Relating physical properties to temperature-induced damage in carbonate rocks

Carbonate rocks have a widespread diffusion in the Earth crust and are extensively used in cultural heritage and buildings. These rocks can be naturally or anthropically exposed to high temperature...


INTRODUCTION
High-temperature gradients drive mechanisms of degradation and weakening of rocks, thus controlling a number of geological processes, engineering applications and cultural heritage (Vagnon et al., 2019 and references therein).
Among various rocks, carbonates are widespread diffused and are extensively used in cultural heritage artefacts and buildings. Large crustal volumes of carbonate rocks are naturally exposed to significant temperature increases in areas with anomalous geothermal gradients. The exposure to high temperatures could also be related to engineering applications. Forecasting their physical evolution under temperature gradients is therefore of utmost importance for many fields of rock mechanics.
While numerous studies have investigated the damageinduced processes by temperature effects on carbonate rocks (Heap et al., 2013;Castagna et al., 2018 and reference therein), less attention has been paid to quantitatively generalise throughout physical parameters evolution of the thermal degradation induced by heating.
A relationship linking physical parameters and temperature (thermal degradation relationship) has been proposed by several authors (e.g. Koca et al., 2006;Dwivedi et al., 2008;Zhao et al., 2012;Musso et al., 2015;Weydt et al., 2018;Vagnon et al., 2019) under the form: where P(T ) is a given physical parameter at temperature T, P 0 is its reference value at 20°C and c is a fitting parameter, depending on the specific rock structure and rock degradation effect. The sign of the exponent is positive if the considered parameter increases with temperature (negative otherwise). Based on experimental tests, several authors (Koca et al., 2006;Dwivedi et al., 2008;Zhao et al., 2012;Vagnon et al., 2019) have proposed similar exponential equations for the thermal degradation relationship with a different c fitting parameter. This study has the main objective of defining a general relationship between physical properties and thermal-induced damage, by way of a multiparametricinduced damage index valid for a broad suite of carbonate rocks.
Six sets of different carbonate rock specimens were tested before and after thermal treatment, with heating/cooling cycles from 105 to 600°C. Density in dry and saturated conditions, porosity, ultrasonic pulse velocity (UPV) and electrical resistivity (ER) were measured. Microstructural observations and both grain-size distribution curves and crack densities were analysed. A unified multiparametric thermally induced damage coefficient was quantified to provide a general law for carbonate rocks.

SAMPLE SETS AND EXPERIMENTAL METHODS
Cylindrical samples obtained from the four different sampling areas (Fig. 1), were classified into six sets: • Seven limestone samples, coming from the fossil hydrothermal system of Las Minas (Mexico), named 'RLM' in the following.
Samples diameter ranged from 40 to 50 mm, and the average length of 95 mm. Samples followed the geometric Vagnon, Colombero, Comina et al.
requirements for standard determination of the analysed physical properties.
To analyse the chemical content of each set, x-ray fluorescence (XRF) and x-ray diffraction (XRD) analyses were conducted (Table 1). It can be observed that RLM and Valdieri samples are mostly calcitic (97·3 and 98%, respectively) while GQ samples are essentially dolomitic. Brazilian samples show transitional compositions between these end members.
Following the experimental procedure detailed in Vagnon et al. (2019), density in dry and saturated conditions, porosity (n), P-and S-wave velocity (V P and V S ) and ER (in saturated conditions, ρ a,WET ) of the 46 core specimens were measured before and after heating (at target     Table 2 summarises the measured parameters, the international standards and experimental methodologies adopted for their determination. The thermal treatment involved a three-stage procedure (Vagnon et al., 2019): (a) sample heating up to the target temperature with a heating rate of 0·06°C/s; (b) 24 h sample exposure to constant target temperature; (c) slow-rate sample cooling down to room temperature (one day on average). The exposure time allows the uniform heating of the samples, ensuring that the surface temperature was the same inside the sample. Even in cooling phase, the time inside the furnace prevents thermal shocks that may influence the sample physical properties, by increasing the thermal degradation effects.
Values of ρ a,WET were also expressed in terms of formation factor, F (Archie, 1942), a dimensionless parameter that represents the ratio between ρ a,WET and the saturating fluid resistivity, ρ fluid .
To analyse the main effects of thermal treatment on the micro-structure of the studied carbonate rocks, 20 × 40 mm thin sections were obtained from natural and thermal-treated extra-samples belonging to the different   sets. Microstructural observations were then performed using a transmitted polarised light microscope. By using the image processing program ImageJ (Schneider et al., 2012), the pre-and post-heating grain-size distribution and crack length (Arganda-Carreras et al., 2010) were measured on thin sections. Crack density, expressed as the ratio between total cracks length and area investigated, was also proposed as a parameter for evaluating thermal damage.

Physical parameter measurements
The thermal treatment induced significant changes in physical properties such as n, UPV and ρ a,WET values for each set of specimens. In Appendix A and Fig. 2    Relating physical properties to temperature-induced damage in carbonate rocks 2000; Koca et al., 2006;Yavuz & Topal, 2007;Peng et al., 2016;Su et al., 2018;Vagnon et al., 2019). Porosity ( Fig. 2(a)) showed an exponential trend with temperature for each set of specimens. In particular, the porosity of RLM limestones was more sensitive to temperature gradients than the other sets of tested specimens.
In general, all the sample sets exhibited the same trends of V P and V S with increasing target temperature (Figs. 2(b) and 2(c)), but with initial P-and S-wave velocity values significantly different.
The formation factor values (F) of each individual set of rock samples is reported in Fig. 2(d). A clear modification in electrical properties is found between different rock samples, with increasing target temperature. In particular, F clearly decreased by increasing temperature.

Discussion and relationships between physical parameters
The previous section has highlighted a strong dependence of each single physical parameter on temperature, repeatable for all lithologies investigated. The main findings can be summarised as follows: • The thermal treatment induced a moderate increase in porosity due to generation of new cracks or re-opening of existing ones at temperatures up to 550°C. At higher temperatures, the porosity increase was likely related to decalcination and decarbonation, leading to increased pore space due to the combination of grain comminution and crack damage (Heap et al., 2013). RLM samples showed a more marked increment in porosity compared to the other samples mirroring the fact that limestones undergo more pronounced textural changes, while marbles, already exposed to high temperatures in their formation history that has led to recrystallisation, maintain a memory of the thermal stresses.
• The increase in porosity is mirrored by a decrease in P-and S-wave velocity and resistivity. With respect to this Valdieri samples showed a slightly different behaviour, since velocities remained relatively constant until 200°C with a significant increase only for higher temperatures. This can be correlated to the presence of dolomite that has been observed (Heap et al., 2013) to strengthen rocks at low temperatures, while decarbonation leads to degradation at higher temperatures.
• Figures 3 and 4 show the inverse power-law relationships between physical parameters and porosities. For the n-V P and n-V S relationships, the general degradation of physical parameters also influenced the mechanical characteristics of rock samples. For n−F relationship that represents Archie's law, the determined parameters for the power law are not in agreement with typical observed values for carbonate rocks (e.g. Ara et al., 2001). However, the application of this relationship to carbonate rocks has been already recognised to be difficult due to the complexity of their voids space (e.g. Talabani et al., 2000).

Microstructural observations
Even if micrographs of thin sections cannot be considered completely as representative of the whole volume of the analysed rock samples, their analysis can be very important for identifying how micromechanical damage induced by heating took place. In this respect, Fig. 5 shows micrographs of thin sections before (a) and after thermal treatment (b) at the highest temperaturethat is, 600°C, for all lithologies investigated. After heating at 600°C, grain expansion leading to crack generation along grain boundaries is observable in all the samples (Fig. 5). Grain-size analyses can also be considered as a good indicator of the thermal effects, given that the decalcination process can reduce the average grain size at high temperature (Heap et al., 2013). Moreover, the propagation of intragranular microcracks can have a double effect either on the crushing of existing grains or the increase in void volume. For these reasons, both grain-size distributions (Fig. 6) and crack length ( Fig. 7 and Table 4) of each micrograph of Fig. 5 were evaluated using the ImageJ code. Moreover, the values of the grain diameter at 50% of the cumulative distribution (D 50 ), the uniformity coefficient (C U ), obtained as the D 60 /D 10 ratio and the crack density were additionally determined (Tables 3 and 4). The analyses highlighted that: • The temperature increase generates a shift of the grain-size distributions to smaller values, strengthening the hypothesis of the formation of microcracks inside initial bigger grains.
• RLM and Valdieri samples experienced higher thermal degradation since they exhibit the highest increase in crack density. For RLM samples this is probably due to the fact that limestone underwent deeper textural changes with respect to metamorphic rocks or carbonates already affected by high-temperature gradients and circulation of high-temperature fluids.

TOWARDS A UNIFIED DAMAGE INDEX
From the above reported results, an induced damage index for carbonate rocks exposed to different temperatures can be proposed. For porosity, the induced damage index can be defined as: where D n is the induced damage index for porosity, n RT is the room-temperature porosity and n(T ) is the porosity evaluated at the different target temperature.
For the other parameters the induced damage index can be written as where D P is the induced damaged index for the generic parameter.  The variation of damage index with temperature is shown in Fig. 8 for each considered parameter. In general, damage indexes gradually increase with temperature following a logarithmic distribution. A dependence on the lithotype is also noticeable in terms of absolute values, while the relative trends remain comparable (Fig. 8). The most plausible explanation may be found in the interplay of bulk composition and strength (dolomitisation and/or grains recrystallisation) and degree of cementation.
The significance of the proposed damage index formulation for carbonatic rocks was assessed by comparing the experimental data with companion results available from literature (Ferrero & Marini, 2000;Sengun, 2013;Yavuz et al., 2010;Brotóns et al., 2013;Zhang et al., 2017). Figure 9 shows the thermal damage trends for fine marble, coarse marble and dolomitic marble (respectively fuchsia dotted, continuous and dashed lines) and limestone (black continuous line) for n ( Fig. 9(a)) and V P (Fig. 9(b)). The trends were evaluated by combining equation (2) (for n) and equation (3) (for V P ) with equation (1) and considering c equals to the fitting parameters shown in Fig. 2. It is possible to see that the experimental results obtained by the majority of the studies fall into these domains, proving the goodness of the proposed unified damage index. However, specific parameter calibration within the proposed limits should be performed for the different materials.

CONCLUSIONS
A series of laboratory tests on six, compositionally and texturally different, carbonate rocks was performed to investigate the variation of multiple physical parameters as a function of increasing temperature.
The main findings of this study can be summarised as • The effect of temperature on physical properties depends mainly on rock texture, bulk composition and grain-size distribution resulting from the interplay of the primary processes of rock formation and recrystallisation. In particular, if the rock was already naturally exposed to high temperatures, a stress memory is preserved and only minor changes in the physical parameters were detected after thermal treatment. As a consequence, limestone samples exhibit a much higher thermal damage compared to marbles already exposed at high temperature and circulation of fluids at high temperature, especially in terms of porosity increase.
These coefficients were calculated as the average of the c values of each rock set considered in this paper.
• A unified coefficient D for quantifying the thermal damage of carbonate rocks has also been proposed and compared with available data from literature.

CONFLICTS OF INTEREST
The authors declare that there is no conflict of interest regarding the publication of this paper.

FUNDING STATEMENT
The study takes partial advantage from analyses (on Mexican samples) founded by the European Union's Horizon 2020 'GE-Mex' research and innovation program under the grant agreement number 727550.