La Reunion, a French island in the southern Indian Ocean, is renowned for its surfing and beautiful beaches. However, this paradise has been suffering from a surge in shark attacks in recent years. Since 2011, there have been at least nineteen attacks, of which seven were fatal. The attacks peaked in 2013, which forced authorities to temporarily ban aquatic activities. As a result, the island’s economy has been strained, with beach-front businesses bearing the heaviest losses.

A solution to the shark problem soon arrived in the form protective barrier cable nets, which were installed on the beaches of Roches Noires and Boucan Canot. The nets consist of a grid of chain, cable, and rope elements tensioned by buoys. At first, the results seemed promising, and other municipalities soon wanted to install such nets on their own beaches. However, due to the urgent need for a solution, their design was a product of common sense rather than theory, and soon the nets began to fail due to the conditions so sought by surfers: heavy wave loading: Holes began to form as individual elements fractured, with the suspected cause being fatigue. Costly daily inspections and maintenance became necessary to keep the net operational, but even then, the beaches were closed for up to ten days per month. Although structural engineers usually associate cable nets with facades and stadium roofs, my master’s research at the Form Finding Lab focused on these relatively “exotic” underwater cable net barriers. Could we understand the phenomena affecting these nets? If so, could we find a better form for the net to make the beaches safer at a lower cost? To answers these questions, I first needed to (numerically) model the mechanical behavior of the nets to understand what was causing them to fail; only with a working model would I be able to glean any design insights and suggest improvements.## Numerical modeling of underwater cable nets

In order to construct an insightful model, I had to make decisions about which phenomena were most relevant. Underwater videos (above) recorded at the Boucan Canot site demonstrate the influence of breaking wave action on the structure’s behavior. The most frequently observed damage is the severing of the horizontal cables, which indicated that the breaking wave action may be responsible for causing the damage. Another possible factor is the direction of flow: The nets form a horseshoe shape along the beach, with the most frequently damaged sections oriented parallel to the wave direction. As a result, I knew I had to characterize the mechanical response due to breaking wave action, and quantify the effect of the net’s mesh topology and orientation on its susceptibility to damage. Furthermore, while there exist a few commercial software packages for modeling underwater cables, none can model breaking waves – I would have to build my own model from scratch.

The shark barrier cable net is a specialized moored structure. The proper design of such structures must consider the environmental loads and the motions they induce. Therefore, the design problem requires dynamic, rather than static analysis. When it comes to forces acting on submerged bodies, many people are familiar with the concept of buoyancy. However, dynamic interactions between waves and cable structures can be more complex. When a structure like a cable net is composed of slender elements whose diameters are much smaller than the wavelengths of the waves affecting them, a special theory known as the Morison equation (originally proposed by Morison *et al.* in 1950) can be used to calculate the resulting forces as functions of the water velocity and acceleration. This is indeed the approach I took for creating my numerical model.

However, in order to use the Morison equation, I would also need to model the breaking wave itself. Simulating fluid flow is an active area of research that I knew little about, but fortunately, a professor in the mechanical engineering department was willing to share some of his latest models with me, which I could scale and adapt for the La Reunion beach site. Even better, because the Morison equation assumes that the net does not disturb the fluid flow, I could run the wave simulation independently of the cable net simulation, thus avoiding the difficult problem of fluid/structure interaction (my current research focus).

With this prerequisite theoretical knowledge and the wave simulation, I implemented and validated (using simple benchmarks against commercial software) my own numerical model of the cable net barrier using a particle-spring approach. This model captures how the net moves under a breaking wave, as well as the tension forces in the cables and chains.

## Design studies

With a working model, I could finally explore some possible design variations of the existing barrier’s “orthogonal” pattern (seen below in the top-left). Any design variants should be simple to construct and maintain. Additionally, the net mesh size must be small enough to keep sharks out (approximately no more than 40 x 40 cm), but large enough to prevent harm to other marine life and unnecessary drag loads.

While my numerical model was useful for studying the effect of the wave breaking action, to perform further design studies, I needed software more powerful than my home-brewed model. By using the commercial package Orcaflex, I could parametrically construct and test many models, though at the expense of excluding the breaking wave effects.

For my design study, I tested each of the above design variants subject to seven possible wave directions. Such parametric studies generate many data, such as tension time-series data for each cable element, and require a suitable method to analyze the results. Since fatigue (weakening of a material due to repeatedly applied loads) was initially suspected as factor in the net’s failure, the cumulative tension of each element was calculated for a full wave cycle. Assuming that all elements experience an equal number of load cycles for a given time interval, this chosen metric can be interpreted as a conservative fatigue estimator.

The results of this study suggested that some patterns are sensitive to wave heading, while others are heading invariant. Comparing the designs by the suprema of their characteristic elements’ cumulative tensions, the original orthogonal pattern experienced the highest cumulative tensions, while the hexagonal pattern experienced the lowest cumulative tensions. While the orthogonal pattern appeared to be heading invariant, the hexagonal pattern achieved lower cumulative tensions for non-perpendicular wave headings. In other words, the highest element-wise cumulative tension in the orthogonal design was up to 12 times greater than in the hexagonal design.

*— Olek Niewiarowski, Form Finding Lab PhD candidate*

### Acknowledgements:

The following people were instrumental in the completion of the above research:

Sigrid Adriaenssens (Department of Civil and Environmental Engineering, Princeton University

Khalid Addi (University of La Réunion, Saint-Denis | Laboratory of Physics and Mathematical Engineering for Energy and the Environment)

Ruy Marcelo Pauletti (Polytechnic School at the University of São Paulo)

Luc Deike (Princeton Environmental Institute | Department of Mechanical and Aerospace Engineering, Princeton University)