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Breach Growth Shape
The shape and progression of the breach depends on the user entered data. Is the User has selected to use the "Simplified Physical Breaching" option, the Breach Growth is dependent upon the user entered Downcutting and Breach Widening rates entered by the user, as well as the event being modeled. If the user has selected the "User Entered Data" breaching method, then the Breach Formation shape is dependent upon the Breach Bottom Width, height of the structure, and the Breach Formation Time. For example, consider a breach with the following parameters: Final Bottom Width is 400 feet, Final Bottom Elevation is 100 feet (top of weir is 200 feet—full breach is 100 feet deep), Formation Time is 4 hours, Breach Progression is Linear. The breach has to grow 400 feet wide in 4 hours so the growth rate is 100 feet/hour (this growth rate is used for both the horizontal and vertical growth rate by default). The breach will start out as a tiny trapezoid (or rectangle if side slopes are zero) at the top of the weir based on the Center Station. The trapezoid will grow such that after one hour, the breach will have just reached the Final Bottom Elevation (100 feet deep) and the breach will be 100 feet at wide (at the bottom). Over the next three hours, the breach will grow horizontally from 100 feet wide to the final width of 400 feet wide, at the bottom. The side slopes of the trapezoid always remain the same. In the less common situation where the breach is deeper than it is wide, the growth rate is based on the vertical depth divided by the formation time—the maximum width would be reached before the maximum depth.
The user has the option to specify a vertical/horizontal growth rate. The default value is 1.0. However, if the user feels the vertical growth rate should be slower or faster than the horizontal growth rate, they can select this option and enter a ration of vertical to horizontal growth rate (e.x. a value of 0.5 would produce a vertical growth rate that is half the speed of the horizontal growth rate).
If the Breach Progression is non-linear, then the horizontal growth will be adjusted, as needed. Progression in the vertical direction will match the horizontal growth (taking into account whether the Same/Proportional option has been selected). For the above example, if data has been entered such that the breach is only 10% (0.1) formed after 25% of the time, then the breach would be 40 feet wide after one hour. It would be 40 feet deep for Same Growth… or, alternately, it would be 10 feet deep for Proportional Growth.
If the Failure Mode is changed to Piping, then the breach starts out as a tiny square (or rectangle) based on the center station and Initial Piping Elevation. For the original example with Same Growth and an Initial Elevation of 120 feet, the sides of the square will grow at the rate of 100 feet/hour. The vertical growth is split between up and down. After 6 minutes, the square will be 10 feet on a side. The top of the square would be at an elevation of 125 feet and the bottom at an elevation of 115 feet. Once the bottom of the square reaches the Final Bottom Elevation, all of the growth is applied upward. When the elevation of the top of the square is higher than the water surface elevation in the breach, it is assumed the breach will cave in. The breach will now be an open rectangle with the current bottom elevation and current bottom width ( the rectangle extending vertically to the top of the weir). If the breach has not yet reached the Final Bottom Elevation, it will grow downward at the full vertical growth rate. The bottom of the breach will continue to grow horizontally at the same rate (or adjusted rate for non-linear). If the side slopes are not zero (vertical), then the side slopes of the rectangle/trapezoid will progress from vertical to the maximum side slope, linearly over the remaining time (or adjusted for non-linear progression based on user selection). So if the Side Slope is 3 and the piping breach becomes an open breach after one hour, then the side slope would be 1 at the end of the second hour, 2 at the end of the third hour, and 3 at the end of the fourth hour. If the water surface remains high enough, then the piping breach will not turn into an open breach until the top of the piping breach reaches the top of the weir. It will then grow to the final trapezoidal shape as previously described.
For a Piping failure with Proportional Growth, the piping breach would be a rectangle that grows vertically at 25 feet/hour. Whether the breach is growing up and down, only up, or only down, is the same as before, as is the open breach behavior and the non-linear growth option.