Hoek-Brown model with softening - PLAXIS UDSM

Hoek & Brown (HB) failure criterion has been often employed over the past decades in practical engineering applications due to its intrinsic capability to capture the non-linear behaviour of different types of rocks. The former idea of HB (Hoek, 1968; Hoek and Brown, 1980), was to link some concepts of fracture mechanics and the macroscopic response resulting from the non-linear trend of the initial yielding. To formulate a mathematical expression of the initial yield surface and describe the rock-mass behaviour, the Uniaxial Compression Strength (UCS) of the intact rock and some dimensionless constants obtained from empirical correlations (i.e., the constants m_b, s and a) have been used to define the HB criterion.

This approach has been further improved by several authors (Marinos et al., 2005) who have used empirical data recorded from field observations at different environmental conditions to characterize the mechanical properties of the rock-mass. For this purpose, the Geological Strength Index (GSI) and the Damage factor (D) have been used to define the material parameters of the HB yield surface.

This Hoek & Brown model implemented in PLAXIS refers to the formulation proposed by Jiang (2017) which can guarantee at the same time smoothness and convexity of the yield surface and plastic potential. The underlying implementation is further enhanced with the following constitutive features:

• The initial non-associativity with the ability to simulate the non-linear evolution of the dilation in the postpeak regime;
• A softening rule implemented through two different formulations;
• A tension cut-off in the tensile regime of the stress space;
• A rate-dependent version of the HB model is here used to solve the mesh-dependency of the numerical solution when the brittle failure is characterized by a strong concentration of strain in narrow shear bands.

With the release of PLAXIS 2D/3D CONNECT Edition V20 Update 1 (January 2020), the PLAXIS User Defined Soil models are delivered with the PLAXIS installation. When enabling the Geotechnical SELECT Entitlement [GSE] when starting the PLAXIS application, this model becomes available in the Parameters tab when selecting "User-defined" for the Material model.