Coastal and port structures represent a large economic investment for society during their lifetime. Therefore, there is a need for proper coastal planning and management. In order to do that, wave and current loads must be considered by determining their level where the coastal structure should resist, otherwise they may suffer extensive damage due to these environmental loads. In this study, a new frame of performance design for coastal structures which includes climate change effects is discussed as a future design methodology. Performance-Based Design considers a coastal structure’s performance determined by the amount of damage. In other words, the structure which is exposed to wave impacts should maintain its serviceability by limiting its damage, so that, its economic, operational, life-safety and environmental impacts are acceptable to the owner. The importance of this method is that it provides a possibility to the owners to work with the engineer in order to establish desired and acceptable levels of wave loads as the basis for a design. Also, it gives an opportunity to the engineer to design structures with their foreknown behavior against the design wave load levels. These performance objectives include two specifications; the hazard levels to which the structure is to be designed, and the permissible amount of damage when the structure is subjected to these hazard levels. This paper aims to explain the performance-based design methodology by giving the deformation-based reliability design for breakwaters and its applicability to the stability design. Since the methodology requires information on the extreme wave-height distribution near the design site, the effect of wave climate change on the performance-based design is investigated.

Introduction

Performance-based design was born from the lessons learned from earthquakes in the 1990s (PIANC, 2001), with the goal to overcome the limitations present in the conventional design process. Conventional design is based on providing capacity to resist a design wave force, but it does not provide information on the performance of a structure when the limit of the force balance is exceeded. Besides, conventional design might cause an uneconomical design when the force-balance is not exceeded for the design waves with a relatively high return period, or it might lead an undesirable (unsafe) design when the structure is subjected to wave forces that are greater than the design waves with a relatively low return period. On the other hand, the performance-based design clearly defines the importance of structures, their performance levels and design basis by considering a design process that systematically specifies the performance requirements of the structures and respective performance evaluation methods.

Performance-based design requires reliability analysis, and the method considering probabilistic nature is quite suitable for coastal facilities because waves are of irregular nature and wave actions fluctuate. However, solely considering the probability of failure is insufficient, when the deformation (damage level) needs to be taken into account (Takahashi, et al., 2015, and Yuksel et al., 2016 and 2018). Therefore, the appropriate design wave levels and corresponding acceptable levels of structural damage must be properly defined.

A few studies in the literature focused on the performance-based design of coastal structures (Ling et al., 1999, PIANC, 2001, Goda, 2004, PIANC, 2014 and Do et al, 2016). However, the definitions for coastal structures under wave loads are still not sufficient. This study aims to fulfill the need of describing the design criteria for port and coastal protection structures with considering different design wave levels during a lifetime of the structures and probabilistic aspects.

Future changes in wave conditions due to climate change will also influence the marine ecosystem, coastal erosion, design of coastal defenses, performance of coastal and port structures, and coastal zone management because changes in wave climate will appear within the service life of coastal structures. Therefore, design wave parameters should be determined by taking into account the projected wave conditions and the projected sea level rise. Performance-based design requires the extreme wave-height distribution near the design site, which is the offshore boundary of a wave transformation model. In this study, new definitions for the inclusion of the effect of wave climate change on the performance-based design is investigated with an application in the eastern Mediterranean Sea.

Methodology: Concept of performance-based design method

The new definitions for the functional classification of port and coastal structures, the definition of performance-damage levels, multi-level design wave levels, and performance objectives are briefly described with respect to the essentials of the performance-based design.

Performance-based design parameters:

  1. Structural classes associated with the expected performance, usage and functional importance,

  2. Performance levels associated with expected damage levels,

  3. Damage levels associated with frequent, rare and very rare wave events,

  4. Performance objectives under different wave return period levels.

Functional classification of structures

Coastal and port structures are classified as special, normal, simple and unimportant structures.

  • Special Structures: Structures to be used for rapid response and evacuation immediately after damage, structures to be used for the marine structures of nuclear power plants, toxic, flammable or explosive materials. Permanent changing of the nature such as inland dredging projects.

  • Normal Structures: Structures where the loss of life and property must be avoided, structures of economic and social significance, structures with difficult and time-consuming post-wave actions repair and retrofit needs, port structures with crane operations.

  • Simple Structures: Less important structures other than those classified in Special and Normal Structures, structures other than those classified as Unimportant Structures, port structures without crane operations such as only berthing usage of fishery ports.

  • Unimportant Structures: Easily replaceable structures, structures not causing life safety risk even extensively damaged such as recreational coastal structures and sunbathing timber piers and temporary structures.

Performance Levels

Performance levels of coastal and port structures are defined with respect to expected damages during a storm wave event.

  • Minimum Damage (MD) Performance Level: This performance level corresponds to a state where no or a very limited damage occurs in coastal and port structures and/or in their elements under a design wave and beyond event. In this case, port operation continues uninterruptedly or if any, service interruptions are limited to a few days.

  • Controlled Damage (CD) Performance Level: This performance level corresponds to a state where non-extensive, repairable damage occurs in port structures and/or in their elements under a design wave. In this case, short-term (few weeks or months) interruptions in related port operations may be expected.

  • Extensive Damage (ED) Performance Level: This performance level corresponds to a state where extensive damage occurs in coastal and port structures and/or in their elements under a design wave. In this case, long-term interruptions or even closures in related port operations may be expected.

  • State of Collapse (CS): This corresponds to the collapse state in port structures and/or in their elements under the over design wave.

Design Wave Levels

Four different levels of storm are defined in terms of their intensity, representing very frequent, frequent, rare and very rare events.

  • (W1) Design Wave Level 1: This design wave level represents very frequent and low-intensity design wave conditions with a high probability to occur during the service life of port structures. The return period of (W1) design wave level is in between 10 and 50 years.

  • (W2) Design Wave Level 2: This design wave level represents relatively frequent but low-intensity design wave conditions with a high probability to occur during the service life of port structures. The return period of (W2) design wave level is in between 50 and 100 years.

  • (W3) Design Wave Level 3: This design wave level represents the infrequent and high-intensity design wave conditions with a low probability to occur during the service life of port structures. The return period of (W3) design wave level is 100 years.

  • (W4) Design Wave Level 4: This design wave level represents the highest intensity and very infrequent design wave conditions. The return period of (W4) design wave level is more than 100 years with a 70% upper limit of the confidence interval for wind waves but 10,000 years for a tsunami wave.

The probability of occurrence of the design wave conditions (R, risk, %) during the service life of the structure should be determined at the design stage according to the service life of the structure (L) and design return period for design conditions (Td),
formula
(1)
The acceptable risk levels for different Td and L values are given in Table 1.

Occurrence probability is identified as an encounter probability of the design wave height during the service life of a structure. The return period can be determined by using the occurrence probability related to the service life of a structure. Hence, the design wave height can be obtained using the return periods defined in Table 2.

Since failures are not considered in the current design process, marine structure engineers do not pay sufficient attention to the extent and consequences of failure, i.e., performance evaluation is limited to the time prior to failure, while that during and after failure is neglected (Takahashi, et al., 2015). However, the damage levels for coastal structures are classified according to their performance in Table 3.

Performance criteria (damage limits) such as displacement, tilting, settlement and slope failure must be known for the coastal structures. Failure modes of typical coastal structures are shown in the Coastal Engineering Manual (CEM, 2003). CEM defines the failure in which damage results in structural performance and functionality below the minimum anticipated by design. Damage is the partial collapse of a structure.

Results and discussion

(i) Damage levels for breakwaters

Van der Meer (1988) defined the value of damage level of rubble mound breakwaters related to their slopes. Damage level is defined with for rock units, where Ae is the area of displaced rocks/stones in cross-section of the armour layer (including pores) above and below the design water level, and D50 is the stone diameter. However, the damage level does not include the functional performance of structural classes. In performance evaluation of the rubble mound breakwaters for the case of ½ slope, the minimum damage (MD), controlled damage (CD), extensive damage (ED) and state of collapse (CS) may be considered as S < 2, S = 2, S = 4, and S = 6, respectively. This classification corresponds to the definitions in Table 3. Thus, damage level of rubble mound breakwaters can be defined with respect to the functional performance of structural classes. As an example, if a rubble mound is a port structure, it must be defined as a normal structure while a rubble mound is a special structure if its functional requirement is protecting a nuclear power plant.

The damage mode of the monolithic vertical breakwaters is identified as horizontal displacement, settlement, and tilting. These modes are characterized by using quantitative damage levels and the damage levels of the monolithic vertical breakwater are summarized according to the performance-based design concept in Table 4. If the designers choose the force-balance based design, the safety factors are only used for the determination of the structure stability. When the performance-based design is considered, it is needed to determine the damage levels of the structures given in Table 4. Moreover, performance-based design can be performed by using advanced analysis, and these performance levels should be validated (calibrated) by physical model tests.

Goda and Takahashi (2001) described performance and reliability design and risk analysis as a new design methodology. Takahashi et al., (2000) concluded that the primary cause of damage is the sliding of the caisson. Any degree of sliding is equated with caisson damage. In practice, however, even if the caisson slides, the breakwater can still be functional, unless the sliding distance impedes the serviceability of the breakwater. The performance-based design method allows a certain amount of sliding during the lifetime of a breakwater (Suh, et al., 2012). Takahashi et al. (2000) defined the allowable expected sliding distance based on structural-functional classes:

  • 3 cm for normal structure

  • 30 cm for simple structure

  • 100 cm for unimportant structure

Moreover, Overseas Coastal Area Development Institute of Japan (2009) defined allowable exceedance probability (%) of allowable sliding distance (cm) and their structural classes in Table 5 where definitions of the classification correspond to the definitions in Table 3.

Breakwaters are not expected to be damaged under design wave condition, however, there is always a risk that a structure may be exposed to above the level of design wave height condition, and these conditions have not been taken into account at the design stage so far. Therefore, the failure performance of the structure under a higher level of the design wave height condition should be designated especially for special structures.

Numerical simulations have an important role in investigating wave transformations and wave actions on structures including wave forces, especially by the introduction of direct simulation techniques (Isobe et al., 1999). Such simulations can explicitly show the process of wave propagation and action, which makes them quite suitable for performance design and use in the design process. Obviously then, both physical model experiments and numerical simulations are important tools in performance design (Takahashi, et al., 2015).

(ii) Effect of wave climate on performance-based design

In the design of coastal structures, waves are usually characterized by the significant wave height (Hs). Other important wave parameters are the mean wave direction () and the mean wave period (Tm) which are used to determine the response of coastal structures to the incident wave conditions.

To investigate the effect of long-term variation of wave parameters, wave climate over the Mediterranean Sea was modeled by a third-generation spectral wind-wave model (MIKE 21SW) using ERA-Interim wind inputs (spatial resolution of 0.25°). The numerical wave model was calibrated with six different buoy measurements (Table 6). As a result of the calibration process, the optimal value of tunable parameter whitecapping dissipation (Cds) was found to be 1.5. The calibration process showed that the default values of other physical processes such as bottom friction, depth induced wave breaking, and nonlinear wave-wave interactions were sufficient. In order to evaluate quantitatively the quality of wave data, Bias (BIAS), Correlation Coefficient (R), Root Mean Square Error (RMSE) and Scattering Index (SI), which is RMSE normalized by the mean measured value, were calculated and presented for both significant wave height and mean period in Table 7. The modeled wave parameters are in reasonably good agreement with the measurements at all stations. Relatively large errors, especially found in modeled wave periods, may be attributed to the uncertainties included in the wind inputs and buoy measurements. In general, the concordance of comparisons for wave parameters was found to be satisfactorily good (Table 7).

Figure 1a and b represents wave climate changes in the last 40 years over the East Mediterranean Sea. This historical model shows that the increase in the annual maximum significant wave height reaches around 1.5 m (corresponding to around 10% increase) and the mean wave period reaches around 0.15 s (corresponding to around 5% increase) in the northeast Mediterranean Sea.

Figure 2 illustrates the frequency distribution of significant wave height at a selected location in Figure 1 (35.835850° longitude E and 36.179073° latitude N) for the first (1979–88) and last decade (2009–18) of the modeled period. Significant wave heights are slightly shifted to larger values in the last decade, with the mode of the distribution increasing from around 0.30 m to around 0.45 m. The values larger than 0.5 m have slightly greater occurrence frequencies in the last decade. For this particular location, the number of relatively large wave heights (>1 m) in the last decade is on average 12% larger than that of the 1979–88 period, calculated based on the ratio between the areas under the dashed and continuous curves for Hs>1 m. This leads to an increase in the average significant wave height from 0.576 m to 0.6 m. These findings indicate that, in addition to an increase in significant wave heights, an increase in the number of extremes is also probable in the future, which should be taken into account in determining design wave conditions.

Damage in coastal structures occurs when the wave forces exceed the design wave conditions. The design wave height is determined by fitting annual maxima to the extreme value distribution. In this study, the Weibull distribution, which has the following cumulative distribution function expression for a random variable x, is used:
formula
(2)
where μ is the location parameter, β is the scale parameter and α is the shape parameter.

Figure 3 shows annual return periods of significant wave height based on the Weibull distribution at the selected location (Figure 1) in the northeast Mediterranean Sea (35.835850°E; 36.179073°N) including 70% confidence intervals (dashed lines). At this site, the design wave height for normal (100-year return period) and special structures (70% upper limit of confidence interval) are around 5.8 m and 6.1 m, respectively, based on Table 3 and Figure 3. The performance level of the normal and special structure is MD (Table 4).

The increase of the annual maximum wave height in 40 years at this site is around 30 cm (Figure 1a). With this 30 cm increase in the maximum wave height, the design wave height for a normal structure (5.8 m) might reach its new value of 6.1 m which corresponds to the design wave condition for special structures. The significant wave height of 5.8 m would correspond to a wave height with a 43-year return period. This indicates that the coastal structure will likely be subjected to waves larger than design waves during the service life, and the risk will increase considerably (Table 2). For instance, the risk is 39% for a normal structure with a service life of 50 years and a return period of 100-years (Table 1 and Table 2). However, reaching the design wave conditions in 43 years increases the risk of damage to 69% for this structure (Eq. 1).

Past climate can be analyzed by using observations (which are sparse in time and space or available by wave modeling). But, to project future waves, future wind condition information is necessary. In this approach, winds derived from general circulation models (GCMs) or regional climate models (RCMs) are used to force a wave model (Chowdhury et al., 2019).

Conclusions

This study defines the performance-based design philosophy and its concept as represented with a flow chart given in Figure 4. In this context, the classification of port structures, the definition of damaged-based performance levels, multi-level design wave actions and performance objectives are briefly described in line with the essential parameters of the performance-based design. As one of the essential parameters, the damage limit should be defined along with design wave parameters for the performance levels of each coastal structure.

Coastal structures are designed based on return levels derived using extreme value theory that provides a statistical description of the maxima of a stationary process, which assumes no change in the frequency of extremes over time. However, global climate change is expected to cause long-term changes in mean sea level, wave height, and storm frequency at time scales longer than the lifetime of many coastal structures. This causes a greater risk of damage to coastal structures than expectations. Therefore, design wave parameters are required to be determined by considering the long-term historical data, the projected wave parameters, and the projected sea level rise.

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