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Table 2.
Orthogonal test table by NHS1 and NHS2
Results
λ
HMCR
PAR
NHS1
NHS2
1
1 (0.85)
1 (0.10)
1 (0.3)
1.3196
1.2938
2
1 (0.85)
2 (0.15)
2 (0.4)
1.3325
1.3276
3
1 (0.85)
3 (0.20)
3 (0.5)
1.3542
1.3321
4
1 (0.85)
4 (0.25)
4 (0.6)
1.3391
1.3413
5
2 (0.90)
1 (0.10)
2 (0.4)
1.3370
1.3079
6
2 (0.90)
2 (0.15)
1 (0.3)
1.3492
1.2917
7
2 (0.90)
3 (0.20)
4 (0.6)
1.3265
1.3298
8
2 (0.90)
4 (0.25)
3 (0.5)
1.3245
1.3057
9
3 (0.95)
1 (0.10)
3 (0.5)
1.3616
1.3235
10
3 (0.95)
2 (0.15)
4 (0.6)
1.2924
1.3223
11
3 (0.95)
3 (0.20)
1 (0.3)
1.3050
1.3134
12
3 (0.95)
4 (0.25)
2 (0.4)
1.3171
1.2783
13
4 (1.00)
1 (0.10)
4 (0.6)
1.3509
1.3327
14
4 (1.00)
2 (0.15)
3 (0.5)
1.3262
1.3298
15
4 (1.00)
3 (0.20)
2 (0.4)
1.2998
1.3144
16
4 (1.00)
4 (0.25)
1 (0.3)
1.2914
1.2903
number of parameters and levels result in different values of
F
0.05
and
F
0.01
, and they
can be determined easily from the existing tables), we can conclude that both parame-
ters are insensitive to the NHS2 analysis. The results obtained by NHS1 and NHS2
are almost identical in this problem.
OHS is trapped by the local minima as shown in Figure 10 with relatively poor re-
sults for the safety factor, though the NEOF required by OHS is smaller than those
required by NHS1 and NHS2. OHS located the safety factor within the range of 1.40
to 1.60 with different number of control variables, on the other hand, NHS1 and
NHS2 find the minimum factor of safety cluster around 1.3 which is much better than
the results by OHS. One special advantage of the harmony search is that the number
of evaluations do not increase sharply with the increase in the number of control vari-
ables (number of slice), and this is a very important reason for the adoption of har-
mony search method for large scale slope stability analysis.
5.2 Example 2
Example 2, as shown in Figure 11, is a slope with three layers where an irregular
weak layer is sandwiched between two strong layers. The geotechnical properties for
layers 1 to 3 are friction angle equal to 20°, 10°, and 20°; cohesion equal to 28.73
kPa, 0.0 kPa, and 28.73 kPa; and unit weight 18.84 kN/m
3
for all three layers. The
Spencer's method is adopted to determine the safety factor. As described above, the
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