Civil Engineering Reference
In-Depth Information
φ
s
are strength parameters required for a safe design, as discussed in
Sec. 18.5. The idea is to reduce the soil strength and then ensure that the slope is
in equilibrium with the lower strength. Values for
F
s
depend on a number of things,
including the consequences of failure and the reliability of the measurements of soil
strength. Typically engineers use values for
F
s
in the range 1.25 to 1.5. This is usually
enough for a safe design but may not be enough to prevent ground movements which
are sufficiently large to damage nearby structures.
Alternatively, engineers apply partial factors to each variable in the analysis. For
undrained, total stress analyses the variables are the slope height and angle, the unit
weight of the soil and the undrained strength and partial factors can be applied to
each. For drained effective stress analyses the variables are the slope height and angle,
the unit weight of the soil, the critical state friction angle and the pore pressure and,
again, partial factors can be applied to each. The values of the partial factors should
reflect the uncertainty with which each variable can be determined.
Usually the slope height and angle and the unit weight of the soil can be deter-
mined reliably and the partial factors for these can be close to 1.0. The critical state
friction angle can also be measured reliably and it is the worst credible value: the
strength will not be less than the critical state strength unless movements are suffi-
ciently large to mobilize the residual strength. In practice measurements of undrained
strength are variable and tend to increase with depth so the partial factor will depend
on whether the values for
s
u
are worst credible, moderately conservative or some
other value. For effective stress analyses the pore pressure must be determined from
a flownet or from considerations of the long term groundwater conditions. It is
usually quite easy to determine the long term pore pressures in which case the par-
tial factor can be 1.0. For effective stress stability analyses it is logical to take
the critical state friction angle, the worst credible pore pressures and apply partial
factors of 1.0: it cannot get worse than the worst credible. In the end, however,
it is for the engineer to choose the design parameters and their associated partial
factors.
where
s
us
and
21.4 Stress changes in slopes
Natural slopes are usually eroded very slowly and the soil is essentially drained so
that pore pressures are governed by steady state seepage from the ground towards the
excavation. Man-made slopes are often constructed quite quickly and in clays the soil
will be essentially undrained during the excavation.
The changes of total and effective stress during undrained slope excavation are illus-
trated in Fig. 21.4. In Fig. 21.4(a) the total stresses on a slip surface are
and
the pore pressure is illustrated by the rise of water in a standpipe. (For simplicity the
excavation is kept full of water so that the phreatic surface is level and the initial and
final pore pressures are the same.)
In Fig. 21.4(b) the total stress path is A
τ
and
σ
→
B; this corresponds to a reduction
in
σ
due to the excavation and an increase in
τ
because the slope height and/or angle
are increased. The effective stress path is A
B
, which corresponds to undrained
loading at constant water content, as shown in Fig. 21.4(c). The exact effective stress
path A
→
→
B
in Fig. 21.4(b) will depend on the characteristics of the soil and its initial
state or overconsolidation ratio, as discussed in Chapter 11.
