Elsevier

Measurement

Volume 160, August 2020, 107832
Measurement

Quantitative study of meso-damage process on concrete by CT technology and improved differential box counting method

https://doi.org/10.1016/j.measurement.2020.107832Get rights and content

Highlights

  • X-ray CT analysis of concrete was carried out.

  • An improved differential box counting (IDBC) method was proposed.

  • The concrete damage process was described using the fractal theory.

  • The relationship between fractal dimension, damage variable and stress were studied.

  • The correlations between area of cracks region and the stress was explored.

Abstract

To study the change of concrete internal structure before and after stress, the meso-mechanical experiment of concrete was conducted using CT technology and a portable dynamic loading device. And CT images of the concrete internal structure change under uniaxial compression condition were obtained. For establishing the relationship between the micro-structure and macro-mechanics of concrete, an improved differential box counting (IDBC) method was proposed to calculate the fractal dimension of the CT images, which could describe the entire damage process of concrete. By comparing the fractal dimension calculated by the two methods, it can be seen that the fitting error of the fractal dimension obtained by the IDBC method is reduced by nearly 50% compared with that obtained by the DBC method. Afterward, the damage variable expression was established on the basis of the fractal dimension. The research results indicated that the damage variable established in this research can describe the damage process of concrete well. That is, the damage variable equaled to 0 during the first scan, and before reaching the peak stress, the damage variable showed a trend of increasing first and then decreasing. After the concrete specimen has completely fractured, the damage variable reached a maximum of one. Furthermore, through extracting the area of CT image cracks region at different stress stages, the relationship between the area of cracks region and the stress was studied. It appeared that the CT technology and fractal theory are promising methods to analyze the evolution of the concrete damage process under static uniaxial compression.

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

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