Non-Erodible Surfaces

Non-erodible surfaces (also known as hard bottoms) may be simulated in HEC-RAS and are specified using a minimum bed elevation, z_b, min, or maximum depth, h_max. In the 2D model the non-erodible surfaces are specified at both cells and faces independently. Non-erodible surfaces are modeled at the subarea scale by limiting the erosion rate so that the minimum bed elevation is preserved (i.e. z_bi ≥ z_b, min. The time stepping scheme is given by $//<![CDATA[ \begin{array}{l}z_{bi}^{n+1}=z_{bi}^{n}+\Delta z_{bi}\end{array} //]]>$ in which z_biⁿ is the previous bed elevation, z_bi^n + 1 is the new bed elevation, and $//<![CDATA[ \begin{array}{l}\Delta z_{bi}\end{array} //]]>$ is the bed change. Assuming that the bed elevation at the current time is higher than the hard bottom (i.e. z_biⁿ ≥ z_b, min). Inserting the above equation into the bed change equation leads to the hard-bottom limited erosion rate

where

$//<![CDATA[ \begin{array}{l}E_{tki, hb}\end{array} //]]>$ = subregion hard-bottom limited fractional erosion rate [M/L²/T]

$//<![CDATA[ \begin{array}{l}D_{tki}\end{array} //]]>$ = subregion fractional deposition rate [M/L²/T]

$//<![CDATA[ \begin{array}{l}ρ_{d1}\end{array} //]]>$ = dry density of active layer [M/L³]

$//<![CDATA[ \begin{array}{l}f_{1ki}\end{array} //]]>$ = grain fractions by weight [-]

$//<![CDATA[ \begin{array}{l}f_{M}\end{array} //]]>$ = morphologic acceleration factor [-]

$//<![CDATA[ \begin{array}{l}\Delta t\end{array} //]]>$ = computational time step [T]

The hard-bottom limited erosion rate is therefore

The bed-slope term and avalanching algorithm are also modified so that only deposition may occur over non-erodible surfaces following an approach similar to that described above.

When simulating multiple grain classes, the bed gradation can significantly change at non-erodible surfaces during a time step. This means that the model may require at least one to two iterations to converge when simulating non-erodible surfaces with multiple grain classes.