Image Processing and Machine Learning to investigate fibre distribution on fibre-reinforced shotcrete Round Determinate Panels

Construction and Building Materials 190 (2018) 870–880

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Image Processing and Machine Learning to investigate fibre distribution on fibre-reinforced shotcrete Round Determinate Panels Mirko Manca ⇑, Ali Karrech, Phil Dight, Daniela Ciancio School of Civil, Environmental and Mining Engineering, University of Western Australia, 35 Stirling Highway, 6009 Crawley, WA, Australia

h i g h l i g h t s
Affordable approach to measure 3D fibre distribution.
Machine Learning algorithm and database to classify fibres’ mode of failure.
Fibre distribution on wet-mix shotcrete.
Point Pattern Analysis with Monte Carlo procedure to test for spatial randomness.

a r t i c l e

i n f o

Article history: Received 10 July 2018 Received in revised form 20 September 2018 Accepted 21 September 2018

Keywords: Image Processing Machine Learning Fibre reinforced shotcrete Statistical distribution of fibres Monte Carlo test

a b s t r a c t Fibres in fibre reinforced concrete (FRC) and fibre reinforced shotcrete (FRS) are known to increase the toughness of the composite material thanks to their ability to transfer tensile stresses even after cracks have opened. However, fibres are deemed responsible for uncertainty in mechanical performance of FRC and FRS. This uncertainty is ascribed to how the fibres are physically located with respect to the crack. In this study a novel approach is presented to measure the distribution of fibres from digital images. A computer code that features Image Processing and Machine Learning algorithms has been developed to extract: i) the 2D location, ii) the mode of failure, iii) the orientation, iv) the pull-out length for each single fibre and v) the total number of fibres bridging the crack. The Machine Learning Algorithm is trained with a database that is attached to this article. This methodology, apart from giving an understanding of how fibres are distributed over the crack, provides the main input of several numerical models that simulate the behaviour of FRC/FRS taking into account the position and orientation of each single fibre. The main advantage of this approach over existing methods is that the hardware required to carry out the analysis consists of a simple smartphone camera while an output with errors within a few thousands parts of the actual measures. The algorithm is employed to analyse the fibres’ distribution for 9 Round Determinate Panels (RDP) made of wet-mix shotcrete. The spatial 2D-location of fibres in the crack is tested for randomness with a Monte Carlo procedure and the fibres’ distribution is found to follow an Independent Random Process. For fibres that pulled-out from one side of the crack, a further 3D investigation has been carried out. The analysis on the fibres’ orientation confirmed the conclusion found by other authors that fibres tend to align perpendicular to the direction of spraying. Furthermore, it is unlikely to find fibres perpendicular to the crack surface. This last conclusion, however, is specific of the properties of fibres tested in this study, and in general, of macro synthetic fibres that tend to snap when their orientation is closer to the direction of the main stress. Finally, in the attempt of examining the representativeness of smaller version round determinate panels, the fibres’ distribution of 3 Mini RDP has been assessed and is found to be comparable to that of full size RDP. This suggests that a similar fibre’s distribution can be achieved even in a panel that is half the weight of the full size RDP. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction

⇑ Corresponding author. E-mail address: [email protected] (M. Manca). https://doi.org/10.1016/j.conbuildmat.2018.09.141 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

The addition of fibres in a concrete mix forms fibre reinforced concrete (FRC) that overcomes the main drawback of (plain) concrete which is its intrinsic brittleness. With particular regards to

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880

macro fibres, while the nature of the concrete itself remains brittle (or more precisely quasi-brittle), the benefit of using fibres comes from their bridging action once the onset of a crack(s) has opened in the concrete matrix, hence imparts an overall ‘‘ductile” behaviour to the structure. This is particularly useful when placing conventional reinforcing steel bars is uneconomical and structural ductility is required. In tunnelling, fibres are extensively used in fibre reinforced shotcrete (FRS) [1]. FRS is a common secondary support system in underground applications [2] where typical conditions result in high rock deformations that are transferred to the shotcrete lining. This would inevitably cause the formation of cracks and, consequently, structural ductility is of utmost importance. Historically, the fibres that are regularly used in FRS are made of steel, however, given that underground there are often highly corrosive environmental conditions, the use of synthetic fibres has recently become the preferred choice by many practitioners [1,3]. Regardless of the kind of fibre, FRC and FRS are a well established materials worldwide and their benefits are largely acknowledged in the construction industry. However, one of the major drawbacks of FRC/FRS remains its high variability in post-peak performance and the associated difficulties when up-scaling laboratory-sized specimen to large structures. The variability is frequently attributed to the fibres themselves, since their position, number, and therefore their contribution, would vary from a specimen to another. It is also documented in literature that the high variability of mechanical performance becomes less evident as the size of the specimen increases [4,5]. This is one of the reasons why panel tests like ASTM C1550 [6] (colloquially known as Round Determinate Panel, or RDP test) or EFNARC [7] are preferred compared to beam tests like EN 14651 [8] or ASTM C1608/1609M [9] which show, in comparison, higher scatter in results. In Australia, for instance, the RDP test is the standard quality control/quality assurance (Q/A and Q/C) tool in the mining sector. Additionally, RDP results are used for design purposes through a modified version of the Barton’s chart [10]. There are, nonetheless, a few complications linked to this approach. Firstly, the size of the standard RDP leads to a specimen that weighs 80 to 90kg, with related handling issues. Smaller and more user-friendly specimens like the MiniRDP is the subject of current studies [11,12], however as mentioned above, smaller specimens might not be representative of the material and therefore not as repeatable because of the higher scatter of results. Secondly, the Barton’s chart is an empirical model. Some authors [13,14] argue that since this chart has been calibrated based on experimental results collected in Norway, it is often used outside of the range and scope which the method was initially intended to cover under different ground conditions. A more scientific approach on this matter is still missing. One way to tackle the problem of variability and a possible path to linking laboratory sized tests like the RDP or smaller versions to real structures would be to examine the sources of variability that are introduced by the use of fibres. Perhaps the most obvious factor that could be responsible for the high scatter of post-peak performance is the number of fibres crossing the crack. This is clearly related to the dosage of fibres per cubic meter, but even with the same load of fibres in the mix design the counting of fibres actively bridging the crack would be different between specimens of the same batch. On this regard, fibre counting has been performed on a large amount of specimens [15] and showed that the number of fibres is strongly correlated to the Coefficient of Variance (COV) in the sample test confirming the trend observed in other studies that larger specimens would have lower variability [4,5]. Besides the fibre counting, considerable effort has been devoted to studying the fibre orientation in cementitious materials and

871

how it is affected by mould size/geometry (wall-effect), rheology, vibration as well as pouring direction [16–20]. The fibre orientation is generally described with a so-called ‘‘orientation factor” which is a scalar that somehow describes the average degree of alignment of fibres and many formulations have been proposed to predict this factor as a function of the above parameters. Given the large use of fibres in the pavement industry, special focus has been dedicated to the orientation of fibres in self compacting concrete where the direction of the flow is found to have a profound influence on the orientation factor [17]. In a further investigation on the effect of the fibre orientation on FRC, a series of tests have been conducted where the authors intentionally induced a preferred fibre orientation on to their sample [21]. The main conclusion, however, was that fibre orientation alone would not be enough to predict the mechanical behaviour of FRC, suggesting that other factors would participate in defining the properties of fibre reinforce concrete. Since most FRC/FRS structures experience bending moments rather than pure tension, a typical cross section manifests stresses of different signs and magnitudes in certain regions. As such, it is intuitive to assume that the position of the fibres plays an important role [3,19,22,23]. On this topic, a study provides an insight on the orientation factor in relation to the spatial coordinates throughout the beam sample as well as counting of fibres by region [22]. Further research also shows a direct comparison of the load– deflection response in a three point bending beam test series with a set amount of fibres at different locations [23]. Additionally, one aspect that is peculiar to synthetic macrofibres is that, depending on the bond developed between the fibre and the concrete matrix, the fibre can either snap (break) or pullout (slip) from one side of the crack surface. Depending on the mode of failure, the way the fibre performs in bridging the crack can vary considerably and this difference can be easily measured with a series of single-fibre pull-out tests [24]. With this in mind, the high scatter of post-peak mechanical performance of FRC/FRS can be attributable to the way fibres are dispersed into the concrete matrix, which will affect their mode of failure, location, orientation, active bridging length and number. While most of these parameters have been addressed individually in many studies, the main focus remains on fibre reinforced concrete and its application. Fibre reinforced shotcrete, which covers an important role in the fibre market, on the other hand, does not share the same amount of attention in the literature in regards to the effects of fibres’ distribution, although the process of spraying concrete on the wall could probably not be compared to conventional cast concrete as far as the distribution of fibres is concerned [3,25]. There are few exceptions where researchers employed X-ray images to study the fibre’s distribution of shotcrete with steel fibres [26,27]. In the present work a method to measure the distribution of fibres across a fracture surface is proposed followed by a direct application on wet-mix shotcrete RDP specimens. This approach extends previous research incorporating the fibre’s mode of failure which is an important characteristic of reinforced macro synthetic fibres. This methodology makes use of Photogrammetry and Machine Learning algorithms and outputs the following parameters:
In-plane coordinates (for each individual fibre in the crack surface)
Mode of failure, classified as ‘‘snap” or ‘‘pull-out” (for each individual fibre in the crack surface)
Embedment length (only for fibres that pulled-out)
3D orientation (only for fibres that pulled-out)
Total number of fibres per crack

872

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880

One of the features of this approach is that accurate results can be achieved with common digital camera like those installed in smartphones and is therefore cheap and can be performed everywhere. In the second part of the paper this method is tested and employed to measure the statistical distribution of fibres on wetmix shotcrete RDP panels. To this end, a Monte Carlo procedure

is performed to test whether fibres tend to be randomly dispersed across the crack surface or tend to cluster. This present methodology can be used in a number of applications, most notably Q/A or Q/C to monitor the fibre distribution in situ. It can represent a viable alternative to study the factors that can alter the distribution of fibres. Finally, the fibre distribution is

Fig. 1. Schematic of the process to obtain the 3D reconstruction of fibres.

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880

873

the plane in which the fibres lie. The process involves the following steps:

Fig. 2. Typical input image. The target (checkerboard) is used to estimate the camera extrinsics. The origin of the world coordinates are taken such that the X-axis coincides with the bottom of the crack and the Y-axis with the wall of the formwork.

employed in numerical/analytical models that simulate fibrereinforced cementitious materials taking into account the contribution of each single fibre [28–34]. 2. Image analysis There are a number of tools available to determine the distribution of fibres; some of them require sophisticated apparatus and utilise magnetic waves [34], electro resistivity [35,36] or X-ray images [16,19,26,27]. Other studies relied on visual inspection [15,37]. Digital images have been also successfully employed to determine, for example, the orientation factor of fibres [16,27]. The method presented in this section receives as input digital images and allows the gathering of a comprehensive set of information about the fibres’ distribution. The proposed methodology has a major advantage in that the analysis can be performed with everyday hardware, such as smartphone cameras and a computer, while achieving high accuracy. The information available on the fibres’ distribution however, are limited to the fibres visible on the crack surfaces. An algorithm has been developed with the software MATLAB (Computer Vision Toolbox) [38]. In this section, we briefly explain the concepts and steps required to perform the proposed analysis. The procedure is presented in a generic manner to make it amenable to translation to other programming languages. A graphical representation of the flowchart is shown in Fig. 1 to illustrate how the algorithm works. More details follow in this Section. The accuracy of this approach has been tested by comparing the numerical outputs with physical measurements on the sample. Typically, the error is within a few thousands parts of the actual measures. 2.1. Fibre Location: photogrammetry A picture is a 2D representation of a 3D scene. From a single image, it is possible to measure the Euclidian distance between two points as long as the points lie in the same plane and the metrics of the plane are known. In order to find out the (world) location ðx; yÞw of each i-fibre (visible in the picture) with respect to the crack surface, a single image is sufficient. The user is required to provide an image of the crack surface with a ‘‘target” of known dimensions (see Fig. 2), that is necessary to calculate the metrics of

1. Identify the target within the image: this step can be automated using edge-detection algorithms that can recognise the grid pattern. 2. Measure the rotation matrix and translation vector (sometimes called camera extrinsics) which contain information about the centre of the camera with respect to the target. The camera extrinsics are calculated performing a projective transformation and are used to determine the metrics of the crack surface which is assumed to be plane. 3. Define the origin of world-coordinate system. The convention followed in this study sees the x-axis parallel to the radial direction of the RDP panel and coincident with the bottom of the crack surface. The y-axis is orthogonal to the x-axis and parallel to the direction of the thickness of the panel with the origin being at the edge of the panel (see Fig. 2). 4. Manually identify the pixel coordinates of each single fibre. Practically, the user would need to click on the image where the fibres are (one click per fibre). 5. Transform pixel coordinates to world coordinates: with the notion of the camera extrinsics the pixel coordinates can be translated into real world coordinates. More details and the mathematics behind this transformation can be found in [39]. Since the calculations are based on the assumption that the crack surface is planar, this approach should not be used if the fracture can not be reasonably considered flat. This makes this methodology particularly suitable for the RDP test where the resulting crack pattern is typically flat. Other tests, like EFNARC or beam tests might show cracks with a higher degree of ‘‘tortuosity” and this approach might produce non-negligible errors. Alternatively, it also is possible to notch the specimen at a predefined location to promote the formation of a planar crack surface. It should be also noted that the above procedure does not take into account lens distortion. This could be an issue depending on the quality of the lens (many modern smartphones, for example, suffer from visible lens distortions), and generally worsens with wide angle lenses and around the edges of the picture (radial distortion is quadratic from the centre of the image). All images in this study have been taken with a calibrated (smartphone) camera and all pictures have been undistorted before processing. 2.2. Fibre mode of failure: Machine Learning Machine Learning (ML) has been successfully employed to a variety of fields that span from medical to robotic applications. In Civil and Structural Engineering ML is relatively new, and has been used to predict the compressive strength and fresh state properties of concrete [40–42], for computational applications [43] and even automatic crack detection [44]. In this example Supervised Learning is exploited to classify the two possible modes of failures for macro synthetic fibres. This process does not require any input and is fully automatic. In order to generate a Machine Learning algorithm, the first step involves the acquisition of a training database, which is, from a practical point of view, a set of images labelled either ‘‘snap” or ‘‘pull-out” showing different poses of various fibres with the appropriate mode of failure. An extract of the database, which consist of 4350 images for each category, is included in Fig. 3. The whole database is attached to this paper. Once a database is available, there are two more steps to take: 1. Select an image feature extraction method: in this example, the method ‘‘Bag of Features” has been chosen for its speed.

874

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880

of the crack and positive sign otherwise). This angle provides insight into the preferential orientation of fibres orthogonal to the direction of spraying. 3. The ‘‘perpendicular” angle h? indicates the angle formed between the fibres and the crack surface. When a fibre is perfectly perpendicular to the crack (corresponding to h? ¼ 0 ) the fibre is aligned to the direction of the main stress. If h? ¼ 90 the fibre lies in the plane of the crack and therefore did not contribute to the bridging of the crack.

Fig. 3. In (a) an extract of the pictures used to train the model showing how snapped fibres look like, similarly in (b) a sample of images showing pulled-out fibres.

Fig. 4. Performance of the Machine Learning algorithm. Each fibre’s mode of failure has been individually assessed before querying the algorithm, when the bounding box around the fibre is green it means that mode of failure has been correctly identified, red otherwise. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

2. Select a Machine Learning Algorithm: the highest accuracy with this database was achieved with Linear Support Vector Machine (SVM) model. An example of the performance of the Machine Learning algorithm is shown in Fig. 4. As is common in these applications, part of the database is used to train the model, in this case 85% (i.e. 3698 pictures), whereas the remaining part (652 pictures) is left to assess the model accuracy. A number of Machine Learning algorithms have been tested and the Linear Support Vector Machine (SVM) model scored the best among the others with an accuracy of about 91%. More sophisticated approaches like Deep Learning, could potentially lead to even higher accuracy but they would also be more computationally expensive. It is worth mentioning that the ability to distinguish a snapped fibre from a pulled-out fibre might not be always an easy task, even for humans. In this regard, 91% accuracy seems satisfactory.

In order to extract 3D information from 2D pictures, it is necessary to analyse at least two images of the same object captured from a different angle. In this case, it is necessary to identify the end point of each fibre that has been classified in the previous step as ‘‘pull-out” noting that the start point (the point at which the fibre pulls-out from the crack surface) should have been already detected when measuring the fibre position (Section 2.1). The relative camera poses (i.e. orientation and translation vector) for the images must also be known and can be automatically processed using the target as mentioned in Section 2.1. This set-up allows the extraction of the 3D world coordinates ðX; Y; ZÞw of the start/end points of each pulled-out fibre i. With reference to Fig. 5, lemb ; hk and h? are calculated as follows:

lemb;i ¼jjv i jj h?;i hk;i

ð1Þ

jjv i ^ njj ¼ arcsin jjv i jj Y end;i  Y start;i ¼ arctan jX end;i  X start;i j

ð2Þ ð3Þ

where

v i ¼½ X end;i  X start;i

n ¼½ 0 0 ðÞ1 

T

Y end;i  Y start;i

Z end;i  Z start;i T

ð4Þ ð5Þ

The vector n can only have the third component non-zero, in line with the assumption of a flat crack surface and following the axis convention as described in Section 2.1.

2.3. Orientation and Embedment Length: triangulation When a fibre snaps, the information concerning its orientation with respect to the crack surface and embedment length can not be retrieved. When a fibre pulls-out, however, these parameters can be obtained from digital images with a method called triangulation. Three main parameters are extracted with this technique (see Fig. 3): 1. The embedment length lemb which corresponds to the length of the fibre pulling out from the crack in the range ½0; lf  with lf ¼ 65mm being the length of the fibre in this study. 2. The ‘‘parallel” angle hk represents the angle between the fibre and the direction parallel to bottom of the crack in the range ½90 ; 90  (with 0° being perpendicular to the spraying direction, negative indicating the fibre inclined towards the bottom

Fig. 5. Definition of hk and h? . The vector v is aligned with the direction of the pulled-out fibre and the vector normal to the cracked surface n is aligned with the Z-axis and is facing ‘‘outward”. Consequently it can have either the same direction of the Z-axis or the opposite direction depending of the side of the crack. Notice that the same reference system is used on both sides of the crack.

875

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880 Table 1 Mix design.

Fig. 6. Fibre counting procedure. Those fibres that have been identified on both sides of the crack (N 12;s ) would have similar world-coordinates and will be counted once. Fibres that have not been matched on the other side of the crack (N 11;s and N 22;s ) are counted individually.

2.4. Fibre counting Once the position, mode of failure, length and orientation angles are measured for each fibre that could be spotted from the images of the two faces of crack, the last step is to perform the fibre counting. Starting with the concept that if a fibre pullsout it would be visible only in one of the two sides of the crack whereas if a fibre snaps, it should theoretically be possible to identify it on both sides, the total number of fibres bridging the crack would be N tot ¼ N 1;p þ N 2;p þ N s , where the number of snapped fibres N s should be identical on both sides (i.e. N s ¼ N 1;s ¼ N 2;s ). Unfortunately this is not always the case. In reality, when a fibre snaps, it often leaves not visible/detectable trace on one side of the crack. A more robust way to count the number of fibres that snapped to avoid double counting of the same fibre is by taking advantage of the scaled reconstruction that has been discussed in Section 2.1. With reference to Fig. 6, the world-coordinates for each snapped fibres are plotted together using the same origin and axis (Fig. 5). Those snapped fibres that left a visible trace on both sides, N 12;s could be easily spotted since they would have very similar world-coordinates. There would also be a number of snapped fibres which coordinates do not match on the other side of the crack or either sides N 11;s and N 22;s . In this case there are two options: 1. the mode of failure has been misjudged, in this case the coordinates of the wrongly assigned snapped fibre would be very similar to the coordinates a pull-out fibre on the other side. 2. the fibre did not leave any visible mark on the other side of the crack.

Component

Actual Dosage for 3 m3

Unit

Water (Batch 1) Water (Batch 2) Cement 7/10 Aggregates Crushed Dust Fine Sand Superplasticizer Stabiliser Accelerator Fibres

610 630 1350 1335 1695 1950 9 9 0 18

l l kg kg kg kg l l l kg

C1550 panel size (800mm diameter and 75mm thickness) and 3 which have different dimensions, 540mm diameter and 100mm thickness. The panels have been sprayed in two batches, approximately 24 h apart, with a different amount of water dosage in the two batches to achieve similar workability (mix design is listed in Table 1). The same mixer and sprayer trucks have been used for the two batches, furthermore all panels have been sprayed by the same operator. After spraying, the panels have been covered and left aboveground (this is often necessary as storing RDP underground can be logistically difficult). After 20 days the panels have been demoulded and sent to the Structure Laboratory at the University of Western Australia for testing. The panels have been tested according to ASTM C1550 (with the exception of the 3 undersize panels) with a Instron Machine rated for 500kN, and the energy absorption at 40mm has been calculated from the load–displacement curve obtained from the machine. After completion of the tests, each panel would be cracked forming three sectors as shown in Fig. 7a with a total of six crack surfaces to analyse per panel. 3.2. Point Pattern Analysis in FRS crack surfaces Knowing of the location of each single fibre in the crack reveals whether fibres can be effectively considered randomly dispersed within the surface. While this is implicitly assumed in many theories, there is no experimental evidence supporting this assumption, at least for an RDP made of wet-mix shotcrete. From an operational perspective, the main goal is to determine whether the spatial distribution of fibres (or points) within the crack area (or study area) follows a so-called Independent Random Process (IRP). This is a common problem encountered in various fields and there is a whole area of study called Point Pattern Analysis (PPA) that formalises different approaches to support whether a 2D distribution

The total counting of snapped fibres is therefore:

Ns ¼ N12;s þ N 11;s þ N22;s

ð6Þ

with:

N11;s ¼N1;s  N12;s

ð7Þ

N22;s ¼N2;s  N12;s

ð8Þ

3. Application: Fibre distribution on wet-mix shotcrete 3.1. Material and testing The method described in Section 2 is used to analyse RDP panels made of shotcrete. The number of panels included in this study amounts to 9 (totalling 27 cracks). Six used the standard ASTM-

Fig. 7. In (a) an example of a tested RDP, in (b) 3D reconstruction of fibre’s distribution obtained from the image analysis software. Since the orientation and pull-out length of the fibres that snapped can not be measured, these fibres (depicted in red) are fictitiously drawn perpendicular to the crack face and with an embedment length equal to half of their length. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

876

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880

Table 2 Unconfined Compressive Strength (UCS) summary. Batch

Slump (mm)

1 2

120 140

*

UCS (Cast Cylinders)

UCS (Cored Sprayed Cylinders)

Energy Absorption at 40mm

Average (MPa)

COV (%)

Average (MPa)

COV (%)

Average (MPa)

COV (%)

43.53 39.56

7.24 2.47

43.91 45.46

7.30 4.18

414.21 431.42*

10.43 23.94

Energy absorption values for batch 2 has been calculated with full size RDP only. MiniRDP were not included in the average.

of points can be deemed statistically random or not. In this Section, the randomness has been assessed looking at a measure proportional to the average distances between fibres with a DistanceBased function called LðdÞ (see [45]). The LðdÞ function incorporates the number of fibres within a certain radius d of a circle drawn around each fibre, which is then extended to all fibres observed in the study area. Following the same notation in [45], the function is defined as:

LðdÞ ¼

rffiffiffiffiffiffiffiffiffiffi KðdÞ

p

d

ð9Þ

with:

KðdÞ ¼

n a 1X #½S 2 Cðsi ; dÞ n n i¼1

ð10Þ

In Eqs. 9 and (10) d means the radius of the circle around each event (fibre) which plays the role of independent variable. The parameter a is the study area (crack surface, since it has been normalised in this case it would be equal to 1) and n the total number of fibres. The term within the summation denotes the number (#) of fibres in the set of location S that belongs to the circle C of radius d centred at the fibre si with S ¼ fs1 ; s2 ; . . . ; sn g. The LðdÞ function of a purely random process, should be centred around zero as per its definition. In order to judge whether the LðdÞ function, measured from the location of the fibres in the sample, can be reasonably considered to describe a IRP, a Monte Carlo analysis has been carried out. The Monte Carlo analysis consists of generating multiple Independent Random Processes with n ¼ N tot (following the notation of Section 2.4) for each crack to analyse. In each simulation, an array of points is generated using the random function built in MATLAB in the range ½0; 1. The number of points is kept equal to the number of fibres identified in the cracked section analysed. The L function is then calculated for this particular set of coordinates.

This step is repeated 106 times (see Fig. 8) for each crack and the corresponding lower/upper 1, 5 and 10 percentile curves are

extracted to graphically assess whether the spatial location of fibres would follow a IRP (or otherwise). Notice from the graph in Fig. 8 that the curves deviate from zero for larger values of d, possibly due to the ‘‘edge effect”. The number of neighbouring fibres for those events (fibres) located close to the edge of the crack decreases since there are no fibres outside the crack area, this results in a biased decreasing LðdÞ function. This highlights the benefits of the Monte Carlo approach since the upper/lower boundaries curves obtained from the analysis would follow the same ‘‘biased” trend as the observed LðdÞ. If the observed LðdÞ function lies within the upper/lower curves forming an envelope calculated through the Monte Carlo procedure with a certain significance value, the spatial distribution of fibres is said to be considered reasonably random. If the observed LðdÞ function goes above (or below) the envelope it would indicate an abnormally high (or low) number of neighbouring fibres which would suggest a clustered (or dispersed) arrangements of fibres.

3.3. Results Due to small deviations from a perfect round shape, difficulties in centering the panels in the testing machine and inhomogeneities in the material, the crack pattern in the RDP does not follow the theoretical 120°. Furthermore, the length of the crack (and consequently its area) in each sector can also be different from panel to panel and even from sector to sector. For this reason, the positions of the fibres have been normalised with respect to the size of the crack. The number of fibres is also divided by the area of the crack (assuming a trapezoidal form) which would allow to compare cracks of different sizes. The results pertaining to every single panel are shown in Fig. 9 with the Monte Carlo simulations (on the left) and frequency plots for the two orientations measured, hk and h? on the right hand side. The number of fibres detected for each single crack and grouped by panel is available in Fig. 10 that also show the ratio of pull-out versus snap fibres.

Fig. 8. Schematic of the Monte Carlo simulation. An array of random points are generated at each simulation (on the left) and the LðdÞ function is calculated. Since the values of the L function are the results of a random process, a sufficiently large number of simulations would produce a set of values that follow a normal distribution as depicted in in the graph on the right.

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880

877

Fig. 9. Fibre distribution results for tested sample. On the right hand side the results from the Monte Carlo procedure,on the right hand side the frequency plots for hk and h? with indication of the fibre length (lf ¼ 65 mm) for each angle. In (a) and (b) the three panels belong to the first and second batch respectively (refer to Table 1 for mix design). In (c) the results for MiniRDP.

878

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880

Fig. 9 (continued)

Fig. 10. Fibre density grouped by crack and panels. Letter ‘‘B” and ‘‘P” are short form of ‘‘Batch” and ‘‘Panel” respectively.

A graphical assessment of the Monte Carlo simulations show that, with some minor exceptions, the observed LðdÞ function lies within the envelope for all panels. This suggests that a random spatial distribution of fibres can be achieved in shotcrete. The frequency plots hk and h? show a clear tendency of fibres to align perpendicular to the spraying direction (hk ¼ 0 ) and to lie in the same plane of the crack (h? ¼ 90 ). The first result has been observed in other studies [26,27], and is deemed to be a consequence of the concrete being sprayed. To explain the second result, fibres tending to be perpendicular to the direction of the main stress (i.e. perpendicular to the crack), it should be noted that h? can only be measured for fibres that pulled-out. It can be argued that fibres closer to a orthogonal orientation with respect to the crack would rather snap. This observation is possibly very sensitive to the kind of fibre and shotcrete mix design adopted in this study. It is also interesting to note that there is no noticeable difference between full size RDP and MiniRDP as far as the distribution of fibres is concerned. The fibre density as shown in Fig. 10 between standard and MiniRDP is also comparable. This suggests that a similar fibre distribution (and representativeness) can be obtained with a MiniRDP

that is half the weight of the full size RPD. This result however needs further research as this study is limited to 3 (MiniRDP) specimens only. It is worth reminding that some of the results showed in this Section, such as orientation, embedment length and ratio of snap versus pull-out fibres, are specific to the fibres and shotcrete mix used in this trial. The location and total number of fibres however is expected to be similar regardless of the brand of fibres as long as the same fibre length (65mm) and dosage (6 kg/m3) is used in the shotcrete mix design. These figures are commonly adopted by shotcrete contractors across Australia. 4. Conclusions In this paper a simple approach based on Image Processing and Machine Learning is employed to capture the distribution of fibres that can be acquired from digital images of cracked surfaces. The software that incorporates the analysis is found to produce accurate results (errors within a few thousands parts of actual measures) with a standard smartphone camera. The software is

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880

ultimately employed on a sample comprising of 6 full size RDP and 3 MiniRDP made of shotcrete. The analysis of the 2D location of the fibres in the sample shows that overall in a RDP, a random spatial distribution of fibres (which is often assumed in many studies) can be achieved. This is checked against a Monte Carlo analysis. In addition to the 2D analysis, the 3D orientation has been retrieved but only for fibres that have pulled-out. According to the results, fibres tend to align perpendicular to the direction of spraying. This is in agreement with previous studies. Furthermore, only ‘‘few” fibres are found to be perpendicular to the crack. This conclusion, however, can be explained by taking into account that fibres perpendicular to the crack tend to snap. Finally, an alternative size of RDP has been tested. Although the sample is limited to three panels only, the results shows that a similar spatial random distribution of fibres, as well as similar orientation and density can be obtained with a smaller version of the full size RDP which is half of the weight but produces a cracked area which is similar (80%) to that of the standard RDP. Conflict of interest The authors declare that there is no conflict of interest. Acknowledgement The authors would like to thank Jetcrete and Sika Australia to organise and fund the trial session and spraying of panels. The first author would like to further thank Sika Australia for his fellowship and supply of synthetic fibres. References [1] S. Yin, R. Tuladhar, F. Shi, M. Combe, T. Collister, N. Sivakugan, Use of macro plastic fibres in concrete: a review, Constr. Build. Mater. 93 (2015) 180–188, https://doi.org/10.1016/j.conbuildmat.2015.05.105. URL https:// www.sciencedirect.com/science/article/pii/S0950061815006194?via%3Dihub. [2] S.V.L. Barrett, D.R. McCreath, Shortcrete support design in blocky ground: towards a deterministic approach, Tunn. Undergr. Space Technol. 10 (1) (1995) 79–89, https://doi.org/10.1016/0886-7798(94)00067-U. URL https:// www.sciencedirect.com/science/article/pii/088677989400067U. [3] J. Kaufmann, K. Frech, P. Schuetz, B. Münch, B. Munch, Rebound and orientation of fibers in wet sprayed concrete applications, Constr. Build. Mater. 49 (2013) 15–22, https://doi.org/10.1016/j.conbuildmat.2013.07.051. URL https://www.sciencedirect.com/science/article/pii/S095006181300665X? via%3Dihub. [4] M. di Prisco, G. Plizzari, L. Vandewalle, Fibre reinforced concrete: new design perspectives, Mater. Struct. 42 (9) (2009) 1261–1281, https://doi.org/10.1617/ s11527-009-9529-4. URL http://link.springer.com/10.1617/s11527-009-95294. [5] S.H.P. Cavalaro, A. Aguado, Intrinsic scatter of FRC: an alternative philosophy to estimate characteristic values, Mater. Struct./Materiaux et Constructions 48 (11) (2015) 3537–3555, https://doi.org/10.1617/s11527-014-0420-6. URL http://link.springer.com/10.1617/s11527-014-0420-6. [6] ASTM C1550, Standard Test Method for Flexural Toughness of Fiber Reinforced Concrete (Using Centrally Loaded Round Panel), ASTM standard C1550 (c) (2012) 1–14. doi:10.1520/C1550-12.2. URL https://www.astm.org/Standards/ C1550.htm. [7] BS EN 14488-5, Testing sprayed concrete -Part 5: Determination of energy absorption capacity of fibre reinforced slab specimens, British Standards Institute. URL https://www.thenbs.com/PublicationIndex/documents/details? Pub=BSI&DocID=279367. [8] BS EN 14651, Test method for metallic fibred concrete – Measuring the flexural tensile strength (limit of proportionality (LOP), residual), British Standards Institute 3 (2005) 1–17. doi:9780580610523. [9] ASTM C1609/C1609M, Standard Test Method for Flexural Performance of Fiber-Reinforced Concrete (Using Beam With Third-Point Loading), 2012. doi:10.1520/C1609. URL https://www.astm.org/Standards/C1609.htm. [10] F. Papworth, Design guidelines for the use of fibre-reinforced shotcrete in ground support, Shotcrete Mag. 1 (2002) 16–21. URL http://imcyc.com/ biblioteca/ArchivosPDF/Fibras de Acero/Design Guidelines for the use of fiber.pdf. [11] D. Ciancio, C. Mazzotti, N. Buratti, Evaluation of fibre-reinforced concrete fracture energy through tests on notched round determinate panels with different diameters, Constr. Build. Mater. 52 (2014) 86–95, https://doi.org/ 10.1016/J.CONBUILDMAT.2013.10.079. URL http://www.sciencedirect.com/ science/article/pii/S0950061813010003?via%3Dihub.

879

[12] D. Ciancio, M. Manca, N. Buratti, C. Mazzotti, Structural and material properties of Mini notched Round Determinate Panels, Constr. Build. Mater. 113 (2016) 395–403, https://doi.org/10.1016/j.conbuildmat.2016.03.025. [13] Y. Potvin, P. Dight, J. Wesseloo, Some pitfalls and misuses of rock mass classification systems for mine design, J. Southern Afr. Inst. Min. Metall. 112 (May) (2012) 697–702. [14] Y. Potvin, J. Hadjigeorgiou, Selection of ground support for mining drives based on the Q-System, in: T.J. Nordlund, A. Eitzenberger (Eds.), Ground Support 2016, no. 1976, Ground Support, Luleå, 2016, pp. 1–16. [15] E.S. Bernard, G.G. Xu, Influence of fibre count on variability in post-crack performance of fibre reinforced concrete, Mater. Struct./Materiaux et Constructions 50 (3) (2017) 169, https://doi.org/10.1617/s11527-017-10355. URL http://link.springer.com/10.1617/s11527-017-1035-5. [16] C. Redon, L. Chermant, J.-L. Chermant, M. Coster, Automatic image analysis and morphology of fibre reinforced concrete, Cem. Concr. Compos. 21 (5–6) (1999) 403–412, https://doi.org/10.1016/S0958-9465(99)00025-6. URL https:// www.sciencedirect.com/science/article/pii/S0958946599000256?via%3Dihub. [17] L. Martinie, N. Roussel, Simple tools for fiber orientation prediction in industrial practice, Cem. Concr. Res. 41 (10) (2011) 993–1000, https://doi.org/10.1016/j. cemconres.2011.05.008. URL https://www.sciencedirect.com/science/article/ pii/S0008884611001608?via%3Dihub. [18] P. Pujadas, A. Blanco, S. Cavalaro, A. De La Fuente, A. Aguado, Fibre distribution in macro-plastic fibre reinforced concrete slab-panels, Constr. Build. Mater. 64 (2014) 496–503, https://doi.org/10.1016/j.conbuildmat.2014.04.067. URL https://www.sciencedirect.com/science/article/pii/S0950061814003845. [19] T. Ponikiewski, J. Katzer, M. Bugdol, M. Rudzki, Steel fibre spacing in selfcompacting concrete precast walls by X-ray computed tomography, Mater. Struct./Materiaux et Constructions 48 (12) (2015) 3863–3874, https://doi.org/ 10.1617/s11527-014-0444-y. URL http://link.springer.com/10.1617/s11527014-0444-y. [20] E.V. Sarmiento, M.R. Geiker, T. Kanstad, Influence of fibre distribution and orientation on the flexural behaviour of beams cast from flowable hybrid polymer-steel FRC, Constr. Build. Mater. 109 (2016) 166–176, https://doi.org/ 10.1016/j.conbuildmat.2016.02.005. URL https://www.sciencedirect. com/science/article/pii/S0950061816300642. [21] I. Sanal, N. Ozyurt Zihnioglu, To what extent does the fiber orientation affect mechanical performance?, Constr Build. Mater. 44 (2013) 671–681, https://doi.org/ 10.1016/j.conbuildmat.2013.03.079. URL https://www.sciencedirect.com/science/ article/pii/S0950061813002894?via%3Dihub. [22] M.G. Alberti, A. Enfedaque, J.C. Gálvez, V. Agrawal, Fibre distribution and orientation of macro-synthetic polyolefin fibre reinforced concrete elements, Constr. Build. Mater. 122 (2016) 505–517, https://doi.org/10.1016/ j.conbuildmat.2016.06.083. URL https://www.sciencedirect.com/science/ article/pii/S0950061816310121?via%3Dihub. [23] M. Manca, D. Ciancio, P. Dight, Effects of fibre location and density on the flexural toughness in FRC beams, in: C.R.C.P. Balkema (Ed.), Mechanics of Structures and Materials: Advancements and Challenges – Proceedings of the 24th Australasian Conference on the Mechanics of Structures and Materials, ACMSM24 2016, vol. 1, CRC Press, Perth, 2016, pp. 249–254. URL http://www. crcnetbase.com/doi/abs/10.1201/9781315226460-36. [24] M. Manca, D. Ciancio, P. Dight, Fibre reinforced concrete in flexure and single fibre pull-out test: a correlation, IOP Conference Series: Materials Science and Engineering, vol. 246, IOP Publishing, 2017, https://doi.org/10.1088/1757899X/246/1/012017. URL http://stacks.iop.org/1757-899X/246/i=1/a=012017? key=crossref.9215747ac5ead94bba37103b009d2646. [25] N. Banthia, J. Trottier, D. Beaupré, Steel–fiber–reinforced wet-mix shotcrete: comparisons with cast concrete, J. Mater. Civ. Eng. 6 (3) (1994) 430–437, https:// doi.org/10.1061/(ASCE)0899-1561(1994) 6:3(430). URL http://ascelibrary. org/doi/10.1061/(ASCE)0899-1561(1994) 6:3(430) http://ascelibrary.org/doi/ 10.1061/%28ASCE%290899-1561%281994%296%3A3%28430%29. [26] L. Segura-Castillo, S.H. Cavalaro, C. Goodier, A. Aguado, S. Austin, Fibre distribution and tensile response anisotropy in sprayed fibre reinforced concrete, Mater. Struct./Materiaux et Constructions 51 (1) (2018) 29, https:// doi.org/10.1617/s11527-018-1156-5. URL http://link.springer.com/10.1617/ s11527-018-1156-5. [27] P.J. Robins, S.A. Austin, P.A. Jones, Spatial distribution of steel fibres in sprayes and cast concrete, Mag. Concr. Res. 55 (3) (2003) 225–235, https://doi.org/ 10.1680/macr.2003.55.3.225. URL http://www.icevirtuallibrary.com/doi/ 10.1680/macr.2003.55.3.225. [28] F.K.F. Radtke, A. Simone, L.J. Sluys, A computational model for failure analysis of fibre reinforced concrete with discrete treatment of fibres, Eng. Fract. Mech. 77 (4) (2010) 597–620, https://doi.org/10.1016/j.engfracmech.2009.11.014. URL http://www.sciencedirect.com/science/article/pii/S0013794409003555? via%3Dihub. [29] V.M.C.F. Cunha, J.A.O. Barros, J.M. Sena-Cruz, A finite element model with discrete embedded elements for fibre reinforced composites, Comput. Struct. 94–95 (2012) 22–33, https://doi.org/10.1016/j.compstruc.2011.12.005. URL http://www.sciencedirect.com/science/article/pii/S0045794911003038?via% 3Dihub. [30] C. Octávio, D. Dias-da Costa, J. Alfaiate, E. Júlio, Modelling the behaviour of steel fibre reinforced concrete using a discrete strong discontinuity approach, Eng. Fract. Mech. 154 (2016) 12–23, https://doi.org/10.1016/j. engfracmech.2016.01.006. URL http://www.sciencedirect.com/science/article/ pii/S0013794416000096?via%3Dihub. [31] A. Yaghoobi, M.G. Chorzepa, Fracture analysis of fiber reinforced concrete structures in the micropolar peridynamic analysis framework, Eng. Fract. Mech.

880

[32]

[33]

[34]

[35]

[36]

[37]

[38]

M. Manca et al. / Construction and Building Materials 190 (2018) 870–880 169 (2017) 238–250, https://doi.org/10.1016/j.engfracmech.2016.11.004. URL http://www.sciencedirect.com/science/article/pii/S0013794416305811?via% 3Dihub http://linkinghub.elsevier.com/retrieve/pii/S0013794416305811. J. Kang, J.E. Bolander, Event-based lattice modeling of strain-hardening cementitious composites, Int. J. Fract. 206 (2) (2017) 245–261, https://doi. org/10.1007/s10704-017-0214-2. URL http://link.springer.com/10.1007/ s10704-017-0214-2. M. Manca, A. Karrech, P. Dight, D. Ciancio, Dual cohesive elements for 3D modelling of synthetic fibre-reinforced concrete, Eng. Struct. 174 (2018) 851– 860, https://doi.org/10.1016/j.engstruct.2018.07.101. H. Al-Mattarneh, Electromagnetic quality control of steel fiber concrete, Constr. Build. Mater. 73 (2014) 350–356, https://doi.org/10.1016/ j.conbuildmat.2014.09.101. URL https://www.sciencedirect.com/science/ article/pii/S0950061814011179?via%3Dihub. N. Ozyurt, T.O. Mason, S.P. Shah, Non-destructive monitoring of fiber orientation using AC-IS: an industrial-scale application, Cem. Concr. Res. 36 (9) (2006) 1653–1660, https://doi.org/10.1016/j.cemconres.2006.05.026. URL https://www.sciencedirect.com/science/article/pii/S0008884606001530?via% 3Dihub. L. Martinie, J.-F. Lataste, N. Roussel, Fiber orientation during casting of UHPFRC: electrical resistivity measurements, image analysis and numerical simulations, Mater. Struct. 48 (4) (2015) 947–957, https://doi.org/10.1617/s11527-0130205-3. URL http://link.springer.com/10.1617/s11527-013-0205-3. R. Gettu, D.R. Gardner, H. Saldívar, B.E. Barragán, Study of the distribution and orientation of fibers in SFRC specimens, Mater. Struct. 38 (275) (2004) 31–37, https://doi.org/10.1617/14021. URL http://www.springerlink.com/index/ 10.1007/BF02480572. MathWorks, MATLAB (R2017b), Computer Vision System Toolbox (2017). doi:10.1007/s10766-008-0082-5. URL http://scholar.google.com/scholar?hl= en&btnG=Search&q=intitle:MATLAB+The+Language+of+Technical+Computing#0

[39] R. Hartley, A. Zisserman, Multiple View Geometry in Computer Vision, 2004, doi:10.1016/S0143-8166(01)00145-2, URL http://www.robots.ox.ac.uk/vgg/ hzbook/ [40] M. Sonebi, A. Cevik, S. Grünewald, J. Walraven, Modelling the fresh properties of self-compacting concrete using support vector machine approach, Constr. Build. Mater. 106 (2016) 55–64, https://doi.org/10.1016/j.conbuildmat. 2015.12.035. URL https://www.sciencedirect.com/science/article/pii/ S095006181530711X. [41] F. Deng, Y. He, S. Zhou, Y. Yu, H. Cheng, X. Wu, Compressive strength prediction of recycled concrete based on deep learning, Constr. Build. Mater. 175 (2018) 562–569, https://doi.org/10.1016/j.conbuildmat.2018.04.169. URL https:// www.sciencedirect.com/science/article/pii/S0950061818309863. [42] Y. Yu, W. Li, J. Li, T.N. Nguyen, A novel optimised self-learning method for compressive strength prediction of high performance concrete, Constr. Build. Mater. 184 (2018) 229–247, https://doi.org/10.1016/j.conbuildmat.2018.06.219. URL https://www.sciencedirect.com/science/article/pii/S095006181831626X https://linkinghub.elsevier.com/retrieve/pii/S095006181831626X. [43] A. Oishi, G. Yagawa, Computational mechanics enhanced by deep learning, Comput. Methods Appl. Mech. Eng. 327 (2017) 327–351, https://doi.org/ 10.1016/J.CMA.2017.08.040. URL https://www.sciencedirect.com/science/ article/pii/S0045782517306199. [44] K. Gopalakrishnan, S.K. Khaitan, A. Choudhary, A. Agrawal, Deep Convolutional Neural Networks with transfer learning for computer vision-based data-driven pavement distress detection, Constr. Build. Mater. 157 (2017) 322–330, https://doi.org/10.1016/j.conbuildmat.2017.09.110. URL https:// www.sciencedirect.com/science/article/pii/S0950061817319335. [45] D. O’Sullivan, D. Unwin, Geographic information analysis, second ed., Wiley, 2010. URL https://www.wiley.com/en-au/Geographic+Information+Analysis% 2C+2nd+Edition-p-9780470288573.