UPC: Armour layer stability tests
Wave Flume tests
The objective of this study is to understand the laboratory effects of storm representation and test repeatability on damage measurements in the armour layer of a breakwater. For that, we study in a smallscale wave flume the effects of storm duration and storm sequencing on the stability of a twolayer cubic block breakwater. We start by simulating a real storm measured in the Mediterranean Sea. Then three different representation models of the real storm are simulated: the classical model (Melby & Kobayashi, 1998) and two ‘Equivalent Magnitude Storm’ (EMS) models with triangular and trapezoidal shapes (MartínHidalgo et al., 2014; Soldevilla et al., 2015). All the four methodologies are repeated at least ten times. For the assessment of the damage in the armor layer of the breakwater, the damage parameter (relative damage) proposed by Van der Meer is used.
The experiments were carried out in the CIEMito wave flume at the Laboratori d'Enginyeria Maritima (LIM) of the Universitat Politecnica de Catalunya (LIMUPC BarcelonaTech). The flume is 18 m long, 0.38 m wide, and 0.56 m deep. It is equipped with a piston type wave paddle, which can generate regular and irregular waves.
The experimental layout used in this work is shown in Figure 1. Here we test a rubble breakwater model placed on a 1:30 smooth slope. The breakwater has a 1:1.5 slope on the seaward, a 0.383 m crest high and a 0.07 m horizontal crest width. Water depth at the front of the paddle was 0.3 m.
A permeable breakwater with two layers of cubes, a filter layer and a core layer has been built.
Figure 1: Experimental layout – CIEMito wave flume configuration (Left) –breakwater crosssection (Right)
Although smallscale models have been extensively used to study the hydraulic behavior of marine structures, there are several uncertainties related to its use. This includes uncertainties related to scale effects, generation of extreme waves (Oliveira et al., 2017 and references cited therein) and test repeatability (Marzeddu et al., 2017), among others.
Wave conditions
There are several methods to reproduce sea states in physical model tests. In this work we aim to simulate a storm measured in the Mediterranean Sea using three storm representation methods named here as i) Real Storm Methodology, ii) Classical Methodology (Melby & Kobayashi, 1998), iii) Synthetic Storm Methodology with triangualr and iv) trapezoidal shapes. The Synthetic Storm model used for these experiments is the ‘Equivalent Magnitude Storm’ (EMS) proposed first by MartínHidalgo and improved later by Martin Soldevilla (MartínHidalgo et al., 2014; Martín Soldevilla et al., 2015). This synthetic storm intends to reproduce the recorded storm with a simple geometric form. Then, at the peak of the simple geometric form is represented by the recorded at the peak of the recorded storm. The duration of the simple geometric form is established such that its magnitude (area describing the storm history above a threshold equals the one of the measured storm.
Figure 2: From top left corner clockwise  Real storm scaled 1/80, propagated at the wave paddle depth  Classical storm methodology  Synthetic triangular storm methodology  Synthetic Trapezoidal storm methodology – All the tested storms (in red) are derived from the measured, scaled and propagated storm (in black) and are discretized in steps of 402s each
Wave height
Significant wave height and peak period have been calculated for all the tests at WG3 at 3.53m from the paddle in order to control the repeatability of the generated waves. Control the repeatability of the generated waves is crucial in order to ensure that the inputs to the system are always the same and the variability on damage results is intrinsic of the wavestructure interaction phenomenon. Low variability of and occurs for the simulations using exactly the 5 same wave time series (same seed number). However, as expected, more significant variability is found when considering 10 times series. For each step of all the storm types the standard deviation of the measured significant wave height has been calculated. Taking into account all the steps it is possible then to compute the mean standard deviation of the measurements for each storm type.
5 time series with same seeding number  All 10 times series  
Storm type  H_{s} (mm)  H_{max }(mm)  T_{p }(s)  H_{s }(mm)  H_{max }(mm)  T_{p }(s) 
Real storm  0.3  1  0.0003  2  9.8  0.002 
Classical  0.4  2.7  0.0004  1.1  6.5  0.001 
Synthetic Triangle  0.3  1.2  0.0003  1.8  5.6  0.001 
Synthetic Trapezoid  0.7  1.9  0.0007  1.8  4.8  0.002 
Table 1: Mean of the standard deviation of the measured significant wave height computed for each test step.
From the results it is possible to note a very small variability due, most probably, to the intrinsic error in the measurement system.
Relative damage measurement
From the pictures taken perpendicular to the breakwater at each step it is possible to calculate the relative damage . Every block has been identified with a unique threedigit number and could be followed numerically so that the position before and after each test can be checked. Van der Meer (Van der Meer, 1999) defines the relative damage as the actual number of units displaced related to a width
where N_{du} is the number of displaced units, D_{n} is the nominal diameter and w is the with of a cross section.
In the case of a wave flume (bidimensional), the complete width of the flume should be considered as a cross section.
Figure 3: Analysed images. On top of the reference image (before the tests  left) has been drawn arrows with the displacement to the final “destination” after a wave attack (after the tests – right). In this case N_{od}=2.7
Ten repetitions of each storm model have been performed and the results will be presented in form of Gaussian probability density function. The decision to present in form of a Normal pdf has been done considering that the number of repetitions (10) was not big enough in order to perform a best fit in between different parametric probability density functions.
Figure 4: Probability density of the damage for all the tested methodology. The end of the test program for Real storm methodology, Synthetic storm methodology with the triangular and trapezoidal shapes has been considered. The 100% step has been considered for the Classical methodology. Ten repetition for each methodology.
The results could also be similarly expressed in terms of mean and standard deviation of the relative damage N_{od} (Table 3).

mean±std 
Std/mean (%) 
min 
max 
max/min (%) 
Real storm 
2.48±1.09 
44 
1.09 
4.71 
432 
Classical methodology 120% 
4.08±1.51 
37 
2.52 
6.6 
261 
Classical methodology 100% 
2.21±0.95 
43 
0.97 
3.24 
334 
Synthetic storm triangle 
2.14±1.23 
57 
0.67 
4.88 
728 
Synthetic storm trapezoid 
1.98±1.09 
55 
0.34 
3.49 
1026 
Table 2: Statistics of the recorded relative damage for all the tested methodologies
References
MartínHidalgo, M., MartínSoldevilla, M. J., Negro, V., Aberturas, P., & LópezGutiérrez, J. S. (2014). Storm evolution characterization for analysing stone armour damage progression. Coastal Engineering, 85, 1–11. https://doi.org/10.1016/j.coastaleng.2013.11.008
Martín Soldevilla, M. J., MartínHidalgo, M., Negro, V., LópezGutiérrez, J. S., & Aberturas, P. (2015). Improvement of theoretical storm characterization for different climate conditions. Coastal Engineering, 96, 71–80. https://doi.org/10.1016/j.coastaleng.2014.11.004
Marzeddu, A., Oliveira, T. C. A., Gironella, F. X., & SánchezArcilla, A. (2017). Variability of wave impact measurements on vertical breakwaters. Journal of Hydraulic Research. https://doi.org/10.1080/00221686.2017.1312576
Melby, J. A., & Kobayashi, N. (1998). Progression and variability of damage on rubble mound breakwaters. Journal of Waterway, Port, Coastal, and Ocean Engineering, 124(6), 286–294.
Oliveira, T. C. A., SanchezArcilla, A., & Gironella, X. (2012). Simulation of wave overtopping of maritime structures in a numerical wave flume. Journal of Applied Mathematics, 2012. https://doi.org/10.1155/2012/246146
Van der Meer, J. W. (1999). Design of concrete armour layers. Proceedings of the International Conference Coastal Structures ’99 : Santander, Spain, 710 June 1999, Volume 1, 213–221.