## 2 X-ray Micro-Tomography and Digital Volume Correlation  
### X-ray Micro-Tomography  
X-ray micro-tomography is a versatile and non-destructive imaging tool that aims at obtaining a three dimensional map of X-ray absorption coefficient of the material components. Basically, the sample is irradiated by a beam coming from an X-ray source. A generally planar detector measures the transmitted intensity. A 2D projection (radiograph) of the sample is therefore obtained, containing information on average attenuations along the different paths from source to detector through the material. Then, this acquisition is performed for various angles. Usually the sample is rotated a fraction of degree along its vertical axis until a 180 or 360-degree turn. The series of acquired 2D radiographs allows a 3D reconstruction through different existing computational methods as filtered back-projection algorithm for instance [30]. The resolution of this 3D map of attenuation highly relies on the configuration of the performed acquisition: size of the sample, size of the focal spot, size of the detector, magnification used (ratio between the sample-to-detector and the sample-to-source distances).. In addition, the X-ray attenuation of a given constituent is linked to its chemical properties (atomic number and density) and to X-ray energy [31]. The attenuation contrast between the constituents should be high enough to be able to identify the microstructure. Acquisitions have been performed at the In Situ Innovative Set-ups under X-ray Micro-tomography (ISIS4D) platform [32] using a computed tomography system Ultra Tom\({}^{R}\) from RX Solutions. This device allows to scan a wide range of material samples and sizes (from hundreds of micrometres up to several tens of centimetres) under various loading conditions thanks to the different X-ray generators, detectors, in situ devices and parameters of acquisition. For this study, the X-ray source is a nanofocus X-ray tube from Hamamatsu. The operation voltage was set at 100 kV in order to discern the constituents of the hard clayey rock. To achieve a voxel size of 4.5 \(\upmu\)m required to investigate its microstructure and its evolution under creep, the filament current was set to 45 \(\upmu\)A (maintaining the focal spot of the X-ray cone beam smaller than the resolution) and the geometrical magnification was a compromise between diameter of the specimen and duration of each acquisition. The specimen, placed the closest to the source, has a diameter limited to 5 mm, a flat-panel detector (1874 \(\times\) 1496 pixels, pixel size 127 \(\upmu\)m) has been selected and 1440 radiographs were taken through a 360-degree turn. We averaged six images at a given angular position to reduced noise. The reconstruction of the tomographic data is performed with a filtered back-projection algorithm using X-act\({}^{R}\) software. It is noticed that in our study, the amplitude contrast mode is used for X-ray imaging. For the studied claystone, the amplitude contrast between the clay matrix and hard inclusion is large enough so that it is not necessary to use the phase contrast mode. Further, the emphasis of our study to investigate the non-uniform strain field during creep test, therefore, the stress field is not investigated.