Breach growth formula (Water Overlay)

Water can flow through Breaches into the hydrological model
The water 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, w_e - H_b) - max(0, w_b - H_b) )

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

ΔW_b = 1.3 * (g^1/2 * Δh^3/2 / cs_b ) * log₁₀ (1 + (0.04 * g / cs_b ) * Δt / 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 + ΔW

Where:

• W_b = The BREACH_WIDTH attribute of the breach.
• H_b = The BREACH_HEIGHT attribute of the breach.
• Wb,t = The calculated breach width, initially equal to W_b.
• w_b = Current water level at breach.
• w_e = Current water level at entry area (external or internal).
• Δh = The difference between the height of the water columns on either side of the breach.
• f_m = Material factor, set to 1.3 (average for sand and clay levees)
• g = Acceleration factor of gravity
• cs_b = The critical BREACH_SPEED attribute of the breach.
• ΔW = The calculated width increase of the breach.
• Δt = Computational timestep.

See also

• Breach