Environmental Engineering Reference
In-Depth Information
σ
n
= 5 kg/cm
2
σ
n
= 3 kg/cm
2
σ
n
= 1 kg/cm
2
σ
n
= 0.5 kg/cm
2
FIGURE 3.24
Peak strength vs. displacement and normal stress.
(From Peck, R. B.,
Proceedings of ASCE, Stability and
Performance of Slopes
Embankments, Berkeley, CA,
1969, pp. 437-451. With permission.)
∆
L
Peak strengths
P
σ
1
σ
3
σ
n
σ
3
σ
3
τ
Tan
=
τ
/
σ
n
FIGURE 3.25
Stresses on a specimen in a confined state.
σ
1
grains until some characteristic stress level is reached at which resistance is exceeded and
rupture occurs. This stress is termed the
peak strength
.
If
σ
1
(for the peak strength) are plotted to define a Mohr's circle at failure, a line
drawn tangentially to the circle passes through the origin at an angle
σ
3
and
as shown in
Figure
3.26
and
Figure 3.27.
Other specimens of the same material loaded to failure, but at different
confining pressures, will have Mohr's circles tangent to the line defined by
φ
. The circle tan-
gent line represents the limits of stability and is termed
Mohr's envelope
. It defines shear
strength in terms of the friction angle
φ
φ
, and the normal or total stresses, and it expressed as
τ
max
σ
n
tan
s
φ
(3.23)
(In actuality, the envelope line will not be straight, but will curve downward slightly at
higher confining pressures.)
φ
Total vs. Effective Stresses (
)
In a fully saturated cohesionless soil, the
φ
vs.
value will vary with the drainage conditions
prevailing during failure. In undrained conditions, total stresses prevail and in drained
conditions, only effective stresses act. The friction angle is expressed as
φ
φ
.
Total Stresses
Saturated Soils
If no drainage is permitted from a fully saturated soil as load is applied, the stress at fail-
ure is carried partially by the pore water and partially by the soil particles which thus
