Test: Terzaghi’s Analysis - Civil Engineering (CE) MCQ

An analysis of the condition of complete bearing capacity failure is termed as a general shear failure, can be made by assuming that the soil behaves like an ideally plastic failure.

Mechanism of Failure:
The shapes of the failure surface under ultimate loading conditions.
The zones of plastic equilibrium represented in this figure by the area may be subdivided into three zones:
1. Zone I of elastic equilibrium
2. Zones II of radial shear state
3. Zones III of Rankine passive state

When load q_u per unit area acting on the base of the footing of width B with a rough base is transmitted into the soil, the tendency of the soil located within zone I is to spread but this is counteracted by friction and adhesion between the soil and the base of the footing.
Due to the existence of this resistance against lateral spreading, the soil located immediately beneath the base remains permanently in a state of elastic equilibrium, and the soil located within this central Zone I behaves as if it were a part of the footing and sinks with the footing under the superimposed load

The concept of failure analysis was first developed by Prandtl, and later extended by Terzaghi, Meyerhof and others.

The parameters Nc, Nq, Nγ are the dimensionless numbers, known as bearing capacity factors depending only on the angle of shearing resistance of the soil.

As the soil compress, φ changes; slight downward movement of footing may not develop fully the plastic planes.

The values of Nγ for φ of 34° and 48° are the original Terzaghi values which were used by Bowles to back compute Kpγ.

In Terzaghi’s analysis the soil is homogeneous and isotropic and its shear strength is represented by Coulomb’s equation.

Local shear failure generally occurs in loose sand while general shear failure occurs in dense sand.

Peck, Hansen, and Thorn burn gave curves for Nq and Nγ for the transition state from φ = 28° and φ = 38°, in which they assumed general shear failure when φ > 28°.

Terzaghi assumed the value of angle ψ = φ, which is not true. Since footings are normally rough, ψ has been found close to 45° + φ/2 than to φ, thus Terzaghi’s bearing capacity equations do not have provision for including depth effects, inclination factors, etc.