Pressure-Dependent Modified Kondner Zelasko (MKZ)
RSSeismic incorporates the pressure-dependent hyperbolic model. The modified hyperbolic model, developed by (Matasovic, 1993), is based on the hyperbolic model by (Konder and Zelasko, 1963), but adds two additional parameters Beta (β) and s that adjust the shape of the backbone curve:
 | Eq. 1 |
where 𝐺0 = initial shear modulus, 𝜏 = shear strength, 𝛾 = shear strain. β, s, and 𝛾 are the model parameters, respectively. There is no coupling between the confining pressure and shear stress. RSSeismic extends the model to allow coupling by making 𝛾r confining pressure dependent as follows (Hashash and Park, 2001):
 | Eq. 2 |
where 𝜎𝑣 ′ is the effective vertical stress. Reference stress is the vertical effective stress at which 𝛾r = Ref. stress. This model is termed as the “pressure-dependent hyperbolic model.” The pressure-dependent modified hyperbolic model is almost linear at small strains and results in zero hysteretic damping at small strains. Small strain damping has to be added separately to simulate actual soil behavior which exhibits damping even at very small strains (Hashash and Park, 2001). The small strain damping is defined as
 | Eq. 3 |
where d can be set to zero in case a pressure independent small strain damping is desired.
In summary, the parameters to be defined in addition to the layer properties are:
- Reference Strain
- Reference Stress
- Stress-strain curve parameter, Beta (β)
- Stress-strain curve parameter, s
- Pressure dependent (reference strain) parameter, b
- Pressure dependent (damping curve) parameter, d