分形理论在混凝土断裂面研究中的应用
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摘要
介绍了对混凝土断裂面进行分形研究的重要性、分形理论及混凝土断裂面分析中几种主要的分数维测量方法;基于激光三角测距原理对试验后的混凝土断裂面进行三维重构.并应用分形几何这一理论工具对重构的断裂面进行分析,得到分数维、粗糙度等断裂面信息;通过探讨分数维与混凝土的力学性能及材料组成的关系,得出在本文试验条件下分数维与混凝土的抗拉强度、峰值应变及峰值弹模存在反比关系,与水灰比、含气量存在正比关系,与胶凝材料用量存在反比关系等一系列结论.
The importance of study on the fracture surfaces, the fractal theory and the measurements of fractal dimensions are introduced. Based on the theory of laser triangulation, the 3-D profiles of the fracture surfaces are reconstructed. Using Fractals, we have analyzed the 3-D profiles and got the information such as fractal dimensions, roughness,etc. The relations between fractal dimensions of the fracture surfaces and mechanical properties of concrete are discussed. The relations, between fractal dimensions of the fracture surfaces
and material parameters are also investigated. The experimental results and theoretical analysis show that the fractal dimensions decrease with the increase of tensile strength, peak-strain and tangent elastic modulus at peak load; and fractal dimensions decrease with the increase of the amount of cementitious material; but the fractal dimensons increase with the increase of water-cement ratio and air content.
The importance of study on the fracture surfaces, the fractal theory and the measurements of fractal dimensions are introduced. Based on the theory of laser triangulation, the 3-D profiles of the fracture surfaces are reconstructed. Using Fractals, we have analyzed the 3-D profiles and got the information such as fractal dimensions, roughness,etc. The relations between fractal dimensions of the fracture surfaces and mechanical properties of concrete are discussed. The relations, between fractal dimensions of the fracture surfaces
and material parameters are also investigated. The experimental results and theoretical analysis show that the fractal dimensions decrease with the increase of tensile strength, peak-strain and tangent elastic modulus at peak load; and fractal dimensions decrease with the increase of the amount of cementitious material; but the fractal dimensons increase with the increase of water-cement ratio and air content.
引文
[1] 冯乃谦.高性能混凝土[M].北京:中国建筑工业出版社,1996．
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[3] Mandelbrot.分形:形、机遇和维数[M].文志英,苏虹译.北京:世界图书出版公司,1999．
[4] 卢春生.断面分形研究中的几个问题[J].力学进展,1996． 26(3) :353～361．
[5] 吴科如,严 安.张 东等.混凝土断裂面参数的测试[J].岩石力学与工程学报,2001,20(2) :1454～1457．
[2] 陈 颙,陈 凌.分形几何学[M].北京:地震出版社,1998．
[3] Mandelbrot.分形:形、机遇和维数[M].文志英,苏虹译.北京:世界图书出版公司,1999．
[4] 卢春生.断面分形研究中的几个问题[J].力学进展,1996． 26(3) :353～361．
[5] 吴科如,严 安.张 东等.混凝土断裂面参数的测试[J].岩石力学与工程学报,2001,20(2) :1454～1457．
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