Topographical analysis of fractured surface roughness of macro fiber reinforced concrete and its correlation with flexural toughness

Macro fibers reinforcement is considered to be an effective way to improve the flexural toughness of the concrete. With growing public interest in wide-spread use of fiber reinforced concrete (FRC), the need for understanding and evaluating micro fiber reinforcement mechanism is on the rise. In this study, concretes were reinforced by various dopant amounts of macro polypropylene (PP) fiber or steel fiber (SF) or their mixtures, topographical analysis was applied on a fractured concrete surface by using a custom-built 3-D laser scanning equipment , and the tested surface was fractured by using a three-point bending beam test. The topographical analysis results were evaluated quantitatively by roughness parameters of roughness number ( RN), fractal dimension ( D ), standard deviation of height distribution ( σ z ), and arithmetic mean deviation of the surface topography ( H a ). Multivariate analysis suggests the most effective of roughness number ( RN) for evaluating the roughness of fractured surface. Furthermore, the RN of fractured surface was further correlated to the flexural toughness of the concrete, the relation between the fractured concrete surface roughness ( RN) and flexural toughness follows an exponential function, which can be employed to quickly estimate its roughness of fractured surface by flexural toughness of the FRC. In conclusion, from the developed topographical analysis method, the hybrid fibers reinforced concrete shows the most significant improvement of the flexural toughness of the concrete, which suggests hybrid fiber reinforcement shall be a future solution for commercialization of the FRC in terms of high toughness and high durability.


Introduction
Concrete is heterogeneous, porous and rough composite material with complicated micro-structures and meso-structures. The previous studies have demonstrated that concrete behavior is mainly determined by the micro-structural heterogeneity. The heterogeneity is produced by the property and proportion of different materials in the concrete and causes the initial local defects such as the micro-cracks and voids. Under the mechanical loading, the voids and micro-cracks propagate and become the macro-cracks [1,2] , and the type of macro-cracks propagation dominates correspondingly the type of failure [3,4] . During all reinforced concretes service life, they work with cracks due to the low tensile capacity of concrete. While the existence of cracks can obviously accelerate the degradation of concrete, due to the intrusion of water inside the concrete with deleterious substances such as chloride and sulphate ions. Moreover, when the crack width is the same, the ease with which fluid penetrates into concrete depends mainly on the fractured surface topography of concrete [5,6] .
As such, the durability of concrete is relevant to the fractured surface topography. Fiber reinforced concrete (FRC) is an increasingly popular construction material during recent years.
The short randomly distributed fibers in the concrete matrix can address some of the concerns related to concrete brittleness, and have long been recognized as an effective way to increase the roughness of fractured surface of concrete and reduce water permeability of fractured concrete [6] . However, the investigation on the effects of fiber on the topography of fractured surface, especially the effects of fiber type and fiber content on the roughness of fractured surface are still very limited.
In recent decades, some researchers have studied the topography characteristic of the cement-based materials employing some instrumental techniques. Different methods have the similar goal that is to acquire the information of fractured surface topography and reconstruct the fractured surface of concrete. The current instruments include focused ion beam [7] , X-ray computed tomography [8] , scanning electron microscopy [9][10][11][12] and confocal microscopy [9,[13][14][15][16][17] .
While the size of the corresponding specimens of these instruments is relatively small (approximately 1-30000 μm) and cannot be suitable for concrete materials. We have a custom-built 3-D laser scanning equipment, and it can be applied to investigate the fractured surface topography of concrete in meso-scale and macro-scale without restriction on the specimen size.
In order to quantify the surface roughness of cement-based materials, some roughness parameters have been calculated by the information of fractured surface topography and employed to reflect the topography of material surface in previous investigations, i.e. roughness number [2,16,[18][19][20][21][22] and fractal dimension [2,4,16,17,23,24] , standard deviations of height distributions [12,25] , arithmetic mean deviation of the surface topography [15,26] , etc. These roughness parameters force on the global character of material surface topography, while it is worth noting that different roughness parameters maybe have different results in quantifying the roughness of the surface. The investigations on selecting the most effective roughness parameter for analyzing the roughness of fractured surface are still very rare.
As a result of crack propagation, the fractured surface topography may reveal the corresponding failure behavior [21,27] . Some investigations have been conducted to analyze the relationship between the fractured surface topography and the mechanical behavior of plain concrete. Issa et al. [4] investigated the correlation between fracture properties and the roughness of fracture surface using the slit-island method. Ficker et al. [18] analyzed the relationship between the roughness of the fractured surface and the compression strength of hydrated cement pastes with the w/c from 0.4 to 1.0 by confocal microscopy. Erdem et al. [2] studied the influence on the fracture-related properties in different types of concrete having different coarse aggregate characteristics. Their results showed that the mechanical behavior of concrete correlated very well with the roughness of fractured surface.
While the review of literatures indicates that the topographical analysis could be used to evaluate the surface roughness of the concrete, and the fractured surface roughness of the concretes could be correlated to their mechanical properties. When the quantitative relationships are obtained, once the mechanical behavior of concrete are known, and then the roughness of fractured surface can be calculated. Meanwhile, some investigations [6,[28][29][30] have verified the relationships between roughness and permeability of crack. Moreover, the tests and methods of mechanical behavior of concrete have been maturely developed. Compared to the durability ( gas/ water permeability) tests, the mechanical tests show the advantages such as simplicity, accuracy and efficiency. If the durability properties of concrete maybe indirectly be estimated by means of the mechanical behavior of concrete, the time and cost of test for measuring the durability properties of concrete will be greatly saved and its accuracy can be obviously improved. However, there is lack of investigations on quantitative analysis of such correlations. In this paper, 3 reinforcements (polypropylene fiber reinforced concrete (PFRC), steel fiber reinforced concrete (SFRC) and hybrid fiber reinforced concrete (HFRC)) and total 9 different proportions were investigated. After the three-point bending test, the fractured surface was scanned by a custom-built 3-D laser scanning equipment, and the topographical features of the fractured concrete surface were converted to be explained by an effective roughness parameter, which was used for a quantitative evaluation of flexural toughness of FRC.

Materials
The P.O 42.5R Portland cement (in line with Chinese Standard GB175-2007 [31] , P.O stands for Ordinary Portland Cement) was used to prepare the FRC. The fly ash, with a specific gravity of 2.0 g/cm 3 was used as an admixture. The fine aggregate was the quartz sand with a fineness modulus of 2.6. The coarse aggregate was the natural crashed gravels with maximum size of 10 mm. The properties and geometry of macro PP fiber and steel fiber are listed in Table 1 and Fig. 1. The mix design of concrete without fiber reinforcement is listed in Table 2. According to the ASTM Standard C143 [32] and C231 [33] , the slump and air content of fresh FRC were tested and listed in Table 3. With the increase of fiber content, a decrease in the slump and an increase in the air content of concrete paste were observed, respectively. And the 28 days compression test showed almost identical compressive strength of FRC specimens.

Test specimens
The beam shape specimens used in this study were cast into steel moulds (100×100×400 mm 3 ). The specimens were demoulded after 24h. Afterwards they were transferred to a moist curing room and stored at 20°C and relative humidity over 90% for 28 days. Before the three-point flexural test, each beam was cut to obtain a 10 mm depth and 3 mm width notch.
Three identical specimens were prepared from the same mixture proportion.

Flexural test
According to RILEM Standard TC162-TDF [34] , the flexural performance of the beam concrete was tested on a setup of MTS Landmark ® test system. The schematic of testing set-up is shown in Fig. 2. All the specimens were tested on a span of 300 mm. The flexural test was determined by the deformation-controlled experiment. A close loop test machine was used and the deformation rate of the mid-span was 0.2 mm/min until the specified end point deflection of 3.5 mm was reached. Two linear variable differential transformers (LVDTs) were applied on the front and back sides for measuring the deflection of mid-span. The IMC Intelligence Data Collecting System was used to collect the experimental data in real time.
The load-deflection curves were employed to evaluate the flexural toughness of FRC.

Acquisition of the surface data
After the flexural test, the specimens were split into two parts along the crack and the connected fibers were cut off to expose the fractured surface. Later on, the custom-built 3-D laser scanning equipment was used to obtain the topographical information of the fractured surface (see Fig. 3). The 3-D laser scanning equipment was a non-contact device which enables to obtain the x, y and z coordinates of the points on the fracture surface and it consisted of the computer, a control system, a data acquisition system, three laser sensors, a power system of laser sensors and a profilometer. Moreover, the laser sensors provided an accuracy of 7μm. The movement of the profilometer with laser sensors was automatically controlled according to a preprogrammed scanning path (see Fig. 4 ). The vertical projection area of scanning region was 100×90 mm 2 .

Roughness parameters
According to the topographic data collected from the fractured surface, four roughness parameters can be calculated, which are intended to be employed to evaluate the roughness of FRC fractured surface. They are listed as follows:

Roughness number
The roughness number (RN) can be extracted from the topographical image (see Fig. 5).
The left part is "wire" model of the reconstructed fractured surface, and the right part is the magnified view of one element in the "wire" model.

Fractal dimension calculated by box-counting method
It is known that the fractured surfaces exhibit fractal behavior [28] , and the fractal dimension can be employed to estimate the roughness of fractured surface. The box-counting method is a widely accepted approach to estimate the fractal dimension. The three-dimensional elements can be used to cover the irregular fractured surface (see Fig. 6).
The size δ of element and the roughness of fractured surface determine the number of elements N (δ) [35] . As the size δ of element is changed, the number of elements N(δ) also changes, and the fractal dimension can be evaluated by the variation ratio of the number N(δ) of three-dimensional elements [26] . The relation between N(δ) and δ follows the power function in Eq. (4) [35] : where F is a constant determined from experimental measurement. D is the fractal dimension calculated by box-counting method.

Standard deviation of height distribution
Every sample has its unique height distributions of z-coordinates of measured points on the scanning area [12] , it means that the standard deviation σ z of height distribution can be used to characterize the dispersion of z-coordinates and then indirectly indicate the roughness of fractured surface. The standard deviation σ z of height distribution can be evaluated from Eq.
wherez is the average value of z-coordinates of all measured points on the scanning area, N is the number of measured points.

Amplitude parameter
Arithmetic mean deviation of the surface topography (H a ) is given as an amplitude parameter to characterize the fractured surface. It describes the deviation of surface heights relative to the mean plane. It is calculated in Eq. (6) [15] : (6) where z(x, y) is the function of topographical image,z is the mean plane of the z-coordinates of all measured points, L and M represent the sides of the projection area in the X-Y plane .

Flexural properties
The load-deflection curves of the specimens (with or without fiber reinforcement) are shown in the Fig. 7, the three-point bending test followed the RILEM TC162-TDF [34] . The flexural strength, ultimate load, energy absorption, equivalent flexural strength and fiber numbers on the fractured surfaces are listed in Table 4   the deflections of (δ L +0.65mm) and (δ L +2.65mm), respectively; f eq,2 and f eq,3 are the equivalent flexural tensile strengths by the deflections of (δ L +0.65mm) and (δ L +2.65mm), respectively; δ L is the deflection corresponds to the F L (mm); F 2 and F 3 are the residual load at the deflections of (δ L +0.65mm) and (δ L +2.65mm), N f is the number of fibers on the fractured surface, respectively.
A comparison of load-deflection of PFRC and SFRC beams is shown in Fig. 7 (a) and Fig. 7 (b), respectively. It can be seen: 1) The load bearing capacity of NC drops suddenly and the failure occurs just after the crack formation. For FRC, the load bearing capacity drops and then stabilizes at post-peak stage.
b) Compared to the SF20, the increment for the number of fibers on the crack surfaces of SF40 and SF60 achieve about 108% and 232%, respectively. c) For SF20 and SF40, the deflection softening behavior is also observed. For SF60, after the first drop of load, the curve possesses a higher flexural load than the cracking load and exhibits the deflection hardening behavior.
From the discussion above, it can be seen that the addition amount of steel fiber of the SF40 and SF60 are 2 and 3 times of SF20, however, according to the fracture surface analysis, the number of fiber at fracture surfaces of SF40 and SF60 are 2.08 and 3.32 times higher than that of SF20. It can be inferred that the increase rate of the number of fibers on the crack surface is higher than the increase rate of fiber content with the increasing of fiber content, PFRC displays a similar behavior. In this case, there is much higher amount of fibers reinforcement at fracture surface of concretes with the increasing of fiber content, this leads to a significant improvement in the post-peak flexural behavior of PFRC and SFRC with increment of fiber content. Meanwhile, in comparison of the load-deflection curves with the same fiber content of macro PP fibers and steel fibers in Fig. 7 (a) and Fig. 7 (b), SFRC exhibits better flexural behavior over the entire deflection range than that of PFRC. From Fig. 7 (c) and Fig. 7 (d) and Table 4, it can be seen: 1) The purple lines in Fig. 7 (c) and Fig. 7  achieves about 11%.
The discussion above demonstrates a positive synergistic effect of hybrid fibers on the post-peak behavior.

Reconstruction of fractured surface
Based on the topographical data of fractured surface obtained by 3-D laser scanning equipment, the fractured surfaces of concrete were reconstructed to gather topographical information of the surface. Fig. 8

Selection of the most effective roughness parameters for crack surface roughness
In order to select the most effective parameter for quantifying the roughness of crack surface, the following analysis is performed.
Four roughness parameters, i.e. roughness number (RN), fractal dimension (D), standard deviation of height distribution (σ z ) and arithmetic mean deviation of the surface topography (H a ), were calculated and listed in Table 5. In order to compare with the four roughness parameters in the same order of magnitude, each parameter is normalized ( the sum of all normalized values of each parameter equals to 1 ). Fig. 9 illustrates the comparison of the mean normalized values of the four roughness parameters of different samples. This implies that all 4 parameters (RN, D, σ z , H a ) are equally useful for the evaluation of the fractured concrete surface. However, considering the significant principle, one significant parameter will be assessed for distinguishing the most representative roughness of fractured surface.
In order to signify the parameters, further analysis is carried out by dividing the nine samples into three groups, and this later-on is found to be useful to distinguish the roughness of fractured surface of different samples. Groups are listed in Table 6. The unsupervised Principal Component Analysis (PCA), a multivariate analysis method for visualization of similarities or differences among data groups, is applied for the data analysis on Table 6. Fig. 10 illustrates the result of the PCA score plots of three groups. The contributions of two principal components (PC 1 and PC 2) equal 85.5% and 7.9% of the variation, respectively. They show a clear classification trend of three groups and demonstrate that the three groups are simultaneously visible to be distinguished. This is a prerequisite for demonstrating that the four parameters can be employed to distinguish the three groups. In order to select the most effective roughness parameter from the four roughness parameters, Random Forest is employed to identify and rank the importance of four roughness parameters in the three groups. Fig. 11 illustrates the relative importance of four roughness parameters by means of Random Forest. Fig. 11. Importance of four roughness parameters by Random Forest.
From Fig. 11, the MeanDecreaseAccuracy value of four roughness parameters is in an order of RN > H a > σ z > D. This means that the RN is the most effective roughness parameter for the evaluation of roughness of fractured concrete surface.

Comparison of the roughness parameter RN of different samples
A comparison of RN of fractured surfaces is shown in Fig. 12, and the results are summarized as follows: In the previous reported studies [36,37] , the roughness of fractured surface of plain concrete had a direct relationship with size and content of coarse aggregate. For FRC, the fibers in concrete matrix play a significant role on the crack trajectory and surface roughness.
Armandei et al. [38] analyzed the effect of fiber on the fractured surface, and the result suggested that the fibers, aggregates and paste of FRC form some "colonies" (see Fig. 13), which may exhibit higher local tensile strength than that of aggregates and pastes, it causes that the cracks can be prevented to propagate into the "colonies" and deviated the trajectory path of crack toward the interval of the "colonies" (Fig. 13 (b)). The fiber and paste of "colonies" work together like a strong "armor" wrapped around the aggregate, and the size of "colonies" is larger than that of aggregate. It is known that the roughness of fractured surface gradually increases with the increasing of size of aggregate [39] , so the "colonies" cause rougher fractured surface than the aggregates. This may explain a much rough surface on the fractured concrete with fibers reinforcement. With increment of fiber content, the domain of "colonies" in FRC matrix expands, which leads to an increment of the roughness of fractured surface. Meanwhile, the high content of fiber could also cause much tortuous trajectory of the cracks.

Relationship between the roughness of fractured surface and the flexural toughness parameters
The roughness parameter RN of the fractured concrete was further correlated to the evaluation of flexural toughness of the concrete (f eq,2 , f eq,3 , F 2 and F 3 ), as shown in Fig. 14  In Fig. 14, it can be seen that the relationships between the roughness parameter RN of fractured surface and the flexural toughness parameters (f eq,2 , f eq,3 , F 2 and F 3 ) correspond well with exponent functions, which can be expressed in following Eq. (7): where m, n and p are the parameters fitted corresponding to the experiment, the variable X is the roughness parameter RN of fractured surface and the Y is the flexural toughness parameters (f eq,2 , f eq,3 , F 2 and F 3 ), respectively. From Fig. 14, it can be seen that the flexural toughness of PFRC, SFRC and HFRC beams presents an exponential growth with increment of roughness parameter RN. The exponential function between flexural toughness and RN roughness was further confirmed by the published data [40] [41] , this indicates the general applicability of the proposed function.  Table 4).
Meanwhile, the increase rate of fractured surface roughness decreases with increment of fiber dosage (see Fig. 12). Therefore, the relationships between the roughness of fractured surface and the flexural toughness agree with the exponent functions rather than the linear functions.
The parameters fitted of Eq. (7) maybe vary depending on the properties of fiber and concrete mix design. Moreover, the functions between flexural toughness and roughness of crack surface can be considered as a tool box to estimate quickly and conveniently the roughness of crack surface by means of the flexural toughness of FRC according to RILEM TC162-TDF [34] . This paper presents a pioneer work in this field. Future study will focus on combining the result in this paper and previous investigations [5,6,28,30] of the relationships between the between crack geometry and permeability, and they will provide the theoretical support of the study between the durability (water/gas permeability) and mechanical behavior of cracked fiber reinforced concrete.

Conclusions
This study proposed a topographical analysis of the fractured surface feature and its correlation to the flexural toughness of FRC, the following conclusions can be drawn: 1. The custom-built 3-D laser scanning equipment was able to be applied to acquire the topographical information of fractured surface of FCR, and the topographical analysis results 4. Synergetic effect was confirmed to significantly improve the flexural behavior and the roughness of fractured surface of the concrete by using hybrid fiber, as compared to the SFRC and PFRC specimens.