HEC-RAS uses two different version of the excess shear equation for cohesive erosion: the dimensional (Kd) form and the "dimensionless" (M) form.
In the dimensional form of the excess shear equation, the erosion coefficient (Kd) is the ratio of the erosion rate to the excess shear stress (e.g. the difference between the bed shear stress and the critical shear stress). It is the slope of the shear-erodibility relationship, normalized by the shear stress.
This is called the "dimensional" form, because the excess shear term has shear stress units, giving the erodibility coefficient units (Mass/Force-time) that are not entirely intuitive.
The alternate form of the excess shear equation normalizes the excess shear component by the critical shear stress, making it unitless. This makes the equation a little less intuitive but gives the erodibility coefficient (M) the same units as the erosion rate, which makes this parameter more intuitive and easier to communicate.
Relationship Between M and Kd
You can convert between the dimensional and dimensionless forms of this equation by multiplying or dividing by 
such that:
Therefore, you can convert between M and Kd by multiplying or dividing by the critical shear stress:
