A swelling pressure cell for X-ray diffraction test

Multi-barrier systems in geological disposal projects are being considered in many countries as a solution to dispose of high-level radioactive waste or spent nuclear fuel (e.g. JNC, 1999; SKB, 2011; Posiva, 2012; METI, 2018). Bentonite, a montmorillonite-rich clay, is widely selected as a candidate material for buffer and backfill materials of the multi-barrier system in Japan because of its low permeability, swelling properties and so on (JNC, 1999). As a parameter for system design, the pressure generated during water absorption of compacted bentonite under the swelling deformation confined condition has been studied extensively (e.g. Pusch, 1980; Sridharan et al., 1986; Komine, 2004; Villar & Lloret, 2008; Tanai et al., 2010; Wang et al., 2012). Herein, the present authors designate the pressure measured for deformation-confined bentonite as apparent swelling pressure (p_s) with the consideration that p_s represents a combination of forces between montmorillonite layers (Warkentin, 1962; Viani et al., 1983) and interactions between montmorillonite particles and non-swelling particles in bentonite. Swelling of montmorillonite has long been known to be the result of water molecule penetration into the interlayer space of montmorillonite and associated basal spacing (d₀₀₁) increase of the sheeted tetrahedral–octahedral–tetrahedral structure (Foster et al., 1954; Norrish, 1954; Fink et al., 1968; Moore & Hower, 1986; Iwasaki & Watanabe, 1988; Watanabe & Sato, 1988; Olis et al., 1990; Sato et al., 1992; Yamada et al., 1994; Moore & Reynolds, 1997; Morodome & Kawamura, 2009, Wang et al., 2020a, 2020b). As shown in Fig. 1(a), swelling of montmorillonite can be classified as osmotic swelling or crystalline swelling. Osmotic swelling relates to diffusions of water molecules due to a concentration difference of exchangeable cations. It has been said (Norrish, 1954; Meleshyn & Bunnenberg, 2005), on the one hand, that osmotic swelling starts from d₀₀₁ = ∼4·0 nm and d₀₀₁ linearly increases with an increase in water content (w). On the other hand, crystalline swelling relates to the hydration of different types of exchangeable cations in the interlayer space and d₀₀₁ increases stepwise, usually up to 1·9 nm, with an increase in w. As illustrated in Fig. 1(b), each step corresponds to a certain arrangement of water molecule (L) from zero layer (0w) to three layers (3w). For both swelling cases, attempts were made to correlate the force between montmorillonite layers with d₀₀₁ using either experimental or theoretical approaches (Warkentin, 1962; Viani et al., 1983; Afzal et al., 1984; Lubetkin et al., 1984; Israelachvili, 2011). However, p_s estimation for compacted bentonite with consideration of d₀₀₁ (or force between montmorillonite layers) behaviours and interactions between montmorillonite particles and non-swelling particles seems to be difficult. Most studies have specifically emphasised p_s at an equilibrium state (e.g. Pusch et al., 1990; Komine, 2004; Kyokawa et al., 2020).

With the objective of providing a useful tool to correlate d₀₀₁ with p_s, this paper presents a swelling pressure cell working on X-ray diffractometers, by which p_s and d₀₀₁ are visible simultaneously. A few similar devices have been developed. Warr & Berger (2007) simultaneously observed d₀₀₁ and water absorption of bentonite specimens with initial dry density up to 1·15 Mg/m³, although p_s was not measured. Takahashi et al. (2015) measured p_s and d₀₀₁ simultaneously for bentonite specimens with initial dry density up to 1·88 Mg/m³, but p_s measurement apparently did not fully match the results of observations conducted by other studies. Moreover, about a month was necessary for each test with the device reported by Takahashi et al. (2015). With the cell introduced in this study, both p_s time histories and d₀₀₁ evolution during water absorption of a compacted bentonite were well observed. The test duration was less than 1 day. The initial dry densities of prepared specimens in the testing programme were up to 1·7 Mg/m³, a comparable value to that of design in the geological disposal project (JNC, 1999). Another test programme was also conducted to measure p_s only by the cell, for which the testing duration for each specimen was also less than 1 day and similar results to those from past studies were obtained.

Commercial bentonite Kunigel V1 (K_V1), which is a sodium (Na)-type bentonite powder and a candidate material for use in Japanese geological disposal projects, was used for all tests conducted for this study. The montmorillonite content was about 50%. The initial water content (w_i) in the laboratory environment (relative humidity = ∼50%, temperature = 23°C) is about 7–9%. Other details are provided in an earlier report (Wang et al., 2020a). Obtaining a very precise value for specific gravity (G_s) of K_V1 seems not to be easy. A test programme was conducted to measure G_s using the pycnometer method based on JGS (2009), with about 50 samples divided into seven groups (tests in the same group were conducted in the same period). The sample mass for each test was reduced to 1·8–6 g, which is ∼10 g recommended by JGS (2009) for clayey soils with the 100 ml pycnometer. This is necessary because the pore air could not be removed easily from K_V1 during tests for a mass greater than 6 g. To remove pore air, samples were first immersed in about 70–80 ml distilled water in pycnometers. Then negative pressure of ∼ 100 kPa was applied for several days. A balance with resolution of 0·1 mg was used for mass measurements in most tests. It was found that water absorption during cooling of the oven-dried samples in the dissector might cause significant G_s value variation. So sample containers were sealed with rubber plugs during cooling for samples in groups 2–5. Results are presented in Fig. 2, where the group number and period for negative pressure application are indicated in the key. Although many efforts and much care were devoted to this test programme, G_s values are widely scattered. It seems that G_s becomes larger for sample masses less than 2·5 g, which might be partially affected by the mass measurement error and mass loss during tests. Negative pressure applications for one day (group 7) seem to be insufficient for removing pore air, although the data variation is less than those in other groups. Additionally, detailed test procedures for samples in the same group were kept almost identical, by which variation in each group implies that material heterogeneity might naturally exist. Nevertheless, G_s = 2·8 was adopted in this study.

The fundamental idea of powder X-ray diffraction (XRD) for clay is that XRD occurs at a specific incident angle (θ_pk) when parallel X-ray beams scan the specimen, as illustrated schematically in Fig. 3(a). This angle reflects the molecular structure of phyllosilicates. By collecting diffracted signals at different angles (2θ), a diffraction peak become visible at θ_pk. The value of d₀₀₁ is calculable using Bragg's law as d₀₀₁ = λ/2sin θ_pk, where λ represents the wavelength of the incident wave ( = 0·15418 nm for Cu Kα). Figures 3(b) and 3(c) depict the swelling pressure cell placed on an X-ray diffractometer stage; Figs 3(d) and 3(e), respectively, depict a plan view and cross-section view of the cell. To achieve X-ray scanning while measuring p_s, the cell includes three main components: a base plate, a middle plate and a top plate. A pressure sensor with diameter (ϕ) of 6 mm was installed at the centre of the base plate. A filter paper and a stainless mesh, as media to transport water to the specimen from water groove, were placed between the specimen and the base plate. Two water inlets connected to a cylindrical water groove were designed: one connected to the water supply bottle; the other connected to a tube for water level observation in the water bottle. The specimen with ϕ of 28 mm and thickness (t) of 2 mm was confined in a stainless specimen ring. This specimen ring was fixed to the middle plate, where a polyester film (t = 6 μm) and a beryllium (Be) plate (t = 0·1 mm) were placed above the specimen. Be plates are often used as X-ray windows because of their high X-ray transmission and mechanical strength. The present authors found that the Be plate can be eroded by wetted bentonite; therefore, the polyester film was further added. For the middle plate, several X-ray tunnels (i.e. slits) were reserved. The tunnel height was about 4 mm, which ensures X-ray passage from 2θ = 0−19°. Apparently, confinement is weaker at the tunnelling area, so the top plate was added to reduce the specimen deformation. Note that water is not sealed for this cell, while no apparent leakage was observed if the water level in the water bottle was not higher than the middle plate surface.

Figure 3 is the latest version of the cell; yet some technical issues found during the development of the cell are worth presenting. The initial version of the middle plate had only one wide tunnel for the passage of X-rays, as presented in Fig. 4. With this plate, some tests were conducted to measure p_s. For case C1, a stainless plate (t = 0·3 mm) was used to confine swelling deformation. For case C2, another stainless plate (t = 2 mm) was fixed to the X-ray tunnel area. For case 3, the middle plate was replaced by a stainless plate (t = 4 mm). K_V1 specimens with initial dry density (ρ_di) of ∼1·50 Mg/m³ were prepared. The results are presented in Fig. 4. Apparently, p_s time history curves obtained in cases 1 and 2 differ from those in case 3. In case 3, p_s experiences four stages during wetting: it first increases sharply to a maximum (peak swelling pressure, p_p), drops to a minimum (valley swelling pressure, p_v), climbs to another maximum (initial swelling pressure for equilibrium, p_ei) and finally reaches an equilibrium state (equilibrium swelling pressure, p_eq). The expressions just given in parentheses are the names of feature points of the p_s curve for convenience, as shown also in Fig. 4. These features have often been observed in past studies, although specimens were often of ϕ = 28–60 mm and t = 10–20 mm (e.g. Pusch, 1980; Komine, 2004; Sun et al., 2013; Wang et al., 2020a). For cases 1 and 2, p_p and p_v are not observed clearly. The reason for the drop in p_s is explained in later sections, whereas, under the weaker confining conditions in cases 1 and 2, large swelling deformation seems to be responsible for invisibility of p_v and for markedly smaller p_eq. With the latest version of the cell, feature points can be observed clearly, as described in later sections.

In considering that the water supply system (groove, filter paper and mesh) in Fig. 3 might not transfer water uniformly to the central part of the specimen, the water content (w) distribution was measured for some specimens after the tests in Fig. 4. The w measurements are presented in Fig. 5. Three specimens in cases C1 and C2 were cut using a circular cutter into three parts, for which w at the centre part is 1–3% higher than other parts. The higher w at the centre part would be attributed to relatively higher swelling deformation when compared to other parts. One specimen in C3, for which the test was terminated when p_s approached p_ei, was cut into five parts, where the w difference was about 3%. However, it seems w at the centre is not necessarily lower than other parts. This difference might also be affected partially by the w measurement accuracy for small samples. Fig. 5 suggests that the current water supply system might induce w distribution variation up to ± 1·5%. Data are not available for comparison with other water supply systems, while the fact observed during tests that p_s increased immediately after water supply implies that the system might not affect p_s measurement to any great degree.

Another technical issue is related to effects of the Be plate and polyester film on the X-ray profile. For parallel beam XRD, in principle, the Be plate and polyester film placed on the specimen top surface (Fig. 3) would not affect the θ_pk position. Some tests were conducted to confirm that fact. Fig. 6(a) shows three X-ray profiles of a compacted K_V1 specimen with w = 7·2% (i.e. water content in the laboratory environment). The top profile was obtained when the specimen was not covered by a Be plate. For the middle one, a Be plate (t = 0·3 mm) was placed on the specimen top surface and the vertical axis origin of the diffractometer (z = 0) was set at the specimen surface. For the bottom one, z = 0 was set at the Be plate surface (default setting for the diffractometer). Note that the y-axis scales of profiles were arbitrarily adjusted for visual convenience (i.e. arbitrary scale) for Fig. 6(a) and other figures without showing the y-axes. Compared to 2θ_pk of the top profile, 2θ_pk is 0·05° smaller for the middle one and 0·25° smaller for the bottom one. In terms of d₀₀₁, they are, respectively, 1·26 nm, 1·27 nm and 1·30 nm. Figure 6(b) shows another example for a K_V1 specimen with w = 51·3%. The specimen was covered by a polyester film to avoid water evaporation during scanning to obtain the top profile. Then either a t = 0·1 mm or a 0·15 mm Be plate was added to obtain the other two profiles (z = 0 at the specimen surface). The value of 2θ_pk increases from 4·58° to 4·63° by adding Be plates, which is opposite to that in Fig. 6(a). The reason remains unclear, but instrumental error at a small angle and broad peak for clayey minerals are possible reasons. The fact that background noise makes an exact determination of the θ_pk position difficult is also a possible reason. For this study, z = 0 was set at the specimen surface, except when presented specifically otherwise. Also, Fig. 6(b) shows that the peak at 2θ_pk = 2·3° cannot be observed clearly by adding Be plates, although it was improved by placement of a thinner plate (i.e. 0·1 mm).

An example demonstrating the effect of a polyester film (t = 6 μm) on a K_V1 specimen with w in a laboratory environment (i.e. it is expected that evaporation can be ignored during scanning) is presented in Fig. 6(c). Results show that 2θ_pk is 0·04° smaller by adding the polyester film. In addition, Fig. 6(d) presents results for a K_V1 specimen with w = 47·1%. The profile was taken first for the case without the polyester film; then the film was placed for another profile. During the first scanning, w would be smaller somehow because of water evaporation (i.e. scanning time was ∼2·5 min), which is expected to result in a larger 2θ_pk during later scanning. However, 2θ_pk, after covering with polyester film, moves from 4·66 to 4·57° (i.e. ∼0·1° smaller) and from 2·45° to 2·25° (i.e. ∼0·2° smaller). Be plate or polyester films (e.g. Mylar film) as an XRD window have often been used to maintain constant water content (Foster et al., 1954; Fink et al., 1968; Ravina & Low, 1972; Viani et al., 1983; Zhang & Low, 1989). However, the present authors were unable to ascertain any particular reasons for the results in Fig. 6. In this study, the film continued to be used in all tests described in later sections to avoid water evaporation and Be plate erosion, although the measured 2θ_pk might differ slightly from its true value.

X-ray scanning was conducted during water absorption while measuring p_s for four compacted K_V1 specimens (hereinafter termed the XRD-p_s test). The specimen and diffractometer information are presented in Table 1. The K_V1 was first oven-dried at 110°C for 24 h, and then it was statically compacted into the specimen ring using a jack. The final dry density (ρ_df) was estimated from the p_s measurement, as explained in later sections. An X-ray diffractometer (RINT-TTR III, Rigaku Corp.) with a parallel Cu Kα beam (source power: 50 kV and 300 mA) was used for this study. Note that the parallel beam, which was developed based on a multilayer technique recently (Harada, 2003), should have a better performance than Bragg–Brentano geometry (BB geometry), which is a popular geometry in powder XRD, in terms of accuracy for low diffraction angles; this is because BB geometry involves some assumptions that are expected to induce more measurement error (e.g. Dinnebier & Billinge, 2008). Scanning speed was 1°/min initially because the profiles changed rapidly at the initial stage of water absorption. This was changed to 0·5 or 0·2°/min later for smoothing profiles. For each test, an initial profile before water supply was taken. After achieving p_eq, the specimen was taken out and scanned by removing the Be plate (the polyester film was retained), and this is assigned as the final profile. All X-ray scanning angles were between 2θ = 0·8 and 10° by rotating incident and detector sides and keeping the specimen horizontal (Fig. 3); this scan range was chosen because the XRD peak of montmorillonite in this range is much easier to distinguish than the one between 2θ = 60 and 65° (e.g. Ravina & Low, 1977).

In addition to the XRD-p_s test, a series of swelling pressure tests were also conducted with the pressure cell, for which X-ray scanning was not applied. In this testing programme, the cell was simplified further as illustrated in Fig. 7. The middle plate, mesh and filter paper were removed. Instead, membrane filters (t = 0·14 mm) with 0·45 μm pore size were used (Wang et al., 2017). The testing programme is shown in Table 2. Four pressure cells were used to conduct tests simultaneously as a group; seven groups were examined. Specimens were prepared similarly by static compaction. The specimen surfaces were trimmed after compaction to leave an equal thickness to that of the specimen ring. All mass measurements were conducted on a balance with a resolution of 0·1 mg. All length measurements (e.g. t and ϕ of specimen ring) were accurate to 1 μm. The initial dry density (ρ_di) was calculated as M/V/(1 + w_i/100), where M and V, respectively, represent the specimen mass and the specimen ring volume. To estimate the specimen dry density after tests (ρ_df), the t value of the cell (i.e. distance between centres of the top surface of the top plate and the bottom surface of the base plate) was measured immediately before water supply and before dismantling the cell using a micrometer, and the t values of the membrane filters were also measured before and after tests. The relations between measured p_eq and t changes of the cell and membranes are shown in Fig. 8. The pressure cell expansion is linearly proportional to p_eq; membrane filter compression is a quadratic function relation with p_eq. Both pressure cell expansion and membrane filter compression were regarded as results of specimen swelling deformation and were considered in the ρ_df calculation. The pressure cell expansion for group 3 and the membrane filter compression for group 1 were not measured, but were estimated using the relations in Fig. 8.

Figure 9 presents results of the XRD-p_s test obtained for four specimens. Each figure part (Figs 9(a)–9(d)) has three components: the p_s time history at the top, typical profiles at the bottom, and an inset graph. The XRD scanned points are indicated on the p_s curve by empty circles and numbered from no. 1, which is the initial profile before supplying water. The closest profiles to the feature points (p_p, p_v, p_ei and p_eq) of the p_s curve are also shown. Typical profiles show that the profile peak starts from 2θ_pk = 9°, which corresponds to a d₀₀₁ value of 0·98 nm. The peak moves to 2θ_pk = 7° (d₀₀₁ = 1·26 nm) immediately after water supply. Thereafter, it moves to 2θ_pk = 5·6° (d₀₀₁ = 1·58 nm) and 2θ_pk = 4·7° (d₀₀₁ = 1·90 nm). Here, as also shown in Fig. 1(b), d₀₀₁ = 0·98 nm, 1·26 nm, 1·58 nm and 1·90 nm are typical values observed in past studies, which were interpreted as four hydration states of exchangeable ions or states with 0 − 3 layers of water molecules (i.e. layer of water L = 0w, 1w, 2w and 3w, respectively) in the interlayer space of montmorillonite (e.g. Moore & Hower, 1986; Watanabe & Sato, 1988; Sato et al., 1992; Yamada et al., 1994; Morodome & Kawamura, 2009; Wang et al., 2020a). Between two consecutive L states, transition profiles are observed either as very broad peaks (e.g. no. 3 in Fig. 9(a)) or bimodal peaks (e.g. no. 9 in Fig. 9(a)). These transition states are expected to be very short in terms of w range because, in most cases, unimodal peaks with 2θ_pk at one of four L states were observed for K_V1 with different w (Fig. 1(b)). With these transition profiles, intensity growth at L = 2w and L = 3w are clearly visible, implying heterogeneity (i.e. co-existence) of L states during water absorption (Cases et al., 1992; Ferrage et al., 2005; Warr & Berger, 2007; Holmboe et al., 2012).

After reaching the maximum intensity at 2θ_pk = 4·7° (no. 16, 16, 17 and 24 for Figs 9(a), 9(b), 9(c) and 9(d), respectively), the reductions associated with intensity increase at 2θ = 2–3° (inset figures). These intensity increases become weaker as the specimen density increases. For the ρ_di = 1·70 Mg/m³ specimen, only a very small reduction at 2θ_pk = 4·7° and increase at 2θ = 2–3° are observed. The final profiles (i.e. profiles after removing swelling pressure and Be plate at the end of the tests) are also added to the inset figures. Note that the final profiles are of different intensity scale from those obtained during water supply. Bimodal peaks at 2θ_pk = 4·7° and ∼2·2° (d₀₀₁ = ∼4·0 nm) are observed from these final profiles, of which the major peak in terms of intensity magnitude changes from 2θ_pk = ∼2·2° to 2θ_pk = 4·7° as the specimen becomes denser. It is expected that the intensity growth at 2θ = 2–3° during water absorption corresponds to peaks 2θ_pk = ∼2·2° on the final profile, which is evidenced by Fig. 6(b). The initiation time of the peak at 2θ_pk = ∼2·2° is not clear, while from the evolution process of the peak from 2θ_pk = 5·6° to 2θ_pk = 4·7°, where no clear peak at 4·7° exists before the peak intensity at 5·6° reaches its maximum, one might infer that the peak component at 2θ_pk = ∼2·2° is not significant before the peak intensity reaches its maximum at 4·7°.

The p_s position corresponding to profiles with maximum intensities at 1w, 2w and 3w are shown on the p_s curve. It is revealed that during movement of the profile peak from 0w to 1w, p_s reaches p_p for relatively loose specimens, while p_p is reached during profile peak movement from 1w to 2w for relatively dense specimens. The p_v appears as the profile peak moves from 2w to 3w; p_ei in most cases is achieved after the profile peak reaches maximum intensity at 3 w, while as the specimen density increases, p_ei may also appear before that. It is clear from Fig. 9 that d₀₀₁ monotonically increases during water absorption, whereas p_s drops to p_v and then increases again to p_ei. It is implied that p_s reduction would be a result of interparticle force reduction rather than force reduction between montmorillonite crystalline layers. These behaviours may be explained schematically by Fig. 10, wherein the montmorillonite particle is symbolised by a spring with arrows and the arrows indicate interparticle force. Initially, the skeleton of non-swelling particles maintains its initial configuration and p_s increases due to swelling of montmorillonite. When p_s reaches a certain magnitude, some particles may move to less stressed positions, which results in a reduction in p_s (i.e. reduction of interparticle force). When the stress environment inside a specimen becomes uniform, further swelling of montmorillonite causes instances of p_s increasing again. With these considerations, a relatively wider p_v area (or longer duration around p_v) for a looser specimen (e.g. Fig. 9(a)) is reasonable, since particle movement can be more active in a relatively larger void space compared to a denser specimen. The last profiles during water supply and the final profiles were extracted and are plotted in Fig. 11. It can be observed that 2θ_pk at 3w is about 0·05° smaller by removing the Be plate and p_s, which would be a result of the Be plate effect on 2θ_pk (i.e. d₀₀₁ did not increase significantly at 3w by releasing p_s), as illustrated in Fig. 6(b). This observation also suggests that montmorillonite swelling up to 3w should not have been obstructed during water absorption.

As described in Fig. 1, swelling of montmorillonite was classified into crystalline swelling and osmotic swelling at d₀₀₁ = ∼4·0 nm (Norrish, 1954; Meleshyn & Bunnenberg, 2005). According to the authors surveyed, this classification was mainly based on the observed stepwise or linear relation between d₀₀₁ and w, thus no clear evidence is available to define montmorillonite behaviours for d₀₀₁ between ∼1·9 nm and ∼4·0 nm, because peaks on X-ray profiles corresponding to this range were rarely clearly observed (Anderson et al., 2010). This gap (i.e. d₀₀₁ between ∼1·9 nm and ∼4·0 nm) was called the forbidden basal spacing by Ravina & Low (1977). Meleshyn & Bunnenberg (2005) studied the mechanism of the forbidden layer spacing of a Na-montmorillonite by the Monte Carlo approach, from which they concluded that a special chain structure would exist between Na ion and water molecule formed at d₀₀₁ = ∼1·9 nm. The structure locked further increase of d₀₀₁ until w increased to a critical level. When w increased further, those chain structures broke, the interlayer space opened to absorb those water molecules and d₀₀₁ jumped to ∼4·0 nm. The forbidden basal spacing is important for this study because 2θ_pk at ∼2·2° (Fig. 11) indicates that the maximum d₀₀₁ (i.e. maximum swelling) for tested specimens under confined condition would be about 4·0 nm (the calculated d₀₀₁ from Fig. 11 is plotted in Fig. 1(b)). It seems from Fig. 1(b) that d₀₀₁ = 4·0 nm is also a step of crystalline swelling for w_f changes from 50·7% to 32·5% (i.e. d₀₀₁ has no clear increase with an increasing w). Together with observations that peak intensity at 2θ_pk = ∼2·2° becomes weaker compared to that at 2θ_pk = 4·7° as ρ_di increases (Fig. 11), and the peak component at 2θ_pk = ∼2·2° may not be significant before the peak intensity reaches a maximum at 4·7° (Fig. 9), even if swelling at d₀₀₁ = ∼4·0 nm is osmotic swelling, one can infer that crystalline swelling might play a major role in the evolution of p_s for the conditions tested.

As possible extensional studies based on the findings in this study, it is also possible to distinguish the water contents of each hydration state in the interlayer space using the technique of XRD profile simulation (Cases et al., 1992; Ferrage et al., 2005; Warr & Berger, 2007; Holmboe et al., 2012) or to predict the p_s curve by combining d₀₀₁ and interactions between swelling and non-swelling particles (Kyokawa et al., 2020).

Typical time histories of p_s are shown in Fig. 12, where ρ_df is presented above the curves. Feature points (p_p, p_v and p_ei) are observed clearly in most cases, but p_p and p_v vanish as ρ_df becomes higher than 1·67 Mg/m³. For these p_s curves, the point with a minimum slope during the initial increase is used as p_p and the point with minimum curvature between p_p and p_ei is used as p_v. Interestingly, the time to reach p_p (t_p) increases as ρ_df increases, whereas it is 1·5–1·7 h to reach p_v and ∼3 h to reach p_ei irrespective of ρ_df, except for some specimens with very small ρ_df. For specimens with ρ_df of less than 1·4 Mg/m³, p_s increases continuously after reaching p_ei, which is not observed for denser specimens. Similar results are also observed from XRD-p_s tests in Fig. 9. Nevertheless, the last p_s measurement was assigned as p_eq for all tested specimens.

Figure 13 portrays the relation between ρ_df and p_p, t_p, p_v and p_ei. The correlations are surprisingly good among all testing data and can be matched by an exponential equation. Similarly, Fig. 14 shows correlation between ρ_df and p_eq, which also suggests a good exponential relation. These relations in Figs 13 and 14 prove to be tools to predict values for feature points of p_s curves. Experimentally obtained results for K_V1 specimens with ϕ = 28 mm and t = 10 mm in Wang et al. (2020c) and specimens with ϕ = 60 mm and t = 20 mm in Tanaka & Watanabe (2019) are also added to Fig. 14. These data are very close to results obtained from the present study. For data reported by Wang et al. (2020c), filter paper compression caused by specimen swelling deformation was not considered in the ρ_df calculations, which may have caused slightly smaller ρ_df values for the same p_eq. Because p_eq increases exponentially with ρ_df, accurate estimation on ρ_df becomes extremely important when estimating p_eq for dense specimens. Additionally, as shown in Fig. 12, the time taken to reach p_ei is about 3 h for most t = 2 mm specimens, which is significantly shorter than the ∼3 days for t = 10 mm specimens in Wang et al. (2020c) and the ∼15 days for t = 20 mm specimens in Tanaka & Watanabe (2019). Tests with t = 2 mm specimens were normally terminated within 24 h, which is sufficiently short to conduct systematic studies to evaluate effects such as the type of bentonite, groundwater, temperature and so on on p_s behaviours. However, apparently, the particle size effect of target materials needs to be considered when employing this pressure cell. Finally, ρ_di and p_eq data measured in XRD-p_s tests are also shown in Fig. 12. Apparently, under the same p_eq, ρ_di is much smaller than ρ_df of specimens in swelling pressure tests. The value ρ_df of four specimens in XRD-p_s tests is estimated using the exponential fitting equation (Table 1). This estimation implies that dry density (ρ_d) may decrease as much as 0·27 Mg/m³ during water absorption for a specimen with ρ_di = 1·70 Mg/m³ in XRD-p_s tests. If this reduction was fully induced by the specimen thickness change, then t of the specimen would increase by ∼0·3 mm, which would seem to be too large. Another reason might be that swelling deformation is greater near the pressure sensor, resulting in density distribution variation.

Correlation between p_eq and w_f among all data, as shown in Fig. 15(a), also seems to be good, although the variation is slightly larger compared to the ρ_df and p_eq relation. The calculated degree of saturation (S_r) of all specimens is shown to Fig. 15(b), which suggests that most of the specimens may not be fully saturated. This is possible, considering observations reported by Wang et al. (2020a) that the w vertical distribution after water supply for 19 days for a t = 10 mm specimen was not uniform (i.e. higher w for the part close to water supply end, and vice versa), although p_eq was achieved in 7 days. Unsaturated conditions are expected to be a reason for worse correlation between p_eq and w_f than that between p_eq and ρ_df. The value S_r of some specimens exceeds 100%, which was often interpreted by the possibility of higher water density (ρ_w) than 1 Mg/m³ for water in the interlayer space of montmorillonite (Pusch et al., 1990; Villar & Lloret, 2004; Jacinto et al., 2012). Herein, another possibility is given: the experimental measurement variation. S_r can be expressed as

By taking a partial derivative, the following is obtained

By setting G_s = 2·8, ρ_w = 1 Mg/m³ and the true value of S_r = 100%, the upper boundary lines for calculated S_r for different ∂w, ∂ρ_d and ∂G_s are shown in Fig. 15(b). Also, ∂G_s and ∂w are set as respectively referring to Figs 2 and 5. For the present study, possible specimen swelling deformation was considered for the ρ_df calculation, while it was also found that membrane filter compression and pressure cell expansion were not very uniform, and that ∂ρ_d = up to 0·02 Mg/m³ would be possible. As shown in Fig. 15(b), S_r > 100% is also possible, even for ρ_w = 1 Mg/m³.

A swelling pressure cell was developed to measure apparent swelling pressure (p_s) as well as basal spacing of montmorillonite (d₀₀₁) simultaneously when compacted bentonite is wetted by distilled water. Test results show that this pressure cell can capture features of the p_s time history curve and d₀₀₁ well. Some technical difficulties remain, however, such as swelling deformation reduction of the dry density of tested specimens, and diffraction peak position changes induced by materials employed as X-ray windows (beryllium plate and polyester film). XRD measurements of initially oven-dried bentonite specimens show that d₀₀₁ moves from 0·98 nm to 1·26 nm, 1·58 nm, 1·90 nm and to ∼4·0 nm gradually as p_s experiences a sharp increase to the peak swelling pressure (p_p), then a drop to a valley swelling pressure (p_v) and another increase to the initial swelling pressure for equilibrium (p_ei), and finally with p_s reaching the equilibrium (p_eq). From these observations, it is concluded that crystalline swell of montmorillonite serves an important role in interpreting the p_s time history for tested specimens. The swelling pressure cell is also used to measure the p_s time history of compacted bentonite specimens that are 2 mm thick. Results suggest that the specimen dry density has a surprisingly good correlation with the feature points of the p_s time history (i.e. p_p, p_v, p_ei and p_eq), which provides a tool of feature point prediction. The test duration of the 2 mm specimen is less than 24 h, which is significantly shorter than those of past studies. Results show that the degree of saturation may exceed 100% of some bentonite specimens after water absorption, for which it can be pointed out that the reason for this might be higher water density in the interlayer space of montmorillonite, while variation in measurements is expected to be another possible source.

Some of this work was performed as a part of the activities of the Research Institute of Sustainable Future Society, Waseda Research Institute for Science and Engineering, Waseda University. Part of this study was supported by the Ministry of Economy, Trade and Industry (METI) of Japan and Waseda University Grant for Special Research Projects (project numbers: 2020C-647 and 2020C-039). Mr Takashi Yoshida and group members of the manufacturing laboratory of Waseda University, Kyowa Electronic Instruments Co., Ltd, Pascal Co. Ltd and Pall Corp. provided important technical support during apparatus development. All XRD tests were conducted and technically supported by the materials characterisation central laboratory, Waseda University (Izutani et al., 2016). Mr Kunlin Ruan provided valuable review comments. The authors express their deep gratitude to all those mentioned above.

0w, 1w, 2w, 3w

no layer, one layer, two layers or three layers of water molecules in the interlayer space of montmorillonite, respectively

d₀₀₁

basal spacing of montmorillonite

G_s

specific gravity

L

layers of water molecules in the interlayer space of montmorillonite

M

specimen mass

p_ei

initial swelling pressure for equilibrium on p_s time history

p_eq

equilibrium swelling pressure on p_s time history

p_p

peak swelling pressure on p_s time history

p_s

apparent swelling pressure of compacted bentonite during wetting

p_v

valley swelling pressure on p_s time history

S_r

degree of saturation

t

thickness

t_p

corresponding water absorption time for p_s to reach p_p

V

inner volume of the specimen ring

w

water content

w_f

final water content

w_i

initial water content

θ

half of the angle between the incident and diffracted X-ray beams of the diffractometer

θ_pk

diffraction angle of a mineral, which equals θ at the peak position of the X-ray scanned profile

λ

wavelength of incident X-ray beams (= 0·15418 nm for Cu Kα source)

ρ_d

dry density

ρ_df

final dry density

ρ_di

initial dry density

ρ_w

water density

ϕ

diameter