The difference in weighted wind fetch from existing conditions to each potential future island design was calculated for Capoli and Harpers Slough HREPs. A simplistic method for calculating sediment suspension probability was also applied to the HREPs in the St. Paul District. This analysis involved determining the percentage of days that maximum orbital wave velocity calculated over the growing seasons of exceeded a threshold value taken from the literature where fine unconsolidated sediments may become suspended.
This analysis also evaluated the difference in sediment suspension probability from existing conditions to the potential island designs. The St. Paul District and the St. Louis District of the U. Using the models developed, UMESC was then asked to perform specific analyses to model weighted wind fetch for HREPs in both districts and also the probability that fine unconsolidated particles would be suspended due to wind-generated waves for the HREPs within the St.
The results of these analyses allow managers to quantify gains or losses between proposed management scenarios. Wind fetch is defined as the unobstructed distance that wind can travel over water in a constant direction. Fetch is an important characteristic of open water because longer fetch can result in larger wind-generated waves. The larger waves, in turn, can increase shoreline erosion and sediment resuspension.
Design issues such as tie-backs, depth of sheets are primarily controlled by geotechnical issues. Given the relationship between wave height and fetch distance across the water body Figure 6. Bulkheads are most common where fetches and wave heights are very small. Seawalls are most common where fetches and wave heights are very large. Revetments are often common in intermediate situations such as on bay or lake shorelines. Seawalls can be rigid structures or rubble-mound structures specifically designed to withstand large waves.
Two very large, rigid, concrete seawalls with recurved tops to minimize overtopping are the Galveston Seawall Figure 6. Such massive structures are not commonly constructed in the US. Vertical sheet pile seawalls with concrete caps are common but require extensive marine structural design. A more common seawall design type in the United States is a rubble-mound that looks very much like a revetment with larger stones to withstand the design wave height.
Thus, the two terms, seawalls and revetments, can be used interchangeably with the former typically used for the larger wave environments. A revetment protecting a coastal highway Bayfront Road, Mobile, Alabama, Types of shore protection walls. Galveston Seawall Seawall Blvd. Seawall protecting a coastal highway. Venice, Florida. Revetments are common on bay or lake shorelines where design waves are short-period, fetch-limited, locally-generated storm waves.
Revetment protecting a highway along a bay shoreline Florida Highway 60, Tampa Bay. Revetments have been criticized for a variety of reasons, including their aesthetics. The engineered seawall is in the middle of the Figure 6. The more aesthetically pleasing seawall Figure 6. This is an example of the evolving nature of seawall design in the United States.
Concrete seawall designed to look like the natural rock formation built on an eroding sea cliff to protect a local road East Cliff Drive, Santa Cruz, California. A well-designed and constructed rubble-mound revetment can protect embankments from waves.
The underlying philosophy of the rubble-mound is that a pile of stones is efficient at absorbing wave energy and robust in design in that damage is often not catastrophic. It also can be relatively inexpensive. Some of the oldest coastal structures in the world are rubble-mounds. They have the inherent ability to survive storms in excess of their design storm.
The required median weight for the outer, or armor layer, stones is:. Steeper slopes require larger stones. However, the range of recommended slopes here is up to horizontal:vertical. The stones have a gradation of weights that varies between 0.
A geotextile that provides rapid transfer of water through the material while holding soil particles and is strong enough to survive the construction process without puncturing by the overlying rocks is recommended.
The modern use of a plastic grid integrally welded to the geotextile can provide some additional strength to bridge soft underlying soils. The geotextile should be designed to not allow the rocks to slide down the surface. The underlayer should have a median weight no smaller than one-tenth that of the armor layer stones USACE Smaller underlayer stones can be pulled out between the gaps of the armor stones. Typical coastal revetment design cross-section. This recommendation is based on interpretation considering the origin of the equation.
Thus, the proper selection of a corresponding wave height statistic from an irregular sea-state is not obvious. The relationships see Table 4. Coastal revetments are often located where the design sea-state is depth-limited, i. To account for the distance over which waves travel as they break, a depth some distance offshore of the toe say one wavelength sometimes is used in Equation 6.
The construction of a revetment, while it protects the upland, does not address the underlying cause of erosion. The depths at the toe of the revetment will likely increase if the erosion process continues. The presence of a revetment or seawall can increase the vertical erosion at its base. The revetment or seawall does not allow the material in the bluff to naturally nourish the beach. Hudson established the K D values such that there was some small level of damage to the structure.
Thus, it is entirely appropriate for some conservatism or factor of safety to be added to the design process based on engineering judgment. This range of design wave heights encompasses many coastal revetments along highway embankments. When design wave heights get very large and the design water depths get very large, problems with the performance of rubble-mound structures can occur. These problems relate in part to wave groupiness back to back large waves , design sea-state specification, constructability and other issues.
One alternative to the two-layer design of Figure 6. A dynamic revetment allows the stones to move in response to storm waves into an equilibrium shape much like a cobble or sand beach.
An alternative to the use of extremely large stones in the armor layer is to use concrete armor units. These typically are lighter since they interlock better than quarrystone and thus have higher K D values.
In these consequences, mathematical models are solved using different numerical techniques and associated schemes. In this manuscript, we aim to review hydraulic principles along with their mathematical equations.
Then we aim to learn some commonly used numerical techniques to solve different types of differential equations related to hydraulics.
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