岩土抗剪强度参数的最优概率分布函数推断方法

发布时间：2018-03-18 16:44

本文选题：抗剪强度参数　切入点：概率分布　出处：《岩土工程学报》2016年S2期 　论文类型：期刊论文

【摘要】：抗剪强度参数最优概率分布形式的推断是保证岩土工程可靠度计算结果精确的基础和前提。现有研究认为大多数抗剪强度参数服从正态或对数正态分布,但是由于岩土参数实际分布区间有限,导致上述分布在使用过程中均存在和实际参数分布区间不匹配的问题。考虑到绝大多数岩土参数存在偏度这一事实,提出以"3?"原理为基础,并考虑偏度进行调整的分布区间确定方法。并基于正态信息扩散原理,提出推断岩土抗剪强度参数概率分布的正态信息扩散法。以水利水电工程中的3组岩基内摩擦角样本作为实例,利用正态信息扩散法推断对应的概率密度函数,并以K-S法进行检验。同时为了考察样本容量对正态信息扩散法以及经典分布拟合法在拟合精度方面的影响,利用蒙特卡洛模拟方法生成已知分布的8组随机样本,样本容量分别为15,20,30,50,100,200,500和1000。研究结果表明:不论对实测样本还是模拟样本,与传统的经典分布拟合法得到的最优分布——对数正态分布相比,正态信息扩散法的检验值均低于对数正态分布,并随着样本容量的增加逐渐趋于收敛,而对数正态分布检验值的收敛趋势相对弱一些。另外,在文中确定的分布区间内,正态信息扩散分布累积概率值的误差约在10-4量级,并且几乎不受样本容量变化的影响;对数正态分布累积概率值的误差在10-3量级,但是受样本容量变化的影响很大,并呈现不规则变化趋势。
[Abstract]:The inference of the optimal probability distribution of shear strength parameters is the basis and prerequisite to ensure the accuracy of the reliability calculation results of geotechnical engineering. It is considered that most of the shear strength parameters are normally or logarithmic normal distribution. However, due to the limited range of the actual distribution of geotechnical parameters, there is a problem of mismatch between the above distribution and the distribution interval of the actual parameters. Considering the fact that most of the geotechnical parameters are biased, this paper puts forward that: "3? "on the basis of the principle, and taking into account the method of determining the distribution interval by adjusting the bias, and based on the principle of normal information diffusion, A normal information diffusion method is proposed to infer the probability distribution of shear strength parameters of rock and soil. Taking three groups of rock foundation friction angle samples in water conservancy and hydropower projects as examples, the corresponding probability density function is inferred by normal information diffusion method. In order to investigate the effect of sample size on the fitting accuracy of normal information diffusion method and classical distribution fitting method, eight groups of random samples with known distribution were generated by Monte Carlo simulation. The sample sizes are 1520 / 30 / 50 / 100 / 100 / 200 and 1000, respectively. The results show that the optimal distribution-logarithmic normal distribution obtained by the classical fitting method is better than that obtained by the classical fitting method for both the measured and simulated samples. The test value of normal information diffusion method is lower than that of logarithmic normal distribution and tends to converge with the increase of sample size, but the convergence trend of test value of logarithmic normal distribution is relatively weak. In addition, in the distribution interval determined in this paper, The error of cumulative probability value of normal information diffusion distribution is about 10-4 order of magnitude, and it is almost unaffected by the change of sample size, while the error of cumulative probability value of logarithmic normal distribution is 10-3 order of magnitude, but it is greatly affected by the change of sample size. And presents irregular change tendency.
【作者单位】：中南大学资源与安全工程学院;
【基金】：国家自然科学基金项目(41102170) 中央高校基本科研业务费专项资金项目(2011QNZT090)
【分类号】：TU43

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