Effects of thermal treatment on acoustic waves in Carrara marble☆
Introduction
Bianco Carrara marble is a popular crystalline rock and frequently used in experimental rock physics to study different physical phenomena, cf. e.g. Refs. [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. Reasons are its high mineral purity, consisting of 98% calcite,4 the low porosity of 0.7%,13 combined with its almost isotropic and homogeneous mechanical behavior on the macroscopic level. All resulting in a very reproducible material for experimental rock studies which was already suggested in 1964 based on a petrofabric analysis of Carrara marble.14
Carrara marble is not only used in its virgin state under ambient conditions but often modified in its microstructure by mechanical or thermal treatments. Both with the aim to initiate microfractures (microcracks). The terms microfractures and microcracks will here be used synonymously as in Refs. 15, 16. The low porosity combined with the nearly mono-mineral composition allows the almost pure study of how microcracks affect the mechanical and hydro-mechanical properties on the macro-scale. Besides the initiation of microcracks by a mechanical load, used, for instance, for the experimental verification of Hudson’s theory,2 the second possibility is to subject the specimens to a thermal treatment.3,9,12 Here, in the simplest case, the specimens are heated-up to a specific maximum temperature, which is held for a certain period until a uniform temperature distribution is ensured. Afterward, the specimens are cooled back to room temperature. In principle, various cooling protocols are available. However, the two extreme cases are to perform the cooling very slowly, for instance, in the switched-off but still closed oven, or very fast, for instance, by quenching the sample in water. For the latter, the term thermal shock is frequently used.17 In both cases, the creation of microcracks can be observed. Recent developments and new investigation methods in the field of experimental rock physics have led to a renewed interest in thermal treatments for the initiation of cracks in Carrara marble.9,12,18 Also in other research areas dealing with the physical weathering of Carrara marble, artificially aging by thermal treatment cycles is still of interest.[19], [20], [21] In a recent work,18 among other crustal rocks, Carrara marble was investigated in regard to its elastic and electrical properties in relation to a varying degree of microfracturing. The microfracturing was achieved by applying different heat protocols (different maximum temperatures) and a slow cooling down (overnight) inside the oven. The effect of rapid cooling instead of slow cooling was not studied and no statistics were considered. Since also thermal shock is a frequently used cooling method,9,12 the question arise how the nature of the initiated cracks and their effect on the macroscopic properties differs. Although recent studies exist for other rock types, e.g., granite [22], [23], [24] and the therein cited literature, a systematic investigation for marble, in particular Carrara marble, does not exist.
The presented research explores, for the first time, as far as the authors know, the different effects of a slow cooling procedure compared to a fast cooling for dry Carrara marble under ambient conditions in a systematic approach. As maximum temperatures the range from 100 °C to 600 °C in 100 K increments is investigated. Further, the influence of the specimen size is taken into account to see if a size effect exists. For this, cylindrical core samples of three different sizes but with the same aspect ratio are investigated. To quantify how the samples are affected by the corresponding thermal treatment on the macro-scale, the bulk volume, the bulk density, as well as P- and S-wave velocity changes are related to the properties before the thermal treatment was applied. For S-wave propagation, shear wave splitting is taken into account to see if a possible anisotropy is caused by the thermal treatments. The results are linked to the changes on the micro-scale in a phenomenological qualitative manner by employing micro X-ray Computed Tomography (XRCT) scans of sub-volumes of selected samples. This allows a three-dimensional (3d) insight into the modified microstructure. From the numerous characterizations, it can be followed that almost independent of the applied cooling procedure and independent of the sample size a logarithm relationship between the relative bulk volume change and the relative change of the ultrasonic velocities exists. This result is the basis of a new model predicting evolving acoustic velocities based on relative bulk volume changes. Moreover, it is discussed how the different thermal treatments are related to each other.
Section snippets
Thermal treatments and samples preparation
As main geometry, cylindrical core samples with a diameter and a length were used. To study a potential size effect, two further specimen sizes were considered. The second sample size has a diameter of and a length of and the third one has a diameter of and a length of . Thus, all three sample geometries have an identical aspect ratio of . The specimen sizes were defined with the consideration that all samples can be examined with identical
Results
The results of the absolute values for the determined density , the P-wave velocity as well as the S-wave velocity , rather and , of each sample, before and after the respective thermal treatment, can be found in Appendix C. Table 2 contains the results for the medium-sized samples, Table 3 for the small ones, and Table 4 for the large samples. From the descriptive statistic of the properties of the untreated samples, classified according to the used raw material blocks, it can
Discussion
The XRCT data sets in Fig. 7 show clearly the effects of the thermal treatments on the microstructure. Independent of the applied cooling method, a crack network was formed crossing the whole sample. The strictly monotonous and smooth curves in Fig. 2 in combination with the XRCT images signal clearly that the bulk volume increase for both thermal treatments is the result of the newly created crack volume and not of irreversible phase transformations. Ref. 18 inferred the same based on their
Summary and conclusions
A systematic study and comparison about the effects of two groups of thermal treatments, distinguishing in the cooling conditions, slow and fast cooling, was carried out for Bianco Carrara marble. As effective properties, the bulk volume, the bulk density, and the P- and S-wave ultrasonic velocities before and after the thermal treatment were determined. For the latter, also shear wave splitting was taken into account. For all measurements, an increase of the bulk volume corresponding with a
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
MR and HS acknowledge funding from the German Research Foundation (DFG) through the project STE 969/13-1. The XRCT images (reconstructed data sets, projection data sets and metadata) of the thermally treated Carrara marble samples and all other measurement data (geometry, mass and ultrasonic measurements) that support the findings of this study are openly available in the Data Repository of the University of Stuttgart (DaRUS) at https://doi.org/10.18419/darus-754,31 //doi.org/10.18419/darus-682
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