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Also, a bias in selecting this angle is introduced by using the square of the random number:
(E.1)
where R is the random number and the angles are as defined in Fig. E.1.
The probability of the location of the initial failure surface segment within an upper and lower
angular limit range that has been subdivided into ten equal sectors is illustrated in Fig. E.2. From
this figure, one can see that the introduced bias results in the initial segment being located within
the sector closest to the lower angular limit for about 32 percent of the cases. The probability for a
segment close to the upper angular limit is only about 5 percent.
This bias leads to initial segments
that are nearer to the lower angular
limit and is introduced primarily to
obtain trial surfaces that are deeper.
During the development of the STABL
program, it was found that a poor
distribution of the factor of safety
values was obtained if the initial
segment was given an equal likelihood
of being oriented in any direction
within the specified angular directional
limits.
Once an initial segment is selected,
the remaining portion of the proposed
circular surface is generated such that it
intersects the ground surface within the
specified termination range. These
Fig. E-2.
Probability of orientation of initial line
circles will all start from the initiation
segment for circular and noncircular
point (near the toe in Fig E.3), have a
surfaces generation
common first segment and be confined
within the region shown in Fig. E.3. All such surfaces are generated so that the termination point is
always above the elevation of the initiation point.
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