Thermal conductivity of compacted Opalinus Clay at different degrees of saturation

. Tunnelling in bedded shale rocks induces damage around the excavation. Consequently, the rock mass in the excavation damaged zone (EDZ) shows different thermo-hydro-mechanical (THM) properties from the intact rock. In turn, the damaged material close to the tunnel wall is affected by seasonal fluctuations in temperature and relative humidity (RH) variations associated with tunnel ventilation, impacting the total suction and the saturation state of the EDZ. The monitoring data at the new Swiss Belchen A2 highway tunnel excavated in Opalinus Clay (OPA) captured these seasonal variations in the total stress acting on the lining associated with this temperature and RH fluctuation. Within this context, assessing the temperature field in the EDZ requires determining the thermal conductivity of the damaged rock at different degrees of saturation. However, obtaining good-quality cores of OPA from the EDZ is not straightforward, and partially desaturating them using controlled RH techniques is time-consuming. Consequently, instead of testing damaged OPA, statically compacted samples of OPA powder at different degrees of saturation have been considered to study the thermal conductivity. In addition, two natural OPA samples (with different bedding orientations) retrieved from the Belchen tunnel have been tested to cross-check the experimental procedure and results, which indicated a consistent increase in thermal conductivity with the degree of saturation.


Introduction
Infrastructure tunnels are a significant part of the mobility transition. They are designed for long service life. However, due to swelling phenomena, several structural damages have been observed in road tunnels constructed in anhydrite-rich rocks or clay rocks [1][2][3][4][5]. While mechanised tunnelling, there are stress redistribution and dilation in the vicinity of the tunnel, which results in the formation of a so-called Excavation Damaged Zone (EDZ). Physically damaged and destructured rock mass in the EDZ shows different thermal, hydraulic and mechanical properties. Additionally, the formation of the EDZ potentially triggers volume change phenomena due to the opening of preferential flow paths in relatively dry materials along the tunnel and pore water disequilibrium due to the excavation-induced unloading and ventilation.
Besides solely hydro-mechanical processes, also temperature plays a significant role in the total stresses acting on the tunnel support system. This was observed at the new Belchen A2 highway tunnel tube (STB) in Northern Switzerland, constructed between 2016 and 2020, and excavated in the argillaceous formation Opalinus Clay and the anhydrite-rich rock Gipskeuper. As the old tunnel tubes were consistently exposed to swelling of the surrounding argillaceous and anhydrite formations since its construction in the 1960s resulting * Corresponding author: nuria.sau@upc.edu in recurring structural damages, the STB was comprehensively equipped with monitoring equipment for short-and long-term measurements. Data [6] clearly show cyclic temperature-driven variations of the radial stress on the tunnel lining induced by seasonal changes. They are around 0.4 MPa for annual temperature changes of 10°C in the Opalinus Clay, the rock mass studied in the present research. Preliminary thermomechanical simulations support the expected impact of thermally-induced expansion and contraction of the Opalinus Clay, but also indicate missing additional influences in the simulations, such as those related to the de-and resaturation of the rock mass around the excavation due to seasonal variations in relative humidity (RH) [6]. Changes in the degree of saturation impact the temperature field distribution around the EDZ of the tunnel lining since water's thermal conductivity is one order of magnitude higher than air. Thereby, characterising the thermal conductivity of the damaged and partially desaturated Opalinus Clay is essential to properly asses the temperature field. However, testing OPA cores from EDZ controlling the degree of desaturation using RH techniques is not straightforward, mainly because obtaining good quality samples at a real construction site requires considerable technical effort and vapour equilibrium is time-consuming. Consequently, instead of testing damaged OPA, statically compacted samples of OPA powder at different degrees of saturation have been used to study the thermal conductivity. In addition, the thermal conductivity of two natural Opalinus Clay samples on two different orientations (heat flow parallel and perpendicular to bedding planes) was also studied. This additional data allowed for building confidence in the experimental setup and procedures since Opalinus Clay has been widely studied as the selected host rock formation for the deep geological repository of heatemitting and long-lived radioactive waste in Switzerland (for instance, [7][8][9][10]).

Experimental program
The sections below present the material tested, a brief description of the testing equipment, and the procedures followed.

Material tested
Opalinus Clay is a Jurassic-aged marine claystone formation. It is composed of several facies and subfacies types according to the amount of quartz, carbonates and clay minerals. The tested Opalinus Clay was retrieved at the construction site of the new Belchen highway tunnel (Jura Mountains in Northern Switzerland), which connects Basel and Lucern. Drilling cores were extracted under consideration of the bedding plane orientation at a depth of around 300 -340 m [11]. The mineralogical analyses showed a similar composition to the shaly facies of Opalinus Clay at Mont Terri Underground Research Laboratory (URL) [12]. The average mass percentage of clay minerals is 64.4%, composed of 22.8-31.4% muscovite/illite, 17.0-21.1% kaolinite, 11.1-16.0% illite/smectite and 4.0-6.5% chlorite. The non-clayey fraction mainly comprises quartz (17.8%) and carbonate minerals (11.6%).
Intact natural samples, parallel and orthogonal to the bedding direction, were prepared from two different drilling cores by reducing the diameter with a lathe and subsequently cutting with a diamond band saw to the final height. Opalinus Clay powder was obtained using a jaw crusher and the dry rock of the drilling core from the intact parallel sample. The material was crushed to pass through the sieve with a maximum diameter of 0.25 mm. For producing artificially prepared samples of Opalinus with different initial degrees of saturation, the corresponding amount of additional water was added to the powder, and the mixture was sealed and homogenised for 24 h. Afterwards, the mixture was statically compacted in a press to a defined volume to reach the target dry density of 2.0 Mg/m³, which resulted in a void ratio of 0.338. To ensure homogeneity on samples, the uniaxial static compaction was performed from both the top and bottom sides. The initial parameters of the intact samples are summarised in Table 1, and of the statically compacted samples in Table 2. The total suction Ψ was measured using a chilled mirror dew-point psychrometer (details of this technique in [13]). The high total suction of the saturated or nearly saturated OPA intact samples results from the large matric suction induced on water-undrained unloading upon retrieval.

Testing setup and protocols followed
Tests were carried out in an experimental setup developed within the context of the Project 'Thermal aspects and their coupled HM effects on Ypresian clays and Boom Clay', a collaboration agreement between ONDRAF/NIRAS (Belgium) and CIMNE (Spain). It was designed to determine the thermal conductivity at high stresses using a rigid PEEK TM cell [14] to reduce radial thermal losses and a lever mechanism to apply vertical stresses. Before and during the thermal tests, high vertical stresses were required to mimic in situ stress conditions (4.5 MPa) at the Belchen tunnel. Thereby, thermal resistivity interferences resulting from stress relief during undrained retrieval of intact samples (opening of bedding planes) or the one occurring on undrained unloading after static compaction (poor contact between the heating cap and sample) were avoided. The cell was designed to apply a controlled high temperature at the top of a cylindrical specimen (38 mm in diameter and 40 mm high). Seven thermocouples continuously monitored the temperature at three internal points of the soil sample and at the top and bottom heat flux sensors. Figure 1 shows a crosssection of the cell. The heat flux sensors made of reference materials (a polycarbonate disc with λpoly=0.20 Wm -1 K -1 and thickness tdisc=1 mm placed between two highly conductive aluminium discs with 209 Wm -1 K -1 ) allowed determining the input qin and output qout heat fluxes using Fourier's law and assuming negligible thermal gradient in the aluminium discs: qin =-λpoly ΔTtop / tdisc and qout =-λpoly ΔTbot / tdisc (1) ΔTtop and ΔTbot are the temperature difference between aluminium discs on both top (thermocouples T1 and T2) and bottom (thermocouples T6 and T7) heat flux sensors.
The water content loss was prevented by covering the soil sample with a neoprene membrane and keeping the testing times as short as possible. Usually, tests lasted 5 hours to reach steady-state conditions.
The cell made of PEEK TM provided radial stiffness and thermal insulation, as previously indicated. In addition, an additional external layer of heat-insulating foam (polyisocyanurate foam) was placed to reinforce thermal insulation.
The thermal conductivity tests were performed at an average maximum temperature close to 45°C and with a change in temperature across the sample around 15°C.   T3, T4 and T5), as observed by [15]. Different phenomena largely associated with local soil volume and water content heterogeneities as well as their changes through the thermal test itself (final water  contents are slightly lower close to the top cap at the higher temperature) lead to temperature differences between equidistant internal points in the soil sample. Nevertheless, the compaction methodology allowed for obtaining relatively homogeneous samples; thus, the temperature differences were small.

Results and interpretation
Under steady-state conditions, the global thermal conductivity λ was computed using Fourier's law: where qave represents the average inflow and outflow heat fluxes, L the sample height and ΔT the difference between thermocouples T2 and T6. Figure 4 displays the thermal conductivity results versus the degree of saturation before the thermal tests. Two phenomena are perceived, the influence of the initial degree of saturation in compacted OPA samples and anisotropic features in intact OPA samples. The data indicate the reduction in thermal conductivity with decreasing initial degree of saturation on compacted samples. Regarding anisotropic features, thermal conductivity determined with heat flow parallel to beddings planes λ║ is higher than the one with heat flow orthogonal to bedding planes λꞱ. The fact is consistent with the observations made by other authors in Opalinus Clay (see Table 3) and in other bedded clay formations such as Boom Clay [16][17][18][19], Ypresian clays [14,15] and Callovo-Oxfordian claystone [18,20,21]. Figure 4 also plots the fitting curve that describes the trend of thermal conductivity with the degree of saturation in compacted samples (solid line). This fitting follows the geometric mean model [22] with: λ = λsat Sr λdry  ; λsat= λs (1-n) λw n ; λdry= λs (1-n) where the subscripts 'sat', 'dry', 's', 'w' and 'a' stand for saturated, dry, solid, water and air, respectively, n is the porosity (n = 0.253), and Sr is the degree of saturation. Figure 4 also presents the evolution of the sample OPA-bed║ (dashed lines) following the same variation with the degree of saturation. Thereby, the value of λ║ at fully saturated conditions would be around 3.0 Wm -1 K -1 . The anisotropy ratio in terms of thermal conductivity (ηT = 1.87) is determined using the values of λ║ and λꞱ at Sr=1 as (refer to Table 3): 4 Discussion and conclusions Table 3 summarises the thermal conductivity values (at two different orientations) and the anisotropy ratio of intact OPA in the present study and state-of-the-art results. This last group of results is obtained from studies focused on investigating the thermal properties and thermo-hydro-mechanical behaviour of Opalinus Clay in the framework of a deep geological repository of radioactive waste (references are reported in the table). These studies were based on data extracted from in situ tests (HE-B, HE-C, HE-D, HE-E and FE experiments) at the Mont Terri Underground Research Laboratory (URL, the overburden height varies between 250 and 320 m) or from samples retrieved from shaly Fig. 4. Thermal conductivity measurements of compacted and intact samples for two different orientations (heat flux orthogonal and parallel to bedding planes) versus the degree of saturation. Table 3. Summary of thermal conductivity data of intact Opalinus Clay. Modified from [14].
Source λꞱ (Wm -1 K -1 ) λ‖ (Wm -1 K -1 ) ηT (-)  Table 3: direct measurements on samples at the laboratory (superscript 1 ), backanalysed from laboratory tests (superscript 2 ) and backanalysed from in situ heating tests at the URL (superscript 3 ). Both laboratory measurements and backanalyses are not free of drawbacks. The lab measurements in Opalinus Clay [23] were performed with a divided bar apparatus under high confining stress, obtaining values comparable to the backanalysed ones. Regarding the backanalysed values, in general, there is a good agreement; just the values reported by [24] differ. These lower values were related to the presence of an intensive fractured zone or a bed of carbonated rock with less quartz content (the HE-C experiment was close to the calcareous sandy facies).
The values determined in this study are slightly higher, but the anisotropy ratio is comparable with the state-of-the-art data. The differences result from slight changes in mineralogical composition and porosity. Mineralogical composition, porosity and degree of saturation strongly affect the thermal conductivity of geomaterials.
Regarding the thermal conductivity of artificially prepared samples, their mineralogy is the same as the intact OPA-bed║ since the dry powder soil belongs to the same core. The differences in the values of intact samples are mainly associated with the soil microstructure (arrangement of grains and pore network). The value of the compacted sample lies close to the mean value of λ║ and λꞱ. Despite the different microstructure generated by compaction at different hydraulic states compared to the natural damaged state, the study allows determining the consistent effects of degree of saturation on the thermal conductivity, which has a crucial role on the material during tunnel ventilation and their associated RH variations.
Nevertheless, as observed in Figure 4, the values graphically fitted for thermal conductivity at saturated and dry conditions were 2.41 and 1.43 Wm -1 K -1 , respectively. These values did not agree with λsat = 2.26 Wm -1 K -1 and λdry = 1.02 Wm -1 K -1 using Equation (3) and the reference values of λw (0.598 Wm -1 K -1 at 20°C), λa (0.026 Wm -1 K -1 at 20°C), and λs = 3.55 Wm -1 K -1 , which was estimated using the simplified version of the geometric mean method proposed by [29] for materials with quartz content q < 0.20: The temperature dependence of thermal conductivity can not justify the fitted values of λsat and λdry. The reference value of λw increases by 6% (0.634 Wm -1 K -1 ) at the average temperature of the tests (40°C). By contrast, the dependence in λs and λa is negligible in this temperature range. Likewise, the changes in Sr and n because of the thermal expansion of the constituents and the irreversible thermal strains were minimal.
A larger value of λs = 3.78 Wm -1 K -1 can also explain the fitted value λsat = 2.41 Wm -1 K -1 . Nevertheless, it does not justify λdry. It may also be assumed that the thermal conductivity of the liquid phase is a combination of adsorbed/ice-like water (λw_ad = 2-3 Wm -1 K -1 , according to [30]) and free water, given the mineralogical properties of OPA. To reach the fitted value of λsat, the thermal conductivity of the liquid phase would be 0.78 Wm -1 K -1 , which agrees with the value reported by [15] when studying the impact of Sr in artificially prepared samples of Ypresian clays. On the other hand, the presence of adsorbed water still bonded to clay particles after oven-drying at 105ºC also affect the value of λdry, increasing its theoretical value. Figure 5 plots the thermal conductivity values of the compacted OPA samples (ρd = 2.0 Mg/m 3 ) together with experimental values measured by different authors on fine-grained clayey materials. A clear influence of the degree of saturation and dry density can be observed. Those results reported by [15,31] were measured with the same testing equipment used in this study and under confined conditions. Their samples had different mineralogical compositions but were statically compacted at the same dry density (1.6 Mg/m 3 ). They aimed to evaluate the impact of the clay mineralogy, quartz content and degree of saturation. Samples with higher quartz and smectite contents (Core-022a-mod-Qz-31%) showed higher thermal conductivity than the denser OPA samples. The values reported by [32] were measured with the needle probe under unconfined conditions on samples with different mineralogy compacted at ρd = 1.5 Mg/m 3 .
In summary, this study's results have revealed that the maximum variation of thermal conductivity at the usual range of the degree of saturation encountered in tunnels (Sr≈70-100%) corresponds to around 0.5 Wm -1 K -1 .