锈蚀钢筋混凝土梁抗剪承载力计算的概率模型

该文针对锈蚀钢筋混凝土（RC）梁抗剪承载力计算的传统确定性模型所存在的缺陷,研究建立了锈蚀RC梁抗剪承载力计算的概率模型。首先综合考虑钢筋锈蚀对箍筋屈服强度、配筋率、配箍率、临界斜裂缝倾角、梁有效抗剪截面积等重要因素的影响,结合修正压力场理论和考虑剪跨比影响的临界斜裂缝倾角模型,建立了锈蚀RC梁抗剪承载力计算的确定性模型;然后综合考虑客观不确定性和主观不确定性的影响,结合贝叶斯理论和马尔科夫链蒙特卡洛（MCMC）法,建立了锈蚀RC梁抗剪承载力计算的概率模型;最后通过与试验数据和传统确定性抗剪承载力计算模型的对比分析,验证了该概率模型的有效性和适用性。分析结果表明,所建立的概率模型不仅可以合理描述锈蚀RC梁抗剪承载力的概率分布特性,而且可以校准传统确定性抗剪承载力模型的计算精度和置信水平,具有良好的有效性和适用性。     

剪切型钢筋混凝土柱抗剪承载力计算的概率模型

现有的钢筋混凝土（RC）柱抗剪承载力计算模型大多属于确定性模型,难以有效考虑几何尺寸、材料特性和外荷载等因素存在的不确定性,导致计算结果的离散性较大,且计算精度和适用性有限。鉴于此,该文结合变角桁架-拱模型和贝叶斯理论,研究建立了剪切型RC柱抗剪承载力计算的概率模型。首先基于变角桁架-拱模型理论,并考虑轴压力对临界斜裂缝倾角的影响,建立了剪切型RC柱抗剪承载力的确定性修正模型;然后考虑主观不确定性和客观不确定性因素的影响,结合贝叶斯理论和马尔科夫链蒙特卡洛（MCMC）法,建立了剪切型RC柱的概率抗剪承载力计算模型;最后通过与试验数据和现有模型的对比分析,验证了该模型的有效性和实用性。分析结果表明,该模型不仅可以合理描述剪切型RC柱抗剪承载力的概率分布特性,而且可以校准现有确定性计算模型的置信水平,并且可以确定不同置信水平下剪切型RC柱抗剪承载力的特征值。     

考虑力学机制和不确定性影响的钢筋混凝土柱概率抗剪承载力模型

为了克服传统确定性抗剪承载力模型无法合理考虑不确定性因素影响所存在的缺陷,研究建立了一种能够综合考虑力学机制和不确定性影响的钢筋混凝土（RC）柱概率抗剪承载力模型。首先基于桁架-拱模型,综合考虑混凝土、箍筋和拱作用的抗剪承载力贡献以及不确定性的影响,建立了RC柱概率抗剪承载力模型的解析表达式;然后结合贝叶斯理论和马尔科夫链蒙特卡洛（MCMC）法,确定了概率模型参数的后验分布信息,并分析了概率模型参数的先验分布信息以及更新批次对概率模型参数后验分布的稳定性和收敛性的影响;最后利用试验数据验证了该概率模型的有效性。分析表明,随着试验数据的增加,概率模型参数的后验分布可以实现不断更新;概率抗剪承载力模型不仅可以合理描述抗剪承载力的概率分布特性,而且可以校准分析传统确定性抗剪承载力模型的计算精度。     

一种箍筋约束混凝土峰值应力的概率模型

该文首先基于多轴受力情况下混凝土材料的极限强度面和Willam-Warnke五参数破坏准则,结合144组箍筋约束混凝土棱柱体的试验数据,建立了箍筋约束混凝土峰值应力的确定性模型;然后综合考虑主观不确定性和客观不确定性的影响,结合贝叶斯理论和马尔科夫链蒙特卡洛法,建立了箍筋约束混凝土峰值应力的概率模型;最后通过与试验数据和传统确定性模型的对比分析,验证了该概率模型的有效性和适用性。分析结果表明,该概率模型不仅能够合理描述箍筋约束混凝土峰值应力的概率特性,而且能够校准确定性模型的置信水平和预测精度,还可以确定具有预定置信水平的箍筋约束混凝土峰值应力的概率特征值。     

一种箍筋约束混凝土峰值应力的概率模型EI北大核心CSCD

该文首先基于多轴受力情况下混凝土材料的极限强度面和Willam-Warnke五参数破坏准则,结合144组箍筋约束混凝土棱柱体的试验数据,建立了箍筋约束混凝土峰值应力的确定性模型;然后综合考虑主观不确定性和客观不确定性的影响,结合贝叶斯理论和马尔科夫链蒙特卡洛法,建立了箍筋约束混凝土峰值应力的概率模型;最后通过与试验数据和传统确定性模型的对比分析,验证了该概率模型的有效性和适用性。分析结果表明,该概率模型不仅能够合理描述箍筋约束混凝土峰值应力的概率特性,而且能够校准确定性模型的置信水平和预测精度,还可以确定具有预定置信水平的箍筋约束混凝土峰值应力的概率特征值。     

基于Bayesian-MCMC方法的深受弯构件受剪概率模型研究

考虑主观、客观不确定性因素的影响,以深受弯构件受剪分析模型为研究对象,基于引入马尔科夫链-蒙特卡洛（MCMC）高效采样方法,通过R语言对深受弯构件概率模型参数进行MCMC随机模拟,给出参数的最优估计值及其对应的可信度,在先验模型基础上建立钢筋混凝土深受弯构件受剪承载力概率模型,完成模型前后的对比分析,并根据不同置信水平确定了深受弯构件受剪承载力的特征值。结果表明:基于MCMC方法得到的受剪承载力概率模型是在50000次迭代分析后产生的结果,能合理地解释影响参数的不确定性,可信度较高;后验概率模型计算结果与试验结果吻合良好,较先验模型更接近试验值,且离散性小。     

剪切破坏型钢筋混凝土柱的抗剪承载力分析模型EI北大核心CSCD

针对传统模型无法考虑轴压比影响和需要引入经验位移延性修正系数所存在的缺陷,研究建立了剪切破坏型钢筋混凝土(RC)柱的改进抗剪承载力分析模型。结合变角桁架-拱模型的变形协调条件和考虑轴压力影响的临界斜裂缝倾角模型,建立了能够综合考虑轴压比影响和桁架-拱模型变形协调条件的改进抗剪承载力分析模型。分析了轴压比对剪切破坏型RC柱抗剪承载力的影响机理,从而有效克服了传统模型无法考虑轴压比影响和需要引入经验位移延性修正系数所存在的缺陷。通过与试验数据和国内外现有模型的对比分析,验证了该模型的有效性和适用性。     

剪切破坏型钢筋混凝土柱的抗剪承载力分析模型EI北大核心CSCD

针对传统模型无法考虑轴压比影响和需要引入经验位移延性修正系数所存在的缺陷,研究建立了剪切破坏型钢筋混凝土(RC)柱的改进抗剪承载力分析模型。结合变角桁架-拱模型的变形协调条件和考虑轴压力影响的临界斜裂缝倾角模型,建立了能够综合考虑轴压比影响和桁架-拱模型变形协调条件的改进抗剪承载力分析模型。分析了轴压比对剪切破坏型RC柱抗剪承载力的影响机理,从而有效克服了传统模型无法考虑轴压比影响和需要引入经验位移延性修正系数所存在的缺陷。通过与试验数据和国内外现有模型的对比分析,验证了该模型的有效性和适用性。     

基于Bayesian理论的弯剪破坏钢筋混凝土柱变形能力概率模型

为了准确预测地震作用下弯剪破坏钢筋混凝土（RC）柱的变形能力,基于Bayesian理论提出了一种建立柱类构件变形能力概率模型的方法。首先对已有RC柱变形能力公式进行评价并选作先验模型,再借助美国PEER柱抗震性能试验数据库中发生弯剪破坏的20根矩形截面RC墩柱的拟静力试验数据作为客观认识,应用Bayesian参数估计方法综合这两类信息进行推断,修正先验模型的偏差从而建立反复荷载作用下弯剪破坏RC柱变形能力的概率模型;采用Bayesian方法剔除影响修正效果不显著的因素以获得模型简化,达到对先验模型的动态更新。最后,讨论了不同形式修正项对修正效果的影响。结果表明,Bayesian方法既继承了先验信息的完备性,又利用了试验数据的准确性,建议的概率模型较已有公式能够更准确地预测弯剪破坏RC柱的变形能力,从而为RC柱抗震设计或评估中考虑能力不确定性提供了便利。     

剪切破坏型钢筋混凝土柱的抗剪承载力分析模型

针对传统模型无法考虑轴压比影响和需要引入经验位移延性修正系数所存在的缺陷,研究建立了剪切破坏型钢筋混凝土(RC)柱的改进抗剪承载力分析模型。结合变角桁架-拱模型的变形协调条件和考虑轴压力影响的临界斜裂缝倾角模型,建立了能够综合考虑轴压比影响和桁架-拱模型变形协调条件的改进抗剪承载力分析模型。分析了轴压比对剪切破坏型RC柱抗剪承载力的影响机理,从而有效克服了传统模型无法考虑轴压比影响和需要引入经验位移延性修正系数所存在的缺陷。通过与试验数据和国内外现有模型的对比分析,验证了该模型的有效性和适用性。     

Probabilistic bond strength model for reinforcement bar in concrete

In order to overcome the disadvantages of traditional deterministic models, a probabilistic bond strength model of reinforcement bar in concrete was presented. According to the partly cracked thick-walled cylinder model, a deterministic bond strength model of reinforcement bar in concrete was developed first by taking into account the influences of various important factors. Then the analytical expression of probabilistic bond strength model of reinforcement bar in concrete was derived by taking into consideration both aleatory and epistemic uncertainties. Subsequently, a probabilistic bond strength model of reinforcement bar in concrete was proposed by determining the statistical characteristics of probabilistic model parameters based on the Markov Chain Monte Carlo method and the Bayesian theory. Finally, applicability of the proposed probabilistic model were validated by comparing with 400 sets of experimental data and four typical deterministic bond strength models. Analysis shows that the probabilistic model provides efficient approaches to describe the probabilistic characteristics of bond strength and to calibrate traditional deterministic bond strength models.     

基于概率的高层建筑地震需求模型与风险评估EI北大核心CSCD

提出了基于贝叶斯理论的地震风险评估方法,综合考虑了地震危险性模型、输入地震动记录、结构参数和需求模型的不确定性,并以云南大理地区1970年-2017年间的地震数据为研究基础进行了详细讨论。在传统基于概率地震危险性分析方法的基础上,提出了基于贝叶斯理论的地震危险性分析方法,通过贝叶斯更新准则,确定了地震概率模型中未知参数的后验概率分布;通过贝叶斯理论建立了基于概率的地震需求模型,并在易损性中考虑了需求模型认知不确定性的影响;以42层钢框架-RC核心筒建筑为例,开展了地震作用下的风险评估。研究表明:基于贝叶斯理论的地震危险性分析方法,能够获得更为合理的危险性模型;忽略需求模型中参数不确定性的影响,将错误估计结构的地震易损性;不同加载工况将对高层建筑的地震风险产生显著影响。提出的概率风险评估方法,提供了可以考虑固有不确定性和认知不确定性的有效途径,有助于推动高性能结构地震韧性评价和设计理论的发展。     

Reliability analysis of structures based on a probability‐uncertainty hybrid model

The traditional reliability analysis method based on probabilistic method requires probability distributions of all the uncertain parameters. However, in practical applications, the distributions of some parameters may not be precisely known due to the lack of sufficient sample data. The probabilistic theory cannot directly measure the reliability of structures with epistemic uncertainty, ie, subjective randomness and fuzziness. Hence, a hybrid reliability analysis (HRA) problem will be caused when the aleatory and epistemic uncertainties coexist in a structure. In this paper, by combining the probability theory and the uncertainty theory into a chance theory, a probability‐uncertainty hybrid model is established, and a new quantification method based on the uncertain random variables for the structural reliability is presented in order to simultaneously satisfy the duality of random variables and the subadditivity of uncertain variables; then, a reliability index is explored based on the chance expected value and variance. Besides, the formulas of the chance theory‐based reliability and reliability index are derived to uniformly assess the reliability of structures under the hybrid aleatory and epistemic uncertainties. The numerical experiments illustrate the validity of the proposed method, and the results of the proposed method can provide a more accurate assessment of the structural system under the mixed uncertainties than the ones obtained separately from the probability theory and the uncertainty theory.     

Quantification of epistemic and aleatory uncertainties in level-1 probabilistic safety assessment studies

There will be simplifying assumptions and idealizations in the availability models of complex processes and phenomena. These simplifications and idealizations generate uncertainties which can be classified as aleatory (arising due to randomness) and/or epistemic (due to lack of knowledge). The problem of acknowledging and treating uncertainty is vital for practical usability of reliability analysis results. The distinction of uncertainties is useful for taking the reliability/risk informed decisions with confidence and also for effective management of uncertainty. In level-1 probabilistic safety assessment (PSA) of nuclear power plants (NPP), the current practice is carrying out epistemic uncertainty analysis on the basis of a simple Monte-Carlo simulation by sampling the epistemic variables in the model. However, the aleatory uncertainty is neglected and point estimates of aleatory variables, viz., time to failure and time to repair are considered. Treatment of both types of uncertainties would require a two-phase Monte-Carlo simulation, outer loop samples epistemic variables and inner loop samples aleatory variables. A methodology based on two-phase Monte-Carlo simulation is presented for distinguishing both the kinds of uncertainty in the context of availability/reliability evaluation in level-1 PSA studies of NPP.     

钢筋混凝土悬臂梁剪切破坏及尺寸效应律研究

相比于混凝土材料,钢筋混凝土构件的破坏模式与机制更为复杂,采用混凝土材料层次的尺寸效应理论难以描述钢筋混凝土构件破坏的尺寸效应行为。为研究钢筋混凝土悬臂梁剪切破坏的尺寸效应行为,从细观角度出发,建立了钢筋混凝土悬臂梁三维细观尺度数值分析模型。结合现有试验数据,验证了细观模拟方法的可行性与合理性,进而拓展模拟与分析了剪跨比及配箍率对钢筋混凝土悬臂梁剪切破坏尺寸效应行为的影响规律,发现:剪跨比对悬臂梁抗剪承载力有较大影响,对尺寸效应的影响很小;配箍率的增大提高了悬臂梁抗剪承载力,同时削弱了梁的抗剪强度尺寸效应。根据剪跨比及配箍率对悬臂梁抗剪强度的影响机制与规律,基于Ba?ant材料层次尺寸效应律,建立了钢筋混凝土悬臂梁抗剪强度尺寸效应理论公式。对比模拟结果及试验数据,验证了所提尺寸效应理论公式的准确性与合理性。     

Treatment of uncertainties in space nuclear risk assessment with examples from Cassini mission applications

By means of several examples from a recent comprehensive space nuclear risk analysis of the Cassini mission, a scenario and consequence representational framework is presented for risk analysis of space nuclear power systems in the context of epistemic and aleatory uncertainties. The framework invites the use of probabilistic models for the calculation of both event probabilities and scenario consequences. Each scenario is associated with a frequency that may include both aleatory and epistemic uncertainties. The outcome of each scenario is described in terms of an end state vector. The outcome of each scenario is also characterized by a source term. In this paper, the source term factors of interest are number of failed clads in the space nuclear power system, amount of fuel released and amount of fuel that is potentially respirable. These are also subject to uncertainties. The 1990 work of Apostolakis is found to be a useful formalism from which to derive the relevant probabilistic models. However, an extension to the formalism was necessary to accommodate the situation in which aleatory uncertainty is represented by changes in the form of the probability function itself, not just its parameters. Event trees that show reasonable alternative accident scenarios are presented. A grouping of probabilities and consequences is proposed as a useful structure for thinking about uncertainties. An example of each category is provided. Concluding observations are made about the judgments involved in this analysis of uncertainties and the effect of distinguishing between aleatory and epistemic uncertainties.