2011-09-30_PERMIT FILE - C1980007A ‎(13)‎

• Permit No: C1980007A
• IBM Index Class Name: Permit File
• Doc Date: 9/30/2011
• Doc Name: Haul Road Geotechnical Design Method
• Section_Exhibit Name: Exhibit 82 Appendix H
• Media Type: D
• Archive: Yes

272 PLASTIC EQUILIBRIUM IN SOILS
Hc =Nsc
which is identical with Eq. 35.3, except that NS depends
not only on (3 but also on (�'. Figure 35.6b shows the
relationship between (3 and N, for different values of (�'.
At a given value of the slope angle (3, N, increases at
first slowly and then more rapidly with increasing values
of (�'. When (�' = (3, N, becomes infinite.
All the points on the curves shown in Fig. 35.6b corre-
spond to failures along toe circles, because theory has
shown that the possibility of a base failure does not exist
unless (�' is smaller than approximately 3 °. Therefore, if
a typical base failure has occurred in a fairly homoge-
neous soil in the field, it can be concluded that it was a
constant volume undrained failure with (� = 0 and c = s,,.
35.9 Irregular Slopes on Nonuniform Soils,
Circular Surface of Sliding
If a slope has an irregular surface that cannot be repre-
sented by a straight line, or if the surface of sliding is
likely to pass through several materials with different
values of c and (�', the stability can be investigated conve-
niently by the method of slices. According to this proce-
dure a trial circle is selected (Fig. 35.7a) and the sliding
mass subdivided into a number of vertical slices 1, 2, 3,
etc. Each slice, such as slice 2 shown in Fig. 35.7b, is
acted on by its weight W, by shear forces T and normal
forces E on its sides, and by a set of forces on its base.
These include the shearing force S and the normal force
P. The forces on each slice, as well as those acting on
the sliding mass as a whole, must satisfy the conditions
of equilibrium. However, the forces T and E depend on
the deformation and the stress - strain characteristics of the
slide material and cannot be evaluated rigorously. They
can be approximated with sufficient accuracy for practi-
cal purposes.
The simplest approximation consists of setting these
forces equal to zero. Under these circumstances, if the
(o)
rb
T„
Ems_' I
Tn..1 0,S
P�
�t
!b)
Figure 35.7 Method of slices for investigating equilibrium
of slope located above water table. (a) Geometry pertaining to
one circular surface of sliding; (b) forces on typical slice such
as slice 2 in (a).
Page H -5 of 5
entire trial circle is located above the water table and there
are no excess pore pressures, a condition corresponding to
a drained failure, equilibrium of the entire sliding mass
requires that
r1 W sin a = rIS (35.5)
If s is the shearing strength of the soil along 1, then
and
from which
s s b
S = -1 =— (35.6)
F F cos a
W sin a = r E sb (35.7)
F cos a
F = 1(sb1cos a) (35.8)
1W sin a
The shearing strength s, however, is determined by
s= c +a tan V
where a is the normal stress across the surface of sliding
1. To evaluate a we consider the vertical equilibrium of
the slice (Fig. 35.7b), from which
and
Therefore
and
Let
Then
a —
W= S sin a +P cos a
P= Pcosa= W — Ssina (35.9)
s =c+(f — �sinoL tangy'
= c +(W —Ftan al tan gy'
c + (Wlb) tan �'
S __ 1 + (tan a tan �')IF (35.10)
ma = (1 + tan a tan (�') cos a (35.11)
I [c + (Wlb) tan (�']b
F = 1W s n, a (35.12)
Equation 35.12, which gives the factor of safety F for
the trial circle under investigation, contains on the right