Deformation field and crack analyses of concrete using digital image correlation method

Abstract

The study on the deformation distribution and crack propagation of concrete under axial compression was conducted by the digital image correlation (DIC) method. The main parameter in this test is the water-cement (W/C) ratio. The novel analysis process and numerical program for DIC method were established. The displacements and strains of coarse aggregate, and cement mortar and interface transition zone (ITZ) were obtained and verified by experimental results. It was found that the axial displacement distributed non-uniformly during the loading stage, and the axial displacements of ITZs and cement mortar were larger than that of coarse aggregates before the occurrence of macro-cracks. The effect of W/C on the horizontal displacement was not obvious. Test results also showed that the transverse and shear deformation concentration areas (DCAs) were formed when stress reached 30%–40% of the peak stress. The transverse and shear DCAs crossed the cement mortar, and ITZs and coarse aggregates. However, the axial DCA mainly surrounded the coarse aggregate. Generally, the higher W/C was, the more size and number of DCAs were. The crack propagations of specimens varied with the variation of W/C. The micro-crack of concrete mainly initiated in the ITZs, irrespective of the W/C. The number and distribution range of cracks in concrete with high W/C were larger than those of cracks in specimen adopting low W/C. However, the value and width of cracks in high W/C specimen were relatively small. The W/C had an obvious effect on the characteristics of concrete deterioration. Finally, the characteristics of crack was also evaluated by comparing the calculated results.

Keywords

deformation filed distribution / crack development / digital image correlation method / mechanical properties / water-cement ratio / characteristics of deformation and crack

Introduction

Concrete has been widely applied in the world due to its advantages such as simple process of production, local availability of the materials, low cost, and good mechanical properties. However, due to its complicated composition and mechanical mechanism, it is difficult to study the deformation characteristics, strain distribution, and crack propagation of concrete elaborately. At present, the strain gauges and linear variable displacement transducers [¹] are always used to study the distribution of deformation field. This method has many advantages such as easy operation and accurate measurement. Nevertheless, the location and quantity of sensors are always limited by space. It can only provide the uniform distribution of deformation fields of the measurement region, which is difficult to further study the properties of concrete at meso-and micro-scales. There were also several methods used to observe and study the crack characteristics of concrete such as ultrasonic, acoustic emission, ray detection, infrared spectrum, piezoelectric impedance, and fiber grating methods [²–⁷]. These methods have some limitations in measuring fine cracks, and it is difficult to analyze cracks quantitatively. Some methods also need special instrument, and they are hard to detect the crack and measure deformation simultaneously. Therefore, developing a better method to study the deformation and crack characteristics has become more and more important.

The digital image correlation (DIC) method is considered as an ideal method due to its full-field feature. It can measure surface deformation of specimen by non-destructive technique (optical technique) [⁸]. The DIC method assumes that the light intensity field remains point-wise unchanged. It captures the initial non-deformed image and subsequently deformed image by camera, tracks random speckle patterns in the specimen surface, and calculates cross-correlation coefficient by using the fundamental photogrammetry and digital image processing rules [⁹]. Subsequently, the displacement of speckle patterns is obtained and data are smoothed, and the strain of specimen can be calculated by using related algorithm. Finally, the characteristics of crack (size, length, and direction, etc.) are detected based on the digital image processing rules. At present, theoretical and experimental studies have been carried out in this field. Chu et al. [¹⁰] developed a theory of the digital image-correlation method and performed several experiments to demonstrate the viability of the DIC method in experimental mechanics. Peters and Ranson [¹¹] utilized digital imaging techniques as a measure of surface displacement components, and presented a solution procedure by a numerical example of a case of uniform tension. Dong et al. [¹²] used DIC technique to investigate the evolution of fracture process zone (FPZ) at the rock-concrete interface. It showed that ligament length significantly affected the FPZ evolution at a rock-concrete interface. The evolution of FPZ of mixed mode fracture in concrete was also studied by DIC [¹³]. It was found that the FPZ evolution was influenced by the specimen ligament length. Doll et al. [¹⁴] studied the fracture behavior of asphalt mixtures by DIC measuring system. It indicated that recycled asphalt shingles had an obvious influence on the load-displacement curves and the crack front parameters. Destrebecq et al. [¹⁵] investigated the influence of the service conditions on the flexural behavior of the full scale concrete beam by using DIC method. It was found that the measured deflection and curvature of the beam given by the DIC method were reasonable. Bolhassani et al. [⁸] used DIC to study the damage and deformability of concrete masonry wall. Test results showed that quantitative mapping of deformation field until the wall capacity was reached was only possible by using DIC. Tung et al. [¹⁶] used DIC method to monitor the full-field deformation of a retaining wall. It was found that this method could accurately evaluate the tendency, location, and quantity of retaining wall’s deformation. In the above studies, the behaviors of concrete specimen (concrete blocks, beams, columns, and walls, etc) were analyzed by DIC method. But the related investigations on the mechanical properties of different concrete phases need to be further performed.

There were few studies on the deformation distribution and crack detection of component of concrete. Shah et al. [¹⁷,¹⁸] applied DIC to measure deformations on the surface of concrete specimens under axial compression. It was found that cracks circumvented the coarse aggregates and propagated parallel to the loading direction. Mao et al. [¹⁹] measured strain distribution together with crack propagation in concrete based on the image analysis method. Wu et al. [²⁰] studied axially compressive behavior of concrete specimens made of demolished concrete blocks and fresh concrete by DIC method. The strain of specimen was approximately uniformly distributed when the external load up to 40%–60% of the peak load, and then microcracks appeared when the load reached 60%–80% of the peak load. Hilal et al. [²¹] used DIC technique to study failure mechanism of foamed concrete. It was indicated that brittleness reduced with inclusion of lightweight aggregate. Li et al. [²²,²³] investigated the deformation distribution and crack propagation of recycled aggregate concrete by DIC. Test results showed that the ITZs were weak links affected micro-crack initiation and propagation of recycled concrete. Maruyama and Sasano [²⁴] obtained strain distributions over the cross section of sliced concrete specimens during drying. It was found that expansive strains existed in the maximum principal strain even though the entire specimen shrank.

However, the deformation field distribution and crack propagation of concrete components (coarse aggregate, cement mortar, and interface transition zones (ITZs), etc.) under compression by DIC method were not systematically analyzed. To the best knowledge of the authors, the study on the influences of water-cement (W/C) ratio and strength on the strain distribution and crack propagation of concrete was very limited. So, an experiment about this field was carried out, and a new analysis program for DIC method was developed. The axial compression tests of sliced concrete were used to study the displacement and strain developments of cement paste, and coarse aggregate and ITZs. The influence of W/C on the deformation behavior and crack development was also investigated.

Analysis process and algorithm model

Cross-correlation coefficient

The cross-correlation coefficient is important to the computation of DIC method. It evaluates the degree of similarity between two images. The theoretical basis of cross-correlation coefficient is described as follows: the initial non-deformed image is referred to as Image A and the subsequently deformed image is referred to as Image B (Fig. 1). To calculate displacement in x and y directions at a selected point on the Image A, an image subset (subimage a) on the non-deformed image is selected. Finding the most similar image subset (subimage b) on the deformed image by using a mathematical function called cross-correlation coefficient. The cross-correlation coefficient defines the degree of similarity between two subimages. The cross-correlation coefficient (R) used in this study can be expressed as (Eq. (1))

(1)R={\displaystyle \frac{{\displaystyle {\displaystyle \sum _{x=-m}^{x=m}}{\displaystyle \sum _{y=-m}^{y=m}\left[f(x,y)-f_m\right]\left[g(x^{\prime },y^{\prime })-g_m\right]}}}{\sqrt{{\displaystyle \sum _{x=-m}^{x=m}{\displaystyle \sum _{y=-m}^{y=m}{\left[f(x,y)-f_m\right]}^{\mathrm{2}}}}}\sqrt{{\displaystyle \sum _{x=-m}^{x=m}{\displaystyle \sum _{y=-m}^{y=m}{\left[g(x^{\prime },y^{\prime })-g_m\right]}^{\mathrm{2}}}}}}}

where f (x,y) and g (x′,y′) are the grayscale values of the subimage a at (x,y) and the subimage b at (x′,y′), respectively. f_m and g_m are the average grayscale values of subimage a and subimage b, respectively. If these two subimages are the same, the cross-correlation is 1. It becomes 0 if there is no correlation between two subimages.

Integer pixel and sub-pixel search

Integer pixel search

The integer pixel search is to find the integer pixel movement in x and y directions at a selected point based on the cross-correlation coefficient. There have been many algorithms developed for the computation of integer pixel shifting. The hill-climbing algorithm [²⁵] was used in this study since its simple, efficient, and accurate.

Sub-pixel search

The data obtained by camera is discrete in nature due to the operational characteristics of video cameras and digitization circuits [²⁶]. So, there is no gray level information available between pixels. However, when specimen is loaded, the movement of point on the non-deformed image is not always integer pixel. To obtain the accurate results, the calculation of sub-pixel shifting is necessary.

There were many algorithms used to measure displacements of objects under loading to sub-pixel accuracy [²⁶]. In this study, bi-cubic spline interpolation algorithm was used to obtain the sub-pixel shifting. This algorithm has been found to be accurate and reliable.

Data smoothing

After integer pixel and sub-pixel search, generally, the calculated results could not be used in the following analysis process directly. That is because the equipment or algorithm used to obtain the data have inherent limitations which manifest themselves as noise in the data [²⁷]. The noise of DIC is always too ambiguous to interpret. So, some techniques and algorithms [²⁸] were required to remove the noise from the data instead of altering the character of underlying data.

In this study, a new smoothing method (Lagrange interpolation polynomial algorithm) was developed and utilized as a noise eliminator. It took the movements of the shared nodes (node 1, 2, 3, etc.) near the adjacent points (point A and point B) as the reference values, and calculated movements of adjacent points (point A and point B) in x and y directions using two-dimensional Lagrange interpolation polynomial fitting method, as illustrated in Fig. 2.

Strain computation

In many mathematical theories and finite element analysis methods, the strain was calculated by using numerical difference method. However, the slight noise in the data could be obviously amplified by using this method in DIC method, which can cause larger errors in the strain computation. To obtain a reasonable strain distribution, the data was calculated by the first derivative of the smooth displacement field [²⁹]. The equation can be expressed as (Eq. (2))

(2){ϵ}_x={\displaystyle \frac{\partial u}{\partial x}},{ϵ}_y={\displaystyle \frac{\partial v}{\partial y}},{\gamma }_{xy}={\displaystyle \frac{\partial u}{\partial y}}+{\displaystyle \frac{\partial v}{\partial x}},

where {ϵ}_x, {ϵ}_y, and γ_xy are the transverse, axial, and shear strains of the specimen, respectively. u and v are the horizontal and axial displacements, respectively.

When the displacement and strain distribution were obtained, the crack data could be analyzed in combination of image information by fundamental photogrammetry and digital image processing rules.

Analysis program

The detailed digital image analysis program is shown in Fig. 3. The Matlab software was employed to code the numerical procedure according to this program. The specific process was as follows. First, obtaining the digital image information of specimens by camera. Secondly, selecting the analysis area of image, and then calculating the integer pixel and sub-pixel movements of selected point. Subsequently, removing the noise from the data using smoothing method. Finally, analyzing the strain distribution and crack development.

Experimental program

To evaluate the deformation distribution and crack propagation of concrete, 18 sliced concrete specimens under axial compression were tested. The main parameter in this study was the water-cement ratio.

Properties of materials

Ordinary Portland cement 42.5R was used in this study. The gravel was chosen as natural coarse aggregate (NCA). The fine aggregate was sand. Table 1 presents the properties of aggregate. The specimen had three mixture proportions, i.e., Cement: Sand: Gravel: Water= 3.69:3.51:8.6:1.48 (W/C= 0.4), 2.95:4.11:8.74:1.48(W/C= 0.5), and 2.46:4.67:8.67:1.48(W/C= 0.6).

Specimen design and testing instruments

Specimen design

Concrete cubes of 100 × 100 × 100 mm³ were cast using different W/C. Three cubes in every group were used to measure compressive strength of specimen. Some cubes were cut into sliced samples (100 × 100 × 15 mm³) for axial compression test. The width-thickness ratio was less than 5. The specimen was in the state of plane stress.

Altogether, 18 sliced specimens were designed and manufactured. The illustration of specimen is shown in Fig. 4. The flat viewing surface is necessary to clear focusing during the image capturing. It should be noted that the specimen was intact and no obvious damage was observed. So, it can be used in the following test and analysis. The details of specimens are given in Table 2. Each group had 6 specimens. Each specimen was named according to the main test parameters. Taking SC2-4 as an example, SC denotes the sliced concrete; the first number represents W/C, 2 is 0.5 W/C; the last number denotes specimen number, 4 denotes the fourth specimen in this group.

Testing instruments

The experimental system consisted of three parts: a 400 kN multi-function electro-hydraulic servo tester, a video system with 1 million resolution industrial camera, and a computer system with image analysis program. The industrial camera was used to capture the digital information of front surface of sliced concrete. The field experimental system is shown in Fig. 5(a).

The arrangement of the strain gauges is shown in Fig. 5(b). Two vertical strain gauges were placed on both sides of specimen to measure axial deformation of sliced concrete. To identify the accuracy of calculated strain field results, two strain gauges were located at the left and right corners of specimen surface. The loading was controlled by the displacement pattern.

Experimental results

The axial stress versus strain curves of sliced concrete under uniaxial compression are shown in Fig. 6 (a). The curves of specimens can be divided into three stages: 1) the elastic stage, the axial stress versus strain curve was almost straight line when the stress up to 30%–40% of the peak stress (f_c); 2) the elasto-plastic growth stage, the relationship between the stress and strain could be characterized by nonlinear; 3) the decline stage, where the axial strain increased with an decrease of stress.

Test results showed that both the peak stress and strain of specimen increased with an decrease of W/C. It indicated that the initial modulus of SC3-3 was lower than those of SC1-2, SC2-5. The W/C had an obvious effect on the mechanical properties of specimen. It was also found that the main failure pattern was the crushing of concrete, and several inclined macro-cracks were formed on the surface of the specimen. The failure patterns of specimens with different W/C were similar.

Discussion and analysis

Error analysis

The comparison between the calculated axial strain and the experimental data are shown in Fig. 6(b). It was found from the figure that the calculated results were in agreement with the experimental ones. The mean value of errors was 0.054 pixels, and the standard deviation was about 0.032 pixels. The error of axial deformation was acceptable. The calculated strain was in agreement with the experimental data.

Displacement field distribution

Axial displacement

The axial displacement contour maps of specimens with different W/C are shown in Figs. 7–8. It could be found that the axial displacement of specimens distributed non-uniformly even at early stage of loading. That can be attributed to the inhomogeneous of materials. The properties (modulus, hardness, and strength, etc.) of coarse aggregate, cement mortar, and ITZ were different, and the geometry of these components was also asymmetrical. The inhomogeneous of specimens leaded to the variation of displacement distribution. The displacements of ITZs and cement mortar were higher than that of coarse aggregate (Figs. 7(a) and 8(a)) in the initial stage of loading, which can be explained as the high strength and modulus of gravel.

With the increase of loading (0.3f_c–0.8f_c), the growth of axial displacements of cement mortar and ITZs was more rapidly than that of coarse aggregate axial displacement (Figs. 7(b) and 8(b)). The reason for this phenomenon is the gravels in concrete form a strong skeleton to bear compressive load. Therefore, the axial deformation of coarse aggregate was relatively small before macro-cracks appeared. When the stress reached f_c, the cracks propagated rapidly, and parts of cement mortars were failed. The deformation of coarse aggregate increased dramatically. This phenomenon is attributed to the crack propagation and the destruction of gravels skeleton, which cause the deformation of coarse aggregate develops rapidly (Figs. 7(c) and 8(c)). After the peak stress, the deformation of coarse aggregate was similar to that of cement mortar due to the failure of gravel skeleton. The axial deformation gradually decreased from the loading end to the fixed end (Figs. 7(d) and 8(d)).

The development tendencies of axial displacements of specimen with different W/C nearly kept the same. But there were also a few differences could be obtained. Comparing with SC1, the differences between the displacement of coarse aggregate and that of cement mortar became small when the SC3 reached f_c (Figs. 7(a)–7(e), 8(c), 8(d)). That is because the higher W/C is, the more cracks of the concrete are (in the peak stress) and the less displacement differences between cement mortar and coarse aggregate are. However, this tendency was opposite in the initial stage of loading.

Horizontal displacement

The horizontal displacement distribution was less affected by the difference between gravel and cement mortar (Fig. 9). In the initial stage of loading, the displacement was approximately symmetric along the middle of specimen (Fig. 9(a)). After the cracking of concrete, the displacement un-uniformly distributed (Fig. 9(b)). The effect of W/C on the horizontal displacement was not obvious.

Strain distribution

Transverse strain

Figure 10 shows the contour description of transverse strain distribution obtained from DIC method (specimen SC3-3). In the initial stage of loading (0.2f_c–0.3f_c), the strain was small and distributed non-uniformly (Fig. 10(a)). That is because the difference of transverse deformations of inhomogeneous materials. With the increase of axial loading (0.4f_c–0.8f_c), large transverse strain appeared in the weak position (locations of voids and initial defects) and the ITZs between coarse aggregate and cement mortar. This is mainly due to the non-uniform displacements between coarse aggregate and cement mortar. During this stage, the large transverse strain increased and formed the discrete deformation concentration areas (DCAs), as shown in Figs. 10(b)–10(c). The discrete DCAs in this stage could be considered as the fracture process zone (FPZ) [¹³] in the fracture mechanics. When the axial load reached f_c, the discrete DCAs were connected gradually and developed an approximate strip region, as shown in Fig. 10(d). The connected DCA not only crossed ITZs, but also obviously appeared in cement mortar. This meant that the damage and fracture of concrete increased, and the cracking of concrete was closed to the unstable development stage. However, the strain of other regions developed slowly. After the peak point, the value of main DCA became larger. There was also a few DCAs appeared in other regions of specimen, which meant the new cracks and FPZ appeared. However, the value of new DCAs was relatively small (Fig. 10(e)). When the external stress dropped to 70%–80% of f_c, the specimen was separated into several parts by the DCAs, and the strain mainly concentrated in DCAs (Fig. 10(f)).

Comparing the transverse strains of specimens under different W/C, it could be found that the development tendencies of transverse strains were similar. Before the obvious cracks occurred, the differences between transverse strains of specimens with different W/C were small. However, when the stress reached/approached the peak value, the number and size of DCAs of concrete with high W/C (SC3) was much more than those of DCAs of concrete with low W/C (SC1). By contrast, the value of DCAs of SC1 was higher those of SC3 (Fig. 11). After the peak point, the number of DCAs in SC3 increased rapidly and the DCAs was spread over the whole surface of specimen. However, the number of DCAs in SC1 was relatively small, and it mainly concentrated in a certain area. This indicated that the W/C had an obvious influence on the strain distribution and the failure of concrete.

Axial strain

The contour description of axial strain distribution obtained from DIC is shown in Fig. 12. In the initial stage of loading (0.1f_c–0.2f_c), the axial strain was small and distributed non-uniformly, which was caused by the difference of axial deformations of inhomogeneous materials. The axial strain of ITZs around coarse aggregate was higher than those of cement mortar and coarse aggregate (Fig. 12(a)). With the increase of loading (0.3f_c–0.4f_c), large axial strain gradually concentrated in the ITZs (Fig. 12(b)). This phenomenon can be attributed to the non-uniformly axial displacement between different concrete phases. The axial strain concentration became more obvious when the stress up to 50%–100% of the peak stress, while the axial strains in other regions of specimen were relatively small. During this stage, the axial DCAs mainly surrounded coarse aggregate, which was different from the distribution of transverse DCAs (Figs. 12(c)– 12(e)). The axial strain of ITZs around coarse aggregate developed more rapidly than strains of other phases. After the peak point, the development of axial DCAs kept the same. The axial DCAs increased with an increase of axial displacement. At the end of test, a small amount of axial DCAs could be observed in the cement mortar (Fig. 12(f)), which was due to the failure of gravel skeleton at the end of loading.

Comparing the axial strains of specimens under different W/C, it could be found that the difference was small in the initial stage of loading. When the axial stress reached/past f_c, the influence of W/C became obvious. The distribution range and number of axial DCAs of specimen with low W/C (SC2) were smaller than those of high W/C specimens (SC3) (Fig. 13). That can be explained as the lower W/C is, the higher cement mortar hardness is, and the lower difference between axial displacement of gravel and that of cement mortar is. However, the value of axial DCAs in SC2 was much higher than that of DCAs in SC3-3. The axial strain of specimen at peak point increased with decreasing of W/C.

Shear strain

Figure 14 presents the contour description of shear strain distribution. When the stress reached 20% of f_c, the strain was small and distributed non-uniformly (Fig. 14(a)). The shear strain concentrated in ITZs, which can be attributed to the differences between the deformation of coarse aggregate and that of cement mortar. With the increase of axial stress (40%–95% of f_c), large shear strain gradually formed the obviously discrete DCA (Fig. 14(b)). The DCAs mainly appeared in ITZs and cement mortar, however, there were also a little of DCAs passed through coarse aggregate. This phenomenon indicated that the increase of FPZs and cracks in concrete, and the cracking of specimen was on the edge of stable development stage. The value of DCAs increased more rapidly when the stress reached the peak point (Fig. 14(c)). Finally, the discrete DCAs connected and formed a main DCA (Fig. 14(d)).

The development tendencies of the shear strains of specimen with different W/C were similar in the initial stage of loading. After the peak point, the differences between shear strain of specimen with low W/C (SC1) and that of specimen with a high W/C (SC3) were obvious. The distribution range and number of DCAs in SC3 were higher than those of DCAs in specimen SC1 (Fig. 15). That can be explained as the higher W/C is, the lower modulus and strength of cement mortar is, and the more difference between deformation of coarse aggregate and that of mortar is. By contrast, the value of DCAs in SC1 was higher than that of DCAs in SC3. The influence of W/C on the deterioration of concrete could be characterized by the high W/C is, the more number of DCAs is, while the less value of DCAs is.

Crack propagation

The crack propagation of concrete was studied by DIC method. The stress state of specimen can be considered as plane state under uniaxial compression. The 2D DIC method was capable of investigating crack propagation of concrete. The comparisons between cracks and deformation field are shown in Figs. 16–17. The crack development of concrete was observed at different stages of compressive loading. It indicated that the failure processes of specimens varied with the variation of W/C.

In the initial stage of loading (20%–30% of f_c), the strain was small and the micro-cracks could be hardly captured by naked eyes, few micro-cracks appeared in ITZs. When the stress reached 40%–50% of f_c, the micro-cracks initiated and developed around ITZ region. However, a few cracks propagated perpendicular to the coarse aggregate surface (Figs. 16(a) and 17(a)). The cracking of specimen was in the stable development stage. As the loading increased (50%–90% of f_c), the micro-cracks developed and most of these cracks were not connected. There were also some cracks appeared in the cement mortar. The cracking of concrete was on the edge of stable development stage. When the stress was about 90%–100% of f_c, the length and width of cracks increased rapidly. Lots of cracks could be captured by naked eyes. Discrete cracks connected and formed continuous cracks. These cracks mainly developed along the ITZs, and parts of cracks even crossed the cement mortar (Figs. 16(b) and 17(b)). After the peak point, the size and number of cracks increased dramatically. The deformation of specimen was obvious. The cracking of specimen was on the edge of unstable development stage. The length and width of cracks developed gradually, even a few cracks passed through coarse aggregate (Figs. 16(c) and 17(c)). Finally, the specimen was crushed and the test finished.

Comparing the crack propagations of specimen under different W/C, it could be found that the propagation of cracks was obviously influenced by the strength differences between coarse aggregate and cement mortar. For SC3 (W/C= 0.6), most cracks passed through the ITZ and cement mortar. Only a few cracks appeared in coarse aggregate (Fig. 17(c)). As for SC1 (W/C= 0.4), the crack crossed ITZs, cement mortar and coarse aggregate (Fig. 16(c)). This phenomenon could be attributed to the differences between the strength and modulus of cement mortar and those of coarse aggregate.

Furthermore, before f_c, the size and number of cracks in specimen with high W/C (SC3) were more than those of specimen with low W/C (SC1). After the peak point, the crack increased with increasing of external load, the number and distribution range of cracks in SC3 were larger than those of cracks in SC1. However, the value and width of cracks in SC1 were obviously higher than those of cracks in SC3 (Figs. 16(c) and 17(c)). The reasons are: the higher W/C is, the more difference between deformation of cement mortar and that of coarse aggregate is, and the larger number and distribution range of cracks are; the smaller number and distribution range of cracks are, the larger width and value of cracks are needed to release internal energy. The effects of W/C on the characteristics of concrete deterioration were obvious.

Conculsions

The deformation distribution and crack propagation of concrete under different W/C were investigated using DIC method. The following conclusions can be drawn.

1)‚The new analysis process for DIC method is developed based on the algorithm model. The related numerical program is also established and validated. The calculated results are in good agreement with experimental ones. The suggested program and process could be applied in the measurement of concrete full-field deformation.

2)‚The axial displacement distributes non-uniformly in the early stage of loading. The axial displacement of cement mortar are higher than that of coarse aggregate before the occurrence of macro-cracks. After that, the difference between the axial displacement of coarse aggregate and that of cement mortar becomes small. After the peak stress, the higher W/C is, the less displacement differences between cement mortar and coarse aggregate are. However, the horizontal displacement distribution is less influenced by the W/C.

3)‚The axial, transverse and shear strains distribute non-uniformly in the initial loading stage. With the increase of loading, the large strain forms DCAs. The transverse and shear DCAs cross the cement mortar, and ITZs and coarse aggregates. However, the axial DCAs mainly surround the coarse aggregate. Furthermore, the higher W/C is, the more range and number of DCA is. However, the value of DCA decreases with an increase of W/C. That can be attributed to the effect of W/C on the properties of cement mortar (modulus, strength, and hardness, etc.).

4)‚The effect of W/C on the crack propagations is obvious. Generally, the micro-crack initiations of concrete mainly occur in the ITZs. For the high W/C concrete, most of cracks cross the ITZ and cement mortar, only a few cracks appear in coarse aggregate. Under the same stress level, the number and distribution range of cracks in high W/C concrete are larger than those of cracks in a low W/C specimen. However, the value and width of cracks in high W/C specimen are relatively small. The W/C has an obvious effect on the characteristics of concrete deterioration.

5)‚The further studies will focus on the quantitative analysis of crack (area, length, size, direction, etc.) under different loading conditions. The elasto-plastic deformation development and the damage evolution of concrete will be studied using the suggested DIC method.

References

[1] Xiao J Z, Li J B, Zhang C. Mechanical properties of recycled aggregate concrete under uniaxial loading. Cement and Concrete Research, 2005, 35(6): 1187–1194

[2] Komlos K. ̆Popovics S, Nurnbergerova T, Babál B, Popovics J S. Ultrasonic pulse velocity test of concrete properties as specified in various standards. Cement and Concrete Composites, 1996, 18(5): 357–364

[3] Ohtsu M, Watanabe H. Quantitative damage estimation of concrete by acoustic emission. Construction & Building Materials, 2001, 15(5–6): 217–224

[4] Morgan D R. Compatibility of concrete repair materials and systems. Construction & Building Materials, 1996, 10(1): 57–67

[5] Atsushi I, Yoshimitsu A, Shuji H. Accurate extraction and measurement of fine cracks from concrete block surface image. In: IEEE the 28th Annual Conference of the Industrial Electronics Society. Sevilla: Institute of Electrical and Electronics Engineers, 2002, 2202–2207

[6] Vieira Filho J, Baptista F G, Inman D J. Time-domain analysis of piezoelectric impedance-based structure health monitoring using multilevel wavelet decomposition. Mechanical Systems and Signal Processing, 2011, 25(5): 1550–1558

[7] Nanni A, Yang C, Pan K. Fiber-optic sensors for concrete strain/stress measurement. ACI Materials Journal, 1991, 88(3): 255–265

[8] Bolhassani M, Hamid A A, Rajaram S, Vanniamparambil P A, Bartoli I, Kontsos A. Failure analysis and damage detection of partially grouted masonry walls by enhancing deformation measurement using DIC. Engineering Structures, 2017, 134: 262–275

[9] Sutton M A, Orteu J J, Schreier H W. Image Correlation For Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications. Boston: Springer, 2009

[10] Chu T C, Ranson W F, Sutton M A. Applications of digital-image correlation techniques to experimental mechanics. Experimental Mechanics, 1985, 25(3): 232–244

[11] Peters L W H, Ranson W F. Digital imaging techniques in experimental stress analysis. Optical Engineering (Redondo Beach, Calif.), 1982, 21(3): 427–431

[12] Dong W, Wu Z M, Zhou X M, Dong L H, Kastiukas G. FPZ evolution of mixed mode fracture in concrete: Experimental and numerical. Engineering Failure Analysis, 2017, 75: 54–70

[13] Dong W, Yang D, Zhou X, Kastiukas G, Zhang B. Experimental and numerical investigations on fracture process zone of rock-concrete interface. Fatigue & Fracture of Engineering Materials & Structures, 2017, 40(5): 820–835

[14] Doll B, Ozer H, Rivera-Perez J J, Al-Qadi I L, Lambros J. Investigation of viscoelastic fracture fields in asphalt mixtures using digital image correlation. International Journal of Fracture, 2017, 205(1): 37–56

[15] Destrebecq J F, Toussaint E, Ferrier E. Analysis of cracks and deformations in a full scale reinforced concrete beam using a digital image correlation technique. Experimental Mechanics, 2011, 51(6): 879–890

[16] Tung S H, Weng M C, Shih M H. Measuring the in situ deformation of retaining walls by the digital image correlation method. Engineering Geology, 2013, 166: 116–126

[17] Choi S, Shah S P. Measurement of deformations on concrete subjected to compression using image correlation. Experimental Mechanics, 1997, 6(3): 307–313

[18] Shah S G, Chandra Kishen J M. Fracture properties of concrete-concrete interfaces using digital image correlation. Experimental Mechanics, 2011, 51(3): 303–313

[19] Mao K, Jun M, Shinobu N, Wu Z. Study of image analysis methods for measuring crack propagation in concrete. Journal of Applied Mechanics, 2014, 70(2): 135–144

[20] Wu B, Liu C, Wu Y P. Compressive behaviors of cylindrical concrete specimens made of demolished concrete blocks and fresh concrete. Construction & Building Materials, 2014, 53: 118–130

[21] Hilal A A, Thom N H, Dawson A R. Failure mechanism of foamed concrete made with/without additives and lightweight aggregate. Journal of Applied Mechanics, 2016, 14(9): 511–520

[22] Li W G, Sun Z, Luo Z, Shah S P. Influence of relative mechanical strength between new and old cement mortars on the crack propagation of recycled aggregate concrete. Journal of Advanced Concrete Technology, 2017, 15(3): 110–125

[23] Li W, Long C, Tam V W Y, Poon C S, Duan W H. Effects of nano-particles on failure process and microstructural properties of recycled aggregate concrete. Construction & Building Materials, 2017, 142: 42–50

[24] Maruyama I, Sasano H. Strain and crack distribution in concrete during drying. Materials and Structures, 2014, 47(3): 517–532

[25] Russell S J, Norvig P. 2nd ed. Artificial Intelligence: A Modern Approach. New Jersey: Prentice Hall, 2003

[26] Bruck H A, McNeill S R, Sutton M A, Peters W H III. Digital image correlation using Newton-Raphson method of partial differential correction. Experimental Mechanics, 1989, 29(3): 261–267

[27] Sutton M A, Turner J L, Bruck H A, Chae T A. Full field representation of discrete sampled surface deformation for displacement and strain analysis. Experimental Mechanics, 1991, 31(2): 168–177

[28] Craven P, Wahba G. Smoothing noisy data with spline functions. Numerische Mathematik, 1978, 31(4): 377–403

[29] Pang X, Xie H M. Full field strain measurement based on least square fitting of local displacement for digital image correlation method. Acta Optica Sinica, 2007, 27(11): 1980–1986 (in Chinese)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature