Quantitative study of meso-damage process on concrete by CT technology and improved differential box counting method
Graphical abstract
Introduction
Concrete is a composite material with multiple phases, which is mixed by aggregate, mortar, and cement in a certain proportion [1]. The failure or fracture of concrete often occurs at an instant after loading due to its brittleness. To some extent, most macro mechanical properties of concrete are intrinsically related to its material structure in the micro and mesoscale [2]. Therefore, it is particularly important to study the change of internal structure (cracks) of concrete from the beginning of the loading to the fracture. However, the understanding of the damage mechanism of concrete is not so profound because of its polyphase and geometric irregularity.
Fractal theory is a simple and useful tool for quantifying the irregularities and roughness of materials [3]. Mandelbrot et al. [4] applied fractal theory to the study of material section characteristics for the first time. Afterward, some researchers observed that fractal theory can be used to describe the fracture roughness and toughness of concrete, and found that the tougher the material, the higher the fractal dimension [3]. Concerning the concrete internal structure, many scholars have researched the change law under various conditions by using the fractal theory. For instance, Saouma et. al [5] examined the relationship between the fracture properties and the fractal dimension by conducting the wedge splitting tests of concrete specimens. The geometric form of concrete at the meso-level was described by the coarse aggregate content and fractal dimension, and indicated that the compressive strength increased with decreasing fractal dimension and increasing coarse aggregate content [6]. Tian et al. [7], [8], [9] have analyzed the geometrical characteristics of meso-crack patterns using digital image – processing (DIP) technique and then estimated the fractal dimension of crack propagation using the DBC method. Furthermore, Yang et al. [10], [11] determined the fractal dimension of each component of the concrete meso-structure and suggested that graded aggregates have a fractal effect is reasonable based on the geometrical characteristics of concrete. Zhou et al. [12] used fractal theory to evaluate the pore structure of waste fiber recycled concrete and showed that the fractal dimension can be used to describe the complexity of the pore structure quantitatively. In addition, many scholars have conducted laboratory tests on mixed-concrete on the basis of the fractal theory to study the fractal characteristic of concrete and revealed that fractal theory can be assumed as the integrative evaluation index for evaluating the characteristics of the pore structure of concrete and its mechanical properties subjected to dynamic or static compression [13], [14], [15], [16], [17], [18], [19], [20]. Indeed, to some extent, more evidence has supported that fractal dimension, as a simple and effective indicator, can characterize the development process of meso-structure [21], [15]. However, the accuracy of the fractal dimension calculation results is directly related to that of quantitative analysis and the applicability of damage variable establishment. Thus, many scholars have made many efforts to improve the DBC method to make the calculation results of the fractal dimension more accurate. Yan et al. [22] attempted to reduce the step size and the fitting error by reducing the number of boxes on the boundary of two adjacent boxes and using all the pixels in the box without ignoring the middle section. The results showed that the fitting error was reduced to 0.012879. Panigrahy et al. [23], [24] believed that the box height was closely related to the gray level change on the image grid, which affected the accuracy of the fractal dimension calculation. Therefore, a new method for estimating the height of the box was proposed without changing the other parameters of the DBC method. In addition, a quantitative texture measurement of gray-scale images was conducted using the improved differential box counting method. Experiment results have shown that the fractal dimension calculated by selecting the appropriate box height was closer to the actual fractal dimension of the image. Furthermore, Nayak et al. [25] improved the DBC method by subtracting the minimum intensity value from the average intensity value of each grid. The findings revealed that the proposed improved method was suitable for various gray scales compared with the existing methods and the fractal dimension was accurately calculated by this new DBC method. Liu et al. [26] solved the problem of excessive counting boxes in z-direction and insufficient counting boxes on the boundary of two adjacent boxes in the DBC method by moving boxes on (x, y) plane and selecting appropriate grid size. The experimental results indicated that the fractal dimension calculated by this method was more accurate than those by other methods. In addition, Li et al. [27] proposed that the DBC method has the following uncertainties: (1) box height selection; (2) box number calculation; (3) image intensity surface partition. Nevertheless, it remains unclear how to choose a suitable method for calculating the fractal dimension, and how to describe the damage process of concrete specimens by using the fractal dimension.
As mentioned above, fractal theory can be used to describe the damage process of concrete. Nevertheless, when stress acts on concrete, microscopic damage within it progresses gradually and macroscopic fractures developed. It is important to make clear the process of micro-damage to apparent fracture for understanding the relationship between microstructure and mechanical properties [28]. Numerous studies have demonstrated that the computed tomography (CT) technology, as a non-destructive testing method, is widely used to explore the internal structure of concrete and its development [29], [30], [31]. Some researchers used high-resolution X-ray computed-microtomography to observe the failure process in high-strength concrete (HSC) specimens under uniaxial compression loading [32]. Researchers who developed 2D meso-scale finite element models with realistic aggregates, cement paste, and voids in concrete by using X-ray CT [33]. Tian examined the evolution of concrete internal damage under freezing-thawing cycles and uniaxial compression with the help of X-ray tomography [34], [35]. Dong investigated the microstructural damage evolution and its effect on the fracture behavior of freeze-thawed concrete samples in three-point bending tests by using the X-ray nano-CT technology and micro-scale cohesive zone model [36]. However, Mao [37] is not satisfied with studying only the changes in the meso-structure of concrete in 2D space, he used CT technology to obtain the volumetric image of a concrete circular cylinder under compression. Furthermore, other researchers who used CT technology to determine aggregate size and distribution, pore or void size and distribution [38], [39]. These researches proved that CT technology is suitable for analyzing the internal structure of concrete.
To address the issues mentioned above, this study manages to tie the CT technology and fractal theory together to research the damage process of concrete under static uniaxial compression tests. First, the CT scanner was performed in the process of the uniaxial compression test of concrete. Then, the process of crack development was described through CT images. After that, an improved DBC (IDBC) method was proposed, and the fractal dimensions were extracted by using the DBC and IDBC method, respectively. The damage variable expression based on the fractal dimension was also established. Last, the relationship between the macro-mechanical properties and micro-structure of concrete was quantitatively analyzed. The research highlights are shown in Fig. 1.
Section snippets
Introduction of the DBC method
D. Stoyan et al. [41] pointed out that DBC is a method for collecting data to analyze complex patterns by dividing a dataset or image into increasingly small box-shaped pieces and then analyzing the pieces at each relatively small scale. The implementation of the DBC method is as follows:
- (a)
The gray image of given M × M is divided into a grid of s × s, taking 1 < s ≤ M/2, and r = s/M, where s is a positive integer;
- (b)
The pixels coordinate is regarded as (x, y) plane, and the grayscale of each pixel
Materials and specimen preparation
The concrete cylinder specimens with 60 mm diameter and 120 mm height were prepared and cured for 28 days under a standard curing scheme (25 °C and relative humidity >95%). The detailed mix proportions of concrete used in this study are listed in Table 1.
The specimen preparations were carried out before conducting test, which is schematized in Fig. 5(a). During the specimen preparations process, the thickness and uniformity of the adhesive largely affect the alignment of the specimen on the
Quantitative analysis of concrete damage process and discussion
This study used MATLAB and Image J software to process and study concrete CT images quantitatively. First of all, concrete CT images were segmented by MATLAB software and then the fractal dimensions of concrete damage process were obtained. Subsequently, the Image J software was used to extract the geometric parameters of the concrete internal structure from CT images, such as aggregates and cracks area, etc. Finally, the relationship between the geometric parameters and the stress was studied.
Conclusions
The meso-damage characteristics of the concrete specimen under static compression were studied by CT technique and fractal theory. Meanwhile, the CT images of the concrete damage process were obtained, and an improved method (IDBC) was proposed on the basis of the existing DBC method. Furthermore, the fractal dimensions D of CT image in different stress stages for the four cross-sections under the uniaxial compression load were acquired by the DBC and IDBC methods. In addition, the expression
CRediT authorship contribution statement
Le Zhang: Investigation, Conceptualization, Methodology, Software. Faning Dang: Conceptualization. Weihua Ding: Testing support. Lin Zhu: Editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This study is financially sponsored by the National Natural Science Foundation of China (No. 51679199, 51979225), the Special Funds for Public Industry Research Projects of the Ministry of Water Resources (No. 201501034-04) and the Key Laboratory for Science and Technology Coordination & Innovation Projects of Shaanxi Province (No. 2014SZS15-Z01). The authors would like to thank the National Natural Science Foundation, Special Funds for Public Industry Research Projects of the Ministry of Water
References (45)
- et al.
Fractal dimension–a measure of fracture roughness and toughness of concrete
Eng. Fract. Mech.
(2003) - et al.
Evaluation of meso-damage processes in concrete by X-ray CT scanning techniques under real-time uniaxial compression testing
J. Nondestr. Eval.
(2019) - et al.
Fractal dimension in concrete and implementation for meso-simulation
Construct. Build. Mater.
(2017) - et al.
Influence of aggregate size on compressive strength of pervious concrete
Construct. Build. Mater.
(2019) - et al.
Mechanical properties of coral concrete subjected to uniaxial dynamic compression
Constr. Build. Mater.
(2019) - et al.
Concrete meso-structure characteristics and mechanical property research with numerical methods
Constr. Build. Mater.
(2018) - et al.
Quantitative texture measurement of gray-scale images: fractal dimension using an improved differential box counting method
Measurement
(2019) - et al.
A modified approach to estimate fractal dimension of gray scale images
Optik
(2018) - et al.
An improved differential box-counting method to estimate fractal dimensions of gray-level images
J. Vis. Commun. Image Represent.
(2014) - et al.
An improved box-counting method for image fractal dimension estimation
Pattern Recogn.
(2009)
Two-dimensional X-ray CT image based meso-scale fracture modelling of concrete
Eng. Fract. Mech.
Pore characteristics (>0.1 mm) of non-air entrained concrete destroyed by freeze-thaw cycles based on CT scanning and 3D printing
Cold Reg. Sci. Technol.
Analysis on meso-damage processes in concrete by X-ray computed tomographic scanning techniques based on divisional zones
Measurement
3D strain evolution in concrete using in situ X-ray computed tomography testing and digital volumetric speckle photography
Measurement
Monitoring macro voids in mortars by computerized tomography method
Measurement
Partial multi-dividing ontology learning algorithm
Inf. Sci.
Fracture behavior and energy analysis of 3D concrete mesostructure under uniaxial compression
Materials
Fractal dimension of concrete incorporating silica fume and its correlations to pore structure, strength and permeability
Constr. Build. Mater.
Fractal character of fracture surfaces of metals
Nature
Fractals, fracture and size effect in concrete
J. Engng. Mech. ASCE
Effect of geometric form of concrete meso-structure on its mechanical behavior under compression
Powder Technol.
Fractal analysis on meso-fracture of concrete based on the technique of CT image processing
J. Basic Sci. Eng.
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