## 3DEC Zone Constitutive Models

### 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-PAC model

The Hoek-Brown failure criterion is an empirical relation that characterizes the stress conditions that lead to failure in intact rock and rock masses. It has been used very successfully in design approaches that use limit equilibrium solutions. The Hoek-Brown-PAC model provides a representation for yielding that accounts for the changing failure condition. 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). This model works well at higher confining stress states, but can produce excessive dilation at low confinement or under tensile-stress conditions.

In the Hoek-Brown-PAC model, the material properties σci, mb, s, and a are assumed to remain constant by default. Material softening after the onset of plastic yield can be simulated by specifying that these mechanical properties change (i.e., reduce the overall material strength) according to a softening parameter. The softening parameter selected for the Hoek-Brown-PAC model is the plastic confining strain component, ep3. Softening behavior is provided by specifying tables that relate each of the properties σci, mb, s, and a to ep3.

This failure criterion was formerly named the Hoek-Brown model.

Hoek-Brown model

The Hoek-Brown model is derived directly from the Mohr-Coulomb model, and, like the Mohr-Coulomb model, can be used to perform factor of safety calculations using the model factor-of-safety command.

The Hoek-Brown model provides a representation for yielding that accounts for the changing failure condition. This model works well at higher confining stress states, at low confinement, or under tensile-stress conditions. The Hoek-Brown model is modified to include a tensile yield criterion, and also allow the user to specify a dilation angle as an input parameter and manually control the level of dilation that develops.

In the Hoek-Brown model, the material properties σci, mb, s, and a are assumed to remain constant by default. Material softening after the onset of plastic yield can be simulated by specifying that these mechanical properties change (i.e., reduce the overall material strength) according to a softening parameter. The softening parameter selected for the Hoek-Brown model is the plastic confining strain component, ep3. Softening behavior is provided by specifying tables that relate each of the properties σci, mb, s, and a to ep3. A length parameter, length-calibration, is available to calibrate Hoek-Brown model softening properties to account for zone size.

This failure criterion was formerly named the Modified-Hoek-Brown model.

### CREEP MODELS GROUP

3DEC 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 for creep analysis.

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.

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