The inter-ramp wall of a pit will consist of a series of stacked benches.  Geotechnical engineers will normally provide the pit slope design criteria based on the inter-ramp angle (“IRA”) for sectors around the pit.  The IRA represents the toe-to-toe slope angle, as shown in the diagram below.

Pit Slope Image for post

The inter-ramp angle can be created in many ways, depending on the bench height (“BH”), bench face angle, and the Catchbench or berm width.  Different combinations of these can be used to develop the same inter-ramp angle.
Typically the bench face angle (“BFA”) will be dictated by the rock strength, the structural fabric, and whether controlled blasting is used to minimize damage to the walls.   Hence the BFA may vary around the pit or in different rock types, but it generally is in the range of 60° to 75°.
The catchbench (“CB”) is used to catch spalling rock and prevent it from rolling down the pit wall and creating a safety hazard.  A rule of thumb is that the catchbench width should be according to the formula 4.5m + 0.2H, where H is the height of the bench.   This means the recommended catchbench width for a 5m high bench should be about 5.5m; for a 10m high bench it should be 6.5m; and for 15m high bench it should be 7.5 metres.
Double benching (or triple benching) is used where the inter-ramp slopes angles are steep enough that single benching would result in an overly flatten slope.   For example if the inter-ramp slope is 50° and the BFA is 70°, then the corresponding calculated catchbench width would be 2.4 metres to achieve the 50° IRA.  However such a small catchbench would be ineffective in catching ravelling rock.  If one double benched (i.e. left a catchbench every 10m instead of every 5m), then the calculated catchbench width would be 4.8 metres.  If one triple benched (i.e. left a catchbench every 15m), then the recommended width would be 7.1 metres.  Hence triple benching would be suggested in this case, assuming the rock mass is of sufficient strength to sustain a 15m high face.
A simple calculator (Bench Slope Calculator) has been prepared to show the relationship between all the factors.  A screenshot of the calculator is shown below.  It allows one either to back-calculate the IRA given a set of bench height, BFA, and catchbench criteria; or calculate the catchbench width given the height, BFA, and IRA criteria.  The yellow shaded cells represent input cells.

Bench Slope Calculator Pic

Single Bench Height (BH):  this is the input height of a single operating bench.
No. of Benches between Catchbenches:   this is the input for single, double, or triple benching.
Total Height (TH):  this is the calculated total height (# of benches X single bench height)
Bench Face Angle (BFA):  this is the input bench face angle, in degrees
Catchbench (CB):  this is the width of the catchbench, either as an input or a calculated value.
Inter-Ramp Angle (IRA): this is the slope angle in degrees, either as a calculated value or an input.
My bottom line is that the inter-ramp angle can be achieved in different ways depending on various components of the slope profile.  Safety is of the utmost importance and therefore the adequate sizing of the catchbench is important, as is the ability to access the benches and clean up the rubble buildup.  Double and triple benching maybe required in some circumstances.

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