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阮永芬, 魏德永, 杨均, 高骏, 刘克文, 彭栓栓. 用Bayes法及后验分布极限确定土力学参数[J]. 岩土工程学报, 2020, 42(3): 438-446. DOI: 10.11779/CJGE202003005
引用本文: 阮永芬, 魏德永, 杨均, 高骏, 刘克文, 彭栓栓. 用Bayes法及后验分布极限确定土力学参数[J]. 岩土工程学报, 2020, 42(3): 438-446. DOI: 10.11779/CJGE202003005
RUAN Yong-fen, WEI De-yong, YANG Jun, GAO Jun, LIU Ke-wen, PENG Shuan-shuan. Determination of soil mechanics parameters based on Bayes method and posterior distribution limit[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(3): 438-446. DOI: 10.11779/CJGE202003005
Citation: RUAN Yong-fen, WEI De-yong, YANG Jun, GAO Jun, LIU Ke-wen, PENG Shuan-shuan. Determination of soil mechanics parameters based on Bayes method and posterior distribution limit[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(3): 438-446. DOI: 10.11779/CJGE202003005

用Bayes法及后验分布极限确定土力学参数

Determination of soil mechanics parameters based on Bayes method and posterior distribution limit

  • 摘要: 岩土力学参数在空间分布上具有很大随机性,现有研究都是从参数小样本去推断大样本,这难免会存在一些失误。若样本数量足够大,正态分布会变得高度集中在某个值附近,勘察失误或偶然因素导致岩土参数统计误差的影响会越来越小,据此提供给勘察设计的岩土力学参数就更准确。根据收集的滇池湖相沉积的离散性高的泥炭质土、粉土及黏土的黏聚力c和内摩擦角φ的大量试验数据,用Bayes大样本法对几种土的力学参数进行分析,充分利用已采集样本带来的先验信息,推求土力学参数的后验信息,并得到贝叶斯估计区间。当Fisher信息量确定后,土力学参数正态分布均值μ验分布可用一个与先验分布无关的正态分布来逼近,就可得到当样本量趋于无穷时参数的收敛取值,并用后验分布极限对土力学参数的相合性及渐近正态性进行检验分析。对滇池湖相沉积土力学指标进行大样本分析,推求土力学指标的收敛值就落在贝叶斯估值区间,充分证明了分析方法的可行性及可靠性。分析结果为地区规范编制及工程经验的积累提供参考,也为设计计算参数取值的合理性提供检验。

     

    Abstract: Geotechnical parameters are of great randomness in spatial distribution, and the existing researches are to infer large samples from small ones, which will inevitably lead to some errors. If the number of samples is large enough, the normal distribution will become highly concentrated near a certain value. The influences of statistical errors of geotechnical parameters will become smaller and smaller resulting from the investigation errors or accidental factors, then the more accurate parameters will be provided during prospective design. According to the collected experimental data of the cohesive force c and the internal friction angle φ of Dianchi Lake facies deposition peat soil, silt and clay with high dispersion, the Bayesian large sample method is used to analyze the mechanical parameters of several soils, the posterior information of mechanical parameters of soils is derived based on the prior information from the collected samples, and the Bayesian estimation interval is obtained. After the Fisher information is determined, the posterior distribution of the mean value μ of the normal distribution of mechanical parameters of soils can be approximated by a normal distribution independent of the prior distribution, and the reliable value of the parameters can be obtained when the sample size tends to infinity. The consistency and asymptotic normality of mechanical parameters of soils are tested and analyzed by the posterior distribution limit. A large sample analysis of the mechanical indexes of the sedimentary soils in Dianchi Lake is carried out. The reliable value of the mechanics index of soils is estimated to fall within the Bayesian evaluation interval, which fully proves the feasibility and reliability of the analytical method. The analysis results may provide reference for the compilation of regional norms and the accumulation of engineering experience, and also a test for the rationality of the design parameters.

     

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