小样本条件下砂砾石坝料级配特征参数的贝叶斯估计方法

筑坝材料干密度具有强烈的级配相关性，受P5含量、最大粒径、曲率系数等级配特征参数的影响尤为显著。然而在实际工程中，坝料级配参数通常是在大坝碾压施工结束后采用筛分法对质量检测试坑挖取的坝料进行筛分得到的。对于某一填筑单元工程而言，碾压区域的挖坑检测数据极少，导致目前大坝碾压智能监控系统中的土石方压实质量评估模型并未能够有效地考虑级配特征参数对压实质量的影响。鉴于此，为构建大坝填筑材料级配特征参数的总体分布，本文以大石门水利枢纽沥青混凝土心墙砂砾石坝的坝壳料碾压质量挖坑检测得到的小样本级配数据为研究对象，通过拟合优度检验确定以威布尔分布为小样本数据的分布模型，并利用参数化Bootstrap方法和非参数核密度估计法确定了小样本数据条件下待估参数的先验分布。进而利用贝叶斯理论结合现场某一碾压单元质量检测挖坑试验数据对先验分布加以修正得出了待估参数的后验分布。最后采用混合Gibbs抽样方法对后验分布进行模拟仿真求解，给出了基于贝叶斯理论的两参数后验威布尔分布估计结果，为大坝填筑施工过程中实时准确评估砂砾石坝料的压实特性提供了重要的数据支撑。

Bayesian estimation method for grading characteristic parameters of sand-gravel dam materi- al under small sample condition

The dry density of dam-building materials has strong gradation correlation,which is particularly affected by some grading characteristic parameters such as P5 content,maximum particle size and curvature coefficient. However,in practical engineering,the grading parameters of dam materials are usually obtained by screening the dam materials excavated from the quality test pit after the rolling construction. For a certain filling unit,there are few detected data from test pits in the filling construction area,so the existing compaction quality model of earthwork in the dam compaction monitoring system cannot effectively consider the impact of gradation characteristic parameters on compaction density. In view of this,in order to construct population distribution of the grading characteristic parameters of the dam filling material,this paper takes the small sample data of grading characteristic parameters obtained from test pits sampling of the asphalt concrete core sand-gravel dam of the Dashimen Water Conservancy Project as the research object. Firstly,the Weibull distribution was selected as the small sample data distribution through goodnessof-fit tests. Secondly,the parameterized Bootstrap method and the non-parametric kernel density estimation method were used to determine the prior distribution under small sample data. Furthermore,the posterior distribution of parameters is obtained by modifying the prior distribution with the Bayesian method combined with the excavation test data of a certain work unit quality inspection on site. Finally,the mixed Gibbs sampling method is used to simulate and solve the posterior distribution,and the estimation results of two-parameter posterior Weibull distribution based on Bayesian theory are obtained,which provides important data support for real-time and accurate evaluation of the compaction characteristics of sand-gravel dam materials during the construction of the dam.