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# Joint Model: Baecher

The Baecher joint network model (Baecher et al., 1978) is a flexible algorithm that can generate intricate joint networks. In this model, joints are assumed to have finite trace lengths, which follow some statistical distribution. The centres of the joints are located in space according to a Poisson point process (i.e. points distributed in the trace plane according to a uniform distribution). The orientations of joints in a Baecher network can either vary according to an orientation distribution or be constant. The number of joints generated in a Baecher network is controlled by a joint intensity measure.

In order to avoid boundary effects for a specified model region, the Baecher algorithm first enlarges the region before generating joints. After generating the joints according to the required joint intensity measure, the algorithm then clips the network with the original bounding region. Joints of the Baecher network generally terminate in intact rock.

Baecher joint network, random joint length and orientation The following input parameters can be defined for the Baecher joint network model.

Orientation Definition

There are two methods of defining the joint orientations: Fisher or Dip/Dip Direction. The input parameters for each method are described below.

Definition Method = Fisher

If you choose Definition Method = Fisher, you can define a 3-dimensional distribution of joint orientations using a Fisher Distribution. A Fisher Distribution describes the angular distribution of orientations about a mean orientation, and is symmetric about the mean. The following input is required to define a Fisher distribution.

Trace Plane Dip Direction

The Trace Plane is simply the cross-sectional plane of your RS2 model. The Trace Plane is assumed to be vertical (i.e. Dip = 90 degrees). Therefore only the Trace Plane Dip Direction is required. This is the direction (i.e. trend or azimuth) of the normal vector of the Trace Plane, measured clockwise from north. Also note, the normal vector is assumed to be pointing INTO the screen (i.e. away from the viewer). RS2 uses the Trace Plane orientation to determine the 2-dimensional traces of the 3-dimensional joint planes, on the trace plane.

Mean Dip / Mean Dip Direction

This is the mean orientation of the joint set you are defining.

Use Std. Dev. = No

If you choose Use Std. Dev. = No, then you must enter a value of the Fisher K coefficient, which defines the variability of the joint orientations around the mean orientation.

Use Std. Dev. = Yes

If you choose Use Std. Dev. = Yes, then you must enter a value of Standard Deviation instead of Fisher K coefficient. The Standard Deviation is related to the Fisher K value, and is an alternative method of defining the variability of the joint orientations around the mean orientation. Standard Deviation is measured in degrees.

See the Fisher Distribution topic for further information.

Definition Method = Dip / Dip Direction

If you choose Definition Method = Dip / Dip Direction, then you can define the joint orientation distribution using either 2-dimensional or 3-dimensional input, according to the setting of the Use Trace Plane option.

Use Trace Plane = No

If you choose Use Trace Plane = No, then only the 2-dimensional Inclination of the joint planes is required. The Inclination is the angle of the joint planes as measured from the x-axis of the model. Values can range between -90 degrees and 90 degrees. You can define the Inclination as a random variable by choosing a Statistical Distribution (Normal, Uniform, Exponential or Lognormal) and entering the distribution parameters. You can also set the Inclination to a fixed value by choosing Distribution = None.

Use Trace Plane = Yes

If you choose Use Trace Plane = Yes, then you can define a 3-dimensional orientation distribution, by choosing a Statistical Distribution (Normal, Uniform, Exponential or Lognormal) for both Dip and Dip Direction, and entering the distribution parameters for each.

Trace Plane Dip Direction

If you choose Use Trace Plane = Yes, then you must also enter the Trace Plane Dip Direction. The Trace Plane orientation is used to determine the 2-dimensional traces of the 3-dimensional joint planes. See above for more information about the Trace Plane.

NOTE:

• When you are defining a 3-dimensional orientation distribution using either the Fisher method or the Dip / Dip Direction method, it is important to remember that the RS2 plane strain analysis is 2-dimensional. RS2 only uses the 3-dimensional information, to determine the 2-dimensional traces of the joint planes on the trace plane. Once this has been determined, the actual analysis is 2-dimensional (i.e. the model will behave as if the joints were perpendicular to the trace plane).
• In general, the Fisher Distribution is preferable for defining a 3-dimensional orientation distribution, because the distribution can be easily defined regardless of the mean orientation. The only parameters required are the mean orientation, and the Fisher K or standard deviation. For the Dip / Dip Direction method, difficulties arise if the mean Dip is near 0 or 90, or the mean Dip Direction is near 0 or 360. Under these circumstances, it may not be possible to properly define the desired orientation distribution.

## Inclination

If the Definition Method = Dip / Dip Direction and Use Trace Plane = No, you will be required to enter the Inclination of the joint planes. See above for details.

## Dip / Dip Direction

If the Definition Method = Dip / Dip Direction and Use Trace Plane = Yes, you will be required to enter the Dip and Dip Direction of the joint planes. See above for details.

## Joint Length

The Joint Length defines the distribution of joint lengths as measured in the trace plane. To define the Joint Length as a random variable, choose a Statistical Distribution (Normal, Uniform, Exponential or Lognormal) and enter the distribution parameters. The default statistical distribution is Exponential.

## Joint Intensity

Joint intensity measures describe the degree of jointing that occurs within a volume of rock mass. There are five measures for joint intensity in two dimensions. These are:

1. P1 = the number of joint traces per unit area of the trace plane
2. P2 = the sum of joint trace lengths per unit area of the trace plane
3. P3 = the sum of joint trace lengths per square root of the trace plane area
4. P4 = the sum of squared joint trace lengths per unit area, and
5. P5 = the square of the sum of joint lengths per unit area.

The last three measures are dimensionless.

## Joint End Condition

For a description of the Joint End Condition option, see the Add Joint Network topic. For further information see the Add Joint Boundary topic.

## Randomize

If you select the Randomize button, the Baecher joint network will be re-generated, using a new sampling of the random variables (e.g. joint orientation, joint length).