Developer’s Tip:
Active or Passive Support Modeling in Slide
Introduction
A variety of support types can be modeled in Slide including soil nails, tiebacks, geotextiles, micropiles
and user-defined support. For each support type, the user may choose the method of force application:
Active or Passive, as shown in the Support Properties dialog below.
A common question we are asked is, “Should I use Active or Passive, and what capacities should be
used?” This developer’s tip aims to clarify the definition of Active or Passive support in Slide and provide
some guidance on the values of support capacity that are recommended for each method.
Slide Support Properties input dialog
Definition of Active and Passive Support
In the most general terms, the Factor of Safety in a limit equilibrium analysis is defined as the ratio of the
forces resisting motion, to the driving forces (Eqn.1).
Eqn. 1
Driving forces include the mass of each slice accelerated through gravity, seismic forces, and water in a
tension crack. Resisting forces arise from the cohesion and frictional strength of the slip surface.
The primary difference between the active and passive support implementation in Slide is as follows.
Active Support is assumed to act in such a manner as to DECREASE the DRIVING FORCE in the Factor
of Safety calculations (Eqn.2).
Eqn. 2
Passive Support is assumed to INCREASE the RESISTING FORCE provided by shear restraint, in the
Factor of Safety calculations (Eqn.3).
Eqn.3
Grouted tiebacks, tensioned cables or rockbolts, which exert a force on the sliding mass before any
movement has taken place, could be considered as Active support.
Soil nails or geotextiles, which only develop a resisting force after some movement within the slope has
taken place, could be considered as Passive support.
Since the exact sequence of loading and movement in a slope is never known in advance, the choice of
Active or Passive force application is somewhat arbitrary (see Appendix 3 of Ref. 1). The user may
decide which of the two methods is more appropriate for the slope and support system being analyzed. In
general, for a given support capacity, Passive support will give a lower Factor of Safety than Active
support. The difference can be quite significant as shown in the following figures.
(A)
(B)
Active (A) and Passive (B) support results for equal support capacity (10,000 lbs / ft).
Note: critical slip circles are different for each method.
Recommended Capacities for Active and Passive Support
Another important question is, “What capacity should I use for my support?”
Duncan and Wright (Ref. 2) offer the following guidelines for active and passive support capacities used
in limit equilibrium slope stability analysis.
Note that the Active and Passive support options in Slide correspond to the Method A and Method B
options described by Duncan and Wright.
For Active support (Method A), because the support forces are included in the denominator of the safety
factor equation (Eqn.2) the support force is NOT divided by the factor of safety calculated during the
analysis. Only the soil strength is divided by the factor of safety. Hence the support capacity input by the
user for Active (Method A) should be the ALLOWABLE support force.
For Passive support (Method B), because the support forces are included in the numerator of the safety
factor equation (Eqn.3) the support forces ARE divided by the factor of safety calculated during the
analysis (i.e. both soil strength and support forces are divided by the factor of safety). Hence the support
capacity input by the user for Passive (Method B) should be the ULTIMATE support force.
According to Duncan and Wright (Ref. 2):
“Method A is preferable, because the soil strength and the reinforcement forces have different sources of
uncertainty... factoring them separately makes it possible to reflect these differences”.
The allowable support force (Method A) allows the user to choose an acceptable safety factor for the
support capacity in advance, and this determines the value (e.g. tensile strength) which is input into the
Support Properties dialog.
For either active or passive support methods, the long-term capacity of the support should be considered
if long term slope stability is important. The long-term capacity of reinforcement may depend on several
factors including creep characteristics, installation damage, durability and other factors (Ref.2).
Active or Passive Support in other Rocscience Software
In the wedge analysis programs Swedge and RocPlane, rock bolt support may be applied using either
active or passive methods of force application. The same issues described in this paper for Slide, are
equally applicable to Swedge and RocPlane which are also limit equilibrium programs.
Swedge support dialog
It is worth noting that in our finite element stress analysis program Phase2, support is automatically
assumed to be active. Therefore, when comparing SSR slope stability analysis results from Phase2 with
limit equilibrium slope stability results from Slide, the active support option should be used in Slide.
Summary
We conclude this developer’s tip by stating that there is no clear “right or wrong” answer with respect to
the choice of active or passive force application for support forces in Slide. Our current thinking is to
recommend the use of Active support application and an allowable support capacity. In our experience
you generally get better convergence properties with active support. However the topic is open for
discussion and we welcome any feedback on this subject.
References
1. Hoek, E. and Bray, J. W. (1981), Rock Slope Engineering (revised 3rd edition), The Institute of
Mining and Metallurgy, Chapman and Hall, London.
2. Duncan, J.M. and Wright, S.G. (2005), Soil Strength and Slope Stability (chapter 8), John Wiley
and Sons Inc.