基桩承载力的可靠度分析及可靠度优化设计研究
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摘要
桩基是土木工程中的重要结构形式之一。考虑不确定因素的影响，是基桩可靠度分析和可靠度优化设计的重要课题。尽管目前诸多学者对基桩承载力和沉降的可靠度开展了大量的研究，但这些工作对不确定因素的研究有待完善，且这些工作对基桩可靠度优化设计和群桩可靠度研究很少。本文着眼于克服这些研究的缺陷，对基桩承载力的可靠度分析方法和可靠度优化设计进行了系统的研究。
基于最大熵原理提出了一种改进的可靠度指标计算方法。采用最大熵原理将可靠度指标的迭代计算转化为熵密度函数的计算。在计算熵密度函数时采用Newton迭代法，同时证明了Newton迭代法的局部收敛性，避免了计算中可能产生的计算迭代不收敛的情况。为了提高计算效率和计算精度，在进行Newton迭代时，采用Newton下山法进行迭代计算。为了验证该方法的计算精度，采用蒙特卡洛模拟法对各种方法的计算结果进行比较。最后通过两个实例验证了该方法的有效性。
针对桩基工程中由于数据较少导致无法精确研究模型不确定性这一问题，基于数理统计理论和贝叶斯统计，提出了桩基工程数据处理和优化方法。利用该方法对打入桩和灌注桩承载力的现场试验数据进行分类和优化。同时利用中心点法、验算点法和蒙特卡洛模拟法计算出承载力的可靠度，根据计算结果和美国桥梁荷载抗力设计规范给出了抗力系数的建议值。最后，研究了参数和模型的不确定性对基桩承载力的影响，引入修正因子，修正了承载力的试计比和变异系数，给出了修正后可靠度指标的计算方法。
利用概率理论，详细地分析了基桩完整性抽样检测的概率分布，建议将总体不合格率作为整批桩质量的评价标准。基于贝叶斯统计，推导出总体不合格率的先验分布和后验分布都服从Beta分布。利用先验分布的期望和方差与后验分布的期望和方差的关系建立了总体不合格率的动态评估模型。同时，利用可靠度理论，给出了基桩完整性检测的可靠度控制模型，使桩基质量控制和结构可靠度设计达到了统一。
提出了考虑基桩完整性的群桩可靠度分析方法。利用贝叶斯统计，推导出缺陷桩的概率分布。同时利用单桩承载力的折减系数和群桩效应推导出缺陷桩群桩的可靠度计算公式和完整桩群桩的可靠度计算公式。基于全概率理论，推导出含有缺陷桩的群桩承载力的失效概率，并通过算例证明了该方法的有效性。另外，整理了国内外确定单桩极限承载力的失效准则，以国内习惯采用的s-lgt失效准则为基准，定义其他失效准则的偏差系数。同时利用群桩效应和偏差系数给出了不同失效准则下群桩可靠度的计算方法，为统一评价桩基安全提供了理论依据。最后利用偏差系数给出了不同失效准则条件下目标可靠度和安全系数的计算方法。
针对目前桩基设计规范规定的定值优化设计法不能解决设计参数不确定性的这一不足，基于可靠度理论，利用现有的优化设计研究成果，提出了基桩的可靠度优化设计方法，并详细地给出了竖向荷载下可靠度优化设计过程。在研究竖向荷载下基桩可靠度优化设计时，提出了一种改进的可靠度优化方法，大大提高了优化计算效率。最后通过实例验证本章方法的有效性。
Pile foundation is one of important structural style in civil engineering. Consideringthe influences of uncertainties is an important topic when studying reliability of bearingcapacity and reliability-design optimaization of piles. Though a large number of researcheshave been conducted to investigate the reiliability of bearing capacity and settlement forpiles, the influences of uncertainties on reliability analysis need to be further studied.Additionally, reliability-based optimization design and reliability analysis of pile grouphave rarely been reported till now. In order to overcome these deficiencies, systemicresearches are carried out in this dissertation to analyze reliability-based optimizationdesign and reliability of bearing capacity of piles.
A modified method for calculating reliability index was put forward based onmaximum entropy principle. To achieve this goal, the maximum entropy principle was usedto transform iterative calculation of reliability index into a maximum entropy densityfunction calculation. Newton iteration method was utilized to calculate entropy densityfunction and its local convergence was proved. The convergence of iteration was ensuredwhen calculating reliability index. To promote calculation efficiency, Newton down-hillalgorithm was incorporated into calculating entropy density function and Monte Carlosimulations were performed to assess the efficiency of the presented method. Finally, twonumerical examples had been presented to verify the validation of the presented method
According to the mathematical statistics theory and Bayesian technique, a method fordata processing and optimization in pile foundation engineering was put forward to solvethe problem caused by model uncertainty due to lack of enough accurate field data. Thepresented method was employed to classify and optimize the field data of the driven pilesand the bored piles. The first order second moment method, the advanced first order secondmoment method and the Monte Carlo simulation were employed to calculate the reliabilityof the bearing capacity, the recommended values of resistance factors were suggestedaccording to the calculated results and American specifications for load and resistancefactor design. Meanwhile, the effects of parameter uncertainties and model uncertainties on bearing capacity of piles were studied, a modification factor was introduced to calibrate thebias factors and coefficients of variance for bearing capacity, and the modified calculationformula of reliability was presented.
Based on probability theory, a systematic method was proposed to estimate theoccurrence probability of defective piles from a site according to non-destructive integrityinspection. The factors influencing on sampling inspection were analyzed based onprobability theory and engineers’ experiences, and the occurrence probability of defectivepiles from a site was suggested to be as the criterion to evaluate the performance of a pilefoundation. To estimate occurrence probability of defective piles, its prior distribution andupdating distribution were deduced to follow Beta distributions, and a dynamic estimationmodel was established based on the relationship between prior mean and variance andupdating mean and variance to calibrate the occurrence probability of defective piles. Thereliability-control method dealing with uncertainties arising from quality assurance ininspection was formalized to judge whether all the bored piles from a site can be accepted,and uniform quality criterion for construction and design in pile foundation engineeringwas established.
A method was presented to evaluate the reliability of pile group considering theintegrity of pile. Based on the Bayesian Statistical Theory, the probability distribution ofdefected piles was deduced. Meanwhile, the calculation formulas of reliability for defectedpile group(DPG) and intact pile group(IPG) were obtained according to the reduction factorand the pile group effect. Finally, the failure probability of the pile group containingdefected piles was formulated using the total probability theory. Additionally, the differentfailure criteria from various countries were examined, and a bias factor defined with respectto s-lgt criterion widely used in China was introduced. Meanwhile, the calculation methodof reliability of pile group considering different criteria was presented using the bias factorsand pile group effect, which provided a theoretical basis to calibrate the reliability levels ofpile foundation associated with various failure criteria. The calculation formula of targetreliability index of bearing capacity of single piles and factor of safety was presented using bias factor.
Currently, deterministic optimization design recommended in prevailing codes for pilefoundations cannot take the uncertainties of design parameters into account. To overcomethis deficiency, based on reliability theory and the existing research achievements ofoptimization design, the reliability-based optimization design of piles was presented, andthe detailed optimization procedures of pile under axial load were established. A modifiedreliability optimization method was put forward to improve the design of piles under axialload, which greatly enhanced the computational efficiency. Finally, the adopted method wasvalidated by a case study.
基于最大熵原理提出了一种改进的可靠度指标计算方法。采用最大熵原理将可靠度指标的迭代计算转化为熵密度函数的计算。在计算熵密度函数时采用Newton迭代法，同时证明了Newton迭代法的局部收敛性，避免了计算中可能产生的计算迭代不收敛的情况。为了提高计算效率和计算精度，在进行Newton迭代时，采用Newton下山法进行迭代计算。为了验证该方法的计算精度，采用蒙特卡洛模拟法对各种方法的计算结果进行比较。最后通过两个实例验证了该方法的有效性。
针对桩基工程中由于数据较少导致无法精确研究模型不确定性这一问题，基于数理统计理论和贝叶斯统计，提出了桩基工程数据处理和优化方法。利用该方法对打入桩和灌注桩承载力的现场试验数据进行分类和优化。同时利用中心点法、验算点法和蒙特卡洛模拟法计算出承载力的可靠度，根据计算结果和美国桥梁荷载抗力设计规范给出了抗力系数的建议值。最后，研究了参数和模型的不确定性对基桩承载力的影响，引入修正因子，修正了承载力的试计比和变异系数，给出了修正后可靠度指标的计算方法。
利用概率理论，详细地分析了基桩完整性抽样检测的概率分布，建议将总体不合格率作为整批桩质量的评价标准。基于贝叶斯统计，推导出总体不合格率的先验分布和后验分布都服从Beta分布。利用先验分布的期望和方差与后验分布的期望和方差的关系建立了总体不合格率的动态评估模型。同时，利用可靠度理论，给出了基桩完整性检测的可靠度控制模型，使桩基质量控制和结构可靠度设计达到了统一。
提出了考虑基桩完整性的群桩可靠度分析方法。利用贝叶斯统计，推导出缺陷桩的概率分布。同时利用单桩承载力的折减系数和群桩效应推导出缺陷桩群桩的可靠度计算公式和完整桩群桩的可靠度计算公式。基于全概率理论，推导出含有缺陷桩的群桩承载力的失效概率，并通过算例证明了该方法的有效性。另外，整理了国内外确定单桩极限承载力的失效准则，以国内习惯采用的s-lgt失效准则为基准，定义其他失效准则的偏差系数。同时利用群桩效应和偏差系数给出了不同失效准则下群桩可靠度的计算方法，为统一评价桩基安全提供了理论依据。最后利用偏差系数给出了不同失效准则条件下目标可靠度和安全系数的计算方法。
针对目前桩基设计规范规定的定值优化设计法不能解决设计参数不确定性的这一不足，基于可靠度理论，利用现有的优化设计研究成果，提出了基桩的可靠度优化设计方法，并详细地给出了竖向荷载下可靠度优化设计过程。在研究竖向荷载下基桩可靠度优化设计时，提出了一种改进的可靠度优化方法，大大提高了优化计算效率。最后通过实例验证本章方法的有效性。
Pile foundation is one of important structural style in civil engineering. Consideringthe influences of uncertainties is an important topic when studying reliability of bearingcapacity and reliability-design optimaization of piles. Though a large number of researcheshave been conducted to investigate the reiliability of bearing capacity and settlement forpiles, the influences of uncertainties on reliability analysis need to be further studied.Additionally, reliability-based optimization design and reliability analysis of pile grouphave rarely been reported till now. In order to overcome these deficiencies, systemicresearches are carried out in this dissertation to analyze reliability-based optimizationdesign and reliability of bearing capacity of piles.
A modified method for calculating reliability index was put forward based onmaximum entropy principle. To achieve this goal, the maximum entropy principle was usedto transform iterative calculation of reliability index into a maximum entropy densityfunction calculation. Newton iteration method was utilized to calculate entropy densityfunction and its local convergence was proved. The convergence of iteration was ensuredwhen calculating reliability index. To promote calculation efficiency, Newton down-hillalgorithm was incorporated into calculating entropy density function and Monte Carlosimulations were performed to assess the efficiency of the presented method. Finally, twonumerical examples had been presented to verify the validation of the presented method
According to the mathematical statistics theory and Bayesian technique, a method fordata processing and optimization in pile foundation engineering was put forward to solvethe problem caused by model uncertainty due to lack of enough accurate field data. Thepresented method was employed to classify and optimize the field data of the driven pilesand the bored piles. The first order second moment method, the advanced first order secondmoment method and the Monte Carlo simulation were employed to calculate the reliabilityof the bearing capacity, the recommended values of resistance factors were suggestedaccording to the calculated results and American specifications for load and resistancefactor design. Meanwhile, the effects of parameter uncertainties and model uncertainties on bearing capacity of piles were studied, a modification factor was introduced to calibrate thebias factors and coefficients of variance for bearing capacity, and the modified calculationformula of reliability was presented.
Based on probability theory, a systematic method was proposed to estimate theoccurrence probability of defective piles from a site according to non-destructive integrityinspection. The factors influencing on sampling inspection were analyzed based onprobability theory and engineers’ experiences, and the occurrence probability of defectivepiles from a site was suggested to be as the criterion to evaluate the performance of a pilefoundation. To estimate occurrence probability of defective piles, its prior distribution andupdating distribution were deduced to follow Beta distributions, and a dynamic estimationmodel was established based on the relationship between prior mean and variance andupdating mean and variance to calibrate the occurrence probability of defective piles. Thereliability-control method dealing with uncertainties arising from quality assurance ininspection was formalized to judge whether all the bored piles from a site can be accepted,and uniform quality criterion for construction and design in pile foundation engineeringwas established.
A method was presented to evaluate the reliability of pile group considering theintegrity of pile. Based on the Bayesian Statistical Theory, the probability distribution ofdefected piles was deduced. Meanwhile, the calculation formulas of reliability for defectedpile group(DPG) and intact pile group(IPG) were obtained according to the reduction factorand the pile group effect. Finally, the failure probability of the pile group containingdefected piles was formulated using the total probability theory. Additionally, the differentfailure criteria from various countries were examined, and a bias factor defined with respectto s-lgt criterion widely used in China was introduced. Meanwhile, the calculation methodof reliability of pile group considering different criteria was presented using the bias factorsand pile group effect, which provided a theoretical basis to calibrate the reliability levels ofpile foundation associated with various failure criteria. The calculation formula of targetreliability index of bearing capacity of single piles and factor of safety was presented using bias factor.
Currently, deterministic optimization design recommended in prevailing codes for pilefoundations cannot take the uncertainties of design parameters into account. To overcomethis deficiency, based on reliability theory and the existing research achievements ofoptimization design, the reliability-based optimization design of piles was presented, andthe detailed optimization procedures of pile under axial load were established. A modifiedreliability optimization method was put forward to improve the design of piles under axialload, which greatly enhanced the computational efficiency. Finally, the adopted method wasvalidated by a case study.
引文
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