一种推断岩体裂隙几何参数概率模型的新方法

A NEW METHOD OF DEFINITION OF PROBABILISTIC DENSITY FUNCTIONS OF GEOMETRY PARAMETERS FOR ROCKMASS FISSURE NETWORK

提出推断岩体裂隙几何参数概率模型的切比雪夫多项式拟合法。基于数值逼近原理,并根据工程现场的样本矩,运用切比雪夫多项式来推断岩体裂隙几何参数的概率密度函数,同时采用精度较高的χ2检验法,从理论上证明所求密度函数的正确性和实用性。研究结果表明,根据切比雪夫多项式方法所得到的逼近表达式非常接近最常用的经典分布曲线(正态分布、对数正态分布、伽马分布、指数分布)。此外,根据样本数据得出的某隧道裂隙岩体产状的概率密度函数,与实际统计所得频率分布非常接近,精度优于传统的经典分布拟合法。

Chebyshe orthogonal polynomial approximation(CPA) method is introduced in this paper.Based on numerical approximation theory,CPA is employed to define the probabilistic density functions(PDF) of the geometry parameters of rockmass fissure network theory from the sample data.χ2 test method is used to verify the availability of this method.Four classical distributions—the normal distribution,the log-normal distribution,the exponential distribution and Gama distribution,are compared with the corresponding CPA density functions generated from the moments.Little differences are found out between classical distribution and its corresponding CPA density function.The density distribution of joint tendency from field data of a freeway tunnel is taken as an example.The results of the case study show that the CPA density function is more accurate than fitting density function by using classical distributions.