## FLAC3D Constitutive Models

##### FLAC3D

FLAC3D includes the following standard nineteen null, elastic, and plastic models. FLAC3D's functionality can be even further expanded by purchasing additional options.

### 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. Example applications: soil, rock, manufactured material such as steel loaded below strength limit.

Elastic, orthotropic Model

The elastic, orthotropic model represents material with three mutually perpendicular (orthogonal) planes of elastic symmetry. Example applications: 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. Example applications: 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.

Mohr-Coulomb model

The Mohr-Coulomb model is the conventional model used to represent shear yielding 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 studies.

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. Example applications: excavation in closely bedded strata.

Ubiquitous-Anisotropic (Caniso) model

This ubiquitous joint model with anisotropic (transversely isotropic) elasticity accounts for the presence of an orientation of weakness (weak plane). The plane of weakness has the same orientation as the plane of elastic isotropy. The criterion for failure on the plane, whose orientation is given, consists of a Coulomb criterion with tension cutoff. This model can be useful in simulation of the elastic and yielding 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 plastic strain. Example applications: post-failure studies involving progressive collapse such as yielding of mining pillars and cave mining.

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 matrix and ubiquitous-joint model properties (cohesion, friction, dilation and tensile strength) as functions of plastic strain. The variation of material strength properties with mean stress can also be taken into account by using the bilinear option. Example applications: post-failure study of laminated rock mass.
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. Example applications: hydraulically placed backfill, lightly cemented granular material.
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. Application example: geotechnical construction on soft clay.

Hoek-Brown model

The Hoek-Brown yield criterion characterizes the stress conditions that lead to failure in intact rock and rock masses. The yield 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. Application example: geotechnical construction in rock mass.

Modified Hoek-Brown Model

A modified Hoek-Brown 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 using a choice of simple flow rules 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. Example application: factor-of-safety calculations in rock mass.

Cap-Yield (CYSoil) Model

This model is a strain-hardening constitutive model for soil characterized by a frictional and cohesive Mohr-Coulomb shear envelope and an elliptic volumetric cap, associated with a shape parameter. The model features include: a cap hardening law, to capture the volumetric power law behavior observed in isotropic compaction tests; a friction-hardening law, to reproduce the hyperbolic stress-strain law behavior observed in drained triaxial tests; and a compaction/dilation law to model irrecoverable volumetric strain taking place as a result of soil shearing.

Compared to the model implemented in FLAC3D 5.0, these features are all built into the updated version. The updated model retains the capability to substitute, by means of tables, alternative user-defined hardening/softening laws for the built-in laws. When a table is declared for a specific model property of friction, dilation, cohesion, tensile strength, or cap-pressure, the associated user-defined law takes precedence over the corresponding built-in law. UPDATED

Simplified CYSoil Model

A simplified version of the CYSoil model with no volumetric cap, 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. Application example: as an alternative to Duncan and Chang model in soil mechanics problems.

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. Application example: geotechnical construction in soils. The model is well established for soil structure interaction problems, excavations, tunneling and settlements analysis, etc. NEW

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 zone property flag-smallstrain on. NEW in 2018

Mohr-Coulomb-Tension (MOHRT) Model
This model requires the same material parameters as the conventional Mohr-Coulomb model. It assumes that a zone can have up to three mutually perpendicular cracks. Each crack completely cuts throughout a zone. If the tensile strength (which is initially isotropic) is exceeded, a crack is formed perpendicular to the principal tensile stress. The tensile strength (which becomes anisotropic) perpendicular to the crack is set to zero, as a result of instantaneous softening. Cracking opening and closing are tracked internally. After the crack closes, the model behaves as if the crack does not exist, except that the tensile strength perpendicular to the crack is zero. Application examples: mining, underground excavation studies, with conservative estimate of surface settlement. NEW

Swell Model

The swell model is based on the Mohr-Coulomb constitutive model. The difference is that the wetting-induced deformations are taken into account by coupling the assumed wetting strains with the model state prior to wetting. The wetting-induced strains follow ether logarithmic or linear function of normalized compressive stress in the (user-defined) principal swelling directions. Application example: soil swelling caused by wetting (other external source). NEW

### CREEP OPTION

This FLAC3D option can be used to simulate the behavior of materials that exhibit creep (i.e., time-dependent material behavior). There are nine material models available with the creep option.

1. Maxwell model - a classical viscoelastic model known as the Maxwell substance;
2. Burgers model - a classical viscoelastic model known as the Burgers substance which composed of a Kelvin model and a Maxwell model;
3. Power model - a two-component power law model used for mining applications (e.g., salt or potash mining);
4. WIPP model - a reference creep model commonly used in thermomechanical analyses associated with studies for the underground isolation of nuclear waste in salt;
5. Burgers-Mohr model - a viscoplastic model combining the Burgers model and the Mohr-Coulomb model;
6. Power-Mohr model - a viscoplastic model combining the two-component power model and the Mohr-Coulomb model;
7. Power-Ubiqitous mdoel - a viscoplastic model combining the two-component power model and the ubiquitous-joint model. NEW
8. WIPP-Drucker model - a viscoplastic model combining the WIPP model and the Drucker-Prager model;
9. WIPP-Salt model - a viscoplastic model modified from the WIPP model, and includes volumetric and deviatoric compaction behavior for salt-like materials.

### DYNAMIC OPTION

The dynamic option permits fully dynamic analysis with FLAC3D. 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.

### THERMAL OPTION

The thermal option of FLAC3D incorporates both conduction and advection models and a thermal hydration constitutive model.

### C++ PLUG-IN OPTION

The C++ Plug-in option of FLAC3D permits you to create, load, and run your own user-defined constitutive model (UDM).

##### Latest News
• International Slope Stability 2022 Itasca is proud to be a Diamond sponsor of Slope Stability 2022 (October 17-21 |...
Read More
• Software Benchmark Tests To help with your hardware configuration decisions, Itasca has created an online benchmark speed test...
Read More
• Meet Our Summer Interns Itasca is pleased to welcome three graduate student summer interns to Minneapolis. They will be...
Read More

##### Upcoming Events
13 Mar
3DEC In-Person Introductory course
Live in-person introductory training course in Minneapolis, Minnesota. This course provides an overview of the capabilities and feature... Read More
27 Mar
FLAC3D In-Person Introductory Course
Live in-person introductory training course. This 3-day course provides general feature training addressing basic concepts and recommen... Read More
30 Mar
Griddle In-Person Introductory Course
Live in-person introductory training course. This course provides an overview of the capabilities and features of Rhino3D CAD software ... Read More