基于Eshelby 夹杂理论的沥青混合料细观本构模型及损伤机理研究

It's difficult to accurately reveal the deformation and damage mechanism of asphalt mixture from the existing meso-mechanical constitutive model because of the insufficient understanding of the applicability of basic meso-mechanical model and the complexity of meso-structure. So, in this research, the undamaged asphalt mixture is treated as a multi-inclusion composite material with high volume fraction, in which aggregates with different sizes and protogenetic air voids are included into asphalt matrix. A stepping algorithm for multi-inclusion problem is proposed based on the Eshelby inclusion theory, and a meso-mechanical constitutive model for undamaged asphalt mixture is established and verified based on the stepping algorithm, which could consider the influences of aggregates shape, gradation and air void characteristics. Then, the hysteromorphous micro-cracks are included into the undamaged asphalt mixture, and the Eshelby tensor of rotational ellipsoid is applied for micro-crack inclusions to establish a meso-mechanical constitutive model for the damaged asphalt mixture with micro-crack inclusions. On this base, the effects of volume fraction and morphological feature of micro-crack inclusions on the macroscopic performances of asphalt mixture are analyzed, as well as the extension behavior of micro-crack inclusions and the effects of viscoelastic property of asphalt matrix. Afterwards, the morphological features the probability distribution characteristics of micro-crack during the creep test are quantitated by CT technology and statistical analysis. According to the morphological feature and distribution function, a statistical damage constitutive model is established and verified for damaged asphalt mixture. Furthermore, the meso-damage evolution law is revealed from the correlation analysis between the extension behavior and the variation of volume fraction of micro-crack inclusions and macroscopic creep damage factor. The achievements in this research could lay the theoretical foundations for the meso-mechanics analysis and numerical simulation of the asphalt pavement.

由于对细观力学基础模型适用性和细观结构复杂性的认识存在不足，现有的沥青混合料细观本构模型还难以准确揭示材料的变形与破坏机制。因此，本项目将无损沥青混合料视为各档集料和原生空隙夹杂于沥青基体的高体分比多类夹杂复合材料，运用Eshelby夹杂理论提出一种分步算法，建立并校验考虑集料形态、级配和空隙特征的无损沥青混合料细观本构模型；再将次生微裂纹夹杂于无损基体中，采用椭球夹杂Eshelby张量进行求解，建立夹杂微裂纹的沥青混合料细观本构模型，在此基础上分析微裂纹体分比和形态对宏观性能的影响，研究微裂纹的扩展行为及沥青粘弹性对其的影响；结合CT技术和统计分析，量化蠕变过程中微裂纹形态和概率密度分布参数，建立并校验考虑微裂纹扩展的统计损伤本构模型，分析微裂纹扩展、体分比变化与宏观蠕变损伤因子的关联特性，进而揭示沥青混合料的细观损伤机理。项目研究成果可为沥青路面细观力学分析和数值模拟奠定理论基础。

由于对细观力学基础模型适用性和细观结构复杂性的认识存在不足，现有的沥青混合料细观本构模型还难以准确揭示材料的变形与破坏机制。因此，本项目以Eshelby夹杂理论为基础，选取5种研究常用细观力学模型，开展了多模型、多尺度、全频域沥青混合料有效动态模量预测的适用性验证。通过引入表征颗粒整体作用强弱的参数，对考虑颗粒相互作用的细观力学J-C模型进行了简化，给出了预测沥青胶浆有效复数剪切模量的细观力学模型。提出了两种描述沥青混合料细观结构特性的径向分布假设（均匀分布和P-Y分布），推导了细观力学J-C模型在两种假设分布下的有效模量精确预测公式。通过假设沥青混合料为以沥青砂浆为基体相，粗集料和空隙为夹杂相的多相复合材料，建立了考虑颗粒相互作用的沥青混合料动态模量两步预测方法，并进行了试验验证。验证结果表明，考虑颗粒相互作用的细观力学模型对沥青胶浆和沥青混合料有效粘弹性能预测具有更高预测精度，均匀分布和PY分布可分别作为J-C 模型预测沥青混合料有效动态模量的上、下界。在此基础上，将次生微裂纹夹杂于无损基体中，采用椭球夹杂Eshelby张量进行求解，建立夹杂微裂纹的沥青混合料细观本构模型，并分析微裂纹体分比和形态对宏观性能的影响。结果表明，微裂纹的存在对沥青混合料起弱化作用，当微裂纹越扩展或者越扁平，弱化作用越明显。最后，提出以复合威布尔分布函数表征沥青混合料中微裂纹的概率密度分布特征，建立并校验考虑微裂纹扩展的统计损伤本构模型。验证结果表明，统计损伤模型能很好地描述混合料的损伤过程，并得到了沥青混合料在不同温度和荷载条件下的损伤演化规律。项目研究成果进一步完善沥青混合料的本构理论，为沥青路面细观力学响应研究及数值分析提供理论基础。