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混凝土多尺度应力响应方程及其数值模拟

EQUATION AND NUMERICAL SIMULATION ON MULTISCALE STRESS RESPONSE OF CONCRETE

  • 摘要: 针对混凝土的多相多尺度材料组成特征及其复杂力学响应问题, 首先, 根据混凝土中各组成材料的几何特征, 将C-S-H凝胶、硬化水泥浆体、砂浆及混凝土细观组成分别视为纳观、微观、亚细观和细观尺度上的复合材料, 并利用颗粒空间堆积方法, 重构了混凝土各尺度复合材料的简化几何模型; 其次, 基于重构的几何模型和等效夹杂理论, 通过等效刚度的升阶计算和应力响应的降阶计算, 建立各尺度复合材料应力响应之间的过渡关系, 推导混凝土多尺度应力响应方程, 并编制相应的计算程序; 最后, 以单轴压缩载荷作用为例, 数值计算载荷作用下混凝土各尺度复合材料中的应力响应, 分析骨料空间位置和相互作用以及水化产物刚度、几何形状和空间取向对其应力响应的影响规律. 结果表明, 单轴压缩载荷作用下, 混凝土细观组成中的应力分布并不均匀; 骨料颗粒之间的距离影响到混凝土中的应力分布, 其有效影响范围约为骨料粒径的6倍; 水泥水化产物的刚度、几何形状和空间取向是影响其应力分布的重要因素, 刚度越大, 所受应力越大, 与载荷作用方向的夹角越小, 长椭球形水化产物沿载荷作用方向的应力越大, 扁椭球形水化产物与之相反.

     

    Abstract: Aiming at the multi-phase and multi-scale composition characteristics of concrete and its complicated mechanical response problem, firstly, according to the geometric characteristics of constituent material in concrete, C-S-H gel, hardened cement paste, cement mortar and meso-scale concrete were respectively regarded as composite materials at different scales of concrete, including the nanoscale, microscale, sub-mesoscale and mesoscale, and their simplified geometric models were reconstructed by using the particle space accumulation method. Secondly, based on the reconstructed simplified geometric model and equivalent inclusion theory, the transition relationship of stress response between composite materials at different scales of concrete was established by using upscaling calculation method of equivalent stiffness and downscaling calculation method of stress response, on this basis, the multiscale stress response equation of concrete under the loading was derived, and the corresponding computing program was compiled. Finally, taking the uniaxial compressive loading as an example, the stress response in composite materials at different scales of concrete under uniaxial compressive loading was numerically calculated, and the influence of spatial position and interaction of aggregate particles, as well as the stiffness, geometric shape and spatial orientation of cement hydration products on their stress response were analyzed. Results show that, the stress distribution in the meso-scale concrete is uneven under uniaxial compressive loading, which was affected by the distance between the aggregate particles, and the effective impact range is about 6 times the radius of aggregate particle. The stiffness, geometric shape and spatial orientation of cement hydration products are important factors affecting their stress distribution under loading, the greater the stiffness, the greater the stress in the hydration products, while the smaller the angle with the direction of loading, the greater the stress in the hydration products of prolate ellipsoids along this direction, however, the stress in the hydration products of oblate ellipsoids is the opposite.

     

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