A mesoscale model based on MonteCarlo method for concrete fracture behavior study.docx

1、A mesoscale model based on MonteCarlo method for concrete fracture behavior study外文参考资料：A mesoscale model based on Monte-Carlo method for concrete fracture behavior studyZHANG NaiLong1, 2, GUO XiaoMing1, 2*, ZHU BiBo3 & GUO Li1, 21.Department of Engineering Mechanics, School of Civil Engineering, So

2、utheast University, Nanjing 210096, China;2.Jiangsu Key Laboratory of Engineering Mechanics, Southeast University, Nanjing 210096, China;2.Daya Bay Nuclear Power Operations and Management Company, Shenzhen 518110, China An aggregate generation and packing algorithm based on Monte-Carlo method is dev

3、eloped to express the aggregate random distribution in cement concrete. A mesoscale model is proposed on the basis of the algorithm. In this model, the concrete con- sists of three parts, namely coarse aggregate, cement matrix and the interfacial transition zone (ITZ) between them. To verify the pro

4、posed model, a three-point bending beam test was performed and a series of two-dimensional mesoscale concrete mod- els were generated for crack behavior investigation. The results indicate that the numerical model proposed in this study is helpful in modeling crack behavior of concrete, and that tre

5、ating concrete as heterogeneous material is very important in frac- ture modeling. cement concrete, fracture, Monte-Carlo method, aggregate generation and packing algorithm, mesoscale models1 Introduction Concrete material is widely used in building, highway, bridge, dam, airport and many other kind

6、s of infrastructural facilities due to its characteristics such as high strength, convenient construction, high plastic property, good fire- proof and corrosion resistance. With the increase of magni- tude of concrete material in infrastructural facilities in re- cent years, a number of cases on str

7、ucture failure in their earlier design life and service extermination can be easily found in concrete constructions. As one of the most com- mon distresses, cracks directly reduce the concrete structure service capacity and lower the mechanical performance. Cracking phenomena pose a severe challenge

8、 to application and design of concrete structures. Understanding the fun-damental mechanisms behind the initiation and the propaga- tion of cracks inside concrete in different cases is a critical step to study the concrete material performance for further design. It is well known that concrete is a

9、heterogeneous compo- site material composed of coarse and fine aggregates, ce- ment paste matrix, interfacial transition zone (ITZ) between the aggregate and cement paste matrix and voids at mesoscale. The size of particles inside concrete can be ranging from a few microns (cement particles) to tens

10、 of millimeters (coarse aggregates). Aggregates usually cover about 85% of the volume of concrete in different sizes, ir- regular shapes and random locations. Mechanical properties of every component in concrete are different obviously. For example, the cement paste matrix is a typical porous mate-

11、rial while its mechanical performances are very sensitive to the cement water ratio, cement hydration degree, curingcondition, porosity and so on. The mechanical properties of concrete are significantly affected by microstructural details and cement content, aggregate type, gradation of aggregate pa

12、rticles, distribution and even orientation of aggregates, the void ratio and so on. Whereas in a macroscale model of concrete, the heterogeneous nature of concrete is ignored and an analytical modeling can be performed based on the linear elasticity. The initiation and propagation of a crack in an e

13、lastic homogeneous medium leads to the development of singular stress field around crack tip and thus disturbs the stress distribution in the region. However, the singular stress field finally results in a finite stress reaching the tensile strength of the weakest component. Therefore, the effects o

14、f different components on the location of crack initiation and the trajectory of crack propagation in concrete are ignored. The complex fracture behaviour of concrete at macroscale is a manifestation of various interlinked mechanisms occur- ring at length scales much smaller than the continuum lengt

15、h scale. Analytical modeling of such systems is diffi- cult to reproduce the effects of different components on the location of crack initiation and the trajectory of crack prop- agation. Continuum models like crack band model, two pa- rameter fracture model, and fictitious crack model have been pro

16、posed in the past but they do not account for heter- ogeneity. Therefore, it is necessary to construct a mesomechanical model containing information of components and micro- structures for simulating the cracking behaviors of concrete more accurately. Sadouki and Wittmann were the first to underline

17、 the importance of studying the material at varying length scales 1. In recent years, a lot of experimental and numerical investigations on crack propagation in concrete have been performed. Some researchers, such as De Souza et al. 2, Kim and Buttlar 3 and Lopez et al. 4, have attached their attent

18、ion to the microstructure effects in the fracture of composite material. Simone et al. applied me- so-model to a four point bending concrete beam to study the fracturing of the heterogeneous specimen 5. Xiao et al. 6 developed a random aggregate model of recycled aggregate concrete to simulate the m

19、eso-structural damage of recycled aggregate concrete under uniaxial compression in a lattice model. Tejchman and Skarzynski 7 investigated fracture process zones (FPZ) at meso-scale in notched concrete beams subject to quasi-static three-point bending. Nguyen et al. 8 developed a meso-model to inves

20、tigate the transition from diffuse damage to localized damage of concrete.The model showed interesting results on the transition from dif- fuse to localized damage and was able to reproduce dila- tancy in compression. Li et al. 9 employed a meso-scale lattice model to predict the primary mechanical

21、properties and the crack paths of the designed cementitious material.The modeling was done based on the meso-structure ofconcrete captured through a micro-CT. Grassl and Jirasek10 proposed a meso-scale model to study the fractureprocess zone of concrete subject to uniaxial tension. Themeso-structure

22、 of concrete was idealised as stiff aggregates embedded in a soft matrix and separated by weak interfaces in the model. Mo et al. presented 2D and 3D meso-level mechanical models for numerical analysis of raveling re- sistance of porous asphalt concrete (PAC) 1121. Many investigators have developed

23、some other mesoscale models in their works. With aggregate generation and packing algorithm based on stochastic Monte-Carlo method, a mesoscale model framework was proposed in this work and applied to the crack initiation and propagation study. A series of tests and numerical simulations on the thre

24、e-point bending of concrete beam were performed to evaluate the mesoscale model.2 Mesoscale heterogeneous model frame In the present mesoscale heterogeneous model, the whole cement mixture solid is divided into three groups of regions, that is, the regions of the aggregates, the region of the ce- me

25、nt matrix and the regions between aggregates and cement matrix, also called ITZ. Therefore, cement concrete here consists of three components. With the aggregate generation by stochastic Monte-Carlo method and packing algorithm, a mesoscale model was developed and used to investigate the effects of

26、microstructure on concrete cracking behavior and capture the trajectory of crack propagation.2.1 Simplification of aggregate gradation In general hydraulic concrete, the fine aggregate is defined as particle, whose mass exceeds 85% passes of a 5 mm sieve, while the coarse aggregate is defined as tha

27、t whose mass exceeds 85% retains on a 5 mm sieve. It is noted that the volume fraction of fine aggregates is low, but their amount is thousands of times that of coarse aggregates or even more. The large number of fine aggregates would greatly increase the element number and go against the computatio

28、nal efficiency, so it is realistic to construct a simplified mesoscale model of cement concrete with con- tinuous gradation. An important issue in this simplification method is to determine the cut-off size between fine aggre- gate and coarse aggregate. Then the fine aggregate is classi- fied into c

29、ement matrix while coarse aggregate is catego- rized into different levels by particle size. By doing so, the difficulty as mentioned previously in modeling will be alle- viated. If we consider 5mm as the cut-off size in this study, the procedure of aggregate gradation simplification is com- pleted.

30、 This simplified aggregate gradation fulfills Fullers curve, from which the Walravens formula is deduced: (1) where Pc is the probability of aggregate whose particle size fulfills DD0 appearing at any point on a section in concrete solid. D0 is the sieve size. Dmax is the diameter of the biggest par

31、ticle. Pk is the volume percentage of all aggregates of concrete solid. The aggregate numbers of different level in the section can be calculated by (2) where Si is the total area occupied by the ith level aggregates; ni is the number of the ith level aggregates and Di is the equivalent diameter of

32、the ith level aggregates. As an example, the simplified aggregate gradation is shown in Table 1.Table 1 Simplified aggregate gradation：Aggregate particle size level (mm) Mass content (%) 25 420615 3210 325 262.2 Aggregate generation and packing Once the number of aggregates of every particle size level is calculated by the method described previously, the next issue is to generate aggregates and pack them in a pre- scribed region. Considering the randomness of the aggre- gate distribution, Monte-Carlo method is employed in ag- grega