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optimizing method in many engineering problems, which is learned from the way of evolution of life,
especially mechanism of genes.
METHODOLOGY FOR ESTIMATION OF SAFETY FACTOR
Response Analysis and Safety Factor
Dynamic response of a slopes is calculated in time domain by
Newmark p method which is one of direct integral methods, in this
study. Viscous boundaries can be adopted for the base and the four
sides of a FEM model As shown in Fig.l, the 3-d model is
connected with four 2-d free field models by viscous boundaries.
The each 2-d model is also connected with two 1-d free field
models by viscous boundaries. The each model has also viscous
boundary at the base.
In conventional 2-d analysis, sliding surface is usually modeled
by a set of lines or an arc. As a natural extension to 3-d analysis,
a sliding surface is modeled by a set of planes or an oval The
modeled sliding surface is divided into many triangle panels for
the numerical calculations. The vertex of the panel is
determined from the intersection of side of FEM element and
the sliding surface. Fig.2 shows two triangle panels, cl-c3-c4
and cl-c2-c3, in an hexahedron element.
Safety factor of the modeled sliding surface is obtained as
the ratio of resistance force to sliding force. The resistance
force working on a triangle panel is calculated by normal stress
to the panel, area of the panel and material strength (cohesion
and internal friction). Sliding force on the panel is also
calculated by shear stress to sliding direction and the area of the
panel Safety factor S/ is obtained as the ratio of total sum of
each force as follows.
Fig.l Free Fields and
Boundary Conditions
Fig.2 Triangle Panels Forming
Sliding Surface
where, RI : resistance on panel i^A\: area of panel f, t: time,0 p 0 2 : directions of excitation and sliding
S l : sliding force on panel z, n : number of the panels, x : a vector of parameter which define a sliding
surface. Minimum value with respect to these parameters is used as a safety factor of a slope or ground.
Optimization by Real Coded Genetic Algorithm
The problem to search the sliding surface with minimum safety margin is formulated as optimization
problem, in which the objective function is safety factor, and design parameters are parameters
providing the sliding surface such as center, radius of the surface, and so on. In this optimization
problems, there might be many local optimum solutions. In that case, local search method such as