A Three Dimensional Study on the Probability of Slope Failure(II)

사면(斜面)의 삼차원(三次元) 파괴확률(破壞確率)에 관(關)한 연구(硏究)(II)

The probability of failure is used to analyze the reliability of three dimensional slope failure, instead of conventional factor of safety. The strength parameters are assumed to be normal variated and beta variated. These are interval estimated under the specified confidence level and maximum likelihood estimation. The pseudonormal and beta random variables are generated using the uniform probability transformation method according to central limit theorem and rejection method. By means of a Monte-Carlo Simulation, the probability of failure is defined as; Pf=M/N N : Total number of trials M : Total number of failures Some of the conclusions derived from the case study include; 1. Three dimensional factors of safety are generally much higher than 2-D factors of safety. However situations appear to exist where the 3-D factor of safety can be lower than the 2-D factor of safety. 2. The F3/F2 ratio appears to be quite sensitive to c and ${\phi}$ and to the shape of the 3-D shear surface and the slope but not to be to the unit weight of soil. 3. In cases that strength parameters are assumed to be normal variated and beta variated, the relationships between safety factor and the probability of failure are fairly consistent, regardless of the shape of the 3-D shear surface and the slope. 4. As the c-value is increased, the probability of failure for the same safety factor is increased and as the ${\phi}-value$ is increased, the probability of failure for the same safety factor is decreased.