Shear Strength of Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 529

τ ff = c + ( σ f - u a ) f tan φ′

or

f′ b + (

τ ff = c ′ + (u a - u w ) f tan φ σ f - u a ) f tan φ′

f′

f′

f′

c 3

c 2

c 1

c ′

0 Net normal stress, ( σ - u a )

Figure 11.11 Horizontal projection of failure envelope onto τ versus σ − u a plane viewed

parallel to matric suction u a − u w axis as contour lines of failure envelope on σ − u a plane.

The inclusion of matric suction in the definition of the
cohesion intercept does not necessarily suggest that matric
suction is a cohesion component of shear strength. Rather,
the matric suction component

tan φ and a slope angle of φ b . The horizontal projection
shows that there is an increase in shear strength as the net
normal stress is increased with matric suction held constant.

u w tan φ b ]
is lumped with effective cohesion c for the purpose
of translating the three-dimensional failure envelope
onto a two-dimensional representative plot. The suction
component of shear strength has also been called the
apparent or total cohesion (Taylor, 1948).
A smooth transition from an unsaturated condition to sat-
urated conditions can be demonstrated using the extended
Mohr-Coulomb failure envelope shown in Fig. 11.9. As the
soil becomes saturated, matric suction goes to zero and the
pore-water pressure approaches the pore-air pressure. The
three-dimensional failure envelope is consequently reduced
to the two-dimensional envelope of τ versus σ

u a −

[i.e.,

11.2.8 Use of σ − u w and u a − u w to Define Shear

Strength
The shear strength equation has thus far been expressed
using σ

u w as the stress state variables. How-
ever, the shear strength equation for an unsaturated soil can
also be expressed in terms of other combinations of stress
state variables, such as σ

− u a and u a −

− u w and u a − u w :

c + σ f − u w f tan φ + u a − u w f tan φ τ ff = (11.14)

where:
σ f −

u w .The
smooth transition between unsaturated and saturated soil
conditions can also be observed in Fig. 11.11. The failure
envelope projection gradually lowers onto the failure enve-
lope for the saturated soil as matric suction decreases. The
cohesion intercept c then becomes equal to the effective
cohesion c .
The extended Mohr-Coulomb failure envelope can also
be projected horizontally onto the τ versus- u a −

−

u w f

= net normal stress state with respect to

pore-water pressure on the failure plane
at failure and

φ = friction angle associated with the matric

suction stress state variable u a − u w f

when using the σ u w

stress state variables in formulating the
shear strength equation.

− u w and u a −

u w plane
(Fig. 11.12). The horizontal projection is made for vari-

ous net normal stresses at failure, σ f − u a f . The resulting

It should be noted that the stress variables and the soil
properties in Eq. 11.14 are changed in such a way that the

contour lines have an ordinate intercept of c + σ f − u a f