# Breach growth formula (Water Overlay)

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.

${\displaystyle \Delta h=abs(max(0,w_{e,t}-H_{b,t})-max(0,w_{b,t}-H_{b,t}))}$

Using the height difference, the breach width increase is calculated.

${\displaystyle \Delta W_{b,t}=f_{m}\cdot ({\sqrt {g}}\cdot {\sqrt {\Delta h^{3}}}/cs_{b})\cdot \log _{10}(1+(0.04\cdot g/cs_{b})\cdot \Delta t/3600)}$

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

${\displaystyle W_{b,t}=W_{b,t-1}+\Delta W_{b,t}}$

Where:

${\displaystyle W_{b}}$ = The BREACH_WIDTH of the breach.
${\displaystyle H_{b,t}}$ = The BREACH_HEIGHT of the breach at time t.
${\displaystyle W_{b,t}}$ = The calculated breach width, initially equal to Wb.
${\displaystyle w_{b,t}}$ = water level at breach at time t.
${\displaystyle w_{e,t}}$ = water level at entry area (external or internal) at time t.
${\displaystyle \Delta h_{t}}$ = The difference between the height of the water columns on either side of the breach at time t.
${\displaystyle f_{m}}$ = Material factor, set to 1.3 (average for sand and clay levees).
${\displaystyle g}$ = Gravity constant, defined for the Water Overlay.
• ${\displaystyle cs_{b}}$ = The critical BREACH_SPEED of the breach (e.g. 0.2 for sand and 0.5 for clay).
• ${\displaystyle \Delta W_{b,t}}$ = The calculated width increase of the breach at time t.
• ${\displaystyle \Delta t}$ = Computational timestep.

## Notes

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)