# 3DEC Zone 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). The stresses within null blocks or null zones (ZONE model null) are set to zero; no body forces (e.g., gravity) act on these zones.

## 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, orthotropic model
The elastic, orthotropic model represents material with three mutually perpendicular planes of elastic symmetry. For example, this model may simulate columnar basalt loaded below its strength limit.

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 (e.g., 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).

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, and 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).

## CREEP OPTION MODELS

This 3DEC 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. Burgers viscoelastic model;
3. Two-component power law;
4. Reference creep formulation (the WIPP model) for nuclear-waste isolation studies;
5. Burgers-creep viscoplastic model combining the Burgers-creep model and the Mohr-Coulomb model;
6. Power-law viscoplastic model combining the two-component power law and the Mohr-Coulomb model;
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 three-dimensional, fully dynamic analysis with 3DEC.