Introduction

Fracture aperture (FA) strongly influences the hydraulic and mechanical behavior of rocks, affecting permeability, transmissivity, and stress distribution1,2,3. Accurate quantification is essential for modeling flow and transport in hydrocarbon reservoirs, geothermal systems, and fractured aquifers4. Several methods have been used over the past several decades to quantify the FA. Earlier studies on FA relied on surface profilometry, both mechanical and optical, which reconstruct opposing fracture surfaces and calculate local FA distributions based on their topography5,6,7. Despite providing high spatial resolution, these methods are often destructive and require meticulous alignment of fracture surfaces, making them unsuitable for dynamic or in situ measurements8. Another class of destructive methods involves the casting of resin, cement, or epoxy inside fractures, followed by mechanical sectioning of the solidified sample to measure local FAs9. However, this method requires fractures that are large enough and interconnected to allow the flow and solidification of viscous fluids within the core. Subsequently, the samples were destructively analyzed by slicing perpendicular to the fractures to measure the local FA fields. Alternative imaging strategies such as digital photogrammetry have also been employed to measure FA in exposed fracture systems. For instance, Torkan et al.10 implemented a photogrammetric approach to extract both FA and roughness from fracture surfaces. However, this method is inherently limited to surface-exposed fractures and cannot resolve internal FA variations critical for volumetric flow modeling. Similarly, other automated image analysis approaches have been proposed for fracture detection, such as the use of grey-level co-occurrence matrices combined with edge detection on borehole imaging logs11. In this framework, the advent of X-ray Computed Tomography (CT) has revolutionized FA characterization by enabling nondestructive, three-dimensional imaging of internal fracture geometries at micrometer to millimeter scales. Johns et al.12 first demonstrated the potential of CT for visualizing fracture voids in crystalline rocks. More recently, high-resolution CT systems have been employed to quantify FA fields with improved accuracy and reduced preprocessing requirements13, or have been integrated with other techniques such as Positron Emission Tomography to achieve multimodal imaging of FA heterogeneity in complex lithologies14. Another significant advantage of employing CT lies in the exceptionally high resolution it offers. Indeed, the variation in FA, even at the scale of a single sample, is an important aspect that will be crucial in future efforts to define the fundamental physics governing the transport of solutes in fractured media, a process that currently remains a significant challenge. As highlighted by Renshaw et al.15, even subtle changes in smaller FAs (\(< {100}{\upmu }\)m) can significantly impact flow and transport pathways, underscoring the need for characterization techniques capable of resolving these fine-scale features. In the scientific literature, several methods have been developed to extract FA from CT data. The standard Full-Width-Half-Maximum (FWHM) method estimates FA at half the gray value range between air and rock16,17,18. FWHM is reliable for features larger than the resolution but its accuracy decreases for narrower fractures influenced by the Point Spread Function, Line Spread Function, or Edge Response17,18,19,20. Alternative approaches that uses signal loss like Missing Attenuation, analyzing the gray value drop area12, and Peak Height, measuring the height between matrix and fracture trough21, are employed. Missing Attenuation suits heterogeneous samples and wider fractures but is orientation-sensitive22,23,24. Peak Height is less noisy for small FAs and orientation-independent but requires homogeneous materials and calibration17,18,24,25, making it sample-dependent. Here, we propose a novel automated method that combines deep learning segmentation with a quantitative FA analysis algorithm. Building on previous automated fracture detection approaches, including image-based feature extraction from borehole logs11 and comparative studies of conventional versus machine-learning-based segmentation for micro-fractures26, and X-ray Micro-CT characterization with deep learning27, this method enables high-resolution, slice-by-slice measurement of FA and infilling thickness (IT) directly from 2D tomography. Fracture networks are extracted with the U-Net architecture, while FA is computed using Gaussian convolution of grayscale intensity, representing density contrast between voids and matrix. This technique enables the quantification of spatially variable aperture fields under non-destructive conditions, extending the principles of pore-scale image analysis for petrophysical modeling demonstrated by Pal et al.28, by applying them to fracture networks and incorporating automated deep learning segmentation to achieve high-resolution, slice-by-slice measurements. To validate the computed measurements, we performed a comparative analysis with 3D image acquisitions obtained using a high-resolution digital microscope on physically sectioned samples, as well as direct manual measurements with a caliper. The proposed method, tested on both open and filled fractures, offers a robust, non-destructive alternative to traditional techniques, and contributes to a refined understanding of fracture-controlled permeability in heterogeneous rock masses. For fractures filled with mineral phases, the analysis of grey-level contrast in the tomography images was further integrated with mineralogical and petrographic techniques to characterize the infilling material.

Materials

Samples preparation and description

Two rock core samples, named S8 and S6, located in the Valleremita area (Marche Region, central Italy, Fig. 1), were selected to evaluate algorithms designed to extract fracture networks and calculate the FA of various types of discontinuities. The samples are sourced from the Lower Turonian-Lutatian Scaglia Rossa Formation, a marly limestone unit ranging in thickness from 150 to 350 m, and the Upper Tithonian-Low Aptian Maiolica Formation, composed of calcilutites, both within the Jurassic-Oligocene Umbria-Marche succession, a sequence shaped by multiple phases of tectonic activity29. Sample S6 is characterized by two primary open fractures, devoid of any filling material, several calcite-filled veins, some of which exhibit partial dissolution, and minor tectonic stylolites containing clay minerals. From De Vallejo et al.30, open fractures are discontinuities where the opposing rock walls remain separated, leaving voids that can act as preferential pathways for fluid circulation. In contrast, fractures with mineral infilling are discontinuities where the void space has been at least partially sealed by secondary mineral precipitation (e.g., calcite, clays, quartz). The presence or absence of filling material strongly influences both the hydraulic conductivity and the mechanical behavior of the rock mass. Accordingly, in this study we refer to aperture when describing open joints, and to infilling thickness when dealing with fractures filled with secondary minerals. Invernizzi et al.31 noted that the presence of clay minerals facilitated the development of stylolites and cleavage during the shortening phases of the Apennine orogeny. The veins represent extensional features filled with a variety of minerals, predominantly calcite in this case, often displaying a fibrous texture. Their formation is typically associated with fluid circulation within preexisting fractures of diverse origins. The development of these veins occurs through the transport and subsequent precipitation of minerals within the fracture space32. Sample S8 is characterized by a major joint filled with clay minerals, inclined at \(70^\circ\), along with minor stylolites and veins. Intersections between stylolites and veins are observed. The calcite-filled veins are concentrated near one face of the sample and intersect the primary joint at a perpendicular angle.

Fig. 1
figure 1

(a) Geological map of the sampled area with the location of the samples indicated; (b) Core boxes from which samples S6 and S8 were extracted, with detailed views showing the different types of discontinuities present.

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Methodology overview

3D X-ray Tomography

The internal characteristics of the limestone samples were investigated and quantified using X-ray computed tomography (CT)33, a non-destructive technique that provides high-resolution, three-dimensional density information. We used a Zeiss Metrotom 1500 system34, which offers a maximum measurement volume of 350 mm in all spatial dimensions. This system features a fixed tube-to-detector distance of 1500 mm and an adjustable X-axis positioning between the tube and rotating platform, enabling voxel size control down to 5 \(\upmu\)m for detailed imaging35. The voxel size determines the spatial resolution of the scan and thus the smallest feature that can be reliably identified in the reconstructed volume. Fractures or infilling materials with dimensions close to or below the voxel size may be affected by partial volume effects, which can blur boundaries and reduce measurement accuracy. A custom-designed support structure ensured stable positioning of the rock sample within the X-ray beam, with its longitudinal axis aligned vertically along the Z-direction of the scanner to maintain consistent orientation throughout the acquisition. This configuration minimized motion artifacts during the \(360^\circ\) rotation and ensured reproducibility across all slices. The tomographic process involves two main phases: scanning, during which the sample is exposed to a cone-beam X-ray source filtered through a diaphragm; and reconstruction, where the transmitted radiation intensities, captured by the detector, are processed to generate a 3D volume. The varying absorption properties of the sample materials result in grayscale projection images acquired over a full rotation36.

Fracture segmentation using U-Net

To extract fracture networks from 2D X-ray tomography images, the U-Net architecture was employed. This fully convolutional neural network, originally developed for biomedical image segmentation37, has proven effective in a range of applications, including the identification of rock discontinuities in tomographic datasets. The U-Net structure consists of a symmetric encoder-decoder architecture. The contracting path captures contextual features through repeated \(3 \times 3\) convolutions with ReLU and \(2 \times 2\) max pooling for downsampling, progressively doubling the number of feature channels. The expansive path restores spatial resolution via \(2 \times 2\) transposed convolutions (upsampling), concatenation with corresponding encoder features, and further \(3 \times 3\) convolutions for refined localization. A final \(1 \times 1\) convolution maps features to the desired classes. The effectiveness of U-Net extends beyond medical imaging, as seen in applications such as bridge failure detection38 and crack detection in masonry39. The dataset used to train the U-Net AI model consisted of a total of 750 images collected by examining buildings with damage during an EU project and from online sources to diversify the types of images in the dataset, and both avoid the problem of overfitting and better generalize the model. The images were labelled manually to ensure the reliability of the labelling. The dataset was divided into training, validation, and test subsets with the following proportions: 80%, 10%, 10%; the model was trained with 130 epochs, reporting an Intersection over Union (IoU) score of 0.991. IoU is a metric used to evaluate segmentation accuracy by measuring the overlap between the predicted and ground truth regions, with a value of 1.0 indicating perfect agreement. Following U-Net segmentation, the resulting binary masks were smoothed using morphological operations to reduce noise and enhance edge continuity. A connected component analysis was then applied to identify discrete pixel clusters corresponding to fracture traces in each 2D slice. For 3D analysis, the segmented slices were aggregated to support point cloud reconstruction and spatial separation of fracture structures, as described in Caputo et al.40. This allowed for the separation of spatially distinct structures and enabled subsequent quantitative analysis of fracture geometry and distribution.

This workflow, ranging from U-Net-based segmentation to 3D reconstruction and clustering, provides an automated and robust framework for the extraction and characterization of complex fracture networks from tomographic data.

Fracture aperture and infilling thickness calculation

To enable a consistent analysis of both open and filled fractures, an algorithm was developed to calculate either the FA or the IT, treating both as equivalent linear measurements. Following the extraction of the fracture clusters from the U-Net segmentation masks, the voxel dimensions were converted into millimeters to allow geometric quantification in physical units. Measurements were carried out on three sub-volumes along the Z-axis of each sample, as well as on the entire segmented volume. For sample S6 (with open fractures), the analyzed Z-range extended from slice 109 to slice 1630, corresponding to 1522 slices and a total thickness of approximately 107.6 mm, based on a voxel size of 70.69 \(\upmu\)m. The volume was subdivided into three equal regions of 507 slices each, corresponding to a thickness of approximately 35.84 mm per portion:

Bottom portion: slices 109–615

Central portion: slices 616–1122

Top portion: slices 1123–1630

For sample S8 (with filled fractures), the analysis was conducted between slice 125 and 1630, totaling 1506 slices and a thickness of approximately 86.59 mm, considering a voxel size of 57.47 \(\upmu\)m. Each of the three sub-volumes consisted of 502 slices (approximately 28.86 mm in thickness):

Bottom portion: slices 125–626

Central portion: slices 627–1128

Top portion: slices 1129–1630

FA or IT was calculated from intensity profiles taken along normals to the fracture trace. Fracture points were identified with 3D clustering, then a fitted spline curve was used to reconstruct a continuous trace of the fracture. This type of curve allows smooth interpolation between discrete points, preserving local geometry while minimizing noise. From the spline, we computed the slope and normal vectors, along which grayscale intensity profiles were extracted to measure contrast with the rock matrix. We applied a thresholding method to each profile to identify the grayscale discontinuities corresponding to the fracture boundaries, by detecting points where the intensity crosses a defined value that separates the rock matrix from the fracture or infilling material. To improve the accuracy of boundary detection, we used Gaussian convolution to enhance grayscale contrast between the discontinuity and the surrounding rock matrix. This technique smooths the intensity profile while emphasizing sharp transitions, allowing for more precise identification of fracture or infilling boundaries. The standard deviation of the Gaussian kernel was empirically set to match the scale of grayscale transitions associated with fracture boundaries, typically corresponding to a few pixels (\(\sigma \approx 2\)–3 px). A sensitivity test was performed by varying \(\sigma\) from 1 to 5 px, and the resulting aperture estimates showed less than 5% variation in mean values across the tested range, indicating low sensitivity of the method to this parameter.The local width was determined by computing the distance between the two threshold-crossing points along the normal and dividing it by two. For each slice, the mean, standard deviation, minimum, and maximum values of the FA or thickness were computed to assess variability. Additionally, a polygonal region was reconstructed using the endpoints of the local width measurements to estimate the total fractured area. This area was calculated numerically and normalized using the voxel size. Eventually, the percentage of fractured area relative to the total cross-sectional area of the core was calculated. The overall core boundary was defined by fitting a circular mask to the sample cross-section, and the fracture density was expressed as a percentage of the fractured area over the total cross-sectional area.

Figures 2, 3 and 4 illustrate the stepwise processing of a representative tomographic slice for sample S6 and sample S8, respectively. Each figure includes the original CT image, cropped region of interest, masked grayscale volume, and spline-fitted fracture trace used for local FA or IT computation. In Fig. 3, a cross-section of the fracture is shown (corresponding to the area identified by the neural network). The grayscale profile is thresholded at an intermediate level between the background and the peak, in order to isolate the fracture while suppressing background noise. The region surrounding the thresholded portion is identified as the fracture.

Fig. 2
figure 2

Processing workflow for sample S6 (open fracture). (a) Original CT slice; (b) cropped region based on ROI; (c) masked slice showing only the segmented rock volume; (d) spline fitted to the fracture trace for FA computation; (e) detail of aperture calculation.

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Fig. 3
figure 3

Gray-level profile across the fracture, showing the applied threshold and the selected region.

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Fig. 4
figure 4

Processing workflow for sample S8 (filled fracture). (a) Original CT slice; (b) cropped region based on ROI; (c) masked slice showing only the segmented rock volume; (d) spline fitted to the fracture trace for IT computation.

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Analysis of infilling characteristics of sample S8

In this study, a multi-technique approach was adopted to investigate the nature and composition of fracture infilling material. The analysis was based primarily on the interpretation of gray-level contrast in 2D X-ray computed tomography images, which were used to distinguish the infill from the host rock. This tomographic method was then validated and complemented by a suite of mineralogical and chemical techniques, including optical petrography on thin sections, powder X-ray diffraction (XRD), and energy-dispersive spectroscopy (EDS) coupled with scanning electron microscopy (SEM). Together, these methods provided a consistent framework for identifying the mineral phases responsible for fracture sealing, with a focus on the infilled discontinuity observed in sample S8.

Grayscale interpretation

This section focuses on the interpretation of grayscale values in CT images of Sample S8, highlighting how grayscale intensity corresponds to material density and aids in distinguishing the mineral phases filling the main fracture. In X-ray computed tomography, grayscale intensity reflects the X-ray attenuation coefficient of the material, which correlates directly with its density and atomic number. Denser phases absorb more radiation and appear brighter in the reconstructed images, while less dense materials produce lower grayscale values. This principle enables the use of grayscale contrast as a non-destructive proxy for identifying and differentiating mineral phases. In sample S8, which contains a fracture filled with minerals, a region of interest was selected within the infill to extract the corresponding grayscale value from the tomographic image. The mean grayscale intensity measured in this area was approximately 158.99 (on an 8-bit scale).

Energy dispersive spectroscopy

Energy Dispersive Spectroscopy (EDS) is a microanalytical technique commonly employed to determine the elemental composition of materials at the microscale. It is typically integrated with a scanning electron microscope (SEM), allowing for the qualitative and quantitative detection of chemical elements within specific areas of a sample, either at the surface or slightly beneath it. In this study, EDS analyses were performed using a Tescan Vega3 scanning electron microscope equipped with an Oxford Instruments INCA x-act EDS detector. Analyses were conducted on carbon-coated polished thin sections under high vacuum conditions. Operating parameters included an accelerating voltage of 20 kV and a working distance of approximately 15 mm. Elemental spectra were collected from fracture-filling phases as well as from the adjacent rock matrix for comparison. Microanalysis as a broader methodological framework includes various techniques aimed at identifying not only the elemental composition of materials, but also, in some cases, their atomic structure, bonding environment, or oxidation state. While EDS does not resolve isotopic compositions or oxidation states, it provides valuable insight into elemental distribution and concentration, particularly when used in combination with mineralogical tools such as X-ray diffraction and optical petrography. In this work, EDS was used to support the mineralogical identification of fracture infilling material in sample S8. The chemical data obtained through this technique played a key role in corroborating the mineral phases inferred from XRD analysis and from observations made under the petrographic microscope.

X-ray diffractometry

X-ray diffractometry (XRD) was used to identify and compare the mineralogical composition of various sandstone specimens. The samples were finely ground using an agate mortar and mounted in a glass sample holder. A Bruker D8 Advance diffractometer, equipped with a Cu radiation tube and a monochromator on the diffracted beam, was employed for the analysis. Diffraction patterns were collected over a \(2\theta\) range of \(^{\circ }\)3 to \(^{\circ }\)70, using a step-scan mode with a step size of \(^{\circ }\)0.02 and a counting time of 2 seconds per step. Phase identification was performed by comparing the resulting patterns with the Mineral Powder Diffraction File databook (Fig. 5).

Validation procedures

To ensure the robustness of the proposed methodology, we validated fracture aperture and infilling thickness measurements using multiple independent techniques. The workflow included comparison with high-resolution digital microscopy and manual caliper measurements, as well as complementary mineralogical and chemical analyses (SEM–EDS and XRD). An overview of the entire validation process is provided in Fig. 6.

Digital microscope

The Leica DVM6 digital microscope was employed to validate the FA and IT calculations for both samples S6 and S8, as described in Section 0.4. This system provides high-resolution 3D imaging and precise dimensional measurement capabilities. One transverse surface was analyzed for each sample, located approximately 32.8 mm from the top of the core in sample S6 and 32.1 mm in sample S8. The microscope was operated with a field of view (FOV) of 12.55 mm and a zoom factor of 1.5×, yielding a spatial resolution of approximately 4.15 \(\upmu\)m. This setup enabled detailed visualization of fracture boundaries and fine-scale features. A high-magnification objective was used to enhance the contrast and definition of the discontinuity edges. FA or IT was estimated by applying the same convolution-based algorithm used for the tomographic analysis to the grayscale intensity profiles extracted from the microscope images. Specifically, grayscale profiles were sampled along directions normal to the fracture trace, and a set of Gaussian kernels was convolved with each profile to identify the most representative fracture width. This automated approach provides a repeatable, operator-independent method for FA estimation based on grayscale contrast.

Figure 5 shows representative examples of this process for samples S6 and S8. For each, the original microscope image and the corresponding cropped ROI with convolution-based aperture identification are shown. Green lines mark the fracture edges, and the red line indicates the center of the discontinuity.

Fig. 5
figure 5

FA and IT estimation from high-resolution microscope images. Panels (a) and (c) show the original transverse surface images of samples S6 (open fracture) and S8 (filled fracture). Panels (b) and (d) display the corresponding ROIs analyzed using convolution-based grayscale profile analysis. Green lines mark the fracture edges, and the red line indicates the center of the discontinuity.

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Caliper

A caliper was used to perform direct measurements of the FA, representing a standard method widely employed in field practice for rock mechanics and structural geology. The measurements were taken at the same sample locations used for the digital microscope analyses, in order to compare the results obtained with the different methodologies. The caliper used in this study has an accuracy of ± 0.05 mm. Measurements were performed on several portions of the fractures and then an average value was calculated.

Fig. 6
figure 6

Workflow from CT acquisition to segmentation, FA/IT measurement, and validation.

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Quantitative results (S6 and S8)

Fracture aperture calculation in sample S6 and infilling thickness in S8

FA in sample S6 and IT in sample S8 were computed slice-by-slice across predefined sub-volumes, as detailed in the Chapter 0.1 and 0.2. For each slice, the pixel coordinates of the segmented fractures were processed to extract a continuous representation of the fracture trace using spline interpolation. Local aperture values were then calculated along the normal directions to the fitted spline by extracting grayscale intensity profiles and applying a Gaussian convolution method to estimate the distance between opposing fracture surfaces. The resulting FA or thickness values were converted from pixel units to millimeters using the known voxel size of each scan. Statistical parameters–including mean, standard deviation, minimum, and maximum values–were computed for three distinct sub-volumes (bottom, central, and top) and for the entire scanned volume, in order to assess the internal variability of discontinuity geometry within each sample. These quantitative results are summarized in Table 1, which includes FA and thickness measurements derived from 2D tomographic analysis, high-resolution digital microscopy, and manual caliper readings. For sample S6, the mean FA measured by 2D tomography ranges from 1.28 mm in the central region to 1.45 mm in the top region, with a standard deviation between 0.16 mm and 0.21 mm. The minimum and maximum values vary from 0.88 mm to 1.69 mm. For the entire sample, the mean FA measured by tomography is 1.34 mm, while microscopy indicates a similar mean value of 1.30 mm, with a slightly higher standard deviation (0.18 mm). The caliper measurement for the whole sample is lower (1.1 mm) compared to the tomography and microscopy results. In sample S8, infilling thickness progressively increases from the bottom (0.80 mm) to the central region (1.15 mm), before slightly decreasing again in the top region (1.10 mm; Table 1). The standard deviation ranges from 0.12 mm to 0.14 mm. The maximum thickness reaches 1.40 mm in the central region, while the minimum is 0.58 mm in the bottom region. For the entire sample, the mean thickness by tomography is 1.02 mm, while microscopy gives a slightly higher mean of 1.173 mm. The caliper measurement is 1.0 mm, slightly lower than both tomography and microscopy values. Overall, the 2D tomography and microscopy measurements are generally consistent, while caliper measurements tend to yield slightly lower mean values for both samples.

Table 1 FA (sample S6) and IT (sample S8) from 2D tomography, high-resolution microscopy, and caliper measurements.
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Mineralogical and chemical characterization of fracture infill in sample S8

SEM and EDS analyzes were first performed to investigate the chemical composition of the fracture-filling material in sample S8. Figure 5a–e show that the fracture infill is mainly composed of calcite, with minor quartz and biotite. In Fig. 7a, a cross-polarized light (XPL) image shows the fracture in a thin section, where the infill appears to be dominated by calcite. The corresponding SEM image of the same fracture is shown in Fig. 7b. EDS analyses were performed on two selected areas, labeled as Spectrum 1 and Spectrum 2, as shown in Fig. 7c. A magnified SEM view of the area corresponding to Spectrum 2 is reported in Fig. 7d. The results of both analyses are summarized in Table 2. Spectrum 2, representative of the main infill phase, shows an elemental composition dominated by calcium (19.4 wt%) and oxygen (49.4 wt%), which supports the presence of calcite as the primary mineral. Notable concentrations of silicon (16.6 wt%), aluminum (6.4 wt%), and potassium (3.1 wt%) indicate the occurrence of a K-bearing aluminosilicate, most likely biotite or illite. Additional minor elements include magnesium (1.2 wt%) and iron (3.9 wt%), consistent with phyllosilicate minerals such as biotite. Minor quartz may also contribute to the silicon signal. The relatively high Al, K, Fe, and Mg contents further support a mica-type phase interpretation. To validate and refine these mineralogical interpretations, powder XRD analysis was conducted on material extracted from the fracture infill. The resulting diffraction pattern, shown in Fig. 7e, reveals a composition dominated by calcite (\(\hbox {CaCO}_{3}\)), accompanied by minor phases of quartz (\(\hbox {SiO}_{2}\)) and biotite. Peak identification was based on standard reference patterns from the Powder Diffraction File (PDF 05-0586, 46-1045, and 80-1106). The strong presence of calcite confirms substantial carbonate precipitation, most likely related to post-depositional fluid flow and fracture sealing. The detection of quartz reflects a residual detrital phase, while biotite likely originates from altered lithic fragments or low-grade metamorphic inputs. Altogether, SEM-EDS and XRD results are in close agreement and indicate that the fracture infill in sample S8 consists mainly of calcite cement, with minor detrital or authigenic phyllosilicates and quartz. This mineral assemblage suggests that the fracture was sealed during diagenesis by carbonate-rich fluids, possibly accompanied by limited introduction of clastic or altered silicate material, resulting in a complex multiphase infill with both authigenic and inherited components. Mineralogical analyses, including XRD and SEM-EDS, identified the fracture-filling material as predominantly composed of calcite (\(\hbox {CaCO}_{3}\)), with minor amounts of biotite and quartz. The theoretical density of calcite is approximately 2.71 \(\hbox {g/cm}^{3}\)41, which aligns well with the observed grayscale level; This correspondence supports the interpretation derived from mineralogical data and highlights the potential of grayscale analysis as a complementary tool for characterizing fracture infill in CT-based studies (Table 3).

Fig. 7
figure 7

Sample S8: (a) Cross-polarized light image of the fracture infill in thin section (performed with ZEISS Axioscope 5 POL); (b) SEM image showing the fracture infill and surrounding matrix; (c) Location of EDS spot analyses; (d) SEM close-up of the fracture infill; (e) XRD pattern of the powdered fracture infill with main peaks indexed for calcite, quartz, and biotite.

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Table 2 SEM-EDS results from Spectrum 1 (rock matrix) and Spectrum 2 (fracture filling). Concentrations are given in weight percent (wt%) and atomic percent (at%).
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Table 3 Comparison between XRD and SEM-EDS results for the fracture infill in sample S8.
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Discussion and comparative evaluation

The results demonstrate the effectiveness of the proposed automated method for quantifying FA and IT by integrating U-Net segmentation with grayscale intensity profile analysis. The workflow operates by first identifying fracture points through a 3D clustering process40 then we applied a curve-fitting procedure to reconstruct a continuous trace of the fracture in each tomographic slice. The local slope and corresponding normal vector are derived to extract grayscale intensity profiles perpendicular to the fracture surface, enabling the evaluation of contrast with the surrounding rock matrix and the measurement of local FA or infill thickness. This workflow that combines U-Net segmentation with a convolution-based measurement algorithm ensures high-resolution extraction of fracture geometries and precise local width measurements throughout the entire sample volume. In fact, the method was successfully validated by comparison with independent high-resolution digital microscope analyses, showing excellent agreement with the tomographic estimates. In both samples, the mean FA or IT values derived from tomography were within 10% of those measured under the microscope, confirming the robustness and reliability of the approach (Table 1). Although caliper measurements are widely used for field surveys due to their simplicity and practicality, it should be noted that it tends to slightly underestimate the mean FA or IT (Table 1). For instance, in sample S6, the mean FA for the entire sample measured by 2D tomography is 1.34 mm, which is very close to the high-resolution digital microscope value (1.30 mm) but higher than the caliper measurement (1.1 mm). A similar trend is observed for sample S8, where the mean IT from tomography (1.02 mm) and high-resolution digital microscope (1.17 mm) is slightly higher than the caliper value (1.0 mm). This underestimation bias arises from the limited resolution of the caliper and the difficulty in ensuring full contact with rough or irregular fracture surfaces, which prevents capturing the true aperture or infilling thickness. Discrepancies between various measurement techniques and caliper methods have also been reported in the literature10, reflecting inherent limitations of contact-based approaches. These methods generally underestimate FAs due to incomplete contact with rough and irregular fracture surfaces. In our study, this underestimation likely arises from the inability of the caliper to fully capture the complex geometry of the fracture and infilling, especially where surface roughness and micro-scale features are present. For what concerns the method used to extract fracture geometries, the workflow presented in this paper, compared to traditional methods such as the FWHM or Missing Attenuation approaches12,18, offers a fully automated solution capable of adapting to complex fracture geometries through the use of a convolutional neural network specifically trained for fracture segmentation. This integration reduces operator bias and enables non-destructive analysis of rock samples, overcoming limitations associated with destructive techniques like resin casting and mechanical sectioning9. An important aspect to consider is the measurement uncertainty and potential error propagation inherent in image-based quantification workflows. In our method, the primary sources of uncertainty stem from the segmentation process and from the grayscale convolution fitting used to compute local widths. Although the U-Net model achieved a high segmentation accuracy (IoU = 0.991), minor misclassifications at fracture boundaries can influence the geometry of the extracted features, particularly for narrow or poorly contrasted regions. These segmentation inaccuracies may propagate during the spline fitting phase, affecting the direction of computed normals and thus the location of intensity profiles used for width calculation. In addition, the convolution-based grayscale analysis, while effective in enhancing contrast, can be sensitive to local grayscale noise and intensity variations, potentially causing slight shifts in boundary detection. Nevertheless, the difference between tomography-based measurements and those obtained from high-resolution microscopy remained within 10%, suggesting that overall uncertainty remains limited. Similarly,42 propose a method based on 2D skeletonization of tomographic slices to separate connected fractures by removing intersection pixels and reconnecting segments according to geometric and orientation criteria, with user-defined thresholds guiding the process. In contrast, our approach leverages U-Net segmentation combined with curve fitting to automatically reconstruct continuous fracture traces and extract normal intensity profiles, facilitating direct, high-resolution measurements of FA and IT. This results in a fully automated and more precise volumetric characterization of fractures. Compared to other recent approaches for aperture quantification, such as grey-level co-occurrence matrix and edge-detection applied to borehole images11, or comparative evaluations of conventional versus machine-learning segmentation for micro-fractures26, our workflow provides a fully automated volumetric characterization directly from CT data. Texture and edge-based methods are effective for 2D borehole logs but cannot capture volumetric variability, while comparative ML segmentation studies often stop at fracture identification without integrating quantitative aperture calculations. In contrast, by combining U-Net segmentation with convolution-based measurement of grayscale intensity profiles, our method directly extracts FA/IT across the entire sample volume. Its main limitations relate to voxel size and grayscale contrast, but multi-method validation demonstrates its robustness. Overall, this approach extends previous image-based methods by providing a reproducible, non-destructive, and statistically supported framework for fracture aperture and infilling thickness measurement. Another important aspect is the ability of the method to resolve internal variations in the FA and infill thickness along the height of the sample, which is critical to evaluating fracture heterogeneity and hydraulic connectivity in fractured media. In sample S6, FA values remained nearly uniform in the bottom and central regions (1.30 mm and 1.28 mm, respectively), while they increased in the top portion (1.45 mm; Table 1). In contrast, caliper measurements are always point-based rather than volumetric; although multiple point measurements can be taken along the core, they cannot capture the full spatial variability and lack the comprehensive resolution provided by volumetric techniques. An important source of uncertainty in the proposed method is related to the voxel size and the physical properties of the materials within the scanned volume. When fractures or infilling material approach the resolution limit of the CT scan, partial volume effects can occur, leading to smoothing or blending of boundaries between the fracture and the surrounding matrix18. When the width of fractures or infilling materials approaches the voxel size, their geometric features may not be adequately captured, leading to possible underestimation or overestimation of the true dimensions. In particular, thin fractures that are only 1–2 voxels wide are subject to thresholding uncertainty and partial volume effects, which can blur the fracture boundaries and reduce segmentation accuracy. This phenomenon causes a smoothing of the grayscale gradient across the boundary, which affects the convolution-based measurement and may systematically bias the estimated aperture. In these cases, voxel size acts as a lower detection threshold, below which precise quantification becomes unreliable. Therefore, for very thin features near the resolution limit, the method may require complementary high-resolution validation (e.g., SEM or digital microscopy) to ensure accuracy. This may cause slight over- or underestimation of the true FA or IT, especially for very thin features. Furthermore, the grayscale intensity used as a proxy for mineralogical identification represents an average value within each voxel and can be influenced by variations in mineral density, impurities, or pore space43,44. Therefore, in cases where minerals with similar X-ray attenuation coefficients or complex intergrowths are present, complementary techniques such as SEM-EDS or XRD analyses remain necessary to ensure accurate phase characterization and to reduce interpretation ambiguity41,45. The grayscale-based convolution method also proved useful for estimating mineralogical characteristics from tomographic images. In the literature, several studies43,44,46,47 have shown that CT scanning can effectively distinguish mineral infills in rocks, but also faces challenges when minerals have similar densities or complex intergrowths. Our study remarks the importance of combining CT with complementary techniques to improve mineral phase identification. In sample S8, the grayscale intensity measured in the fracture fill was consistent with the density of calcite (2.71 \(\hbox {g/cm}^{3}\)41). However, this value should be considered an average estimate, as the actual density can vary slightly depending on the specific geological context, mineral impurities, and rock fabric45. This correspondence suggests that grayscale analysis can be used not only for geometric measurements, but also as a proxy for phase identification in future applications. The proposed method is fully automated and non-destructive, enabling continuous, spatially resolved measurement along fractures with minimal user intervention, avoiding physical sample damage, reducing operator subjectivity, and applicable to both open and mineral-filled discontinuities without the need for sample preparation or destructive sectioning. However, its performance may be affected by poor grayscale contrast or very thin features approaching the resolution limit of the scan. In such cases, complementary mineralogical or microscopic validation remains essential. Overall, the ability to accurately and efficiently measure FA and IT using tomography opens new perspectives for improving fracture characterization in geomechanical and hydrogeological modeling. The combination of spatially resolved measurements and mineralogical insights offers a powerful toolset for understanding fracture-controlled processes in heterogeneous lithologies. For future work, we recommend validating this method across other lithologies and fracture types, including formations with complex mineral infill, and integrating it with multimodal imaging (e.g., \(\upmu\)CT combined with PET) to enhance resolution for sub-millimeter features. Another valuable direction is the automatic recognition of mineralogical phases by leveraging advanced grayscale classification supported by machine learning, building on the consistency demonstrated here between CT grayscale levels and mineral phases confirmed by SEM-EDS and XRD Figure 7 and Table 2. In summary, the integration of deep learning, X-ray tomography, and multi-technique validation proves to be an effective strategy for characterizing rock discontinuities, overcoming the known limitations of traditional methods, and opening new perspectives for applications in hydrogeology, geomechanics, and structural geology. Compared to existing aperture and infill thickness measurement techniques, such as point-based caliper surveys, FWHM, Missing Attenuation, or 2D skeletonization methods, the proposed approach offers several key advantages. It provides fully automated, volumetric, and spatially resolved measurements, reduces operator bias, and avoids destructive sample preparation. Unlike contact-based or threshold-dependent methods, it captures the full heterogeneity of fracture geometry and infilling, enabling more accurate and reliable characterization across complex fracture networks.