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Active and Passive Force Application

When a support force is applied, the force may be applied as either an Active or Passive force in the Limit Equilibrium analysis.

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 block accelerated through gravity, seismic forces, external loading, and water pressure. Resisting forces arise from the shear strength of the block sliding planes.

Active support force is included in the analysis as in Eqn.1.

Eqn1: Factor of Safety Equation including Active Support Force
Eqn1: Factor of Safety Equation including Active Support Force

Where:

TN = normal component of the support force

TS = shear component of the support force

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 modeling supports such as tensioned cables or rock bolts, which exert a force on the block before any movement has taken place, then this could be considered as Active support.

Passive support force is included in the analysis as in Eqn.2.

Eqn2: Factor of Safety Equation including Passive Support Force
Eqn2: Factor of Safety Equation including Passive Support Force

Where:

TN = normal component of the support force

TS = shear component of the support force

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

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

Since the exact sequence of loading and movement of a block is never known in advance, the choice of Active or Passive Force application is somewhat arbitrary. Active support can influence the failure mode and/or sliding direction of a block, while Passive support does not have any impact on failure mode or sliding direction. The user may decide which of the two methods is more appropriate for the block 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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