Simulation on Cracking of Random Aggregate Model of Concrete Three-Point Bending Beam

doi:10.12068/j.issn.1005-3026.2024.07.016

Abstract

Abstract:

Accurate description of concrete crack propagation is of great significance to practical engineering. This paper adopts the cohesive zone model （CZM） to investigate both the macro?mechanical properties and the micro?cracking damage behavior of concrete beams in a three-point bending test. Throughout the study of damage under loading in the three-point bending test， parametric examinations are conducted on five key factors controlling the cracking of cohesive elements regarding the case of circulate aggregate， namely type I fracture energy， type II fracture energy， shear strength， tensile strength and elastic modulus （stiffness）. Through the test results of macro-mechanical properties and micro-cracking， the test results of a group of specimens and the results of parametric models are reversely analyzed， and the applicable parameter range of control factors in three-point bending simulation is obtained. Three computation models with different aggregate areas are established by taking account of the quantitative aggregate data from specimens with different mix proportions. The parameter range is then applied to derive quantitative results related to crack propagation. Eventually， the accuracy of the parameter range is validated against both the mechanical properties and quantitative crack data obtained from simulations and experiment.

Key words: cohesive zone model, fracture parameter, three-point bending test, crack expanding, meso-scale

CLC Number:

TU 528

Qing-yuan WANG, Ying XU, Sheng QIAN. Simulation on Cracking of Random Aggregate Model of Concrete Three-Point Bending Beam[J]. Journal of Northeastern University(Natural Science), 2024, 45(7): 1037-1046.

Figures/Tables 25

Fig. 1 Two scale meso‐model cohesive element grid diagram

Table 1 Concrete mix ratios and mechanical parameters

组号	水	水泥	水灰比	细骨料	粗骨料	减水剂	压缩强度	弹性模量
组号	kg·m^-3	kg·m^-3	水灰比	kg·m^-3	kg·m^-3	kg·m^-3	MPa	GPa
C30	200	279	0.72	1025	838	0.4	34.40	19.52
C40	195	463	0.42	867	866	3.8	42.37	21.02
C60	153	512	0.30	642	1071	6.2	63.43	23.00

Fig. 2 Schematic diagram of post‐treatment of cracks in three‐point bending test

Table 2 Material parameters of baseline model

参数	骨料	砂浆	ITZ	MII
弹性模量/GPa	72	28	24	26
平面内泊松比	0.16	0.2	—	—
最大容许拉应力/MPa	—	—	2.6	4
最大容许切应力/MPa	—	—	12	30
Ⅰ型断裂能/（N·mm^-1）	—	—	0.025	0.1
Ⅱ型断裂能/（N·mm^-1）	—	—	0.625	2.5
准则材料系数	—	—	1.2	1.2

Fig. 3 Cohesive elements simulating crack expanding

Fig. 4 Inversion method diagram

Fig. 5 Effect of tensile stress of cohesive elements

Fig. 6 Damage images of different tensile stress models（a）—0.6倍；（b）—0.8倍；（c）—1.0倍；（d）—4.0倍.

Fig. 7 Summary diagram of crack area‐load curves with change of tensile stress of cohesive elements

Fig. 8 Effect of shear stress of cohesive elements on mechanical properties

Fig. 9 Damage images of different shear stress models（a）—0.6倍；（b）—0.8倍；（c）—1.0倍；（d）—4.0倍.

Fig. 10 Summary diagram of crack area‐load curves with change of shear stress of cohesive elements

Fig. 11 Effect of type Ⅰ fracture energy on mechanical properties

Fig. 12 Damage patterns of different type Ⅰ fracture energy models（a）—0.6倍；（b）—1.0倍；（c）—2.6倍.

Fig. 13 Effect of type Ⅰ fracture energy on crack area‐load case

Fig. 14 Effect of type Ⅱ fracture energy on mechanical properties

Fig. 15 Damage patterns of different type Ⅱ fracture energy models（a）—0.6倍GⅡ模型；（b）—1.0倍GⅡ模型；（c）—2.6倍GⅡ模型.

Fig. 16 Effect of type Ⅱ fracture energy on crack area?load

Fig. 17 Effect of elastic modulus on mechanical properties

Fig. 18 Damage patterns of different elastic modulus models（a）—0.6倍K模型；（b）—1.0倍K模型；（c）—4.0倍K模型.

Fig. 19 Effect of stiffness change on crack area‐load case

Fig. 20 Appropriate intervals of macroscopic mechanical properties and key parameters of micro?cracking

Table 3 Calculation results of aggregate area with different percentages

组别

骨料总面积

占比

粗骨料

（5~10 mm）

细骨料

（1~5 mm）

Fig. 21 Load‐CMOD variation for three sets of specimens tested and simulated

Fig. 22 Crack area?load of three groups of specimens tested and simulated

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