# Back Analysis of Support Force

The Back Analysis option in the Support menu, allows the user to determine the critical slip surface which requires the maximum amount of support force in order to achieve a specified factor of safety. This information can then be used as a starting point for the design of a support system.

To use this option:

1. Select the Back Analysis option in the Support menu.

2. Select the "compute reinforcement load" checkbox.

3. Enter a desired factor of safety, and elevation (y-coordinate), and select OK.

4. To indicate that the Back Analysis option is in effect, a horizontal arrow will be displayed on the model at the specified elevation, along with the required safety factor. NOTE that this force arrow is ONLY applicable for the Back Analysis calculation, and has NO effect on the main slope stability analysis.

Force arrow to indicate Back Analysis option is in effect

When you select Compute to run the Slide analysis, the Back Analysis is performed as follows:

1. For each slip surface that you are analyzing, the Back Analysis option will automatically determine the support force which is required to achieve the specified factor of safety.

The Back Analysis uses the limit equilibrium equations. Rather than iterating to find the factor of safety, the factor of safety is set to the user specified value, and the force required to achieve the specified factor of safety, is solved for.

1. The program keeps track of which surface requires the MAXIMUM support force, to achieve the specified factor of safety, and these are the final results which are reported for the Back Analysis.

2. The Back Analysis option can only be used in Slide, with the following limit equilibrium analysis methods – Bishop, Janbu and Janbu Corrected. It is not available for other analysis methods.

3. The force is assumed to be HORIZONTAL. However, the user may specify an Elevation (y-coordinate) for the force. NOTE:

• The elevation will only have an effect on the results for the Bishop Analysis method. This is because a Bishop analysis uses moment equilibrium, and the elevation of the force determines the moment arm.

• It will NOT affect results for the Janbu (or Janbu Corrected) analysis methods, because the Janbu method considers only force equilibrium; since the force is horizontal, the location of the force does not enter into the analysis.

1. The Back Analysis calculation is performed completely independently of the main Slide stability analysis. If you are performing a slip surface search, the search results are NOT affected by the Back Analysis option. The required support force determined by the Back Analysis is NOT included, and does not affect the results of the main Slide analysis, in any way.

2. The results of the Back Analysis are viewed in the Slide Interpret program. The slip surface(s) and the required force are displayed. NOTE: the required force can be assumed to act as either an ACTIVE or a PASSIVE force. When the Back Analysis is carried out, the required force is calculated using BOTH assumptions, and both results will always be available in Slide Interpret.

3. For a discussion of the significance of ACTIVE versus PASSIVE support force application, see the topic – Active / Passive Force Application (in the Support Properties section of the Help system).

To summarize – the Back Analysis option calculates:

• a total HORIZONTAL force magnitude

• at the specified elevation

• which gives the specified factor of safety

• for a particular slip surface (the slip surface which requires the MAXIMUM support force to achieve the specified factor of safety).

It is up to the user, to use this information, to help with the design of a support system. The force magnitude determined by the Back Analysis, can be used to estimate the spacing and capacity of support. The slip surface which is determined, can be used to estimate the required LENGTH of support (i.e. the user should ensure that the support has sufficient embedded length beyond the slip surface, which can supply the required support force).

Example

The MINIMUM required length of support can be estimated as follows: 1) In the Slide Interpret program, use the Filter Surfaces option to display ONLY the slip surfaces with a Factor of Safety LESS THAN the Factor of Safety specified for the Back Analysis. 2) The display of these slip surfaces will then define an "envelope" of surfaces which require support. 3) This "envelope" defines the MINIMUM length of support which is required at any location. 4) The actual length of support will depend on your support properties, spacing, and the location of the critical slip surface determined by the Back Analysis (i.e. the surface which requires the maximum amount of support force to achieve the factor of safety).