**1. Introduction**

### *1.1. Alkali-Silica Reaction (ASR)*

Despite decades of research, the problem of harmful alkali-silica reaction (ASR) in the field of concrete construction has not ye<sup>t</sup> been satisfactorily solved. For the first time in 1940, Stanton [1] reported damaging strains within concrete due to chemical reactions of cement and aggregate. In the 1950s, Powers and Steinour [2,3] developed initial models of ASR's damage mechanism. In the 1970s, Locher and Sprung [4] identified opal and porous flint as alkali-sensitive aggregates and developed theories on their reaction mechanisms. In the 1980s, various researchers conducted in-depth studies on the influence of alkali metal salts on the swelling pressures of the ASR gel [5,6]. The current state of knowledge in the field of ASR has also been extensively described in number of recent publications [7,8].

During the ASR process, the reactive SiO2 within aggregates reacts with alkalis (supplied from the cement paste or from an external source) in the presence of water to form expansive alkali silicate hydrates (ASR gels). Because the tensile strength of road surface concrete is often significantly lower than the swelling pressures caused by ASR gels, cracking can be induced [9]. The progression and the extent of the resulting cracking processes are determined to a large extent by the type of aggregate. For example, fast-reacting aggregates (among others, flint, opaline sandstone and mudstone) are characterized by gel and crack formation emanating from the transition zone between the grain and the mortar matrix [7]. On the other hand, in the case of the slow-reacting aggregates (for instance greywacke or quartz porphyry), which were of primary of interest in this project, the gel formation takes place above all inside the aggregate itself, which results in the formation of internal aggregate cracks [7].

The severity of the ASR degradation process is thought to be partially dependent on the amount of porosity within a given aggregate that is accessible to liquid penetrating from the sample surface. Against this background and to evaluate the alkali sensitivity of the aggregate, the influence of the specific surface area on the solubility behaviour of four di fferent aggregates in 0.1 M potassium hydroxide solution without and with defined addition of NaCl at a temperature of 80 ◦C was thoroughly investigated in a joint project [10]. To quantify this relationship, a non-destructive method is needed for measuring both the external surface area of aggregates and the internal surface area of aggregate cracks and pores, including a di fferentiation of internal voids connected to the sample surface from those isolated from the surface. The primary focus of this publication is devoted to the crack detection method. A detailed analysis of the implications for ASR damage, including a comparison of the CT results with those from other porosity measurement methods, such as mercury porosimetry and the Brunauer–Emmett–Teller (BET) method, can be found in Oesch et al. 2020 [11] and in Weise et al. 2019 [10].

### *1.2. X-Ray Computed Tomography (CT)*

The development of X-ray computed tomography (CT) began in the 1960s and clinical X-ray CT investigations have been widely conducted since the 1970s [12,13]. Since that time, many di fferent reconstruction algorithms have been developed for clinical use, including algorithms based on the algebraic reconstruction technique (ART), filtered back projection (FBP), and iterative reconstruction (IR) [14]. Medical X-ray CT scanning systems are, however, unsuitable for many applications in materials science given their lower X-ray energy characteristics and coarser resolution compared to specialized laboratory-based X-ray CT systems used for materials research [15]. These di fferences occur both because the size of the intended scanning objects tends to significantly di ffer between clinical and materials science applications and because the X-ray absorption characteristics of live tissues are much lower than those of materials such as concrete and steel.

X-ray CT has been used in non-destructive concrete research applications for more than 30 years [16,17]. In this scanning method, a sample is placed on a rotating table between an X-ray source and an X-ray detector [18]. By adjusting the distances between the X-ray source, the sample and the X-ray detector, it is possible to vary the voxel (i.e., 3D pixel) resolution in the resulting images. The penetration of the sample by the X-ray beam causes an X-ray attenuation image of the sample to be projected upon the detector. By recording these projected images during the 360◦ rotation of the sample, the projections can be inverted using volume reconstruction algorithms, which produce a 3D representation of X-ray attenuation within the sample [19]. X-ray attenuation is approximately proportional to local material density and can be used to identify single objects within a material (or structure) and to individually separate and analyze those objects.

Previous research has shown that X-ray CT scans can be taken during incremental testing. This includes mechanical testing (such as unconfined compression, split cylinder, triaxial, and reinforcing bar pull-out testing [20–24]), chemical testing (such as the measurement of progressive corrosion in reinforced concrete during repeated exposure to chloride [25] and the transport of water [26–28]) and thermal testing (such as water migration in heated concrete [29]).

### *1.3. Crack Detection and Quantification*

Crack detection and quantification is important for understanding and modelling a series of material behaviours. Precise measurement of crack surface area is needed, for instance, in order to calculate the fracture energy expended during damage processes using basic fracture mechanics relationships [30]. The crack orientations have also been observed to exhibit a behaviour that is highly dependent on the anisotropy of the material structure, such as fibre orientation within fibre-reinforced concretes [31].

Crack detection and quantification within X-ray CT images have been the subject of extensive past research. Most of these crack detection methods have leveraged one or more unique characteristics of cracks, which differentiate them from the surrounding material. Possibly the most popular research approaches have focused on the use of template-matching methods in order to separate cracks from the surrounding materials [32,33]. This method of crack detection relies on the similarity of cracking structures to certain template shapes, such as small planes or discs. Although impressive results have been demonstrated using the template-matching method, the template parameters are not universal and must generally be tailored for each material and each imaging scenario.

Research was recently carried out by Paetsch (2019) [34] with the goal of partially overcoming these challenges related to using template matching approaches. This research indicated that the results of a series of analyses carried out using different template shapes can be combined in order to obtain a greater accuracy of the detected cracks. However, Paetsch (2019) [34] has underlined that further problems remain to be solved that are common to most template-matching methods, such as difficulties detecting cracks in areas where significant crack branching or widening occurs.

Another method that takes advantage of the narrow shape characteristics of cracks is a Hessian-based approach [35,36], which identifies regions that exhibit sharp changes in image intensity. Percolation methods have also shown significant promise in detecting cracks across a range of materials [37]. These methods leverage the fact that most cracks are continuous, narrow objects with relatively consistent (low) density. Percolation methods have proven insufficient, however, to accurately detect complex cracks of varying size in most materials. Impressive results have also been obtained through a combination of the Hessian and percolation-based methods into the Hessian-driven percolation approach, although the processing time required for such an analysis remains prohibitive for most high-resolution CT images [32].

Many methods have also been employed that leverage the unique characteristics of a specific material or damage scenario. One excellent example of this approach is the use of digital volume correlation (DVC) to detect cracks in samples subjected to in-situ loading [38–40]. DVC is used to measure strains within samples by calculating voxel movements between subsequent CT images (such as images calculated before and after a loading increment). Cracks can, thus, be identified as areas of either high strain or poor correlation within DVC images or through more complex analysis methods, such as phase-congruency analysis. Although these methods appear to exhibit a relatively high accuracy (even sub-pixel, see [41]), they are only useful for detecting cracks caused by progressive in-situ testing with simultaneous CT. They do not provide any benefit for detecting cracks that are already present in specimens prior to testing. Phase congruency can, however, also be used to detect edge features (including cracks) within the greyscale images without direct reference to DVC [42].

Another example of a material-specific crack detection approach is the leveraging of typical wood structure within logs to identify cracks. These cracks typically run perpendicular to the growth rings of the logs and can, thus, be easily identified by their orientation characteristics [43].

Despite the many promising crack detection methods outlined here, a series of obstacles remain that have prevented the implementation of consistent, accurate, and quantitative crack analyses as part of CT scanning. First, most of these methods require some amount of tailoring for specific material properties (as in the case of template matching and percolation) or specific crack conditions (such as measuring only those arising from in-situ testing using DVC methods). Second, none of these methods

has been successfully validated for the quantitative determination of crack properties (such as surface area) based on other standard measurement techniques.

In this study, we will show, on the example of di fferent aggregate types, how the obstacles mentioned above can be circumvented by a novel data fusion strategy.

### **2. Materials and Methods**

### *2.1. Sample Selection*

For this testing series, a group of aggregates from four different categories were selected and analysed. These categories were selected in order to include stones with a variety of di fferent mineralogical compositions, deterioration conditions, and alkali-sensitivity characteristics (Table 1 and Figure 1) [44]. All stones included in this analysis were in the 8 mm to 16 mm size range: During the sieving process, the individual stones passed successfully through a sieve with a 16 mm mesh but were unable to pass through a sieve with an 8 mm mesh [45].



For the categories GK1 and GK4, the selected stones were sieved from a natural river gravel. Such river gravels are typically characterized by significant mineralogical deterioration due to naturally occurring weathering processes. In order to characterize these river gravels, which have a heterogeneous mineralogical composition, the primary types of rock (7 types in total) occurring in GK1 and GK4 were determined and 10 individual grains of each type were selected for CT analysis.

For the categories GK2 and GK3, the selected stones were sieved from crushed stone chips that were quarried from solid rock deposits. Such quarried stones are typically characterized by greater mineralogical integrity than river gravels because they have not been exposed to significant weathering. Due to the homogeneity of the quarried stone, the selection of individual grains was limited to 10 each for GK2 and GK3. Thus, combining all the individual grains from each of the four stone categories included in this research study, a total of 90 di fferent individual grains were investigated.

### *2.2. CT Scanning*

During this research program, an acceleration voltage of 130 kV and current of 180 μA were used for the X-ray source. The X-ray beam was also filtered using a 0.5 mm thick Copper plate immediately upon leaving the source in order to remove (unwanted) photons of small energies from the X-ray beam, thereby increasing the contrast of the resulting images. The flat panel detector used for this scanning contained a 2048 × 2048 pixel field.

Individual aggregates were sorted based on mineralogical characteristics and placed within corresponding plastic tubes with small pieces of foam separating the aggregates from one another. As a result of heating and deterioration of the target material within the X-ray tube as well as changes in detector sensitivity over time, significant variations in the measured X-ray beam intensity and distribution can occur. To compensate for these variations, "dark-field" and "bright-field" images, which correspond to blank images (i.e., containing no sample) acquired with no illumination and full illumination, respectively, were acquired prior to the scanning of each plastic tube of samples. These images were then used to calibrate the X-ray images of the samples.

The CT machine was pre-programmed to collect a complete scan of each aggregate before repositioning the plastic tube using a manipulator and beginning the scan of the next aggregate. Thus, the scanning conditions for all stones within any given plastic tube were identical. All scanning conditions other than resolution were also held constant for all plastic tubes.

It was important to maintain scanning conditions that were as consistent as possible to ensure that the results of the crack analysis would be comparable. In spite of this, the resolution was maximised for each stone type, if they significantly varied in size and shape. This was done by adjusting the distance between the plastic tube and the X-ray source. The corresponding voxel sizes were then calculated directly from the measured distances between the X-ray source, the sample holder and the X-ray detector for each individual set of scans.

Although these variations in image resolution are known to directly a ffect measurements of crack properties, such as surface area (increased surface area is generally detected with decreasing voxel sizes), some estimation of the magnitude of this e ffect can already be accounted for based on a recent study [46]. The results of this study indicate that even a doubling of voxel size does not appear to generally change the measured crack surface area by more than a factor around two. We will see below that the small voxel size variations had little influence on the much larger variations in measured crack surface area among the di fferent aggregate types, so that comparisons could be made, and conclusions drawn.

### *2.3. Image Analysis*

### 2.3.1. Data Fusion Approach

In such an environment, where many analysis methods are readily available, but no individual method is su fficiently accurate to provide the needed measurements, the use of a data-fusion inspired approach becomes very promising and attractive. Data fusion enables researchers to combine data from multiple sources in order to produce more consistent and accurate results than those provided by any single source [47]. In non-destructive testing, the di fferent sources used in data fusion typically result from di ffering non-destructive measurement approaches. Such data-fusion based approaches have even been successfully applied to the application of crack detection [48].

It is, however, often the case that researchers only possess meaningful data from a single measurement technique, such as CT (often indeed used as a reference), or do not have access to further non-destructive testing equipment. Even in this case, it should be possible to use the theory behind the data fusion approach to improve the overall quality of the quantitative determinations resulting from image analysis. Rather than relying on a wide variety of physical measurement techniques, data fusion in this approach would be carried out by using the output from an array of di fferent image analysis techniques. Since such an approach relies on the fusion of di fferent computationally generated data sources resulting from the same original CT image rather than on a variety of di fferent physical measurement techniques, it can be more appropriately described as virtual data fusion. This is similar to the process that is thought to occur when an expert identifies cracks using the human eye. The expert has only one measurement technique (a visual image), but by considering its many di fferent aspects (such as coloration, shape, and relationship to surrounding objects or planes of stress), the expert is able to quite easily and accurately detect a crack on the surface of a specimen.

Figure 2 shows a diagram of this virtual data fusion approach. In the diagram, the characteristics of a crack are displayed in dark grey boxes and the image processing steps for identifying objects with those characteristics are depicted in light grey boxes. The list provided here is only meant to serve as an example and is by no means exhaustive. It is clear, however, that results obtained through a fusion of the results from twelve such independent analyses will be much more accurate and resilient to varying material conditions than the results from any single analysis technique. An example of how such a step-by-step approach can identify individual cracks within a generic concrete sample is shown in Figure 3.

**Figure 2.** Virtual data fusion web linking cracks (black) with their characteristics (dark grey) and image analysis techniques for identifying objects with those characteristics (light grey).

**Figure 3.** Step-by-step isolation of cracking by means of virtual data fusion. CT image of a concrete sample (**a**), voids identified using a greyscale threshold (**b**), voids identified in (**b**) added to interfacial zones identified using a gradient-based analysis (**c**), removal of small connected components (noise and isolated pores) from image (**d**), and elimination of components with small specific surface areas from image (**e**). Raw data courtesy of U.S. Army Engineer Research and Development Center (ERDC).
