A SLOPE STABILITY CASE IN ARCADIA: Notes on the analyses of translational slides
The back analyses have been performed using the limit equilibrium method programmed in a spreadsheet
application.
The initial data required for the analyses include information on the: a) ground surface geometry, b) subsoil
stratigraphy geometry, c) piezometric level (as measured in the piezometers), d) slip surface geometry (as
measured in the inclinometers) and e) unit weight of the encountered materials.
The user has to divide the slope into slices and to record the following information on slice geometry: a)
slice average height, h, b) piezometric level average height (measured from slice base), hw, c) slice width, b,
and d) the angle formed between the base of the slice and the horizontal, a (see Figure 1).
The user searches the residual strength parameters that result to a factor of safety FoS=1. Typically, the
cohesion is assumed zero (cr’=0) and the only unknown is the residual mobilized angle of shearing
resistance (φr’).
The methods used are the: a) conventional and b) the horizontal force equilibrium.
Equation of the conventional method
All forces are resolved normal and parallel to the base of the slice and the factor of safety is computed by
comparing forces acting parallel to the base of the slice (e.g., Equation 12.19 in Knappett & Craig, 2012):
n
FoS 
 cl  W cos a  U  tan  
i
i 1
n
 W sin a 
i 1
i
where:
n:
l:
W:
U:
a:
number of slices
inclined length of the slice base (in m)
total weight of the slice (in kN)
pore water force (in kN)
inclination of the slice base (in degrees)
Equation of the horizontal force equilibrium method
The factor of safety is computed by considering equilibrium of forces in the horizontal direction (e.g.
Equation 5 in Fredlund et al., 1981):
n
FoS 
cl   N  U  tan   cos a
i
i 1
n
  N sin a 
i 1
i
where:
n:
l:
N:
U:
a:
number of slices
inclined length of the slice base (in m)
total normal force on the slice base (in kN)
pore water force (in kN)
inclination of the slice base (in degrees)
b
Ground
water level
h
hw
a
l
Figure 1. Slice geometry
References
Knappett, J.A. and R.F. Craig [2012]. “Craig’s Soil Mechanics”, 8th Ed. (1st Ed. 1974), Spon Press, London, UK.
Fredlund, D.G., J. Krahn and D.E. Pufahl [1981]. “The Relationship between Limit Equilibrium Slope Stability
Methods”, Proceedings of the 10th Int. Conf. on Soil Mechanics and Foundation Engineering, Stockholm,
June 15–19.