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

If the shape of the surface of sliding is such that it
cannot be represented even approximately by an arc of
a circle, the procedure must be modified according to the
methods described in Article 35.10 in connection with
composite surfaces of sliding.
35.6 Procedure for Investigating Stability of
Slopes
To investigate whether or not a slope on soil with known
shear characteristics will be stable, it is necessary to deter-
mine the diameter and position of the circle that represents
the surface along which sliding will occur. This circle,
known as the critical circle, must satisfy the requirement
that the ratio between the shearing strength of the soil
along the surface of sliding and the shearing force tending
to produce the sliding must be a minimum.
After the diameter and position of the critical circle
have been determined, the factor of safety F of the slope
with respect to failure may be computed by means of the
relation (Fig. 35.1)
F, = sr dle2 (35.2)
Will — W212
wherein r represents the radius of the critical circle and
diet the length of the surface of sliding.
Like the passive earth pressure of a mass of soil, the
stability of a slope may be investigated by trial or, in
simple cases, by elementary analytical methods. To make
the investigation by trial, different circles are selected,
each representing a potential surface of sliding. For each
circle, the value F (Eq. 35.2) is computed. The minimum
value represents the factor of safety of the slope with
respect to sliding, and the corresponding circle is the
critical circle.
The elementary analytical solutions can rarely be used
to compute the factor of safety of a slope under actual
conditions, because they are based on greatly simplified
assumptions. They are valuable, however, as a guide for
estimating the position of the center of the critical circle
and for ascertaining the probable character of the failure.
In addition, they may serve as a means for judging
whether a given slope will be unquestionably safe,
unquestionably unsafe, or of doubtful stability. If the
stability seems doubtful, the factor of safety with respect
to failure should be computed according to the procedure
described in the preceding paragraph.
The solutions are based on the following assumptions:
Down to a given level below the toe of the slope, the
soil is perfectly homogeneous. At this level, the soil rests
on the horizontal surface of a stiffer stratum, known as
the firm base, which is not penetrated by the surface of
sliding. The slope is considered to be a plane, and it is
located between two horizontal plane surfaces, as shown
in Fig. 35.2. Finally, the weakening effect of tension
Page H -2 of 5
ARTICLE 35 STABILITY OF SLOPES 269
cracks is disregarded, because it is more than compen-
sated by the customary margin of safety. The following
paragraphs contain a summary of the results of the
investigations.
35.7 Slope Failures under Undrained Conditions
The average shearing resistance s per unit of area of a
potential surface of sliding in homogeneous clay under
undrained conditions (Article 20) is referred to as the
mobilized undrained shear strength. That is,
s = s„ (mob) (18.5)
If s„ (mob) is known, the critical height H, of a slope
having a given slope angle R can be expressed by the
equation,
H� = NS s„ (mob) (35.3)
y
In this equation the stability factor NS is a pure number.
Its value depends only on the slope angle R and on the
depth factor nd (Fig. 35.2b), which expresses the depth
at which the clay rests on a firm base. If a slope failure
occurs, the critical circle is usually a toe circle that passes
through the toe b of the slope (Fig. 35.2a). However, if
the firm base is located at a short distance below the level
of b, the critical circle may be a slope circle that is tangent
to the firm base and that intersects the slope above the
toe b. This type of failure is not shown in Fig. 35.2. If
a base failure occurs, the critical circle is known as a
midpoint circle, because its center is located on a vertical
line through the midpoint m of the slope (Fig. 35.2b).
The midpoint circle is tangent to the firm base.
The position of the critical circle with reference to a
given slope depends on the slope angle R and the depth
factor nd. Figure 35.3 contains a summary of the results
of pertinent theoretical investigations. According to this
figure, the failure of all slopes rising at an angle of more
than 53° occurs along a toe circle. If P is smaller than
53 °, the type of failure depends on the value of the depth
factor nd and, at low values of nd, also on the slope angle
P. If rtd is equal to 1.0, failure occurs along a slope circle.
If nd is greater than about 4.0, the slope fails along a
midpoint circle tangent to the firm base, regardless of the
value of P. If nd is intermediate in value between 1.0
and 4.0, failure occurs along a slope circle if the point
representing the values of nd and R lies above the shaded
area in Fig. 35.3. If the point lies within the shaded area,
failure occurs along a toe circle. If the point is below the
shaded area, the slope fails along a midpoint circle tangent
to the firm base.
If the slope angle (3 and the depth factor nd are given,
the value of the corresponding stability factor N, (Eq.
35.3) can be obtained without computation from Fig.
35.3. The value of N, determines the critical height H,
of the slope.