Modified Harmony Methods for Slope Stability Problems - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 141

y

x U

x n+1

x L

y i,max

V n+1

y=y g (x)

…

x u

x n , y n

x l x 1

V n

V 1

x i , y i α i

x 2 , y 2

V i y=R(x)

V 2

y i,min

0

x

Fig. 1. A typical slip surface obtained by conventional procedure

+ −
=+

x x

xx

n 1 1

×− = ( i 1), i 2, ..., n (1)

i 1

n

()
()

⎧
⎨ ⎩

y = y x

i ,max g i

, i = 2, ..., n (2)

y = R x

i ,min i

The unacceptable slip surface as shown in Figure 1 (dash line) is obtained by random
numbers. In order to render it to be kinematical, a correcting procedure is proposed.

x n+1

y

V n+1

V n

( x n , y n )

y 2max

x l

β n+1

V 1

V 3

β 2

V 2

( x 3 , y 3 )

( x 2 , y 2 )

y 2min y = R ( x )

x

Fig. 2. Procedure for generating trial slip surface