Environmental Engineering Reference
In-Depth Information
Shear Strength Factors (see also
Section 3
.4)
Strength Parameters
The basic strength parameters are the angle of internal friction
φ
and cohesion
c
. Frictional
resistance based on
is a function of the normal stress, and the maximum frictional shear
strength is expressed as
φ
S
max
N
tan
φ
(9.2)
Cohesion
c
is independent of the normal stress and acts over the area of the failure sur-
face.
Total and Effective Stresses
In the total stress condition, the measured stress includes both pore-water pressures and
stresses from grain-to-grain contact. In the effective stress condition, stresses from grain-
to-grain contact are measured, which increase as pore pressures dissipate. Effective stress
equals total stress minus pore pressure.
Pore-water pressures (
U
for total,
u
for unit pressures) are induced either by a load
applied to a saturated specimen, or by the existence of a phreatic surface above the sliding
surface. They directly reduce the normal force component
N
, and shearing resistance is
then expressed as
S
max
(
N
U
)tan
φ
(9.3)
In
Figure 9.66,
therefore, if pore pressures become equal to the normal component of the
weight of the block, there will be no shearing resistance.
Failure Criteria
The Mohr-Coulomb criterion defines failure in terms of unit shear strength and total
stresses as
s
c
σ
n
tan
φ
(9.4)
The Coulomb-Terzaghi criterion accounts for pore-water pressures by defining failure in
terms of effective stresses as
s
c
'
σ
n
'tan
φ
'
(9.5)
where
c
' is the effective cohesion;
p
-
u
) with
p
total nor-
mal stress. In a slope, the total pressure
p
per unit of area at a point on the sliding surface
equals
h
z
σ
n
' the effective normal stress (
γ
t
/cos
2
θ
, where
h
z
is the vertical distance from the point on surface of sliding to
top of slope,
the inclination of surface of
sliding at point with respect to horizontal; u the pore-water pressure, in a slope
u
γ
t
the slope unit weight of soil plus water, and
θ
h
w
γ
w
,
the piezometric head times the unit weight of water; and
' the effective friction angle.
The strength parameters representing shearing resistance in the field are a function of
the material type, slope history, drainage conditions, and time. Most soils (except purely
granular materials and some normally consolidated clays) are represented by both param-
eters
φ
and
c
, but whether both will act during failure depends primarily on drainage con-
ditions; and, the stress history of the slope.
φ
