# Staying Dry: Numerical modeling of flexible pressurized storm surge barriers

Relative to all other natural disasters, storm surges are the leading cause of damage and loss of life in the United States of America; think Hurricane Sandy in 2012 – with 20 billion dollars in damage in New York City alone – and Hurricane Harvey in 2017, with 200 billion dollars of total damage (Brown 2017).

Due to changing atmospheric conditions and the accompanying sea-level rise associated with climate change, the intensity of the average storm surge has increased in recent years; this trend is expected to continue (Lin et al. 2016). Many potential solutions – large steel gates and huge masses of concrete, for example – have been proposed and implemented, but realistically none are efficient with physical material or appropriate in form. Such current strategies reduce beachfront property values and are very costly, with an estimate of NYC’s “Big U” having a price tag of \$540 million (Cohen 2016).

A more cost effective and less intrusive proposed solution for coastal flood defense is a storable, inflatable membrane. These lightweight, prestressed membrane dams have been estimated to have anywhere from 30 to 50% of the lifecycle cost of other coastal protection strategies (van Breukelen 2013). Pneumatic membranes have already been employed as effective riverway dams and have been extensively studied in the linear static regime due to quasi-static loads from standing water. The effectiveness of such inflatable membranes for hydrostatic loads has been established and can be seen in the following video:

These inflatable barriers are not a novel idea; they have already been verified and deployed in the hydrostatic case on a small scale. That said, the extension to a larger scale to protect coastlines from storm surge loads has yet to be realized. For this coastal protection design to be implemented and for the optimum form to be found, a reliable method of analysis must be created that appropriately models the complex loads on the barrier and its structural response. Unlike the cable net system in one of our other projects, this pneumatic barrier will interrupt the hydrodynamic flow. As a result, the analysis must consider fluid-structure interaction. This is a relatively complex physical phenomenon and requires a numerical model to find a solution.

Before we consider the impounding hydrodynamic flow, we must first solve the challenges associated with modeling the barrier alone. The barrier (as seen in the rendering in Figure 1) is made from a rubber-like material (a nonlinear, hyper-elastic material model), will deform significantly, and has an internal fluid (compressed air) which all need to be included in the model.

The deformation of the barrier (or its position at static equilibrium) can be computed by minimizing the total potential energy (TPE) of the system, comparable to finding the equilibrium position of a pendulum under the force of gravity. The TPE can be written abstractly to capture all the forces acting on the system:

$\Pi = \Pi_{int} - \Pi_{ext} - \Pi_{air}$

Where $\Pi_{int}$ , $\Pi_{ext}$ , and $\Pi_{air}$ represent the internal strain energy from stretching the barrier itself, the energy from the external force, and the compressed air energy, respectively.

Each term in the equation above can be written as a function of known and unknown physical quantities, but is highly nonlinear when fully expanded. Thus, a numerical approach is necessary; we chose the well-known finite element method to obtain the solution.

For example, if we apply an external distributed load in the center of a three-dimensional strip of this barrier (modeled in Python using the FEniCS package), we see a deformation as modeled in Figure 2.

Given some arbitrary loads, the model can produce a reliable analysis of the behavior of the barrier. However, the loads are not actually known to the designer and must be modeled based on what we know of storms and their natural processes. By using atmospheric data and simulations, the water velocity profile of a storm can be estimated at a certain distance from the coast. We can then use this fluid flow information as boundary conditions for the fluid solver – employing the Navier-Stokes equations to simulate hydrodynamic flow – where the physical domain includes the inflatable barrier. The pressures acting on the barrier at every time step may then be applied as forces on the barrier which will in turn deform and change the physical boundary conditions in the fluid solver. The results of this algorithm are shown in Figure 3.

We can see the fluid-structure interaction of the deformable membrane with the fluid flow and how the flow is affected by the structure and the structure, itself, deforms due to the loads from the flow.

The initial profile can be varied to model different shapes (as seen in Figure 4) which may prove to be more efficient structural systems. In the pursuit of the best form for the inflatable (rather than a simple cylindrical shape), future work will consist of parametrically varying the initial profile and internal air pressure to optimize the structure’s effectiveness as a storm surge barrier, with respect to criteria such as over-topping, rupture, and stability.

For more details on the modeling of the membrane action of the barrier, the fluid solver, and the coupling strategy (Arbitrary Lagrangian Eulerian with strong spatial coupling), you can check out our upcoming conference paper here.

– Andrew Rock, Form Finding Lab, MSE

### References:

Brown, N., 2017. Harvey Vs. Sandy: Comparing the Hurricanes by the numbers. AM New York.

Cohen, M., 2016. NYC May Get a Big Ugly Wall Instead of Bjarke Ingels’ Storm Protection System. Policy, Technology, Urban Design.

Lin, N. et al., 2016. Hurricane Sandy’s flood frequency increasing from year 1800 to 2100. In Proceedings of the National Academy of Sciences. pp. 12071–12075.

Niewiarowksi A., Rock A., Adriaenssens, S., Chiaramonte M. ‘Pneumatic storm surge barriers subject to hydrodynamic loading’, in IASS 2018: Creativity in Structural Design, Massachusetts, 2018.

van Breukelen, M., 2013. Improvement and scale enlargement of the inflatable rubber barrier concept. Delft University of Technology.