Civil and Building Engineering.

This discussion of the mechanics involved in the shear strength of soils begins with fundamental concepts based on Amonton’s law of friction. A block resting on a horizontal plane is shown in Figure 3.30. A vertical force N and a shearing force F are applied to the block. If the shearing force F is gradually increased until sliding occurs, then F exceeds the friction force holding the block in place. The magnitude of F is

Relationship Between Principal Stresses at Failure. The relationship between the principal stresses at failure when the failure envelope has a cohesion intercept is obtained by solving Eq. 3.94 for the desired principal stress and then using the trigonometric identity
The resulting equations are
Equations 3.99 and 3.100 apply to circles tangent to linear failure envelopes whether the envelopes are expressed in terms of total stresses or effective stresses, provided, of course, that the symbols are adjusted for the type of stress used and for the type of test.