# How is the minimum bench width computed for a particular slope angle?

Here we'll go through the calculation for a particular point on a Minimum Bench Width Plot (blue line in the image below).  The plot is taken from the tutorial file attached to this article.

Minimum Bench Width Plot (blue line)

At 60 degrees, the Minimum Bench Width is 6.64m.  The Minimum Bench Width is the minimum bench width that would be required to contain the spill from the above bench taking into account the backbreak distance on the current bench due to any wedge failure.  How does the program compute the backbreak distance?

1. For a particular slope angle, the program tries to create numsamples wedges (value in Project Settings).  From the wedges created, it looks at wedges whose FS is less than the design FS.  From this it constructs a distribution of backbreak distance.  You can see this distribution in Swedge using the attached file.  Create a histogram of Wedge Width to Crest on Upper Face.

Right-click in the plot and choose the Filter Out Safe Wedges option.  You should see the plot below.  This is the distribution of backbreak distances.

Distribution of backbreak distances

2. It then computes the backbreak distance at which 80% (the design threshold) of all backbreak distances are less than this value.  To see this in Swedge, plot a Cumulative plot of Wedge Width to Crest on Upper Face.  Make sure you Filter out Safe Wedges.  If you look at the value at a probability of 0.8 (80%), it's around 2.75m (see the figure below).  So the probability that all backbreak distances are less than 2.75m is 80%.

Cumulative plot of Wedge Width to Crest on Upper Face

We now have the backbreak distance for a design threshold of 80%.  However, we also need the spill width.  This is because it is the backbreak distance plus spill width that gives you the minimum bench width.

Bench width

How do we compute spill width?  For each wedge that has a FS less than the design FS, you can compute the spill width that it would create using the equation in Gibson's paper.  In the same way as backbreak distance you can create a cumulative distribution of spill width.  If you do this in Swedge, you get the cumulative plot shown below.  The value of spill width at which 80% of all spill widths are less than this number is 3.9m.  80% of all computed spill widths are less than 3.9m or the probability that a spill width will be less than 3.9m is 0.8.

Cumulative distribution of spill width

The minimum bench width is then the backbreak distance (at 80%) + the spill width (at 80%).  This gives 3.9+2.75 = 6.65m, which is what the Minimum Bench Width plot is showing.

The program then does this for all the slope angles that you ahve specified to get the plot.