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Numerical simulation of fracture propagation of heterogeneous material Zeqi Zhu1,2, a, Qian Sheng2,b and Xiaodong Fu2,c 1 Key Laboratory of Hydro-Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, China 2 State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China azhuzeqi2005@tom.com, bQsheng@whrsm.ac.cn, c fxd_scu@163.com Keywords: digital image processing; heterogeneous material; fuzzy clustering; fracture process; numerical simulation Abstract.
Therefore, the images, as a kind of information resource, are able to reflect meso structures perfectly base on different gray scales and colors, and are used to study the interior structures and defects of materials during the DIP.
While the image attributes for different interior materials are not quite distinguished, the method of fuzzy cluster analysis was introduced into digital image processing in this paper.
Then, the softening model is applied in software FLAC3D to simulate the rock failure of brittle material such as granite in this paper, and the mechanical parameters for different materials in Three Gorges granite are seen in Reference[3].
Chinese Journal of Geotechnical Engineering 27, 956 (2005) [5] Kwan A K H, Mora C F, Chan H C.

The basic parameters of two materials are in Table 1 [5, 6].
Wen: submitted to Chinese Journal of High Pressure Physics (2008) (In Chinese) [2] S.H.
University of Science and Technology of China(2000) [3] G.Z.
Scruggs, et al: submitted to International Journal of Impact Engineering (2002) [5] Z.H.
The Nanjing University of Science and technology (2006) [6] G.R.

It advantageously improves the material various properties, for example strength, hardness, toughness, microwave absorption properties, thereby utilizing widely in chemical engineering, materials science and other fields[2-5].
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Materials and Methods Semantan bamboo (Gigantochloa scortechinii) culm's outer skins were used in this study.
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Mangeron, No. 59A, 700050, Iasi, Romania 2Technical University “Gheorghe Asachi” of Iasi-Romania, Department of Materials Science and Engineering, Blvd.
Rosetti, no. 31, Sector 2, Bucharest, Romania 4Technical University “Gheorghe Asachi” of Iasi-Romania, Department of Materials Science and Engineering, Blvd.
Mangeron, No. 59A, 700050, Iasi, Romania 5Technical University “Gheorghe Asachi” of Iasi-Romania, Department of Materials Science and Engineering, Blvd.
To obtain these materials has been chosen different gas blowing method (N2, SO2 and C4H10).
Journal of Materials Processing Technology, 212, (2012), 181–187.

The sol-gel method is widely used due to its simple equipment, easy operation, low raw material cost and easy loading of specific materials [14-16].
Weber: Journal of Materials Science Letters Vol. 19(8) (2000), p. 683
Sun: Journal of Materials Science: Materials in Electronics Vol. 27(2) (2015), p. 2103
Journal of Sol-Gel Science and Technology Vol. 29(2) (2004), p. 81
Hrabovský: Journal of Sol-Gel Science and Technology Vol. 63(3) (2012), p. 294

However in case of a heterogeneous material model, the identification procedure has to be able to quantify the aleatory uncertainties capturing the variability of the material properties.
This contribution concentrates on identification of aleatory uncertainties in the context of heterogeneous materials, their character causes spatial variations of mechanical parameters (such as elastic modulus, yield stress or tensile strength) affecting the structural system behaviour under the loading.
Acknowledgement This outcome was financially supported by the Czech Science Foundation, project No. 16-11473Y, and the Grant Agency of the Czech Technical University in Prague, grant No.
Marzouk, Bayesian inference with optimal maps, Journal of Computational Physics, 231 (2012) 7815-7850
Pregibon, Exchangeability and data analysis, Journal of the Royal Statistical Society.

The raw mineral material base of the construction industry currently consists of two types of raw materials: natural and industrial materials (industrial byproducts) [4].
International Journal of the Physical Sciences, 5 (2010) 1952-1963
Building Materials: Properties, Performance and Applications, Nova Science Publishers.
International Journal of Innovative Research in Science, Engineering and Technology, 1(3) (2014) 8390- 8397
Australian Journal of Crop Science, 1 (2008) 37-42

There are three ways for methane biosynthesis: firstly, methane biosynthesis is based on acetic acid as raw materials; secondly, methane biosynthesis is based on hydrogen and carbon dioxide as raw materials; thirdly, methane biosynthesis is based on methyl compounds as raw materials.
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Experimental Materials.
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