基于改进差分盒维数法的混凝土细观损伤定量研究

Quantitative Study of Concrete Mesoscopic Damage Based on The Improved Differential Box Counting Method

为了从细观角度定量研究混凝土材料的宏观力学特性,以单轴压缩条件下获得的混凝土CT图像作为研究对象,应用差分盒维数法(Differential Box Counting method,或DBC)对混凝土破损过程进行了定量描述.在分析传统差分盒维数法优缺点的基础上,提出了改进的差分盒维数法(Improved Differential Box Counting method,或IDBC),并分别用DBC和IDBC方法对混凝土破坏过程中4个断面不同应力阶段CT图像进行了对比分析.分析表明,IDBC方法计算所得分形维数的标准差、方差和拟合误差均较小.说明用IDBC方法算出的分形维数较DBC方法更为准确.因此用IDBC方法计算得到的分形维数建立了损伤变量表达式,并计算得到了4个断面各个应力阶段的损伤变量.结果表明加载初期试件完整,损伤变量为0,随着应力增大,由于混凝土内部孔洞经历了压密的过程,损伤变量稍有减小,随后一直增大直到混凝土完全破裂时损伤变量达到最大.损伤变量的变化能够较好地反映出混凝土材料损伤演化规律,可将其作为定量的损伤状态参数来描述混凝土在单轴压缩条件下裂缝的演化过程.

In order to quantitatively study the macroscopic mechanical properties of concrete materials from a microscopic point of view, the concrete CT images obtained under uniaxial compression tests are taken as the research object, and the concrete damage process is quantitatively described using the Differential Box Counting method(DBC).Based on the analysis of the advantages and disadvantages of the traditional differential box counting method, an improved Differential Box Counting Method(IDBC) is proposed, and the CT images of different stress stages of four sections in concrete failure process are compared and analyzed by DBC and IDBC methods, respectively.The analysis shows that the standard deviation, variance and fitting error of the fractal dimension calculated by IDBC method are smaller than that of DBC method.It reveals that the fractal dimension calculated by IDBC method is more accurate than that by DBC method.Therefore, the fractal dimension calculated by IDBC method is used to establish the damage variable expression, and the damage variables of each stress stage of the four sections are calculated.The results indicate that the specimen is intact at the initial loading stage and the damage variable is 0.As the stress increases, the specimen undergoes a compaction process, and the damage variable decreases slightly, and then increases until the damage variable reaches the maximum when the concrete is completely broken.The change of damage variable can better reflect the damage evolution law of concrete material, which can be used as a quantitative damage state parameter to describe the evolution process of concrete under uniaxial compression.