Fundamentals of Friction Circle Method in Civil Engineering

The friction circle method is commonly used in civil engineering to analyze and design slopes, retaining walls, and other structures that involve the interaction between soil and structures. One of the key components of this method is the friction circle, which helps in determining the stability of the structure against sliding.

Understanding the Friction Circle

The friction circle is a graphical representation of the shear strength of the soil and the applied forces acting on the structure. It is a circle drawn on a Mohr's circle, which is a graphical representation of stress states. The radius of the friction circle represents the shear strength of the soil, while the center of the circle represents the normal stress acting on the soil.

Radius of the Friction Circle

The radius of the friction circle is a crucial parameter in the friction circle method. It is directly related to the shear strength of the soil and can be determined using various methods, such as laboratory tests or empirical correlations. However, in the context of this question, the radius of the friction circle is given by the equation r*sinθ, where r represents the effective normal stress and θ represents the angle of internal friction.

Explanation of the Correct Answer

The correct answer to the given question is option 'C', which states that the radius of the friction circle is given by r*sinθ. This equation is derived from the trigonometric relationship between the radius, normal stress, and angle of internal friction.

Trigonometric Relationship
The relationship between the radius (r), normal stress (σ), and angle of internal friction (θ) can be expressed as follows:

r = σ * tanθ

To convert this equation into the form r*sinθ, we can use the trigonometric identity:

tanθ = sinθ / cosθ

By substituting the value of tanθ in the equation for r, we get:

r = σ * (sinθ / cosθ)

Simplifying the equation further, we can cancel out the common factor of cosθ:

r = σ * sinθ

Therefore, the radius of the friction circle is given by r*sinθ, which corresponds to option 'C' as the correct answer.

Conclusion

In the friction circle method used in civil engineering, the radius of the friction circle is a critical parameter that represents the shear strength of the soil. It can be calculated using the equation r*sinθ, where r is the effective normal stress and θ is the angle of internal friction. This equation is derived from the trigonometric relationship between the radius, normal stress, and angle of internal friction.