# COV

## 1. Introduction

This tutorial introduces the ability to define variability on the shear strength of a material itself. It has two important advantages:

- It eliminates the need to define variability on multiple individual parameters for a material, particularly helpful in cases where parameter-specific data may be sparse.
- It can be applied to all material strength types, including Shear/Normal Function, all Anisotropic options, and Discrete Strength Function.

We will start this tutorial by importing the corresponding COV tutorial from Slide2.

After opening *Slide3*, select **File > Import > Import Slide Project**. Navigate to the following location: C:\Users\Public\Documents\Rocscience\Slide3 Examples\Tutorials\Probabilistic COV

Double-click on **Tutorial 39 COV – starting file.slmd** to import, select the master scenario when prompted, and click OK. Click OK as well for the suggested extrusion depth, and the Import Information dialog.

You should see the following extruded open pit section:

Delete the search limit item in the Visibility Tree on the left by clicking on the garbage can beside it – this is not necessary here since it envelops the entire slope.

You can click on Analysis > Project Settings to see that the Spencer method is selected. You can also click on Surfaces > Slip Surface Options to see that Particle Swarm ellipse search is selected.

## 2. The Model

Select Materials > Define Materials. You will notice that the yellow material is a Shale with a Shear/Normal Function strength type. You can click “Edit” to see the Shear/Normal function. The green material uses the Generalized Anisotropic Strength Type. You can click Edit to see that the function is defined by two other materials:

Click Cancel and select the Anisotropic Linear material. You will see this follows an anisotropic surface. Slide3 automatically converted the Slide2 Anisotropic Linear strength type to Generalized Anisotropic in Slide3 by adding the additional materials. It also automatically extruded the anisotropic surface to a plane. Click Cancel.

Click Analysis > Compute to run the analysis. Once done, select the Results tab to view the results. You will notice a minimum surface that intersects all three materials, with a Factor of Safety of about 1.2.

The factor of safety and the surface are in good agreement with the corresponding Slide2 results:

## 3. The COV option

To use the COV option, we first have to enable Probabilistic analysis. To do this select Analysis > Project Settings and click on the Statistics tab. Check the “Probabilistic Analysis” box. Then set the number of samples to 1000 and the Analysis Type to Global Minimum as shown.

Now the Statistics tab will appear in the menu bar. Select Statistics > Material Statistics. You will notice the “Define shear strength using COV” button. Check this to enable the option for the Shale material. You will see two input fields appear as shown:

This means that the shear strength of the Shale will vary according to a lognormal distribution, with a coefficient of variation of 0.2. The coefficient of variation is defined as standard deviation divided by the mean. Because the shear strength value changes according to location, the user only needs to define the standard deviation as a fraction of the mean. We will enter a COV value of **0.1** for the Shale material.

Now click on Generalized Anisotropic in the sidebar and check the COV box. Select a Uniform distribution. You will notice that the COV box is replaced by a range. This is because certain distributions (uniform, triangular, exponential) do not take a standard deviation (and hence a COV) input. Change the range to 0.75 and 1.25:

The meaning of this is that in each simulation the shear strength value calculated at a given location will be multiplied by a value between 0.75 and 1.25. Hence, we are saying that the shear value determined by the material input parameters may not be exactly that, and we want to consider some plus/minus variability in the shear strength.

Now select the Anisotropic Linear material and define a COV random variable with Lognormal distribution and a COV of 0.2.

Notice that you can also define random shear for Soil Mass and Bedding materials, which make up the Generalized Anisotropic material, as well as Base and Bedding materials which make up the Anisotropic Linear material. Keep in mind that if you do so, these random variables will be independent of the random shear in their respective Generalized Anisotropic materials, meaning they will not be *derived* from the Generalized Anisotropic material’s random shear.

We will stick with these three random variables. Click OK. Now Click Analysis > Compute.

We see that the Probability of Failure is 7.2%.

An important note is warranted here: the random shear option means that the shear strength at each x,y,z point in the slope follows the distribution defined by the user throughout the 1000 simulations. It does *not* mean that the anisotropic angle is random. For example if you were to take the shear strength value at a point in the Generalized Anisotropic material and make a histogram of the shear strength at that point from the 1000 simulations, you would see the distribution shape defined for the Generalized Anisotropic material.

This distribution can be viewed from Statistics > Histogram Plot. Plot the Shale Shear Strength Factor. You will see the lognormal distribution originally defined:

The mean is 1.0: shear strength is multiplied by 1.0 in the deterministic case. Right click on the plot and select “Change plot data.” Switch to Generalized Anisotropic Shear Strength Factor and you will see the uniform distribution we defined. Now switch to factor of safety and click Plot.

These are the 1000 factor of safety values computed: they range between approximately 0.8 and 1.8.

This concludes the COV tutorial.