4.2 Relationship between particle size of bentonite pellets and SWCC
The SWCCs of PCMs with different particle sizes are illustrated in Fig. 9. In the low suction range (20–1150 kPa), the smaller the particle size, the higher the water content of the PCM with the same suction. However, with the increase in suction, the SWCCs of PCMs with different particle sizes tended to be consistent. In the high suction range (4200–309000 kPa), the particle size had little effect on the water retention of the PCM. The SWCC can reflect not only the relationship between suction and water content, but also the pore state in soil (Fredlund and Rahurdjo 1993). The SWCCs of PCMs with different particle sizes were different in the low suction range, indicating that although the bentonite pellets became homogeneous with the bentonite powder on the macro-level after saturation, the interior of the PCM was still inhomogeneous on the micro-level.
Hoffmann et al. (2007) analyzed the SWCC of the FEBEX PCM with a dry density of 1.50 g/cm3. Zhang et al. (2014) determined the SWCC of the GMZ bentonite-sand mixture with a dry density of 1.50 g/cm3 and a sand content of 30%. The two curves were compared with the SWCCs of the GMZ PCMs in this work (see Fig. 10). The SWCC of the FEBEX PCM was above the SWCC of the GMZ PCM, but the tendency was similar. The main reason that the SWCCs of these two bentonites could not be completely coincided was due to the inconsistency of mineral composition, resulting in different specific surface areas and surface charge densities of particles (Tripathy et al. 2014; Fattah et al. 2017), which would show different water retention. Furthermore, GMZ bentonite-sand mixture is a feasible buffer backfill block material for the HLW disposal in China (Tan et al. 2019; Zhang et al. 2019; Tan et al. 2020). In the low suction range, the water content of the PCM was more than that of the bentonite-sand mixture under the same suction. However, in the high suction range, there was no significant difference in the water content between the two materials under the same suction. It could be inferred that the PCM as the joint sealing material has better water retention in the low suction range than the buffer backfill block material, and is not prone to shrink and crack in the dry environment of the underground disposal repository. And there is little difference between the water retention of the PCM and that of the buffer backfill block material in the high suction range.
4.3 Hydraulic conductivity
4.3.1 Selection of SWCC model
Three commonly used models, namely Fredlund-Xing model (Fredlund et al. 1994), Gardner model (Gardner 1958), and Van Genuchten model (Genuchten 1980), were selected to fit the SWCC obtained from the test. It was found that the Fredlund-Xing model had a poor fitting effect, and the Gardner model had a good fitting effect, with the correlation coefficients above 0.90, which was the most suitable model for fitting the SWCC of PCM. For space reasons, only the fitting curves of the three models for the SWCC of the PCM with a dry density of 1.60g/cm3 and a particle size of 0.5–1 mm are presented in Fig. 11. The correlation coefficient of the Gardner model was 0.997.
The Gardner model is generally applicable to sand, and the Fredlund-Xing model and Van Genuchten model are generally applicable to silt and clay (Gardner 1958; Genuchten 1980; Fredlund et al. 1994). The particle size of bentonite pellets in the PCM was 2 mm maximum and 0.25 mm minimum, and the pellet percentage was 70%, so the PCM belonged to sand. Therefore, the Gardner model was the most suitable model to fit the SWCC of PCM.
The Gardner model is expressed as follows (Gardner 1958):
(1)
where φ is the suction, kPa; θs is the saturated volumetric water content, %; θr is the residual volumetric water content, %; a is the parameter related to the air-entry value; and n is the parameter related to the pore size distribution. The fitting parameters of the Gardner model for the SWCC of the PCM are given in Table 4. The dry density and particle size had a great influence on a, but had little effect on n. Among them, with the increase in dry density, a had a greater trend.
Table 4
Fitting parameters of the Gardner model
Particle size of bentonite pellets / mm
|
Dry density / (g/cm3)
|
a
|
n
|
R2
|
1–2
|
1.50
|
20198.26
|
0.73
|
0.997
|
1.60
|
17002.92
|
0.74
|
0.996
|
1.80
|
31257.96
|
0.76
|
0.996
|
0.5–1
|
1.50
|
13615.49
|
0.78
|
0.995
|
1.60
|
14041.81
|
0.78
|
0.997
|
1.80
|
26422.64
|
0.71
|
0.994
|
0.25–0.5
|
1.50
|
16962.26
|
0.74
|
0.996
|
1.60
|
17739.19
|
0.71
|
0.990
|
1.80
|
41460.37
|
0.67
|
0.998
|
4.3.2 Prediction of unsaturated hydraulic conductivity
Gardner proposed a two-parameter model by considering the pore size distribution and pore geometry (Gardner 1958; Fredlund and Rahurdjo 1993):
(2)
where ks is the saturated hydraulic conductivity. a and n were obtained by fitting the SWCC of PCM with the Gardner model, and it has just been proved that the Gardner model has a good fit. Therefore, it was feasible to predict the unsaturated hydraulic conductivity of the PCM by using the two-parameter model proposed by Gardner.
The saturated hydraulic conductivity of 6 groups of PCMs was determined by the variable head permeability test as shown in Table 5. At the same dry density, the saturated hydraulic conductivity of the PCMs with different particle sizes was in the same order of magnitude. But as the particle size increased, the saturated hydraulic conductivity of the PCM increased and the impermeability decreased. Moreover, the effect of dry density on the saturated hydraulic conductivity of the PCM was more significant than that of particle size. When the particle size was the same, the dry density of the PCM increased from 1.50 g/cm3 to 1.80 g/cm3, and the saturated hydraulic conductivity of the PCM decreased from 5.31×10-11 m/s to 1.61×10-12 m/s, an order of magnitude difference. With the increase in dry density, the saturated hydraulic conductivity decreased and the impermeability increased.
Table 5
Saturated hydraulic conductivity of the PCM
Specimen No.
|
Particle size of bentonite pellets / mm
|
Dry density
/ (g/cm3)
|
Saturated hydraulic conductivity / (m/s)
|
1
|
1–2
|
1.60
|
3.79×10− 11
|
2
|
0.5–1
|
1.60
|
2.77×10− 11
|
3
|
0.25–0.5
|
1.60
|
2.38×10− 11
|
4
|
0.5–1
|
1.50
|
5.31×10− 11
|
5
|
0.5–1
|
1.80
|
1.61×10− 12
|
The unsaturated hydraulic conductivity of the PCM was obtained by combining the model with the saturated hydraulic conductivity (see Figs. 12 and 13). Ye et al. (2009) carried out an unsaturated hydraulic conductivity test on the compacted GMZ bentonite with a dry density of 1.70 g/cm3, and the unsaturated hydraulic conductivity ranged from 1.13×10− 13 m/s to 8.41×10− 15 m/s (see Fig. 12). In this work, the unsaturated hydraulic conductivity of PCMs with a particle size of 0.5-1 mm ranged from 1.27×10− 12 m/s to 9.88×10− 15 m/s. The unsaturated hydraulic conductivity of the compacted GMZ bentonite with a dry density of 1.70 g/cm3 was between that of the PCM with a dry density of 1.60 g/cm3 and that of the PCM with a dry density of 1.80 g/cm3. Besides, the hydraulic conductivity of the PCM agreed well with that of the compacted bentonite (Hoffmann et al. 2007). Therefore, it could be considered that the method used in this work was reliable to predict the unsaturated hydraulic conductivity of the PCM.
The variation of the unsaturated hydraulic conductivity of the PCM with increasing suction could be divided into two stages (see Figs. 12 and 13). The suction of 0–1000 kPa belonged to the rapid decline stage, and the suction of 1000–30000 kPa belonged to the slow decline stage. In the rapid decline stage, i.e. in the low suction stage, the pore water mainly existed in the inter-aggregate pores, with large pores and good connectivity. When the PCM varied from a saturated state to an unsaturated state, with only a small suction, the pore water in the soil could be discharged quickly, and the unsaturated hydraulic conductivity of the PCM decreased significantly. In the slow decline stage, i.e. in the high suction stage, the pore water was mainly in the intra-aggregate pores. With the continuous increase in the suction, the flow path of the pore water became smaller and narrower. The pore water was mainly adsorbed on the surface of the soil particles in the form of pellicular water, and the unsaturated hydraulic conductivity of the PCM decreased slowly and smoothly.
The unsaturated hydraulic conductivity of the PCMs with different dry densities and a particle size of 0.5–1 mm ranged from 1×10− 12 m/s to 1×10− 15 m/s (see Fig. 12). At the same suction, the unsaturated hydraulic conductivity of the PCMs with dry densities of 1.50 g/cm3 and 1.60 g/cm3 varied in the same order of magnitude, but the unsaturated hydraulic conductivity of the PCM with a dry density of 1.80 g/cm3 was one order of magnitude smaller. The results showed that the dry density had a significant effect on the unsaturated hydraulic conductivity of the PCM. With the increase in dry density, the unsaturated hydraulic conductivity of the PCM decreased.
The unsaturated hydraulic conductivity of the PCMs with a dry density of 1.60 g/cm3 and different particle sizes ranged from 1×10− 12 m/s to 1×10− 14 m/s (see Fig. 13). With the increase in particle size, the unsaturated hydraulic conductivity increased. Comparing the variations in Figs. 12 and 13, it could be found that the effect of dry density on the unsaturated hydraulic conductivity was greater than that of particle size.
4.4 Influence mechanism of SWCC and hydraulic conductivity
There are two types of pores in bentonite, i.e. inter-aggregate pores and intra-aggregate pores in the PCM, as shown in Fig. 14 (Lloret and Villar 2007; Agus et al. 2010). The pores with pore sizes larger than 0.2 µm are inter-aggregate pores, while those with pore sizes smaller than 0.2 µm are intra-aggregate pores. Figure 15 shows the pore size distribution curves of the PCWs with different dry densities and a particle size of 0.5–1 mm after the SWCC tests. The PCM presented a bimodal pattern in which the intra-aggregate pores and inter-aggregate pores were dominant. The first peak corresponded to the pore size of 0.06 µm, which was the pore size of the intra-aggregate pores. Compaction did not affect on it, and it did not vary with the dry density. The pore size corresponding to the second peak was 12 µm, which was the pore size of the inter-aggregate pores. With the decrease in dry density, the size and number of the inter-aggregate pores increased.
The inter-aggregate pores have a great impact on the low suction (Fredlund and Rahurdjo 1993; Hoffmann et al. 2007; Wang et al. 2013). The PCM with low dry density had a lot of large inter-aggregate pores. It could store a large amount of free water and capillary water in the saturated state, and had a high water content in a high saturation state (low suction range). Due to compaction, the size and number of the inter-aggregate pores in the PCM with a high dry density became smaller, and the water content was low at high saturation. In addition, within the high suction range, the pores affecting the water retention and suction are the intra-aggregate pores (Fredlund and Rahurdjo 1993; Hoffmann et al. 2007; Wang et al. 2013). With the variation of dry density, the size and number of intra-aggregate pores remained unchanged. And in the high suction range, pore water is mainly adsorbed on the mineral surface by intermolecular forces, and compaction can hardly vary the influence of mineral adsorption capacity on water (Fredlund and Rahurdjo 1993). Therefore, in the high suction range, the dry density had little effect on the SWCC of the PCM. Since compaction has no significant effect on the size and number of the intra-aggregate pores in bentonite powder compacted samples after the SWCC test (Zhang et al. 2014), it can be inferred that the compaction has no obvious effect on the size and number of the intra-aggregate pores in bentonite pellets after the SWCC test.
After the SWCC test, the microstructures of the PCMs with a dry density of 1.60 g/cm3 and different particle sizes are shown in Fig. 16. During the saturation process of the PCM, the high-density bentonite pellets in the PCM were not homogeneous with the surrounding bentonite powder. The results showed that the water molecules did not completely enter into the laminated body of the high-density bentonite pellets, and the internal aggregates of the high-density bentonite pellets did not fully swell, which had the potential of continuous swelling and healing. The microstructure of the saturated FoCa PCM and MX-80 PCM were tested, and similar conclusions were obtained (Pusch et al. 2003; Van Geet et al. 2005). Moreover, the bentonite pellets were not in contact with each other, but were suspended in the bentonite powder and wrapped by the bentonite powder. The interface between the bentonite pellets and powder had no noticeable shrinkage and cracking, indicating that the PCM is effective as a sealing material for the HLW disposal.
The SEM images were binarized to obtain the apparent porosity and average pore area. When the particle size was 1–2, 0.5–1, and 0.25–0.5 mm, respectively, the apparent porosity of the PCM at 500 times magnification was 4.1, 4.5, and 4.7%, respectively, and the average pore area was 138, 112, and 102 µm2, respectively. According to the pore size in the SEM images, the pores corresponded to the inter-aggregate pores. Therefore, under the same dry density, as the particle size decreased, the total volume of the inter-aggregate pores did not change significantly, but the average area of the inter-aggregate pores decreased from large to small, thus the water flow of the inter-aggregate pores became more inconvenient and the water retention of the PCM increased. In other words, in the low suction range, the smaller the particle size, the higher the water content of the PCM when the suction was the same. In addition, for the sample preparation of the PCM with the same dry density, the compaction effect was different due to the different particle sizes. However, it was previously found that the compaction had no significant effect on the size and number of intra-aggregate pores in the bentonite powder compacted samples and bentonite pellets after the SWCC test. And the dry density and microstructure of bentonite pellets with different particle sizes before compaction were all consistent. Thus, under the same dry density and different particle sizes of the PCMs, the intra-aggregate pores in the bentonite pellets and bentonite powder were identical. In the high suction range, the particle sizes had little effect on the water retention of the PCM.
After the SWCC test, the PCM was unsaturated, and its microstructure could also be used to analyze the influence mechanism of the unsaturated hydraulic conductivity. The increase in dry density decreased the size and number of inter-aggregate pores in the PCM under compaction, and the intra-aggregate pores did not vary significantly. Therefore, in general, the increase in dry density of the PCM led to the deterioration of pore connectivity, thus the hydraulic passage per unit section decreased, the unsaturated hydraulic conductivity decreased, and the impermeability increased. Furthermore, with the increase in particle size, although there was no obvious variation in the intra-aggregate pores of the PCM, the area of the inter-aggregate pores increased, resulting in the better connectivity between the inter-aggregate pores and the increase in the hydraulic passage per unit section. Therefore, the unsaturated hydraulic conductivity of the PCM increased and the impermeability decreased.