Application |
PLAXIS Designer, PLAXIS 3D LE |

Version |
CONNECT Edition V21 |

Date created |
25 January 2021 |

Date modified |
25 January 2021 |

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### Introduction

Slope stability analysis is often targeted at topographically complex sites whose features vary greatly in three dimensions, or seemingly simple surface topology with strong and weak internal layers that vary across the site. For these types of sites, it can be difficult to determine where the location of the failure is most likely to be. Typically, an engineer would be required to perform tedious and time-consuming analysis at multiple different locations in sequence in order to find the location of the failure. PLAXIS 3D LE supports a new feature called *Multi-Plane Analysis (MPA)* that enables rapid, thorough, and simple to perform analysis of a 3D site at many different locations simultaneously.

*MPA* requires a 3D model of the site, which may be created through PLAXIS Designer or PLAXIS 3D LE. When executing the solver, each location and direction (i.e., plane) undergoes full limit equilibrium analysis through PLAXIS 3D LE, with a choice of either 2D or 3D analysis being available. This approach allows users to quickly and easily create many different 2D slices or rotated 3D models of the site in an automated manner, while still using the same underlying analysis method that they are familiar and comfortable with. Once the location of the failure surface is located through *MPA*, standard search methods can be performed as follow-up to refine the solution, if desired.

### Setup

In order to demonstrate the feature, we will briefly look at the process of analyzing a tailings dam site with curved banks on both sides of the crest, and varying underground material layers. There is a weak layer that varies in thickness and depth across both banks.

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*Figure 1: 3D projection of results.*

*MPA* is defined by creating a number of planes across the model. Each plane defines a 2D slice of the model and contains configuration parameters such as the slope limits and slip surface search methods. The entire plane configuration process is designed such that it is quick to perform on one or many planes at once. For example, the slope limits may be defined for all planes at once by simply drawing a polygon that encloses the area of interest on the 3D model. The slip surface search method is automated, with some options available to the user.

Figure 1 shows the example model with a series of planes already defined. The planes are represented by the light gray lines projected on top of the model. There are multiple ways to create planes. The most common one, and the one used in this case, is to simply select a point on each of the two banks. Planes are then created along the slope automatically, at configurable distance intervals. The direction for each plane is set automatically based on the surface geometry. Each plane can be set to use multiple similar directions so that the critical direction is more likely to be found.

### Results

The *MPA* solver makes full use of all CPU power available on the system, which allows for rapid iteration. The solver collects the results of each individual analysis and aggregates them into the original 3D model for visualization.

#### 2D Results

Figure 2 shows the results of 2D analysis projected onto the 3D model. The factor of safety for each plane is shown and contoured, which gives an overview of slope stability results throughout the model. Each line represents the extents of the 2D critical slip surface transformed onto the coordinates of the 3D model. In this example, the top left area of the model has the lowest factor of safety due to the weak layer being dominant in that region. As well, for similar reasons, the right bank has some areas with a lower factor of safety than their surroundings.

The shape and size of each slip surface can also be visualized for one or more planes at once.

Figure 2 shows the shape of the 6 slip surfaces with the lowest factor of safety at each location. The slip surfaces were raised by the user above the model for visualization purposes, since the lines would normally be below the ground surface.

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*Figure 2: Visualization of shape and FOS of all analyzed slip surfaces.*

#### 3D Results

Analysis of each model may be performed in 3D simply by setting the *MPA* mode to 3D and uses the same model setup procedure. Switching from a 2D *MPA* analysis to 3D, or vice versa, takes seconds.

Figure 3 shows the results of the same tailings dam model after being analyzed in 3D. Critical slip surfaces are now shown on the model as outlines indicating their extents on the top surface. Each trial can also be selected with its full 3D ellipsoid visualized. In addition, a Factor of Safety Map is draped onto the top surface. The color at each location on this map indicates the lowest factor of safety of any trial surface that has passed through that location.

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*Figure 3: Visualization of shape and FOS of 3D slip surfaces.*

### Summary

The *Multi-Plane Analysis (MPA)* feature is an additional feature that works by allowing the user to specify and analyze many sections of a 3D model at once. Additional help about the specifics of this implementation is available in the User Manual.