Pore structure characteristics of coral reef limestone: a combined polarizing microscope and CT scanning study

Coral reef limestone is a special class of geological medium formed through long-term deposition following the death of reef-building coral groups. Because it retains the skeletal structure of marine organisms during its formation, its pore structure is hyper-developed and complex. Deciphering the pore structure of the coral reef limestone is important because it is closely related to its macroscopic physical and mechanical properties. This study conducted a comprehensive analysis of the pore structure features of two types of coral reef limestone collected from the construction site of a nuclear power station located in the South China Sea using a combination of polarizing microscopy and CT scanning technologies. The fractal dimension of the pore structure of the treated reef limestone image was calculated, and the pore structure characteristics were statistically analyzed by considering several parameters including porosity, pore size, pore equivalent radius, shape factor, etc. In addition, the directional feature of the pore structure was explored. The results show that the improved watershed segmentation algorithm can accurately segment the pore structure of reef limestone images; both coral reef limestone specimens are loose of high porosity; the fractal dimension of pore structure lay between 1.58∼1.75, indicative of a high self-similarity; the pore size of the two coral reef limestone specimens is quite different, and the distribution of equivalent pore radius conforms to the normal distribution law; the pore structure of the two samples had obvious directionality, which can be quantified using a directional tensor. This study sheds light on future investigations linking the microscopic structure and macroscopic properties of coral reef limestones.


Introduction
The physical and mechanical properties of porous rocks are intricately related to their pore structure.Coral reef limestone (CRL), which serves as a typical porous medium, possesses distinct features such as a complex pore structure, high porosity, low density, and strength owing to its unique formation principles, setting it apart significantly from other terrestrial rocks [1].Furthermore, the pore structure of the coral reef limestone exhibits clear anisotropy.
As the exploration of the physical and mechanical properties of coral reef limestone has advanced, an increasing number of scholars have recognized the pivotal role played by the pore structure in influencing its physical and mechanical behavior.According to Tian et al. [2], based on the observed correlation between the P-wave velocity, porosity, and density characteristics of coral reef limestone obtained by drilling in a reef in the Nansha Sea area, it can be concluded that the porosity and pore structure type are the predominant factors influencing the P-wave velocity of coral reef limestone extracted in the Nansha region.Wu et al. [3] conducted visual and quantitative analyses of the microscopic-scale crack morphology characteristics of coral reef limestone after experiencing triaxial shear failure.This analysis revealed that the failure mode of the sample was influenced by the pore structure and cemented skeleton and that the distribution of pores had an impact on the final failure mode.Wu et al. [4] analyzed the uniaxial compression behavior and pore structure characteristics of four different structural types of coral reef limestone.This study revealed significant variations in terms of uniaxial compressive strength (UCS), deformation characteristics, elastic modulus, and failure modes among the coral reef limestone samples with distinct structures.It was concluded that the primary determinant of the mechanical behavior of coral reef limestone specimens lies in their pore structure.
Therefore, this study focuses on the internal pore structure of coral reef limestone.A comprehensive analysis of the pore structures in the two types of coral reef limestones was conducted using polarizing microscopy and CT scanning technology.This study employs a watershed segmentation algorithm based on the extended minimum label to segment the pore structure within coral reef limestone, and subsequently quantitatively characterizes its pore attributes.

Sample preparation
This study is based on the coral reef limestone tunnel project at a nuclear power plant in Hainan, China.Two types of coral reef limestone samples with distinct appearances were obtained through onsite engineering drilling.After processing, the samples were transformed into two circular specimens measuring 50 mm×25 mm each, as shown in figure 1.Specifically, specimen (a) exhibits a conspicuous coral reef growth line structure with a light yellow color and irregular surface pores.On the other hand, the (b) specimen has a denser structure, numerous small pores, and an overall whitish appearance.The coral reef limestone samples with coarse and fine pores were designated CRC and CRF, respectively.The dry density of the CRC was 0.955 g/cm 3 , which is lighter than that of water, causing the specimen to float when placed in water.However, the CRF had a dry density of 1.29g/cm 3 , indicating a significant difference in the internal structure between the two specimens.The mineral compositions of the two types of coral reef limestones were examined using X-ray diffraction (XRD).The analysis results indicated that in the CRC, the mass fraction of the aragonite phase was 98.2%, whereas that of the silica phase was 1.8%.In contrast, the CRF exhibited only the presence of the aragonite phase.This suggests that the mineral composition of the coral reef limestone is closely mono, with a high degree of purity.By conducting measurements with a hydrometer, the specific gravity of the coral reef limestone was determined to be 2.87 g, resulting in calculated porosity values of 66.63% for the CRC and 55% for the CRF.This indicates that both types of coral reef limestone have a low density and high porosity.

Polarizing microscope
Thin sections for polarizing microscopy were prepared from the remaining blocks of selected samples after cutting.Specific locations with typical features were chosen for single polarized light and orthogonal polarizing microscope observations, yielding microscopic images of the two types of coral reef limestone.From the images obtained under orthogonal polarized light, it is evident that the thin sections of both specimens exhibited relatively uniform colors, indicating a relatively homogeneous material composition of the coral reef limestone.Using the corresponding scale, it can be determined that the pore structures in the coral reef limestone generally exceed 30μm, with fewer structures below this size.

CT scanning
The CT scanning system used in this experiment was the YXLON FF85 CT computer tomography scanning system capable of providing high-precision helical scanning [5].During the scanning process, the scanning voltage was set at 209.4 kV, the scanning current at 115.5μA, and the scanning accuracy at 18.4174μm/pixel.During the scanning process, CRF obtained 1370 slices, whereas CRC obtained 1360 slices.

Morphological image processing
Before calculating and analyzing the microscopic pore characteristics of the coral reef limestone, it was necessary to convert the image into a binary image.First, images from the orthogonal polarizing microscope were converted to grayscale images.Subsequently, a thresholding method was applied to segment the images and obtain binary images.
Owing to the presence of small cracks and noise in polarized light microscope images, this portion can lead to the inaccurate recognition of pore structures.Therefore, before analyzing the pore feature parameters, it is necessary to perform morphological operations on the polarized light microscope images to remove small cracks and noise.In this study, MATLAB programming was used to apply morphological operations to binary images obtained using a polarizing microscope.These operations included dilation, erosion, removal of small objects, and other operations to retain more clearly defined primary pore structures.

Watershed segmentation based on extended minimum labelling
The watershed algorithm [6] treats an image as a geographical landscape, where the watersheds represent the boundaries in the image.The fundamental idea behind watershed segmentation is to start by identifying local minimum points within the image.It then simulates the flow of water from these points, gradually filling up low-lying areas, and creating watershed lines between elevated regions.Thus, each segmented area within the image is linked to a local minimum point.The watershed segmentation algorithm is frequently used for segmenting porous structures and similar applications.
Watershed segmentation is highly sensitive to noise and edge irregularities Owing to the high number of pixels occupied by pores in the polarized microscopy images of reef limestone, coupled with the pronounced irregularity of their edges, local minima tend to be generated more frequently.Although some reduction in the local minima can be achieved through distance transformation and morphological operations, their effectiveness is not particularly pronounced.Therefore, in this study, an approach is introduced to further reduce over-segmentation by marking local minima through the extension of minimum values, building upon distance transformation and morphological operations [7].The extended minima essentially represent the regional minimum values derived from the minimum transform.Whereas the minimum transform aims to reduce the number of local minima, the extended minima transform selectively retains only the local minima, eliminating those that exceed this minimum threshold.The refined segmentation effect following this correction is shown in figure 3.

Pore Characterization Analysis Based on Polarized Microscope Images
In this study, six key indicators were selected to characterize the pore structures: fractal dimension, equivalent radius, area, shape factor, aspect ratio, and orientation.The fractal dimension [8] was calculated using the box-counting method to assess the irregularity and complexity of the pore shapes.
The equivalent pore radius is the radius of a circle with the same area as the pore and is used to measure the pore size.The shape factor [9] quantifies the shape characteristics of the pore structures and their proximity to a circle; a larger shape factor indicates a more regular and circular pore structure.In addition, the pore area represents the actual area of the pores.The pore structures were also fitted with ellipses to obtain the major and minor axes of the fitted ellipses.The angle of the major axis of the fitted ellipse was used to determine the pore orientation.This allowed the calculation of the aspect ratio between the major and minor axes.Aspect ratios between 1 and 1.5 were categorized as equiaxial pores, those between 1.5 and 10 as non-equiaxial pores, and those exceeding 10 as elongated pores.
The calculated average fractal dimension for CRF was 1.2036, whereas the average fractal dimension for CRC was 1.3326.CRC had a slightly larger fractal dimension.Based on the fractal dimension, it can be concluded that the pores in coral reef limestone are relatively complex and exhibit fractal characteristics.
As shown in figure 4(a), the equivalent radius of CRF is mainly concentrated between 40 to 100 μm, and its distribution pattern follows a normal distribution.The distribution of CRF's area shows that as the size increases, the proportion gradually decreases, with the majority of areas distributed below 3×10 4 μm 2 .The distribution of the pore shape factors after watershed segmentation and the corresponding Gaussian fitting curves are shown in figure 4(c).The pore shapes were mainly concentrated between equilateral triangles and circles.The distribution patterns of CRF and CRC were similar, with CRC exhibiting slightly greater irregularities.Both CRF and CRC have a main range of aspect ratios between 1 and 2, with non-equiaxed pores being predominant and equiaxed pores being secondary.Aspect ratio.Because of the relatively low number of pores in the polarized microscope images of the CRC, there was no clear distribution pattern; therefore, the corresponding curves were not plotted for equivalent radius and area analysis.For CRC's pore analysis in the Area category, the minimum area is 2861.1 μm 2 , the maximum area is 460374.59μm 2 , and the average area is 160399.64μm 2 .In terms of equivalent radius, the minimum value is 30.18μm, the maximum value is 382.81 um, and the average value is 217.23 μm.Compared with CRF, CRC has pore areas that are an order of magnitude larger and equivalent radii that are more than twice as large as CRF.
From the two-dimensional dip distribution map of the coral reef limestone, it can be concluded that the pore dip angle of the coral reef limestone has clear directivity.Compared with the pore structure of the CRF, the heterogeneity of the CRC is greater, whereas the CRF is more uniform; however, it also has obvious directivity.In comparison, the anisotropy of CRC was more obvious.
In previous research, many scholars solely conducted qualitative analyses of rock pore structure and morphology using a polarizing microscope without delving into the quantitative analysis of pore characteristics.Furthermore, comparative analysis across different methodologies was often lacking.
Thus, this study integrates polarizing microscopy observations with CT scanning to provide a comprehensive analysis of the pore characteristics of coral reef limestone.

CT scan image processing
Before calculating the pore characteristics in the CT scan images, it is necessary to preprocess the images [10].This involves adjusting the image contrast to enhance edge clarity, applying median filtering to filter the image, and reducing the impact of noise generated during the scanning process.A combination of "Interactive Thresholding" and "Top-hat Thresholding" methods in Avizo is used to determine a more accurate threshold segmentation result, resulting in a binary image.This binary image was then utilized for three-dimensional pore structure reconstruction and feature analysis.The results of the image preprocessing and threshold segmentation are depicted in figure 5.

Pore characteristics analysis based on CT scan images
After three-dimensional reconstruction, the calculated porosities of the CRC and CRF were 61.5% and 52.0%, respectively.When compared with the theoretical values, there was a difference of 7.6% for CRC and 5.4% for CRF.The reasons for these differences are twofold.First, errors can arise during density and volume calculations.Second, inaccuracies in CT scanning and threshold segmentation can also contribute to errors in porosity calculations.Consequently, there is a disparity between the calculated and actual porosities.By calculating the fractal dimensions of 1000 slices, it was observed that the fractal dimensions of the two types of coral reef limestones primarily range between 1.58 and 1.75.CRC exhibited more noticeable fluctuations in its fractal dimension, whereas the fractal dimension of CRF appeared to be relatively consistent.In comparison, the CRF had a higher fractal dimension, indicating that it exhibited better self-similarity and a higher level of complexity in its pores than the CRC.In summary, both have relatively high fractal dimensions, indicating complex pore structures with certain fractal characteristics and self-similarity.
To conduct a more comprehensive analysis of the pore characteristics of coral reef limestone, CT scan images were selected at regular intervals.Five slices were chosen each for CRC and CRF, with slice numbers of 180, 430, 680, 930, and 1180.Pore characteristic calculations were performed on the selected slices, and the calculation results for the CRF are shown in the following figure .Based on the plotted curves in figure 6, it can be observed that the pore equivalent radius of CRF is mainly concentrated between 50-100μm, following a Gaussian distribution pattern.Pores with an equivalent radius exceeding 200um are very few, and nearly 90% of the pore structures have an area below 8×e 4 um 2 .As the area increases, the number of pores gradually decreases.After segmenting the pores, it was found that 50% had a pore shape factor lower than 0.625, indicating that the majority of the pore shapes were irregular triangles, triangles, and quadrilaterals, with some pore structures approaching circular shapes.Furthermore, analysis of the ratio between the long and short axes of the fitted ellipses shows that the proportions of equiaxial and non-equiaxial pores in the segmented CRF pore structures are similar, whereas elongated pore structures have a very low proportion.Owing to limited space, the calculated results for CRC are not presented in the text.The equivalent pore radius for CRC is primarily concentrated in the range of 100-500 μm, following a Gaussian distribution pattern.Some larger pore structures with equivalent radii exceeding 1200 μm exist within CRC.The pore area distribution for the CRC followed a pattern similar to that of the CRF, with a decreasing proportion as the pore area increased.Furthermore, the pore areas in the CRC were significantly larger than those in the CRF, showing a difference of several orders of magnitude.The pore shape factor mainly falls within the range of 0.35 to 0.65, and compared to CRF, the pore shapes in CRC exhibit greater irregularity, which is consistent with the results from CT scan slices.Analysis of the pore aspect ratios indicates that CRC predominantly consists of non-equidimensional pores, with non-equidimensional pores accounting for nearly 65% of the total pores, whereas equidimensional pores account for approximately 35%.Based on the directional curve distribution in figure 7, the CRF exhibits a relatively uniform directional distribution, with a few prominent directions superimposed on this uniform distribution.In contrast, the CRC pore structure displayed a more pronounced directional pattern, primarily concentrated in the range of 50° to 100° along the growth lines of the coral skeleton, with greater anisotropy.
By comparing the results of CT scanning with those of the polarizing microscope analysis, it can be concluded that the pore area, shape factor, equivalent radius, and aspect ratio obtained from the polarizing microscope were numerically and systematically similar to those obtained from CT scanning.This demonstrates the accuracy of both methods for identifying and calculating the pore characteristics of coral reef limestone.

Conclusions
Through a comprehensive analysis of images obtained from polarizing microscopy and CT scanning of the coral reef limestone, this study revealed the following findings: • Both types of coral reef limestone exhibited loose and porous characteristics, with high porosity and complex pore shapes.The fractal dimensions of their two-dimensional pore structures fall within the range of 1.58 to 1.75, indicating fractal and self-similar features.• A watershed segmentation algorithm based on extended minimum value marking was proposed, which can accurately segment pore structures within coral reef limestone.The quantitative analysis of the pore characteristics of coral reef limestone reveals that the equivalent pore radius of CRF was mainly concentrated between 50-100μm, while that of CRC was mainly concentrated between 100-500μm.Both followed a normal distribution pattern.Additionally, the pore structures in coral reef limestone exhibit significant directional characteristics.• A comparison of the results from polarizing microscopy and CT scanning validated the accuracy of the pore identification and feature calculations in coral reef limestone, providing a feasible method for the recognition and analysis of rock pore structures.• In this study, we focused solely on analyzing two-dimensional pore structure characteristics without delving into the intricacies of three-dimensional aspects.We aimed to explore the threedimensional pore characteristics of coral reef limestone using data obtained from CT scanning.
In addition, we plan to investigate the potential correlations between these pore characteristics and the macroscopic features of the limestone.

Figure 1 .
Figure 1.Sample images: (a) CRC; (b) CRF.The dry density of the CRC was 0.955 g/cm3 , which is lighter than that of water, causing the specimen to float when placed in water.However, the CRF had a dry density of 1.29g/cm 3 , indicating a significant difference in the internal structure between the two specimens.The mineral compositions of the two types of coral reef limestones were examined using X-ray diffraction (XRD).The analysis results indicated that in the CRC, the mass fraction of the aragonite phase was 98.2%, whereas that of the silica phase was 1.8%.In contrast, the CRF exhibited only the presence of the aragonite phase.This suggests that the mineral composition of the coral reef limestone is closely mono, with a high degree of purity.By conducting measurements with a hydrometer, the specific gravity of the coral reef limestone was determined to be 2.87 g, resulting in calculated porosity values of 66.63% for the CRC and 55% for the CRF.This indicates that both types of coral reef limestone have a low density and high porosity.

Figure 2 .
(a), (b), and (c) show the results under single polarized light, whereas (d), (e), and (f) show the results under orthogonal polarized light.

Figure 3 .
Figure 3. (a) Traditional watershed segmentation results; (b) Watershed segmentation results based on extended minimum value labeling.

Figure 4 .
Figure 4. Distribution of pore characteristics: (a) Equivalent Radius; (b) Area; (c)Shape factor; (d)Aspect ratio.Because of the relatively low number of pores in the polarized microscope images of the CRC, there was no clear distribution pattern; therefore, the corresponding curves were not plotted for equivalent radius and area analysis.For CRC's pore analysis in the Area category, the minimum area is 2861.1 μm 2 , the maximum area is 460374.59μm 2 , and the average area is 160399.64μm 2 .In terms of equivalent radius, the minimum value is 30.18μm, the maximum value is 382.81 um, and the average value is 217.23 μm.Compared with CRF, CRC has pore areas that are an order of magnitude larger and equivalent radii that are more than twice as large as CRF.From the two-dimensional dip distribution map of the coral reef limestone, it can be concluded that the pore dip angle of the coral reef limestone has clear directivity.Compared with the pore structure of the CRF, the heterogeneity of the CRC is greater, whereas the CRF is more uniform; however, it also has obvious directivity.In comparison, the anisotropy of CRC was more obvious.In previous research, many scholars solely conducted qualitative analyses of rock pore structure and morphology using a polarizing microscope without delving into the quantitative analysis of pore characteristics.Furthermore, comparative analysis across different methodologies was often lacking.

Figure 6 .
Figure 6.Distribution of pore characteristics of CRF: (a) Equivalent Radius; (b) Area; (c)Shape factor; (d) Aspect ratio.Owing to limited space, the calculated results for CRC are not presented in the text.The equivalent pore radius for CRC is primarily concentrated in the range of 100-500 μm, following a Gaussian distribution pattern.Some larger pore structures with equivalent radii exceeding 1200 μm exist within CRC.The pore area distribution for the CRC followed a pattern similar to that of the CRF, with a decreasing proportion as the pore area increased.Furthermore, the pore areas in the CRC were significantly larger than those in the CRF, showing a difference of several orders of magnitude.The pore shape factor mainly falls within the range of 0.35 to 0.65, and compared to CRF, the pore shapes in CRC exhibit greater irregularity, which is consistent with the results from CT scan slices.Analysis of the pore aspect ratios indicates that CRC predominantly consists of non-equidimensional pores, with non-equidimensional pores accounting for nearly 65% of the total pores, whereas equidimensional pores account for approximately 35%.

Figure 7 .
Figure 7. Pore dip distribution: (a) CRF; (b) CRC.Based on the directional curve distribution in figure7, the CRF exhibits a relatively uniform directional distribution, with a few prominent directions superimposed on this uniform distribution.In contrast, the CRC pore structure displayed a more pronounced directional pattern, primarily concentrated in the range of 50° to 100° along the growth lines of the coral skeleton, with greater anisotropy.By comparing the results of CT scanning with those of the polarizing microscope analysis, it can be concluded that the pore area, shape factor, equivalent radius, and aspect ratio obtained from the polarizing microscope were numerically and systematically similar to those obtained from CT scanning.This demonstrates the accuracy of both methods for identifying and calculating the pore characteristics of coral reef limestone.
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