The U.S. coastline is under attack! But not in the way many would assume; our coasts are under attack by the constantly changing environment, rise in sea level and increased severe-weather events. Although storms, floods and erosion have always been hazards, they now occur on top of higher sea levels. Combined with coastal development, these hazards now threaten approximately $1 trillion in real estate along U.S. coasts. According to the “2022 Sea Level Rise Technical Report,” the average global sea level rose around 10-12 inches during the last 100 years and is predicted to rise an additional 10-12 inches during the next 30 years. With more than 60,000 miles of U.S. roads and bridges in coastal floodplains, coastal designers will need to work fast to protect our valuable infrastructure.
When it comes to battling floods and sea level, one country stands out: the Netherlands. With about a third of the country sitting below sea level, the Dutch have become masters of controlling floodwaters and the impacts of the sea. One of the greatest Dutch accomplishments is the construction of the Afsluitdijk, a 20-mile dam and causeway. The Afsluitdijk was built in 1932 to close off the Zuiderzee (South Sea) to protect against flooding that was occurring due to storm surges. With a core of glacial till and armored by natural basalt columns, the dam had a height of approximately 26 feet above mean sea level, and the 3.5H:1V slope face was designed for 8-foot-high waves. During the last 90 years, however, the basalt columns have eroded and, coupled with increasing water levels and wave heights, led to the need to strengthen the Afsluitdijk. The rehabilitation included increasing the crest level to reduce the wave overtopping and reinforce the armor layer on both sides of the dam.
To strengthen the dam, the Rijkswaterstaat (the Dutch Ministry of Infrastructure and Water Management) desired to maintain the structure’s historic value and visual appearance. The rehabilitation contract included several unique aspects, including an approach that required the design to be adaptable for wave overtopping following actual sea-level rise.
The contract also motivated contractors to develop designs that would minimize new material use, minimize the use of the protected Wadden Sea area and maximize existing material reuse. Overall, the armor system would need to be placed in a regular pattern, the crest raised 6.6 feet and the dam designed for a significant wave height of 13.8 feet, a 68-percent increase. To meet the design requirements and provide an installation with lower carbon impact than the baseline concrete-cube reference design, a new concrete armor unit, XblocPlus, was developed.
New Armor Unit
The XblocPlus is a further improvement to the widely used single-layer armor unit, Xbloc. The XblocPlus offers high resilience to climate change, increased stability, low concrete consumption, fast and safe block placement, and reduced material quantities and CO2 emissions. These enhancements provide better economics with lower project lifecycle cost. In addition, placement on a regular grid simplifies installation and makes verification of installation much easier.
The XblocPlus shape can be described as a bird with a beak, a tail and two wings. Shape development focused on minimizing uplift pressures on the beak, using the wings to increase the distance between blocks, and creating gaps and openings to dissipate wave energy and reduce uplift pressures. Extensive numerical modeling was conducted using ANSYS CFD to study the velocities and wave pressures as well as the impact on variations in unit shapes. Each shape modification was tested in an 80-foot-long wave flume. In the final form, a hole was introduced in the center of the block. The hole greatly reduces the destabilizing forces and increases the hydraulic stability of the units.
The stability of concrete armor units is defined by the stability number, Hs/ΔDn where the significant wave height is divided by the relative density times the nominal diameter. The significant wave height is the mean of the highest one-third of the waves at the toe of the structure.
In the physical model testing of XblocPlus, no extractions or rocking occurred—even during a 200-percent overload case. The XblocPlus units rest on the slope and on two units in the row below. They are further stabilized by two units in the row above. This above-and-below interaction interlocks the units. The large interlocking capacity of the units provides a design stability number of 2.5. While a higher stability number could have been selected based on the physical model testing, a value lower than other armor units was selected to provide more resilience and safety in design. When wave heights increase due to climate change, the XblocPlus system will have reserve capacity.
The XblocPlus system provides a visually smooth aesthetic appearance, however, the units have large open spaces, resulting in a large influence factor for roughness (γf). The roughness factor for XblocPlus units on a permeable core is 0.45.
Design of the Afsluitdijk
The design and crest level were originally determined using the 2018 EurOtop Manual (an overtopping manual based on European research). The required armor unit size for protection against wave attack is determined mainly by the design wave conditions. Additional considerations for project geometry, geotechnical parameters and water depth were used to ensure correct sizing of the units.
The recommended formula for determining the required volumetric unit size is shown in Equation 1. If more than one of the additional considerations for correction factors exist, then the largest value should be used as a starting point for physical model tests. Based on the wave height, the XblocPlus stability coefficient of 2.5, and project correction factors, an XblocPlus size of 6.6 U.S. tons was selected. To armor the new 2H:1V slope of the Afsluitdijk, eight rows of XblocPlus units are required with a total of approximately 75,000 units needed for the armoring. An artist rendering of the new Afsluitdijk protection system is shown in Figure 3.
A special feature of the Afsluitdijk design is the berm that lies approximately at the high-water level. This is very effective to reduce wave overtopping, but it poses a large challenge for the hydraulic stability of the top block on the lower slope: the wave loads are high at the water level, whereas the top block lacks the added stability that would be provided by blocks above. Therefore, a customized XblocPlus unit, the berm block, is applied at the top of the lower slope. This block is an XblocPlus unit with increased mass, weighing 12 U.S. tons instead of the normal 6.6 U.S. tons. The berm blocks also have extra voids to release the wave pressure between the units and the asphalt of the bicycle lane on the berm.
The average wave overtopping discharge can be predicted from Equation 2 (EurOtop 2018) where q = average overtopping discharge; Rc = freeboard; α = slope angle; ζm-1,0 = breakwater parameter; γb = the influence factor of the berm; γf = the influence factor for the roughness of the slope; γβ = the influence factor for oblique waves; and γv and γ* = influence factor for a wall on top of the slope.
With the composite slope of the Afsluitdijk, the roughness influence factor, γf, is difficult to predict as it depends upon the amount of wave overtopping and wave steepness. Therefore, physical modeling was needed to better estimate the overtopping.