Civil Engineering Reference
In-Depth Information
The limit equilibrium method combines features of the upper and lower bound
methods. The geometry of the slip surfaces must form a mechanism that will allow
collapse to occur, but they may be any shape so they need not meet all the requirements
of compatibility (see Sec. 19.3). The overall conditions of equilibrium of forces on
blocks within the mechanism must be satisfied, but the local states of stress within the
blocks are not investigated. Although there is no formal proof that the limit equilibrium
method leads to correct solutions, experience has shown that the method usually gives
solutions that agree quite well with observations of the collapse of real structures and
the method is firmly established among the techniques of geotechnical engineering.
20.2 Simple limit equilibrium solutions
Two simple problems, one for drained loading and one for undrained loading, are
shown in Figs. 20.l and 20.2. These illustrate the general principles of the limit equi-
librium method. Figure 20.1(a) shows part of a very long slope in soil where the pore
pressures are zero. The problem is to determine the critical slope angle
i
c
when the
Figure 20.1
Limit equilibrium solution for stability of an infinite slope for drained loading.
Figure 20.2
Limit equilibrium solution for the bearing capacity of a foundation for undrained
loading.
