# Stability of Finite Slope

In the Stability of Finite Slope early 1900, Swedish scientist, W.Fellenius, proved the surface of earth slopes resembles the shape of a circular arc. These slides are termes as rotational slides. These can be divided into

1. Face Failure⟹ these type of failure occur when slope angle β is quite high and soil near the toe possesses high strength.
2. Toe Failure⟹ the failure occurs when the soil mass of the slope is homogenous above and below the base, the angle β is moderate. For dams, this is the most common failure pattern. (14° <β <53° )
3. Base Failure⟹ β is quite low and the soil below the base is softer and more plastic than the soil above the base.

### Taylor Stability Number

Taylor publishes a chart having stability numbers as a function of slope and angle of internal friction. Also hence for different values of β, C,γ,H, we can find a factor of safety and also for different ‘H’ we have different ‘Fs’ and minimum Fs gives us the critical height of the slope.

IF β>530 then failure will be toe failure, if β<530 it can be any type of failure.

#### Culmann Method ⟹

Culmann Method is of historical importance only, as he assumes that rupture will occur in a plane since the actual failure surface is curved.

Culmann’s method permits one to determine graphically the magnitude of the earth pressure and to locate the most dangerous rupture surface according to Coulomb’s wedge theory. Culmann Method is of historical importance only, as he assumes that rupture will occur in a plane since the actual failure surface is curved.

Lay off on AE distances AV, A1, A2, A3 etc to a suitable scale to represent the weight of wedges ABV, AB1, AB2, AB3, and so on.

Select the point C’ on pressure locus such that the tangent to the curve is parallel to the

line AE.

### Failure planes makes an angle of θc, with the horizontal

• Swedish Circle Method or Method of Slices
• This is a limit equilibrium technique to find the most critical plane
• he masses above an assumed rupture surface of failure is divided into a number of vertical slices and assuming the forces on opposite sides of each slice are equal and opposite, a statically determinate problem is obtained.
• a trial slip circle is ASC is drawn with O as a center and OC=OA=R A number of trial slip circles are chosen and the factor of safety with respect to each of them is computed. The slip circle corresponding to the minimum factor of safety is identified. This is the potential slip surface and the corresponding factor of safety against failure of the slope AB.

Friction Circle Method⟹ This method is based on the assumption that the resultant force R (the resultant of the normal and frictional forces along the surface of sliding.) on the rupture surface is tangential to a circle of radius, Rain, which is concentric with the trail slip circle and we take total stress to analyze the slip circle.
the following quantities are known.
1. the magnitude and direction of weight of sliding wedge (W)
2. The direction of resultant reaction (R)
3. The direction of total cohesion

The factor of safety with respect to cohesion based on the assumption that frictional strength has been fully mobilized is given by
1. A number of slip circles are analyzed and the lowest factor of safety is the likely failure plane.

Stability of the slopes of earth dam⇒ There are three generally recognized critical stages based on pore pressure for which the stability of the embankment should be ascertained. These three situations are

(i) end of construction, (ii) steady-state seepage, and (iii) rapid drawdown.