Environmental Engineering Reference
In-Depth Information
-12
0
Debris dike
6.1
m
12
0.875
1
0.875
30.5
m
1
San Francisco Bay
mud
24
36
Firm soil
s u from in situ vane shear
tests (kPa)
s u from UU tests on 35 mm
trimmed (kPa)
s u from UU tests on 70 mm
untrimmed (kPa)
0
15
30
45
0
15
30
45
0
15
30
45
0
0
0
5
5
5
c 0 = 9.11
b =1.04
s x = 0.18
c 0 = 1.10
b =1.30
s x = 0.21
c 0 = 0.05
b =1.17
s x = 0.21
10
10
10
15
15
15
20
20
20
Two bad
points
removed
25
25
25
30
30
30
Figure 9.7 Underwater excavated slope in San Francisco Bay mud, and the average s u profile, described by
s u = c 0 + by, and the ± 1 Std. Dev. lines.
UU triaxial tests on untrimmed 70 mm specimens, respectively. For comparison, the cor-
responding F s values for critical circular slip surfaces were 1.23, 1.19, and 1.03, respectively,
slightly higher than those of the critical noncircular slip surfaces. It was noted that measured
strength values were affected by the disturbance and rate of loading effects. Subtle errors
were also caused by extrapolation of the undrained shear strength ( in situ and lab tests data,
available only for the upper 21 m of the Bay mud, from depth 6 m to depth 27 m; Figure
9.7 ) to the full depth of underwater excavation. Since the midpoint of a slip circular arc is at
about the two-thirds depth, this means that in limit equilibrium slope stability analysis, half
the slip surface was based on extrapolated strength.
In the probabilistic analyses by Low and Duncan (2013), FORM analyses based on log-
normal distributions and critical circular slip surfaces produced failure probability values
(by Equation 9.5 ) of 9.7, 19.4, and 45.6%, for undrained shear strength from field vane tests,
UU triaxial tests on trimmed 35 mm specimens, and UU triaxial tests on untrimmed 70 mm
specimens, respectively. These P f values are much higher than the P f of about 0.6% implied
by the commonly required β of 2.5, or P f of 0.14% for a target β of 3.0. Hence, a failure was
not unlikely, and did happen.
FORM analyses can be performed easily with search for the reliability-based critical non-
circular slip surfaces , producing probabilities of failure (by Equation 9.5 ) a few percent-
ages higher than the above-mentioned 9.7-45.6% range (circular slip surfaces) for the three
 
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