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

WI11 — W212
T =
r ab n
Then, on the basis of the known values of [s,,]1, [s„]2,
[su]3, etc., we compute the average value of s„ (mob) of
the soil along the sliding surface. The factor of safety of
the slope against sliding along the circular trial surface is
F = s„ (mob) (35.4)
The value of F is inscribed at the center of the circle.
After values of F have been determined for several trial
circles, curves of equal values of F are plotted (Fig. 35.5).
These curves may be considered as contour lines of a
depression. The center of the critical circle is located at
the bottom of the depression. The corresponding value
F,ni„ is the factor of safety of the slope with respect
to sliding.
If it is not obvious which of two layers may constitute
the firm base for the critical circle, trial circles must
be investigated separately for each possibility and the
corresponding values of F,w,, determined. The smaller of
the two values is associated with the firm base that gov-
erns the failure and is the factor of safety of the slope.
35.8 Slopes on Soils with Cohesion and Internal
Friction
If the shearing resistance of a soil located above water
table can be expressed approximately by Eq. 26.3
s= c +Q tan ('
the stability of slopes on the soil can be investigated by
the procedure illustrated by Fig. 35.6a. The forces acting
on the sliding mass are its weight W, the resultant cohesion
C, and the resultant F of the normal and frictional forces
acting along the surface of sliding. The resultant cohesion
C acts in a direction parallel to the chord de and is equal
to the unit cohesion c multiplied by the length L of the
chord. The distance x from the center of rotation to C is
determined by the condition that
Cx= cLx =cder
from which x = de r1L. Therefore, the force C is known.
The weight W is also known. Since the forces C, W, and
F are in equilibrium, the force F must pass through the
point of intersection of W and C. Hence, the magnitude
and line of action of F can be determined by constructing
the polygon of forces.
If the factor of safety against sliding is equal to unity,
the slope is on the verge of failure. Under this condition
each of the elementary reactions dF in Fig. 35.6a must
be inclined at the angle 4' to the normal to the circle of
sliding. As a consequence, the line of action of each
4
n
0` B
s
0
0 6
m
e�
390' BO' 70' 60' SO' 40' 30' 20' /0' 0'
Valaes of Slope Angle, A
Page H -4 of 5
ARTICLE 35 STABILITY OF SLOPES 271
Figure 35.6 Failure of slope in material having cohesion and
friction. (a) Diagram illustrating friction- circle method; (b) rela-
tion between slope angle R and stability factor Ns for various
values of (�' (after Taylor 1937).
elementary reaction is tangent to a circle, known as the
friction circle, having a radius
rf = r sin ('
and having its center at the center of the circle of sliding.
The line of action of the resultant reaction F is tangent
to a circle having a radius slightly greater than rf, but as
a convenient approximation we assume that at a factor
of safety equal to unity the line of action of F is also
tangent to the friction circle. The corresponding error is
small and is on the safe side.
For a given value of (�' the critical height of a slope
that fails along a toe circle is given by the equation,
FAA
A
umia�■
mrJEN
ME
EVA
MEN
ENEEMPUMME
MONUMEMEN
MONEMEEME
MEMMMMEMIN
NEOMM
MMEMEMME
■
Figure 35.6 Failure of slope in material having cohesion and
friction. (a) Diagram illustrating friction- circle method; (b) rela-
tion between slope angle R and stability factor Ns for various
values of (�' (after Taylor 1937).
elementary reaction is tangent to a circle, known as the
friction circle, having a radius
rf = r sin ('
and having its center at the center of the circle of sliding.
The line of action of the resultant reaction F is tangent
to a circle having a radius slightly greater than rf, but as
a convenient approximation we assume that at a factor
of safety equal to unity the line of action of F is also
tangent to the friction circle. The corresponding error is
small and is on the safe side.
For a given value of (�' the critical height of a slope
that fails along a toe circle is given by the equation,