基于XFEM的骨料分布对混凝土有效模量的影响

混凝土的弹性模量是结构设计中最基本的参数，在计算方法上需要保证足够的准确性。基于现有的3层球壳解析模型，将骨料、界面过渡区和薄层砂浆组成的整体先行处理为等效夹杂体，并根据解析模型获得相应的弹性模量，随后将混凝土视为由此等效而来的夹杂体与基体砂浆组成的二相复合材料。在固定背景网格体系中，采用无附加自由度的扩展有限元方法计算不同级配和骨料含量的混凝土等效弹性模量。当混凝土的骨料分布发生变化时，无附加自由度的扩展有限元方法能够在程序设计上避免整体刚度矩阵的维度变化问题。此外，为了能在获得不同的骨料分布的同时获得较高的骨料含量，混凝土的级配采用固定的粒径分布形式。结果表明：骨料含量同为47.12%的3种级配的混凝土弹性模量基本相同，说明级配对混凝土弹性模量的影响可以忽略；解析解可较准确地预测稀疏骨料分布情况下的混凝土等效弹性模量，但骨料增加后其预测值出现较大偏差；混凝土弹性模量随硬骨料含量的增加线性增大，随软骨料含量的增加线性减小。

Influence of Aggregate Distribution on the Effective Elastic Modulus of Concrete Based on XFEM

Elastic modulus of concrete plays an important role in civil engineering design, thus it is important to keep the accuracy of its computation. Based on the on-hand three-layered spherical-shell model, an equivalent inclusion that consists of the aggregate, the interfacial transition zone and cement mortar was made, and its elastic modulus was calculated by the three-layered spherical-shell model. Then, the concrete was seen as a two-phase composite, which consists of the equivalent inclusion and basic cement mortar. Under the fixed-grid background, the extended finite element method without augmented degree of freedom was used to calculate the effective modulus of two-dimensional two-phase concrete composed of equivalent inclusions and cement mortar. This kind of XFEM can avoid the problem of dimensional inconsistency after aggregate distribution being changed. And the aggregate degradation was obtained through giving different aggregate diameters. It was shown that the aggregate degradation has no influence on the effective modulus of concrete, and the analytical solutions for predicting the effective modulus of concrete are only reliable when aggregate content is low, and the effective modulus of concrete has a linear relationship with aggregate content.