A Bingham plastic can absorb some stress without deforming the material. Deformation (strain) only occurs after stress exceeds a minimum threshold. That minimum threshold required before stress causes strain, is the yield stress (\tau_y), which is the intercept of the stressstrain relationship. HECRAS provides three methods for yield stress:
 Userspecified constant
 Exponential formulation
 MohrCoulomb formula
Exponential
A widely used formula to estimate the yield stress is the exponential formulation (Chien and Ma, 1958; Dai et al., 2014; O'Brien and Julien, 1988)
where a and b are calibration coefficients, and C_v is the volumetric concentration between 0 and 1.
Table: Yield stress parameters for the Exponential equation from Julian (1995)
Material  a (Pa)  b 
"Typical soil"  0.005  7.5 
Kaolinite  0.05  9 
Sensitive Clays  0.03  10 
Bentonite  0.002  100 
The exponential equation works relatively well for hyperconcentrated flows with concentrations between 5% and 30%. However, for high concentrations or very low concentrations the formulation does not work as well. For example a zero concentration produces a yield stress equal to the coefficient a and does not go to zero as it should theoretically.
MohrCoulomb
The MohrCoulomb yield stress model is given by

\sigma = ( \rho_m  \rho_w ) g h \cos^2 \theta 
where c is the cohesion or cohesive strength, \mu is the Coulomb friction coefficient, \sigma is the normal stress at the bottom of the mixture, \theta is the bed slope angle, h is the vertical flow depth, and \phi is the internal friction angle. The normal stress is computed assuming the flow is parallel to the bed as in Hergarten and Robl (2015). In addition the mixture is assumed to be fully saturated. The internal friction angle depends on mixture but its values are typically between 2.5º and 15º.