Civil Engineering Reference
In-Depth Information
Ultimate stability of soil structures
using bound methods
19.1 Introduction
In previous chapters I considered the behaviour of single elements of soil, either in the
ground or in laboratory tests, and I developed simple theories for strength of soil and
simple constitutive equations relating increments of stress and strain. What we have to
do now is to apply these theories to the behaviour of geotechnical structures such as
foundations, slopes and retaining walls. As discussed earlier, solutions for problems in
mechanics must satisfy the three conditions of equilibrium, compatibility and material
properties. It is fairly obvious that complete solutions, satisfying these conditions with
the material properties for soil, will be very difficult to obtain, even for very simple
foundations and slopes.
First, I will consider the conditions of ultimate collapse where the important material
property is the soil strength. Remember that, as always, it is necessary to distinguish
between cases of undrained and drained loading. For undrained loading the strength
of soil is given by
τ
=
s
u
(19.1)
where
s
u
is the undrained strength. For drained loading where pore pressures can be
determined from hydrostatic groundwater conditions or from a steady state seepage
flownet the strength is given by
τ
=
σ
tan
φ
=
φ
(
σ
−
u
) tan
(19.2)
φ
is a friction angle. As discussed in Sec. 9.2 soil has a peak strength, a crit-
ical state strength and a residual strength which are mobilized at different strains or
displacements. The factors which determine which strength should be used in stability
calculations are discussed in Chapter 18.
Even with these relatively simple expressions for soil strength it is still quite dif-
ficult to obtain complete solutions and the standard methods used in geotechnical
engineering involve simplifications. There are two basic methods: the bound methods
described in this chapter and the limit equilibriummethod described in the next chapter.
Both methods require approximations and simplifications which will be discussed in
due course.
where
