Effects of Thermal Treatment on Acoustic Waves in Carrara Marble

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 thermal treatments, differing in the applied maximum temperature and the applied cooling condition (slow versus fast cooling) are experimentally studied for dry Bianco Carrara marble under ambient conditions. Two sizes of cylindrical core samples are investigated to identify a potential size effect. As effective quantities on the core-scale, the bulk volume, the bulk density, and the Pand 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, and the propagation velocities significantly drop. 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 sample 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.

bulk volume, the bulk density, and the P-and S-wave velocities, including shear wave 23 splitting, are examined. To obtain a three-dimensional insight into the mechanisms 24 occurring on the micro-scale level, micro X-Ray Computed Tomography (μXRCT) 25 imaging is employed. For both cooling conditions, with increasing maximum temper-26 ature, the bulk volume increases, and the propagation velocities significantly drop. To systematically study the effects of the different thermal treatments, each sam-177 ple was characterized before and after the respective thermal treatment. All measure-178 ments were performed under ambient (laboratory) conditions. To distinguish between 179 the moment of the measurements, we introduce the superscript "(0)" for the measure-180 ments before the thermal treatment, and the superscript "(1)" for the measurements 181 after. In Figure 2 • µXRCT imaging (one sub-sample) thermal treatment treated state measurements (t1) is not studied.

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To identify a possible induced anisotropy, shear wave splitting was taken into account as done, for instance, in Peacock et al. (1994) and de Figueiredo et al. (2013). This means, that by polar measurements a potentially existing shear wave splitting was identified, and in the positive case, the velocities V S,1 and V S,2 of the faster and the slower traveling S-wave determined. To quantify the state of anisotropy, Thomsens's anisotropy parameter is introduced (Thomsen, 1986)  The results of the absolute values for the determined density ρ, the P-wave ve-228 locity V P as well as the S-wave velocity V S , rather V S,1 and V S,2 , of each sample, before 229 and after the respective thermal treatment, can be found in Appendix C.     is evidence that the raw material is slightly anisotropic perpendicular to the wave     is up to 350 • C depending on the peak temperature and above more or less constant.

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In Figure 5(b) the ratio of V  cooling procedure, we obtain nearly the same results independent of the sample size.

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However, for the fast cooling procedure, the drop of the propagation velocity for the 327 small samples is for all thermal treatments slightly lower.  where the error between the "3PM -all data" and the "lin. regression -all data" is less than 15 %. on the bulk volume changes. The fact that all data points in the semi-log plots lie 345 approximately on a straight line motivates to employ a logarithmic model approach. 346 Therefore, we propose for the relative P-wave and S-wave velocity changes ∆V i with 347 i = {P, S,1, S,2}, as a function of the relative bulk volume change ∆V rel. , following 348 approach: The parameters m i , c i and b i are corresponding fit parameters. Therefore, we refer instead of the specif one is less than 2.5 % for the P-wave model and less than 4.6 % for 376 the S,1/S,2-wave models. In Figure 7(b), 7(d) and 7(f) the region is highlighted, where 377 the relative error between the 3PM and the linear regression is less than 15 %. This 378 corresponds to relative bulk volume changes greater than 4.1 × 10 −4 (0.041 %) for the 379 P-wave velocity changes and 5.9 × 10 −4 (0.059 %) for the S-wave velocity changes. For employing the ultrasound velocities of the untreated samples and the relative bulk volume change. In combination with the associated modified bulk volume density

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The μXRCT data sets in Figure 8 show clearly the effects of the thermal treat- temperature of the subsequent thermal treatment, cf. Figure 5(b). Since the transmit-539 ted pulse of the S-wave transducer always includes P-wave portions, the first arrival 540 of the S-wave is superimposed more and more by parts of the P-wave arriving before. In the through-transmission technique, there are two probes, one on either side of the sample, whereby one transmits a pulse while the other receives the pulse after a certain travel time. With the current sample length l (here l (0) or l (1) ) and the related travel time ∆t s of the pulse within the sample, the wave propagation velocities can be derived. The employed experimental setup is shown in Figure A1. For the 663 coupling of the transducers to the sample surface, an adequate couplant was used. All measurements were performed under an identical contact pressure of 0.25 MPa.

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The related force was adjusted using a scissors-lift table and a mechanical load cell.

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As ultrasonic square wave pulser/receiver, the Olympus-Panametrics 5077PR unit in    The resulting time ∆t is larger by the system time ∆t sys. than the pure travel time within the sample ∆t s , ∆t s = ∆t − ∆t sys. holds. The system times ∆t sys. were experimentally determined for the two setups using two aluminum standards with a different length (l 1 and l 2 ) made out of the same semi-finished product. Since in both standards the speed of sound must be equal, the system time follows from the two measured time periods ∆t 1 and ∆t 2 : To achieve a plane wave approximation, the basic requirement of ultrasonic measure-685 ment is that the sample diameter is much larger than the transducer diameter (Zhang hold. Therefore, with the absolute quantities for the density given in Table C2 and   734   Table C3, the relative change of the density ∆ρ rel. and the relative change of the bulk 735 volume ∆V rel. can be determined.

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The relative changes for the P-and S-wave velocities are defined as to the used raw material blocks, are given in Table C1. The absolute determined 741 quantities for bulk density as well as velocities are given in Table C2 for the large 742 samples and for the small ones in Table C3. For the measurements before the thermal 743 treatment the superscript "(0)" and after the thermal treatment the superscript "(1)" 744 is used.