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methods will face similar problems in the choice of parameters, but the present modi-
fied proposals have greatly reduced this limitation which is critical for the original
formulation.
The comparisons of results among OHS, NHS1 and NHS2, as seen in Figure14,
show that the OHS results locate much higher than those by NHS1 and NHS2, al-
though the NEOF required by OHS is smaller than those used by NHS1 and NHS2.
This is mainly because, after
N
2
iterations, there is no improvement on the safety fac-
tor obtained so far, which is called precocity. On the other hand, the NHS1 and NHS2
can improve the results found so far within
N
2
iterations, so the NEOF used by them
is always larger than that used by OHS. The largest one is not more than 30,000 and
this is acceptable as the solution time is less than 5 minutes.
Fig. 14.
Comparison of safety factor and NEOF with different number of slices
5.4 Example 4
Example 4, as shown in Figure 15, is an interesting problem which is worth consid-
eration. The second layer of soil is only 1 mm thick so that it cannot be seen from the
8
7.5
7
6.5
6
5.5
5
4.5
4
3.5
3
2.5
2
0
1
2
3
4
5
6
7
8
9
10
11
12
Fig. 15.
Failure surface without domain transformation method (safety factor = 1.486)
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