Modified Harmony Methods for Slope Stability Problems - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 150

Table 1. Geotechnical parameters for example 1

(kN/m 3 )

γ

Layers c' (kPa) φ ' (degree)

1 19.0 15.0 20.0

2 19.0 17.0 21.0

3 19.0 5.00 10.0

4 19.0 35.0 28.0

slope geometry
NHS1
NHS2

51

49

47

45

43

41

15 40

10 20 25 30 35

Fig. 8. Geotechnical profile and critical solution for example 1

Figure 8 while the soil parameters are given in Table 1 ( ' means the unit

weight, effective cohesive strength and effective friction of soil). Soil layer 3 is a thin
irregular weak layer and the Spencer method [21] is used to calculate the factor of
safety. Since soil layer 3 is thin with poor soil parameters, many control variables
should lie within this region which is not easily determined automatically from the
OHS. This situation is particularly important when the number of control variables is
large which will be demonstrated. The results shown in Figure 10 have clearly illus-
trated that the performance of the OHS is poor under this case, while the improved
harmony method give much lower factor of safety with similar critical slip surface as
shown in Figure 8.
All stochastic optimization methods rely on the use of some parameters which are
difficult to be determined for general case. In general, these parameters are based on
the statistics from large number of numerical tests. Due to the special problems in
slope stability analysis as mentioned in previous section, the authors view that the
performance of the algorithm with respect to the use of optimization parameters is
very important and a statistical check has been carried out in this chapter. The ran-
domly generated 50 series of parameters are used to check the robustness of the pre-
sent algorithm. From Figure 9, the results corresponding to the 50 series of parameters
are mainly located in the range of 1.28 to 1.33, with only one result higher than 1.40
and two results higher than 1.35. The average value of the 50 factors of safety is 1.31
and the average number of NEOF is 11,617.

γ , c' and φ