基于分形理论的混凝土统计损伤本构模型研究
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摘要
由于混凝土材料具有原料丰富、耐久性好等优点,在建筑结构中得到广泛的使用。但混凝土材料不同于钢材等各向同性均质材料,它作为一种复合材料,在微细观上体现出明显的多相性、多孔性以及非均质性,而在宏观上又体现出力学性能的离散性和随机性,凡此种种对于建筑结构的受力以及抗震性能有着复杂的影响。与普通混凝土相比,超高强高性能混凝土中水泥浆体强度较大,甚至与骨料相当,表现出较高的脆性,或者是较强的均匀性,不过其力学性能的随机性和离散性仍旧无法避免。针对混凝土材料的上述力学性能,本文进行了如下研究:
基于随机损伤研究领域常用的单轴受压随机损伤弹簧模型,引入Weibull分布以及对数正态分布的概率密度函数用以描述微元体弹簧的极限应变分布规律,通过对比分析建立了可用分维表示材料的均质度,并且同时适用于普通混凝土以及超高强高性能混凝土的单轴受压细观统计损伤本构模型;利用应变等效假设将经典损伤变量定义转化为损伤破坏过程中混凝土弹性模量的变化量与初始弹性模量的比值,通过混凝土CT无损扫描试验以及单轴压缩试验,确定了已建立模型中的参数。
基于杜荣强提出的“损伤因子”,将建立的单轴应力状态下的损伤演化方程推演至多轴应力状态下,进而得到多轴应力状态下的细观统计损伤本构模型。将本文所提出的单轴以及多轴损伤本构模型与试验结果以及数值模拟算例进行对比分析发现,它们可以较为准确地反映混凝土的损伤演化规律。
考虑到试验验证的需要,本文配制了三组不同强度等级的超高强高性能混凝土以及普通混凝土,简要介绍了超高强高性能混凝土配合比试验,分析了超高强高性能混凝土水胶比、胶凝材料用量以及粗骨料级配等参量对混凝土力学性能的影响;而后基于CT无损扫描试验、采用差分盒维数法研究了各强度等级混凝土的分形断裂特性,分析了以上各参量对断裂面分形维数的影响,并就其分形断裂机理作出了合理解释。
本研究为深入研究超高强高性能混凝土的力学性能提供了一定的理论基础,有助于工程技术人员对混凝土内部组份之间的作用机理进行认识和理解,将为进一步研究混凝土细观损伤作用机理以及多轴应力下的力学性能提供参考。
For the opulence and good durability of raw material, the concrete is widely used in many types of building structures. However, as a kind of composite material, it is different from the isotropic homogeneous material, for example, steel. It reflects polymorphism, porosity and heterogeneity in mesoscopic level, and discreteness, randomness of mechanical properties in macroscopic level. All of these special performance will seriously effect the mechanical behavior and seismic capability of the structures.
Compared with the Ordinary Concrete, the strength of cement paste in Super High Strength and High Performance Concrete (SHSHPC) is higher, almost eaqual to the strength of aggregate, which makes SHSHPC reflect higher brittleness and stronger uniformity. But in the area of mechanical properties, the randomness and discreteness of SHSHPC still cannot be avoided. According to the mechanical properties of the concrete material mentioned above, this paper do research as follows:
Based on the uniaxial compression stochastic damage spring model which is widely used in the area of stochastic damage, the probability density function of the weibull distribution and the logarithmic normal distribution are introduced to describe the probability density of the ultimate strain of meso-element, and then a uniaxial compression stochastic damage constitutive model of meso-statistics which applied to not only the Oridinary Concrete, but also to the SHSHPC, using the fractal dimension as a representation of homogeneous degree, is established by means of comparing the two types of distribution probability density function; the damage variable is defined as a ratio of elastic modulus variation during the damage process of concrete and the initial elastic modulus on the basis of strain equivalence hypothesis, then the parameters in the model are fixed via CT scanning test and uniaxial compression experiment.
Based on the“damage factor”put forward by Du Rongqiang, the damage evolution equation under uniaxial stress state is deduced to the axial stress state. Therefore, the statistics stochastic damage constitutive model of meso-statistics under the multi-axial stress is developed. The uniaxial and multiaxial damage constitutive model put forward in this paper can accurately reflect the damage evolution regularity of concrete by comparing them with the test results and other research results.
Considering the need of experimental verification, three kinds of SHSHPC with different strength grade are prepared , at the same time, the mix proportion of SHSHPC is briefly introduced, the effect of water-binder ratio, the consumption of cementitious material and the coarse aggregate gradation etc on the mechanics properties of SHSHPC is analyzed; the differential box counting theory is applied to count the fractal dimension of concrete to research the relationship between the dimension of fracture surface and the parameters mentioned above on the basis of computed tomography (CT) scanning test, and then the mechanism of fractal damage of SHSHPC is reasonably explained.
This research provides not only the theoretical basis for the application of SHSHPC, but also the knowledge to understand the mechanism of the internal components of the concrete. The research of this paper is useful on further research of the mesoscopic damage mechanism of concrete and the mechanical properties of concrete under multiaxial stress.
基于随机损伤研究领域常用的单轴受压随机损伤弹簧模型,引入Weibull分布以及对数正态分布的概率密度函数用以描述微元体弹簧的极限应变分布规律,通过对比分析建立了可用分维表示材料的均质度,并且同时适用于普通混凝土以及超高强高性能混凝土的单轴受压细观统计损伤本构模型;利用应变等效假设将经典损伤变量定义转化为损伤破坏过程中混凝土弹性模量的变化量与初始弹性模量的比值,通过混凝土CT无损扫描试验以及单轴压缩试验,确定了已建立模型中的参数。
基于杜荣强提出的“损伤因子”,将建立的单轴应力状态下的损伤演化方程推演至多轴应力状态下,进而得到多轴应力状态下的细观统计损伤本构模型。将本文所提出的单轴以及多轴损伤本构模型与试验结果以及数值模拟算例进行对比分析发现,它们可以较为准确地反映混凝土的损伤演化规律。
考虑到试验验证的需要,本文配制了三组不同强度等级的超高强高性能混凝土以及普通混凝土,简要介绍了超高强高性能混凝土配合比试验,分析了超高强高性能混凝土水胶比、胶凝材料用量以及粗骨料级配等参量对混凝土力学性能的影响;而后基于CT无损扫描试验、采用差分盒维数法研究了各强度等级混凝土的分形断裂特性,分析了以上各参量对断裂面分形维数的影响,并就其分形断裂机理作出了合理解释。
本研究为深入研究超高强高性能混凝土的力学性能提供了一定的理论基础,有助于工程技术人员对混凝土内部组份之间的作用机理进行认识和理解,将为进一步研究混凝土细观损伤作用机理以及多轴应力下的力学性能提供参考。
For the opulence and good durability of raw material, the concrete is widely used in many types of building structures. However, as a kind of composite material, it is different from the isotropic homogeneous material, for example, steel. It reflects polymorphism, porosity and heterogeneity in mesoscopic level, and discreteness, randomness of mechanical properties in macroscopic level. All of these special performance will seriously effect the mechanical behavior and seismic capability of the structures.
Compared with the Ordinary Concrete, the strength of cement paste in Super High Strength and High Performance Concrete (SHSHPC) is higher, almost eaqual to the strength of aggregate, which makes SHSHPC reflect higher brittleness and stronger uniformity. But in the area of mechanical properties, the randomness and discreteness of SHSHPC still cannot be avoided. According to the mechanical properties of the concrete material mentioned above, this paper do research as follows:
Based on the uniaxial compression stochastic damage spring model which is widely used in the area of stochastic damage, the probability density function of the weibull distribution and the logarithmic normal distribution are introduced to describe the probability density of the ultimate strain of meso-element, and then a uniaxial compression stochastic damage constitutive model of meso-statistics which applied to not only the Oridinary Concrete, but also to the SHSHPC, using the fractal dimension as a representation of homogeneous degree, is established by means of comparing the two types of distribution probability density function; the damage variable is defined as a ratio of elastic modulus variation during the damage process of concrete and the initial elastic modulus on the basis of strain equivalence hypothesis, then the parameters in the model are fixed via CT scanning test and uniaxial compression experiment.
Based on the“damage factor”put forward by Du Rongqiang, the damage evolution equation under uniaxial stress state is deduced to the axial stress state. Therefore, the statistics stochastic damage constitutive model of meso-statistics under the multi-axial stress is developed. The uniaxial and multiaxial damage constitutive model put forward in this paper can accurately reflect the damage evolution regularity of concrete by comparing them with the test results and other research results.
Considering the need of experimental verification, three kinds of SHSHPC with different strength grade are prepared , at the same time, the mix proportion of SHSHPC is briefly introduced, the effect of water-binder ratio, the consumption of cementitious material and the coarse aggregate gradation etc on the mechanics properties of SHSHPC is analyzed; the differential box counting theory is applied to count the fractal dimension of concrete to research the relationship between the dimension of fracture surface and the parameters mentioned above on the basis of computed tomography (CT) scanning test, and then the mechanism of fractal damage of SHSHPC is reasonably explained.
This research provides not only the theoretical basis for the application of SHSHPC, but also the knowledge to understand the mechanism of the internal components of the concrete. The research of this paper is useful on further research of the mesoscopic damage mechanism of concrete and the mechanical properties of concrete under multiaxial stress.
引文
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