Breach growth formula (Water Overlay): Difference between revisions

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Water can flow through [[breach (Water Overlay)|breach]]es into levee protected areas. These breaches often start small and grow over time<ref name="breachgrow"/>.  
Water can flow through [[breach (Water Overlay)|breach]]es into levee protected areas. These breaches often start small and grow over time<ref name="breachgrow"/>.  
TODO: THIS SECTION IS OUTDATED, NEEDS UPDATE!


The water flowing through breaches can originate from an external area outside the project area or an input area within the project area.
The water flowing through breaches can originate from an external area outside the project area or an input area within the project area.
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First, the difference in height of the water on either side of the breach is calculated.
First, the difference in height of the water on either side of the breach is calculated.


: <math>\Delta h = abs( max(0, w_{e,t} - H_{b,t}) - max(0, w_{b,t} - H_{b,t}) )</math>
: <math>\Delta h_{t} = abs( w_{o,t} - max(w_{i,t}, H_{b,t}))</math>


Using the height difference, the breach width increase is calculated.
Using the height difference, the breach width increase (m/s) is calculated per time step.


: <math>\Delta W_{b,t} = ((f_1 * f_2) / ln(10)) * ((g * H)^1.5 / cs_b^2) * (1 / (1 + (f_2 * g * t) / (3600 * cs_b)))</math>
: <math>\Delta W_{b,t} = ((f_1 * f_2) / ln(10)) * ((g * \Delta h_{t})^1.5 / cs_b^2) * (1 / (1 + (f_2 * g * t) / (3600 * cs_b)))</math>


The current breach width is then equal to the last calculated breach width, plus the calculated breach width increment.
The current breach width is then equal to the last calculated breach width, plus the calculated breach width increment.
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: <math>H_{b,t}</math> = The [[Breach height (Water Overlay)|BREACH_HEIGHT]] of the breach at time t.
: <math>H_{b,t}</math> = The [[Breach height (Water Overlay)|BREACH_HEIGHT]] of the breach at time t.
: <math>W_{b,t}</math> = The calculated breach width, initially equal to W<sub>b</sub>.
: <math>W_{b,t}</math> = The calculated breach width, initially equal to W<sub>b</sub>.
: <math>w_{b,t}</math> = Inner water level at breach area at time t.
: <math>w_{i,t}</math> = Inner water level at breach area at time t.
: <math>w_{e,t}</math> = Outer water level at input area (or external) at time t.
: <math>w_{o,t}</math> = Outer water level at input area (or external) at time t.
: <math>\Delta h_{t}</math> = The difference between the height of the water columns on either side of the breach at time t.
: <math>\Delta h_{t}</math> = The difference between the height of the water columns on either side of the breach at time t.
: <math>f_1</math> = Material factor, set to 1.3 (average for sand and clay levees).
: <math>f_1</math> = Material factor, set to 1.3 (average for sand and clay levees).

Revision as of 09:00, 7 September 2022

Water can flow through breaches into levee protected areas. These breaches often start small and grow over time[1].

The water flowing through breaches can originate from an external area outside the project area or an input area within the project area.

First, the difference in height of the water on either side of the breach is calculated.

Using the height difference, the breach width increase (m/s) is calculated per time step.

The current breach width is then equal to the last calculated breach width, plus the calculated breach width increment.

Where:

= The BREACH_WIDTH of the breach.
= The BREACH_HEIGHT of the breach at time t.
= The calculated breach width, initially equal to Wb.
= Inner water level at breach area at time t.
= Outer water level at input area (or external) at time t.
= The difference between the height of the water columns on either side of the breach at time t.
= Material factor, set to 1.3 (average for sand and clay levees).
= Constant, set to 0.04.
= Gravity constant, defined for the Water Overlay.
  • = The critical BREACH_SPEED of the breach (e.g. 0.2 for sand and 0.5 for clay).
  • = The calculated width increase of the breach at time t.
  • = Computational timestep.

Notes

See also

For an example of the breach growth, take a look at the Demo Breach Project available in all domains.

Related

The following topics are related to this formula.

Features
Breach
Formulas
Breach flow formula
Models
Surface model

References

  1. ↑ Verheij, H.J. ∙ Aanpassen van het bresgroeimodel in HIS-OM: Bureaustudie ∙ found at: http://resolver.tudelft.nl/uuid:aedc8109-da43-4a03-90c3-44f706037774 ∙ (last visited 2019-03-08)
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