Fundamentals of Engineering Design
Numerous methods are available for predicting the stability of stream banks. Most methods used
employ the concept of limited equilibrium analysis. The use of limited equilibrium analysis explicitly
accounts for the major factors that influence the shear stress and shear resistance of a slope, and employs
the comparison between resisting forces (FR) and driving forces (FD). The slope under consideration is
considered stable as long as the resisting forces are greater then the driving forces (FR > FD). Both mild
and steep slopes can be analyzed employing the concept of limited equilibrium analysis.
The resisting force, FR, is derived from the shear strength of the soil, and keeps the slope from
moving. The shear strength of a soil is defined by Eq. (5.36):
J ' c % F tan N
shear strength of the material;
normal stress on the failure surface; and
Equation (5.36) is known as the Revised Coulomb Equation. The angle of internal friction ( ) and cohesion
(c) are known as the shear strength parameters. Each shear strength parameter can be determined from
laboratory tests on soil samples or back-calculated after failure of a stream bank occurs.
Forces tending to cause movement of the slope, or the driving forces (FD) include the weight of the
soil mass and any external loading. External loading may be additional loading on the top bank or a
surcharge of pore-water pressure. The ratio between resisting and driving forces define the factor of safety
(FS) and is determined by Eq. (5.37):
The factor of safety can also be considered as the ratio of the critical bank height to the actual bank height,
as represented by Eq. (5.38).
where: Hc = critical bank height; and
H = actual bank height.
Failure is anticipated when the factor of safety is less then unity. Figures 5.47a and 5.47b depict the
fundamental failure geometry associated with limited equilibrium bank instability for a low steep