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

270 PLASTIC EQUILIBRIUM IN SOILS
Z° /
?. y
if
9
AMEN
.�a
� 7
M M M W, 011-0
0
h
� 6
0
� 5
a
390 60 70 60 SO 40- 30° 20- W 0'
Vo,lues of slope onq /e /d, deg
Figure 35.3 Relation between stability factor N, and slope
angle [3 for different values of depth factor nd (after Taylor
1937).
If failure occurs along a toe circle, the center of the
critical circle can be located by laying off the angles a
and 28, as shown in Fig. 35.2a. Values of a and 9 for
different slope angles R are given in Fig. 35.4a. If failure
occurs along a midpoint circle tangent to the firm base,
the position of the critical circle is determined by the
horizontal distance n_LH from the toe of the slope to the
circle (Fig. 35.2b). Values of n, can be estimated for
different values of nd and [3 by means of the chart
(Fig. 35.4b).
If the clay beneath a slope consists of several layers
with different average undrained shear strengths, [s„] i,
1412, etc., or if the surface of the ground is irregular (Fig.
35.5), the center of the critical circle must be determined
by trial and error. Inasmuch as the longest part of the
real surface of sliding should be located within the softest
stratum the trial circle should also satisfy this condition.
If one of the upper layers is relatively soft, the presence
of a firm base at considerable depth may not enter into
the problem, because the deepest part of the surface of
sliding is likely to be located entirely within the softest
stratum. For example, if the undrained shear strength 1412
of the second stratum in Fig. 35.5 is much smaller than
the undrained shear strength [su]3 of the underlying third
layer, the critical circle will be tangent to the upper surface
of the third stratum instead of the firm base.
For each trial circle we compute the average shearing
stress T which must act along the surface of sliding to
balance the difference between the moment W1 l 1 of the
driving weight and the resisting moment W212. The value
Of T is
5
0
C4
0 30
20
/0
J
l4
a
�3
�2
0
Page H -3 of 5
h qh" M"
PAAF
MEN
Values of J3
A
,
3
r�
_
,I
tea.
/o
_
r
MENS
Z° /
?. y
if
9
AMEN
.�a
� 7
M M M W, 011-0
0
h
� 6
0
� 5
a
390 60 70 60 SO 40- 30° 20- W 0'
Vo,lues of slope onq /e /d, deg
Figure 35.3 Relation between stability factor N, and slope
angle [3 for different values of depth factor nd (after Taylor
1937).
If failure occurs along a toe circle, the center of the
critical circle can be located by laying off the angles a
and 28, as shown in Fig. 35.2a. Values of a and 9 for
different slope angles R are given in Fig. 35.4a. If failure
occurs along a midpoint circle tangent to the firm base,
the position of the critical circle is determined by the
horizontal distance n_LH from the toe of the slope to the
circle (Fig. 35.2b). Values of n, can be estimated for
different values of nd and [3 by means of the chart
(Fig. 35.4b).
If the clay beneath a slope consists of several layers
with different average undrained shear strengths, [s„] i,
1412, etc., or if the surface of the ground is irregular (Fig.
35.5), the center of the critical circle must be determined
by trial and error. Inasmuch as the longest part of the
real surface of sliding should be located within the softest
stratum the trial circle should also satisfy this condition.
If one of the upper layers is relatively soft, the presence
of a firm base at considerable depth may not enter into
the problem, because the deepest part of the surface of
sliding is likely to be located entirely within the softest
stratum. For example, if the undrained shear strength 1412
of the second stratum in Fig. 35.5 is much smaller than
the undrained shear strength [su]3 of the underlying third
layer, the critical circle will be tangent to the upper surface
of the third stratum instead of the firm base.
For each trial circle we compute the average shearing
stress T which must act along the surface of sliding to
balance the difference between the moment W1 l 1 of the
driving weight and the resisting moment W212. The value
Of T is
5
0
C4
0 30
20
/0
J
l4
a
�3
�2
0
Page H -3 of 5
h qh" M"
PAAF
MEN
Values of J3
160° 6-0° 404 30° 200 /00 0°
values of 13
Figure 35.4 (a) Relation between slope angle 0 and para
ters a and 6 for location of critical toe circle when R is greater
than 53 °; (b) relation between slope angle R and depth factor
nd for various values of parameter n,, (after W. Fellenius 1927).
rirm acz5e
Figure 35.5 Base failure in stratified cohesive soil.
A
,
3
r�
_
,I
tea.
/o
_
r
160° 6-0° 404 30° 200 /00 0°
values of 13
Figure 35.4 (a) Relation between slope angle 0 and para
ters a and 6 for location of critical toe circle when R is greater
than 53 °; (b) relation between slope angle R and depth factor
nd for various values of parameter n,, (after W. Fellenius 1927).
rirm acz5e
Figure 35.5 Base failure in stratified cohesive soil.