Shear Strength of Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 535

The cohesion intercepts c at various matric suctions can be
computed using Eq. 11.28 and plotted on the shear strength
versus matric suction plane (Fig. 11.16) in order to obtain
the angle φ b . Knowing the strength parameters c , φ , and
φ b , the parameters for the stress point envelope (i.e., d , φ ,
and ψ b ) can also be computed.

At low matric suctions, the soil specimen remains saturated.
Under these conditions the effect of pore-water pressure and
total normal stresses on the shear strength are characterized
by the friction angle φ . Both the pore-water pressure and
the total normal stresses are referenced to the same exter-
nal air pressure, as expressed by the stress state variables
u a −

u a . The shear strength behaves as a satu-
rated soil with a friction angle φ . The shear stress versus
matric suction envelope has a slope angle φ b equal to φ .
This condition is maintained as long as the soil is saturated.
Water is drawn out of the pore spaces once the air-entry

u w and σ −

11.2.10 Nonlinearity of Failure Envelope
A linear shear strength theory has been presented for an
unsaturated soil using an extended Mohr-Coulomb failure
envelope. As a wider variety of soil types have been tested
over a wider range of soil suctions, it has become increas-
ingly apparent that the shear strength versus matric suction
relationship should not be limited to a linear relationship.
Shear strength test results on compacted glacial till by Gan
(1986) showed that the shear strength envelope was curved.
Figure 11.18 illustrates the nonlinear matric suction failure
envelope measured by Gan (1986). The φ b angle appears
to be equal to φ at low matric suctions and decreases to a
lower value at high matric suctions. Consequently, the φ b
angle appears to be a function of matric suction. Similar
curved suction versus shear strength envelopes were earlier
presented by Escario and Saez (1986).
An examination of the effect of increasing matric suc-
tion from an initially saturated condition suggests that it is
reasonable for the shear strength versus matric suction rela-
tionship to be nonlinear. Let us consider a shear strength
test performed using the axis translation technique over a
wide range of matric suctions. The tests can start from an
initially saturated condition with the soil consolidated under
a designated confining pressure σ . The initial matric suction
is maintained at zero (i.e., pore-water pressure in the soil is
equal to externally applied pore-air pressure).
The total confining pressure can be referenced to the exter-
nal air pressure σ

value of the soil specimen, u a − u w b , is exceeded. As the

matric suction in the soil is increased, the soil begins to
desaturate. The pore-water pressure is referenced to the pore-
air pressure (i.e., u a − u w ), which is now both external and

internal to the soil since the soil becomes unsaturated. The
total normal stress is similarly referenced to the pore-air
pressure through the σ

u a stress state variable.
The pore-water occupies only a portion of the pore spaces
in the soil as indicated by a degree of saturation which is
less than 100%. A further increase in matric suction is not
as effective in increasing shear strength as is an increase
in net normal stress. As a result, it is necessary for the
φ b angle to reduce to a value lower than φ when matric
suction is increased beyond the air-entry value of the soil,

−

u a −

u w b . The effects of net normal stress and pore-water
pressure on the shear strength of an unsaturated soil take
on independent roles in terms of the stress state variables
σ u w .

The air-entry value of a soil largely depends on the grain
size distribution of the soil. Coarse-grained soils such as
sands desaturate at lower matric suctions than fine-grained
clayey soils. Test results have shown that there is a rela-
tionship between the air-entry value of the soil and the pore
sizes in the soil. Sands often have an air-entry value less
than 10 kPa whereas clayey soils can have an air-entry value
well beyond 100 kPa. The air-entry value of a soil may also
depend to some extent on the net confining pressure applied
to the soil. The air-entry value provides an indication of the
point where the shear strength versus matric suction starts
to exhibit nonlinear shear strength behavior.
The study of shear strength results on soils tested over
a wide range of suction values has clearly revealed that
the suction versus shear strength envelope bears a relation-
ship to the SWCC for a soil. The φ b angle with respect to
matric suction is more clearly understood by considering the
amount of water in the pores of the soil. Curvature of the
shear strength versus matric suction envelope is related to
the air-entry value of the soil and residual conditions.
Several empirical procedures have been proposed whereby
the SWCC can be used to estimate the shape of the shear
strength function for an unsaturated soil. The proposed pro-
cedures are presented later under the section on the estima-
tion of the unsaturated soil shear strength envelope (i.e., the
beginning of Chapter 12).

− u a and u a −

u a . Assuming that the φ and c param-
eters are known, the soil shear strength under the initial con-

−

ditions is equal to c + σ u a tan φ . Let us now increase

the applied air pressure (i.e., producing a positive matric suc-
tion) while keeping the net normal stress σ

−

− u a constant.

250

(

σ f - u a ) f = 72.7 kPa

f′ = 25.5 °

200

150

100

( σ f - u a ) f tan f′ = 34.7 kPa

50

c ′ = 10 kPa

0

0 100 200 300 400 500

Matric suction ( u a - u w ), kPa

Figure 11.18 Direct shear test results exhibiting nonlinear behav-
ior for failure envelope projected onto τ versus u a − u w plane (after
Gan, 1986).