岩土参数概率密度函数的正交多项式推断

Assessment of Probability Distribution of Mechanical Parameters of Rock & Soil by using Legendre Polynomials

岩土参数的概率密度函数在岩土工程可靠性的分析中有很重要的作用。文章基于数值逼近原理,直接根据试验样本矩,运用勒让德正交多项式来拟合岩土随机参数的概率密度函数。并且用χ2法进行检验,根据有限比较法确定其中的最佳分布概型,在理论上证明该方法的正确性和实用性。通过算例表明,所得到的逼近表达式有很好的拟合性能,数值计算稳定,可以满足岩土工程可靠性分析的要求。

The probabilistic distribution function of random variables （e.g. parameters of rock and soil） is very important for stochastic reliability analysis in rock and soil engineering. Legendre polynomial approximation （LPA） method is presented to define the probabilistic density functions of the parameters of rock and soil in this paper. Based on numerical approximation theory, Legendre polynomial is introduced to match the probabilistic density function of the parameters of rock and soil froum the sample data. a test is carried out to verify the availability of this method,then the optimum fit of probabilisfic model can be generated by using finite contrast method（FGM）. The LPA density function of a soil cohesion is generated using the moments about the origin. The results of the case study show that the LPA density hmction is accurate and can be used in stochastic reliability analysis of rock and soil engineering.