2. 4.1 Introduction
Slope: -any natural or man made earth mass, whose
surface forms an angle with the horizontal.
Hills and mountains, river banks, etc. are common
examples of natural slopes.
Examples of man made slopes include fills, such as
embankments, earth dams or cuts, such as highway
and railway , canal banks, foundations excavations.
Natural forces (wind, rain, earthquake, etc.) change
the natural topography often creating unstable slopes.
3. Failure slopes have resulted in much death
and destruction.
In assessing the stability of slopes,
geotechnical engineers have to pay
particular attention to geology, drainage,
groundwater, and the shear strength of the
soils.
In this chapter, we will examine the stability
of earth slopes in two dimensional space
using limit equilibrium methods.
4. Introduction…..
If the ground surface is not horizontal, a component of
gravity will cause the soil to move downward.
Mohr-Coulomb failure criterion applies and the shear
strength parameters used correspond to the peak
strength.
Objective of slope stability analysis
In a slope stability analysis the objective is to locate the
circle (or any type of the sliding surface) that yields the
minimum factor of safety.
This usually requires that an iterative procedure be
employed.
12. Types of slope movements
All movements of land masses is referred to as earth materials
movement or mass movement.
All types of earth materials’ movements can be classified into 3:
1) Earth flow
2) Landslide
3) Subsidence
Any earth material movement along the slope is known as slope
movement. Therefore earth flow and landslides are slope movements.
1) Earth flow is the down ward movement of the earth material along
the slope, in which the movement is distributed through out the
displaced mass.
13. Continued…
2. Landslide is the down ward movement of earth materials along the
slope, in which the movement is confined to a definite failure plane.
Figure : typical examples of landslide (a) transitional slide (b) rotational
slide
(a)
(b)
14. 5.4 Factor of Safety
• The task of analyzing slope stability is to
determine the factor of safety which is
generally be defined as:
m
f
s
FS
Where
FSs = factor of safety with respect to strength
τf = average shear strength of the soil
τm = average shear stress developed along the potential
failure surface
(1)
15. 4.4 Two-Dimensional Slope Stability Analysis
Slope stability can be analyzed using one or more of
the following:
the limit equilibrium method,
limit analysis,
finite difference method, and
finite element method.
Limit equilibrium is the most widely used method for
stability analysis. In the following sections, we will
learn some of the commonly used slope stability
analysis methods that are based on the limit
equilibrium.
16.
17. W = (volume of the soil element)X(unit weight of soil) = bz
The weight, W, can be resolved into two components:
Force perpendicular to the plane AB= Na
→Na = Wcos αs = bzcos αs
Force parallel to the plane AB, Ta
→ Ta = W sin αs = bzsinϕ → force that tends to cause the
slip along the plane
shear forces X j and Xj+1 on the sides, the normal forces Ej and
Ej+1 on the sides,
If seepage is present, a seepage force Js = i bz γw develops, where
i is the hydraulic gradient. For a uniform slope of infinite
extent.To continue with the limit equilibrium method, we must
now use the equilibrium equations to solve the problem.
34. Example
• For the slope shown in Figure, find the factor of
safety against sliding for the trial slip surface AC.
Use the ordinary method of slices.
35. Solution
• The sliding wedge is divided into seven slices.
• Other calculations are shown in the table.
