混凝土尺寸效应理论研究与断裂参数分析
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摘要
如何对混凝土材料的力学行为进行恰当和准确的描述是力学难题之一，其理论和应用研究一直受到人们的重视。本文采用有限元理论、随机理论、统计理论、能量理论和分形理论等方法对混凝土材料的断裂参数及尺寸效应理论的若干问题进行了研究。主要内容如下：
(1)对Weibull尺寸效应统计理论、Bazant尺寸效应理论与Carpinteri分形尺寸效应理论的研究现状进行了回顾、分析、比较和评论。
(2)采用随机骨料模型，以有限元为计算手段，从应力、应变和裂纹发展过程等多方面分析了混凝土材料的细观力学性能，得到一些有益的结论。
(3)采用数值方法对不同尺寸的试件进行了分析，揭示出混凝土强度具有明显的尺寸效应现象。并采用Bazant尺寸效应律和Carpinteri分形尺寸效应律对数值分析结果进行了验证，得到与试验分析相一致的结论。
(4)在对混凝土断裂能的各种影响因素进行探讨的基础上，建立了混凝土断裂能的单因素和多因素统计模型，并进行了验证分析。
(5)对混凝土断裂能尺寸效应现象进行了深入的分析。认为断裂过程区大小随试件尺寸的变化而变化是产生断裂能尺寸效应现象的根本原因。
(6)综合考虑试件尺寸和材料细观结构特征对断裂能的影响，建立了混凝土断裂能尺寸效应的分形模型，并进行了验证分析。
(7)使用分形理论建立了Ⅰ型分形裂纹尖端处的应力强度因子计算模型；模型使用的计算公式可以退化为经典的Ⅰ型裂纹尖端处的应力强度因子公式。
(8)在对应力强度因子的计算方法进行评述的基础上，对应力强度因子的计算误差进行了分析，提出了一个使用有限元方法求解应力强度因子的误差指标参数。
The description of mechanical properties about concrete is a difficult problem in mechanics. The studies about it are going on by researchers. Some problems on mechanical parameters and size effects of concrete are studied in this dissertation. The main contents are as follows.(1) Three size effect laws are reviewed, analyzed and commented. They are Weibull statistical size effect law, Bazant size effect law and Carpinteri size effect law.(2) The micro-mechanical properties are studied by Random Aggregate Model.(3) Various size components are analyzed by Random Aggregate Model. It is showed that the concrete components have the characters of size effect. Then the analysis data are compared with Bazant size effect law and Carpinteri size effect law.(4) The affect factors to fracture energy of concrete are discussed. Then some statistical models are developed. The multi-factors statistical model in above models is a feasible and correct model. This conclusion is built on the basis of analysis.(5) The resource of fracture energy is studied. The size effect of fracture energy results in the change of fracture process zone in various size components.(6) A fractal model of fracture energy is built with fractal theory. The size of component and the fractal dimension of crack are involved in this model. The analysis to the model indicates it is a feasible and correct model.(7) A fractal model of SIF is also built with fractal theory. The analysis indicates it is a feasible and correct model.(8) The error of SIF is discussed too. Then an index to estimate error of SIF is advised. The analysis shows it is a feasible and correct parameter.Size effect, Numerical analysis, Statistical theory, Energy theory, Fractal theory
(1)对Weibull尺寸效应统计理论、Bazant尺寸效应理论与Carpinteri分形尺寸效应理论的研究现状进行了回顾、分析、比较和评论。
(2)采用随机骨料模型，以有限元为计算手段，从应力、应变和裂纹发展过程等多方面分析了混凝土材料的细观力学性能，得到一些有益的结论。
(3)采用数值方法对不同尺寸的试件进行了分析，揭示出混凝土强度具有明显的尺寸效应现象。并采用Bazant尺寸效应律和Carpinteri分形尺寸效应律对数值分析结果进行了验证，得到与试验分析相一致的结论。
(4)在对混凝土断裂能的各种影响因素进行探讨的基础上，建立了混凝土断裂能的单因素和多因素统计模型，并进行了验证分析。
(5)对混凝土断裂能尺寸效应现象进行了深入的分析。认为断裂过程区大小随试件尺寸的变化而变化是产生断裂能尺寸效应现象的根本原因。
(6)综合考虑试件尺寸和材料细观结构特征对断裂能的影响，建立了混凝土断裂能尺寸效应的分形模型，并进行了验证分析。
(7)使用分形理论建立了Ⅰ型分形裂纹尖端处的应力强度因子计算模型；模型使用的计算公式可以退化为经典的Ⅰ型裂纹尖端处的应力强度因子公式。
(8)在对应力强度因子的计算方法进行评述的基础上，对应力强度因子的计算误差进行了分析，提出了一个使用有限元方法求解应力强度因子的误差指标参数。
The description of mechanical properties about concrete is a difficult problem in mechanics. The studies about it are going on by researchers. Some problems on mechanical parameters and size effects of concrete are studied in this dissertation. The main contents are as follows.(1) Three size effect laws are reviewed, analyzed and commented. They are Weibull statistical size effect law, Bazant size effect law and Carpinteri size effect law.(2) The micro-mechanical properties are studied by Random Aggregate Model.(3) Various size components are analyzed by Random Aggregate Model. It is showed that the concrete components have the characters of size effect. Then the analysis data are compared with Bazant size effect law and Carpinteri size effect law.(4) The affect factors to fracture energy of concrete are discussed. Then some statistical models are developed. The multi-factors statistical model in above models is a feasible and correct model. This conclusion is built on the basis of analysis.(5) The resource of fracture energy is studied. The size effect of fracture energy results in the change of fracture process zone in various size components.(6) A fractal model of fracture energy is built with fractal theory. The size of component and the fractal dimension of crack are involved in this model. The analysis to the model indicates it is a feasible and correct model.(7) A fractal model of SIF is also built with fractal theory. The analysis indicates it is a feasible and correct model.(8) The error of SIF is discussed too. Then an index to estimate error of SIF is advised. The analysis shows it is a feasible and correct parameter.Size effect, Numerical analysis, Statistical theory, Energy theory, Fractal theory
引文
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