Environmental Engineering Reference
In-Depth Information
some of the normal stress from grains to pore water and comprehensively reducing shear
strength.
Plastic
and
liquid limits
define thresholds of increasing water content at which
the mass deforms, first plastically or then as a viscous fluid (Figure 13.11). They also
depend on particle size character, void ratio and proportion of clay minerals, but plastic
and fluid behaviour is not restricted to fine-grained soils. Under exceptional water
pressures, large boulders and grains may become fluidized and move rapidly downslope
as
debris flows
when grain collisions replace water as the buoyancy source. Water
content also fluctuates with the weather and the seasons. Intense precipitation or spring
melt may induce pore water pressures to rise rapidly. Steep slope angles and the
proximity of rock walls generate rapid runoff which readily infiltrates slope colluvium.
Drainage is
MOHR-COULOMB FAILURE CRITERIA
key concepts
The parameters of the Mohr-Coulomb equation are now summarized in Figure 1. Any
point on the solid line indicates the shear stress needed to exceed the shear strength
related to specific values of normal stress, σ, cohesion,
c
, and friction angle, . This line,
however, shows 'ideal'
intact rock mass strength
(IRS), and the presence of
discontinuities and water in slopes substantially reduces shear strength. Discontinuities
remove cohesion between intact blocks. As water infiltrates the mass, any downslope
component increases shear stress,
v
, and provides an uplifting force
u
. This reduces
normal stress to
effective
stress and may reduce the friction angle by
x
to a residual value.
Their collective impact is shown by
discontinuous rock mass strength
in dry (DRS
d
)
and wet (DRS
w
) states and the Mohr-Coulomb equation is modified to
or simplified to
where τ′ = effective shear stress, increased by the weight of water. This restates the
balance of shear stress and strength but has not yet formally introduced the significance
of slope angle and still relates only to rock mass. However, the modified equation applied
to discontinuous rock mass is also a reasonable approximation for debris and soil on
slopes, with a little qualification. Cohesion = 0 in discontinuous rock mass and applies
equally to large, loose blocks or uncohesive soil grains on a sloping surface. We can
apply remaining Mohr-Coulomb criteria to such a block or grain and see its
sliding
resistance
, R, on a slope of known angle, given as
where
c
= cohesion (zero),
A
is the block/grain-to-slope contact area,
W
= block/grain
weight,
B
= slope angle and = friction angle. However, part of the mass is mobilized
downslope by gravity and limiting equilibrium reflects a balance between
perpendicular
and
tangential
forces. In the case shown in Figure 2, water behind and beneath the block,
respectively, exerts shear stress and reduces effective stress.
