Breach growth formula (Water Overlay)

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 . 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, w_e - H_b,t) - max(0, w_b,t - H_b,t) )

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

ΔW_b,t = f_m * (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_b,t

Where:

• W_b = The BREACH_WIDTH attribute of the breach.
• H_b,t = The BREACH_HEIGHT attribute 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.
• Δh_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
• cs_b = The critical BREACH_SPEED attribute of the breach.
• ΔW_b,t = The calculated width increase of the breach at time t.
• Δt = Computational timestep.

Notes

• The Breach height H_b,t can be defined over time.

See also

• Breach