Breach growth formula (Water Overlay)

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

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.

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

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

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

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

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

Where:

$W_{b}$ = The BREACH_WIDTH of the breach.

$H_{b,t}$ = The BREACH_HEIGHT of the breach at time t.

$W_{b,t}$ = The calculated breach width, initially equal to W_b.

$w_{b,t}$ = water level at breach at time t.

$w_{e,t}$ = water level at entry area (external or internal) at time t.

$\Delta h_{t}$ = The difference between the height of the water columns on either side of the breach at time t.

$f_{m}$ = Material factor, set to 1.3 (average for sand and clay levees).

$g$ = Acceleration factor of GRAVITY, defined for the Water Overlay.

• $cs_{b}$ = The critical BREACH_SPEED of the breach.
• $\Delta W_{b,t}$ = The calculated width increase of the breach at time t.
• $\Delta t$ = Computational timestep.

Notes

• The breach height H_b,t can be defined over time, by configuring the BREACH_HEIGHT as an attribute array.

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

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