Before the calibration test, the vacuum saturation cylinder is first filled with air-free water. Then, the inner chamber components are placed into the water, and pre-vacuuming is performed, effectively preventing the presence of air in the inner chamber. There are two main reasons for underwater assembly: (1) The phase that the inner chamber components entering into air-free water brings new air into the air-free water. Also, the air in the component pipes, joints, and rubber ring grooves cannot be completely removed. (2) Directly filling the inner chamber with air-free water without underwater assembly leaves air bubbles in the top of chamber.

Figure 6 shows a comparison of the inner chamber components before and after vacuuming. Although the water in the vacuum saturation cylinder is air-free water, there are still many bubbles adhering to the surface of the components after vacuuming. This is because placing the inner chamber components into air-free water introduces air. Before underwater assembly, the components need to be gently shaken underwater and brushed to remove the air bubbles on the surface. Figure 7 shows that the loading ram at the top of the specimen can be divided into two parts. After vacuuming, the loading ram was unscrewed, and air-free water was injected using the controller to ensure there was no residual air in the pipeline. After removing the bubbles, the inner chamber components were assembled underwater.

After all components were assembled underwater (as shown in Figure 8), the inner chamber was placed in the triaxial outer chamber for airtightness testing. The drainage pipe at the top of specimen was connected to the back pressure controller, and the water stop cap of the inner chamber was closed to completely seal it. Subsequently, the drainage joint “a” at the bottom of the inner chamber was opened, and whether liquid flows out of the joint “a” in Figure 9 was observed. If there is water flowing out of joint “a”, it indicates that the chamber has not been completely sealed (which may be related to whether the bolts are tightened), and it needs to be reassembled underwater.

The calculation equation for the change in the immediate volume of the inner chamber is as follows: ∆ V i − c e l l = ∆ V − ∆ V c + s π r 2 (1)

Where r is the radius of the loading ram, s is the axial displacement, and the specimen compression direction is positive. ∆ V represents the total immediate volume change of the measurement system, ∆ V i − c e l l represents the immediate volume change of the inner chamber, and ∆ V c represents the immediate volume change of the controller (including pipelines).

The volume of the solid metal specimen changes little with the increase in pressure (Yin, 2003). Therefore, the solid metal specimen is widely used in volume change systematic error calibration tests (Ng et al., 2002; Yin, 2003; Zhang et al., 2014; Chen et al., 2019). Using solid metal specimens can eliminate the influence of soil specimens and calibrate only for the systematic errors of the instrument itself. The dimensions of the stainless specimen are 50 mm × 100 mm. The stainless specimen was installed in the inner chamber following the installation procedure for the soil specimen. During the volume change measurement, the cell pressure of both the inner and outer chambers and the back pressure were first increased to 100 kPa and maintained for a period of time. Then, the cell pressure of both chambers was simultaneously increased by 30 kPa, while the volume of backpressure controller remained unchanged. The B-value was checked and found to be 0.99. After the B value detection was completed, the volume change calibration was performed.

The immediate volume change calibration was based on a back pressure of 100 kPa, with cell pressure increased in steps (the pressure of the inner and outer chambers increases by 50 kPa each time). During the test, the drain valve of the back pressure joint was closed to keep the water volume in the membrane unchanged. At this time, the volume change of the inner chamber caused by the increase in confining pressure is considered the immediate volume change. Calculated by Equation 1, Figure 10A shows the relationship between the volume change of the inner chamber ∆ V i − c e l l and the net confining pressure (the difference between cell pressure and the initial cell pressure) σ i − c e l l . Under net confining pressure of 400 kPa, the volume change of the inner chamber is 0.072 cm³. Since the volumes of triaxial specimens of different standard sizes vary, the measurement error percentage results are compared. In this test, the volume of the stainless specimen is 196.35 cm³, leading to a volume change error of 0.072/196.35 = 0.037%. Figure 10A shows that whether underwater assembly is performed significantly influences the test results. The immediate total volume change of ∆ V , measured without underwater assembly, is significantly higher than that measured with underwater assembly.

The creep calibration was performed after the immediate volume change calibration was completed, with both the inner and outer pressures maintained at 100 kPa for one week. Figure 10B shows the creep result of the inner chamber over this period. The volume changes rapidly during the first 24 h, after which the changes exhibit a linear trend.

Table 1 compares the measurement errors of the double chamber system designed in this study with others existing double-chamber systems. The net confining pressure increases from 0 kPa to 400 kPa. “a” represents specimen diameter 50 mm, height 100 mm; “b” represents specimen diameter 38 mm, height 76 mm; “c” represents specimen diameter 100 mm, height 200 mm.

This design minimizes the volume of the inner chamber and improves the measurement accuracy. However, since the load cell is located outside the inner chamber, there is friction between the inner chamber top cover and the vertical loading ram, causing the value measured by the load cell to be the sum of the friction and the actual strength of the specimen. To reduce friction, the contact surface is coated with Teflon and Vaseline, and the friction is calibrated using a high-precision dynamometer. First, the weight of the loading ram was measured by the dynamometer (as shown in Figure 11A), with an average result of 6.18 N from five tests. Then, after assembling the inner chamber, the dynamometer was pulled to raise the loading ram at a uniform speed to measure the sum of the friction force and weight (as shown in Figure 11B), yielding an average of 10.32 N from five tests. The friction force is approximately 4.14 N, resulting in an initial axial stress due to friction of only 2.11 kPa. Using silicone oil or applying lithium-based grease on the contact surface can further reduce friction. (David Suits et al., 2005). During the testing, the initial axial stress is 2∼2.5 kPa without the inner chamber; therefore, initial axial stress of 6.5 kPa was pre-applied at specimen of the double-chamber triaxial test. The direction of friction calibration must be set according to the axial strain direction under other loading stress paths.

Tests were conducted using solid rubber specimens (50 mm in diameter and 100 mm in height) both with and without the inner chamber. The test was carried out using two different loading methods: (1) stress loading, where the axial stress is increased to 130 kPa within the same time period and the stress is controlled to be the same; (2) strain loading, the displacement increased to 1.7 mm within the same time period, and the final position was consistent; Friction calibration was performed under different effective confining pressures. The tests were divided into those with and without the inner chamber. In this study, “Friction” indicates the presence of the inner chamber during the calibration test, while “Frictionless” indicates the absence of the inner chamber. Figure 12 shows the test results, indicating that increasing the initial axial stress to 6.5 kPa has little effect on the results.

Due to the metal specimens used during calibration testing, all components of the inner chamber and the specimen can be assembled in air-free water and then placed in the triaxial inner chamber. However, in the soil specimen test, the procedure is slightly adjusted. First, the specimen was installed on the inner chamber base in the atmosphere. After the specimen assembly was completed, the tri-leaflet valve used to protect the specimen was not disassembled (see Figure 13). Instead, as an external constraint, it continued to protect the specimen during the vacuuming. Thus, the specimen has little deformation in both radial and axial directions, avoiding any change in the volume of the specimen when the vacuum was applied. Then the remaining components of the inner chamber and the soil specimen ware placed in a vacuum saturation cylinder for pre-vacuuming. After the vacuum was drawn, the inner chamber was assembled underwater and then placed in the triaxial outer chamber.

Generally, in saturated soil drained tests, the volume change of the specimen can be represented by the specimen drained volume. In order to test the measurement precision and accuracy of the apparatus, a drained monotonic shear test was carried out, and the volume change of the inner chamber was compared with the volume of water drained from the specimen. Due to its slower drained shear rate, clay is more susceptible to being influenced by system creep. Therefore, undisturbed soil specimens of soft clay were chosen, sourced from a foundation pit located in Hangzhou, China (see Figure 14). The British GDS stress path triaxial apparatus was used to carry out the consolidation drained shear test. Figure 14 shows the location of the soil utilized in this test and the typical geotechnical profile at that location. The basic physical parameters of the soil specimen are presented in Table 2. Figure 15 shows the particle size distribution curve of soft clay, the diameter of the specimen is 50 mm and the height is 100 mm. To ensure high saturation, in this study the soft clay specimen was saturated under a back pressure of 300 kPa (Wang et al., 2016; Wang et al., 2017; Wu et al., 2017, 2022) and a confining pressure of 310 kPa. The saturation time was not less than 24 h. The B-value was checked and found to be 0.97.

Figure 16A shows that during consolidation, the drained volume of the soil specimen was measured to be ∆ V 1 = 23.135 cm³. According to the calibration results, the influence of immediate volume change and creep on shear tests must be considered, therefore the volume change of the inner chamber was ∆ V 2 = 22.934 cm³. The error between specimen drained volume and chamber volume change is 0.201 cm³, which is 0.102% of the specimen volume.

After consolidation was completed, the “Advanced Loading” test module was used to conduct the drained shear test, with a shear rate of 0.005%/min. Since the confining pressure remains unchanged during shearing, the influence of creep is mainly considered. Figure 16B shows the variation curve of specimen volume with shear time. When shearing is completed, the drained volume of the specimen ∆ V 1 = 13.934 cm³; the volume change of the inner chamber ∆ V 2 = 14.065 cm³, and the measurement error is 0.131 cm³, which is equivalent to 0.067% of the soil specimen volume.