3d imaging and analysis of cracks in loaded concrete samples

Concrete plays a central role as the standard building material in civil engineering. Experimental characterization of the concrete microstructure and a description of failure mechanisms are important to understand the concrete’s mechanical properties. Computed tomography is a powerful source of information as it yields 3d images of concrete specimens. However, complete visual inspection is often infeasible due to very large image sizes. Hence, automatic methods for crack detection and segmentation are needed. A region-growing algorithm and a 3d U-Net showed promising results in a previous study. Cracks in normal concrete and high-performance concrete that were initiated via tensile tests were investigated. Here, the methods are validated on a more diverse set of concrete types and crack characteristics. Adequate adaptions of the methods are necessary to deal with the complex crack structures. The segmentation results are assessed qualitatively and compared to those of a template matching algorithm which is well-established in industry.


Introduction
Concrete is a common construction material used in buildings, bridges, and roads.To guarantee safety and durability, it has to meet high quality standards.Investigating loaded concrete has been an active field of research in civil engineering since the 19th century.However, a characterization of crack systems forming under load is often restricted to visual inspection of the specimens' surfaces.A more insightful approach to analyze crack structures in concrete is via micro-computed tomography (µCT) [5].Depending on the sample size, specialized µCT hardware is necessary.Gulliver -a dedicated XXL CT having an X-ray energy of up to nine megaelectronvolts and being able to scan concrete samples of up to 30 centimeters in diameter and six meters in length during bending tests -is currently being built at RPTU in Kaiserslautern.Gulliver will generate CT images of up to 10 000 2 × 2 000 voxels and several hundreds of gigabytes.This amount of data renders manual inspection for cracks infeasible.Hence, automatic and robust methods for crack detection and segmentation are needed.First explorations of crack segmentation methods for 3d CT images date back to 2011 [9,16,17].They were developed as part of a cooperation of the Federal Institute for Materials Research and Testing (BAM) and the Zuse Institute Berlin (ZIB).Recently, methods from machine and deep learning have successfully been used for image segmentation tasks, too.In [3], we have analyzed and compared several methods from classical image processing and machine learning.The methods were trained and evaluated based on semi-synthetic image data and the corresponding ground truths.The best-performing methods were Hessian-based percolation [9] and the 3d U-net [6].Subsequently, both approaches were successfully adapted to real CT data of concrete [4,14].Cracks in concrete can occur due to various causes such as mechanical load [11,12], alkali-silica reaction (ASR) [28,29], freezeand-thaw cycles [27], corrosion [21,26] or fire exposition [20].As a result, cracks exhibit diverse characteristics regarding thickness, roughness, and topology.Here we focus on cracks in mechanically and chemically loaded concrete samples.The goal is an accurate crack segmentation with the previously explored segmentation methods.The results are compared with those of a template matching algorithm, a well-proven method in industry [25].Robustness, limitations, and the optimization of the methods with respect to runtime are investigated based on CT images taken at BAM and the High-Energy X-ray Imaging facility at the Fraunhofer EZRT.
12th Conference on Industrial Computed Tomography, Fürth, Germany (iCT 2023), www.ict2023.orgThis work is structured as follows.Section 2 describes the concrete samples and the test setup for crack initiation.In Section 3, we summarize the µCT imaging setup including details on the hardware and imaging parameters.Section 4 provides insight into the methods that were used for crack segmentation.The segmentation results are discussed and compared with each other in Section 5.In Section 6, we give a conclusion and an outlook to future work.

Concrete samples 2.1 Fiber-reinforced concrete sample
Bending tensile strength tests were carried out on hardened high-performance concrete with polypropylene fibers (PP) Master-Fiber 235 SPA [15].The tests were conducted on beam specimens of dimensions 100 × 100 × 400 mm 3 in accordance with EN 14651 [1].In the tests, we used the classical measurement method recording force and deflection.Simultaneously, for the measurements of beam deformation, we applied the test method of crack mouth opening displacement (CMOD), which has recently been suggested for the experimental investigation of HPFRC [18,22].For this purpose, a notch with a depth of 17 mm and a width of 5 mm in the middle of the span was milled on the bottom surface of the beam specimens according to the procedure in EN 14651 [1] for determining the strain during the crack initiation.Metal plates were glued near the notch to attach a clip gauge which measures the displacement between the two opposite edges of the crack [13].The stresses f L were calculated according to the fib Model Code 2010 [2] as where F represents the cylinder force (in N); b and h are the width and height of the specimens, respectively; and l = b/0.3 is the distance of the supports.Dimensions are provided in mm.Based on the experimental stress-strain curves, the parameter f L was evaluated at four different CMOD values: 0.5, 1.5, 2.5, and 3.5 mm (Figure 1).The influence of the fiber dosage on the residual bending tensile strength is studied in [11,12].Here, we focus on the segmentation of cracks that were initiated in a sample with a fiber dosage of 25 kg/m 3 .

Graywacke sample
The second sample is a cylindrical sample whose concrete mixture contains a water/cement ratio of 0.45.It has a diameter of 70 mm.The sample was part of a study of the ASR research group 1498, AKR-Reaktionen in Betonteilen bei gleichzeitiger zyklischer Beanspruchung und externer Alkali-Zufuhr.ASR is a common chemical reaction in cementitious materials.It is triggered by moisture exposition of the basic and alkalicontaining cement matrix and the concrete's aggregates that are often naturally rich in silica.As a result, silica gel is produced which is prone to swelling.Consequently, damage processes are initiated and cracking occurs.A comprehensive overview over the reaction mechanisms during ASR is given in [23].
The sample under investigation contains graywacke which has a relatively high alkali reactivity [28].ASR was triggered by storing the sample in a fog chamber for nine months at 40 °C according to the DAfStb alkali guideline [8].As a result of ASR, cracks were initiated.
Copyright 2022 -by the Authors.Licensed under a Creative Commons Attribution 4.0 International License.

CT imaging and image data
CT measurements on large concrete specimens require a high X-ray energy due to the high density of 2.6 g/cm³.Additionally, for samples with reinforcements, e.g. of iron (7.6 g/cm³), this requirement increases even further, so that measurement is not possible even with X-ray tubes of the highest energy (600 kV).

Imaging of the fiber-reinforced concrete sample
The sample was scanned at the Fraunhofer EZRT, Germany.The dimension of the sample allowed for the application of an 300 kV microfocus X-ray tube from Hamamatsu Photonics.The sample was scanned at 290 kV.The detector has a sensitive area of approx.42 x 42 cm² and a pixel size of 139 µm.The sample was positioned on a rotary axis for measurement and imaged onto the detector with a magnification factor of 2.3.This results in an effective voxel size of 60.4 µm in the object.For the 3d reconstruction, 3 600 angles were acquired along a complete rotation of the sample with an exposure time of 0.8 s each.The total measurement time was 48 min.

Imaging of the graywacke sample
The sample was scanned by a laboratory µCT device at BAM, Germany.It consists of an X-RAY WorX GmbH XWT-225-SE X-ray tube and a PerkinElmer Inc. XRD1620 detector.A tube voltage of 210 kV was used.The 3d reconstruction is obtained from 2 400 angles along the complete rotation of the sample and 2 seconds exposure time per angle.

Image and crack characteristics
Gray value ranges and sizes of the reconstructed images are summarized in Table 1.As large parts of the images do not contain any cracks, we restrict to manually cropped out regions. Figure 2 shows two slices of each of the two images.The crack characteristics differ significantly.As a result of the bending test, the crack opening in the fiber-reinforced concrete sample is relatively large (approx.350 voxels in height in the reconstructed images).It propagates from left to right through the complete specimen, becoming thinner on the right.Several branches exist, most of them having a thickness of only a few voxels.Within the crack, we observe some loose concrete chunks that were separated from the sample during crack propagation.Cracks in the graywacke sample appear on a scale of 1-8 voxels.Instead of one connected crack, we observe a set of individual, unconnected crack structures.Most cracks appear inside aggregates.In some parts they also propagate into the cement matrix.

Crack segmentation methods
The performance of several crack segmentation methods has been analyzed and compared on simulated cracks in 3d CT images of concrete [3].Based on these results, the methods have successfully been adapted to authentic cracks [4,14].Here, our goal is a qualitative comparison of the methods with those previously developed for industrial purposes [25].Our focus lies on analyzing the methods' robustness, i.e., the ability to perform equally well for a range of different crack and cement characteristics.In the following, I : R 3 → R denotes a 3d image.
Copyright 2022 -by the Authors.Licensed under a Creative Commons Attribution 4.0 International License.

Hessian-based percolation
Hessian-based percolation [9,30] is an algorithm that consists of two steps.First, a preselection of voxels is computed that are considered part of the crack structure.Classically, such a preselection can be obtained by analysing the eigenvalues of the Hessian matrix of the input image.Second, the selected set of voxels is grown iteratively.The region-growing process is initiated from every candidate voxel.After each iteration, the grown region is evaluated based on a shape criterion.A good preselection is crucial for the algorithm to perform well.Examples of Hessian-based filters that can be used for preselection are the sheet filter [9,24] and the Frangi filter [10].Candidate crack voxels are obtained by thresholding the filter responses.
In a large-scale simulation study [3], the Frangi filter showed a better performance than the sheet filter with respect to recall values.As we want to avoid false negatives in the preselection step, we choose the Frangi filter to compute the candidate voxels.This filter is defined as follows.
The Hessian matrix H(p, σ ) of an image I at voxel p is calculated from the convolution of I with the second derivatives of an isotropic Gaussian kernel with standard deviation σ ≥ 0.
These terms are combined to a plateness measure for dark structures on a brighter background via The Frangi filter is then defined as In practice, multiple scaling parameters, 0.5 ≤ σ min ≤ σ ≤ σ max , are considered to detect multiscale structures.α, β , η σ are weighting parameters.Hysteresis thresholding is then applied to the filter values F(p) ∈ [0, 1): Choose two thresholds 0 ≤ τ 2 ≤ τ 1 ≤ 1. Voxels with F(p) ≥ τ 1 ∈ R give an initial set of foreground voxels.The set is then grown iteratively.In every iteration, voxels with F(p) ≥ τ 2 ∈ R that are adjacent to the foreground are added to the foreground.The iteration stops when no more voxels are added.The procedure results in a binary image.We denote the final set of foreground voxels by H.This set then serves as input for the percolation algorithm given in Algorithm 1. Set P = {p} and t = I(p) + ε.

3:
while boundary of window of size (2W + 1) 3 with center p is not reached do 4: for every neighbor q of P do 5: if I(q) ≤ t then 6: Add q to P.

7:
end if 8: end for 9: Set t = max(max p∈P I(q),t) + ε.Compute 12: if F 3D ≥ f then 13: P is part of the crack 14: end if 15: end for 16: Discard voxels which were detected at most t times.We choose α = β = 0.5 to process the concrete images.By visual inspection, the crack widths in the fiber-reinforced concrete sample are estimated to range from 1 to approx.350 voxels.The parameter σ is tuned accordingly and with the same reasoning as in [14].We set σ min = 0.5, σ max = 175 and choose a σ -step size of 0. 12th Conference on Industrial Computed Tomography, Fürth, Germany (iCT 2023), www.ict2023.orgto decrease run-time.In the graywacke sample, the crack thickness ranges from 1 to approx.8 voxels.Here, we use σ min = 0.5 and σ max = 4 with a σ -step size of 0.5.The parameter η σ is supposed to suppress noise.A classical choice is η σ = 2(max p R(p, σ )) 2 [10].A previous study has shown that this choice also suppresses thin crack structures if the concrete matrix contains bright artifacts [14].Therefore, we use η σ = 2(R 0.99 (p, σ )) 2 for both images where R 0.99 (p, σ ) is the 99%-quantile of the empirical distribution of R given in Equation (1).For the voxel preselection, we choose the hysteresis thresholding parameters τ 1 = 0.8 and τ 2 = 0.15 for the fiber-reinforced concrete sample and τ 2 = 0.4 for the graywacke sample.The parameters for the percolation step are ε = 0, f = 0.2, W = 3, t = 0 in both cases.For the fiber-reinforced concrete image, we extracted the largest connected component to remove background noise.We did not apply connected component extraction on the graywacke image due to the disconnected crack structures.

3d U-Net
As a representative of deep learning methods, we used the 3d U-Net [6], see Figure 3 for a sketch of the network architecture.In the left part of the network, the input is processed by convolutional layers (kernel size three) and max pooling layers.The blue rectangles symbolize the convolutional layers, the green ones max pooling layers.In the gray rectangles the input is concatenated with the corresponding feature map from the encoder and is upsampled.The sizes of the rectangles relate to shrinkage/enlargement of the input image.The numbers below show the output filters of each layer.
To train the 3d U-Net, 3d semi-synthetic images with simulated cracks of fixed widths of one, three, and five voxels are used.The cracks are simulated on images of normal and high performance concrete, see [3] for details.We trained the network for 20 epochs.The 3d images of size 256 3 are tiled into patches with a size of 64 3 to lower the computational cost of the training.Patches have a 14 voxel overlap to reduce edge effects.We used transfer learning [19] to improve our network and we fine-tuned [7] it on semi-synthetic data with multiscale cracks, where the crack thickness ranges from 1 to 20 voxels and cracks have smaller branches.While the basic training of our neural network requires at least 20 epochs, fine-tuning takes only 10 epochs.In this way, the network was adapted to be able to detect thicker cracks.To segment cracks in the fiber-reinforced concrete sample, we ran the model on the image downscaled to {0.0625, 0.09375, 0.125} times the original size and applied the fine-tuned model to predict the crack at each scale.Afterwards, we rescaled the images to the original size by using spline interpolation and computed the voxelwise maximum of the three segmentations to obtain the final result.In this way we obtained the segmentation of the big, main crack.To get the results for the thin cracks, we applied the model trained on the cracks of fixed width on the images downscaled for scales in {0.125, 0.25, 0.375, 0.5}.We used the same interpolation to restore the original image size.We combine the two results for the thick and the thin cracks and apply threshold 0.5.The results for the graywacke sample were obtained by running the model trained on the images with fixed crack width on the downsampled images for scales in {0.125, 0.25, 0.375, 0.5}.We use spline interpolation to restore the original image size, compute the voxelwise maximum of the four segmentation results to obtain the final results and apply a threshold of 0.5.

Template Matching
The idea behind template matching is to find a certain pattern, given as an image T (the template), in the image I.For this purpose, the template T is moved over the image I, and at each position, the similarity between T and the subimage of I covered Copyright 2022 -by the Authors.Licensed under a Creative Commons Attribution 4.0 International License.
12th Conference on Industrial Computed Tomography, Fürth, Germany (iCT 2023), www.ict2023.orgby T is measured.This can also be regarded as a convolution.The similarity of images is measured via the correlation coefficient where N is the number of voxels of the template T , Ī, T are the means and σ I , σ T are the standard deviations of grey values in I and T , respectively.On a small scale a crack can be regarded as a plate or disc where the plate is represented as zeros and the surrounding area by ones, assuming that a crack is dark while the surrounding material is brighter than the crack.A 2d example of a template oriented horizontally looks like the following matrix: To ensure that cracks of arbitrary orientation are detected, the template T is rotated stepwise by five degrees in both directions (azimuth, elevation, 180 degrees each) and for every resulting template the correlation coefficient is computed.The highest coefficient for every position is then stored.Since cracks vary in width, not only the orientation of the template but also the size and width of the template have to be changed.The template matching method for segmenting cracks has been implemented in ZIBAmira [25], a modular visualization and data analysis system.It is an academic version and a superset of the commercially available visual analysis system Amira™.Within this framework the crack detection featuring template matching is carried out in three steps: • Crack completion in areas where cracks bifurcate or branch (a weak point of that approach) [optional] • Application of a mask discriminating between the inside area of the cylindrical sample and outside regions surrounding it to overcome false positives at the borders.Big pores are manually classified and also regarded as outside [optional].
A median filter was applied to both images as preprocessing.The template choices for segmenting the images are summarized in Table 2.
The resulting correlation coefficients were binarized with a threshold of 0.5.Small components less than 500 voxels were removed.The crack completion as the last post processing step was carried out by marking voxels adjacent (with respect to the 26-neighborhood) to crack voxels as crack if their correlation coefficients deviate no more than 10% from the primary threshold.This step is repeated until the boundary of a 25 3 window is reached.
Copyright 2022 -by the Authors.Licensed under a Creative Commons Attribution 4.0 International License.

Results
A ground truth for validating the segmentation results is not available.Due to the image sizes of order 1 000 3 , manual labelling of crack voxels is unfeasible.Hence results can only be discussed qualitatively after visual inspection of 2d slice views and 3d renderings.We discuss the results for the two samples separately.Slices for the fiber-reinforced concrete sample are shown in Figure 5, while 3d renderings are shown in Figure 6.From the renderings, one can notice that the general crack shape looks similar for Hessian-based percolation and the 3d U-net.The large crack opening is segmented accurately.The template matching algorithm assumes cracks to be thin, planar structures.Therefore, only thin templates are matched to the structure and the crack opening is not segmented.Polypropylene fibers exhibit low grayvalues in CT images.As a result, all methods partially misclassify fibers as cracks.As can be seen from renderings, this effect seems to be most prominent for template matching.Hessian-based percolation also misclassifies ring artifacts.
From the slice views, we observe that Hessian-based percolation performs better than the 3d U-net in segmenting thin branching cracks near the crack opening.These thin cracks were removed by the downsampling scheme which is used for the 3d U-net.The thin cracks were also segmented accurately via template matching.
The result from the 3d U-net is smoother than the result from Hessian-based percolation and the edges of the crack opening are segmented more precisely.Concrete chunks inside of the crack opening are falsely segmented as cracks for both methods.However, these regions may still be regarded as concrete failure which makes their detection worthwhile in practice.12th Conference on Industrial Computed Tomography, Fürth, Germany (iCT 2023), www.ict2023.orgSlices for the graywacke sample are shown in Figure 7, while 3d renderings are shown in Figure 8.Since this sample contains many small and subtle cracks, we can observe many disconnected components in the renderings.The segmented structures look similar for the 3d U-net and Hessian-based percolation, but for the latter there are fewer holes in the segmented crack structures.Template matching segments cracks very smoothly and with very few noise voxels, especially compared to the other two methods.
The reason for this is that only templates with a length of more than 32 voxels were used, such that smaller structures are less likely to be segmented.
From the slice views we can validate the previous claim: Cracks segmented by the 3d U-net are less connected than for Hessianbased percolation (Figure 7b).Additionally, the 3d U-net seems to be more sensitive to the boundaries between aggregates and cement paste and classifies them as cracks (Figure 7c).These boundaries in some cases are part of the crack, which makes their detection indeed worthwhile.For template matching we can observe that fewer noise voxels are classified as cracks and that generally cracks are more continuous than for the 3d U-net and Hessian-based percolation (Figure 7d).Although template matching seems to be more suitable for very thin cracks, some of these still remain undetected.
Even though most cracks appear inside the aggregates due to ASR, they sometimes propagate through the cement matrix as well.
These cracks tend to be thinner and have a lower contrast than the cracks within the aggregates, thus being more likely to be overlooked by all three methods.The run-time of the Frangi filter is 70 (graywacke image) and 100 minutes (fiber-reinforced concrete image) for a single σ .In practice, the filters for several σ can be computed simultaneously depending on the hardware used.The run-time for Hessianbased percolation heavily depends on the window size W and the amount of preselected voxels.With our choice of W = 3 the algorithm finished in 1 minute for the graywacke image and 50 minutes for the fiber-reinforced concrete image.Template matching took approx.80 minutes per template.
For the 3d U-Net, the training took around 2 days and the complete segmentation of the fiber-reinforced concrete sample took around 27 minutes (on the image downscaled by factor 2).For the graywacke sample it took around 30 minutes to get the segmentation results.12th Conference on Industrial Computed Tomography, Fürth, Germany (iCT 2023), www.ict2023.org

Conclusion
In this work, several crack segmentation methods were tested on two different samples: a high-performance concrete reinforced with polypropylene fibers and a concrete mixture with graywacke.Cracks in the fiber-reinforced concrete sample were induced by flexural tensile strength testing, while cracks in the graywacke sample are due to a chemical reaction (ASR).As a consequence, the cracks in these two samples differ fundamentally with respect to their shape and topology.The fiber-reinforced concrete sample is dominated by a large crack opening with several thin crack branches surrounding it.The graywacke sample features many small and thin cracks which spread over the sample.The crack segmentation methods of choice were 3d U-net, Hessianbased percolation, and template matching.Compared to previous studies [3,4,14], their parameters were only varied marginally to validate the methods' robustness.However, some adaptions are necessary to account for the cracks' scales.The 3d U-net was trained on synthetic cracks in concrete images which differ from the ones evaluated in this study.Therefore, it is remarkable that it is able to segment most crack structures accurately.
For the fiber-reinforced concrete sample, the 3d U-net and Hessian-based percolation successfully segment the dominant crack opening.Template matching is unable to do so.Larger and differently-shaped templates would be necessary to detect these large crack openings.However, this would make the approach computationally even more demanding and render it unpractical on very large images.On thin cracks, template matching performs better, similar to Hessian-based percolation.The 3d U-net performs worse as it has been applied on downscaled versions of the image.For the graywacke sample, Hessian-based percolation and 3d U-Net perform well except for some discontinuities in the segmented cracks.For this sample, template matching worked better as the continuity of cracks is preserved.However, very thin cracks with a low contrast remain a main challenge for all methods.Moreover, dark boundaries between aggregate and cement paste also cause confusion for our methods.However, these regions may sometimes be actually considered as cracks.
In combination with the findings in [3,4,14], our results give evidence that the crack segmentation methods are able to robustly and reliably segment various types of cracks in various types of concrete with only minor adjustments.Thin cracks still represent the main limitation, especially in combination with very thick cracks, such as crack openings initiated from flexural tensile testing.Also, fibers with grayvalues similar to those of the cracks often yield false positives in the segmentations.These are particular challenges and limit the accuracy and precision of the methods discussed here.A refinement of the methods or suitable postprocessing may be necessary to improve the results.Another constraint is the significantly increased run-time of our methods for increasing image size.To solve this problem, methods for the preselection of potential regions with cracks could turn out very helpful.
To conclude, the segmentation methods discussed here may be used to detect cracks in 3d images of concrete semi-automatically.
A visual estimation of the range of crack thickness is necessary for choosing the scaling parameter of the Frangi filter, the downsampling scheme of the 3d U-Net, and the template sizes of the template matching algorithm.The remaining parameters were only varied marginally compared to previous studies, rendering the methods a good choice to segment multiscale cracks on different concrete types in a robust way.Still, challenges deteriorating the results have been identified and refining the methods with respect to these is subject to future work.

Figure 1 :
Figure 1: Left: Stress-strain curves of the beam test-series with different fiber dosages MasterFiber 235 SPA (PP).Clip gauge strain in accordance with EN 14651 [1].The vertical axes are CMOD 0.5 to CMOD 3.5.Right: Picture from the beginning of the test and from the end of the test.

Figure 3 :
Figure3: The architecture of the 3d U-Net.In the left part of the network, the input is processed by convolutional layers (kernel size three) and max pooling layers.The blue rectangles symbolize the convolutional layers, the green ones max pooling layers.In the gray rectangles the input is concatenated with the corresponding feature map from the encoder and is upsampled.The sizes of the rectangles relate to shrinkage/enlargement of the input image.The numbers below show the output filters of each layer.

Figure 4 :
Figure 4: Principle of Template Matching: Template outside crack (left) Template on crack (center) Template fitted to crack (right)

1 .
Image preprocessing like smoothing (e.g.3d median filter) [optional] 2. Template matching 3. Postprocessing of the result such as • Binarization of each correlation coefficient and computation of the pointwise maximum of the outputs • Removing of very small segments [optional] (a) original (b) Hessian-based percolation (c) 3d U-Net (d) template matching

Figure 5 :
Figure 5: From left to right: Slice y = 1 000 of the input fiber-reinforced concrete image and segmentation results for Hessianbased percolation, the 3d U-Net and template matching overlayed over the input image in cyan color.

Figure 6 :
Figure 6: From left to right: Rendered segmentation results for the fiber-reinforced concrete image for Hessian-based percolation, the 3d U-Net and template matching.

Figure 7 :
Figure 7: From left to right: Slice z = 550 of the input graywacke sample image and segmentation results for Hessian-based percolation, the 3d U-Net and template matching overlayed over the input image in cyan color.

Figure 8 :
Figure 8: From left to right: Rendered segmentation results for the graywacke sample for Hessian-based percolation, the 3d U-Net and template matching.

Table 1 :
Information on the µCT image data.