摘要
主裂缝亚临界扩展所形成的虚拟裂缝区的粘聚力是影响混凝土断裂韧度尺寸相关性的重要因素。根据混凝土准脆性材料的断裂特性,建立了一种基于虚拟裂缝模型的求解混凝土等效断裂韧度的实用解析方法。首先根据复合材料力学和线弹性断裂力学的基本原理,将虚拟裂缝的粘聚力作为相应的边界条件,运用修正的剪滞理论,分区引入变异层,建立了分层剪滞模型;然后根据能量法则,推导出求解混凝土等效断裂韧度的解析计算模式;最后针对相关试验的数值解,得到了混凝土等效断裂韧度的解析解。结果表明,对于不同的子层数,体积系列试件的混凝土等效断裂韧度均方差和变异系数分别低于0.0398和0.0384,高度系列试件的混凝土等效断裂韧度均方差和变异系数分别低于0.0394和0.0363,从而证明了混凝土等效断裂韧度是与试件尺寸无关的断裂参数;且与数值解相比,解析解的均方差和变异系数更小,证明了本文解析方法具有更好的鲁棒性。由此得出结论,基于虚拟裂缝模型所建立的解析模式为求解混凝土等效断裂韧度提供了一种可靠的、实用的解析方法。
The cohesive strength of the fictitious crack generated by the sub-critical growth of main crack is an important factor affecting the size dependence of the fracture toughness of concrete. According to the fracture property of the quasi-brittle material of concrete, a practical analytical method, to solve the equivalent fracture toughness of concrete is established based on fictitious crack model. At first, according to the basic principles in the composite material mechanics and the linear elastic fracture mechanics, the cohesive strength of the fictitious crack is taken as the boundary condition. Based on the modified shear lag theory and by introducing the variable layer in different zones, the layered shear lag model is built. Then based on the energy law, an analytical form to solve the equivalent fracture toughness of concrete is derived. Finally, against the numerical solutions of the related experiments, the analytical solutions of the equivalent fracture toughness of concrete are obtained. The results show that in the case of varying sub-layers, the mean square deviation and the coefficients of variation of the equivalent fracture toughness of concrete of the volume series specimens are lower than 0.0398 and 0.0384 respectively. The mean square deviation and the coefficients of variation of the height series specimens are lower than 0.0394 and 0.0363 respectively. It proves that the equivalent fracture toughness of concrete is a size-independent fracture parameter. Compared with the numerical solutions, the mean square deviation and the coefficients of variation of the analytical solutions are smaller, which demonstrates that the proposed analytical method is more robust. A conclusion is drawn that the proposed analytical form based on the fictitious crack model provides a reliable and practical analytical method to solve the equivalent fracture toughness of concrete.
出处
《工程力学》
EI
CSCD
北大核心
2006年第11期91-98,共8页
Engineering Mechanics
基金
国家杰出青年科学基金(50425824)
关键词
混凝土
等效断裂韧度
虚拟裂缝模型
粘聚力
剪滞理论
解析解
concrete
equivalent fracture toughness
fictitious crack model
cohesive strength
shear lag theory
analytical solution
