Test: Friction Circle Method - Civil Engineering (CE) MCQ

In the friction circle method, it is assumed that the resultant reaction is tangential in the friction circle, since the error involved in this assumption is of small magnitude.

• This method is based on total stress analysis, but it enables the angle of shearing resistance to be taken into account.
• It is convenient approach for both graphical and mathematical solutions.
• It should be noted that some soils, such as saturated silts and unsaturated clays, do exhibit a Φ value under un-drained condition.
• The friction circle method assumes a circular slip surface; it is in the form of a circular arc of radius R with its centre at ‘O’ and radius of slip circle is Rsinϕ as shown in the figure below.

The friction circle having radius r sin φ is also called as φ-circle.

Friction circle method:

This method is also based on total stress analysis in which shearing angle of ϕ is used to analyse the stability of finite slope.
The principle of the method is that the inter granular forces are in an obliquity of ϕ to the circular surface at failure, where ϕ is the angle of the internal friction of the soil.
When the length of the arc is divided into small elements, the line of action of the inter granular forces acting on these elements can be defined by a tangent to the friction circle drawn around the centre of the sliding circle.
The radius of this friction circle is given by R sinϕ
Where,
R is the radius of the sliding circle.

Thus, the friction circle is agraphical tool that defines the line of action of the intergranularforces at any given point on the sliding circle in a convenient way.In geotechnics, the method is used primarily for slope-stability investigations in homogeneous soil when both cohesive and frictional components have to be considered.

The circle giving minimum factor of safety Fc is considered as a critical slip circle.

Similar to Culmann’s method, the friction circle method also assumes the failure surface as the arc of circle.

The factor of safety with respect to cohesive strength, based on the assumption that frictional force has been fully mobilized, and the equation is given by FC = C / Cm.

The factor of safety Fc with respect to cohesive strength, based on the assumption that the frictional strength has been fully mobilized, is given by FC = C / Cm.

The forces acting on a sliding wedge are i) the weight of the wedge ii) the total frictional resistance or resultant, and iii) total cohesive resistance along the slip circle.

In the frictional circle radius of Kr sin φ, the factor K depends on the central angle δ of the slip arc.