# Probabilistic analysis - COV

## 1.0 Introduction

Probabilistic Analysis can be performed using **Slide3** for various applications of slope stability. This tutorial covers a slope geometry with different complex material types including varying anisotropic materials assigned to the slope stability analysis. The objective of this tutorial is to introduce the use of **Coefficient of Variation (COV)**
in Slide3 and the associated interpretation of the results.

The finished product of this tutorial can be found in the *Tutorial 39 COV - Final file.Slide3m2* data file. All tutorial files installed with Slide 3 can be accessed by selecting **File > Recent Folders > Tutorials Folder** from the Slide 3 main menu.

## 2.0 Project Settings

We will first check for methods.

- Open the
**Project Settings**dialog from the toolbar or the**Analysis**menu - Click on
**Methods**to see that the Spencer method is selected - Open
**Surfaces > Slip Surface Options**to check**Particle Swarm****Search**is selected as the**Surface Search Method**

## 3.0 The Model

- Select
**Materials > Define Materials** - You can click the
**Pencil**icon to see the Shear/Normal function.

You will notice that the yellow material is a **Shale** with a **Shear/Normal Function** strength type.

There is also the green material, **Generalized Anisotropic (Angle)**, and red material, **Generalized Anisotropic (Surface)**
using the **Generalized Anisotropic** as the **Failure Criterion**. If you click the Pencil icon, you will see that their strength function is defined by two other materials as shown below:

## 4.0 Compute

- Save the file
- Click
**Analysis > Compute**to run the analysis - Select the
**Results**workflow tab to view the results.

You will notice a minimum surface that intersects all three materials, with a Factor of Safety of about 1.31 as it can be seen in the column viewer option below:

## 5.0 COV OPTION

To use the **COV option**, we first must enable **Probabilistic Analysis**. To do this:

- Select
**Analysis > Project Settings**in the menu - Click on the
**Statistics**tab - Check the
**Probabilistic Analysis**box - Then set the
**Sampling Method**to**Latin-Hypercube**, the**Number of Samples**to**1000**and the**Analysis Type**to**Global Minimum**as shown - Click
**OK** - Select
**Statistics > Material statistics**. - You will notice the
**Define shear strength using COV**box. Check this to enable the option for the Shale material. You will see input fields appeared as shown: - Now select
**Generalized Anisotropic (Angle)**material and check the**COV**box - Select a
**Uniform Distribution**and change the range to 0.75 and 1.25: - Select the
**Generalized Anisotropic (Surface)**material and define the shear strength of this material as a random variable with Lognormal Distribution and a COV of 0.2. - Click
**OK** - Select
**Analysis > Compute**and then**OK**in the dialog to proceed. - Select
**Statistics > Histogram Plot** - Select the
**Highlight Data**and set the data to**Factor of Safety - Spencer with comparison < 1** - Click
**Plot**, then you will see the following result with histogram shown below:

As indicated in the graph, the highlighted sections are probability of failure where Factor of Safety was < 1 (with Probability of Failure = 0.5%).This can also be shown through scatter plot as well.

- Select
**Statistics > Scatter Plot**. - Select the Highlight Data and keep the values as default. (Factor of Safety - Spencer < 1)
- Select
**Statistics > Cumulative Plot**. - Click
**Plot**and you will see the cumulative Factor of safety for cumulative probability of failure as shown.

Now the Statistics menu will appear in the menu bar,

This means that the shear strength of the **Shale**
will vary according to a **Lognormal Distribution**, with a coefficient of variation of 0.1. The coefficient of variation is defined as the 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.

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.

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

We will stick with these three random variables.

We see that the result as shown below with Spencer FOS of 1.31 with Probability of Failure (PF) of 0.5% as shown below:

## 6.0 Results

If you look at the top toolbar in Slide3, you will see three result icons with statistics. Those can also be found by selecting:

**Statistics > Histogram plot / Scatter plot / Cumulative plot**.

We will first look at the histogram of this model.

Here you see the scattered plot of Generalized Anisotropic (Surface).

Now we will look at the cumulative plot of the result.

You will be prompted by this dialog.

If you hover over to the Spencer FOS around 1, you can double check that probability of failure below FOS = 1 is around 0.5%.