水泥砂浆断面形貌像素点法与投影法分形的计算对比研究

Comparison on Surface Fractal Dimension of Cement Mortar Section by Pixel Covering Method and Projective Covering Method

为对比分析像素点覆盖法和投影覆盖法计算水泥砂浆断口分形维数的优缺点,采用这2种方法分别计算水泥砂浆在3种不同养护龄期下的断面分形维数,探索分形维数与抗压强度之间的关系。结果表明,像素点覆盖法计算得到的断口分形维数为2.258 0～2.265 6,相关系数为0.988 6～0.989 3,计算精确度高,数值变化区间小;投影覆盖法计算得到的断口分形维数为2.856 0～2.918 9,相关系数为0.921 4～0.935 2,计算精度较差,但数值变化区间大,有利于实际应用,与抗压强度呈良好相关性。

Relative merits between pixel covering method and projective covering method about calculating the fractal dimension of cement mortar were focused.The fractal dimension of cement mortar fracture with three different maintenance time were figured out.The relationship of surface fractal dimension and compressive strength was characterized based on the two methods.The results show that the pixel dimension is between 2.258 0 and 2.265 6,correlation coefficient is between 0.988 6 and 0.989 3.It indicates that the precision is high but the numerical change interval is small.The projective dimension is 2.856 0～2.918 9 and the correlation coefficient is 0.921 4～0.935 2.The precise is poor but the change scale is larger.The projective dimension presents better dependence with the compressive strength,which indicates that it is better for practical applications.