Probabilistic density function estimation of geotechnical shear strength parameters using the second Chebyshev orthogonal polynomial

A method to estimate the probabilistic density function (PDF) of shear strength parameters was proposed. The second Chebyshev orthogonal polynomial(SCOP) combined with sample moments (the origin moments) was used to approximate the PDF of parameters. χ~2 test was adopted to verify the availability of the method. It is distribution-free because no classical theoretical distributions were assumed in advance and the inference result provides a universal form of probability density curves. Six most commonly-used theoretical distributions named normal, lognormal, extreme valueⅠ, gama, beta and Weibull distributions were used to verify SCOP method. An example from the observed data of cohesion c of a kind of silt clay was presented for illustrative purpose. The results show that the acceptance levels in SCOP are all smaller than those in the classical finite comparative method and the SCOP function is more accurate and effective in the reliability analysis of geotechnical engineering.