# Joint Shear Strength

If you are performing a Probabilistic analysis with **RocPlane**, the Joint Shear Strength can be defined as a random variable as follows:

- Select
**Input Data**and select the**Strength**tab in the**Probabilistic Input Data**dialog. - Select the
**Shear Strength Model**(e.g.,**Mohr-Coulomb**,**Barton-Bandis**,**Power Curve**). - Select the method of defining shear strength as a random variable from the
**Random Variables**drop-down:**Parameters**or**Strength**(see definitions below). - Enter the probabilistic shear strength parameters as described below.

## Random Variables = Parameters

If **Random Variables = Parameters**, you can define a **Statistical Distribution** for each parameter used in the strength criteria.

### CORRELATION COEFFICIENT

If you are using the **Mohr-Coulomb** as the **Shear Strength Model**, you can define a **Correlation coefficient between cohesion and friction angle**. For details, see Correlation Coefficient in a RocPlane Probabilistic Analysis.

If you are using **Barton-Bandis** or **Power Curve** **as the Shear Strength Model**, then you CANNOT define a correlation between the statistical sampling of the strength parameters (i.e., the statistical sampling of each parameter is performed independently of the sampling of any other random variables).

## Random Variables = Strength

If **Random Variables = Strength**, the shear strength (tau) is defined directly as a random variable rather than defining the individual parameters of the strength criterion as random variables. For a given normal stress, a random value of shear strength is generated. This works as follows:

- Set the
**Random Variables**=**Strength**. - Enter the mean values of the strength criterion parameters (e.g.,
**Cohesion**and**Friction Angle**for the**Mohr-Coulomb**criterion). - Choose a
**Statistical Distribution**for the shear strength. Only Lognormal and Gamma distributions are allowed because these distributions are only defined for positive values and therefore ensure that randomly generated values of shear strength are always positive. - Enter the
**Coefficient of Variation**for the shear strength. The**Coefficient of Variation**is equal to the standard deviation divided by the mean shear strength.

**NOTE:** Typical values of shear strength CV range from 0.15 to 0.35 [Miller et.al. (2000)].

- When the analysis is computed, random values of shear strength are generated as follows:

- The normal stress on a joint plane is computed.
- Using the mean values of the strength criterion parameters (e.g. cohesion and friction angle), the mean shear strength is calculated. This defines a point on the mean strength envelope.
- Using the mean shear strength, coefficient of variation, and the selected statistical distribution (Lognormal or Gamma), a random value of shear strength is generated, for the given normal stress. This will be the actual value of shear strength used in the
**RocPlane**safety factor calculation. - The above steps are repeated for each probabilistic simulation until the required number of samples are generated.

The random shear strength option is schematically illustrated in the following figure for the **Mohr-Coulomb** criterion. Essentially, you are defining a variability of shear strength about the mean strength envelope. This is intuitively simpler to grasp than defining variability of individual strength parameters.

The random shear strength option is particularly useful for **Barton-Bandis** or **Power Curve** strength models, since it eliminates the need for defining statistical distributions for individual strength parameters (which may be difficult to obtain or unavailable). Furthermore, the issue of statistical correlation of the strength parameters is avoided (i.e., you do not have to worry about generating unrealistic combinations of strength parameters, since variability is defined with respect to the mean envelope).

*Random shear strength option (Mohr-Coulomb envelope)*