混凝土断裂面多重分形谱的二次拟合研究

STUDY ON QUADRATIC FITTING OF MULTI-FRACTAL SPECTRUM OF FRACTURE SURFACE IN CONCRETE

基于混凝土断裂面的分形特性,采用Weierstrass-Mandelbrot(W-M)分形曲面法构造了具有不同分形特征参数的混凝土分形断裂面;对比研究了混凝土分形断裂曲面的多重分形特性,得到了混凝土分形断裂面的多重分形谱曲线。针对混凝土多重分形谱曲线的几何特性,利用最小二乘法对混凝土分形断裂面的多重分形谱进行了二次拟合;对拟合结果进行了定量分析,并对拟合函数进行改进,从而实现了对混凝土断裂面多重分形谱曲线的简化计算。试验结果与拟合结果的对比研究显示,该文所提出的多重分形谱拟合方法能够较好地实现对混凝土断裂面的多重分形谱曲线的模拟,并对多重分形谱的变化规律和趋势进行较为精确的表达。研究成果对研究混凝土断裂面的形成规律乃至混凝土结构或构件的优化设计提供了一种新的思路和方法。

Based on fractal characteristics of the fracture surface of concrete, a series of Weierstrass-Mandelbrot （W-M） fractal surfaces of concrete satisfying certain fractal conditions are built. The multi-fractal characteristics of the W-M fracture surface of concrete are studied to calculate the multi-fractal spectrum of fracture surface of concrete. Considering the geometrical properties of the multi-fractal spectrum of concrete, the method of minimum squares is applied to the quadratic fitting of multi-fractal spectrttm of fracture surface. The fitted function is quantitatively analyzed to simplify the calculation of multi-fractal properties of concrete. Comparisons between test results and theoretical calculation results verify that the quadratic fitting method of multi-fractal spectrum fits the multi-fractal spectrum of fracture surface of concrete well, and the evolution rules and trend are forecasted accurately. The research results can be applied in further research about mechanism of fracture surface formation in concrete and the optimization design of concrete structure.