20-10-2012, 05:30 PM
Advance Methods of Slope-Stability Analysis for Economical Design of Earth Embankment
Advance Methods of Slope-Stability Analysis for Economical Design of Earth Embankment.pdf (Size: 2.14 MB / Downloads: 114)
ABSTRACT
The concept and theory involved in different methods of slope stability analysis of earth embankment have been discussed.
The mathematical equations and the methodology for calculating the factor of safety of earth slope of any specified(chosen)
slip circle by various methods has been given. By repeating the process for different slip circles, the minimum factor of
safety can be calculated and critical slip circle obtained. The forces which act within a soil mass have been discussed. The
inter slice normal and shear forces which are being also considered in many methods of analysis, have been explained and
mathematical equations given to calculate them for the analysis.
The specified function f (x) (including half-sine function) and applied function ratio denoted by ‘λ’ has been explained. A
simple example of earth embankment has been analyzed to illustrate the methodology. The results as obtained by
mathematical calculations proceeding ab-initio have been compared with the output using a soft ware for such analysis.
For the purpose of direct comparison and easy explanation the critical circles were first established by the computer
software by various methods of analysis and to illustrate the method only these circles were analyzed through independent
mathematical equations and computations using Microsoft Excel program for the iterating process. It could be seen that
without the use of computer for the analysis, particularly the iterating process, it would have been very cumbersome and
time consuming to do the same by manual calculations. But it is possible to do complete analysis by Excel as explained in
this paper. Graphical method can be used for marking the circle and various slices as is the normal practice for slopestability
analysis. Graphical method of analysis can be used to draw force polygon to obtain various forces and computing
factor of safety, but this paper has dealt with mathematical equations only for the analysis part. Since the main emphasis is
on explaining and demonstrating the various methods, set of minimum forces (such as seismic, pore water pressure, some
external force etc. not taken) have been considered, however, without any loss of merit for the methodology.
INTRODUCTION
The slope stability analysis is usually done by
Fellenius method also called Ordinary or Swedish Circle
method. It does not take into consideration inter slice
force and considers only moment equilibrium and not
force equilibrium conditions and thus provides only
moment factor of safety and not force factor of safety.
It also does not provide the closed force polygon in free
body force diagram for the individual slice within the
failure zone of earth mass. It, therefore, does not satisfy
the equilibrium conditions. It provides the factor of safety
on lower side and thus results into a more conservative
design of earth slope. The Bishop Simplified method
which is sometimes used takes into consideration only
inter slice normal force, but does not take the inter slice
shear force. This also gives moment factor of safety
only. Here also force polygon does not close.
DEFERENT THEORIES FOR ANALYSIS
The failure of a slope could be slippage of earth
mass along a slip surface (generally circular). Coulomb
(1776) considered a wedge failure in his theory of
earth pressure, Rankine (1857) considered zone of
failure where each element is at the verge of failure.
All the methods of slope stability analysis in practice
consider discretization of failure zone into slices. A slice
of earth will be subjected to the forces shown in Fig.1.
None of the present methods takes into consideration
the strain compatibility of the slices within the zone of
failure. All methods are covered within the ambit of
Limit Equilibrium Analysis (LEA). The LEA further
comprises of Moment Equilibrium and Force Equilibrium
and provide Moment factor of safety and/or Force
factor of safety depending on the method of analysis.
Corps of Engineers #1 Method
In this method,the resultant inter slice force is
assumed to act parallel to the line joining entry point
with exit point as shown in Fig. 5. As the inclination of
resultant is constant (parallel to the same line) the ratio
of inter slice shear force to inter slice normal force
remains same for all the slices. In other words this will
compare with constant function of Morgenstern-Price.
However this method considers only force equilibrium
and provides only force factor of safety. Incase of Corps
of Engineers # 2 method the resultant inter slice force is
assumed to be parallel to the embankment slope as shown
in Fig. 6. That is it will have only inter slice normal force
and no shear force where the embankment surface at
slice top is horizontal. Rest of the things remains the
same as in Corps of Engineers #1 method.