Effects of thermal treatment on acoustic waves in Carrara marble

https://doi.org/10.1016/j.ijrmms.2022.105205Get rights and content

Highlights

  • Thermal treatments of Carrara marble lead to significant bulk volume increase correlating with the initiated crack volume.

  • High cooling rate systematically amplifies the observable results of slow cooling.

  • Thermally created cracks can initiate or amplify shear wave splitting.

  • The specimen size affects the resulting acoustic velocities for a high cooling rate.

  • Independent of the cooling rate and specimen size, the relative bulk volume change is a suitable parameter to predict the acoustic velocities.

Abstract

Many physical processes in the field of rock physics are influenced by the presence of fractures and microcracks. Therefore, intact rock samples are often used for reproducible experimental studies, and cracks are artificially created by various methods. For this, one possibility is the use of thermal treatments. In this work, twelve different thermal treatments are experimentally studied for dry Bianco Carrara marble under ambient conditions. The focus is primarily on the influence of the cooling rate (slow versus fast cooling) in combination with different applied maximum temperatures. This also raises the question of the influence of the specimen size, which has never been systematically investigated in this context before. Therefore, three sizes of cylindrical core samples are investigated to identify a potential specimen size effect. As effective quantities on the core-scale, the bulk volume, the bulk density, and the P- and S-wave velocities, including shear wave splitting, are examined. To obtain a three-dimensional insight into the mechanisms occurring on the micro-scale level, micro X-ray Computed Tomography (μXRCT) imaging is employed. For both cooling conditions, with increasing maximum temperature, the bulk volume increases, the propagation velocities significantly drop, and shear wave splitting increases. This behavior is amplified for fast cooling. The bulk volume increase is related to the initiated crack volume as μXRCT shows. Based on comprehensive measurements, a logarithmic relationship between the relative bulk volume change and the relative change of the ultrasound velocities can be observed. Although there is a size effect for fast cooling, the relationship found is independent of the specimen size. Also the cooling protocol has almost no influence. A model is derived which predicts the relative change of the ultrasound velocities depending on the initiated relative bulk volume change.

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 (μXRCT) 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 d=29mm and a length l=72.5mm were used. To study a potential size effect, two further specimen sizes were considered. The second sample size has a diameter of d=12mm and a length of l=30mm and the third one has a diameter of d=48mm and a length of l=120mm. Thus, all three sample geometries have an identical aspect ratio of l/d=2.5. 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 ρ, the P-wave velocity vP as well as the S-wave velocity vS, rather vS,1 and vS,2, 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 μXRCT 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 μXRCT 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 μXRCT 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

References (62)

  • ClarkeD.R.

    Microfracture in brittle solids resulting from anisotropic shape changes

    Acta Metall

    (1980)
  • VagnonF. et al.

    Effects of thermal treatment on physical and mechanical properties of valdieri marble - NW Italy

    Int J Rock Mech Min Sci

    (2019)
  • Sheremeti-KabashiF. et al.

    Determination of structural anisotropy of carrara marble with ultrasonic measurements

  • VlassenbroeckJ. et al.

    Software tools for quantification of X-ray microtomography at the UGCT

    Nucl Instrum Methods Phys Res A

    (2007)
  • RufM. et al.

    Effects of thermal treatment on acoustic waves in Carrara marble [preprint]

    (2021)
  • PeacockS. et al.

    Seismic velocities in fractured rocks: An experimental verification of Hudson’s theory

    Geophys Prospect

    (1994)
  • MahmutogluY.

    Mechanical behaviour of cyclically heated fine grained rock

    Rock Mech Rock Eng

    (1998)
  • SchubnelA. et al.

    Transient creep, aseismic damage and slow failure in carrara marble deformed across the brittle-ductile transition

    Geophys Res Lett

    (2006)
  • SchubnelA. et al.

    Quantifying damage, saturation and anisotropy in cracked rocks by inverting elastic wave velocities

    Pure Appl Geophys

    (2006)
  • Delle PianeC. et al.

    Influence of strain history on the mechanical and micro-fabric evolution of calcite rocks: Insights from torsion experiments

    Swiss J Geosci

    (2008)
  • KandulaN. et al.

    Dynamics of microscale precursors during brittle compressive failure in carrara marble

    J Geophys Res: Solid Earth

    (2019)
  • LissaS. et al.

    Digital rock physics applied to squirt flow

    Geophysics

    (2021)
  • SaroutJ. et al.

    Stress-dependent permeability and wave dispersion in tight cracked rocks: Experimental validation of simple effective medium models

    J Geophys Res: Solid Earth

    (2017)
  • KimK. et al.

    Effect of rapid thermal cooling on mechanical rock properties

    Rock Mech Rock Eng

    (2013)
  • PimientaL. et al.

    Variations in elastic and electrical properties of crustal rocks with varying degree of microfracturation

    J Geophys Res: Solid Earth

    (2019)
  • El BoudaniM. et al.

    Marble characterization by ultrasonic methods

    Procedia Earth Planet Sci

    (2015)
  • El BoudaniM. et al.

    Marble ageing characterization by acoustic waves

    Physics Procedia

    (2015)
  • SiegesmundS. et al.

    Physical weathering of marbles caused by anisotropic thermal expansion

    Int J Earth Sci

    (2000)
  • GaoJ. et al.

    Effects of cooling thermal shock on the P-wave velocity of granite and its microstructure analysis under immersion in water, half immersion in water, and near-water cooling conditions

    Bull Eng Geol Environ

    (2021)
  • FanL. et al.

    Investigation of three different cooling treatments on dynamic mechanical properties and fragmentation characteristics of granite subjected to thermal cycling

    Undergr Space

    (2022)
  • Rodriguez-NavarroC. et al.

    Thermal decomposition of calcite: Mechanisms of formation and textural evolution of CaO nanocrystals

    Am Mineral

    (2009)
  • Cited by (0)

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