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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 the fractal characteristics of the fractured surface of concrete, fractal fractured surfaces of concrete with different fractal characteristic parameters were constructed by Weierstrass-Mandelbrot (WM) fractal surface method. The fractal characteristics of fractured fractured surfaces of concrete were compared and the fractal surface of fractured surface of concrete Multifractal spectrum curve. According to the geometrical characteristics of the curve of multifractal spectrum of concrete, the multifractal spectrum of the fractal surface of the concrete was quadratic fitted by the least square method. The fitting results were quantitatively analyzed and the fitting function was improved. A SIMPLIFIED CALCULATION FOR MULTIPLICATION OF CONCRETE FRACTURE SURFACES. The experimental results and the fitting results show that the multifractal spectrum fitting method proposed in this paper can well simulate the multifractal spectrum curve of the concrete fracture surface, and the variation rules and trends of the multifractal spectrum More accurate expression. The research results provide a new idea and method for studying the formation rule of concrete fracture surface and even the optimal design of concrete structure or component.