# Strength Properties

In the Material Properties dialog, the **Strength Parameters** allow you to define:

- the failure (strength) criterion for a material
- the material type (elastic or plastic)

## Failure Criterion

The following strength criteria are available in *RS3* for defining the strength of your rock mass or soil:

Elastic/Plastic

Softening/Hardening

- Cam-Clay
- Modified Cam-Clay
- Mohr Coulomb with Cap
- Softening Hardening Model
- Barcelona Basic
- Norsand

Dynamic

- Bounding Surface Plasticity
- Manzari and Dafalias

Anisotropic

- Jointed Mohr-Coulomb
- Jointed Generalized Hoek-Brown
- Snowden Mod.Anisotropic Linear
- Anistropic Linear
- Generalized Anisotropic

Slide Models

FLAC

PLAXIS

See below for information about each failure criterion.

NOTE: for the Mohr-Coulomb, Hoek-Brown or Generalized Hoek-Brown criteria, you can link directly to *RocData* to help determine values of input parameters.

## Material Type

You may select either **Elastic** or **Plastic** for the Material Type.

### ELASTIC MATERIAL

If you choose Material Type = **Elastic**, then the failure criterion parameters that you enter will only be used for the calculation and plotting of strength factor within the material. Although an Elastic material cannot "fail", the failure envelope allows a degree of overstress to be calculated.

### PLASTIC MATERIAL

If you choose Material Type = **Plastic**, the strength parameters you enter will be used in the analysis if yielding occurs. This is unlike Elastic materials, where the strength parameters are only used to obtain values of strength factor, but do not affect the analysis results (i.e. stresses and displacements are not affected).

If you define a material to be Plastic then you may also define residual strength parameters and a dilation parameter, depending on the strength criterion.

- If the residual strength parameters are equal to the peak parameters, then you are defining an "ideally" elastic-plastic material.
- The
**dilation**is a measure of the increase in volume of the material when sheared (see below for more information).

NOTE: if you define a material as **Plastic**, then you are restricted to **Isotropic** elastic properties for that material. You cannot combine plasticity with Transversely Isotropic or Orthotropic elastic properties.

## Mohr-Coulomb

For the Mohr-Coulomb criterion you must define the following parameters:

- Cohesion
- Friction Angle
- Tensile Strength

If you are not considering pore pressure in the analysis, then the cohesion and friction angle are total stress parameters. If you are considering pore pressure, then cohesion and friction angle are effective stress parameters.

If the Material Type = Plastic, you will also be able to define:

- Dilation Angle
- Residual values of cohesion, friction angle and tensile strength

#### Link to RocData

For assistance with determining Mohr-Coulomb parameters you can startup *RocData* by selecting the button, and paste applicable data from *RocData* by selecting the button. See below for further information.

## Hoek-Brown

The **Hoek-Brown** strength criterion in *RS3* refers to the original Hoek-Brown failure criterion [Hoek & Bray (1981)], described by the following equation:

Note that this is a special case of the **Generalized Hoek-Brown** criterion, with the constant a = 0.5. See below for definition of the parameters in this equation.

The original Hoek-Brown criterion has been found to work well for most rocks of good to reasonable quality in which the rock mass strength is controlled by tightly interlocking angular rock pieces.

For lesser quality rock masses, the Generalized Hoek-Brown criterion can be used.

### LINK TO ROCDATA

For assistance with determining Hoek-Brown parameters you can startup *RocData* by selecting the button, and paste applicable data from *RocData* by selecting the button. See below for further information.

## Generalized Hoek-Brown

For the **Generalized Hoek-Brown** criterion you must define the following parameters:

- The intact uniaxial compressive strength (UCS) of the rock
- parameters mb, s and a

If the Material Type = Plastic, you will also be able to define:

- Dilation parameter
- Residual values of mb, s and a

The Generalized Hoek-Brown strength criterion is described by the following equation:

where:

- mb is a reduced value (for the rock mass) of the material constant mi (for the intact rock)
- s and a are constants that depend upon the characteristics of the rock mass
- is the uniaxial compressive strength (UCS) of the intact rock pieces
- and are the axial and confining effective principal stresses respectively

In most cases it is practically impossible to carry out triaxial or shear tests on rock masses at a scale that is necessary to obtain direct values of the parameters in the Generalized Hoek-Brown equation. Therefore some practical means of estimating the material constants mb, s and a is required. According to the latest research, the parameters of the Generalized Hoek-Brown criterion [Hoek, Carranza-Torres & Corkum (2002)], can be determined from the following equations:

where:

- GSI is the Geological Strength Index
- mi is a material constant for the intact rock
- the parameter D is a "disturbance factor" which depends upon the degree of disturbance to which the rock mass has been subjected by blast damage and stress relaxation. It varies from 0 for undisturbed in situ rock masses to 1 for very disturbed rock masses.

### PARAMETER CALCULATOR

The parameters GSI, mi, D and UCS can be estimated for your material using the Parameter Calculator dialog, which is available by selecting the GSI button in the **Material Properties** dialog. Values of mb, s and a are automatically calculated from the above equations, and the rock mass modulus is also calculated. See the Parameter Calculator topic for more information.

### LINK TO ROCDATA

For assistance with determining Generalized Hoek-Brown parameters, you can startup *RocData* by selecting the button, and paste applicable data from *RocData* by selecting the button. See below for further information.

## Drucker-Prager

The **Drucker-Prager** strength parameters are:

- Tensile Strength
- q parameter
- k parameter

If the Material Type = Plastic, you will also be able to define:

- Dilation parameter
- q (residual), k(residual)

NOTE: to calculate equivalent Drucker-Prager parameters based on Mohr-Coulomb parameters, you can use the following equations:

## Cam-Clay

Specification of the **Cam-Clay** model requires five material parameters, and the initial state of consolidation. These parameters are summarized below. For a theoretical overview of the Cam-Clay and Modified Cam-Clay strength models, see the Theory section.

### LAMBDA

### KAPPA

### CRITICAL STATE LINE SLOPE (M)

The slope (M) of the Critical State Line (CSL) in space.

### SPECIFIC VOLUME (N OR GAMMA)

There are two possible methods for defining the specific volume parameter. The N parameter defines the specific volume of the normal compression line at unit pressure. The Gamma () parameter defines the specific volume of the CSL at unit pressure.

### ELASTIC PARAMETERS

There are two possible methods of defining the elastic parameter for a Cam-Clay material. You may enter either the Shear Modulus or Poissonâ€™s Ratio in the Stiffness tab of the **Material Properties **dialog.

### INITIAL STATE OF CONSOLIDATION

There are two possible methods for defining the initial state of consolidation. The Overconsolidation Ratio (OCR) is the ratio of the previous maximum mean stress to the current mean stress. Or you can specify the Preconsolidation Pressure (Po).

## Softening and Hardening

## Modified Cam-Clay

The **Modified Cam-Clay** strength model in *RS3* has the same input parameters as the Cam-Clay model, but uses the Modified Cam-Clay equations. See above for a summary of input parameters.

For a theoretical overview of the Cam-Clay and Modified Cam-Clay strength models, see the Theory section.

## Dilation Parameter

A **dilation** parameter can be defined for Mohr-Coulomb, Hoek-Brown, Drucker-Prager, Barton-Bandis materials, if the Material Type = Plastic.

Dilatancy is a measure of how much volume increase occurs when the material is sheared.

- For a Mohr-Coulomb and Barton-Bandis material, dilation is an angle that generally varies between zero (non-associative flow rule) and the friction angle (associative flow rule).
- For Hoek-Brown materials, dilation is defined using a dimensionless parameter that generally varies between zero and m.

Low dilation angles/parameters (i.e. zero) are generally associated with soft rocks while high dilation angles/parameters (i.e. phi or m) are associated with hard brittle rock masses. A good starting estimate is to use 0.333*m or 0.333*phi for soft rocks and 0.666*m or 0.666*phi for hard rocks.

## Jointed Mohr Coulomb

Jointed Mohr-Coulomb strength model allows users define Mohr-Coulomb material with jointed option defined within the material setting. From the previous versions of *RS3*, this is similar to Mohr-Coulomb failure criterion with joint material option selected. In the latest version, this is introduced as a separate failure criterion.

## Jointed Generalized Hoek-Brown

Jointed Generalized Hoek-Brown strength model allows users define Generalized Hoek-Brown material with jointed option defined within the material setting. From the previous versions of *RS3*, this is similar to Generalized Hoek-Brown failure criterion with joint material option selected. In the latest version, this is introduced as a separate failure criterion.

The Barton-Bandis failure criterion is an empirical relationship widely used to model the shear strength of rock discontinuities (e.g. joints). It is very useful for fitting a strength model to field or laboratory shear test data of discontinuities. The Barton-Bandis criterion is non-linear, and relates the shear strength to the normal stress using the equations described below.

The original Barton equation for the shear strength of a rock joint is given by Eqn.1:

Eqn.1

where is the *basic* friction angle of the failure surface, **JRC** is the joint roughness coefficient, and **JCS** is the joint wall compressive strength [Barton, 1973, 1976].

The suggested values for **JRC** is based on appearance of discontinuity surface provided in Practical Rock Engineering, under 'Field estimates of JRC' section. Figure 5 shows suggested coefficient values with respect to the surface roughness.

The suggested values for **JCS** is provided in Figure 7 of Practical Rock Engineering. It provides relationship between joint wall compressive strength to Schmidt hardness test.

is based on appearance of discontinuity surface provided in Practical Rock Engineering, under 'Field estimates of JRC' section. Figure 5 shows suggested coefficient values with respect to the surface roughness.

On the basis of direct shear test results for 130 samples of variably weathered rock joints, Barton and Choubey revised this to Eqn.2:

Eqn.2

where **(Phi r) **is the *residual* friction angle of the failure surface [Barton and Choubey, 1977]. Barton and Choubey suggest that can be estimated from Eqn.3:

Eqn.3

where r is the Schmidt hammer rebound number on wet and weathered fracture surfaces and R is the Schmidt rebound number on dry unweathered sawn surfaces. Equations 2 and 3 have become part of the Barton-Bandis criterion for rock joint strength and deformability [Barton and Bandis, 1990].

For further information on the shear strength of discontinuities, including a discussion of the Barton-Bandis failure criterion parameters, see Practical Rock Engineering (Chapter 4 - Shear Strength of Discontinuities) on the Rocscience website.

If Mateirl Type = Plastic, You will be able to define the **dilation angle. **The suggested dilation angle generally varies between zero (non-associative flow rule) and the friction angle (associative flow rule).

## Link to RocData

If you have the program *RocData* installed on your computer, you can start up these programs directly from the **Material Properties** dialog. You can then use *RocData* to help determine parameters for the Mohr-Coulomb, Hoek-Brown or Generalized Hoek-Brown criteria (e.g. by curve fitting lab test data, for example).

- To start up
*RocData*select the button in the Define Material Properties dialog. If you have both programs installed on your computer, then*RocData*will be opened. - To paste applicable results from
*RocData*into*RS3*, first select the**Copy Data**option in*RocData*, and then select the paste button in the**Material Properties**dialog in*RS3*. Applicable data will be pasted into the dialog. If applicable results for the selected strength criterion are not found, an error message will be displayed.

For information about RocData see the Rocscience website.

Additional information can be located in the Material Model Manuals:

- Preliminaries on Constitutive Models
- Elastic Models
- Elastoplastic Constitutive Models
- Druker-Prager Model
- Mohr-Coulomb Model
- Hoek-Brown Model
- Duncan-Chang Model
- Cam Clay and Modified Cam Clay Model
- Jointed Rock Model
- Mohr-Coulomb with Cap Model
- Softening-Hardening Model
- User Defined Material Model
- ChSoil Model (FLAC)
- CySoil and Double Yield Model (FLAC)
- Hardening Soil Model (PLAXIS)
- Hardening Soil Model with Small Strain Stiffness (PLAXIS)
- Soft Soil Model (PLAXIS)
- Soft Soil Creep Model (PLAXIS)
- Swelling Rock Model (PLAXIS)
- Slide- Isotropic Model
- Slide- Anisotropic Model