Calibrating Thermomechanical Triaxial Cells for Transient Thermal Loads

The thermo-hydro-mechanical behavior of soils has been assessed considering fully undrained or fully drained conditions in laboratory experiments (Campanella 1965; Campanella and Mitchell 1968; Plum and Esrig 1969; Baldi et al. 1985; Hueckel and Pellegrini 1992; Kuntiwattanakul et al. 1995; Savvidou and Britto 1995; Delage, Sultan, and Cui 2000; Cekerevac and Laloui 2004; Abuel-Naga, Bergado, and Bouazza 2007; Abuel-Naga et al. 2007; Vega et al. 2012; Lima et al. 2013; Coccia and McCartney 2016a) or numerical models (Baldi, Hueckel, and Pellegrini 1988; Hueckel and Baldi 1990; Robinet et al. 1996; Sultan, Delage, and Cui 2002; Laloui and Cekerevac 2003; Sheng, Sloan, and Gens 2004; Coccia and McCartney 2016b; Ghaaowd et al. 2017). The fully undrained conditions mimic instantaneous changes in the soil temperature that do not allow time for the excess pore water to flow out of the soil. This condition is typically assessed by preventing water flow from the soil boundaries while measuring the fully undrained thermally-induced pore water pressures. On the other hand, fully drained conditions correspond to very slow rates of change in the soil temperature that ensure no thermally-induced pore pressures develop in the soil; under this condition we typically measure the fully drained thermally-induced volumetric strains. Thus, we currently consider instantaneous (fully undrained) or very slow (fully drained) changes in the soil temperature when we assess the thermo-hydro-mechanical behavior of soils. In other words, current practices overlook the effects of realistic transient thermal loads on the soil response.

Under these realistic transient thermal loads (i.e., gradual changes in the soil temperature), a soil mass experiences both thermally-induced pore water pressures and volumetric strains corresponding to a partial drainage condition (Vega et al. 2012; Olgun et al. 2015; Zeinali and Abdelaziz 2021). The magnitudes of the thermally-induced pore water pressure and volumetric strains depend on the temperature change rate, the soil’s hydraulic conductivity, the thermal expansion coefficients of the different soil constituents, and the drainage length from the drainage boundary. For example, the thermally-induced pore water pressure that will develop near the drainage boundaries is less than the pressure that would develop at locations far away from the drainage boundaries. However, a soil element near a drainage boundary will experience more thermally-induced volumetric strains than an element at a farther distance from the drainage boundary. In order to better understand and develop robust models for the soil response under the partial drainage conditions triggered by the transient thermal loads, we need reliable laboratory results that mimic such conditions. In these experiments, we need to measure the thermally-induced pore water pressure at a specific distance from the drainage boundary while measuring the thermally-induced volumetric strain experienced by the tested soil. One possible way to achieve these goals is to change the temperature of soil specimens in thermomechanical triaxial cells with one drained boundary and another undrained boundary. This technique will allow us to measure the thermally-induced pore water pressure at the undrained boundary while measuring the thermally-induced volumetric strains drained out of the drained boundary. If needed, we will also be able to use comparable soil specimens with different heights to determine the distribution of the thermally-induced pore water pressure over the distance from the drainage boundary.

However, conducting these lab experiments requires calibrating the test equipment for the effect of the transient thermal loads. The conventional corrections of measured thermally-induced pore pressures and volumetric strains at the data processing stage are not acceptable (Zeinali and Abdelaziz 2021). These methods rely on having the system at a constant temperature, i.e., neglecting the transient phase of the test, which represents the transient thermal load considered in this study. Therefore, a calibration that incorporates the effect of the transient thermal loads within the transient stage of the load is needed.

As a result of this, we present a modified technique to perform thermomechanical triaxial experiments under transient thermal loads. We first present the system components needed to perform these experiments. Then, we present the detailed steps of system calibration used to measure robust thermally-induced pore pressures and volumetric strains under the considered transient thermal loads. We then present two experiments in which kaolinite clay specimens were subjected to different heating rates under partial drainage conditions. Finally, we discuss the impact of heating rate on the thermally-induced pore pressure and volumetric strains based on the experimental results.

The thermomechanical triaxial system used in this study uses the thermomechanical triaxial cell developed by Jaradat and Abdelaziz (2020). Briefly, Jaradat and Abdelaziz (2020) modified a conventional Trautwein GeoTAC triaxial cell by replacing the acrylic chamber wall with an aluminum chamber wall where six bipolar thermo-electrical devices were attached. Regulating the electrical current powering these bipolar thermo-electrical devices allows (1) heating or cooling soil specimens by switching the cathode and the anode of the current and (2) controlling the temperature change rate of the specimen by ramping the voltage up or down. A TC-720 temperature control unit, provided by thermo-electric (TE)-Technology, was used to regulate the TE devices’ electrical current. Jaradat and Abdelaziz (2020) presented a detailed description and system calibration for the used triaxial cell.

Two calibrations are typically used for thermomechanical triaxial cells: a calibration for the specimen temperature against the system control temperature and another calibration for the temperature effects on system components. For the specimen’s temperature calibration, the temperature of a sacrificial soil specimen is correlated to the system control temperature (e.g., fluid or external chamber temperatures). In this study, the specimen’s temperature calibration is the same as that reported by Jaradat and Abdelaziz (2020).

The calibration for the temperature effects on the system components includes measuring the impact of the changing temperature on the pore pressure transducer and the water volume filling the drainage lines. This system calibration is essential when transient thermal loads are considered to obtain accurate measurements of thermally-induced pore pressures and volumetric strains during the thermal ramp. For this purpose, the conventional correction of measured thermally-induced pore pressures and volumetric strains at the data processing stage is not acceptable (Cekerevac, Laloui, and Vulliet 2005; François and Laloui 2010; Coccia and McCartney 2012; Jaradat and Abdelaziz 2020). These post-experiment corrections mean that the thermally-induced pore pressures and volume changes recorded during the temperature ramp will be inaccurate. That is because during the temperature ramp, transient thermal loads induce a partial drainage condition in the soil specimen. During the temperature ramp, some thermally-induced pore water pressure (less than the pore pressure developed under full undrained condition) will develop, along with some thermally-induced volumetric strains (less than that developed in fully drained thermal tests). The temperature effects on the system affect the measured thermally-induced pore water pressure and volumetric strains. If conventional calibration methods are used, the measured pore pressures and volumetric strains during the transient thermal load will impact the measured pore pressures and volumetric strains. Thus, calibrating triaxial systems for accurate measurements of the thermally-induced pore pressures and volumetric strains requires integrating system corrections within the testing steps. In other words, thermally-induced pore water pressures and volumetric strains due to system components are corrected during real-time testing. This integration was performed by separating the top and bottom drainage lines, which allowed water flow in and out of the system components at the two boundaries in real time. Each drainage line was connected to a separate backpressure pump (see fig. 1 ) controlled independently using Trautwein DigiFlow software.

We performed this calibration by mounting a solid acrylic specimen sandwiched between filter papers and porous stones in the triaxial cell (see fig. 1 ). The drainage lines were saturated, and the desired effective stress was applied. The system was calibrated under three different effective stresses (100, 400, and 900 kPa) to determine the calibration dependency on effective stress. The backpressure corresponding to the desired effective stress was applied at the specimens’ boundaries by pressure-controlling the top and bottom flow pumps to ensure uniform effective stress. After stabilizing the applied effective stress and completion of the system consolidation, the temperature of the system was initially stabilized at 20°C; then it was raised to 70°C using a carefully controlled rate matching the temperature change rate measured at the center of a sacrificial clay specimen used in the thermal calibration (Jaradat and Abdelaziz 2020). Furthermore, three different heating rates (0.08°C/min, 0.15°C/min, and 0.35°C/min) were used under 400 kPa confining stress to determine the dependency of the calibration results on the heating rate. For each of the considered confining stress and heating rate conditions, water volumes drained from the top and bottom lines were recorded over time. The calibrations under each stress and temperature rate combinations were repeated five times to confirm the repeatability of the results.

Figures 2  and 3  present the drained volumes from the top and bottom drainage lines during system calibrations up to 70°C under different heating rates and confining stresses, respectively. Table 1  summarizes the obtained rates of drained volumes, transition points, and maximum drained volumes for each of the considered conditions. The number of transition points and their coordinates (i.e., time and volume change) shown in figure 2  were determined using the least square of errors for each drained volume curve. Table 1  summarizes the start and end times for the different transition points for each linear segment shown in figure 2 , the volume change rate for each line segment, the maximum drained volume over each of the segments (V_max.), and the total drained volume, V_max.total (i.e., the summation of V_max.). The fluctuation observed in the drained volume in figure 2 , specifically at low heating rates, is believed to result from the potential two-way water movement in the drainage lines as the temperature stabilizes. Moreover, it appears in figure 2  and Table 1  that the maximum water volumes drained from the top or bottom lines at given effective stress are independent of the applied heating rate, despite a minor difference noticed in figure 2C  for 0.35°C/min, which is within the variations observed for the other two rates in figure 2A  and 2B . However, the maximum volume drained from the top drainage line is less than that drained from the bottom line. This difference is potentially because of the higher thermal expansion coefficient of the top plastic drainage lines compared to that of the bottom aluminum lines; this, in turn, allows the top drainage line to accommodate more of the thermal expansion of the water filling the line without draining it out.

Figure 3  presents the calibration results at different effective stresses. As shown in this figure, the water volume drained from the top drainage line is less than that drained from the bottom line for all considered effective stresses; this agrees with the observations in figure 2 . However, figure 3  shows that the maximum drained volumes from the top and bottom drainage lines depend on the applied effective stress. It appears that the higher the applied effective stress, the more the drained water volume from the top and bottom system components, as presented in Table 1 . The large drained volumes under higher effective stresses are justified since higher stresses constrain the expansion of system components more than lower stresses.

It should be noticed that the aforementioned calibrations were repeated five times under the different stresses and temperature ramps with a variation of less than ±1 %, ensuring the repeatability of the results presented in figures 2  and 3 . The results of the aforementioned calibrations are used in triaxial thermal tests to correct for the system effects during the application of the thermal load. For fully undrained thermal loads, water volumes drained from the top and bottom drainage lines (see figs. 2  and 3 ) are to be drained using the separate top and bottom flow pumps, controlled using Trautwein DigiFlow version 1.2.0 software. Once the calibrated maximum drained volumes stabilize, the top and bottom valves are to be closed, allowing measurements of accurate thermally-induced pore water pressures during and after the thermal load, i.e., without the effect of the water filling the system components. On the other hand, the calibrated volumes of water drained from the top and bottom drainage lines are to be subtracted from the respective water volumes drained from soil specimens during the data processing stage for fully drained thermal loads.

The unique capability of the calibration performed in this study is the ability to obtain robust measurements of thermally-induced pore water pressures and volume changes of soil specimens subjected to transient thermal loads. One boundary of the soil specimen will be drained for these transient thermal loads, while the other will be undrained. For the undrained boundary, the water volume drained of this boundary during system calibration will be withdrawn during testing using the respective flow pump. On the other hand, the water volume drained during the calibration from the specimen’s drained boundary is to be subtracted from the total drained volume of the specimen at the data processing stage. Applying this technique allows accurate measurements of the thermally-induced pore water pressure at the undrained boundary and robust estimates of the thermally-induced volumetric strains at the drained boundary under the transient thermal load. This technique is adopted in the following experiments to demonstrate the system’s capability of performing transient heating tests on clay specimens.

The experiments performed in this study aim to demonstrate the ability to measure accurate thermally-induced pore water pressures and volumetric strains under transient thermal loads. The following sections present the sample preparation technique, procedure adopted to perform transient heating tests, and results and discussion.

The kaolinite clay used for the tests reported in this study is the Edgar Plastic Kaolin (EPK) clay. The liquid and plastic limits of the EPK kaolinite are 67 % and 32 %, respectively (Darbari, Jaradat, and Abdelaziz 2017; Jaradat et al. 2017; Zeinali and Abdelaziz 2021). Therefore, this clay classifies as high plasticity, fat clay according to the Unified Soil Classification System.

The tested clay specimens were reconstituted by mixing a kaolinite powder with water at a 1.5 liquid limit following Jaradat et al. (2017) and Darbari, Jaradat, and Abdelaziz (2017). The slurry was poured into a mold with a height of 200 mm and diameter of 100 mm. Then, to minimize piping (Mitchell and Soga 2005; Head 2006), the slurry was left under the weight of the loading cap for 24 hours. Afterward, the bulk sample was subjected to one-dimensional consolidation by doubling the vertical stress up to 100 kPa using an automated loading frame. At the end of primary consolidation, the bulk clay samples were extracted and trimmed to the desired specimen dimensions (∼35.6 mm in diameter and ∼50 mm in height).

Two specimens were considered in this study (see Table 2 ). The specimens were backpressure saturated to a minimum B-value of 0.95. Then, the temperature of each specimen was stabilized at 20°C, after which the specimens were isotropically consolidated under 400 kPa. After that, the temperature of each specimen was raised at a controlled heating rate of 0.15°C/min. or 0.35°C/min. up to ∼60°C under partial drainage conditions. Table 2  summarizes the dimensions, porosity after consolidation, consolidation pressure, and heating rate for each tested specimen.

The top and bottom boundaries of the specimens in Table 2  were drained and undrained, respectively, during the application of the heating load. These boundary conditions facilitated applying a transient partial drainage thermal load to the considered specimens, which is the focus of this study. For the bottom undrained boundary, the water volumes drained from the bottom drainage line during the calibration—see figure 2B  and 2C  for 0.15°C/min and 0.35°C/min, respectively—were withdrawn using the bottom flow pump. Once the system’s desired drained water volume stabilized, after 280 and 195 min for 0.15°C/min and 0.35°C/min, respectively (see Table 1 ), the bottom drainage valve was closed. On the other hand, the water volumes drained during the calibration from the top drained boundaries of the specimens were subtracted from the total volume drained from each specimen at the data processing stage.

Figure 4  presents the measured thermally-induced pore water pressures at the bottom of the specimens in Table 2 . As shown in figure 4 , thermally-induced pore water pressures develop at the bottom of the two specimens as the specimens’ temperature increases. However, Specimen 1, heated at 0.35°C/min, experienced a higher thermally-induced pore water pressure at the bottom of the specimen than that measured at the bottom of Specimen 2, heated at 0.15°C/min. The higher pore pressure corresponding to a faster heating rate was expected since the faster heating rate does not allow enough time for the pore water to flow out of the specimen from the top drained boundary. Furthermore, we observed that the maximum thermally-induced pore water pressures measured in the two specimens occurred before the specimens’ temperature reached the maximum desired value (i.e., 60°C), which was shown to be due to the temperature-dependent water and soil properties (Zeinali and Abdelaziz 2021). Moreover, we noticed a plateau in the thermally-induced pore water pressure in Specimen 2, suggesting a quasi-static state for the thermal pore pressures. This quasi-static state occurs when the rate at which thermally-induced pore pressures develop in a soil specimen is equal to the rate at which water flows out of the specimen; in other words, the generation and dissipation rates of thermally-induced pore water pressures are balanced. Finally, the thermally-induced pore water pressure at the bottom of the specimens begins to dissipate over time as the specimens’ temperature increases and after it stabilizes at the maximum desired temperature.

Figure 5  presents the thermally-induced volumetric strains due to temperature changes in the two considered specimens over time. As shown in this figure, the ultimate thermally-induced volumetric strain, which occurs when the specimen temperature stabilizes at the maximum set value, is independent of the temperature change rate. However, the rate at which these thermally-induced strains develop in the specimens depends on the temperature change rate. A closer look at the thermally-induced strains reveals that their magnitudes depend on the absolute value of the temperature, which depends on the temperature change rate. Finally, the thermally-induced volumetric strains did not stabilize for the two specimens, even though the specimens’ temperature stabilized at the maximum desired temperature because of the expected thermal creep (i.e., continuous volume changes under constant stress at elevated temperature) at the high temperature (Mitchell and Campanella 1964; Paaswell 1967; Campanella and Mitchell 1968; Fox and Edil 1996).

This paper presents a robust calibration method for transient thermal testing of soils. This method is integrated with the testing steps such that the recorded test results are the actual thermal behavior of a soil specimen, thus tackling the problems involving post-experiment correction of the results. Two backpressure pumps were separately connected to the top and bottom drainage lines of the triaxial system. The system was calibrated under three different effective stresses (100, 400, and 900 kPa) and three different temperature change rates (0.08°C/min, 0.15°C/min, and 0.35°C/min). The results showed the dependency of system volume change on effective stress; however, the differences in the results obtained under different heating rates were negligible. The proposed method was then utilized to perform two transient thermal tests on two kaolinite clay specimens under the same effective stress of 400 kPa but two different heating rates of 0.15°C/min and 0.35°C/min.

This material is based upon work supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under contract numbers W911NF-20-1-0238, W911NF-16-1-0336, W911NF-17-1-0262, and W911NF-18-1-00068. The discussions and conclusions presented in this work reflect the opinions of the authors only.