# Generalized Anisotropic

The **Generalized Anisotropic Strength** model allows you to define Anisotropic strength properties for a material using any combination of failure criteria applied over user defined orientations. There are two methods of defining the anisotropy:

**Dip/DipDirection**- you can define one or more planes of anisotropy, with 3-dimensional orientation defined by Dip and DipDirection, OR**Surface**- you can define a general 3D anisotropic surface (e.g. to follow the orientation of folded bedding strata).

Each anisotropic plane or surface can be assigned its own failure criterion, within a specified angular range defined by A and B parameters. The rock mass is also assigned a failure criterion. The strength of any failure plane through the anisotropic material can then be calculated, using a linear interpolation method, as described below.

To define a Generalized Anisotropic Strength Function:

- Set the Failure Criterion:
**Anisotropic > Generalized Anisotropic**in the Material Properties dialog. - Select the
**Edit**button beside the failure criterion combo box. - You will see the
**Define Generalized Strength Function**dialog.- To
**edit**an existing Generalized Anisotropic Strength function, select the Function Name from the list at the left of the dialog.

- To create a new Generalized Anisotropic Strength function, select the
**Add**button at the lower left corner of the dialog, and enter a Function Name.

- To
- Select the
**Base Material**for the function. This will represent the strength properties of the rock mass, for failure planes which are not within the defined orientation range of the anisotropic plane(s) or surface. - Select the
**Anisotropy Definition**-**Dip/DipDirection**or**Surface**. For each plane or surface, assign a material and enter the required parameters as described below. - When all data has been entered, select
**OK**, and you will be returned to the Material Properties dialog. The Name of the function you have just defined will appear in the Generalized Function list. By selecting a Function Name from this list, you can now apply a Generalized Anisotropic Function to any material in the model. - By default, one anisotropic plane will be defined. Enter the
**Dip**and**Dip Direction**of the anisotropic plane, and enter the A and B parameters (see below for details), and select a Material for the anisotropic plane. - If you have more than one anisotropic plane, select the
**Insert Row**button to add the required number of rows. Enter the Dip, DipDirection, A and B parameters for each plane. **DipDirection**is measured from**North**, with clockwise positive convention. The y-axis of your model represents the North direction.**Dip**is measured from the**horizontal**, with downward positive convention.- If the normal vector of the column base is
**WITHIN**radius A of the normal vector of the anisotropic plane, then the strength model selected for the**Anisotropic Plane**is applied (in the above example the "weak bedding plane" material). - If the normal vector of the column base is
**OUTSIDE**radius**B**of the normal vector of the anisotropic plane, then the strength model selected for the**Base Material**is applied (in the above example the "rock mass" material). - If the normal vector of the column base is
**OUTSIDE**radius**A**and**WITHIN**radius**B**, then the strength applied is based on a linear transition between the**Anisotropic Plane**strength and the**Base Material**strength, as shown in the figure below. - The material with the maximum cumulative angular range in 2D is defined as the base material in 3D.
- All other materials that are part of the 2D generalized anisotropic description are translated as Anisotropic directions in 3D.
- The 3D dip is equal to the 2D (Angle From + Angle To)/2.0.
- The A value is equal to the 2D (Angle To - Angle From)/2.0
- B value is A+5 degrees.
- you must first define the Anisotropic Surface using the Anisotropic Surfaces option in the Surfaces menu.
- you will then be able to assign this surface to the Generalized Anisotropic material, with A and B parameters.
- NOTE: only ONE anisotropic surface can be assigned to a Generalized Anisotropic material.
- For a given column base, the NEAREST point on the Anisotropic Surface is first determined.
- This gives a
**local value**for the**Dip/DipDirection**of the**anisotropic surface**. - The angle between the column base plane and the local anisotropic surface orientation is determined.
- The calculation of shear strength for the column base, then proceeds as described above for the planar Dip/DipDirection option.
- One material for the Generalized Anisotropic material.
- One material for the rock mass strength assignment.
- One material for the anisotropic plane or surface strength assignment.

NOTE: in the Material Properties dialog you must also define the material strength properties for the rock mass and anisotropic plane(s) assigned in steps 4 and 5.

Anisotropy Definition - Dip/DipDirection

The **Anisotropy Definition** = **Dip/DipDirection** option allows you to define one or more planes of anisotropy, with orientation defined by Dip and Dip Direction. The A and B parameters define the angular range of the anisotropy as described below.

2-dimensional representation of two anisotropic plane orientations

Definition of Dip / DipDirection

The definition of Dip and Dip Direction follows the standard convention:

NOTE: if you are using **Anisotropy Definition** = **Dip/DipDirection**, the alignment of your model must correspond to the plane orientation measurements. Since Dip Direction is measured from North, your model must be aligned accordingly. In *RS3*, the y-axis corresponds to the North direction. Therefore your model must be oriented in its true direction with respect to North (or grid North), or else the anisotropic plane orientations will be incorrect.

Definition of A and B Parameters for Generalized Anisotropic Function

The definition of the input parameters for the **Generalized Anisotropic** strength model is described below. For example, let's assume a rock mass has a single well defined plane of anisotropy, such as a bedding plane, with input as shown below.

A 2D representation of the A and B parameters is shown below. If a shear plane (column base) lies within the A angle, the anisotropic plane strength is applied. If a shear plane lies outside of the B angle, the rock mass strength is applied. If a shear plane lies between the A and B angles, a linear transition between the rock mass strength and the anisotropic plane strength is applied.

2D representation of A and B angle parameters

The best way to illustrate the definition of the A and B parameters is with the aid of a stereonet. The 3-dimensional orientation of an anisotropic plane is given by entering the **Dip** and **Dip Direction** of the plane. On a stereonet, a plane can be represented as a great circle with corresponding pole (normal vector) as shown below. *Anisotropic plane and pole displayed on a stereonet*

The A and B parameters define the angular radius of two cones centered on the pole vector of the anisotropic plane, as shown in the following figure.

Definition of A and B parameters for anisotropic plane

The Generalized Anisotropic Strength model is applied as follows. For a given column in a sliding mass, the orientation (dip and dip direction) of the base of the column is determined. The normal vector to the base of the column is then determined.

The following figure illustrates how the shear strength is derived for a Generalized Anisotropic material. Within angular radius A the shear strength of the anisotropic plane is applied. Outside of angular radius B the base material (rock mass) strength is applied. For angles between A and B the transition of shear strength is assumed to be linear.

NOTE: the calculation of shear strength for the **Generalized Anisotropic** model in *RS3*, is based on the Anisotropic Linear strength model in *Slide*, with a more general definition of failure criteria. In *RS3 *you may use any available failure criteria, you are not limited to Mohr-Coulomb.

Anisotropic strength properties from RS2 to *RS3*

In *RS2,* anisotropic strength properties are assigned with simple angular measurement. Since RS2 does not contain 3D orientation of the planes with weakness defined by dip and dip direction, there are few assumptions when creating a 3D model from a 2D model with the anisotropic strength properties. Firstly, dip direction is aligned to the East-West direction. This is due to 2D model extruded along the north direction. The angular range is then converted to Dip and A and B factors.

Here are the rules for importing and converting a RS2 generalized anisotropic function:

Dip and Dip Direction are always adjusted so that Dip is positive.

Multiple Anisotropic Planes

If more than one anisotropic plane has been defined, the algorithm first determines which anisotropic plane is nearest to the orientation of a given column base. Then the calculation proceeds as described above, only considering the nearest anisotropic plane. Other anisotropic planes are ignored.

Anisotropy Definition - Surface

The **Anisotropy Definition** = **Surface** option allows you to assign a surface which corresponds to the mean orientation of a non-planar anisotropic region. For example as illustrated in the figure below. For simplicity this is illustrated in 2D however the actual surface is 3-dimensional.

In order to use this option:

The **Anisotropic Surface** option is useful because it allows you to assign a single anisotropic material type, to a non-planar material zone with variable anisotropic orientation. The determination of shear strength is exactly the same as described above for the planar Dip/DipDirection option, with the following additional step:

Generalized Anisotropic Material Assignments

A **Generalized Anisotropic** material in *RS3 *will always require at least three material assignments:

The Generalized Anisotropic material is really a composite material with a rock mass strength component and one (or more) anisotropic strength component(s). If the Anisotropy definition = Dip/DipDirection, and more than one anisotropic plane is defined, then each plane may have a different material assigned. This is illustrated below.

Failure Criteria for Base Material and Anisotropic Planes

You may use any material strength model for the base material (rock mass) and anisotropic planes. For example, you might use:

- Generalized Hoek-Brown (for the rock mass)
- Barton-Bandis (for anisotropic planes or surface)

You are not limited to the Mohr-Coulomb strength model when using the Generalized Anisotropic material option in *RS3*.

Tensile Strength

See the Tensile Strength topic.