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3
SLOPE STABILITY PARAMETERS
3.1
Loading conditions and shear strength parameters
Coulomb (1776) observed that the cohesive component of the shearing strength remained
constant for a given soil and is independent of the applied stress. The second component of
the shear strength is the frictional resistance: the angle of shearing resistance, which was
further investigated by Mohr in 1900. Mohr (1900) produced circles - Mohr circles - using the
principal stresses at failure (𝜎1 and 𝜎3 ) to represent the state of stress at a point. A line drawn
tangential to a series of Mohr circles shows the Mohr failure envelope which identifies that, at
failure, the shear stress is equal to the shearing strength. The Mohr failure hypothesis thus
identifies the point of tangency of the Mohr failure envelope as the inclination of the failure
plane, i.e. the angle of shearing resistance (Ranjan & Rao, 2007).
𝜏
𝜎1
𝜎3
𝜎𝑓
𝜏𝑓
𝜎3
𝜏𝑓
𝜎3
𝜎1
Figure 3.1: Soil element at failure
𝜎3
𝜎1 𝜎𝑓
𝜎
𝜎1
Figure 3.2: Mohr failure circles and Mohr failure envelope
The Mohr-Coulomb failure criterion incorporates both shear strength parameters: cohesion (c)
and angle of shearing resistance (𝜙) in an equation for the shear strength at failure (𝜏𝑓 ):
𝜏
c
𝜏𝑓 = 𝑐 + 𝜎 tan 𝜙
𝜙
3.1
𝜎
Figure 3.3: Mohr-Coulomb failure criterion
19