单桩竖向承载力的贝叶斯估计及可靠度研究
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摘要
随着经济的快速发展,高层建筑和桥梁大量兴建,可靠性问题在工程中的重要性日益突出。桩基因其承载力高、沉降小、施工方便等优点被广泛地用作为土木工程的基础形式。因此,桩基承载力的可靠性研究具有重要的工程实际意义。但是,目前基桩承载力可靠度研究存在着以下两个问题：(1)基桩承载力的确定没有考虑类似工程的影响,白白浪费了工程经验数据。(2)考虑到工程实际因素,在进行基桩承载力可靠度研究时,收集到的静载荷试验数据的离散性较大,计算出的可靠度指标的误差较大,会给工程造成隐患。本文基于极差理论和贝叶斯统计理论,针对以上两个问题进行了较为系统的研究工作。
由于经济和工期原因,基桩的静载荷试验数据往往很少,并且数据的离散性很大,大大增加了承载力可靠度分析的难度。本文利用数理统计中的极差理论,根据静载试验结果,计算出总体样本的均值和方差。然后,给出了基桩竖向承载力服从对数正态分布时的可靠度计算方法。通过算例分析表明,该方法的计算精度满足工程需要,并为桩基设计人员根据实测结果确定设计值提供了参考。
在桩基工程中,基桩承载力的设计值取决于静载荷试验结果。但是由于工期、经济效益等因素的影响,试桩数往往较少,且离散性较大,由此确定的承载力设计值的误差较大。贝叶斯统计将随机变量的总体信息、样本信息和先验信息有机地结合起来,估计出的变量值更加接近实际值。本文基于数理统计中的极差理论和贝叶斯统计原理,给出的基桩承载力均值的先验分布为正态分布,并利用贝叶斯统计推导出承载力的后验分布也服从正态分布；充分利用工程地质资料的丰富信息和静载试验的结果,推导出基桩承载力设计值的贝叶斯估计的计算公式。
本文的研究成果不仅使基桩承载力的设计取值达到安全可靠、经济合理的目的,而且为设计值的确定提供了理论依据,可供工程设计人员参考。
High-rise buildings and major bridges are increasingly constructed with rapid development of economy. Accordingly, reliability of structures plays a significant role in engineering practice. Pile foundation is widely useed as the foundation of the structures due to its high bear capacity, small settlement and convenient contruction. Therefore, reliability analysis is highly important in engineering practice. However, there are two problems in existing researches, they are:(1) the data from similar projects are discarded, they are not adopted to determine the bearing capacity of pile; (2) the error of reliability index may be relatively large due to the great discreteness of data from the static load tests, which may cause relatively significant loss to the project. Considering the above two problems, following studies have been conducted in this dissertation.
Due to high cost and long construction period of the project, the data from static load tests of piles are often scarce and their dispersion degree is very large, which brings more difficulties to reliasbility analysis of bearing capacity. In this dissertation, the mean and variance of population sample are calculated based on the concept of range extremity difference and the results from static load tests. Then the calculation formula of reliability is presented on the condition that the vertical bearing capacity of pile follows log-normal distribution. The results from case studies show that the calculation accuracy is satisfactory and it can provide good references to designers to determine the design parameters according to testing piles.
The design value for bearing capacity of pile is usually determined from the static load tests in pile foundation engineering. However, the error of the design value obtained from static load tests is large due to limited number of testing piles and great discreteness arising from many adverse factors including possible delays and high cost. The value of a random variable can be more accurately evaluated using Bayesian statistic because the general information, sampling information and prior information are systematically associated in Bayesian framework. Based on Range theory and Bayesian statistics principle, the prior distribution of the mean of bearing capacity of pile is presented to be normal distribution, and posterior distribution also follows a normal distribution according to Bayesian statistics. The calculation formula of design value is obtained using the abundant information of soil exploration and the results from the static load tests in the Bayesian framework,
The achievements in this dissertation not only can meet the requirements of safety and economy for pile foundation, but also provide a theoretical basis to determine the design value and references for designers.
由于经济和工期原因,基桩的静载荷试验数据往往很少,并且数据的离散性很大,大大增加了承载力可靠度分析的难度。本文利用数理统计中的极差理论,根据静载试验结果,计算出总体样本的均值和方差。然后,给出了基桩竖向承载力服从对数正态分布时的可靠度计算方法。通过算例分析表明,该方法的计算精度满足工程需要,并为桩基设计人员根据实测结果确定设计值提供了参考。
在桩基工程中,基桩承载力的设计值取决于静载荷试验结果。但是由于工期、经济效益等因素的影响,试桩数往往较少,且离散性较大,由此确定的承载力设计值的误差较大。贝叶斯统计将随机变量的总体信息、样本信息和先验信息有机地结合起来,估计出的变量值更加接近实际值。本文基于数理统计中的极差理论和贝叶斯统计原理,给出的基桩承载力均值的先验分布为正态分布,并利用贝叶斯统计推导出承载力的后验分布也服从正态分布；充分利用工程地质资料的丰富信息和静载试验的结果,推导出基桩承载力设计值的贝叶斯估计的计算公式。
本文的研究成果不仅使基桩承载力的设计取值达到安全可靠、经济合理的目的,而且为设计值的确定提供了理论依据,可供工程设计人员参考。
High-rise buildings and major bridges are increasingly constructed with rapid development of economy. Accordingly, reliability of structures plays a significant role in engineering practice. Pile foundation is widely useed as the foundation of the structures due to its high bear capacity, small settlement and convenient contruction. Therefore, reliability analysis is highly important in engineering practice. However, there are two problems in existing researches, they are:(1) the data from similar projects are discarded, they are not adopted to determine the bearing capacity of pile; (2) the error of reliability index may be relatively large due to the great discreteness of data from the static load tests, which may cause relatively significant loss to the project. Considering the above two problems, following studies have been conducted in this dissertation.
Due to high cost and long construction period of the project, the data from static load tests of piles are often scarce and their dispersion degree is very large, which brings more difficulties to reliasbility analysis of bearing capacity. In this dissertation, the mean and variance of population sample are calculated based on the concept of range extremity difference and the results from static load tests. Then the calculation formula of reliability is presented on the condition that the vertical bearing capacity of pile follows log-normal distribution. The results from case studies show that the calculation accuracy is satisfactory and it can provide good references to designers to determine the design parameters according to testing piles.
The design value for bearing capacity of pile is usually determined from the static load tests in pile foundation engineering. However, the error of the design value obtained from static load tests is large due to limited number of testing piles and great discreteness arising from many adverse factors including possible delays and high cost. The value of a random variable can be more accurately evaluated using Bayesian statistic because the general information, sampling information and prior information are systematically associated in Bayesian framework. Based on Range theory and Bayesian statistics principle, the prior distribution of the mean of bearing capacity of pile is presented to be normal distribution, and posterior distribution also follows a normal distribution according to Bayesian statistics. The calculation formula of design value is obtained using the abundant information of soil exploration and the results from the static load tests in the Bayesian framework,
The achievements in this dissertation not only can meet the requirements of safety and economy for pile foundation, but also provide a theoretical basis to determine the design value and references for designers.
引文
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