for the breakwater layout and its location are part of the system (macro-level). The selection of breakwaters type and the economic optimization of the cross-section correspond to the meso and micro level respectively. Economic Optimization of Breakwaters 2

15 Being the length of the breakwater an important contribution for the construction costs of a port, the assessment of the location and layout of breakwaters is crucial. There are no formal rules or guidelines for selecting the breakwaters layout. However some recommendations should be kept in mind (Ligteringen & Velsink, 2012): The length of the breakwater should always be minimized in order to reduce costs without disregarding the following aspects: Along alluvial coastlines breakwaters should reach beyond the corresponding breaker zone water depth; The direction, the magnitude of the littoral transport and the corresponding accretion rate at the breakwater should be considered. The configuration of the entrance should limit wave penetration. The breakwaters should provide space immediately behind the heads for three main reasons: Avoiding hard structures close to the channel boundaries; Vessels need lateral space for passing from cross-current conditions into still water; Reduction of wave penetration due to the enhancement of diffraction effects. When the wave climate is such that the littoral transport is unidirectional one breakwater may suffice. Further discussion on the macro-level is out of the scope of this study. These and other strategic decisions are considered as already taken. From here onwards focus is given on the component breakwater and on the elements of its cross-section that are subjected to economic optimization. As stated before, a high-quality design should consider not only technical aspects but also social, environmental and economic factors. Nearly always there are conflicts in between those factors and optimization is needed. Optimization of a breakwater is a very challenging task since the optimum is subjective and can be different depending on the point of view. A breakwater can be optimized with respect to amongst others, construction costs, construction time, material reduction, environmental impacts and total cost. In this report the economic optimization is considered. The definition of optimum design used from here on is given by (Van de Kreeke & Paape, 1964). A breakwater design is optimum when it results in a structure that meets the requirements at minimum total cost. The total cost is defined as the cost of construction plus the anticipated damage and economic loss due to failure of the structure. In order to assess the cost, the cross-section of the breakwater has to be determined. The type of the structure and the dimensions of the cross-section have to be selected. The breakwater types and the selection process are presented in the following section. Additional Master Thesis 3

16 2.1. Breakwater Types The breakwaters can be divided into three main structural types: Sloping or mound type, vertical type (including composites) and special types (Takahashi, 2002). Table 2-2 indicates the breakwaters structural types. Table Structural types of breakwaters. Sloping or mound Vertical and composite Special (non-gravity) Rubble mound breakwater Multi-layer rubble mound breakwater Rubble mound armoured with concrete blocks Berm breakwater Icelandic-type berm breakwater Low-crested (submerged) breakwater and reef breakwater Monolithic concrete breakwater Concrete caisson breakwater Caisson breakwater with a berm (horizontally composite breakwater) Cellular block breakwater Block masonry breakwater Sloping top caisson breakwater Perforated front wall caisson breakwater Curtain-wall breakwaters Steel pile breakwaters Horizontal plate breakwaters Floating breakwaters Pneumatic breakwater Hydraulic breakwater A rubble mound breakwater, also known as conventional type, is simply a pile of elements such as, stones, gravel, and concrete blocks. The conventional multi-layer rubble mound breakwater is statically stable which means that the initial cross-section is not changing in time although displacement of armour units can be allowed. Basically two types of armour units can be applied: rocks or concrete blocks. The breakwater can also have a berm which is not the same as a berm breakwater; both types are described in details afterwards. A particular case of the latter is the Icelandic-type berm breakwater. Low-crested breakwaters, as the name indicates, are structures with a lower crest level which can be overtopped frequently or even be entirely submerged. Examples of it are the detached (reef) breakwaters. The original concept of the vertical breakwater was to reflect waves, while that for the rubble mound breakwater was to break them (Takahashi, 2002). The monolithic breakwaters can be made of caissons, masonry, cellular block and others. The invention of caissons made vertical breakwaters more reliable and it is now the most commonly used. From this point forward, reference is made only for caisson breakwaters and its variations. The monolithic structures can be placed on top of a rubble mound foundation. These are the so called composite breakwaters. The height of the mound can vary dividing the composite breakwater in two subcategories: high-mound composite breakwater and low-mound composite breakwater. The horizontally composite breakwaters have stones or concrete blocks placed in front of the caisson to dissipate the wave energy reducing the wave forces on the wall and the amplitude of the reflected wave. The sloping top and the perforated front wall caisson breakwaters are design alternatives that aim to reduce wave forces. Economic Optimization of Breakwaters 4

17 The special type breakwaters are used, as the named states, only in special situations and therefore are not very common. Floating, pneumatic, hydraulic, pile, horizontal plate and curtain-wall breakwaters are examples of it. The exceptional conditions at which each of these solutions may be feasible are presented afterwards. The choice of the breakwater type is an important phase of the design. It is a complex assignment and depends on a great amount of factors. A considerable however nonexhaustive list of variables that influence on the selection of the breakwater type is given in Table 2-3. Table 2-3 Aspects to be taken into account when selecting a breakwater type. Technical aspects Functional requirements Site conditions Construction Economics Social Environmental Limit overtopping Reduce waves inside port (transmission, reflection, diffraction) Guide currents Provision of quay, mooring and/or other installations Provision of access road Design life of the structure Tolerable downtime Acceptable risk during the lifetime Maintenance strategy Adaptability Hydraulic boundary conditions (Wave climate, currents, tides) Topography, Bathymetry and Geotechnical data Meteorology Construction time (urgency of the project) Material and equipment availability Knowhow of local companies Weather and seasonal limitations Space for precast yards and storage Funding Maintenance costs Financial constraints Acceptable operational risks Safety Use of local labors Recreational areas Mitigate potential environmental impacts Minimization of carbon footprint Use of renewable materials Reduce visual pollution Make use of an aesthetic design The advantages and disadvantages of each type of breakwater are reported in the subsequent section considering factors listed in Table 2-3. Additional Master Thesis 5

18 Aspects related to breakwater type Sloping or mound breakwaters Rubble mound breakwaters: are the most commonly applied type of breakwaters. Some of the reasons that favor their choice are here stated. The outer slope forces the waves to break dissipating the wave energy therefore reducing the wave reflection. Construction is relatively easy, highly skilled professionals and specialized equipments are not compulsory for a successful execution which allows for the use of local labors. Foundation requirements are less than for a comparable vertical structure. The rubble mound structures can be considered flexible given that differential settlements can be tolerated. From an environmental point of view an advantage is that long period waves are transmitted through the breakwater allowing more water exchange compared to a vertical breakwater. A disadvantage is that the slopes require more material than the vertical walls. In addition, especially in deep water, the footprint on the seabed is higher increasing the impacts on seabed life. On the other hand, the rubble mound slope is suitable for sea life. A variation of the conventional rubble mound breakwater is the use of a crown wall on its crest. The crown wall can be designed for reducing overtopping. Additionally, this crest element usually incorporates a roadway which can be used for access to the roundhead and for structure maintenance. It can also provide space for port operations when for example a quay is included at the lee side of the structure. The armour layer of rubble mound breakwaters can be made of stones or concrete units. Armourstone is applied when natural blocks with adequate weight to stand the loads for the given wave climate are available within economically viable distances. When the design conditions are exceeded damage occurs. The damage increases gradually when armourstone is used. Usually the structure doesn t fail abruptly, allowing repairs before the complete collapse. When sufficient amount of heavy natural blocks is not available or when the weight limit for quarystones is exceeded (rough wave climates) the use of concrete armour units is required. Different shapes of concrete blocks are available. Depending on the type of block they can be placed on single or double layers. The interlocking property of some blocks allows them to be lighter and more slender. A disadvantage of the concrete units compared to the natural blocks is the not so gradual degradation. Movement of blocks during a storm can lead to breakage. The resultant broken blocks are more susceptible to damage, therefore, once damage begins it increases rapidly, anticipating the failure compared to a good quality armourstone. Berm breakwaters: this type is an alternative to the situations when stones are available but there are not sufficient heavy natural blocks and concrete armour units are dismissed Heavy concrete armour units can be difficult to cast especially in places with lack of space or in countries with lack of technology or skilled labors. A general characteristic of berm breakwaters is the allowance for the stones of the outer slope to move and reshape into a stable profile. These berm breakwaters can be divided into statically stable and dynamically stable reshaped structures (PIANC/MARCOM 40, 2003). The statically stable reshaped structures allow the slope to reshape into a stable profile so that the individual stones are also stable. For a dynamically stable reshaped structure, the reshaped profile is also stable; however individual stones are allowed to move up and down the slope. The disadvantage of allowing this reshaping is that more material is required to maintain the functionality of the breakwater. Thus, the viability of this type of structure depends very much on the costs of the quarry material. The reduction of construction costs, by eliminating the need to build the slope at a specific angle because it is going to reshape anyhow, is an advantage of this method. Economic Optimization of Breakwaters 6

19 Icelandic-type berm breakwaters: are considered statically stable non-reshaping structures. The difference between the Icelandic-type berm breakwater and a conventional multi-layer rubble mound breakwater with a berm is that the former is built of several stone classes and usually have a dedicated quarry for the project. The general method for designing an Icelandic-type berm breakwater is to tailor-make the structure around the design wave load, possible quarry yield, available equipment, transport routes and required functions (Sigurdarson, Gretarsson, & Van der Meer, 2008). One of the advantages of this type of breakwater is that it is less voluminous than the dynamic reshaping berm breakwater. Furthermore, narrowly graded armour classes are used increasing the stability of the structure due to the higher permeability obtained. Low-crested/submerged breakwaters: can be applied in areas of low tide range and when overtopping is highly acceptable. It is also an alternative when one of the requirements is horizontal visibility. A mound of stones or concrete can also be considered non-aesthetic. The disadvantage of it is that it represents a non visible hazard to swimmers and boats. Reef breakwaters: its main objective is the prevention of beach erosion reducing the wave heights at the shore. They are in principle designed as the conventional rubble mound structures (either multi-layer or homogeneous) but with submerged crests. Their location is parallel to the shore and the mounds can be stable or reshaping. Concrete units can also be applied as the amour layer. A procedure for deciding between a conventional rubble mound breakwater and a berm breakwater (and which type of it) is given in Sigurdarson, et al. (2004) Jacobsen, Smarason, & Bjørdal (2004). It takes into account the availability of rocks and the designed stone weight. The first option is a conventional rubble mound structure, which has its financial viability assessed. In case of a dedicated quarry, the possibility of using all quarried material or selling it to other projects has to be taken into account. The following step involves an economic comparison between the previous solution and an Icelandic-type breakwater with the largest stone class similar to that of the conventional rubble mound. The Icelandic-type usually requires cover stones with less weight than that for conventional rubble mound breakwaters but the total demand for stones is higher. When a quarry is dedicated to the project the Icelandic-type is more economical than a conventional rubble mound structure. If large stones to withstand the design wave height are not available, then a wider and more voluminous berm breakwater of the statically stable reshaped type should be considered. If the beforehand mentioned options are not possible, the feasibility of a still wider and more voluminous berm breakwater design of a dynamically stable structure may be verified. Vertical breakwater If the availability of quarried stones is limited, a caisson breakwater could be an alternative. In case both options are feasible there are some aspects to consider when selecting a sloping mound or a vertical breakwater. The vertical breakwater has a main advantage over the conventional rubble mound breakwater especially in deep water: less material is needed for constructing it. Additionally, the smaller breakwater footprint causes less impact on seabed life and also dredged material can be reused to fill the caisson, which are advantages regarding the environmental aspects. The water depth at which a caisson option becomes more economical varies according to the location, but there is a general preference for caisson breakwaters, including composite caissons, where the water depth is 15 m or more (CIRIA/CUR/CETMEF, 2007). However, the experience of the contractors should always be taken into account. The possibility of using the lee side as a quay wall is also an advantage since vessels can berth alongside the breakwater. If construction time is an important aspect caisson breakwaters could be an alternative if skilled labor is available. Furthermore, enough space for the precast yard for caissons is needed. The stability during construction is higher than the rubble mound breakwaters. In the latter case, the core could be exposed to a storm during construction and the need to protect the inner layers could Additional Master Thesis 7

20 cause delays. Since the failure of vertical breakwater is more brittle, no partial damage is admitted to the structure. Hence, the maintenance costs are usually less than compared to a conventional breakwater. However, this reduced maintenance cost does not guarantee that the total costs are less. The variations of the caisson breakwaters are described separately below. Low-mound composite breakwater: is the conventional type of caisson breakwaters. The caisson is placed on top of a relative thin stone bedding layer which is essential to stabilize the foundation against the wave force and the caisson weight. High-mound composite breakwater: this option can be more economical in deep waters. However, scouring and wave-generate impulsive pressures due to wave breaking have to be considered. This makes the low-mound composite breakwaters more common than the high ones. Horizontally composite breakwater: is composed by a caisson and concrete blocks or a rubble mound structure placed in front of it. The effects of the presence of the mound are reduced wave reflection, breaking wave force on the vertical wall and overtopping. The height of the reflected wave is also decreased. Sloping-top composite breakwater: the aim of this type of vertical breakwater is to provide a reduced wave force in a much more favorable direction on the structure. However, the sloping-top gives higher overtopping rates than a vertical wall with same crest height (Steven A. Hughes, 2002). Perforated front wall caisson breakwater: The perforated front wall has the purpose to dissipate wave energy thereby reducing wave forces and wave reflection Technical aspects Provision of quay on the lee side: vertical breakwaters can facilitate this requirement. Provision of access road: vertical breakwaters, composite breakwaters or rubble mound breakwaters with a crown wall are possible solutions. Construction time: usually vertical breakwaters are faster to construct than rubble mound breakwaters, especially in deep areas were a huge amount of stones is needed to construct the mound. Material availability: the availability of rocks can determine the decision between a vertical breakwater, a rubble mound with concrete armour units or natural stone blocks, a berm breakwater or an Icelandic-type berm breakwater. The list is ordered from the lowest to the higher availability of rock, ending with a dedicated quarry in case of an Icelandic-type breakwater. Knowhow of local companies: usually the contractors have preference for a type of structure based on previous experiences. For instance, if the company has a large portfolio of built caisson breakwaters, the tendency is to design and construct breakwaters of the same type. Also, the preference of a national developed concrete unit can induce the selection of a specific breakwater type Economic aspects The economic aspects can influence the decision on safety levels of the structure. In some countries, where interest rates are high, it can be wiser to construct a structure with lower safety requirements and save funds for repairs that may be necessary during structure lifetime, instead of investing more in the initial project. However, the decision of having frequent repairs of the structure influences the choice of the breakwater type. Vertical breakwaters have a more brittle kind of failure which doesn t allow for small repairs. Additionally, repair of caissons, depending on the damage, is not an easy task. Sometimes Economic Optimization of Breakwaters 8

21 removal of the damaged caisson and replacement for a completely new one is needed. When no spare caisson is available and considering that the repair operation itself is already time consuming, the downtime due to damage/failure might be significant and can lead to high economic losses. Alternatively, rubble mound breakwaters have a more ductile failure mode, allowing for more time to repair before complete failure, especially for natural blocks armour layer. Concrete armour units, particularly the ones that are applied in single layers, can increase the damage rate being the ductile nature reduced. Therefore, if an option for reducing the safety level and allowing repairs during the lifetime is made, a rubble mound breakwater is preferred to a vertical breakwater. The functionalities of the breakwater have to be guaranteed by the layout of the breakwater, the breakwater type and the structural design of its cross section. As already stated, the layout of the breakwater is not discussed in this report. With respect to the selection of the breakwater type, usually few alternatives are selected by eliminating clearly unfeasible options. The most promising alternatives should be economically optimized and the results should be compared in order to assess the best solution. A breakwater design is considered optimum when it results in a structure that meets the requirements at minimum total cost. Two methods for economic optimization are introduced in the following sections. The first method was applied in Part II of this report (Case study) and will be explained in more detail. The second method, which considers a full probabilistic economical optimization, is concisely presented. Additional Master Thesis 9

22 2.2. Economic Optimization of Breakwaters The total cost is defined as the cost of construction plus the anticipated damage and economic loss due to failure of the structure. When designing a structure, the return period has to be established and the respective design wave should be determined. Given that the design wave is a stochastic value, there is always a probability of this value to be exceeded. An increase of the design wave value leads to a raise on the costs of construction. Nevertheless, by selecting a higher design wave, the probability of exceedance of this new value is reduced hence the capitalized anticipated damage and economical losses become smaller. The sum of these values (cost of construction plus capitalized anticipated damage and economic losses) is calculated in order to identify the optimum design wave at which the total costs are minimized. Figure 2-1 presents graphically the functions of construction costs (C C ), capitalized anticipated damage (C D ) and the total cost (C). Costs C Costs of construction (C C ) Capitalized anticipated damage (C D ) Total cost (C) C(H) =C C (H) +C D (H) C C C D H o Design wave height (H) Figure 2-1 Total costs as a function of the design wave height. The optimum design wave height gives the minimum total cost and is represented by H o. The two dashed purple lines are equidistant from H o. It can be noticed that when designing a safer breakwater, the construction costs are higher but the associated damage is lower resulting in a slightly more expensive project. However, when the breakwater is designed for a more vulnerable situation, the construction costs are lower nevertheless the damage costs are considerably higher resulting in an even more expensive project. Usually this is the total cost curve (C) behavior: at the left side of the optimum point the total cost decreases rapidly while at the right side it increases gradually. Hence, it is better, financially speaking, to be at the safer side. This optimization method is especially good when ranking structures of the same type, since for example errors in construction costs or damage are incorporated equally for all alternatives. When different breakwater types are compared, the optimum design wave height can be considerably different for every case due to the differences in failure modes. For example, a caisson breakwater would result in a higher optimum design wave height than a conventional rubble mound breakwater due to the more brittle failure type. For rubble mound breakwater, the x axis (design wave height) can also be expressed in terms of the mass of the armour units. At relatively low values of H, natural blocks can still be used. As the design wave height increases the mass of the armour units also increases. However, due to the limit on the mass of natural blocks, at a certain point the use of concrete units becomes necessary. In Europe the limit is approximately 10 to 15 tons but it can vary significantly at other regions. For example, in Japan it is difficult to obtain rocks heavier than Economic Optimization of Breakwaters 10

23 2 to 3 tons (Matsumoto, Mano, Mitsui, & Hanzawa, 2012). The consequence of that on the C C function is a step on the costs at the natural stones mass limit, since concrete units are more costly. It is important to mention that in this study the optimum design is considered as the one with minimum total costs. However, this is not the absolute true, since the optimum design can vary for different situations. For example, in public projects the obtainment of funds is usually a hindrance, thus, any requirement for extra money in the future should be avoided. Whenever possible, expending more money at the present and preventing future outlays on repair may be a solution in this case. Changes of government and their policies may also be an obstacle for engineering projects which reinforces the decision on an initially more expensive design. When a private project is involved, it may be more appropriate to reduce initial costs at the present and invest it in order to have sufficient funds in the future to expend with potential repairs, especially when the interest rates are high. Nonetheless, for the sake of this report, the optimum is considered the minimum total cost. The calculation methods used for the constructions costs and capitalized anticipated damage are summarized in the following subsections Construction costs The construction costs can be assessed by designing cross sections that meet the functional requirements for different design wave heights (H). Each H is related to one return period. After designing the cross sections by means of a deterministic approach, the material volumes per meter of breakwater have to be calculated and used to compute the material costs. The man and equipment hours needed for constructing the breakwater and its respective costs also have to be assessed. A fixed value for mobilization and others have to be considered. The construction costs are therefore: Where: H C C (H) C CF C CV (H) C C (H) = C CF + C CV (H) Design wave height used for deterministic design Total construction costs Fixed construction costs (mobilization and others) Variable construction costs Capitalized anticipated damage and economic losses The capitalized anticipated damage has to be calculated in order to make it possible to compare different alternatives. Since the repair of the damage is a future expense, this amount has to be brought to the present and the interest rate should be discounted. Also, the probability of expending this amount in the future should be considered. There are different ways of dealing with the damage. The following scenarios can be assumed: Any damage is repaired immediately Damages are accumulated but only when the ULS is exceeded repair is done Damages are accumulated and repaired in accordance to the maintenance strategy In the first case no accumulation of damage is taken into account since repairs are carried immediately after damage. For the second case an Ultimate Limit State (ULS) is established and repairs are only made after this limit is reached. Usually the costs of repair are high and downtime costs should be taken into account. Additional Master Thesis 11

24 An example of RLS is a stage of damage which allows access of a crane on the crest of the structure (Burcharth, 2009). The damage criteria of the respective limit states should also be known. Table 2-4 presents an example of limit state damages and the respective repair strategy based on Burcharth (2009). Table Limit state damages and respective repair strategies (Burcharth, 2009). Lower boundary Upper boundary Armour damage Repair strategy Initial No damage SLS 5% No repair Minor damage SLS RLS 5-15% Major damage RLS ULS 15-30% Failure ULS - >30% Repair of the armour Repair of armour and filter 1 Repair of armour, filters 1 and 2 The maintenance strategy is drawn up based on these limit states. In the preceding example (Table 2-4) no repairs are needed while the Service Limit State (SLS) is not reached. After crossing this limit, minor repairs should be held. When a Repairable Limit State (RLS) is taken into account, this is the boundary between minor and major repairs. The latter costs more than the former but the probability of exceeding this threshold is lower. The Ultimate Limit State (ULS) is related to failure of the structure. Repairing costs as well as the economic losses due to downtime are then considered. The probability of exceeding the SLS, RLS and ULS thresholds need to be assessed to calculate the capitalized anticipated costs of repair and economic losses. The following formula is then applied (Burcharth, 2009): T L 1 C D (H) = C R1 (H) P R1 (t) + C R2 (H) P R2 (t) + C F (H) P F (t) (1 + r) t t=1 Where: H T L C D (H) C R1 (H) C R2 (H) C F (H) P R1 (t) P R2 (t) P F (t) r Design wave height used for deterministic design Design life time Total capitalized anticipated damage and economical losses Costs of repair for minor damage when SLS is exceeded Costs of repair for major damage when RLS is exceeded Costs of failure including downtime costs when ULS is exceeded Probability of minor damage in year t Probability of major damage in year t Probability of failure in year t real rate of interest Economic Optimization of Breakwaters 12

25 Different approaches can be used to assess the probabilities of minor damage, major damage and failure. One of the methods is here described. As already mentioned, in order to access the optimum solution, cross sections are calculated for different design wave heights (H). For every cross section there is a design wave height related to a no damage situation (H S0 ), damage will occur when this value is exceeded. A relation between the displacement of armour units (damage), the no damage design wave height (H S0 ) and the actual significant wave height (H S ) can be established (Van de Kreeke & Paape, 1964). Therefore, the occurrence of a certain amount of damage can be related to the probability of occurrence of a certain significant wave height. Ranges of damage can be stipulated, for example the already cited limit states and the H S associated with this damage values can be determined. For example, the probability of major damage in a certain year is the probability of occurrence of significant wave heights that cause the damage within the predefined major damage range. Referring to the examples of Table 2-4, the probability of major damage is equal to the probability of occurrence of significant wave heights which causes damage in the range of 15 to 30% of displaced units. In this way, the probabilities of initial damage, minor damage, major damage and failure can be assessed. The optimum design can then be determined from the minimization of the total costs function (Figure 2-1) Full Probabilistic Economic Optimization of Breakwaters In the previous approach, the cross-section design for each design wave height is obtained by a deterministic calculation and the only failure mode considered is the armour layer instability. In the Full Probabilistic Economic Optimization, other design variables such as crest height, the water depth at the toe and others can also be optimized. Every combination of these design variables (usually geometry properties) gives a different total construction cost and total failure probability, which is determined by a reliability analysis. The analysis combines individual failure modes such as excessive overtopping, toe instability, excessive wave transmission and others. The optimum design is obtained by the minimization of the total costs as a function of the design variables that are being optimized. The total costs in this approach are also the construction costs plus the expected costs of failure. A list of publications where the full probabilistic economic optimization method is applied for different breakwater types is given below. Rubble mound breakwaters: Viet, Verhagen, Vrijling and van Gelder (2008) Composite breakwaters: Castillo, Mínguez, Castillo and Losada (2006) Vertical breakwaters: Voortman (1997). Additional Master Thesis 13

26 PART II (Case Study) NORTHERN BREAKWATER PORT OF CONSTANTZA

27

28 3. CASE STUDY DESCRIPTION The city of Constantza is located in the Dobruja region of Romania, on the western Black Sea coast, 185 miles from the Bosphorus Strait. Constantza is an ancient metropolis; its history started some 2,500 years back, and is today the third largest city in Romania. The Port of Constantza is the Romania s largest sea port. It is located at the crossroads of the trade routes linking the markets of the landlocked European countries to Transcaucasus region, Central Asia and the Far East. The port has connections with the Central and Eastern European countries through the Corridor IV (rail and road), Corridor VII - Danube (inland waterway), to which it is linked by the Danube-Black Sea Canal, and Corridor IX (road), which passes through Bucharest. The Danube-Black Sea Canal connects Port of Constantza to the TEN-T (trans-european transport network) Rhine/Meuse-Main-Danube inland waterway. The port covers 3,926 ha, of which 1,313 ha is land and 2,613 ha is water. The two breakwaters located northwards and southwards shelter the port. The present length of the North breakwater is 8,344 m and the South breakwater is 5,560 m. Constantza Port has a handling capacity of over 100 million tons per year and 156 berths, of which 140 berths are operational. The total quay length is km, and the depths range between 8 and 19 meters. This case study focuses on the Northern breakwater, particularly the so called offshore breakwater which was built between 1976 and Figure 3-1 presents the location of the study area. Offshore Breakwater Extension 1.100m Figure 3-1 Location of the study area. In the original design the offshore breakwater should be 5,900m long. However, due to budget restrictions the project was stopped in 1990 with only 4,800m of its extension being completed. Economic Optimization of Breakwaters 14

29 Figure 3-2 View from the crown wall of the offshore breakwater. The armour layer consists of 25 tons stabilopodes at the sea side slope and 4.5 tons at the port side (Figure 3-2). In 2001, the offshore breakwater was repaired by a local company as part of the Constantza Port Rehabilitation Project. The repair was done by replacing the removed units with new or reused stabilopodes of the same dimensions as the initial ones. Additionally, 15 tons Antifer cubes were placed at the toe of the sea side slope at highly damaged locations. On February 2013 the Romanian Ministry of Transport has awarded Van Oord the contract to complete the project. The remaining 1,100m of the offshore breakwater is currently being constructed by Van Oord. The aim of this project is to enhance the Romania s national port commercial role by delivering the wave protection needed and improving safety conditions for the ships entering the port. The existing part of the northern breakwater is however damaged. The goal of this case study is to perform an optimization of the maintenance costs, identifying the less costly maintenance strategy. In order to do so the following steps were performed: The breakwater was divided into segments with similar hydraulic boundary conditions. Information on the Constantza Port Rehabilitation Project (from 2001) was analyzed in order to understand the damage processes. Damage models were implemented and compared with the existing data. Maintenance strategies were proposed and optimized. Conclusions and recommendations are given. These steps are described in the following chapter. The data provided by Van Oord to be used in the case study is listed below: Design wave conditions of the northern breakwater extension project. Original cross-section of the offshore breakwater. As-built drawings of the Constantza Port Rehabilitation Project from Additional Master Thesis 15

30 4. METHOD APPLIED ON THE CASE STUDY 4.1. Introduction First of all, in paragraph 4.2, the hydraulic boundary conditions were verified by analyzing the design wave conditions report prepared by ARCADIS to Van Oord (ARCADIS, 2013), which is referent to the offshore extension breakwater project. Then, the section of the existing offshore breakwater to which this same boundary condition is applicable was selected based on the As-built elevations (paragraph 4.3). This selection was validated analyzing the damage repaired in 2001, which was checked at the entire breakwater extension. After having selected the breakwater section, the origin of the damage repaired in 2001 was investigated (paragraph 4.4). The first examined hypothesis was that one storm had caused the damage at the offshore breakwater. The second analyzed hypothesis was that the not a single storm resulted in the witnessed damage but the accumulation of damage since the end of its construction (1990). The probability of the actual damage repaired in 2001 to occur in 11 years of damage accumulation was checked. Other hypotheses for the damage were raised. In paragraph 4.5 the maintenance strategy is introduced. The costs of repairing the damaged breakwater and of rebuilding a new one in case of failure were estimated (paragraph 4.5.1). Simulations of damage evolution were run and the maintenance strategies were applied (paragraph 4.6). In order to assess the optimum strategy, the costs of each simulated repair were discounted and added over a period of 100 years (total costs). The probabilities of exceedance of the total costs were assessed for every different repair threshold. Finally conclusions recommendations are given in paragraph 5. Economic Optimization of Breakwaters 16

31 4.2. Design wave height return period The Peak over Threshold approach was applied by ARCADIS to derive the extreme offshore conditions which were fitted by a Weibull distribution. The probability of exceedance for the direction section with the most severe significant wave heights is presented in Figure 4-1 (from ARCADIS, 2013, page 22). Figure 4-1 Weibull fit applied for directional sector 45 N~75 N on wave height. The propagation to the nearshore was carried out with SWAN 2D. The maximum wave height at the toe of the structure was obtained in a location with 22.7m depth, for waves with offshore incoming direction of 60º (being 0ºN and 90ºE). Combining the results of the distribution fitting and the wave propagation, the information given in Table 4-1 was derived (ARCADIS, 2013). Table 4-1 Offshore and nearshore design wave characteristics for different return periods (adapted from ARCADIS, 2013). Return Offshore Nearshore period dir Hm0 Tp Hm0 Tm-1,0 Tp Dir (yr) ( N) (m) (s) (m) (s) (s) ( N) Additional Master Thesis 17

32 Considering this information and the parameters of the Weibull distribution for offshore significant wave heights, Figure 4-2 was derived. It illustrates the return period of the offshore conditions and the associated nearshore conditions (between brackets). Figure 4-2 Return period of the design wave height (m). Nearshore values presented between brackets. The design wave condition considered in the offshore breakwater extension is indicated by the dashed red lines. In the current study, these wave statistics were used in the attempt to reproduce the offshore breakwater damage repaired in 2001, as well as to make damage predictions Selection of the section to be analyzed As previously mentioned, the wave statistics were obtained at a location with a depth of 22.7m. Since the wave conditions are strongly related to the bathymetry (wave-topography interactions) the preceding results cannot be applied to the entire offshore breakwater. In shallower sections of the breakwater the design wave conditions are probably less severe. As-built drawings of the offshore breakwater were provided by Van Oord. The cross-sections (every 10m) contain valuable information on the elevations and the number of concrete units that were used for the Rehabilitation Project in An example of these as-built drawings can be visualized in Figure 4-3. The armour layer at the sea side slope is composed by stabilopodes of 25 tons (Figure 4-4). The stabilopodes have a shape similar to the tetrapods except for the protuberance located at the tip of its legs. Since no geometry relations are known for the stabilopodes, the cube length is approximated to that corresponding to a tetrapod. For a 25 tons tetrapod the nominal diameter is equal to 2.22 m. This value is used also for the stabilopodes under consideration. Economic Optimization of Breakwaters 18

33 Figure 4-3 Example of available As-built drawing. Additional Master Thesis 19

34 Figure View from the Crown Wall of the offshore breakwater around km Stabilopodes 25 tons. From the as-built drawings, the water depth at the toe of the structure and the crest level were obtained. This information is presented in Figure 4-5. Figure 4-5 As-built elevations of the existing Offshore Breakwater. Economic Optimization of Breakwaters 20

35 The green line represents the depth at which the nearshore wave conditions were derived. The orange dashed line is an offset of 5m from the design wave depth. The dashed vertical black line shows the limit of the selected breakwater section to be analyzed (from km to km 4+800). The maintenance strategy of these 2800 meters of the offshore breakwater is optimized in this case study. Other information obtained with the as-built drawings was the number of stabilopodes that were replaced during the rehabilitation project in This number was obtained for strips of 10m of breakwater and was translated into number of replaced stabilopodes within a strip of one nominal diameter (D n ) in order to compare the measured values with the damage level (N od ) considered in the breakwater design formulas. Figure 4-6 presents the number of replaced stabilopodes within a strip of one nominal diameter (D n ) at the sea side slope of the offshore breakwater. Figure 4-6 Number of replaced stabilopodes within a strip of one nominal diameter (D n ). The blue dots represent the information given every 10 meters. The red crosses are averages over 500m. The horizontal thick black line gives the average for the selected breakwater section. The average is equal to 3.6 replaced units every 2.22 m. The observed damage of the sea side slope before the rehabilitation is considered to correspond to a N od of 3.6. This value represents 162 removed units in 100m of breakwater and 4540 removed units at the considered breakwater section (2800m). Additional Master Thesis 21

36 4.4. Causes of the observed damage in 2001 After having selected the breakwater section, the origin of the damage repaired in 2001 is investigated. The first examined hypothesis is that one storm had caused the damage at the offshore breakwater. The second analyzed hypothesis is that the not a single storm resulted in the witnessed damage but the accumulation of damage since the end of its construction (1990). Other hypotheses for the damage are also raised. In order to verify the first hypothesis, the wave height that the breakwater can stand (in terms of armour layer stability) was calculated. Since no formulations for the design of breakwaters using stabilopodes was indentified, and taking into consideration the already mentioned shape similarity with tetrapods, the design formulas derived for tetrapods are applied to the stabilopodes in this case study. The use of tetrapode formulas is an approximation and possible discrepancies are not investigated in this study. The well-known formulae for tetrapods by Van der Meer (1988) valid for surging waves and by De Jong (1996) for plunging waves were applied. However both formulas are valid for a slope angle of 1:1.5. The stability formula proposed by Suh and Kang (2012) for tetrapods which incorporates the slope effect was also applied. Figure 4-7 copied from the original project of the offshore breakwater shows for the sea side a slope angle of 4:7 or 1:1.75. Figure 4-7 Original design of the offshore breakwater cross-section. The as-built drawings were also used to measure the actual (2001) sea side slope. Some cross sections slipped resulting in a gentler slope and others are even stepper than in the original project. The slope angles range from 1:2.5 to 1:1.4 with an average of 1:1.73, so the original value of 1:1.75 can be adopted. Stability formula for tetrapods (Van der Meer, 1988), valid for surging waves only (Van der Meer, 2000): 0,5 H S 0,2 = 3,75 N od D 0,25 n N s om Z Economic Optimization of Breakwaters 22

37 Stability formula for tetrapods (De Jong, 1996), valid for plunging waves: 0,5 H S = 8.6 N od D 0,25 n N s om 0,2 Z With: H S Significant wave height N od Number of units displaced out of the armour layer within a strip of one D n N z Number of waves D n Nominal diameter Δ Relative mass density s om Wave steepness, s om = 2πH s gt2 p Stability formula for tetrapods (Suh & Kang, 2012) incorporating slope effect: 0,5 H S = max 9.2 N od D 0,25 n N ξ m 0,4, 5.0 N od 0,25 Z N (cot θ)0.45 ξ 0,4 m Z 0,5 With: ξ m Surf similarity or breaker parameter, ξ m = θ Slope angle tan θ H s L0 and L 0 = gt m 2 2π Suh and Kang (2012) stability equation only differs from those of Van der Meer (1988) and De Jong (1996) by the slope angle term and the first coefficients which are slightly larger. The transition from plunging to surging waves can be calculated using: ξ mc = 9.2 N 0,5 od 0,25 N Z 5.0 N 0,5 od 0,25 N (cot θ)0.45 Z 1.25 The relative density is equal to 1.26 for a water density of 1018 kg/m³ and concrete density of 2300 kg/m³. The nominal diameter is 2.22m. Relations for the significant wave height (H s ) and periods (T p and T m ) were obtained using the values of Table 4-1. The number of waves (N z ) was calculated based on a storm duration of 6 hours and the wave period. Iterations were performed in order to obtain the design wave height equivalent to different values of damage (N od ) considering the preceding formulas. The results of these calculations are summarized in Table 4-2. Gray cells correspond to plunging waves and white cells to surging waves. Additional Master Thesis 23

38 Table 4-2 Values of significant wave height in meters (m) for different damages N od. Nod VDM and De Jong Suh and Kang Taking into account the slope effect a higher wave is needed to result in the same damage, therefore a more stable situation seems to occur. However, the more conservative results given by Van der Meer (1988) and De Jong (1996) are chosen to be used. For the no damage criterion a significant wave height of 5.84m is given. The return period of this wave is about 17 years (Figure 4-8). Nevertheless, no damage at all is a very strict criterion (Van der Meer, 2000). A N od of 0.5 is suggested as a more economical criterion. The significant wave height in this case is 7.19m with a corresponding return period of about 77 years. This value is much closer to the design wave height of the breakwater extension (7.5m and 100 years). The result given for a N od equal to 3.6, representing the damage repaired by the rehabilitation project in 2001, is a 10.80m significant wave height with a return period of more than 4000 years (Figure 4-8). Evidently, this was not the wave condition that caused the damage to the breakwater. If such a significant wave height happened between 1990 and 2001 this event would be in the dataset used to derive the design wave height for the breakwater extension and the distribution would be different resulting in a much smaller return period for the same value of significant wave height. Figure 4-8 Significant wave heights, return periods and associated damage. Given the excessively high value of significant wave height required to cause the damage repaired in 2001, the hypothesis that one storm has originated the damage is discarded. Economic Optimization of Breakwaters 24

39 Cumulative damage The second hypothesis, which considers the accumulation of damage given by subsequent waves, is now evaluated. The formulas of Van der Meer (1988) and De Jong (1996) were obtained for a unique event, the slope was rebuilt after each test. With the purpose of using the same formulas to consider the cumulative effects of multiple events, Van der Meer (2000) propose the following procedure: 1. Calculate the damage for the first wave condition. 2. Calculate for the second wave condition how many waves would be required to give the same damage as caused by the first wave condition. 3. Add this number of waves to the number of waves under the second wave condition. 4. Calculate the damage under the second wave condition with the increased number of waves. 5. Calculate for the third wave condition how many waves would be required to give the same damage as caused by the previous wave conditions and so on. However, the existing formulas are only valid for numbers of waves between about 700 and 5000 (Van der Meer, 2000). This limitation was ignored in this study case. First of all, the number of storms per year has to be known. The same interval between storms over the threshold (H s = 2m) considered to determine the return periods of the design wave is used to determine the number of storms per year. The average interval is 6.5 weeks, which gives on average 8 storms per year. Since there is no information about other repairs realized between 1990 and 2001, about 88 storms occurred during this period and the damage caused by each of these storms is calculated and accumulated. A significant wave height series of 100 years, with 8 storms per year, is randomly generated as a function of the Weighbull distribution. Only waves higher than 5.84m (which is the limit for no damage) are considered from this point onwards. The increase in damage is set to zero for waves smaller than this limit. The number of waves needed to cause the accumulated damage (associated to the previous wave conditions) with the actual wave condition is calculated using the following formulas: For surging waves: N Z = 3,75 max N od(yr 1), N od (i 1, yr) 0.5 H S 0,2 D n s 0.85 om 4 For plunging waves: N Z = 8.6 max N od(yr 1), N od (i 1, yr) 0.5 H S 0,2 D n s 3.94 om 4 The total number of waves to be used in the accumulated damage calculation is obtained with: N z = N z (i) + N z Additional Master Thesis 25

40 N Z (i) is calculated for a storm duration of 6 hours and the period associated to the significant wave height. In the case of the first wave condition, N Z is equal to zero given that the starting damage is also zero. The accumulated damage can now be calculated with the stability formulas of Van der Meer (1988) and De Jong (1996) for surging and plunging waves respectively. The maximum result is saved and used in the calculations of the next wave condition. The general calculation flow of this procedure for one lifetime cycle (100 years) is presented in Figure 4-9. Significant wave height distribution yr = 1 to 100 i = 1 to 8 Hs(i,yr) Hs(i,yr) > 5.84 NO YES N od (i-1,yr) > N od (yr-1) NO YES Equivalent wave number N z required to Hs(i,yr) to cause accumulated damage N od (yr-1) Equivalent wave number N z required to Hs(i,yr) to cause accumulated damage N od (i-1,yr) N z = N z (i) + N z N od (i,yr) = máx (N od (plunging), N od (surging)) N od (yr) Plunging and surging equations. N od after one lifetime cycle Economic Optimization of Breakwaters 26

41 Figure 4-9 Calculation flow for one lifetime cycle. Matsumoto et al. (2012) performed a similar calculation for accumulation of damage on horizontally composite breakwaters. They state that the expected value of N od can be calculated by repeating the process more than 2,000 times. As a first estimate 5,000 repetitions of the lifetime cycle (100 years) were simulated. The number of runs was doubled to 10,000 samples presenting the same result. Since the calculation time did not increase significantly, the results obtained with 10,000 samples were used. This large number of repetitions is considered to properly account for the stochastic behavior of storm intensities over time. An example of cumulative damage results for 10,000 samples is shown in Figure Figure 4-10 Cumulative damage in 100 years (10000 runs). The statistics of the accumulated damage can be derived from those simulations. Figure 4-11 shows the probability of damage occurrence in time, starting in The repair performed in 2001 is not included in these simulations. Therefore, results for accumulated damage after 2001 should not be derived from this graph. Additional Master Thesis 27

42 Figure 4-11 Probability of damage occurrence in time The vertical dashed black line represents year The probability of having damage equal or greater than 3.6 in that year was about 7%. In other words, 7% is the probability that the damage repaired in 2001 was caused by hypothesis 2 (damage accumulation). Despite of the small probability, this hypothesis cannot be discarded. In the following section more factors that could have contributed to the damage witnessed in 2001 are presented. Economic Optimization of Breakwaters 28

43 Other possible damage contributors In the previous calculation for damage accumulation the breakage of the stabilopodes was not accounted for. However, this issue can have an important contribution to the damage. Once the concrete units start to break they become more susceptible to movements due to their decreased weight. Further, the smaller parts that are detached from the concrete units can easily be moved and induce even more breakage when shocking with other units. The protuberance located at the tip of the stabilopodes legs can be considered an unfavorable component since the extra weight far from the center of mass favors rocking hence breakage. Additionally, this kind of geometric discontinuities can result in stresses concentration, being the protuberance a weak spot. Even though this particular form may increase interlocking between blocks, the disadvantages might probably prevail. Figure 4-12 is a snapshot of a movie registered during the visual inspection of the northern breakwater held in 21/05/2013. It can be seen that many stabilopodes are broken, especially around the water line. Additionally, some freshly broken parts can be identified (blue arrow). The inclusion of the breakage effect to the damage accumulation would probably lead to a more rapid increase in the damage with time. Figure 4-12 Snapshot of visual inspection video. The quality of the concrete is also a factor that can contribute to the breakwater damage. In this study, only the density of the concrete is included, hence, other concrete properties are not taken into account. Figure 4-13 presents a closer view to the 25 tons stabilopodes at the sea side slope of the offshore breakwater. Additional Master Thesis 29

44 Figure tons Stabilopodes at the sea side of the offshore breakwater. The as-built drawings also provide interesting data on other possible failure modes. It is possible to check how the slope has adapted from the original situation to the one observed in For example, looking at the number of Antifers that were placed at the toe of the sea side slope to support the replaced stabilopodes can give an idea of the locations where the profile has significantly changed. This could have happened due to either toe instability or slope instability. The number of 15 tons Antifers placed at the toe of the sea side slope was quantified and compared with the number of stabilopodes replaced at the same location. Figure 4-14 shows the number of replaced stabilopodes and placed Antifers every 10m at the offshore breakwater. It is noticed that the location of the stabilopodes peaks indeed coincides with the Antifers peaks indicating that significant changes in the profile (damage) happened at those crosssection. The slope stability and toe instability failure modes could be better investigated in order to improve the prediction of future damages. It is likely that it was not a single storm which caused the damage observed in Rather, it is more plausible that a combination of the second hypothesis (accumulated damage) and some other factors like breakage and toe instability were the causatives of the damage. Assuming that the rehabilitation project in 2001 has eliminated the toe and slope instabilities, the method for accumulation of damage will be applied to predict future damage and to optimize the maintenance strategy of the offshore breakwater. For the sake of simplicity the units breakage contribution was not included in this case study. A description of possible maintenance strategies is introduced in the next section, followed by the costs estimate and the choice of the optimum strategy. Economic Optimization of Breakwaters 30

45 Figure 4-14 Number of stabilopodes replaced at the sea side slope and antifers placed at the toe of the sea side slope. Additional Master Thesis 31

46 4.5. Maintenance strategy The maintenance strategy is based on the repair strategy given for different damage levels together with a predefined threshold for repair. The damage levels were based on (Burcharth, 2009), Table 2-4. The damage was translated from percentage of armour units to N od (number of displaced units within a strip of the breakwater length corresponding to the width of one nominal diameter). Table 4-3 presents the damage levels and respective repair strategies adopted. Table 4-3 Limit state damages and respective repair strategies (adapted from Burcharth, 2009). Lower boundary Upper boundary Damage N od Repair strategy Initial No damage SLS 0<Nod<0.5 No repair Minor damage SLS RLS 0.5 Nod<2.5 Major damage RLS ULS 2.5 Nod<5 Failure ULS - 5 Repair of the armour Repair of armour and filter 1 Repair of armour, filters 1 and 2 For minor and major damage, the repair is done in the traditional way, as it was done in 2001, replacing the damaged stabilopodes with new ones. Nevertheless, different aspects have to be considered when maintaining and repairing breakwater armours then when constructing a new one. Ensuring interlocking in between the newly placed units and the ones already present in the damaged breakwater is a challenge.it is known from experience with dolos breakwaters that repairs performed using similar dolosse in structures with broken dolos units has shown unfavorable results (Turk & Melby, 1997). No information about the performance of stabilopode breakwater repairs is available, however it might be expected that when the damage is too large, repairing the breakwater with similar stabilopodes may not be the best solution. Thus, when failure occurs, repair is done by removing all the stabilopodes and replacing them with a new Core-Loc single layer armouring. The choice for the Core-Loc elements was made because these blocks have shown favorable results when used for repairing damaged dolosse breakwaters. Additionally, they seem to be less sensitive to strict placing rules, indicating that repairs of local damages could be easier with Core-Locs (Van der Meer, 2000). Therefore, repair of the failed segment can be performed with Core-Locs in such a way that the interlocking feature with the adjacent segments is maintained. Since Core-locs are applied in a single layer it is also a more economic solution than other double layer concrete units. The preceding limit state damages can be combined with a threshold that gives the limit for the decision of carrying out or not a repair. For example, every time that the damage in the breakwater exceeds the value of 1, repair will be done (the repair threshold in this example is set to 1). If the damage is equal to 1.5 the costs of repair are associated to minor damage costs. If the damage is 3, the costs of repair are calculated based on major damage costs. If the damage is higher than 5, the cost of repair is equal to the failure cost. Although, the threshold for repair can also be selected as 5 (repair is only done in case of failure). In this case, the repair cost is equal to the cost of reconstructing the entire armour layer. Economic Optimization of Breakwaters 32

47 The total lifetime cost of different threshold possibilities is evaluated later in this report. First, functions for the costs of minor damage, major damage and failure are derived Costs In 2004 Jan Wagner performed a research on costs of armour units. His objective was to find the most economical armour unit for the armour layer of the breakwaters of IJmuiden. It was investigated the total costs of construction of three different armour units, consisting of the production costs and the placement costs. The production costs is of the costs of moulds, storage area, equipment, labour and material costs, being the concrete costs the main share of it (Wagner, 2004). His work was used as the base for the repair costs estimation. The costs of minor repair were approximated as follows: 1. The concrete volume and costs per unit were calculated; 2. The production costs were estimated as 15% of the concrete costs; 3. The placement costs were estimated as 20% of the concrete costs; 4. The costs of moulds were estimated as 10% of the concrete costs. The concrete price was estimated in 2014 in 125 per m³. Since placement, production and moulds costs are calculated as percentages of the concrete costs, no correction in the prices has to be done. Major damage includes, aside from the concrete units replacement, the repair of the first filter layer. In order to account for this additional cost, the total cost per block unit associated to minor repair was multiplied by a factor 1.5. Those are the variable costs of repair (minor and major) which are dependent on the damage level (N od ). Additionally, a fixed cost for mobilization and demobilization is considered. This cost was obtained from Wagner (2004) and corrected to present value. Table 4-4 presents the results of the costs estimate for minor and major repair. Table 4-4 Repair costs estimate Minor repair Stabilopode 25t unit per unit per block concrete 11 m³ 125 1, production 1 unit placement 1 unit moulds 1 unit total per block 2, , Major repair per block total per block (Minor repair) 2, additional factor due to filter repair 1.5 3, total per block (Major repair) 3, Fixed costs per unit per repair mob. + demob. 1 unit 1,200,000 1,200, Additional Master Thesis 33

48 Notice that these costs correspond to Dutch prices. They may differ from Romanian prices. However, since the optimum repair threshold is aimed to be selected, the difference in prices would be included in all different simulations, so the pattern of results is assumed to be preserved. The functions used to calculate the costs of damage are as follows. If N od is larger than 0.5 and smaller than 2.5: C minor_repair = L N od D n If N od is larger than 2.5 and smaller than 5: C major_repair = L N od D n With: L Length of the breakwater (2810m) N od Number of units displaced out of the armour layer within a strip of one D n averaged over L D n Nominal diameter (2.22m) In order to estimate the failure costs,he design of a new armour layer composed by a single layer of Core-Loc blocks was performed considering the design wave height of the breakwater extension (7.5m). The crest level was maintained as in the existing situation. A Hudson type formula is used to estimate the concrete armour unit stable weight. H S = (K D D cot α) 1 3 n50 With: K D Stability coefficient α Slope angle M 50 Mass of Core-Loc armour unit M 50 = ρ c (D n50 ) 3 Equivalent length of cube having same mass as Core-Loc, D n50 D n50 = M 50 ρc 1 3 Turk and Melby (1997) recommend a stability coefficient of 16 for trunk sections. This value is valid for slopes from 1V:1.33H to 1V:2H. They also state that this coefficient should give a conservative estimate and that final designs should be validated with three-dimensional physical models replicating local bathymetry and actual design wave conditions and directions. Considering a slope of 1:1.5 a stability number of 2.88 and a D n50 of 2.06m are obtained. The Core-Loc design guide table was used to select the standard cube that is immediately larger than the calculated one. That is a 10m³ Core-Loc with a D n50 of 2.15m. The reverse calculation was performed in order to assess the highest wave that can be stand with these blocks for the no damage condition (7.8m) and for the failure condition (8.5m). The failure condition was obtained by considering a under prediction of 10% in the wave height and using a safety factor of 1.3 (Van der Meer, 2000). Therefore, after reconstructing the breakwater, an 8.5m significant wave height is considered to cause a new failure in the breakwater. Economic Optimization of Breakwaters 34

49 According to the Core-Loc design guide table the number of units per square meter for this specific block is equal to (u/m²). With that information and the surface area of the breakwater, the total number of units needed for the reconstruction of the breakwater is obtained. The volume of the filter layer that has to be placed as well as the volume of the old filter layer that has to be removed were also assessed. Figure 4-15 shows in a cross-section where these removals are required. Figure 4-16 shows a sketch of the new cross-section. Figure 4-15 Stabilopodes and filter layer to be removed. Additional Master Thesis 35

50 Figure 4-16 Cross-section used for the breakwater reconstruction. The underlayer stone weight is in the order of one-fifth of the weight of the overlying unit as recommended by Steven A. Hughes (2002a) which results in a HM A stone class. The costs of failure were estimated as shown in Table 4-5. The cost for removing concrete units was considered twice the price of placing it. Table 4-5 Calculation of reconstruction costs Reconstruction of the Breakwater Removal per unit Stabilopode 25t unit 1,100 24,200, removal 1 unit 1,100 1, per unit 2-4 ton ton 110 6,149, removal 1 ton Construction per unit Core-Loc 23t unit 1,820 43,680, concrete 10 m³ 125 1, production 1 unit placement 1 unit moulds 1 unit total per unit 1, mob. + demob. 1 unit 1,200,000 1,200, Quarry material per unit HM A ton 77 31,408, ton 1 ton transport 1 ton placing 1 ton total per ton mob. + demob. 1 unit 1,200,000 1,200, TOTAL Variable costs 105,437, Fixed costs 2,400, Total 107,837, ,000, No downtime costs are considered since there are no quays on the lee side of the breakwater at the section that is being studied. Assessing the probability of blocking the access channel of the Port is out of the scope of this study. Additionally, the construction time is not taken into account neither the probability of failure during construction. If N od is larger than 5 (failure) the following formula applies: C failure = 108,000,000 Economic Optimization of Breakwaters 36

51 4.6. Optimization of the threshold for repair The optimization of the costs of maintenance for a period of 100 years starting in 2014 is presented in this section. As a starting point, the actual damage in 2014 has to be assessed. The cumulative damage model derived in paragraph is used to accumulate the damage from 2001 since no repairs were conducted after the rehabilitation project. Figure 4-17 presents the results of the damage accumulation starting in 2001 with no damage. The probability of exceedance of damages that are boundaries of the damage levels is shown in time. Figure 4-17 Probability of damage occurrence in time. The dashed black vertical line represents year The blue line represents the probability of occurrence of a damage larger than 0 (90% in 2014). The red line shows the probability of having a damage greater than 0.5 (~ 60% in 2014), the magenta line greater than 2.5 (~15% in 2014) and the green line greater than 5 (<5% in 2014). It is very likely that the damage in 2014 is higher than 0.5. The next two figures help to identify how much larger this damage could be. Figure 4-18 shows the probability of occurrence of the maintenance strategy damage levels. In 2014 the highest probability is that a minor damage (blue line) is present (0.5 N od <2.5). However, there is still a lot of difference between a damage of 0.5 and 2.5.Figure 4-19 zooms in the damage between 0 and 2. The blue line shows that the highest probability for 2014 is a damage level between 0 and 0.5. Therefore, based on the results of the given accumulation damage model, the damage value of 0.5 is assumed to be the current N od at the northern breakwater (2014). Additional Master Thesis 37

52 Figure 4-18 Probability of damage level occurrence in time Figure 4-19 Probability of occurrence of damage between 0 and 2 Economic Optimization of Breakwaters 38

53 From this starting point (2014 with N od = 0.5) 10,000 simulations of 100 years with 8 stochastically generated storms were performed for every selected threshold for repair. In total 41 thresholds for repair were simulated from 1 to 5 varying by 0.1. Every time that the accumulated damage exceeds the threshold, the simulated N od value is applied to the formulas derived in the previous paragraph for the costs. It is important to highlight that after a reconstruction is carried, the cumulative damage model changes. For the Core-loc breakwater no damage is computed and waves higher than 8.5m cause a new failure. Some examples of those simulations are given in the next figures. Figure 4-20 shows the damage accumulation when a threshold for repair of 1 N od is selected. For this specific simulation, around year 2060 failure occurs. Before that, the repair threshold was crossed 3 times. Notice that after a reconstruction no damage occurs again. In other words, no waves higher than 8.5m occurred in this simulation after the reconstruction was carried out. Figure 4-21 presents the costs of repairs and reconstruction related to this simulation. Additional Master Thesis 39

54 Figure 4-20 Example of lifetime simulation results - repair threshold equal to 1. Figure 4-21 Maintenance costs given the previous cumulative damage. Economic Optimization of Breakwaters 40

55 Figure 4-22 presents one of the simulations run with a repair threshold of 3 N od. The respective costs are given in Figure In this particular simulation, no failure has occurred and in 100 years two repairs were done when the damage was higher than 3. Figure 4-22 Example of lifetime simulation results - repair threshold equal to 3. Figure 4-23 Maintenance costs given the previous cumulative damage. Additional Master Thesis 41

56 Figure 4-24 shows a particular simulation run with a repair threshold of 4 N od. In that specific run failure occurred around year The related costs are presented in Figure Figure 4-24 Example of lifetime simulation results - repair threshold equal to 4. Economic Optimization of Breakwaters 42

57 Figure 4-25 Maintenance costs given the previous cumulative damage. In order to demonstrate other possibilities, Figure 4-26 shows another simulation run with the same threshold repair which resulted in two failures of the breakwater. It was reconstructed near year 2020 and failed again around The probability of such a situation to happen is minor and this case is only presented with the intention of indicating that when 10,000 runs are simulated all possible results are covered. Figure 4-27 show the costs of both reconstructions. Figure 4-26 Example of lifetime simulation results - repair threshold equal to 4. Additional Master Thesis 43

58 Figure 4-27 Maintenance costs given the previous cumulative damage. Figure 4-28 shows one simulation result when the threshold of 5 is set. For this specific threshold no repair with stabilopodes is done. Only when failure occurs the breakwater is reconstructed with Core-Locs. The costs related to the presented simulation are given in Figure Economic Optimization of Breakwaters 44

59 Figure 4-28 Exam ple of lifetime simulation results - repair threshold equal to 5. Figure 4-29 Maintenance costs given the previous cumulative damage. Many other situations, different from the presented ones, can occur. For example, there is also the possibility that no expenses occur in 100 years. This example is shown in Figure In this simulation, the selected threshold of 5 was not exceeded in 100 years, thus, no maintenance costs are associated with this run. Additional Master Thesis 45

60 Figure 4-30 Cumulative damage for repair threshold equal to 5. In order to assess the most economic (optimum) threshold the costs of every simulation were discounted and added over the entire simulation period (100 years) resulting in the total lifetime cost. This procedure was repeated for different interest rates (2, 3 and 4%). For the interest rate equal to 2%, 100,000 simulations were run and the median results were compared with those of 10,000 simulations in order to investigate if 10,000 runs were enough. No significant differences were found between the results obtained with 10 thousand or 100 thousand runs, hence 10 thousand simulations were considered sufficient and the results could be evaluated. Because of the spread in the simulation results (due to the stochastic behavior of the wave climate), median and expected values are not so representative. Therefore, probability distributions of expected total costs were derived. The following figures present the results obtained. The colors represent the probability of exceedance of a certain total discounted cost. The total lifetime costs are represented by the vertical axis and the repair thresholds by the horizontal axis. The probability of exceedance can be thought as the probability that is accepted for having expenses higher the calculated value. For every selected threshold, the expected lifetime costs are higher if the acceptable chance to be exceeded is low and decrease with increasing accepted probability of exceedance. In Figure 4-31 it is possible to visualize that for all thresholds the upper limit (for which only 5% of the costs are greater) is almost the same. In other words, the probability of having extremely high costs is uniform and independent of the chosen repair threshold. Thus, no optimum threshold for repair can be selected based on an acceptable exceedance of 5%. Economic Optimization of Breakwaters 46

61 Figure 4-31 Probability of exceedance of total lifetime costs for an interest rate of 2% For an acceptable probability of exceedance of 15% a slightly increase in total lifetime costs can be noticed for higher thresholds (over 4.5). When considering a tolerable probability of exceedance of 30%, the optimum threshold for repair lays between 3.5 and 4.5. However, if the acceptable exceedance of the lifetime costs is even higher, for example 50%, by selecting a threshold greater than 4.5 there is 50% of chance that no expenditures are needed in 100 years. It can be concluded that there is not a sharp optimum threshold of repair. The selection of the optimum threshold is highly dependent on the accepted probability of exceedance. However, it is clear that acceptable exceedance below 20% (bluish values) gives roughly constant costs for all different thresholds with slightly increasing expenses for thresholds closer to the failure limit (N od over 4.2). For these acceptable probabilities of exceedance the conclusion is that any threshold smaller than 4.2 gives approximately the same expected lifetime costs. For probabilities of exceedance between 20 and 40% (greenish and yellowish values), additionally to the slightly increase of expected total lifetime costs for thresholds above 4, an increase can also be expected for lower threshold values. For these range of tolerable probabilities of exceedance, the optimum lays between 3.5 and 4.5, thus, it can be concluded that performing repairs with a damage smaller than 3.5 can lead to total lifetime costs higher than when waiting for the damage to be inside the previously mentioned optimum range. Values of tolerable exceedance higher than 50% are not reasonable so the last accepted probability of exceedance to be analyzed is 50%. In this situation, the expected total life time costs decrease almost linearly with increasing thresholds for repair. The minimum is reached when a threshold of 4.5 is applied. Based on the analysis of all acceptable probabilities of exceedance it can be concluded that the threshold that meets the optimum requirements for ranges below 20% and between 20 and 40% is a N od equal to 4. However, if a probability of having the expected costs exceeded of 50% is tolerated the threshold goes up to a N od of 4.5. Additional Master Thesis 47

62 The increase in expected total lifetime costs for probabilities of exceedance of 5 and 15% from a threshold of 4 to 4.5 is in the order of 2 million Euros (which corresponds to less than 2% of the failure costs). Therefore, it can be concluded that a threshold for repair of 4.5 fulfills the requirements of all accepted probabilities of exceedance equal or smaller than 50%. Hence, the optimum threshold for repair is a N od of 4.5. However, this damage corresponds to the major damage level and for this situation the repair is done in the traditional way, by replacing the removed stabilopodes with new ones. Nevertheless, when letting the repair threshold getting too close to the failure (N od = 5) it is recommended to reconsider the repair solution. In the given example there is a sharp transition (N od = 5) between repairing with similar stabilopodes and reconstructing the entire armour layer. In reality no sharp transition between major damage and failure exists and since a damage of 4.5 N od corresponds to the displacement of 28% of the armour units, the possibility of performing the reconstruction with Core-Locs already for this value has to be evaluated. It is recommended to monitor the damage of the breakwater and as soon as the structure either reaches the threshold of 4.5 N od or starts losing its functionality the reconstruction of the affected segment with Core-Locs should start. A N od of 4.5 corresponds to on average 220 stabilopodes removed in 100m of breakwater length. The time needed to design, to raise funds and to initiate the reconstruction should also be taken into account when deciding to start the actions. This conclusion is based on the judgment that the difference between 4.5 and 5 is relatively small (about 25 units in 100m) and for this situation it is wiser to perform the repair by reconstructing it. In reality, the threshold for failure could also be optimized. In Figure 4-32 and Figure 4-33, with an interest rate of 3% and 4% respectively, the same pattern can be noticed. Beyond the fact that the total lifetime costs have an overall decrease due to the increased interest rate, a shift of the optimum threshold to the higher values can be observed. This is evident for the 30% exceedance probability, for which the minimum values are around 4.5 for an interest rate of 3% and over 4.5 for 4% (against 3.5 to 4.5 for 2%). The threshold for which there is a probability of 50% of having no costs in 100 years is equal to 4.5 for all simulated interest rates indicating that the choice for a threshold of 4.5 is not very sensitive to changes in the interest rate. Another conclusion that doesn t depend on the interest rate is that, for small acceptable probabilities of exceedance, the expected cost is high and roughly constant for all thresholds for repair. Additionally, for tolerated chances of exceedance higher than 30%, the expected total lifetime costs increases with decreasing threshold for repair. Economic Optimization of Breakwaters 48

63 Figure 4-32 Probability of exceedance of total lifetime costs for an interest rate of 3% Figure 4-33 Probability of exceedance of total lifetime costs for an interest rate of 4%. Additional Master Thesis 49