基于分形渗流模型的导电沥青混凝土的分维计算

Estimation of fractal dimensions of conductive asphalt concrete based on fractal and percolation model

引入分形理论研究导电通路的分布特征,利用分形维数描述导电沥青混凝土从绝缘体到导体的转换过程。基于Matlab平台,结合常规的图像处理方法,获取图像的盒维数信息,分析分维与导电相材料体积掺量之间的关系。研究结果表明:导电通路的分布图具有明显的统计意义的自相似性,分形维数在二维平面内随石墨掺量增加而增大,变化趋势类似于电阻率与石墨掺量的依赖性。说明分形维数可明确地、定量地表征导电沥青混凝土中形成导电渗流途径的连通程度。

This paper introduces the fractal theory to the study on the distribution characteristics of the conduc-tive paths of asphalt concrete by using fractal dimension to describe the conversion process when asphalt concrete are changed into conductor.Based on Matlab,the images information of the box -counting dimension combined with the conventional image processing method is obtained.The relationship between fractal dimension and vol-ume content of the conductive material was also analyzed.The results show that：the conductive path of asphalt concrete has obviously statistical significant similarity on fractal,and fractal dimension increases by the graphite content at two -dimensional plane.In addition,the change trend of fractal dimension is similar to the depend-ence of resistivity and graphite content.The results indicate that fractal dimension can describe the degree of connectivity clearly and quantitatively when conductive asphalt concrete forming a percolation path.