Breach growth formula (Water Overlay): Difference between revisions
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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. | ||
: ''Δh = abs( max(0, w<sub>e</sub> - H<sub>b</sub>) - max(0, w<sub>b</sub> - H<sub>b</sub>) )'' | : ''Δh = abs( max(0, w<sub>e</sub> - H<sub>b,t</sub>) - max(0, w<sub>b,t</sub> - H<sub>b,t</sub>) )'' | ||
Using the height difference, the breach width increase is calculated. | Using the height difference, the breach width increase is calculated. | ||
: ''ΔW<sub>b</sub> = f<sub>m</sub> * (g<sup>1/2</sup> * Δh<sup>3/2</sup> / cs<sub>b</sub> ) * log<sub>10</sub> (1 + (0.04 * g / cs<sub>b</sub> ) * Δt / 3600)'' | : ''ΔW<sub>b,t</sub> = f<sub>m</sub> * (g<sup>1/2</sup> * Δh<sup>3/2</sup> / cs<sub>b</sub> ) * log<sub>10</sub> (1 + (0.04 * g / cs<sub>b</sub> ) * Δt / 3600)'' | ||
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. | ||
: ''W<sub>b,t</sub> = W<sub>b,t-1</sub> + ΔW'' | : ''W<sub>b,t</sub> = W<sub>b,t-1</sub> + ΔW<sub>b,t</sub>'' | ||
Where: | Where: | ||
* W<sub>b</sub> = The [[Breach width (Water Overlay)|BREACH_WIDTH]] attribute of the breach. | * W<sub>b</sub> = The [[Breach width (Water Overlay)|BREACH_WIDTH]] attribute of the breach. | ||
* H<sub>b</sub> = The [[Breach height (Water Overlay)|BREACH_HEIGHT]] attribute of the breach. | * H<sub>b,t</sub> = The [[Breach height (Water Overlay)|BREACH_HEIGHT]] attribute of the breach at time t. | ||
* | * W<sub>b,t</sub> = The calculated breach width, initially equal to W<sub>b</sub>. | ||
* w<sub>b</sub> = | * w<sub>b,t</sub> = water level at breach at time t. | ||
* w<sub>e</sub> = | * w<sub>e,t</sub> = water level at entry area (external or internal) at time t. | ||
* Δh = The difference between the height of the water columns on either side of the breach. | * Δh = The difference between the height of the water columns on either side of the breach. | ||
* f<sub>m</sub> = Material factor, set to 1.3 (average for sand and clay levees) | * f<sub>m</sub> = Material factor, set to 1.3 (average for sand and clay levees) | ||
* g = Acceleration factor of gravity | * g = Acceleration factor of gravity | ||
* cs<sub>b</sub> = The critical [[Breach speed (Water Overlay)|BREACH_SPEED]] attribute of the breach. | * cs<sub>b</sub> = The critical [[Breach speed (Water Overlay)|BREACH_SPEED]] attribute of the breach. | ||
* ΔW = The calculated width increase of the breach. | * ΔW<sub>b,t</sub> = The calculated width increase of the breach. | ||
* Δt = Computational timestep. | * Δt = Computational timestep. | ||
Revision as of 11:25, 15 April 2019
Water can flow through Breaches into levee protected areas. These breaches often start small and grow over time. The speed by which they can grow has been described in [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.
- Δh = abs( max(0, we - Hb,t) - max(0, wb,t - Hb,t) )
Using the height difference, the breach width increase is calculated.
- ΔWb,t = fm * (g1/2 * Δh3/2 / csb ) * log10 (1 + (0.04 * g / csb ) * Δt / 3600)
The current breach width is then equal to the last calculated breach width, plus the calculated breach width increment.
- Wb,t = Wb,t-1 + ΔWb,t
Where:
- Wb = The BREACH_WIDTH attribute of the breach.
- Hb,t = The BREACH_HEIGHT attribute of the breach at time t.
- Wb,t = The calculated breach width, initially equal to Wb.
- wb,t = water level at breach at time t.
- we,t = water level at entry area (external or internal) at time t.
- Δh = The difference between the height of the water columns on either side of the breach.
- fm = Material factor, set to 1.3 (average for sand and clay levees)
- g = Acceleration factor of gravity
- csb = The critical BREACH_SPEED attribute of the breach.
- ΔWb,t = The calculated width increase of the breach.
- Δt = Computational timestep.
See also
References
- ↑ 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)