Studied sample

This study focuses on independent measurements of deformation and variations in the elastic properties in granular rocks caused by water sorption mechanisms. I conduct the experimental study on the outcrop Bentheim sandstone from the Gildenhausen quarry, Germany. The outcrop is composed of 95% quartz, 3% kaolinite, and 2% orthoclase. This sandstone is nearly isotropic and homogeneous with round to subround quartz grains sized 50–500 µm (Klein et al., 2000). Some elastic anisotropy effects may exist, but they are likely to be of second

order compared to those considered in this study. The porosity of the outcrop is ~24%, measured from the mass difference between a fully water-saturated sample and the same sample dried in a vacuum chamber under 60 °C. Two samples are prepared for measurement. The primary sample, of a cubic shape with an edge size of approximately 5 cm, is used for deformation and ultrasonic measurements. The second sister sample of an arbitrary shape is used to estimate variation in the saturation with adsorption/desorption of water.

4.2.2 Control of saturation

I regulate the sorption process by maintaining the samples in a surrounding atmosphere with controlled RH. The samples are placed into a desiccator, an enclosed container with a presence of various salt solutes called desiccants (e.g., Greenspan, 1977). The type of desiccant and temperature define the RH. To minimise the influence of variations in the temperature on the results of the experiment, I conduct the measurements in an air-conditioned room with temperature

T = 24 ± 1°C. The desiccants used and the corresponding RH values at room

temperature are summarised in Table 6. I continuously record variations in the temperature and humidity of the atmosphere around the samples with the data logger EL-USB-2-LCD+ (Lascar) placed inside the desiccator. The logger provides accuracy of temperature and RH measurements of ±0.5 °C and ±3%.

Table 6 The list of salts used for the sorption experiment with the corresponding range of relative humidity (RH) at room temperature.

Salt Formula RH at 24 °C

Potassium Sulfate K2SO4 97−98 %

Potassium Chloride KCl 86−88 %

Sodium Chloride NaCl 76−78 %

Magnesium Nitrate Mg(NO3)2 52−55 %

Potassium Carbonade K2CO3 44−47 %

Calcium Chloride CaCl2 26−31 %

Potassium Acetate KC2H3O2 23−26 %

4.2.3 Measurements of deformation

The schematic of the experimental set-up is shown in Figure 26. I have glued a semiconductor strain gauge (Type KSP-6-350-E4, Kyowa Ltd.) to a face of the primary sample to measure the deformation of the sandstone caused by sorption of water. The deformation of the sample leads to the deformation of the gauge. To precisely measure the following change in the resistance, the strain gauge is connected to the Wheatstone electrical bridge. Reading the voltage difference between two legs of the bridge allows accurate measurements of the changes in gauge resistance and calculation of deformation (e.g., Hoffmann, 1986). The acquisition system comprises a digital multimeter 34461A 6½ (Keysight Ltd.) and a PC, which enables continuous monitoring and recording of the strain gauge readings during the sorption process (Figure 27). In designing the experiment, I attempted to minimise the influence of any external factors on the strain gauge readings. I used the air conditioner to maintain the same temperature (±0.5 °C) in the area and covered a desiccator to prevent illumination by light (which can also affect strain gauge readings) and the influence of any unwanted air gusts.

4.2.4 Ultrasonic measurements

Ultrasonic velocity measurements are conducted using the pulse transmission technique (e.g. Birch, 1960). Two piezoelectric shear transducers V153 1 MHz/0.5 in. (Olympus Panametrics-NDTTM) are glued to the opposite faces of the primary sample. The acquisition system includes a rectangular form electrical pulser/receiver 5077PR (Olympus Ltd.) and a digital phosphor oscilloscope TDS 3034C (Tektronix Ltd.). A waveform of the ultrasonic pulse transmitted through the sample is recorded and processed to obtain P- and S-wave velocities (e.g., Lebedev

et al., 2013). The dead time of the electronics is taken into account during processing

Figure 26 Top: schematic of the experimental setup for measurements of sorption-induced deformation and variations in the elastic properties of rocks. Bottom: image of the experimental setup.

4.2.5 Hydration procedure

The stabilisation of the RH inside the enclosed desiccator takes 3–7 days (Figure 27). Meanwhile, it is reported that the final saturation of high-porous sandstones due to the sorption process is reached within several hours after RH stabilisation (e.g., Pimienta et al., 2014). The strain gauge readings show that the deformation caused by sorption generally follows a change in RH (Figure 27). Therefore, I conduct ultrasonic velocities measurements and proceed to the next desiccation stage only after strain gauge readings are stabilised, which usually takes up to one week.

The sorption process is started with the driest possible state. First, I keep the samples inside a vacuum chamber under a temperature of 60 °C for 24 hours. Then I

place the samples in the 13% RH atmosphere, the driest state that can be reached with the given set of desiccants. After stabilisation of strain gauge readings and conducting of velocity measurements, I change the desiccant to set 97% RH around the sample and measure the deformation and ultrasonic velocities again. Then, starting from this wet state, I follow the desorption path back to 13% RH through the intermediate humidity states (Figure 28a) measuring strain, and P- and S-wave velocities. Afterwards, desorption is followed by an adsorption path through the same stages.

Figure 27 Readings from the strain gauge and the data logger for the adsorption process with 97% RH potassium sulfate desiccant.

4.3 Results