Stilling wave basins for overtopping reduction at an urban vertical seawall – The Kordon seawall at Izmir

Ocean Engineering 185 (2019) 82–99

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Stilling wave basins for overtopping reduction at an urban vertical seawall – The Kordon seawall at Izmir Dogan Kisacik a, *, Gulizar Ozyurt Tarakcioglu b, Cuneyt Baykal b a b

Institute of Marine Sciences and Technology, Dokuz Eylul University, Haydar Aliyev Boulevard 32, 35430 Inciralti, Izmir, Turkey Department of Civil Engineering, Middle East Technical University, Ankara, Turkey

A R T I C L E I N F O

A B S T R A C T

Keywords: Wave overtopping Sea walls Vertical structure Stilling wave basin (SWB) Impulsive waves

Reduction of wave overtopping at urban coastal structures is a significant concern as uncontrolled flooding, and the wave forces disrupt the daily flow of the urban life causing damage to people, structures and economy. However, the design of these structures needs to consider the spatial and visual demands of the urban function that restrict the crest heights. Therefore, crest modifications such as a storm wall, a bullnose or a combined structure like Stilling Wave Basin (SWB) can be used to optimize the crest height for lower overtopping values. Although reduction factors of these modifications have been studied for sloped structures in EurOtop (2016), there is relatively limited dataset regarding the vertical structures. This paper presents the results of wave overtopping experiments for an urban vertical wall with low crested Stilling Wave Basin structure with foreshore, under impulsive wave conditions. Over 150 tests have been carried out using a model of a seawall and prom­ enade combined structure based on the urban vertical seawall of Kordon, Izmir. A variety of design parameters such as the pattern of gaps, blocking coefficients, and promenade are investigated under constant hydraulic conditions to optimize SWB design for this urban vertical wall structure. The hydrodynamic conditions for overtopping experiments are designed to test the applicability of the empirical formulas of overtopping over vertical walls for impulsive waves in EurOtop (2016). A method, calculating reduction factors, is determined for the finalized SWB design for a broader spectrum of hydraulic boundary conditions (0:40 � Hm0 =dw � 0:90, 1:22 � Tm 1;0 � 2:02 s, and 0:106 � dw � 0:20 m) of the impulsive wave with 0:708 < Rc =Hm0 < 2:091.

1. Introduction Coastal zones with high population density such as coastal cities are vulnerable to storms and wave overtopping which hinders economic and social activities from time to time. In extreme events, the outcome be­ comes severe as significant damages might occur and human lives can be lost. Impacts of climate change are expected to reduce the resilience of coastal cities as the storms become intense with higher wave heights. Therefore, extensive research has been carried out to increase the resilience of coastal areas through coastal protection structures by reducing the wave overtopping. In Turkey, where the largest and economically important areas are coastal cities with highly urbanized shorelines, the vulnerability asso­ ciated with wave overtopping is significant. In addition to the economic significance, these shorelines have been an essential part of the social fabric as social and recreational activities take place frequently. The shoreline of Turkish coastal cities typically consists of a promenade

protected by either revetments or seawalls. ‘Kordon’ in Izmir is a wellknown example of seawall and promenade (see Fig. 1). Behind the promenade, main city roads and apartment buildings including shops and restaurants are present. As the promenade is dominantly used for recreational purposes, very low wall heights (usually less than 50 cm) are designed to satisfy the visual quality. Table 1 shows the character­ istics of the cross-sections of Kordon Seawall and Promenade which are measured at seven different locations (1–7 in Fig. 1b). From these crosssections, a simplified representative cross-section is defined for the experimental tests (Table 1). However, during storm conditions (usually every winter), these promenades, and the adjacent areas are flooded, as the crest of the seawall is not high enough to reduce the wave overtopping (Fig. 2). Although increasing the crest heights of these structures would be the most straightforward measure to implement, people and the local gov­ ernments do not accept any obstruction to the scenery. Additionally, urbanized shoreline usually restricts the landward spatial extension.

* Corresponding author. E-mail addresses: [email protected] (D. Kisacik), [email protected] (G.O. Tarakcioglu), [email protected] (C. Baykal). https://doi.org/10.1016/j.oceaneng.2019.05.033 Received 10 June 2018; Received in revised form 28 February 2019; Accepted 19 May 2019 Available online 1 June 2019 0029-8018/© 2019 Elsevier Ltd. All rights reserved.

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Ocean Engineering 185 (2019) 82–99

Therefore, other measures such as the landward expansion of the promenade cannot be applied. Stilling Wave Basin (SWB) concept is one measure that can be designed to consider both the spatial and visual restrictions as the wave energy is dissipated between a partially permeable seaward wall and a landward wall where both walls can be designed with low heights. The promenade can be utilized as the basin between the walls during the winter storm conditions with no allowance for public use. Stilling Wave Basin (SWB) on the crest of smooth dike slopes under non-breaking conditions have been studied, and their effect on wave overtopping is presented in EurOtop (2016). EurOtop (2016) also pre­ sents several key points for wave overtopping at vertical structures such as seawalls. The influence of the foreshore, wave breaking conditions, and low crest heights are taken into consideration, and related design formulas are presented. However, the combination of seawalls and Stilling Wave Basin on the crest has not been studied much, to the best knowledge of the authors. As more urban coastal areas are expected to experience changes in the hydrodynamic conditions due to climate change, the level of over­ topping is also expected to deviate from the initial design consider­ ations. Therefore, modification to the present structures will be required for many urban areas, and SWB might be an effective solution for lo­ cations similar to Kordon, Izmir. Therefore, the primary objective of this study is to present and discuss the wave overtopping at a seawall with

low crested SWB modification with foreshore as an alternative to mod­ ifications with higher crest heights for urban coastal areas. To achieve the main objective, at first, the design of low crested SWB structure is optimized specifically for the simplified model of urban seawall of Kordon, Izmir (Table 1). Then, over 150 2D model tests have been carried out for a broader range of hydrodynamic conditions to analyze wave overtopping under impulsive wave conditions (as described in EurOtop (2016)) for a vertical wall as well as SWB modification to the urban vertical wall. Although the experiments are performed for one optimized cross-section design of SWB, results of the broader spectrum of hydrodynamic conditions highlight the possible use of SWB modifi­ cation across different locations. A comprehensive literature study about SWB is given in section 2. A detailed overview of the design and execution procedure of the experi­ ments and of the test database is presented in section 3. The test matrix was based on a broader spectrum of hydraulic boundary conditions which also cover the condition along the Kordon seawall and promenade in Izmir Bay. The overtopping type and characteristics were discussed in section 4. Then, the optimized SWB design was tested using the whole test matrix of the vertical wall experiments to determine the reduction factor, γSWB.

Fig. 1. a) Top view of Kordon Seawall and Promenade in Izmir, b) Positions of the seven cross-sections along the Kordon Seawall, c) Simplified cross-sectional sketch of Kordon Seawall and Promenade. 83

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2. Literature study

q pffiffiffiffiffiffiffiffi ¼ 2:7 � 10 h2* g:h3

In the literature, methods of quantifying the wave overtopping discharge are widely discussed in many guidance manuals such as TAW (2002), EurOtop (2007, 2016) in addition to the national guidelines of many countries. One of the widely used guidelines is EurOtop (2016) which presents the latest techniques and approved methods for estab­ lishing overtopping hazards and flooding for an extensive range of structure types. One of the earliest formula on wave overtopping discharge is based on Owen, 1980. The general form of wave overtopping discharge, q, on many kinds of structures (see Fig. 3) can be described as in Equation (1), in which q decreases exponentially as the crest freeboard, Rc, increases. � � q Rc qffiffiffiffiffiffiffiffiffiffi ¼ a exp (1) b Hm0 gH 3mo

h*

Rc < 0:02 Hm0

(5)

The newly proposed formulas in EurOtop (2016) are described below: No influence of foreshore (deep water, h =Li > 0:5Þ at the location of the structure. Li is the wavelength calculated from the dispersion rela­ tion based on Tm 1;0 at water depth h. " � �1:3 # q Rc qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:047:exp (6) 2:35 Hm0 g:H 3 m0

Influence of the foreshore, but no wave breaking, (non-impulsive,

h2 Hm0 Lm

1;0

> 0:23).

q qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:05 exp g:H 3m0

The h* parameter is used as a measure of “impulsiveness” with a transition from non-impulsive to impulsive overtopping conditions at the wall taking place over the range 0:2 � h* � 0:30 (Van der Meer and Bruce, 2014). Based on the variation of h* parameter, a comprehensive method for wave overtopping at vertical seawalls was proposed in EurOtop (2007) as follows: Non-impulsive condition, h*>0.3 � � q Rc qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:04 � exp 0:1 < Rc =Hm0 < 3:5 2:6 (3) Hm0 g:H 3m0

Rc 0:03 < h* < 1:0 Hm0

2:7

(i) a clear separation of situations based upon the existence of an influencing foreshore in front of the vertical structure; (ii) an adjusted “discriminator” to identify impulsive overtopping conditions is used by replacing the previous h* parameter; (iii) a clearer integration of methods for composite vertical structures with plain vertical structures.

(2)

Impulsive condition, h* � 0:2 � � 3:1 q R pffiffiffiffiffiffiffiffi ¼ 1:5 � 10 4 exp h* c 2 3 Hm0 h* g:h

� � Rc h* Hm0

Further research was performed in light of available datasets such as CLASH (De Rouck et al., 2009) and the results lead to new consider­ ations on wave overtopping for vertical walls. For example, Goda (2000) showed significant peaks for some shallower (relative) water depths and found that local water depth on a foreshore is important. In the new edition of the EurOtop (2016), the standard equations for wave over­ topping at vertical walls as described in the first edition of EurOtop (2007) were reformulated. The aim was to integrate the proposed equations into a more unified, physically rational framework of pre­ diction tools spanning a greater breadth of structure types and wave conditions. The principal changes in EurOtop (2016) are:

where Hm0 is the spectral significant wave height, and a and b are fitting coefficients. The equation gives a straight line on a log-linear graph with two coefficients for fitting the data. Early work by Franco et al. (1994) proposed a ¼ 0.2 and b ¼ 4.3 for relatively deep water, while Allsop et al. (1995) determined a ¼ 0.05 and b ¼ 2.78 in conditions of shal­ lower water when Equation (1) is applied in the case of vertical structures. However, it is not possible to describe all hydrodynamic conditions in front of a vertical seawall by simple exponential form equations like Equation (1). Allsop et al. (1995) used data from model studies where wave breaking occurred on the structure to propose a new empirical equation showing a power-law decrease in overtopping discharge with freeboard, rather than an exponential one. Therefore, a discriminating parameter h* was introduced (Equation (2)) to determine whether an exponential or a power law should be used. h 2πh h* ¼ 1:35 Hm0 gT 2m 1;0

4

� 2:78

Rc Hm0

� (7)

where, Lm 1;0 being the deep water wavelength based on Tm (Lm 1;0 ¼ gT2m 1; 0 =2π). Waves break at the structure, (impulsive,

� �0:5 � q Hm0 qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:011 :exp hsm 1;0 g:H 3 m0

h2 Hm0 :Lm

1;0

(4)

� 0:23).

� Rc 2:2 ; 0 < Rc =Hm0 < 1:35 Hm0

�0:5 � � 3 � q Hm0 Rc qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:0014 ; Rc =Hm0 � 1:35 hsm 1;0 Hm0 g:H 3m0

1;0

(8)

(9)

where sm 1;0 is the wave steepness (2πHm0 =gT2m 1;0 ). For a design or assessment approach, it is strongly recommended to increase the average discharge by about one standard deviation (σ).

Broken waves

Table 1 Summary of the Kordon Seawall and Promenade characteristics. Cross-sections #

dw (m)

df (m)

dw þ df (m)

xr (m)

hb (m)

wb (m)

Rc (m)

sf ( )

1 2 3 4 5 6 7 Representative Cross-section

2.35 2.10 1.85 2.00 2.30 1.80 1.25 2.36

0.95 0.96 0.90 0.79 0.88 0.89 1.07 1.00

3.30 3.06 2.75 2.79 3.18 2.69 2.32 3.36

7.90 8.12 7.96

0.350 0.340 0.350 0.360 0.320 0.380 0.230 0.288

0.61 0.60 0.60 0.60 0.60 0.62 0.57 0.48

1.30 1.30 1.25 1.15 1.20 1.27 1.30 1.29

12 19 16 32 19 19 10 20.00

7.88 8.29 8.00

84

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Thus, Equation (10) and Equation (11) presented below should be used in design and safety assessments. � �0:5 � � q Hm0 Rc qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:0155 :exp 2:2 ; 0:1 < Rc =Hm0 < 1:35 hsm 1;0 Hm0 g:H 3m0 (10) �0:5 � � 3 � q Hm0 Rc qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:0020 ; hsm 1;0 Hm0 g:H 3m0

Rc =Hm0 � 1:35

(11)

All the proposed equations show that the amount of overtopping discharge strongly depends on the crest freeboard (Rc ) under constant hydraulic conditions. Therefore, increasing Rc seems to be a solution for reducing the overtopping discharges. However, direct implementation of this solution may not be possible for some locations where the stakeholders are against higher crest heights due to visual implications. Additionally, landward expansion of the seawall might be impossible, since buildings are often close to the seawall (Geeraerts et al., 2006). To overcome these limitations, the crest modifications of the vertical sea­ walls can be designed as a Stilling Wave Basin (SWB). EurOtop (2016) defined Stilling Wave Basin as an area designed in front of the crest or capping wall, where a part of the up-rushing wave may remain without overtopping. The SWB is made up of a partially permeable seaward storm wall, a sloping promenade (basin) and a landward storm wall. The seaward storm wall may consist of a double row of shifted storm walls or a single storm wall with some gaps to allow drainage of the water in the basin. Landward and seaward storm walls may have bullnose geometries of different angles (Geeraerts et al., 2006; Van Doorslaer et al., 2009). This crest design is based on the principle of energy dissipation. The incoming wave dissipates most of its energy by hitting the seaward storm wall and through the basin before it reaches the landward storm wall. Consequently, the landward wall is overtopped less in comparison with an unmodified crest, even though the crest height has not been increased (Van Doorslaer et al., 2015). The SWB concept was used in different configurations with coastal protection structures as follows:

Fig. 3. Definition sketch for assessment of overtopping at vertical seawalls (EurOtop, 2016).

the first systematic model studies for overtopping performance was made by Aminti and Franco (2001). The data by Aminti and Franco were then re-analyzed by Cuomo et al. (2005) to compare them with the prediction computations of the CLASH Neural Network. They proposed a reduction factor due to the SWB as a function of the relative basin’s dimensions. On the basis of physical 2-D model tests, Burcharth and Andersen (2006) discussed the design and performance of breakwaters with the front reservoir and the sensitivity of the overtopping discharge to the width of the reservoir (Fig. 4). It is demonstrated that breakwater cross-sections with the front reservoir are very efficient and economical when low structure crest levels are demanded.

a) SWB concept of sloping structures The application of SWB at the top of smooth impermeable dikes was �nchez-Naverac (1978) and was even first described by Aguado and Sa tested for run-up performance by Ceniceros and Medina (2001). Then,

Fig. 4. The principle of front reservoir structure (Burcharth and Ander­ sen, 2006).

Fig. 2. Photos of Kordon Seawall and Promenade during storm conditions. 85

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Ocean Engineering 185 (2019) 82–99

Geeraerts et al. (2006) investigated the application of SWB at the top of smooth impermeable dikes to reduce wave overtopping (Fig. 5). Fig. 5a shows both a standard dike and a dike with SWB built in the crest where both structures have the same crest heights. The influence of geometric variations of SWB on top of a dike on wave overtopping can be summarized as (Van Doorslaer et al., 2015; Grossi et al., 2015): - The effect of the height of the seaward wall, γ wall is dominant, while the effect of the basin’s width, γ promenade is present but less pronounced. - The slope angle and the wave period have a minor influence on the reduction of wave overtopping. - A reduction factor of γ SWB is found to be around 0.45 for SWB ge­ ometry, and can be used to quantify wave overtopping over a dike slope with SWB (EurOtop, 2016).

Fig. 6. Conceptual design of crest drainage dike (not to scale), see Nieuwenhuis et al. (2005).

Kortenhaus et al. (2007) introduced the concept of crest drainage dike by installing an “Overtopping Buffer Basin” in the dike crest. This concept was developed by Nieuwenhuis et al. (2005) initiated by the European ComCoast project to reduce the wave load and wave over­ topping of a dike. Overtopping Buffer Basin is a concrete U-Profile which serves as a SWB, in the dike crest (Fig. 6). Most of the overtopping water will be collected in this buffer basin and water will drain out through drainage pipes towards landward or seaward side of the dike between overtopping events. They mentioned that the seaward drainage systems could be preferable in extreme events since it could drain more water than landward drainage designs. Cappietti and Aminti (2012) experimentally measured the wave overtopping on scale models of rubble mound marina breakwaters to assess the effectiveness of building an overspill basin in front of the breakwater wave wall (Fig. 7). The concept of SWB and overspill basin has similar characteristics. They observed that the design with SWB decreases overtopping by up to a factor of 2 compared to a classically shaped breakwater within the range of experimental conditions tested. Veale et al. (2012) and Altomare et al. (2014) performed wave overtopping and pressure tests to determine the optimal geometry of wave return walls to be constructed on the existing sloping sea dike at Wenduine-Belgium. For overtopping tests, they considered three cases; (i) a storm wall located either at the seaward, (ii) at the landward edge of the vertical dike and (iii) both storm walls together, which is defined as Stilling Wave Basin, SWB (Fig. 8). They indicated that the storm wall located at the landward edge of the vertical dike showed a better per­ formance for reducing mean overtopping discharge than the case where the storm wall located at the seaward edge. However, the best result was obtained from the SWB case. The Storm Surge Protection (SPP) wall (Kortenhaus et al., 2002), which consists of an underwater Stilling Wave Basin can be considered as another example of a related structure. However, it is not further

Fig. 7. Schematic layout of the tested breakwater models characterized by overspill basins of different volumes. Units are cm, and the measurements are related to the scaled model (Cappietti and Aminti, 2012).

discussed because of its different hydraulic effect. b) SWB concept on vertical structures In the 1960s, the Principality of Monaco built the vertical breakwater of Fontvieille (Fig. 9) with a SWB at the crest. This combination was designed to overcome the lack of hinterland and the significant water depths (30–40 m) at the location of the breakwater (Bouchet, 1992). This is one of the earliest examples of a SWB concept combined with vertical structures. Similarly, Di Risio et al. (2006) studied vertical composite break­ waters with several different parapet walls and an overspill basin by means of a 2D physical model with the scale of 1:35 in non-breaking wave conditions. Instead of the term “Stilling Wave Basin,” they used the term “Overspill Basin.” The composite breakwater was made of a caisson over a quarry stone mound (Fig. 10). They observed better overtopping performance with the parapet walls than using an Overspill Basin. Later, Crema et al. (2009) conducted laboratory measurement of the wave by wave overtopping volumes and mean overtopping discharges at a plain vertical wall breakwater with and without an Overspill Basin to investigate the effect in the reduction of the wave overtopping dis­ charges and volumes. The model was tested for nine different configu­ rations, including the overspill basin in Fig. 11, of an almost non-impulsive overtopping regime under irregular waves. Therefore, they interpolated the experimental measurements by using the non-impulsive formulation (Equation (3)) for the plain vertical wall in EurOtop (2007), where the reduction factor (γSWB ¼ 0:69) have been calibrated for the configuration with Overspill basin. � � q Rc 1 qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:04 � exp 2:6 (12) Hm0 γ SWB g:H 3m0 γ SWB ¼ 0:69 is related to the experimental ranges in 1:18 < Rc =Hm0 < 1:85. Within the range of the experiments, they concluded that the effect of the overspill basin in reducing the mean overtopping discharges is poor. This is mainly due to the use of a smaller capacity basin, which is built by considering a relatively lower seaward storm wall.

Fig. 5. a) Simple, smooth dike slope (left) compared to a dike slope with SWB built in the crest (right), b) Side view of Stilling Wave Basin, (model scale and dimensions in mm), (Geeraerts et al., 2006). 86

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Fig. 8. Schematic of dike geometry with SWB (Veale et al., 2012).

Fig. 9. The sketch of the Fontvieille breakwater (Bouchet, 1992).

Fig. 11. Stilling Wave Basin (SWB) with a vertical breakwater (Crema et al., 2009).

modification of vertical seawalls under the breaking wave condition. 3. Methodology The experimental work is primarily designed to understand the wave overtopping over a low crested SWB structure on a vertical seawall located at an urban coastal area. Therefore, a parametric survey study of SWB geometry is performed to optimize the cross-section of SWB for lower overtopping values considering the limitations due to being part of urban fabric such as low crest heights for visual aesthetics. The optimization tests for SWB modification were performed under the wave condition used in the initial design of the vertical wall. Then, both the optimized SWB cross section and the initial vertical seawall were tested under a boarder range of hydrodynamic conditions (impulsive condi­ tions) to highlight the possible effects of the performance of such crest modification across different urban areas. Physical model tests have been carried out in the wave flume of Coastal and Harbour Engineering Laboratory, Department of Civil En­ gineering of Middle East Technical University (METU, Turkey). The wave flume is 26 m in length, 6 m in width and 1.0 m in depth. An inner channel with glass side walls (18 m in length, 1.5 m in width) is con­ structed in the wave flume to reduce the size of the cross-section and the effects of reflection occurring due to concrete sidewalls (Fig. 12a and Fig. 13a). A slope of plastic wire scrubbers acting as wave absorbers is installed at the end of the flume as passive absorption system (Figs. 12b and 13b). A piston type wavemaker, which is capable of generating irregular waves at water depths of 0.30–0.60 m, is placed at the other end of the wave flume. The wavemaker frequency is between 0.05 Hz and 2.0 Hz, and the maximum stroke length is 290 mm. Each time series of the experiments contained 500 irregular waves with Bretschneider spectrum. Romano et al. (2015) stated that a wave train of at least 500

Fig. 10. The sketch of the composite vertical breakwater with Overspill Basin (Di Risio et al., 2006).

The reduction factor (γSWB ) for the overtopping discharge due to the SWB depends on parameters like basin height, width, and permeability. Therefore, it is difficult to set a single value of γSWB since geometry may vary a lot. However, it is possible to define the SWB geometry based on a parametric survey study. In addition, the literature on SWB dominantly focuses on sloped structures such as dikes. According to the authors’ knowledge, the information for the combined vertical structures with a SWB crest modification is limited, and the existing ones mainly considered the non-breaking wave conditions. Therefore, there is still a research gap on the reduction coefficient (γ SWB ) for SWB crest 87

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Fig. 12. Flume model set-up, used for irregular wave tests. a) is the top view, b) is the side view of the without structure case, c) is the side view of the simple vertical seawall case (Model-A) and d) is the side view of the vertical seawall with SWB case (Model-B).

waves could be used in overtopping tests to achieve a comparable ac­ curacy for which the confidence interval difference is less than 20% with those obtained for 1000 waves. The Froude model scale was set as 1:16 after considering possible water depth in the flume and wavemaker capacity to ensure correct reproduction of all wave processes. The model was instrumented with ten wave gauges, and three video cameras were used to capture the wave overtopping process. The overtopped water was collected in an over­ topping tank (Figs. 12c and 13c). The models were located 18 m away from the wave paddle on a uniform foreshore slope, 1 =sf (Fig. 12d). The set-up was used to analyze (i) the case without structure, (ii) the simple vertical seawall (Model-A), (iii) the optimization of SWB cross section of a vertical seawall and (iv) the vertical seawall with optimized SWB (Model-B). The models were built from wooden and plastic materials (Fig. 13d). The incident waves at the location of the structure (i.e., undisturbed wave conditions generated using the set-up without the structure) were used to calculate the wave overtopping. The incident spectral significant wave heights (Hm0 ) and wave periods Tm 1;0 were measured at wave gauges 8, 9 and 10 (Fig. 12) by utilizing the standard 3-gauge-procedure of Mansard and Funke (1980), while L was determined by linear wave theory for any depth. Hm0 =L is the wave steepness based on spectral wave height and period. There are a number of different measurement techniques which enable a direct quantification of wave overtopping (e. g., Kortenhaus et al., 2004; Troch et al., 2004). In this study, the over­ topped water was collected over a specific crest width that drained into a tank down a chute. The accumulated water in the tank was measured at the end of each test and the mean wave overtopping discharge q (m3 =s per m width) was calculated.

water depth at the structure, df is the vertical distance between SWL and promenade, hb is the seaward storm wall height, wb is the seaward storm wall width and xr is the horizontal width of the promenade. The seaward storm wall is one piece of continuous wall without gaps on it. The total crest freeboard is Rc ¼ hb þ df. The geometric dimensions of the simple vertical seawall model (Model-A, Table 2) are scaled from the di­ mensions of the representative cross-sections along the Kordon seawall and promenade (Table 1). 3.2. Optimization of SWB for an urban seawall To optimize the SWB cross-section with lower overtopping discharge in an urban setting, the parametric survey considered several parame­ ters that control the amount of the overtopping water such as the pattern of the gaps in the storm walls, the blocking coefficients (Cb), the storm wall order, the horizontal gap between the seaward storm walls (Δx), the horizontal width of the promenade (xr), the height of the landward storm wall (hr) and the height of the seaward storm wall (hb). Fig. 15 shows the different configurations of SWB (Table 3) at the model scale at a constant water depth (dw ¼ 0.163 m and df ¼ 0.047 m). Since SWB is proposed as a crest modification to a present vertical seawall, the test hydrodynamic condition was kept constant (Hm0 ¼ 0:827 m and Tm 1;0 ¼ 1:33 s) which reflects the 100 year return period storm con­ dition of Izmir Bay used in the design of the vertical seawall. Horizontal and vertical dimensions are normalized with deep water wave length (Lm 1;0 ) and wave height (Hm0 ) at the model location, respectively. For each set-up, the cumulative overtopping discharge per meter q ðl=mÞ after 500 waves is presented in Table 3. Although the reduction in the overtopping discharge (as discussed in this section) was the main focus in optimization, the aesthetic considerations imposed by the urban setting such as the height of storm walls, limit the range of dimensions to be tested for the optimization of SWB. Therefore, it is important to state that the optimized SWB structure (Model-B) modeled from the para­ metric study is not optimized for lowest overtopping values under the hydrodynamic condition tested, but it is an optimized design for lower wave overtopping for urban settings with similar functions and uses,

3.1. Vertical seawall (Model-A) Fig. 14 shows the details of the simple vertical seawall model (ModelA), which represents the simplified model of the existing Kordon seawall and promenade in Izmir-Turkey (Kisacik et al., 2017). Here, dc is the water depth at the paddle, ft is the foreshore slab thickness, dw is the 88

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Fig. 13. Flume model set up photos. a) visualization of the inner channel with glass side walls at the dry condition, b) visualization of the installed plastic wire scrubbers acting as wave absorbers, c) visualization of the overtopping tank, d) visualization of the scaled model of SWB.

Fig. 14. Details of the simple vertical seawall model (Model-A).

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Table 2 Summary of the Model-A characteristics. f t ðmÞ

dw þ df (m)

hb (m)

wb (m)

xr (m)

sf( )

Prototype Scale

6.400

3.360

0.480

8.000

20

Model Scale

0.390

0.210

0.000 0.288 0.640 0.000 0.018 0.040

0.030

0.500

20

compared to the use of high crested structures. Each tested parameter and the respective configurations named as cases a-g are described below. For cases a-e, the heights of the seaward and landward storm walls are kept constant (hb =Hm0 ¼ hr =Hm0 ¼ 0:363). For cases e-g, the seaward storm wall arrangement is kept constant as two-rows of walls where the front wall has Cb ¼ 66:7 %, the second wall has Cb ¼ 33% and the distance between the two rows are Δ x =Lm 1;0 ¼ 0:014 m. a. The arrangements of the block units of the seaward storm wall are defined as the pattern of gaps. From fine to very coarse, four different patterns were considered Fig. 15a). In the pattern analysis, a constant blocking coefficient of Cb ¼ 50% and the wall height of hr =Hm0 ¼ 0:363 was used for all the patterns. Limited variations were observed among the tested patterns (row-a, in Fig. 15). Therefore, it is concluded that the influence of pattern variations is negligible. b. The blocking coefficient (Cb) is the ratio of the closed part of the seaward storm wall. For a proper design, the structure should allow inflow to the basin as low as possible, while maximum outflow from the basin. Four different blocking coefficients Cb ¼ 33, 50, 66.7 and 76.6% were considered through the optimiza­ tion process (Fig. 15b). Increasing the Cb resulted in lower over­ topping discharge (row b in Fig. 15). However, it was observed that rapid drainage was not maintained for the highest Cb. Therefore, a blocking coefficient of Cb ¼ 66.7% for the most seaward wall was determined as optimal. c. Two rows of the wall were further considered to increase the reduction of the wave overtopping compared to cases a and b. As it is mentioned above, the blocking coefficient of the outer seaward storm wall was Cb ¼ 66.7%. Then, the blocking coefficient of the second row is arranged such that walls on the second row mirror the gaps of the first row without any overlap. This leads to a blocking coefficient of Cb ¼ 33.3% (100% 66.7% ¼ 33.3%) for the second row. Then, the order of the rows was changed and, tests were repeated (Fig. 15c). It was observed that the order of the rows did not have any significant influence on the results (row c in Fig. 15). d. Four different values for the horizontal gap between the rows of the seaward storm walls, (Δx =Lm 1;0 ¼ 0:007; 0:011; 0:014 and 0:018 for Lm 1;0 ¼ 2:759 m) were considered (Fig. 15d). Variation of Δx did not generate a significant difference on the amount of over­ topping discharge (row d in Fig. 15). As accumulated water over the promenade from previous overtopping events may have a negative influence on the wave overtopping measured at the landward storm wall, an optimal value (Δx =Lm 1;0 ¼ 0:014 ) was defined which was observed to allow rapid drainage. e. The horizontal width of the promenade (xr) has an influence by reducing the energy of the flow on the sloping promenade as the water reaches to the landward storm wall. Additionally, increasing the storage capacity of this area that acts like a basin decreases the overtopping discharge. Optimization tests were performed for three different normalized values of Xr =Lm 1;0 ¼ 0:127; 0:181 and 0:232 where Lm 1;0 ¼ 2:759 m (Fig. 15e). The results from Xr =Lm 1;0 ¼ 0:181 and 0:232 were close to each other (row e in Fig. 15). Xr =Lp0 ¼ 0:181 was defined as an optimal value in light of the spatial limita­ tions for urban areas.

Fig. 15. Details of the parametric survey for the vertical seawall with SWB in prototype scale, a) variation of the patterns, b) variation of the blocking co­ efficients (Cb), c) variation in the storm wall order, d) variation of the horizontal gap between the seaward storm walls (Δx), e) variation of the horizontal width of the promenade (xr).

f. The landward storm wall height (hr) is another critical parameter for the optimization. Veale et al. (2012) mentioned that the stakeholders accept the wall height not more than 0.7 m for aesthetic reasons. Therefore, optimization tests considered three different normalized hr values (hr =Hm0 ¼ 0:363; 0:484 and 0:605, where Hm0 ¼ 0.0827 m). Although the case of hr =Hm0 ¼ 0:605 had the least overtopping discharge (row f in Fig. 15), hr =Hm0 ¼ 0:484 was selected as an optimal value considering the visual implications and the stakeholder acceptance (hr =Hm0 ¼ 0:529). 90

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Table 3 Parametric survey results of SWB (Model-B), model scale. Test#

a b c d

q ðl=mÞ 1

2

3

4

Fine, Cb ¼ 50% 108, 112 Cb ¼ 33% 120, 120 Δx ¼ 0:050 mΔx =Lm 54

Medium, Cb ¼ 50% 94, 110, 104, 103 Cb ¼ 50% 94, 110, 104, 103 Δx ¼ 0:050 mΔx =Lm 54

Coarse, Cb ¼ 50% 101.4 Cb ¼ 66.7% 84, 84

Very Coarse, Cb ¼ 50% 101 Cb ¼ 76.7% 80, 80

Δx ¼ 0.040 m Δx =Lm 1;0 ¼ 0:014

Δx ¼ 0:050 mΔx =Lm

1;0

¼ 0:018

Δx ¼ 0.020 m Δx =Lm 1;0 ¼ 0:007

1;0

¼ 0:018

Δx ¼ 0.030 m Δx =Lm 1;0 ¼ 0:011

50, 56 Xr ¼ 0.350 m Xr =Lm 1;0 ¼ 0:127

48, 52 Xr ¼ 0:500 mXr =Lm

f

80, 76 hr ¼ 0:030 mhr =Hm0 ¼ 0:363

52, 48 hr ¼ 0:040 mhr =Hm0 ¼ 0:484

50, 48 hr ¼ 0:050 mhr =Hm0 ¼ 0:605

g

52, 48 hb ¼ 0:020 mhb =Hm0 ¼ 0:242

22, 22 hb ¼ 0:030 mhb =Hm0 ¼ 0:363

10, 10 hb ¼ 0:040 mhb =Hm0 ¼ 0:484

40, 36

28, 28

22, 22

e

1;0

¼ 0:181

g. The seaward storm wall height (hb) is the last parameter considered in the optimization process. Similar to the landward storm wall height, hb must be designed as low as possible for community acceptance, but must also restrict the overtopping by limiting mean overtopping discharge to tolerable discharge criteria. Tests were done for three different normalized wall heights (hb =Hm0 ¼ 0:242; 0:363 and 0:484) and hb =Hm0 ¼ 0:484 was selected as the final dimension which meets the stakeholder expectations while limiting the overtopping discharge (row g in Fig. 15).

52, 48 Xr ¼ 0:640 mXr =Lm

1;0

¼ 0:232

1;0

¼ 0:018

50, 54

whole width of each row of shifted storm walls. The promenade is located behind the storm walls with a seaward slope 1 =sr ¼ 1=40 which is the standard value of the cross slope of a public road. hr is the height of the landward storm wall which is located at the end of the promenade. The landward storm wall is sloped seaward direction with a 45� angle. The total crest freeboard, R’c, is the vertical distance between SWL and the crest of the hr. The results of the parametric survey discussed in detail in Section 3.2 was used to optimize the design of Model-B (Table 4). Fig. 16 shows the dimensions of the finalized design of Model-B which was tested for a broader range of hydrodynamic condi­ tions to assess the reduction in wave overtopping.

3.3. Vertical seawall with optimized SWB model (Model-B) Fig. 16 shows the details of the vertical seawall with SWB model (Model-B). The partially permeable seaward storm wall consists of a double row of shifted storm walls (1. Wall and 2. Wall) with a horizontal gap, Δx. The layout of the seaward storm walls is determined with a blocking coefficient, Cb, which is the ratio of the closed parts to the

3.4. Test matrix The test matrix is based on hydraulic boundary conditions present along the Kordon seawall and promenade in Izmir (Ozyurt Tarakcıoglu et al., 2015), but opened up to a broader spectrum of relevant

Fig. 16. Details of the vertical seawall with SWB (Model-B), a) side view and b) top view. 91

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Table 4 Summary of the Model-B parametric survey characteristics. ft (m)

dw þ df (m)

hb (m)

wb (m)

xr (m)

Δx (m)

hr (m)

Cb (%)

sf –

sr –

Pattern –

Prototype Scale

6.400

3.360

0.320 0.480 0.640

0.480

5.600 8.000 10.240

0.320 0.480 0.640 0.800

0.480 0.640 0.800

33 50 66.7 76.7

20

40

Fine Medium Coarse Very coarse

Model Scale

0.040

0.210

0.020 0.030 0.040

0.030

0.350 0.500 0.640

0.020 0.030 0.040 0.050

0.03 0.04 0.05

33 50 66.7

20

40

Fine Medium Coarse Very coarse

parameters to have a good base for analysis (e.g. from small to large wave periods, from small to large dimensionless freeboards) of a reduction factor for SWB structures. Both Model-A and Model-B were

tested with irregular waves for six different water depths (dc). For each water depth, six different values of wave periods (Tm 1;0 ), measured in front of the seawall, were considered. Three different hb values were

Table 6 Test parameter matrix for irregular waves. Test #

dc(m)

dw(m)

df(m)

Hm0 (m)

Prototype Scale

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

9.600 9.296 9.008 8.704 9.600 9.296 9.008 8.704 8.400 9.300 9.000 8.700 8.400 8.100 9.008 8.704 8.400 8.096 9.000 8.700 8.400 8.100 9.000 8.700 8.400 8.100

3.200 2.896 2.608 2.304 3.200 2.896 2.608 2.304 2.000 2.900 2.600 2.300 2.000 1.700 2.608 2.304 2.000 1.696 2.600 2.300 2.000 1.700 2.600 2.300 2.000 1.700

0.160 0.464 0.752 1.056 0.160 0.464 0.752 1.056 1.360 0.460 0.760 1.060 1.360 1.660 0.752 1.056 1.360 1.664 0.760 1.060 1.360 1.660 0.760 1.060 1.360 1.660

1.295 1.203 1.104 1.071 1.413 1.364 1.322 1.210 1.129 1.662 1.474 1.348 1.220 1.196 1.511 1.437 1.345 1.282 1.686 1.564 1.466 1.368 1.822 1.728 1.642 1.524

Model Scale

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

0.600 0.581 0.563 0.544 0.600 0.581 0.563 0.544 0.525 0.581 0.563 0.544 0.525 0.506 0.563 0.544 0.525 0.506 0.563 0.544 0.525 0.506 0.563 0.544 0.525 0.506

0.200 0.181 0.163 0.144 0.200 0.181 0.163 0.144 0.125 0.181 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106

0.010 0.029 0.047 0.066 0.010 0.029 0.047 0.066 0.085 0.029 0.048 0.066 0.085 0.104 0.047 0.066 0.085 0.104 0.048 0.066 0.085 0.104 0.048 0.066 0.085 0.104

0.081 0.075 0.069 0.067 0.088 0.085 0.083 0.076 0.071 0.104 0.092 0.084 0.076 0.075 0.094 0.090 0.084 0.080 0.105 0.098 0.092 0.086 0.114 0.108 0.103 0.095

92

Tm

1;0 (s)

Model-A

Model-B

Rc1 (m)

Rc2 (m)

Rc3 (m)

R’c (m)

5.03 5.03 4.90 5.03 5.48 6.01 5.32 5.82 5.48 6.42 6.42 6.42 6.42 6.89 6.89 6.65 6.65 6.65 6.89 7.16 7.16 7.16 8.09 8.09 8.09 8.09

0.160 0.464 0.752 1.056 0.160 0.464 0.752 1.056 1.360 0.460 0.760 1.060 1.360 1.660 0.752 1.056 1.360 1.664 0.760 1.060 1.360 1.660 0.760 1.060 1.360 1.660

0.448 0.752 1.040 1.344 0.448 0.752 1.040 1.344 1.648 0.748 1.048 1.348 1.648 1.948 1.040 1.344 1.648 1.952 1.048 1.348 1.648 1.948 1.048 1.348 1.648 1.948

0.800 1.104 1.392 1.696 0.800 1.104 1.392 1.696 2.000 1.100 1.400 1.700 2.000 2.300 1.392 1.696 2.000 2.304 1.400 1.700 2.000 2.300 1.400 1.700 2.000 2.300

1.000 1.304 1.592 1.896 1.000 1.304 1.592 1.896 2.200 1.300 1.600 1.900 2.200 2.500 1.592 1.896 2.200 2.504 1.600 1.900 2.200 2.500 1.600 1.900 2.200 2.500

1.26 1.26 1.22 1.26 1.37 1.50 1.33 1.45 1.37 1.61 1.61 1.61 1.61 1.72 1.72 1.66 1.66 1.66 1.72 1.79 1.79 1.79 2.02 2.02 2.02 2.02

0.010 0.029 0.047 0.066 0.010 0.029 0.047 0.066 0.085 0.029 0.048 0.066 0.085 0.104 0.047 0.066 0.085 0.104 0.048 0.066 0.085 0.104 0.048 0.066 0.085 0.104

0.028 0.047 0.065 0.084 0.028 0.047 0.065 0.084 0.103 0.047 0.066 0.084 0.103 0.122 0.065 0.084 0.103 0.122 0.066 0.084 0.103 0.122 0.066 0.084 0.103 0.122

0.050 0.069 0.087 0.106 0.050 0.069 0.087 0.106 0.125 0.069 0.088 0.106 0.125 0.144 0.087 0.106 0.125 0.144 0.088 0.106 0.125 0.144 0.088 0.106 0.125 0.144

0.063 0.082 0.100 0.119 0.063 0.082 0.100 0.119 0.138 0.081 0.100 0.119 0.138 0.156 0.100 0.119 0.138 0.157 0.100 0.119 0.138 0.156 0.100 0.119 0.138 0.156

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Ocean Engineering 185 (2019) 82–99

assessed in Model-A setup through 78 successful tests which result in three different sets of Rc (Rc1, Rc2 and Rc3). Then, twenty six tests, repeated twice, were successfully performed for Model-B with a fixed cross-section geometry. Table 6 shows the whole test matrix for irregular waves (0:067 � Hm0 � 0:114 m, 1:22 � Tm 1;0 � 2:02 s and 0:106 � dw � 0:200 m).

vertical seawall with a SWB. These photographs are obtained from camera recordings. Photographs a1 and b1 depict the test set-up with drawings. The horizontal white line in the middle represents the level of still water level (SWL). The free water surface at the starting instant is marked with a white color. Fig. 17-a1 to a5 show the free surface profiles of an approaching non-impulsive wave. The approaching wave is tending to break. The water level on the wall starts below the SWL, and it rises to the level (Fig. 17-a1). Accelerated water, which is rising on the vertical wall, reaches the impact point before the arrival of the approaching wave crest. Therefore, the approaching wave cannot break, and it is a non-impulsive wave. Then, the following wave run-up levels are high enough for the water to reach and pass over the crest of the seaward storm walls (Fig. 17-a2). This is defined as the ‘green water’ overtopping case where a continuous sheet of water passes over the crest of the seaward storm walls. Then, the incoming wave dissipates most of its energy by hitting the seaward storm wall and through the basin before it reaches the landward storm wall (Fig. 17-a3). A secondary impact occurs on the landward storm wall (Fig. 17-a4). However, this

4. Overtopping characteristics The wave condition at a vertical seawall may be non-impulsive (sometimes referred to as “pulsating’“) or impulsive (breaking). Nonimpulsive waves result in “green water” overtopping whereas impul­ sive waves result in violent (splash or spray type) overtopping. However, the combination of SWB at the crest of a vertical seawall tested in this research is expected to affect the type and characteristics of overtopping that is usually observed on simple vertical walls. Fig. 17 shows five photos in a sequence indicating the developments of water surface variations during overtopping through the crest of a

Fig. 17. Sequential photos of the water surface variations during the overtopping at the crest of a vertical seawall with a SWB. a) Green water overtopping, b) splash or spray type overtopping. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) 93

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impact is different from the first one and creates a splash type over­ topping ((Fig. 17-a5). Finally, accumulated water in the basin evacuates back through the double row of shifted seaward storm walls. From this example, it is seen that even if the overtopping starts as a green water overtopping type at the seaward storm wall, it may end up as a splash type overtopping at the landward storm wall where the overtopping water is collected. This shift will be influenced by the amount of the green water overtopping discharge from the seaward storm walls and the drainage capacity of the basin. Fig. 17 (b1 to b5) shows the free surface profiles of an approaching impulsive wave. The onset of breaking occurs at a distance before the wall location (Fig. 17-b1). White spikes are evidence that waves already start to lose some energy. The wave collides on the vertical seawall with a more parallel or curved face. Air is enclosed in the curve of the wave face. Wave crest and trapped air break up into pieces very soon and sends splashes/sprays (Fig. 17-b2). These droplets are carried over the sloping promenade under their own momentum (Fig. 17-b3 and b4). Some of these droplets may pass the landward storm wall, and other reflected back (Fig. 17-b5). The splash and spray type overtopping will be strongly influenced by the onshore winds. EurOtop (2016) suggests a maximum increase of factor 3–4 for the lowest discharges. However, the effect of wind on this type of discharge was not modeled in this research.

SWB. The test set-up, measuring devices and techniques were kept con­ stant for both Model-A and Model-B experiments to guarantee good comparison and to diminish the model effects. Little or no scale effect is expected in the overtopping results of this research as measurements from large scale laboratory tests for steeply-battered (10:1 and 5:1) nearvertical walls under impulsive (breaking) conditions indicate that there is good agreement at both small- and large-scales (Pearson et al., 2002). Pullen et al. (2004) and Pearson et al. (2001) also support these obser­ vations through a comparison of the field and laboratory measurements. 5.1. Overtopping at a vertical seawall (Model-A) Model-A serves as the reference case to determine the reduction factor of the Stilling Wave Basin (Model-B). The measured overtopping values are used to plot the performance of Model-A to compare with simple vertical wall formulations of EurOtop (2016). The test conditions are summarized in Tables 2 and 7 for three different Rc values All the tested waves break at the structure, generating “impulsive” overtopping d2

conditions (Hm0 :Lwm

1;0

� 0:23) following the definitions given in EurOtop

(2016). Data is within the range of 0:113 < Rc =Hm0 < 1:924. In addi­ tion, most of the data is defined as a low freeboard condition ðRc =Hm0 < 1:35Þ. The data points from high freeboard condition are marked with a ‘*’ in Table 7. Fig. 18 shows the relative overtopping discharge qffiffiffiffiffiffiffiffiffiffiffiffi 0:5 3 (ðq= g:Hm0 Þ =ðHm0 =dw sm 1;0 Þ ) plotted against the relative freeboard

5. Results The mean overtopping discharge (q) is a key design parameter for many coastal structures which are designed to limit overtopping below a selected admissible discharge (Van der Meer and Bruce, 2014). There­ fore, the mean overtopping discharge q is measured carefully from the collected water in the overtopping tank after each successful test. The discussion on the simple vertical seawall model (Model-A) is presented as a reference case to calculate the reduction in overtopping due to SWB (Model-B). Then, the effect of SWB on overtopping is described as a reduction factor (γSWB ). Discussion on tolerable over­ topping discharge is included for a complete assessment of the effect of

(Rc =Hm0 ) on Model-A following the approach presented in EurOtop (2016). Trend lines, which are the regression means, are fitted through the data for both low and high freeboard conditions. The test results are compared to the predicted values using Eqs. (3)–(5) for EurOtop (2007) and Eqs. (8) and (9) for EurOtop (2016). Fig. 18 shows that the for­ mulations of EurOtop (2016) predict significantly better than the first edition of the manual (EurOtop, 2007). The main differences between the two versions of the EurOtop Manual on vertical wall structures are

Table 7 Test results of the vertical seawall (Model-A) in model scale. Test #

Hm0 (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

0.081 0.075 0.069 0.067 0.088 0.085 0.083 0.076 0.071 0.104 0.092 0.084 0.076 0.075 0.094 0.090 0.084 0.080 0.105 0.098 0.092 0.086 0.114 0.108 0.103 0.095

a

Tm

1;0 (s)

1.26 1.26 1.22 1.26 1.37 1.50 1.33 1.45 1.37 1.61 1.61 1.61 1.61 1.72 1.72 1.66 1.66 1.66 1.72 1.79 1.79 1.79 2.02 2.02 2.02 2.02

dw (m)

0.200 0.181 0.163 0.144 0.200 0.181 0.163 0.144 0.125 0.181 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106

dw Li

d2w Hm0 :Lm

0.124 0.117 0.114 0.103 0.112 0.096 0.103 0.087 0.086 0.089 0.084 0.078 0.073 0.062 0.078 0.076 0.070 0.064 0.078 0.070 0.065 0.059 0.065 0.061 0.057 0.052

0.200 0.176 0.164 0.125 0.155 0.109 0.116 0.083 0.076 0.079 0.071 0.061 0.051 0.033 0.061 0.053 0.043 0.032 0.054 0.042 0.034 0.026 0.036 0.030 0.024 0.019

Rc1 (m)

Rc1 Hm0

0.010 0.029 0.047 0.066 0.010 0.029 0.047 0.066 0.085 0.029 0.048 0.066 0.085 0.104 0.047 0.066 0.085 0.104 0.048 0.066 0.085 0.104 0.048 0.066 0.085 0.104

0.124 0.386 0.681 0.986 0.113 0.340 0.569 0.873 1.205 0.277 0.516 0.786 1.115 1.388a 0.498 0.735 1.011 1.298 0.451 0.678 0.928 1.213 0.417 0.613 0.828 1.089

1;0

q1 (l/ m/s)

1.544 0.730 0.370 2.354 1.431 0.694 0.369 3.547 1.839 0.919 0.435 0.248 2.602 1.518 0.864 0.420 3.371 2.040 1.172 0.564 3.901 2.613 1.612 0.806

High freeboard condition.ðRc =Hm0 � 1:35Þ 94

Rc2 (m)

Rc2 Hm0

q2 Rep1 (l/m/ s)

q2 Rep2 (l/m/ s)

q3 Rep3 (l/m/ s)

Rc3(m)

Rc3 Hm0

q3 (l/ m/s)

0.028 0.047 0.065 0.084 0.028 0.047 0.065 0.084 0.103 0.047 0.066 0.084 0.103 0.122 0.065 0.084 0.103 0.122 0.066 0.084 0.103 0.122 0.066 0.084 0.103 0.122

0.346 0.625 0.942 1.255 0.317 0.551 0.786 1.111 1.460a 0.450 0.711 1.000 1.351a 1.629a 0.688 0.935 1.225 1.523a 0.621 0.862 1.124 1.423a 0.575 0.780 1.004 1.278

1.780 0.816 0.381 0.194 2.557 1.460 0.895 0.417 0.187 2.361 1.191 0.581 0.218 0.128 1.464 1.038 0.561 0.267 2.608 1.282 0.743 0.352 2.883 1.883 1.037 0.496

1.817 0.871 0.362 0.192 2.496 1.455 0.853 0.379 0.199 2.368 1.206 0.581 0.218 0.130 1.464 1.024 0.561 0.253 2.571 1.358 0.717 0.326 2.889 1.859 0.991 0.473

2.001 0.828 0.375 0.164 2.878 1.599 0.959 0.423 0.175 2.523 1.351 0.601 0.238 0.145 1.686 1.094 0.627 0.323 2.834 1.559 0.864 0.409 3.232 2.073 1.206 0.611

0.050 0.069 0.087 0.106 0.050 0.069 0.087 0.106 0.125 0.069 0.088 0.106 0.125 0.144 0.087 0.106 0.125 0.144 0.088 0.106 0.125 0.144 0.088 0.106 0.125 0.144

0.618 0.918 1.261 1.584a 0.566 0.809 1.053 1.402a 1.772a 0.662 0.950 1.261 1.639a 1.924a 0.921 1.180 1.487a 1.798a 0.830 1.087 1.364a 1.681a 0.768 0.984 1.218 1.509a

1.229 0.494 0.222 0.095 1.872 1.112 0.642 0.315 0.131 1.911 0.919 0.435 0.184 0.090 1.239 0.818 0.491 0.210 2.073 1.237 0.716 0.304 2.569 1.651 0.998 0.461

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Ocean Engineering 185 (2019) 82–99

qffiffiffiffiffiffiffiffiffiffiffiffi (ðq= g:H3m0 Þ =ðHm0 =dw sm

0:5 1;0 Þ )

plotted against the relative freeboard

(Rc =Hm0 ) of the Model-B. The green water type of overtopping is shown in the green color corresponding to low freeboard (0:708 � Rc =Hm0 < 1:35) whereas; splash/spray type (q < 10 l =m) is shown in red color for high freeboard (1:35 � Rc =Hm0 � 2:091) condition. As it is discussed before, one σ increased version of EurOtop (2016) equations (Equation (10) and Equation (11)) can fairly estimate the regression mean of the measurements from Model-A. Therefore, this line is used as the reference value to assess the impact of SWB on overtopping discharge. Fig. 19 shows the reduction impact of SWB on the overtopping discharge for both the low and high freeboard conditions under the 2

impulsive waves (Hm0 :Lh m

Fig. 18. Variation of the relative (non-dimensional) overtopping discharge plotted against the relative freeboard for simple vertical wall – comparisons to EurOtop (2007) and EurOtop (2016).

enhanced in this research set-up and conditions, therefore better pre­ diction capability of EurOtop (2016) is highlighted. On the other hand, there are some differences between data trend lines and the mean value approach of EurOtop (2016). Model effect, the differences in the number of waves in one run and the wave generation spectrum type will be the main source of the differences. However, the trend lines of the dataset (Fig. 18) coincide with the results of Equation (10) and Equation (11) in EurOtop (2016) which increase the average discharge by about one standard deviation (σ) for low and high freeboard conditions. Therefore, one σ increased version of EurOtop (2016) (Equation (10) and Equation (11)) is considered to represent data set.

y¼

1;0

1 q �0:5 � 0:0155 qffiffiffiffiffiffiffiffi3ffiffiffiffi H g:H m0 hsmm01;0

(14)

Then, the equation can be simply written as � � Rc y ¼ exp 2:2 Hm0

The Stilling Wave Basin (Model-B) is tested under the conditions summarized in Table 5 and Table 8. Waves break at the structure, and the dataset is within the reliability range of impulsive overtopping d2

� 0:23). This effect of SWB can be expressed

The right side of the equation can be denoted as

5.2. Overtopping at the crest of the vertical seawall with SWB (Model-B)

(Hm0 :Lwm

1;0

by a reduction factor for every test case by comparing the measured discharge value of Model-B to the expected discharge value of Model-A for same freeboard condition, Rc =Hm0 using the respective equation for low and high freeboard conditions as described below: a) For low freeboard condition ( 0:1 < Rc =Hm0 < 1:35), the reference formula has an exponential form (Equation (10)), and it can be rearranged as � � 1 q Rc ¼ exp 2:2 (13) � � 0:5 0:0155 qffiffiffiffiffiffiffiffi3ffiffiffiffi H Hm0 g:H m0 hsmm01;0

(15)

After taking the natural logarithm of both sides, the expression is rewritten as

� 0:23), low and high freeboard conditions. Data is within the

range of 0:708 < Rc =Hm0 < 2:091. Most of the data is defined as a low freeboard condition ðRc =Hm0 < 1:35Þ. The data points from high free­ board condition are marked with a ‘*’ in Table 8 and they are all below 0:01 l =m=s. It is hard to determine one reduction formula that can be applied to SWB since many variations in the geometry of the SWB are possible. Therefore, the optimized SWB geometry of Model-B was tested under the identical hydrodynamic conditions that Model-A was tested (Table 7) to propose a reduction factor for structures with similar geometries. The mean overtopping discharge was measured from the collected water in the tank. However, the mean overtopping discharge would be the result of either green water or splash/spray type overtopping, since both types may be observed during a run with 500 irregular wave train. So it is hard to determine which type of overtopping is responsible for the accumu­ lated water in the tank. However, it is seen that waves in the range of high freeboard condition ðRc =Hm0 � 1:35) mainly result in splash or spray type of overtopping whereas waves in the range of low freeboard condition ðRc =Hm0 < 1:35) mainly result in green water type over­ topping. The splash or spray type of overtopping discharges are q < 0:01 l =m=s and their type are also confirmed by visual observations. Fig. 19 shows the relative overtopping discharge

lnðyÞ ¼

2:2

Rc Hm0

(16)

For a known HRm0c value, the presence of the SWB reduces the average

overtopping discharge from y to y1 by a reduction factor (HRm0c lnðy1Þ ¼

� � Rc 1 2:2 Hm0 γ SWB

1 ). γSWB

(17)

y is the calculated theoretical value from Equation (16), while y1 is the value considering measured q from Model-B with SWB. Then, the reduction factor (γSWB ) for low freeboard condition can be written as 2:2 Rc ¼ γ SWB lnðy1Þ Hm0

(18)

b) For high freeboard condition (Rc =Hm0 � 1:35), a similar procedure to low freeboard conditions is followed. The reference formula (Equation (11)) has a power form, and it can be re-arranged as

Table 5 Summary of the finalized Model-B characteristics.

Prototype Scale Model Scale

ft (m)

dw þ df (m)

hb (m)

wb (m)

xr (m)

Δx (m)

hr (m)

Cb ð%Þ

sf –

sr –

6.400 0.400

2.560 0.160

0.640 0.040

0.480 0.030

8.000 0.500

0.640 0.040

0.640 0.040

66.7 66.7

20 20

40 40

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Ocean Engineering 185 (2019) 82–99

Table 8 Test results of the vertical seawall with SWB (Model-B), in model scale. Test #

Hm0 (m)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

0.081 0.075 0.069 0.067 0.088 0.085 0.083 0.076 0.071 0.104 0.092 0.084 0.076 0.075 0.094 0.090 0.084 0.080 0.105 0.098 0.092 0.086 0.114 0.108 0.103 0.095

a

Tm

1;0 (s)

dw (m)

1.26 1.26 1.22 1.26 1.37 1.50 1.33 1.45 1.37 1.61 1.61 1.61 1.61 1.72 1.72 1.66 1.66 1.66 1.72 1.79 1.79 1.79 2.02 2.02 2.02 2.02

0.200 0.181 0.163 0.144 0.200 0.181 0.163 0.144 0.125 0.181 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106 0.163 0.144 0.125 0.106

dw Li

d2w Hm0 :Lm

0.124 0.117 0.114 0.103 0.112 0.096 0.103 0.087 0.086 0.089 0.084 0.078 0.073 0.062 0.078 0.076 0.070 0.064 0.078 0.070 0.065 0.059 0.065 0.061 0.057 0.052

0.200 0.176 0.164 0.125 0.155 0.109 0.116 0.083 0.076 0.079 0.071 0.061 0.051 0.033 0.061 0.053 0.043 0.032 0.054 0.042 0.034 0.026 0.036 0.030 0.024 0.019

R’c (m)

R’c Hm0

qSWB Rep1 (l/m/s)

γSWB –

qSWB Rep2 (l/m/s)

γSWB –

0.063 0.082 0.100 0.119 0.063 0.082 0.100 0.119 0.138 0.081 0.100 0.119 0.138 0.156 0.100 0.119 0.138 0.157 0.100 0.119 0.138 0.156 0.100 0.119 0.138 0.156

0.772 1.084 1.442a 1.771 0.708 0.956 1.204 1.567a 1.949a 0.782 1.086 1.409a 1.803a 2.091 1.054 1.319 1.636a 1.954a 0.949 1.215 1.501a 1.827a 0.878 1.100 1.340 1.640a

0.09220 0.00954

0.45 0.40

0.09538 0.00874

0.46 0.39

0.26003 0.08789 0.02105 0.00103 0.00015 0.27919 0.04235 0.00536 0.00002

0.53 0.51 0.49 0.19 0.12 0.52 0.47 0.26 0.06

0.23811 0.08656 0.01805 0.00110 0.00010 0.28646 0.03986 0.00548 0.00001

0.52 0.51 0.48 0.19 0.11 0.52 0.47 0.27 0.05

0.12221 0.01925 0.00223 0.00030 0.30065 0.06704 0.00978 0.00026 0.47972 0.16040 0.02471 0.00514

0.56 0.49 0.22 0.14 0.62 0.55 0.31 0.11 0.60 0.57 0.48 0.25

0.09358 0.01684 0.00283 0.00006 0.29253 0.06704 0.01006 0.00022 0.43130 0.15464 0.02570 0.00415

0.53 0.48 0.24 0.08 0.61 0.55 0.31 0.11 0.59 0.56 0.48 0.23

1;0

High freeboard condition.ðRc =Hm0 � 1:35Þ

� y1 ¼

Rc 1 Hm0 γSWB

�

3

(22)

y is the calculated theoretical value from Equation (21), while y1 is value considering measured q from Model-B with SWB. Then, the reduction factor (γSWB ) for high freeboard condition can be written as pffiffiffiffiffi Rc 1=3 y2 ¼ γSWB Hm0

(23)

Individual reduction factors, obtained for the 26 tests on Model-B, are calculated using Equation (18) and Equation (23), and the results are presented in Table 8. Fig. 20 shows the variation of calculated reduction factors for both low and high freeboard conditions. Regression Fig. 19. Variation of the relative (non-dimensional) overtopping discharge plotted against the relative freeboard for SWB geometry – comparison to EurOtop (2016).

� � 1 q Rc �0:5 ¼ � q ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 0:002 Hm0 g:H 3m0 hsHmm01;0

3

(19)

The right side of the equation can be denoted as y¼

1 q �0:5 � 0:002 qffiffiffiffiffiffiffiffi3ffiffiffiffi H g:H m0 hsmm01;0

(20)

Then, the equation can be written as � � 3 Rc y¼ Hm0

(21)

For a known HRm0c value, the presence of the SWB, reduces the average

overtopping discharge from y to y1 by a reduction factor (HRm0c

Fig. 20. Variation of the reduction factor γSWB with the variation of HRm0c . Blue values represents the results from low freeboard condition whereas red values represent the results of high freeboard condition. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

1 ). γSWB

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Ocean Engineering 185 (2019) 82–99

lines of reduction factors are drawn for low and high freeboard condi­ tions to assess the sensitivity of the reduction factor to the change of freeboard. Equation (24) and Equation (25) represent the regression means. For low and high freeboard conditions, the reduction factor variation is in the range of 0:39 � γSWB � 0:62 and 0:05 � γSWB � 0:31, respectively. It is observed that SWB designed as Model-B presents higher efficiency in reducing the overtopping for high freeboard conditions. Also, for the tested SWB geometry, the reduction factor is more sensitive to the change of freeboard condition in the zone of high freeboard condition. Still, the scatter of the data has to be considered. Low freeboard condition (Greenwater type) γ SWB

low

¼

0:0615

Rc þ 0:577; Hm0

0:708 �

Rc < 1:35 Hm0

Table 9 Limits for overtopping for people and vehicles (EurOtop, 2016). Hazard type and reason

Mean discharge, q (l/ m/s)

Max volume, Vmax (l/m)

People at structures with possible violent overtopping, mostly vertical structures

No access for any predicted overtopping

No access for any predicted overtopping

0.3 1 10–20 No limit

600 600 600 No limit

People at seawall/dike crest. Clear view of the sea. Hm0 ¼ 3 m Hm0 ¼ 2 m Hm0 ¼ 1 m Hm0 < 0.5 m

(24)

High freeboard condition (splash/spray type) γ SWB

high

¼

0:3812

Rc þ 0:828; Hm0

1:35 �

Rc � 2:09 Hm0

(25)

If Equation (24) and Equation (25) integrated into the EurOtop equations (Equation (10) and Equation (11)), the new forms of nondimensionalised exponential and power form equations can be written as � �0:5 � � q Hm0 Rc 1 qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:0155 :exp 2:2 ; 0:708 < Rc =Hm0 hsm 1;0 Hm0 γ SWB low g:H 3m0 < 1:35 (26) �0:5 � � � q Hm0 Rc 1 qffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:0020 hsm 1;0 Hm0 γSWB high g:H 3m0

3

1:35 �

Rc � 2:09 Hm0

Fig. 22. Variation of the overtopping discharge [q (l/m/s)] as a function of the spectral significant wave height, Hm0 for tolerable overtopping.

(27)

have access to these structures all the time. Therefore, the experimental results are discussed in light of the concept of a tolerable overtopping discharge for people and vehicles defined in EurOtop (2016) as pre­ sented in Table 9. Tolerable overtopping strongly depends on wave height in addition to maximum overtopping volume. Fig. 22 shows the variation of the overtopping discharge [q ðl=m=sÞ] as a function of the spectral signifi­ cant wave height, Hm0 . The plots compare the measured values of q from Model-A and Model-B with tolerable overtopping discharge limits for people proposed in EurOtop (2016). In the experiments, the wave heights ranged from 1 m to 2 m which corresponds to tolerable over­ topping discharges from 20 to 1 l =m=s respectively (see Table 9). However, due to the absence of sufficient data, it is not clear about the form of the function between Hm0 ¼ 1 2 m (EurOtop, 2016). As it is seen from the figure, the measured values for Model-A are mostly above the tolerable values. These results accurately depict the negative consequences of over­ topping observed every year during winter storms (Kisacik et al., 2017). However, SWB modification of Model-B significantly decreases the overtopping discharge for Hm0 < 1:6m which enhances the applicability of such modification in real life. it should be strongly noted that the values plotted in Model-B belong to overtopping behind the landward seawall not in the basin of the SWB which is the promenade. If such a modification is realized on site, precautions must be taken to inform people about the use of promenade under storm conditions.

Then, trend lines from Equation (26) and Equation (27) are plotted with the SWB data for low freeboard (Greenwater type) and high free­ board (Splash/spray type) conditions in Fig. 21. Within the parameters range, a good agreement is observed for the specified geometry of the SWB. 5.3. Tolerable overtopping for people Tolerable overtopping discharge is the amount of water passing over a structure that is considered safe. The structures presented in this paper are primarily designed and tested to limit overtopping that might cause flooding in an urban setting. Therefore, the direct hazard of overtopping to people and cars is a meaningful discussion to consider since people

6. Conclusions Over 150 tests have been carried out to investigate wave overtopping at a vertical wall with low crested Stilling Wave Basin structure with foreshore and under impulsive conditions in an urban coastal area. Reduction of wave overtopping in the optimized SWB modification compared to simple vertical seawall is discussed for a range of wave conditions correspond to impulsive conditions defined by EurOtop

Fig. 21. Variation of the relative (non-dimensional) overtopping discharge plotted against the relative freeboard for SWB geometry – comparison to EurOtop (2016). 97

Ocean Engineering 185 (2019) 82–99

D. Kisacik et al.

(2016). Conditions limiting the modification of existing coastal struc­ tures in urban settings for wave overtopping are reflected in the experiment design. The performance of SWB in terms of tolerable overtopping in an urban setting is also discussed for the tested hydro­ dynamic conditions. A parametric survey with 23 different geometries was performed under constant hydrodynamic conditions (100 year return period storm condition of Izmir Bay) to optimize SWB geometry as a crest modifica­ tion for the vertical seawall. The results of the parametric study indicate that essential parameters in the design of SWB are the height of the storm walls, the number of rows on the seaward edge and an optimal blocking coefficient. Moreover, as the width of the promenade increases, its effect on wave overtopping decreases exponentially. A simplified model of an existing seawall and promenade, wellknown as `Kordon’ in Izmir, Turkey was tested to analyze the perfor­ mance of the structure under impulsive conditions. These experiments showed that a single non-impulsive wave generally produces green water overtopping at low freeboard condition, whereas splash or spray type overtopping is seen at high freeboard condition for an impulsive wave. However, it was observed that the existence of SWB changes the overtopping type and characteristics. With SWB, two sequential over­ topping types take place for one single wave. The first one occurs on the seaward and the second one occurs on the landward storm walls, and the overtopping type may shift from one type to the other one when it is passing from seaward to the landward walls. The final measured over­ topping discharge in the tank will belong to the second overtopping type, which appears on the landward storm wall. As both green water and splash/spray types of overtopping was observed to occur in each run with a wave train of 500 irregular waves. The green water type of overtopping corresponds to low freeboard (0:708 � Rc =Hm0 < 1:35) whereas; splash/spray type corresponds for high freeboard (1:35 � Rc = Hm0 � 2:091) condition. Differences between measured data trend lines and the mean value approach of EurOtop (2016) were observed. The model effect, the dif­ ferences in the number of waves and the wave generation spectrum type might be the primary sources of the differences. However, the trend lines of the experiment dataset coincide with the results of EurOtop (2016) which increase the average discharge by about one standard deviation σ for low and high freeboard conditions. The effect of SWB modification is expressed by a reduction factor for every test case by comparing the measured discharge value of Model-B to the expected discharge value of Model-A for same freeboard condi­ tion, Rc =Hm0 using the respective equations of EurOtop (2016). Regression mean lines of reduction factors are drawn for low and high freeboard conditions of individual reduction factors obtained for the 26 tests on Model-B. Low freeboard condition (Greenwater type) γ SWB

low

¼

0:0615

Rc þ 0:577; Hm0

0:708 �

# �0:5 " � q Hm0 Rc 1 qffiffiffiffiffiffiffiffiffiffiffi ¼ 0:0020 hsm 1;0 Hm0 γSWB high g:H3m0

high

¼

0:3812

Rc þ 0:828; Hm0

1:35 �

1:35 �

Rc � 2:09 Hm0

This SWB crest modification on vertical seawall performs similarly to dike modifications presented by Cavani et al. (1999); Aminti and Franco (2001) and Geeraerts et al. (2006). The reduction coefficient proposed in this study can be directly used with the formula of EurOtop (2016); however, it is specific to the test geometry. For a general design, opti­ mization of the SWB under different hydrodynamic conditions is also necessary. Although the reduction factors presented in this study has limited applicability for general design of SWB, both the parametric study and the reduction observed under broader hydrodynamic conditions indi­ cate that modifying the crest of a vertical seawall with a double row shifted storm walls on the seaside, a promenade and a landward storm wall with bullnose (SWB) lead to a significant reduction of the over­ topping discharge while preserving the original outline of the seawall and promenade. It should also be noted that such “innovative” geometry of the overspill basin in an urban setting is relatively easy and cheap to be made, especially in existing structures with large low crest berms, where some rocks in front of the wave wall could be shifted seaward to create a higher outer crest and a rear dissipating basin (Grossi et al., 2015).Therefore, SWB modification of seawalls can be an efficient alternative solution to adapting to the possibility of higher overtopping conditions in urban settings. Acknowledgments The support of MSc student Banu Keles¸ Benli during field survey is gratefully acknowledged. This project is funded by Middle East Tech­ nical University (Turkey), Scientific Research Projects Funds (METUBAP) Grant No: BAP-08-11-2015-036 and Dokuz Eylül Üniversitesi (Turkey), Scientific Research Projects Funds (DEU-BAP) Grant No: 2016. KB.FEN.014. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.oceaneng.2019.05.033. References Aguado, A., Sanchez-Naverac, V., 1978. Nuevo tipo de secci� on para diques en talud con espald� on, vol. 1978. Revista de Obras Pùblicas. Mako, pp. 353–359. Allsop, N.W.H., Besley, P., Madurini, L., 1995. Overtopping Performance of Vertical Walls and Composite Breakwaters, Seawalls and Low Reflection Alternatives. Final Rep. Of Monolithic Coastal Structures Project. Univ. of Hannover, Hannover, Germany. Altomare, C., Verwaest, T., Suzuki, T., Trouw, K., 2014. Characterization of wave impacts on curve faced storm return walls within a stilling wave basin concept. In: Lynett, P. (Ed.), Proc. 34th Conference on Coastal Engineering, Seoul, Korea, 2014. Coastal Engineering Proceedings, vol. 34, pp. 1–12. Aminti, P., Franco, L., 2001. Performance of overspill basin on top of breakwaters. In: International Conference in Ocean Engineering (Chennai). Bouchet, R., 1992. New Types of Structures for Attenuating Waves and Breakwaters. Proc. Coastal Structures and Breakwaters. Thomas Telford Publishing, London, ICE, pp. 95–110. https://doi.org/10.1680/csab.16729.0006. Burcharth, H.F., Andersen, T.L., 2006. Overtopping of rubble mound breakwaters with front reservoir. Proc. 30th Int. Conf. on Coastal Engineering. World Sci. 4605–4615. https://doi.org/10.1142/9789812709554_0386. Cappietti, L., Aminti, P.L., 2012. Laboratory investigation on the effectiveness of an overspill basin in reducıng wave overtoppıng on marına breakwaters. In: Proc. 32nd Conf. On Coastal Engineering, vol. 2012, pp. 1–10. Santander, Spain. Cavani, A., Franco, L., Napolitano, M., 1999. In: Losada, I., Balkema (Eds.), Design Optimization with Model Tests for the Protection of Gela Caisson Breakwater Coastal Structures ’99, Proc. Int.Conf. CS’99 - Santander (Spain) 7-10 June 1999, vol. 2, pp. 927–935 (Rotterdam). Ceniceros, J., Medina, J.R., 2001. Redes neurales para el diseno de diques con baja cota de coronacion (in Spanish). VI Jornadas Esp. Ing. costas y puertos. Crema, I., Cappietti, L., Aminti, P.L., 2009. Laboratory measurements of wave overtopping at plain vertical wall breakwaters in presence of an overspill stilling

Rc < 1:35 Hm0

High freeboard condition (splash/spray type) γ SWB

3

Rc � 2:09 Hm0

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