NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-17-127-2017Wave simulation for the design of an innovative quay wall: the case of
Vlorë HarbourAntoniniAlessandroArchettiRenatarenata.archetti@unibo.ithttps://orcid.org/0000-0003-2331-6342LambertiAlbertoCoastal, Ocean and Sediment Transport Research Group – Plymouth
University – Marine Building, Drake Circus, Plymouth, Devon, PL4 8AA, UKDICAM, University of Bologna, Bologna, 40136, ItalyCONISMA, Consorzio Nazionale Interuniversitario per le Scienze del
Mare, Rome 00196, ItalyCIRI Edilizia e Costruzioni, University of Bologna, Bologna, 40100,
ItalyRenata Archetti (renata.archetti@unibo.it)30January201717112714214May201613June20165October201627October2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://nhess.copernicus.org/articles/17/127/2017/nhess-17-127-2017.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/17/127/2017/nhess-17-127-2017.pdf
Sea states and environmental conditions are basic data for the
design of marine structures. Hindcasted wave data have been applied here
with the aim of identifying the proper design conditions for an innovative
quay wall concept.
In this paper, the results of a computational fluid dynamics model are used to
optimise the new absorbing quay wall of Vlorë Harbour (Republic of
Albania) and define the design loads under extreme wave
conditions. The design wave states at the harbour entrance have been
estimated analysing 31 years of hindcasted wave data simulated through the
application of WaveWatch III. Due to the particular geography and topography
of the Bay of Vlorë, wave conditions generated from the north-west are
transferred to the harbour entrance with the application of a 2-D spectral wave
module, whereas southern wave states, which are also the most critical for
the port structures, are defined by means of a wave generation model,
according to the available wind measurements. Finally, the identified extreme
events have been used, through the NewWave approach, as boundary conditions
for the numerical analysis of the interaction between the quay wall and the
extreme events. The results show that the proposed method, based on
numerical modelling at different scales from macro to meso and to micro,
allows for the identification of the best site-specific solutions, also for a
location devoid of any wave measurement. In this light, the objectives of
the paper are two-fold. First, they show the application of sea condition
estimations through the use of wave hindcasted data in order to properly
define the design wave conditions for a new harbour structure. Second, they
present a new approach for investigating an innovative absorbing quay wall based
on CFD modelling and the NewWave theory.
(a) Location of Vlorë, (b) wave hindcast
extraction point (red star), Vlorë Harbour (yellow star), wind data
measurement point (blue star); (c) view of Vlorë Harbour.
Introduction
The development of global trade and ship transportation often requires that
the existing docks must be upgraded, consolidated or enlarged in order to
face effectively the increasing demand of people and freight traffic. With such
aims, quays built above absorbing rubble mounds can be used to enlarge or rebuild structures in the existing docks. Generally, the
rubble mound structures assure low reflection in the port basins, which is very
important for mooring and manoeuvring but they lead to the construction of
very wide superstructures. The construction of these superstructure is not always possible due to the
restrictions in the available spaces and financial sources. The use of
vertical walls as berthing structures is an alternative often used in port
areas: in fact this kind of solution represents a compromise between the
simplicity of construction and the need to occupy a small area.
Nevertheless, vertical quay walls present a drawback of undesirable high-wave reflection into the port areas. A low-reflecting quay might sort out the
reflection issue in port areas by means of porous or open structures that
dissipate part of the incident wave energy. Therefore, several different
vertical dissipative solutions have been proposed during the last decades as
a result of research studies from all over the world.
The availability of wave data is necessary for pursing the design
of innovative harbour parts, as the quays and docks. For several remote
locations direct measurements are not always available and series of
hindcasted waves are necessary for defining the proper conditions at the harbour
entrance. The most common operative wave models are WaveWatch III, WAM and
SWAN (The WAMDI Group, 1988; Monbaliu et al., 2000; Booij and Holthuijsen, 1999).
The WaveWatch III model (http://polar.ncep.noaa.gov/waves/wavewatch/wavewatch.shtml), developed by
the National Weather Service (NWS) and National Oceanic and Atmospheric
Administration (NOAA) is operational at DICCA, University of Genoa. The
model covers the whole of the Mediterranean basin with a resolution equal to
0.1∘ (Sartini et al., 2014, 2015a, b). The model chain,
extensively validated by Mentaschi et al. (2015a), is forced with the
National Centers for Environmental Prediction Climate Forecast System
Reanalysis data at 0.5∘ resolution. In this paper, the design wave
conditions are estimated by means of extreme wave analysis applied to the
numerical results. An extreme event analysis can be based on different
methodologies (Mazas et al., 2014; Masina et al., 2015) while the historic
and most used design approach leads to the use of the peak over threshold
technique to select sample data (Mathiesen et al., 1994; Garcia-Espinel et
al., 2015).
To attenuate wave reflection various structures have been designed,
Jarlan-type structures (Jarlan, 1961) being the most widely used. However, all the
existing absorbing solutions for vertical maritime structures have the
drawback that their exiguous efficacy reduces the reflection of low-frequency waves (i.e. wave periods larger than 25 s). To overcome this
technical problem, the design of a vertical structure can be based on a
multi-cell circuit concept which is considered to be especially effective to
reduce the wave reflection of wind waves and oscillations associated with
intense storms and resonance waves in port basins (Medina et al., 2010). Furthermore, Altomare and Gironella (2014), Matteotti (1991)
and Faraci et al. (2012) investigated, by means of physical model
tests, several quay walls consisting of prefabricated caissons with frontal
openings and internal rubble mounds. In the paper, a similar solution is
shown, consisting of a retaining wall realised by a combi-wall structure
and a frontal opening with internal rubble mounds. Throughout the paper, the use
of hindcasted data are used to properly define the design conditions at the
entrance of Vlorë Harbour, while the quay wall structure is investigated
using CFD simulations (CD-ADAPCO, 2013; Lamberti et al., 2014).
Site description
The city of Vlorë, in the Republic of Albania, is located on a coastal plain
in the north-eastern part of the bay. The bay is approximately 17 km long and
10 km wide with a depth that reaches 55 m. It is open to the Adriatic Sea
through the north-western side and is bordered by tall and craggy mountain peaks on
the southern and western sides. The bay is also partially protected from the
swells coming from the north-west by the presence of Sazan Island, located at the
northern part of the bay, and by the shallow water next to the mouth of the
Vjosa River (see Fig. 1a). The investigated port is located in the small
northern stretch of the coast in the inner part of the bay. The location of
the new harbour is presented in Fig. 1b with a yellow star.
In the surrounding area some port infrastructures are already presented.
Some of them are still working and others are disused. The facilities
include an offshore berth for tankers called New Port and the historic Old
Port of Vlorë. The harbour under investigation is characterised by the
presence of two piers, as shown in Fig. 1c, called the west wharf and east pier.
The first is primarily intended for docking ferry passengers while the
second is used for berthing cargo vessels.
Design wave conditions
No measured wave data are available for the Bay of Vlorë; therefore wave climate
is defined as 31 years (1999–2010) of hindcasted wave data
supplied by the University of Genova (Sartini et al., 2015a; Mentaschi et
al., 2015b). The extraction point (red star in Fig. 1b) is selected in order
to represent the wave climate outside the gulf. The wave rose at
the extraction point is shown in Fig. 2.
Wave rose at the entrance of Bay of Vlorë (coord. 40∘30′ N, 19∘12′ E.)
Two main directional sectors are evident: the first sector between
-120 and +40∘ N, associated with the axis
direction of the Adriatic, and the second sector between 160 and
200∘ N, providing information on southern waves. The dominant wave condition is related
to the sector between 155 and 170∘ N, whereas the maximum occurrence
frequency, i.e. 15 %, of the northern events is related to 300∘ N. The maximum northerly wave height is equal to 5.75 m, with a peak period of 10 s.
Due to the particular geography and topography of the bay, southern
hindcasted wave data are not representative of the actual conditions in the
vicinity of the port. Consequently, the definition of southern wave states
(S–SW) requires other data sources like wind measurements to be partially available
inside the bay.
In order to define the design wave conditions at the harbour entrance, two
different approaches have been undertaken according to the propagation
direction. For both the interested directions, the exercise and extreme
conditions are defined according to return periods of 2 and 100 years,
respectively. A return period event of 2 years is accounted for by the limit
of ordinary operation, i.e. the limit condition for which there should not be
any malfunction of the harbour infrastructure. A return period event of
100 years is considered for the design condition of the structures, i.e. the
event for which only the structures should resist. The northern wave
conditions are established by the extreme wave analysis, performed on the
hindcasted wave data. The southern wave conditions are estimated by applying
the wave generation model, Mike21-SW on the Bay of Vlorë, by imposing a local wind
intensity with TR= 2 years and TR= 100 years.
Design waves from NW
The peak over threshold method (POT) has been applied to the northern storm
time series (N–NW) in order to select independent storm peaks. The technique
is a well-established statistical approach, based on the following steps:
(i) the application of a proper threshold, (ii) the selection of homogeneous
independent events and peaks which exceed the selected threshold, (iii) the
identification of the probability model that best represents the exceedances
and (iv) a determination of values within a given return period.
Interpretation of the wave data at the study
area: (a) empirical and analytical PDF and (b) empirical
and analytical CDF for the identified peak values.
The POT analysis has been applied to the wave data, providing the results
illustrated in Fig. 3, in which the empirical frequency histogram and
cumulative distribution function (PDF and CDF) are given along with the
corresponding Gumbel distribution with the best-fit scale parameter (σ) and location parameter (μ) equal to 0.58 (95 % lower and upper
bounds parameter fitting: 0.55–0.61), 2.51 (95 % lower and upper bounds
parameter fitting: 2.48–2.55), respectively. The threshold used to define an
individual storm has been established according to Boccotti's method
(Boccotti, 2000). The method is based on the identification of a wave height
threshold, namely 1.5 times the annual average HSy, that is equal
to 1.0 m for the available wave data: the adopted threshold value is
therefore equal to 1.50 m. The application of the described approach led to
the detection of 355 independent events from the direction -120 to
+40∘ N. The northern sector is between 285 and 345∘ N. It is worth
remarking that the significant wave height (HSTR30) of the
estimated 30-year return period (TR= 30 years) is equal to
5.8 m, in good agreement with the maximum hindcasted wave height equal to
5.75 m. The resulting values of HS for the selected wave heights
are listed in Table 1. The analyses have provided the significant wave height
(Hs) and the mean peak period (Tp), with values given
in Table 1 with reference to return periods of 2 years and 100 years. The
mean peak periods associated with the predicted significant wave heights have
been calculated using a scatter plot of simulated peak periods versus
significant wave height as proposed by Viselli et al. (2015) and Schweizer et al. (2016). The parameters
a and b in Eq. (1). turn out to be equal to 2.36 (0.30, 4.42) and 0.72
(0.43, 1.01), respectively; values in parentheses indicate the lower and
upper bounds of the 95 % confidence interval.
Tp=a⋅Hsb
The numerical model Mike 21-SW was then applied to propagate such conditions
from the offshore location to the entrance of the port. The spectral wave
model simulates the growth, decay and transformation of wind-generated
waves. MIKE21-SW is a third-generation spectral wave model, as it does not
require any parameterisation of either the spectral or the directional
distribution of power. The modelled physical processes comprise: (a) energy
source-dissipation processes (wind driven interactions with atmosphere,
dissipation through wave breaking and white-capping and bottom
friction-induced dissipation), (b) non-linear energy transfer conservative
processes (resonant quadruplet interactions, triad interactions) and (c) wave
propagation-related processes (wave propagation due to the wave group, depth
induced refraction, shoaling). The models compute the evolution of wave
action density by solving the action balance equation as described by Booij
et al. (1999). Numerical propagation has been completed by means of
unstructured triangular meshes as recently applied by Samaras et al. (2016)
and Gaeta et al. (2016). The adopted bathymetric and shoreline data result
from the digitisation of nautical charts acquired from the Italian
Hydrographic Institute. The triangular mesh dimension is homogeneous over the
entire domain, resulting in a mesh of 102 995 elements with a mean dimension
of 600 m2. The adopted grid is shown in Fig. 4.
Bathymetry of the wave model (a) and close-up of the
bathymetry and mesh at the harbour entrance area (b).
Wave field for the design wave condition HS= 4.40 m,
Tp= 8.5 s, Dir = 310∘ N. (a) Entire
domain, (b) harbour entrance. The blue bullet is the extraction
point location; its UTM coordinates are 371221∘ E,
4478470∘ N.
Interpretation of extreme events using the hindcasted northern wave
data at the selected location off the Bay of Vlorë.
Wave fields of HTR2 and HTR100 are presented in
Figs. 5 and 6, in which reduction of the wave height due to the shoaling is
shown. The design conditions at the harbour entrance at 13.5 m water depth
(UTM coord. 371221∘ E, 4478470∘ N; Fig. 6) are shown in Table 2.
Wave field for the design wave condition HS=6.85, Tp=11,
Dir = 310∘ N. (a) Entire domain, (b) harbour entrance. The blue
bullet is the extraction point location; its UTM coordinates are 371221∘ E,
4478470∘ N.
Wave conditions extracted at the harbour entrance (UTM coord.
371221∘ E, 4478470∘ N).
Hs [m]Tp [s]Dir [∘ N]TR= 2 years1.008.5260TR= 100 years1.7011.0265Design waves from S
Southerly design wave conditions are not easily estimated, as direct
measurements of waves inside the Bay of Vlorë were not available and wind
data were also relatively scarce. Such conditions, which are also the most
critical for the port structures, were defined by a wave generation model,
MIKE21-SW, after an empirical extrapolation of the wind intensity based on
2 years of measured data.
The approach is well known and shortly summarised here: wind-wave generation
is the process by which the wind transfers energy into the water body,
generating waves. The wind input is based on Janssen's (1989, 1991)
quasi-linear theory of wind-wave generation, in which the momentum transfer
from the wind to the sea not only depends on the wind stress, but also on the
sea state itself. The source function describing the dissipation due to white
capping is based on the theory of Hasselmann et al. (1985) and
Janssen (1989), while the source function describing the bottom-induced wave
breaking is based on the well-proven approach of Battjes and Janssen (1978)
and Eldeberky and Battjes (1996). More details on the wave generation
model are provided in
the DHI Manual (2011). The generation model was forced with
TR= 2 and TR= 100 wind intensity values (see
Table 3).
Wind conditions used as input to the MIKE21-SW wave generation
model, Lamberti et al. (2015).
U [m s-1]Dir [∘ N]TR= 2 years22215TR= 100 years41215
Wind data measurements were supplied by SIAP-MICROS s.r.l., the anemometer
was installed on the Albania coast at point of coordinate
40∘ 30′51.98′′ N,
19∘ 23′36.69′′ E, presented on Fig. 1b with a blue star; the
resulting wind rose is shown in Fig. 7. The measurement protocol followed the
standard, measuring every 10 min. The instrument has been working for
2 years (July 2006–August 2008). The statistical analysis of the data was
preceded by a quality control check of all data in order to remove the
outliers and to interpolate over small data gaps that may be present.
Overall, the corrected data were of sufficient quality, with less than
3 % of the data removed as outliers or unacceptable values; Belu and
Koraicn (2009). The highest measured value is equal to 22.8 m s-1,
while a gust reduction factor equal to 0.96 is applied in order to define the
effective wind velocity (El-Hawary, 2000). The minimum effective southern
wind duration for the Bay of Vlorë is estimated through the
SMB (Sverdrup–Munk–Bretschneider) method and is equal to 1 h for an effective
fetch of 10 km length (US Army corps of engineers, 1984). Under the
hypothesis of a constant difference between wave heights characterised by two
consecutive return periods of different orders of magnitude (i.e. ΔHs=(HsTR10-HsTR1)=(HsTR100-HsTR10)=1.35 m)
the centennial wave state was estimated to be equal to a significant wave
height of 3.8 m and peak period of 6.1 s. Within the inverse SMB procedure,
the centennial wind intensity is estimated to be equal to 41 m s-1.
Wind rose (July 2006–August 2008).
It should be said that the dearth of data and the empirical nature of the
stated procedure might produce uncertainty of the calculated values.
Therefore, in order to validate the adopted method, the wave field forced by
the mentioned wind conditions was generated through the wave generation
model of the MIKE 21 SW. The results are presented in Table 3 and in Figs. 8
and 9, while the extracted wave conditions at the harbour entrance are
presented in Table 4. The final results of the design waves are a set of four
wave conditions for the two incoming wave directions (i.e. north-west and
south-west) and the two return periods (i.e. 2 and 100 years); Table 4.
Wave field for the design wave condition generated by southern wind
U=22 m s-1, Dir 215∘ N, TR=2 years. (a) Entire
domain, (b) harbour entrance. The blue bullet is the extraction point location; its UTM
coordinates are 371221∘ E, 4478470∘ N.
Wave field for the design wave condition generated by southern wind
U=41 m s-1, Dir 215∘ N, TR=100 years. (a) Entire
domain, (b) harbour entrance. The blue bullet is the extraction point location; its UTM
coordinates are 371221∘ E, 4478470∘ N.
Absorbing quay wall section, plan and frontal views.
Simplified section and cad representation of the tested
structures.
CFD modelling of the quay wall
The quay wall structure, consisting of steel sheet-pile foundation and an
absorbing wave chamber, is investigated through CFD model by means of the
commercial code STAR-CCM+, already widely used for design, as in Antonini
et al. (2016a, b, c). The innovative design is presented in Fig. 10, while
the optimum site-specific geometry is defined through the comparison of three
geometries. The changes made during the analysis are related to the
following:
the length of the absorbing wave chamber;
the extension of the gap between front reflective surface and free surface;
the arrangement of the armour slope inside the cell.
The aim of the site-specific absorbing quay wall design is the maximisation
of the wave energy dissipation according to the exercise wave condition
(described in Table 4). The goal is reached using a cell length as close as
possible to the quarter of the considered wavelength; therefore only a single
wave state is adopted to optimise the geometry of the cell. In this light,
the optimisation of the absorbing cell is carried out according to the
exercise wave condition from the south-west, i.e. wave no. 3 (Hs= 1.80 m, Hmax= 3.2 m, Tp= 4.5 s,
Ts= 4.2 s), while for waves no. 1 and 4 the performances of
the optimised quay wall are investigated.
The chamber width, which will be varied through the design phase, is filled
with a rubble mound in order to induce dissipation due to the breaking wave.
With an aim to not affect the rubble mound stability, the top of the slope is
always kept under the seawater level according to three main restrictions:
(i) the design diameter of the natural stone, (ii) the maximum allowed
steepness and (iii) the limited chamber length. The geometry of structure 1
has a cell length equal to 5.47 m and the frontal reflective surface extends
from -7.5 to -2.5 m. The armour slope extends from the front sheet pile
up to the rear beam installed on top of rear sheet pile, with a nominal
diameter (DN50) equal to 1.0 m, (Fig. 11a). The geometry of
structure 2 has cell length equal to 5.80 m and the front reflective surface
extends from -7.5 to -3.0 m. The armour slope extends horizontally from
the frontal sheet pile up to 2.70 m inside the cell where a slope of 1:4
reaches the rear sheet pile and the nominal diameter of the stones is 1.0 m.
An underlayer with a nominal diameter of 0.50 m is designed in order to
separate the rocks and the bottom sand (Fig. 11b). The geometry of structure
3 presents the same geometrical characteristics of structure 2 in terms of
length and depth of the cell but there are some differences in the
arrangement of the armour slope, which extends from the frontal sheet pile up
to the rear one with a slope equal to 1:2. The stone nominal diameter is
1.0 m. (Fig. 11c).
Modelling set-up
A k-ω SST (shear stress transport) turbulence model (Menter,
1994) is applied with a two-layer all y+ wall treatment model, and a second
order implicit scheme was utilised for time marching. The transient SIMPLE
algorithm is applied to linearise the equations and to achieve
pressure–velocity coupling. A volume of fluid (VOF) method is applied to
describe the free surface. The calculation is performed on a fixed grid and
free surface interface orientation and shape are calculated as a function of
the volume fraction of the respective fluid within a control volume.
A right-handed Cartesian coordinate system is located at the intersection
between frontal structure surface, the undisturbed water surface and the
medium vertical section of the domain. The longitudinal x axis points
towards the outlet boundary, the z axis is vertical and points upwards, and
the undisturbed free surface is the plane z=0 (Fig. 12).
The domain region is 2.62 m wide (-1.31 m ≤y≤1.31 m, i.e.
structure pile centre to pile centre distance), 38.75 m high
(-7.75 m ≤z≤31.0 m) and its length varies according to the
simulated wave group length (λg) (i.e. -3/4λg≤x≤6), while the seabed is given 7.5 m below the
mean water surface. A superposition of linear wave velocity profile is
specified at the up-wave boundary in order to generate an extreme focused
wave group at the structure location.
Four boundary conditions have been used to describe the fluid field at the
domain bounds. They involve (i) a no-slip wall, (ii) a velocity inlet,
(iii) a pressure outlet and (iv) a symmetry plane condition. The no-slip wall
boundary condition represents an impenetrable, no-slip condition for viscous
flow and such a boundary is used to describe the structure surface and the
bottom (z=-7.5 m). The velocity inlet boundary represents the inlet of the
domain at which the flow velocity is known according to the required wave
profile. This condition is used to model the up-wave boundary at x=-3/4⋅λg and the top (z=31.0 m) of the domain. Lateral
boundaries (y=-1.31 and y=1.31 m) are defined by means of symmetry
planes. The pressure outlet boundary is a flow outlet boundary for which the
pressure is specified and the proposed model adopts the condition of a calm water
surface. Such a status is specified at the boundary above the structure (x=6 m) only for the air
phase.
Domain, boundary conditions and structure details. Tank inlet is
the velocity inlet boundary, Tank outlet is the pressure outlet boundary.
Modelling of the armour slope
The proposed armour slopes within the absorbing cell are modelled through the
insertion of two solids communicating with the fluid field. By means of these
volumes, dissipations due to the inertial and viscous forces are imposed by
means of two coefficients. These two terms were subjected to many
investigations as demonstrated by several authors (Burcharth and Andersen,
1995; Cruz et al., 1997; Engelund, 1953), who proposed different methods to
calculate them according to the size and type of the modelled element.
According to the Burcharth's method and considering the armour design
condition, the adopted values are 6.4 kg m-3 s-1 for viscous
dissipation coefficient and 1221 kg m-4 for the inertial coefficient,
while for the underlayer, the adopted values are 26 kg m-3 s-1
for viscous dissipation coefficient and 2440 kg m-4 for the inertial
one. The porosity value is assumed to be 0.38 and is kept constant for the
porous domains.
Simulated wave conditions
Three different wave conditions have been simulated with two characteristics
of exercise conditions (wave no. 1 and wave no. 3 in Table 4) and one dealing
with extreme conditions (wave no. 4 in Table 4). We assume that the modelling
of extreme condition from the north-west (i.e. wave no. 2) is not necessary
as the wave state is significantly less intense than the southern one, as
highlighted in the wave climate study. The wave groups are generated by a
superposition of eight linear components, each of them characterised by its
own amplitude, period and phase. The input signals are calculated according
to the Boccotti or NewWave theories; Boccotti (1983), Boccotti et al. (1993)
and Tromans et al. (1991). The procedure allows us to define an extreme
focused wave group coherent with a random sea state described by a spectral
distribution. In this study a Jonswap spectral shape with a peak enhancement
factor equal to 3.3 is adopted, while the maximum wave height at the focusing
point is identified through Goda's method (i.e. wave no. 1
Hmax=1.80 m; wave no. 3 Hmax=3.24 m; wave no. 4
Hmax=5.40 m; Fig. 13); Goda (2000).
Imposed surface elevation at the generation
boundary: (a) wave no. 1, (b) wave no. 3, (c) wave
no. 4.
Grid generation
The domain mesh and prism layer grid are generated using the mesh generator
in STAR-CCM+. Grid resolution is finer near the free surface and around the
quay wall structure to capture both the wave dynamics and the details of the
flow around the structure; Fig. 14. Prism-layer cells are generated along the
structure's surface, and the height of the first layer is set so that the
value of y+ (60 to 400) satisfies the turbulence model requirement by
solving the velocity distribution outside the viscous sublayer, i.e. log-law
regions are solved as presented in Demirel et al. (2014) and Schultz and
Swain (2000). Regular hexahedral cells define the whole domain, while four
thinner areas are used to capture free surface movements and the interaction
between the wave group and the structure (Vw1, Vw2,
VS1, VS2). The grid refinements across the water
surface are realised by the volumetric controls, VW1and
VW2, proposed along the whole domain. The size of VW2
is equal to the maximum simulated wave height, while the dimension of
VW1 is 50 % larger (see longitudinal section in Fig. 14).
VW2's horizontal grid size is determined according to the
shortest generated wavelength (λi1) (i.e. Δx=Δy=λi1/60), while the vertical grid size is adjusted according to
the smallest generated wave height (Hi1) (Δz=Hi1/20). Refinements around the structure present the same grid
dimension of those used to discretized the water surface but their dimensions
are set in order to include a gap between the structure surface and the
volumetric control edges; the dimensions are equal to 1.0 m for
VS1 and 5.0 m for VS2. These mesh characteristics
contribute to generating a grid of variable cell numbers from
2.0 × 106 to 3.5 × 106, according to the incident
wave condition. To assure the numerical stability and to take the requested
Courant number into account, a time step equal to Tp/400 is
adopted in the study. All the RANS simulations are carried out on the work
station at the hydraulic laboratory of the University of Bologna, using a
double compute node consisting of hexa-core 2.00 GHz Intel Xeon E5. For a
mesh made of 2.0 × 106 elements, it takes about 36 h on
12 cores to complete the entire wave group attack.
General domain grid and grid detail around the absorbing quay
wall structure.
Example of the adopted window.
Comparison of reflected wave spectrums for wave no. 3.
Results
The results are presented in terms of mean values of reflection coefficient
(cr) and pressures acting on the most significant parts of the
structure. The pressure results are analysed only with respect to the extreme
conditions. Surface elevation is measured through six wave gauges placed
along the domain axis (y= 0) and at different distances from the quay
wall (i.e. x=-18; -16; -14; -12; -10; -8 m). The gauge
distances from the quay wall are at least 1/4 of the peak wavelength in
order to exclude the effects of stationary oscillations, which cannot be
explained through the adopted reflection analysis method (Zelt and
Skjelbreia, 1992).
Reflection coefficients results
Wave reflection induced by the quay wall is quantified by the reflection
coefficient, defined as follows:
cr=m0im0r=HiHrm0=∫0.5/fp1.5/fpS(f)⋅f0⋅df,
where Hr and Hi are the reflected and incident wave
heights, and m0r and m0i are the related zero-order spectral
moments calculated between 0.5 and 1.5 times the peak frequency.
The calculation of the reflection coefficient is carried out through the
spectral analysis of a non-stationary signal, since the generated wave group
is represented by a short non-stationary time series. The approach implies
the use of a time-fixed window (i.e. along the time series vector), centred
on both incident and reflected wave groups. A trapezoidal-shaped window is
used to reach this scope. Its length is defined according to the shape of the
signal; i.e. the window begins with the first value above 0.05 m identified
within the incident wave and closes after the last value above 0.05 m
identified within the reflected signal. The window shape is characterised by
two linear slopes between 0 and 1. The slope length is equal to 5 % of
the group's envelope (Fig. 15). This approach is based on the assumption that
the reflection phenomenon is linear, thus reflected and incident spectral
shapes will not change except for the reduction of energy.
Figure 16 shows the comparison of the reflection coefficients for the three
structures: it is clear that structure 3 is the best in terms of reducing the
reflection. In fact it can be noticed that there is a generalized reduction
of the reflected wave energy for whole range of analysed frequencies. With
regard to the lower frequencies, i.e. incident wave periods longer than
4.5 s, the required wave attenuation cannot be guaranteed only by the
resonance phenomenon of the cell. In this light the presence of the rocks
inside the cell becomes more important. The arrangement of the geometry with
the smaller armour slope (structure 2, red line in Fig. 16) does not induce
the expected general improvement, whereas it becomes important for structure 3.
With regard to the higher frequencies with incident wave periods shorter than
4.5 s, the significant improvement associated with structure 3 is mainly due
to the variable length of the absorbing cell generated by the inner slope
that faces the incoming waves. With regard to the central frequencies, i.e.
incident wave periods around 4.5 s, the largest improvement is between
structures 1 and 2 because of the increased length of the absorbing cell.
Structure 1 presents a ratio between its own length and wavelength equal to
0.18 while for structure 2 it is 0.195, facilitating the establishment of
resonance conditions inside the cell. In order to validate the reflection
coefficient results and highlight the capability of the numerical model to
reproduce the dissipation due to the wave breaking on the rubble mound a
comparison with the experimental results proposed by Liu and Faraci (2014)
and Faraci et al. (2014) is presented in Fig. 17. The experiments, carried
out at the Hydraulics Laboratory of the University of Messina, analysed a new
combined caisson, including an open window on the front wall and an internal
rubble mound with a slope. The caisson was made of steel and was composed by
a double chamber in the wave crest direction and a vertical bulkhead in the
front part. The inner part of the caisson was filled with rubble mound in
order to simulate a rock armour. A comparison between the numerical solution
and the experimental data is given in Fig. 17, in which it can be seen that
the agreement between the CFD results and the experimental data is
reasonable.
Comparison between physical results (Liu and Faraci, 2014) and CFD
results for geometry 3, where b is absorbing chamber width, L is the
wavelength, d is the water depth at the structure toe, hswl is
the submerged depth of the front wall, bswl is the width of the
surface piercing rubble mound at the still water.
A synthesis of the reflection coefficients is presented in Table 5, in which
we can consider the averaged reflection coefficient obtained for structure 3
to be satisfactory. Therefore, structure 3, presented in Fig. 10, has been
selected as the optimum structure for the future quay wall of Vlorë
Harbour.
(a, b, c) Comparison between CFD results and empirical
formulas proposed by McConnell et al. (2004) solid
line refers to deterministic formula results while dotted line refers to
probabilistic formula results. (d) Comparison between pressure
distribution on the frontal sheet pile; orange refers to the CFD result and green
refers to the well-known Goda's method.
Pressure results
This section presents the pressure and force values acting on different parts
of the structure. In order to validate the numerical results, the forces
acting on the upper structure are compared with the empirical results
obtained according to McConnell's method (Fig. 18a, b, c, McConnell et
al., 2004), whereas the pressure distribution on the front sheet pile is
compared with the distribution calculated according to Goda's method (Goda,
2010); Fig. 18d.
Measurements of pressure were carried out using virtual pressure gauges:
eight pressure gauges were used to measure the uplift pressure acting on the
frontal beam (Fig. 18a), 20 pressure gauges were used
to measure the uplift pressure acting on the internal beam (Fig. 18b), 4
pressure gauges were used to measure the horizontal unitary force acting on
the frontal beam (Fig. 18c) and 16 pressure gauges were used to identify the
pressure distribution on the frontal sheet pile (Fig. 18d).
Two main activities were carried out in order to reduce the effect of
high-frequency loads and at the same time consider all wave gauges positioned
on the investigated structure area. Firstly, the average pressure signal is
calculated. Secondly, a low-band filter is applied with a cutting frequency
equal to 2 Hz, which is roughly the natural period of the analysed
structures. Then, the considered design pressure values are the maximum
values of each filtered signal, while the pressure distribution on the
frontal sheet pile is calculated according to the maximum value of each
single-filtered pressure signal (Table 6).
This paper presents a study case in which the hindcasted wave data have been
used to define the sea conditions with the aim of estimating the design wave
states for an effective dock design based on an innovative quay wall concept.
Through a specific study case, the results provide a methodology, based on
advanced numerical tools, to approach the design of coastal structures, focusing
on the optimization of an innovative quay wall.
Design wave conditions are identified on the basis of the wind measurements
and hindcasted wave data. Because of the different directions and periods,
the identified wave conditions are distinguished in southerly and northerly
waves. According to this classification two limit conditions were assessed:
the limit of the exercise conditions for which the service condition has to
be ensured, and the extreme limit for which the only requirement is the
resistance of the structures. Once the wave conditions have been identified,
the structure performance is analysed in terms of reflection coefficients by
means of a CFD code. The optimisation of the absorbing cell is carried out
only for the southerly wave conditions, while the complete reflection
analysis is completed for the other two identified wave states. The resulting
structure is a quay wall with an absorbing cell characterised by a ratio
between its own length and wavelength equal to 0.195, filled with a 1:2
armour slope realised on the entire absorbing cell extension. The main
findings are three values of reflection coefficients CR 0.56,
0.33 and 0.4 for wave no. 1, 3 and 4. The result of the reflection
coefficients, which is used to select the best design of the reflective quay
wall, is also compared with experimental data in order to validate the
numerical studies. The comparison shows a good agreement. With the same code
the loads acting on the main structural parts of the quay wall are evaluated
under the extreme southern conditions. Furthermore, a comparison of the
numerical results with empirical formulas is proposed in order to validate
the calculated pressure values. A general good agreement for the results is
recognised through the compared pressure values. In conclusion sea data
strongly supported the correct engineering design of the quay wall at
Vlorë Harbour.
Data availability
The observational data used to carry out this research are free and available on request by writing to the authors.
The authors declare that they have no conflict of interest.
Acknowledgements
The authors gratefully acknowledge Giovanni Besio and Carlo Zumaglini,
SIAP-MICROS s.r.l., for providing waves and wind data, and Piacentini,
Ingegneri s.r.l., for the discussion on the quay design. Italian Flagship
Project Ritmare IV (SP3_LI3_WP1) is gratefully acknowledged for partially
supporting the research. Edited by:
I. Federico Reviewed by: L. Martinelli and one anonymous referee
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