The Toffaleti transport function was not developed for these large particles or high gradient systems and has a numerical artifact that can arise under these conditions. Yaw et al. (2019) demonstrated a load discontinuity, under certain shallow, large particle settings. This discontinuity is native to the Toffaleti equation so it can show up in the original formula or its hybrid with MPM which was designed to extend the approach to larger particle sizes. As long as the hydraulic radius is roughly an order of magnitude larger than twice the particle size the form of the Toffaleti equation works. But as 2dsi approaches Rh11.24 the denominator of the reference unit sediment discharge (see Mi equation in Toffaleti Section) goes to zero (generating infinite transport) and then negative as grain size continues to increase relative to shallow depths.
But particles that invert the Toffaleti transport denominator are unlikely to be suspended. These particles will almost always be limited to bed load. So HEC-RAS added a "Toffaleti limiter" that uses Julian's (2002) Rouse number, suspension test, that a grain class is likely to be suspended if the fall velocity (w) is less than 40% of the shear velocity (u) (u/w>0.4). Therefore, HEC-RAS checks the Rouse number (u*/w) of each grain class in each time step and sets the transport capacity to zero for all transport ones where Rouse number is less than or equal to 0.4,
