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Active / Passive Force Application

When a support force is applied in the UnWedge analysis, the force may be included in the analysis as either an Active or a Passive force. In UnWedge:

  • Bolt or shotcrete support is always considered passive (i.e. bolts or shotcrete which are explicitly modeled using the Add Bolt or Add Shotcrete options).
  • However, if the Pressure Support option is used, the user may choose the method of Force Application – Active or Passive. Remember that Pressure support in UnWedge can be used to simulate the equivalent support pressure of any type of support system or loading. The significance of the Force Application method is as follows.

Active versus Passive Support

In general terms, the Factor of Safety is defined as the ratio of the forces resisting motion, to the driving forces. Driving forces include the mass of a wedge accelerated through gravity, seismic forces, and water pressure. Resisting forces arise from the cohesion and frictional strength of the wedge sliding planes.

Active Support is included in the UnWedge analysis as in Eqn.1.

Factor of Safety Equation 1 Eqn.1

where is the normal component and is the shear component of the force applied to the rock, by the support.

Active Support is assumed to act in such a manner as to DECREASE the DRIVING FORCE in the Factor of Safety calculation. If you are using the Pressure support option to model support such as tensioned cables or rockbolts, which exert a force on the wedge before any movement has taken place, then this could be considered as Active support.

Passive Support is included in the UnWedge analysis as in Eqn.2.

Factor of Safety Equation 1 Eqn.2

By this definition, Passive Support is assumed to INCREASE the RESISTING FORCE provided by shear restraint, in the Factor of Safety equation.

If you are using the Pressure support option to model support such as shotcrete, grouted dowels, wire mesh or steel sets, which only develop a resisting force after some movement of the wedge has taken place, then this could be considered as Passive support.

NOTE: Remember: bolts or shotcrete which are explicitly modeled in UnWedge using the Add Bolt or Add Shotcrete options, are always considered as Passive support.

Since the exact sequence of loading and movement of a wedge is never known in advance, the choice of Active or Passive Force Application is somewhat arbitrary. The user may decide which of the two methods is more appropriate for the wedge and support system being analyzed. In general, Passive support will always give a lower Factor of Safety than Active support, and will therefore result in a more conservative estimate of support design requirements.

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