# FLAC Constitutive Models

## NULL MODEL GROUP

Null model
A null material model can be assigned to zones to represent material that is removed or excavated (holes, excavations, regions in which material will be added at later stage). This is more advantageous than deleting zones because zone materials can be changed later (for instance, to represent backfill in a construction stage).

## ELASTIC MODEL GROUP

Elastic, isotropic model
The elastic, isotropic model provides the simplest representation of material behavior. This model is valid for homogeneous, isotropic, continuous materials that exhibit linear stress-strain behavior with no hysteresis on unloading (manufactured materials such as steel, for instance, loaded below strength limit; factor-of-safety calculation).

Elastic, transversely isotropic model
The elastic, transversely isotropic model gives the ability to simulate layered elastic media in which there are distinctly different elastic moduli in directions normal and parallel to the layers (laminated materials loaded below strength limit).

## PLASTIC MODEL GROUP

Drucker-Prager model
The Drucker-Prager plasticity model may be useful to model soft clays with low friction angles. However, this model is not generally recommended for application to geologic materials. It is included here mainly to permit comparison with other numerical program results (implicit finite-element).

Mohr-Coulomb model
The Mohr-Coulomb model is the conventional model used to represent shear failure in soils and rocks. Vermeer and deBorst (1984), for example, report laboratory test results for sand and concrete that match well with the Mohr-Coulomb criterion. Example applications: general soil or rock mechanics for slope stability and underground excavation general soil or rock mechanics.

Ubiquitous-joint model
The ubiquitous-joint model is an anisotropic plasticity model that includes weak planes of specific orientation embedded in a Mohr-Coulomb solid (excavation in closely bedded strata).

Caniso model
The Caniso model combines the logic of an elastic, transversely isotropic (anisotropic) model with that of the ubiquitous joint model. The model has a single orientation of weakness, which matches the orientation of the plane of elastic isotropy, and the criterion for failure is a local Mohr-Coulomb yield criterion. The model can be useful in simulation of the behavior of layered (laminated) materials.  NEW

Strain-hardening/softening model
The strain-hardening/softening model allows representation of nonlinear material softening and hardening behavior based on prescribed variations of the Mohr-Coulomb model properties (cohesion, friction, dilation, tensile strength) as functions of the deviatoric plastic strain (studies in post-failure (e.g., progressive collapse, yielding pillar, caving)).

Bilinear strain-hardening/softening ubiquitous-joint model
The bilinear strain-hardening/softening ubiquitous-joint model allows representation of material softening and hardening behavior for the matrix and the weak plane based on prescribed variations of the ubiquitous-joint model properties (cohesion, friction, dilation and tensile strength) as functions of deviatoric and tensile plastic strain. The variation of material strength properties with mean stress can also be taken into account by using the bilinear option (studies in post-failure of laminated materials).

Double-yield model
The double-yield model is intended to represent materials in which there may be significant irreversible compaction in addition to shear yielding, such as hydraulically placed backfill or lightly cemented granular material (hydraulically placed backfill).

Modified Cam-clay model
The modified Cam-clay model may be used to represent materials when the influence of volume change on bulk property and resistance to shear need to be taken into consideration, as in the case of soft clay (geotechnical construction on clay).

Hoek-Brown model
The Hoek-Brown failure criterion characterizes the stress conditions that lead to failure in intact rock and rock masses. The failure surface is nonlinear, and is based on the relation between the major and minor principal stresses. The model incorporates a plasticity flow rule that varies as a function of the confining stress level (geotechnical construction in rock mass).

Modified Hoek-Brown model
A modified Hoek-Brown model (the mhoek model) provides an alternative to the Hoek-Brown model with a stress-dependent plastic flow rule, described above. The modified model characterizes post-failure plastic flow by simple flow rule choices given in terms of a user-specified dilation angle. This model also contains a tensile strength limit similar to that used by the Mohr-Coulomb model. In addition, a factor-of-safety calculation based on the shear-strength reduction method can be run with the modified Hoek-Brown model (factor-of-safety calculations in rock mass).

Cysoil model
The cap-yield (Cy)soil model provides a comprehensive representation of the nonlinear behavior of soils. The model includes frictional strain-hardening and softening shear behavior, an elliptic volumetric cap with strain-hardening behavior, and an elastic modulus function of plastic volumetric strain. The model allows a more realistic representation of the loading/unloading response of soils (geotechnical construction in soft soils).

Simplified Cysoil model
A simplified version of the Cysoil model, called the Chsoil model, offers built-in features including a friction-hardening law that uses hyperbolic model parameters as direct input, and a Mohr-Coulomb failure envelope with two built-in dilation laws (alternative to Duncan and Chang model).

Plastic Hardening model
The Plastic Hardening (PH) model is a shear and volumetric hardening constitutive model for the simulation of soil behavior. The model is characterized by a hyperbolic stress-strain relationship during axial drained compression (while unlodaing/reloading is elastic) and stress-dependent stiffness described by a power law. It also includes shear and volumetric hardening laws and adopts Mohr-Coulomb failure criterion. The model is straightforward to calibrate using either conventional lab or in situ tests. It is well established for soil structure interaction problems, excavations, tunneling and settlements analysis, etc. (geotechnical construction in soils).

To take soil strain-dependency into account, a PH small-strain (PHSS) stiffness formulation is now available for the Plastic Hardening model. Whereas the PH model assumes an elastic material behavior during unloading and reloading for very small strains, with the small-strain formulation soil stiffness behaves nonlinearly with increasing strains. The PHSS formulation is enabled by the model property flag flag_small 1. NEW IN 2019

Swell model
The swell model is based on the Mohr-Coulomb constitutive model with nonassociated shear and associated tension flow rules. It accounts for wetting induced deformations by means of coupling wetting strains with the model state prior to wetting (geotechnical construction in expansive soils).

## CREEP OPTION MODELS

This FLAC option can be used to simulate the behavior of materials that exhibit creep (i.e., time-dependent material behavior). There are eight creep material models available with this option.

1. Classical viscoelastic model;
2. Two-component power law;
3. Reference creep formulation (the WIPP model) for nuclear-waste isolation studies;
4. Burgers-creep viscoplastic model combining the Burgers-creep model and the Mohr-Coulomb model;
5. Power-law viscoplastic model combining the two-component power law and the Mohr-Coulomb model;
6. Power-law viscoplastic model combining the preceding model (5) with ubiquitous joints logic;
7. WIPP-creep viscoplastic model combining the WIPP model and the Drucker-Prager model; and
8. Crushed-salt constitutive model.

## DYNAMIC OPTION MODEL

The dynamic analysis option permits two-dimensional, plane-strain, plane-stress or axisymmetric, fully dynamic analysis with FLAC. This option includes the Finn constitutive model for dynamic pore pressure-generation. This model includes both the Martin, Finn, and Seed formulation and the simpler Byrne formulation.