Sarma Non-Vertical Slices
Sarma (1979) developed a limit equilibrium analysis method for non-vertical slices, and the
angle of each slice is found as part of the solution. In this method, the critical acceleration
factor 𝐾𝐾𝑐𝑐 is calculated, with the assumption that under the influence of the force 𝐾𝐾𝑐𝑐 𝑊𝑊𝑖𝑖 , the
factor of safety on the slip surface is equal to one.
Where the symbols are defined as:
•
•
•
•
•
•
•
•
•
𝑐𝑐̅ is the average cohesion on the side of the slice
� is the average friction angle on the side of the slice
ɸ
𝛼𝛼 is the angle of the base of the slice (relative to the horizontal axis)
𝛿𝛿 is the angle of the side of the slice (relative to the vertical axis)
𝑊𝑊 is the weight of the slice
𝑙𝑙 is the length of the base of the slice
𝑑𝑑 is the length of the side of the slice (from slip surface to ground surface)
𝑈𝑈 is the force due to pore water pressure on base of slice
𝑃𝑃𝑃𝑃 is the force due to pore water pressure on the side of the slice
The factor of safety (𝐹𝐹𝑠𝑠 ) is then calculated through an iterative process where the strength
parameters are reduced until a critical acceleration of zero is reached:
For more information about this method see Sarma, S.K., “Stability Analysis of
Embankments and Slopes,” J. Geotech. Eng. Div. ASCE 105, No. 12, 1979, pp. 1511-1524.
Number of Slices
The Number of Slices is the number of non-vertical slices into which the sliding mass for
each slip surface will be divided. The default number of 25 slices is sufficient to obtain an
accurate solution for most problems.
For non-circular failure surfaces the Use minimum # of slices option automatically selects
the number of slices. Slice boundaries will be located at points where the failure surface
changes slope, and where it intersects a material boundary. Using the minimum number of
slices will generally improve the angle optimization results, but it is recommended to use
this option with caution. For circular failure surfaces the minimum number is set to a
constant value of 25 slices.
Slice Angles
The factor of safety depends on the set of values of slice boundary angles (𝛿𝛿). The objective
is to find the critical set, which is defined as the set of angles that results in the lowest
factor of safety. See Slice Angles topic for more detail.
Sarma Interslice Strength Options
The factor of safety is also dependant on the cohesion and frictional angle along the slice
boundary. These strength parameters are determined using the Sarma Interslice Strength
Options.
Usage
Active-passive wedge failures such as those which occur in spoil piles on sloping foundations
or in clay core dam embankments can be analyzed using this method. In a model with
anisotropic material, unlike other limit equilibrium methods, the factor of safety is affected
when the slices are aligned with the direction of the weak layers.
Limitations
Currently Excess Pore Pressure and Rapid Drawdown Analyses cannot be performed using
Sarma non-vertical method. In addition, the line of thrust cannot be drawn for Sarma nonvertical.