Fractal characteristics of meso-failure crack in recycled coarse aggregate concrete based on CT image
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摘要: 为深入研究再生混凝土的破坏形态和内部裂纹扩展情况与普通混凝土之间的差异，以不同再生粗骨料(RCA)取代率的再生混凝土为研究对象，利用Phoenix v | tome | x s240微焦点工业CT获取再生混凝土加载到90%预估破坏荷载的二维扫描图像，借助Photoshop CS6图像处理软件，对材料内部破坏裂纹进行提取，进而基于分形几何理论，以分形维数及多重分形谱表征裂纹的分形扩展规律，建立分形维数和多重分形谱特征参数与RCA取代率和再生混凝土抗压强度的关系。结果表明：再生混凝土的细观受力破坏模式与普通混凝土不同，其受力破坏形态不仅取决于粗骨料与水泥浆体的界面黏结强度，还取决于RCA自身性能，当裂纹发展至天然粗骨料或强度较高的RCA时会绕过骨料表面继续发展，发展至强度较低的RCA时会贯穿骨料；分形维数可定量描述混凝土材料内部细观裂纹的整体扩展情况，即裂纹越丰富，分形维数越大；多重分形谱可反映从局部到整体不同层次的细观裂纹特征，裂纹分形维数和多重分形谱特征参数均与RCA取代率呈线性下降关系，与抗压强度呈线性增长关系；本研究可为再生混凝土在大型结构工程中的广泛应用奠定理论和实验基础。Abstract: The work aims to study the difference between recycled coarse aggregate concrete and normal concrete in failure mode and internal crack propagation. The recycled coarse aggregate concretes with different recycled coarse aggregate (RCA) replacement rates were used as the research object. Using the micro-focus industrial CT (Phoenix v | tome | x s240), 2D scanning images of recycled coarse aggregate concrete under 90% predicted failure load were obtained. With Photoshop CS6 image processing software, the failure crack in material was extracted. After that, based on the fractal geometry theory, the fractal dimension and multi-fractal spectrum were used to characterize the fractal propagation law of crack. Finally, the relationship between fractal dimension, multi-fractal spectrum characteristic parameters and RCA replacement rate and compressive strength was established. The results show that the meso-failure mode of recycled coarse aggregate concrete is different from that of normal concrete. The failure form of recycled coarse aggregate concrete depends on the interfacial transition zone (ITZ) between the coarse aggregate and the cement paste and the properties of RCA itself. When the crack develops to the natural coarse aggregate (NCA) or the RCA with higher strength, it will continue to develop around the surface of the aggregate, and it will penetrate through the aggregate when it is developed to the RCA with lower strength; The fractal dimension can quantitatively describe the overall propagation of meso-crack inside the concrete materials, that is, the richer the crack, the larger the fractal dimension; Multi-fractal spectrum can reflect the characteristics of meso-crack at different levels from local to global; The fractal dimension and multi-fractal spectrum characteristic parameters of crack have a linear negative correlation with the RCA replacement rate, and have a linear positive correlation with the compressive strength; This study can lay a theoretical and experimental basis for the wide application of recycled concrete in large-scale structural engineering.
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图 1 天然粗骨料(NCA)(a)和再生粗骨料(RCA)外观(b)和RCA组成成分((c)–(e))
Figure 1. Appearance of natural coarse aggregate(NCA)(a) and recycled coarse aggregate(RCA)(b) and composition ((c)–(e)) of RCA
图 5 不同RCA取代率下的混凝土抗压强度
Figure 5. Compressive strengths of concrete with different replacement rates of RCA
图 6 RCA取代率为50%的再生混凝土CT扫描图像
Figure 6. CT scanning image of recycled concrete with 50% replacement rate of RCA
图 7 90%预估破坏荷载下再生混凝土的破坏形态
Figure 7. Failure modes of recycled concrete under 90% predicted failure load
图 8 不同RCA取代率下的混凝土细观破坏裂纹lnN(r)-lnr关系曲线
lnN(r)—Logarithm of number of square boxes containing crack(N(r)); lnr—Logarithm of side length of square box(r)
Figure 8. lnN(r)-lnr curves of meso-failure crack of concrete at different replacement rates of RCA
图 9 不同RCA取代率下的混凝土细观破坏裂纹分形维数平均值
Figure 9. Average fractal dimension of meso-failure crack of concrete with different replacement rates of RCA
图 10 RCA取代率为100%的再生混凝土的ln χq(ε)-ln ε曲线
Figure 10. ln χq(ε)-ln ε curves of recycled concrete with 100% replacement rate of RCA
ln χq(ε)—Logarithm of the partition function(χq(ε)); ln ε—Logarithm of the side length of square box(ε); q—Weighting factor
图 11 不同RCA取代率下的混凝土细观破坏裂纹的多重分形谱
Figure 11. Multi-fractal spectra of meso-failure crack of concrete with different replacement rates of RCA
图 12 细观破坏裂纹分形维数D与RCA取代率R及混凝土抗压强度fc的关系
Figure 12. Relationship of D with R and fc
D—Fractal dimension of meso-failure crack; R—Replacement rate of RCA; fc—Compressive strength of concrete
图 13 细观破坏裂纹多重分形谱特征参数与RCA取代率R及抗压强度fc的关系
Figure 13. Relationship of multi-fractal spectrum parameters, R and fc
表 1 粗骨料基本性能
Table 1. Properties of coarse aggregate
Aggregate
typeCrushing
index/%Natural stacking
density/(kg·m−3)Voidage/% Apparent density/
(kg·m−3)Water absorption
of 24 h/%RCA 20.2 1 073 56 2 425 6.73 NCA 6.3 1 479 46 2 750 0.57 
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表 2 再生混凝土配合比
Table 2. Mix proportions of recycled aggregate concrete
Code R/% mw/mc Mix proportion/(kg·m−3) Cement Sand NCA RCA Water Fly ash Silica fume Superplasticizer R0 0 0.50 288 726 1 184 0 180 54 18 7.2 R25 25 0.50 288 726 888 296 180 54 18 7.2 R50 50 0.50 288 726 592 592 180 54 18 7.2 R75 75 0.50 288 726 296 888 180 54 18 7.2 R100 100 0.50 288 726 0 1 184 180 54 18 7.2 Notes: R—Replacement rate of RCA; mw/mc—Water-to-cementitious material ratio.
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表 3 工业CT系统技术参数
Table 3. Technical parameters of industrial CT system
Parameter Result Maximum tube voltage/kV 240 Maximum tube power/W 320 Detail resolution/μm 1
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表 4 不同RCA取代率的混凝土细观破坏裂纹的多重分形谱参数
Table 4. Parameters of multi-fractal spectrum of meso-failure crack of concrete with different replacement rates of RCA
αmin αmax αmean f (αmin) f (αmax) Δf (α) f (α)max R0 1.3655 1.5835 1.4745 0.8479 1.2056 0.3577 1.4648 R25 1.2571 1.5088 1.3830 0.6516 1.0229 0.3713 1.3376 R50 1.3110 1.5262 1.4186 0.8034 1.1018 0.2984 1.3694 R75 1.1791 1.3922 1.2857 0.6479 0.8794 0.2315 1.2486 R100 1.1640 1.4330 1.2985 0.6943 0.8958 0.2015 1.2506 Notes: In multi-fractal spectrum f ( α )- α: αmin, αmax, αmean—Minimum, maximum and mean of α ; f (αmin), f (αmax)—Corresponding to αmin and αmax ; Δf (α)=f (αmax)–f (αmin); f (α)max—Maximum of f (α).
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