Introduction

Freeze-thaw cycles are often involved in the erosion and collapse of steep rock surfaces in cold environments. According to Hall (1999), this process involves the repeated freezing and thawing of water in the pores, fissures, and fractures of the rock. However, frost weathering as an important geomorphological agent is not restricted to the cold climates of permafrost and periglacial regions or high mountains. It is also a common process in temperate climates (Gage et al. 2022). This phenomenon occurs at different spatial scales and results in processes such as granular disintegration, spalling, and micro-fracturing, known as ‘microgelivation’, as well as the propagation of macrofractures and the formation of larger debris, known as ‘macrogelivation’ (Matsuoka 2001). Volumetric expansion weathering occurs when pore water expands upon freezing, creating internal pressure and generating tensile stresses capable of fracturing saturated rock (Matsuoka 2008). Freeze-thaw processes also contribute to rock weathering through the growth of ice crystals, where liquid water migrates towards freezing centres within porous rock. This results in the formation of ice lenses within the rock, which can lead to fracturing as discussed by Matsuoka in 2008. In rocks with pre-existing fractures, tensile stresses tend to accumulate at the crack tips. The resistance to shear forces within a fracture is influenced by factors such as its surface roughness, cohesion due to intermolecular bonding, and the concentration of clay minerals in the joint. The growth of segregated ice weakens the shear strength of fractures by generating tensile stress, which has the potential to break intermolecular bonds, expand the rock mass, and reduce the effect of joint roughness (Hales and Roering 2007).

A full understanding of both internal and external factors, such as material properties, humidity, or temperature conditions, is essential when studying the effects of weathering processes within rock materials (Deprez et al. 2020; Hall 1999). Although the latter two factors are highly variable and closely related to the local environment and its climate, material properties can be defined relatively precisely (Deprez et al. 2020). Parameters such as pore volume (total porosity), degree of interconnectivity, and pore size distribution (PSD) determine the ability of the porous medium to transport fluid within the porous material (Hall and Hoff 2002), as well as the intensity and location of internal stresses induced by the phase transition from water to ice. It is a well-established fact that as the pore size decreases, the freezing point of water also decreases, as pointed out in several studies by Huang et al. (2018a, b, c) and Zheng et al. (2021). In recent decades, extensive research has been conducted to explore the thermodynamics of freezing in pore water, mainly based on the Gibbs-Duhem equation (Moran et al. 2010). The phase equilibrium of pore water can also be elucidated by considering the chemical potential. At a given temperature and pore size, if the chemical potential of ice becomes lower than that of liquid water, the pore water will freeze (Matsuoka 2008). The freezing point of pore water is only minimally lowered when dealing with micrometre-sized pores but is significantly lowered when the pore size reaches the nanometre range (Yang 2013; Zeng 2011). Consequently, for cemented materials with a significant proportion of nanopores, ice formation continues to increase until the temperature drops to around − 40 °C or − 50 °C (Gong and Maekawa 2018; Johannesson 2010; Sun and Scherer 2010). In contrast, for rock materials with typically larger pores, ice freezing occurs more rapidly at temperatures below 0 °C (Eslami et al. 2018; Huang et al. 2018a, b, c). Consequently, the volume of ice and the extent of freezing expansion are closely linked to the pore size distribution (PSD) and local temperature conditions, as highlighted by Sellevold and Bager in 1980. This requires a more accurate estimation.

Porosity, also referred to as void fraction, is a measure of the empty spaces within a rock, expressed as a value between 0 and 1 or as a percentage ranging from 0 to 100%. Various methods are available to determine porosity in rock samples, such as saturation or imbibition techniques (Hu et al. 2001), gas expansion (He pycnometry) (Keulen 1973; Maľa et al. 2022), gas adsorption (BET) or mercury intrusion porosimetry (Ondrášik 2004; Fagerlund 1973c).

In addition to conventional methods, non-destructive imaging techniques such as X-ray computed tomography (µCT) have recently become widespread. The result of a standard CT scan is a collection of 3D slices that form a grid of voxels. Voxels are essentially 3D pixels and each voxel contains a calculated grey value which depends on the density, atomic number of the materials present, and the energy of the x-rays used during the scan (Wildenschild and Sheppard 2013). The voxel size determines the highest achievable measurement resolution. There are several works dealing with the use of µCT image processing techniques in the study of weathering processes, such as progressive fracture propagation induced by repeated freeze-thaw cycles (F-T cycles) (De Kock et al. 2015), microscale changes in the internal structure of limestones and igneous rocks induced by F-T cycles (Dewanckele et al. 2013; Park et al. 2015; Maľa et al. 2022), or salt crystallization dynamics in building rocks (Derluyn et al. 2015). The pore space segmented by different segmentation algorithms can be used to generate a pore network model (PNM). A PNM is a simplified way of representing the primary voids in a material, where the basic shapes, such as spheres, represent pores, while cylinders depict connecting passages in the structure of the material at the microscopic level (Sadeghnejad et al. 2021). The intricate pore network systems guide the movement of fluids and have important implications in various fields, including fluid transport (Held and Celia 2001; Ferraro et al. 2016), filtration processes (Shire and O’Sullivan 2017), migration of ions (Mohajeri et al. 2010), and carbon dioxide storage (Li et al. 2006). None of these methods is without limitations or drawbacks and may not be applicable to all lithological types of rocks or other porous media.

Previous studies linking cryogenic processes with PSD have been hindered by the use of destructive tests, specifically mercury intrusion porosimetry (MIP), for quantifying the pore size distribution of rocks. While MIP is a standard test, it does not allow for quantification of pore size distribution and porosity on the same sample before and after freezing. The main objective of this work is to establish the relationship between thermocryogenic processes and changes in the pore network system using experimental and non-destructive techniques. The focus is on using a set of standards to achieve this goal. In March 2011 and November 2012, two rock niche collapses occurred at Brhlovce village, in a culturally protected reserve of folk architecture. A large tuff rock block collapsed due to water freezing in rock discontinuities and cracks (Fig. 1, right). Additionally, scaling of the rock surface of the dwellings was observed in several walls due to freeze-thaw action on saturated rock. This site was therefore deemed suitable for the research of cryogenic action on porous rock. This study is aimed at a detailed quantification of microstructural changes after 100 F-T cycles using non-destructive and experimental sample testing. Specifically, this study applies spontaneous imbibition method, a newly developed indicative rock pore structure method (IRPS method) (Ondrášik et al. 2017, 2019), together with X-ray computed µTomography (µCT) imaging. Tuff samples were cycled using a specially designed VLAP 04 thermodilatometer, which allowed us to determine latent heat generation and diffusion during ice crystallization, as well as strain behaviour during freezing and thawing. Based on these results, we were able to apply the principles of poromechanics and determine the size of the pores in which the crystallization started, as well as the corresponding crystallization pressure. The direct effect of frost weathering on pore network systems can be seen in detail by studying the evolution of PNMs before and after 100 F-T cycles. Collectively, this is the first time such a scientific approach was used to study frost weathering in the Central European region.

Fig. 1
figure 1

Rock dwellings in Brhlovce (left); destruction of one of the dwelling niches which occurred in November 2012 (right)

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Materials and methods

Site characterization and rock preparation

This study is focused on pyroclastic rocks, specifically volcanic tuffs from the rock dwellings at Brhlovce (Slovakia) (Fig. 1 left). The investigated site is built on Neogene andesite volcanic Badenian and Sarmatian bedrock. The rock dwellings were excavated in pyroclastic rocks (volcanic tuffs) and redeposited tuffite sediments forming the peripheral parts of the Štiavnica stratovolcano, dating back 15 million years (Brestenská 1982). All volcanoclastic complexes are very heterogeneous with respect to grain size, matrix type, cementation, etc. The lithological composition of andesite tuff consists of a variable proportion of volcanic glass matrix and crystalline sand-sized fine grains. Remnants of plants and wood were identified inside the tuff rocks as well. The volcanic sedimentary sequences are positioned horizontally at the studied locality (Boháč et al. 2013).

These volcanic rocks are usually quite variable in structure; they are easy to work and are often used as building or façade materials and are therefore exposed to variations in temperature and humidity. Their matrix grain sizes typically range from fine clay minerals to silt-sized materials (ash form) in which lithic and igneous fragments are embedded (Wedekind et al. 2012; Chen et al. 2004). Their porosity can vary by up to 50% (Deprez et al. 2020), as can their pore size distribution. These characteristics make the material less resistant to weathering processes induced by moisture or F-T cycling. This was confirmed in a study by Boháč et al. (2013), who monitored moisture using a new moisture sensor connected to RTM electronics to understand weathering processes of rock dwellings in Brhlovce. In March 2011 and November 2012 (Fig. 1, right), two collapses of rock niches occurred according to Boháč et al. (2013). Large rock blocks collapsed due to the effect of water freezing in rock discontinuities and cracks.

The rock dwellings were built in the sixtenth and sevententh centuries as a means of ‘hiding’ the village from Turkish raids. There was no point in building normal houses on the ground because they would have been visible for miles around. The stone formations around the village have been home to people for more than three centuries. The historical and cultural value of these structures is that they represent a way of life and a way of living in the past. They document the symbiosis of human settlement with the natural environment and the influence of natural, climatic, economic, and social conditions on the way of life of the inhabitants. The rock dwellings in Brhlovce are the last remaining examples of this type of folk building in Slovakia and require permanent conservation and maintenance. In 1983, the government declared the dwellings a reserve of folk architecture. About 10 years later, a museum of cave dwellings was opened, and in 1994, the Tekov Museum in Levice was awarded the Europa Nostra prize as the first institution in the Slovak Republic to present the cave dwellings in Brhlovce. Currently, the owners of the houses use them as storerooms, summer kitchens, chambers, cellars, etc. (Fig. 1 left).

Fifteen cylindrical core samples were used in this study. The samples were 5.0 cm long and 3.2 cm in diameter. These samples were cut and machined from a single tuff block without any visible alteration collected from rock mass in Brhlovce (Slovakia), hereafter referred to as BR(Tf) (Fig. 2A).

Fig. 2
figure 2

(A) Macrophoto of the BR (Tf) specimen. (B) Mineralogical composition on standard polished section by SEM. Abbreviations: Ilm, ilmenite; Pl, plagioclase; Smkt, smectite; Ap, apatite; Opx, orthopyroxene; Glass, volcanic glass

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SEM and XRD analysis

The solid phase, which governs the mechanical strength of rocks and construction materials via cementation and mineral bonding, underwent analysis with scanning electron microscopy (SEM) using a standard polished thin section with a conductive surface achieved by vacuum vapour deposition of a thin gold layer.

The mineral content was quantitatively analysed by X-ray diffraction (XRD) of the rock samples. The fine-grained fractions (clay) were also extracted adopting standard procedures for separation of fine fractions (Šucha et al. 1991) and quantitative X-ray powder diffraction analysis was conducted on sediment samples, which were prepared following the methods described by Środoń et al. (2001) and Eberl (2003).

Determination of pore network characteristics

There is considerable evidence highlighting the influence of petrophysical properties on the frost resistance of rocks. A comprehensive understanding of the porosity and pore size distribution is crucial for evaluating the freeze-thaw-induced alterations in pore structure. Understanding the water absorption capacity of the rock matrix and pore system and estimating potential ice formation under specific environmental conditions are essential for interpreting internal frost weathering damage mechanisms.

This knowledge was obtained through the use of standard techniques for obtaining detailed data on the rock’s initial properties. The methods outlined in detail in Maľa (2021) allowed us to determine bulk density, total porosity, and pore size distribution. Additionally, we obtained data on the distribution of representative pore radii through the traditional approach of mercury intrusion porosimetry (MIP) as a reference.

Non-destructive techniques such as helium pycnometry (effective porosity), spontaneous imbibition testing (pore interconnectivity) and experimental rock pore structure identification (pore size distribution) can be used to measure changes in the geometric and topological aspects of pore spaces following repeated freeze-thaw cycles. These methods are advantageous due to their speed, non-intrusive nature and ability to be applied repeatedly to the same sample. It should be noted that these methods lack standardization. Nonetheless, their non-destructive nature and the ability to perform them repeatedly on the same specimens make them ideal for assessing the effects of freeze-thaw cycling on specific porous materials. The non-destructive methods mentioned above were applied to all 15 samples before and after 100 F-T cycles.

Effective porosity was evaluated using helium pycnometry, a technique that uses helium gas to determine the particle density of finely ground samples. In this process, a rock of cylindrical shape is positioned in a chamber with a predetermined volume, VC. Helium gas is then introduced until the desired pressure, p1, is attained. Once the inlet is sealed, the gas proceeds to invade all of the rock’s effective pores until it achieves equilibrium at pressure p1. The valve is subsequently opened to an adjacent chamber of known volume VA, allowing the helium to expand and the pressure to fall to a new equilibrium at pressure p2, in accordance with Boyle’s law of gas expansion (p1 − V1 = p2 − V2). Each sample measurement is preceded by thorough purging of helium. The data is obtained by calculating the average of ten stable p1:p2 ratios with a maximum deviation of ± 0.001 (Maľa et al. 2022).

Pore size distribution

Two distinct approaches were employed for assessing the pore structure of the rocks. The distribution of representative pore radii was analysed by mercury intrusion porosimetry in compliance with STN 72 1011 norm, the prevalent technique as previously stated. Furthermore, a recently proposed experimental method, which is explained in Ondrášik et al. (2019), was used to characterize the rock’s pore structure. This innovative methodology is founded on the hypothesis that water absorption (including sorption and uptake) within rock pores is impacted by the internal pore framework. Therefore, through the study of water absorption under carefully controlled conditions, it is possible to define the specific properties of the pore structure of the rock. These controlled conditions are achieved through three distinct adsorption tests: 72 h of water vapour adsorption at 98% relative humidity, 48 h of water adsorption at atmospheric pressure, and 24 h of vacuum water adsorption. These tests result in the identification of four distinct categories of rock pores based on their size and accessibility to water, namely micropores and mesopores, readily accessible macropores, partially accessible macropores, and closed pores of varying sizes. The categorization of pore dimensions into micropores, mesopores, and macropores adheres to the guidelines established by the International Union of Pure and Applied Chemistry (IUPAC) (Sing 1985). A major benefit of this methodology is its non-destructive nature, which makes it suitable for repeated use prior, during, and after subjecting the sample to F-T cycles.

Pore connectivity by the spontaneous imbibition method

Spontaneous imbibition is commonly used as a non-destructive test to evaluate pore connectivity in rocks, which is a crucial aspect of their topological structure. The test involves exposing one side of a sample to water and monitoring the resulting increase in mass uptake over time (Hu et al. 2001). This method employs the principle of diffusion, where, for uniform materials (disregarding gravitational impacts), the distance to the wetted front expands proportionally to the square root of time (l ~ t0.5). In this research, a revised testing procedure was employed to address prospective inaccuracies related to buoyancy forces and evaporation effects, in comparison to the methodology used by Hu et al. (2001). In this updated methodology, a larger water tank was utilized for the sample testing, in contrast to the Petri dish technique described by Hu et al. (2001). After drying the sample at 105 °C for 48 h, it was wrapped in polyethylene (PE) foil, exposing only the base of the core to water to reduce evaporation losses. The sample was then placed in a desiccator and tested while suspended under a balance, which automatically recorded data every second for the duration of 15 min. To conduct the imbibition test (SI), a glass water tank measuring 202 × 122 × 125 mm was filled with distilled water up to a height of 65 mm. Subsequently, the tank was mounted on a support in order to enable the rock sample to come into contact with the water in the reservoir, with the sample being submerged to a depth of about 1 mm. The temperature was maintained at 23.0 ± 1 °C. The imbibition (SI) tests were performed thrice for each sample, whereby the sample was dried for 48 h at 105 °C between tests. Data from each test were analysed plotting the cumulative height of water absorption (in millimetres) against the square root of time (in minutes) on a logarithmic scale. The imbibition slope, which characterizes the rate of water imbibition into the sample, was determined through the apparent slope of the linear regression curve C(I). This relationship, which originates from Handy’s model (Handy 1960), is solely applicable to small samples in the absence of gravitational influence, as is the scenario in this case. Two individual imbibition slopes were determined for distinct intervals of 0.1 to 1 min and 1 to 10 min. The imbibition slopes for the rapid 0.1–1-min interval were designated \({C\left(I\right)}_{\text{f}}^{0}\) for the initial state and \({C\left(I\right)}_{\text{f}}^{100}\) after 100 freeze-thaw cycles. The slopes for the intermediate time range of 1–10 min were marked as \({C\left(I\right)}_{\text{m}}^{0}\) and \({C\left(I\right)}_{\text{m}}^{100}\) correspondingly.

Processing of µCT images

CT reconstruction of scanned specimen before and after repeated freezing and thawing was conducted on an industrial µCT Phoenix | tome | x L 240, as described by Maľa et al. (2022). Image processing utilized multiple visualization techniques in ORS Dragonfly software on a single specimen and is summarized in several processing steps in Fig. 3.

Fig. 3
figure 3

Flowchart showing µCT image post-processing. (A) Image filtering (1); image binarization (2); pore space separation (3); porosity and PSD calculation (4); pore network modelling (5); absolute permeability simulation (6). (B) A pore-throat schematic diagram

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  1. 1.

    Filtering of acquired images by using Unsharp filter

    This filter enhances the edges of elements without amplifying any noise by applying a Gaussian filter to a duplicate of the original image and then merging it with the original image.

  2. 2.

    Pore space separation by image binarization

    Selecting objects or features within an image is a fundamental requirement. This task often entails scrutinizing every pixel in the raw image to determine its relevance to the object of interest. Defining a range of brightness values in the original image is one simple method of doing this. Pixels within the specified range were deemed part of the foreground, which corresponds to the region of interest in our study — the pore space. The rest of the pixels were classified as part of the background or solid phase. We applied thresholding to make this selection, which is a commonly used technique. Following this process, the resulting image was presented in a binary or two-level format, utilizing black and white to distinguish between the two regions. Image segmentation represents a crucial stage in image processing since it prominently impacts subsequent analyses such as pore network generation or extraction. This process refers to labelling each pixel of an image with a unique number, so that pixels which bear the same label also share similar features (Beg 2021).

  3. 3.

    Using watershed segmentation algorithm for separation of interconnected pore space

    Watershed segmentation techniques, commonly referred to as immersion methods, simulate water rise and the consequent flooding impact from a specific group of markers or locations. The initial markers used for watershed segmentation in this scenario are derived from the initial segmentation that serves as their foundation. The data segmentation process was finalized with the use of the island removal algorithm, which had the sole purpose of removing pores that had less than 26 connected voxels.

  4. 4.

    Porosity calculation and pore size distribution determination

    Porosity in the tested sample was determined by comparing the pore area to the total segmented volume. An ideal pore assumes the shape of a sphere, with the same volume as an irregularly shaped real pore. We grouped the results into predefined bins and measured the frequency of pore size distributions. As pore shapes can be irregular, the cumulative volume of pore clusters is estimated by using the total volume of all voxels within the cluster. The model assumes that the pore clusters’ volumes represented by voxels are similar to perfect spheres with an equivalent radius (Req) calculated as:

    $${R}_{\text{eq}}=\sqrt[3]{\frac{3{N}_{\text{Veq}}}{4\pi }},$$
    (1)

    where \({N}_{\text{Veq}}\)  represents the equivalent volume size of the spherical pore. These idealized pores are positioned in alignment with the actual locations of the real pores (Beg 2021).

  5. 5.

    Pore network model extraction using Open PNM pore network modelling package (Gostick et al. 2016)

    PNM, or pore network modelling, is a reliable and established technique for simulating transport in porous materials. The basic premise of pore network modelling is to depict porous materials as a network or graph of pores, with nodes representing pores, while branches depict links or edges. A pore network model generated via Dragonfly software with the integrated Open PNM package and PoreSpy (an open-source toolkit for the analysis of images of porous media; Gostick et al. 2016) can evaluate the connected void space, solid space, or multiple phases within each space.

    The SNOW algorithm, integrated into PoreSpy, adopts a watershed segmentation approach to determine the regions which correspond to pores and throats, according to their proximity to the solid region. The described pore network extraction was conducted using the µCT images that have been pre-processed and segmented as stated above. For watershed segmentation, the algorithm utilized a Gaussian filter, with a sigma of 0.4, in order to remove any spurious peaks in the distance transform. The following step involved applying a maximum filter with a radius of 4 to recognize the markers that function as the core points of the pores.

  6. 6.

    Effective permeability estimation using Open PNM

    Within a PNM, two adjacent voids are considered to be authentic and linked through a passage. The resulting flow connecting these voids is considered to be the flow within a channel, the properties of which are explained by a variety of analytical solutions depending on the geometry associated with the channel. A popular approach is to employ the Hagen-Poiseuille equation to simulate single-phase flow in a cylindrical conduit (Gostick et al. 2016): 

    $$q=\frac{\pi {R}_{\text{i}-\text{j}}^{4}({P}_{\text{i}}-{P}_{\text{j}})}{8\mu {L}_{\text{i}-\text{j}}},$$
    (2)

    where Pi and Pj are the pressures in pores i and j, Li−j and Ri−j are the length and radius of the throat (pipe) connecting pores i and j, and µ is the fluid viscosity (Fig. 3).

    After creating the PNM, we calculated the effective permeability. Permeability is a property of the porous medium itself. It is independent of the properties of the fluid. Hence, any fluid with a specific viscosity value can be employed as the flowing phase in the network. In our case, we used water. We determined the network’s permeability by implementing the Stokes flow algorithm. To determine the permeability in the Z direction, a fixed pressure boundary condition was enforced at both the bottom and top points (Z direction) of the network. Ultimately, the permeability was computed with the use of Darcy’s law: 

    $${K}_{\text{abs}}=\frac{Q}{A}\frac{\mu L}{\varDelta P}$$
    (3)

    where Q is the inlet flow rate, A is the inlet area, and L is the distance between the inlet and outlet.

Freeze-thaw test

To comprehend the structural transformations within the sample caused by the damaging mechanisms during ice crystallization, freeze-thaw conditions were simulated using a custom-designed VLAP 04 thermodilatometer.

After analysing the pore space characteristics, we dried the specimen for 48 h at 60 °C, measured its weight, and then saturated it with distilled water in a vacuum for 48 h until maximum water saturation was reached. The specimen was weighed again and enclosed in low-density polyethylene foil to prevent moisture loss. It was then inserted into the thermal chamber of the VLAP 04 thermodilatometer.

Generally, the temperature conditions of the natural environment are simulated in the range of − 20 °C to + 200 °C with temperature oscillation rates of 0.3 °C/min to 2 °C/min, and according to several authors (Widhalm et al. 1996), the temperature rate of 2 °C/min is a limiting rate for thermal shock. Our thermodilatometer can control temperature changes between − 17 °C and + 60 °C. To prevent thermal shock, we simulated temperature changes ranging from − 10 °C to + 10 °C at cooling and subsequent heating rates of − 0.18 °C/min and 0.21 °C/min, respectively. We monitored temperature using a control thermocouple, placed along the central rotational axis of a cylindrical dummy sample, made from the same lithological material as the other specimens tested.

Excessive pressure during the F-T cycle induces porosity changes consequently resulting in residual strain. Monitoring of length changes and observation during ice crystallization allow quantification of damage. Measurements were taken with a VLAP 04 thermodilatometer using two HIRT-LVDT-T101 F linear variable differential transformer sensors.

Results

SEM and XRD results

According to SEM and XRD results, the BR(Tf) tuffs are composed of pumice material with the fragments of unsorted pumice (37 wt%), plagioclases (26.4 wt%), hematite (0.1 wt%), and ilmenite (1.1 wt%) spread chaotically in the matrix. The matrix is formed mainly by a clay-swelling mineral group of smectite — montmorillonite (24.2 wt%) and kaolinite (3.4 wt%) (Fig. 2B) and (Table 1).

Table 1 X-ray diffraction (XRD) results on tuff samples. Abbreviations: Hem, hematite; Ilm, ilmenite; Kfs, K-feldspar; Kln, kaolinite; Plg, plagioclase; Qtz, quartz; Sm, smectite. + — mineral is present. DoF (‘degree of fit’) — a statistical parameter expressing the quality of the analysis. Its value should be < 0.1
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Montmorillonite is a mineral with a 2:1 layer structure. These minerals consist of two tetrahedral sheets and one octahedral sheet. According to Pötzl et al. (2018), the swellability of clay minerals can play a decisive role in the weathering process and affects the length change behaviour of rocks during ice crystallization inside the pores.

Changes in pore network characteristics after F-T cycling

The mineral composition and the fabric (structure and texture) determine the petrophysical properties of the rocks (Ruedrich and Siegesmund 2007).

The pyroxene-rich andesite tuffs found in the Brhlovce locality exhibit remarkably high porosity levels. This is a distinctive quality of tuffs composed predominantly of unsorted and chaotically deposited pumice material in a fine-grained matrix. The effective porosity average for these tuffs was 30.1%, which increased to 31.2% on average after undergoing 100 F-T cycles. The average total porosity increased from 31.3 to 32.5% after cycling (Fig. 4a, b, c, d).

Fig. 4
figure 4

Petrophysical properties of 15 tuff samples determined before and after 100 F-T (freeze-thaw) cycles: change in effective (a) and total (b) porosity prior to and after freeze-thaw cycling; values of effective porosity (c) and total porosity (d); average imbibition slopes recorded before and after 100 cycles of F-T (freeze-thaw) for fast (e) and medium (f) imbibition time window

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The pore size distribution pattern is bimodal and represents a wide range of pore sizes, with a large volume of pores with a radius smaller than 1 × 101 nm and larger than 1 × 104 nm (Fig. 5).

Fig. 5
figure 5

Pore size distribution obtained from MIP and a comparison with micro-CT resolution

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The porosity of Brhlovce tuffs is high due to their genesis, mineral composition, and structure. Of the total porosity, 5.93% is accounted for by easily accessible pores (Nbulk), while micro- and mesopores (Nads) make up 5.70%. However, there are smaller volumes of hard-to-access pores (Nvoid = 2.73%) and closed pores (Nc = 3.98%). This suggests that the tuffs have a relatively open pore structure and are more susceptible to the effects of frost weathering. The content of micro- and mesopores has decreased by 0.14% points to 5.56, while the pores that are not easily accessible to water have decreased by 0.85% points to 1.87%, and the content of closed pores has decreased by 3.50% points to 0.57%. However, these declines were countered by a 4.61% point increase in pores which are easily accessible to water, resulting in a final value of 10.54%.

Based on the results of spontaneous imbibition, it can be concluded that the pore structure of the BR(Tf) tuff under examination is extensively interconnected. This outcome is predominantly owing to its unique distribution of pore sizes, wherein larger macropores, easily accessible to water as mentioned earlier, dominate, while micro- and mesopores connect them. The C(I) values are therefore high, with an initial and average \({C\left(I\right)}_{\text{f}}^{0}\) = 0.700 which increased to \({C\left(I\right)}_{\text{f}}^{100}\) = 0.838 after F-T cycling, thus representing an increase of 19.6 pp.

In contrast, the imbibition slope after F-T cycling decreased in the medium time frame. The value \({C\left(I\right)}_{\text{m}}^{0}\) = 0.547 decreased to \({C\left(I\right)}_{\text{m}}^{100}\) = 0.492 after 100 F-T cycles, which was decrease by 10.1 pp (Fig. 4e, f).

Pore network modelling and permeability calculations

CT scanning of rock core samples, which measured 51 mm ± 1 mm in length and 32 mm ± 1 mm in diameter, resulted in a voxel size of 34 μm. As a result, only macropores were detectable within the analysed sample, as shown in Fig. 4g. One hundred freeze-thaw (F-T) cycles, with temperature oscillations ranging from 10 °C to −10 °C, cause substantial microstructural alterations in pore spaces and result in fracture formation. The equivalent diameter (ED) of each pore structure was measured before and after F-T cycling to determine dimensional changes, which revealed a considerable increase in porosity of the scanned specimen (BR(Tf) 10)) from an initial 13.1 to 35.58%, or an increase of 173.2% points (Fig. 6). The total length of the conduit throat decreased from the initial 13.2 × 103 μm to 10.2 × 103 μm after cycling. Additionally, the initial median throat length was 1989.8 μm, which increased to 3742.6 μm after cycling (Fig. 6).

Fig. 6
figure 6

Pore network modelling results showing changes in PSD (a) after 100 F-T as well 3D rendering of connected pore space showing an increase in total porosity from 13.1 to 35.5% together with effective permeability from 3.28 × 10−8 to 8.57 × 10−4 (b)

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The microstructural development of the fracture occurs in all three dimensions within a three-dimensional space. Changes in sample porosity are strongly linked to alterations in pore connectivity and confirm the results from spontaneous imbibition.

As mentioned previously, permeability was assessed from µCT image analysis by implementing the Stokes flow algorithm in the Z direction. These changes occur by creating new pathways for fluid flow, increasing the permeability from an initial 3.28 × 10−8 m s−1 to 8.57 × 10−4 m s−1 after cycling.

However, it is important to note that the rock permeability we calculated is only associated with the constructed pore network models. The sensitivity of these models is limited by the maximum resolution of CT images and does not consider a whole range of pore sizes.

Freeze-thaw test

The strain and temperature behaviour during the F-T cycling was plotted as strain versus time diagrams in Fig. 7 and divided into four, respectively, five characteristics zones — I; II; III (a, b); and IV. A modified division by Ruedrich and Siegesmund (2007) was applied. Above the freezing point, the strain curve was in zone I. Expansion, which started below the freezing point, was caused by crystallization of the ice (zone II). Within this zone, the water-ice phase transition occurred. In this section, the latent heat released from solid ice to liquid is greater than the heat removed from the system; therefore, the overall temperature of the system increased. Zone III was characterized by a pronounced contraction of the specimens. A secondary expansion was observed in zone IIIb and was followed by a contraction in zone IV.

Fig. 7
figure 7

Record of temperature and strain behaviour of the BR(Tf) samples. (a) Temperature and strain path during 100 F-T cycles. (b, c) Detailed records of temperature and strain vs. time sample behaviour during the 2nd and 95th F-T cycles. (d, e) Detailed records of strain vs. temperature paths during the 2nd and 95th F-T cycles

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Specifically, in zone I, the strain path curve has a constant course or exhibits slight expansion even at positive temperatures. This can be explained by the swelling of clay minerals, specifically clay minerals of the smectite group. In zone II, a minimal expansion occurs at about − 2.5 °C, followed by an observable pronounced contraction in zone IIIa with a peak at around − 7 °C. This contraction is followed by a second expansion in IIIb with a peak around − 10 °C. Subsequently, a contraction with limited intensity occurs in zone IV with a peak at − 5 ° C (Fig. 7).

Applying principles of poromechanics, when assuming a spherical crystal with a radius equal to a given pore radius, a Kelvin freezing point depression can be calculated by the following equation:

$${{T}}_{\text{f}}=-273\frac{2{{\upsigma }}_{\text{s}\text{l}/\text{s}\text{v}}}{{r}{\uprho }{L}},$$
(4)

where r is the radius of the spherical ice crystal; ρ is the density of the ice density (ρ = 917 N m−1); L is the latent heat of fusion (L = 333,550 J kg−1), and \({\sigma }_{\text{sl}/\text{sv}}\) are surface tension characteristics of the solid-liquid interface (σsl = 0.033 N m−1) and solid-vapour interface (σsl = 0.109 N m−1) (Camufo 1998). The ice crystal radii, which correspond to the freezing temperatures of − 3.5 and − 8.6 °C (temperature inside the VLAP 04 thermal chamber), are 16.8 nm (− 3.5 °C) and 6.8 nm (− 8.6 °C) respectively. The upper pore radii, calculated from the surface tension of the ice-vapor interface, were 55.5 and 22.6 nm respectively. The corresponding crystallization pressures were derived by Eq. (7):

$${P}_{\text{c}}=\frac{2\gamma \cos{\Theta }}{r},$$
(5)

where 𝛾 is the surface tension at the ice-water interface, \({\Theta }\) is the contact angle between the crystal and the pore wall, and r is the radius of a spherical ice crystal. So, the crystallization pressures calculated for these derived radii were 3.9 MPa for temperature of − 3.5 °C and 9.6 MPa for temperature − 8.6 °C.  In the case that the crystallization pressure exceeds the local tensile strength of the frozen rock, a cracking of the rock material will occur (Eq. (7)).

$${\upsigma }\approx \text{b}.{S}_{C}.{P}_{C},$$
(6)
$${\upsigma }>\frac{{{\upsigma }}_{\text{z}}}{\sqrt{3(1-2{\upnu })}},$$
(7)

in which b is the Biot coefficient, Sc is the ice crystal saturation degree, σz is the tensile strength, and ν is the Poisson’s ratio. The tensile strength and Poisson’s ratio used in this calculation were according to the engineering geological atlas of the Slovak Republic σz = 1.21 MPa and ν = 0.15. Based on Eq. (7), the macroscopic stress σ needed to exceed the tension failure strength is 0.438 MPa. To obtain this resulting stress with the above-derived crystallization pressure, local fractions of ice crystals have to be 22.3% (− 3.5 °C) and 9.09% (− 8.6 °C) respectively, assuming the Biot coefficient equals 0.5.

Discussion

The Brhlovce tuff is highly susceptible to damage from ice crystallization within its pore spaces, making it a vulnerable rock type. A critical factor in determining this susceptibility is the distribution pattern of its pores. The BR(Tf) tuffs exhibit a pore size distribution with a substantial quantity of micropores as well as larger pores above 10 μm. When the temperature of the pore network system reaches the freezing point, heterogeneous nucleation (crystallization) takes place. Due to the pressure of the water within the pores, the freezing point decreases as the pore size decreases. Everett (1961) states that it is more advantageous for the water to initiate crystallization in larger pores and, if there is sufficient interconnectivity between the pores, water can diffuse from the micropores to the forming ice front in the macropores. Micropores can act as a substantial reservoir for initiating ice crystal growth, leading to the generation of negative pore pressure and consequent sample contraction. This phenomenon is influenced by the dissimilarity in chemical potential between water and ice. However, our research, which utilized the Kelvin freezing point depression equation, indicates that crystallization initiates within nanometric micropores (6–55 nm). The second phase of expansion occurs in zone IIIb. This was caused by a crystallization pressure of approximately 9.6 MPa leading to residual strain generation after 100 F-T cycles. This contradicts the observed increase in porosity, pore interconnection, and changes in pore size distribution, resulting in rapid rise in the number of pores that easily allow water access. Besides Everett’s theory, several other models elucidate the pressures within the pore network during crystallization. One theory is the volumetric expansion model, which assumes that water is forced away from the solidification front in the macropores, increasing the hydraulic pressure in the medium as the space that can be occupied by water is limited (e.g. in micropores or when pore interconnection is too low). According to Scherer (1999), the pressure in the pore water (PL) during thermodynamic equilibrium is computed using the subsequent equation:

$${P}_{\text{L}}-{P}_{\text{c}}=-\frac{2{\gamma }_{\text{CL}}}{({r}_{\text{p}}-\delta )},$$
(8)

where PL is the equilibrium pressure of the vapor, \({ \gamma }_{\text{CL} }\) is the interfacial energy between the ice crystal and the liquid, rp is the radius of cylindrical pore, and \(\delta\) is the water film between the ice crystal and the pore wall. In these conditions, the crystallization pressure (Pc) cannot overcome the negative value of the capillary pressure. The reason is the negative contraction of the sample (Scherer 1999; Scherer and Valenza 2005). But according to Sun and Scherer (2010), despite the contraction and subsequent compression, a sample can degrade by means of fatigue cracking or subcritical cracking. Another possible explanation is the development of negative pore pressure due to the presence of clay minerals. Rocks with advanced swellable clay minerals are characterized by the hygric swelling process. According to Ruedrich et al. (2011), this process can contribute to the weathering and deterioration of natural rocks and building materials. Water located between intermediate layers of swelling clay minerals can migrate during ice crystallization to the forming ice crystals located in larger pores, and thus swelling pressure decreases, and this results in sample shortening (Ruedrich and Siegesmund 2007; Ruedrich et al. 2011). Boháč et al. (2013) investigated the feasibility of a novel monitoring sensor for quantifying moisture levels in porous materials, specifically in Brhlovce volcanic tuffs. The sensor employed the hot ball method to measure thermal conductivity, which is contingent on the moisture content of the pores. When the interstitial spaces are occupied by air/vapour, water, or ice, the thermal conductivity of the porous structure varies. Furthermore, laboratory research also included in situ monitoring of the temperature and humidity levels found within the Brhlovce rock dwellings at depths of 10, 50, 70, and 182 cm. Starting in 2011, this monitoring was conducted for 1 year and yielded intriguing findings. The moisture saturation in the deeper parts of the rock mass was between 50 and 58%. Similarly, the surface probe indicated a saturation of 58.6% at a depth of 10 cm and 68.2% at 50 cm. This study verifies that the moisture content in the tuff mass exceeded 50%. Throughout the year, these values fluctuated, peaking in the spring season. Given that Brhlovce tuff matrix primarily consists of smectite minerals, which are prone to swelling and vulnerable to wetting and drying cycles, moisture expansion could play a critical role in triggering instability of the rock dwelling. This issue is likely intricate and may rely on a combination of various factors, such as in situ stresses, frost weathering, thermal cycling, or biological aspects. Future research will incorporate dilatometric monitoring, surface and borehole temperature monitoring, and laboratory investigations of thermophysical properties. Subsequently, the thermomechanical and frost weathering rate modelling of rock wall erosion will be conducted. This experiment will elucidate whether rockfall is impacted by volumetric expansion due to short-term freezing or ice segregation, both affected by moisture supply.

Conclusion

In this study, we exposed volcanic tuff from Brhlovce, an unstable rock formation, to multiple freeze-thaw cycles. The rock formation contains rock dwellings with considerable historical and cultural importance. Our investigation aimed to examine the microstructure of these rocks utilizing non-destructive and experimental methods, including spontaneous imbibition, indicative rock pore structure, and helium pycnometry. Saturated rock specimens were cycled in a VLAP 04 thermodilatometer which was specifically constructed for this study. The thermodilatometer was equipped with two HIRT-LVDT sensors to gather data, and the changes in pore network models were quantified using post-processed µCT images. Our findings illustrate that:

  • Brhlovce tuffs are highly susceptible to frost damage. This type of rock is characterized by high porosity and high pore interconnectivity. In addition to the large number of micropores, there is a substantial portion of macropores easily accessible to water present within this rock type.

  • The strain and temperature behaviour during freezing is characterized by two expansions, which occurred at temperatures of  − 3.5 °C and − 8.6 °C. This means that ice crystallization starts at nanometric sized pores with corresponding crystallization pressure of 3.9 and 9.6 MPa. The crystallization pressures generated in nanometric sized pores can exceed the local tensile strength of tuff, which are characterized by low tensile strength of 1.21 MPa, consequently leading to rock micro-fracturing. Fracture opening is mainly located on the boundaries of the grains and in the smectite matrix as observed on the µCT images.

  • After 100 F-T cycles, the total porosity increased only slightly by 1.1 pp. However, according to the pore network model analysis, there was a significant increase in macroporosity of 22.4 pp. This is consistent with the results of the indicative rock pore structure identification method, which showed that the volume of pores easily accessible to water increased by 4.61 pp, while the content of micropores decreased.

  • The freeze-thaw cycles cause significant changes in the geometric and topological characteristics of the pore network, resulting in a rise in rock permeability. After F-T cycling, pore interconnectivity changes significantly to 19.6 pp for C(I)f and 10.1 pp for C(I)m respectively and permeability simulated by PNM rises from an initial 3.28 × 10−8 m s−1 to 8.57 × 10−4 m s−1.

  • The residual strain after 100 F-T cycles and the overall contraction of the sample can be attributed to two factors. Firstly, the crystallization pressure is unable to overcome the negative value of the capillary pressure. Secondly, negative pore pressure develops in micropores due to the diffusion of water moving torward the forming ice front.

Overall, the described changes in petrophysical and hydraulic properties could lead to alterations in the distribution of moisture within rock bodies after repeated freezing and thawing, potentially causing stability problems in the long term. However, further studies are required to fully understand this phenomenon, including the role of clay minerals in the tuff matrix during frost weathering.