Probabilistic structural analysis and the Gaussian transformation of random variables

Young, D. S.
Organization: Society for Mining, Metallurgy & Exploration
Pages: 5
Publication Date: Jan 1, 1987
The random variable transformation technique was introduced to make probabilistic structural analysis simple for such structures as slopes, dams, foundations, or retaining walls, where two shear strength parameters are required to analyze their stability by deterministic engineering methods. The Gaussian transformation was performed by using the Hermite orthogonal polynomial function. This transforms the experimental histogram into the standard normal distribution, whose mean is zero with a variance of one. Then, the transformed standard Gaussian variable was used for the bivariate normal probability analysis on the structure. The Gaussian transformation technique and the Hermite polynomial functions were chosen because the bivariate joint normal distribution is well-known and easily available for engineers. The binormal probability analysis was made on the probability region of a certain confidence level by superposing the critical line on the same probability region that divides the region into two zones: stable and unstable zones. The critical line was determined from the back calculation of the deterministic engineering method of the structural design. Finally, the probability of structural failure at a desired confidence level was calculated by simply integrating the volume of the binormal density surface above the unstable zone in the probability region. A simple case of slope analysis is introduced to illustrate this probabilistic approach, and its effectiveness and simplicity is demonstrated.
Full Article Download:
(343 kb)