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4.5
Limitations of limit equilibrium methods
Wright, Kulhawy, & Duncan (1973) state that limit equilibrium methods are “…subject to
criticism on theoretical grounds” since assumptions are employed that result in the normal
stress calculated using only conditions of static equilibrium, without consideration of the
stress-strain characteristics of the soil. The GEO-SLOPE SLOPE/W Stability Modelling
(2008) document states that “…this has two consequences, one is that local variations in
safety factors cannot be considered, the other is that the calculated stress distributions are
often unrealistic”. To overcome this issue, stresses can be found using the upper and lower
bound theorem methods, or by finite element analysis then incorporated in the stability
analysis to compute a factor of safety. Alternatively, the factor of safety can be analysed using
probabilistic analyses to account for local variations in soil properties.
Wright, Kulhawy & Duncan (1973) also state that most limit equilibrium methods assume
that the factor of safety for each slice is the same however this would only be true at failure
when each slice has a factor of safety of one.
4.6
Computer modelling
4.6.1
GeoStudio™ SLOPE/W
GeoStudio™ SLOPE/W (2012) is a computer modelling program which uses limit
equilibrium methods to determine a factor of safety of soil embankments. SLOPE/W was
used for the deterministic analyses to calculate factors of safety and also used for the
probabilistic analysis to determine the probability of failure using Monte Carlo simulations.
The GEO-SLOPE Slope Modelling (2008) document states “…the SLOPE/W results must
always be judged in context of what can exist in reality”.
4.6.2
Microsoft Excel™
Microsoft Excel™ spreadsheets can be used for simple limit equilibrium methods to obtain
factors of safety. Spreadsheets have been developed by the author for Bishop’s simplified
method and Fellenius’ method for undrained and drained conditions. Both methods have
limitations in that the width, height, and angle of the base of each slice are unknown and need
to be specified beforehand. The number of slices and iterations also has to be manually
entered.
The spreadsheets are not able to determine the location of the slip circle. This is a significant
limitation as each potential failure surface will need to be analysed separately to determine
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