## 2 Modified Porosity of Smectite as a Function of Temperature
### Smectite Shrinkage and Swelling Caused by the Hydration State of the Interlayer  
[PERSON] and [PERSON] [43] and [PERSON] and [PERSON] [44] proposed a porosity (\(\phi\)) modified equation for porosity based on the hydration state of smectite [39]. The porosity of soil is defined as  
\[\phi\equiv\frac{V_{v}}{V_{T}}=\left(\frac{M_{p}}{\rho_{w}}\right)/\left( \frac{1}{\rho_{b}}\right)=\left(\frac{W_{c}M_{s}}{\rho_{w}}\right)\rho_{b} \tag{11}\]  
where \(\phi\) is porosity, \(V_{v}\) is void volume of soil (cm\({}^{3}\)), \(V_{T}\) is bulk volume of soil (cm\({}^{3}\)), \(M_{p}\) is mass of water released through heating per unit mass of soil (g), \(M_{s}\) is mass of dry soil after dewatering through heating per unit mass of soil (g), \(W_{c}\) is ratio of water mass to dry soil mass, \(\rho_{w}\) is pore water density (g/cm\({}^{3}\)), and \(\rho_{b}\) is soil bulk density (g/cm\({}^{3}\)). \[\left\{ \begin{array}{c}M_{p}+M_{s}=1\\ W_{c}=\frac{M_{p}}{M_{s}}\end{array} \right.\quad\Rightarrow\ M_{s}=\frac{1}{1+W_{c}} \tag{12}\]  
[PERSON] and [PERSON] [43] argued that traditional porosity determinations for smectite-bearing sediments can be corrected through partitioning H\({}_{2}\)O between pore spaces and smectite interlayers. Interlayer water may be vaporized through heating in such a manner that the definition of smectite porosity in (11) may overestimate porosity. The modified porosity equation of hydrous smectite is expressed as  
\[\phi_{\alpha}=\frac{\rho_{b}\left(\frac{\varphi\rho_{w}}{M_{s}\rho_{b}}-\frac {A\alpha}{1-\alpha}\right)}{\rho_{w}\left(1+\frac{\varphi\rho_{w}}{M_{s}\rho_ {b}}\right)} \tag{13}\]  
where \(\alpha\) is the mass fraction of interlayer H\({}_{2}\)O in the hydrated smectite, and \(A\) is the ratio of the heated dry smectite mass to the heated dry soil mass. Approximate nominal values of a for fully hydrated smectite in subsurface systems are 0.1, 0.2, and 0.25 for smectite hydrates with interlayer spacings of 12.6, 15.7, and 18.3 A, respectively [43; 44]. The physical interpretations of buffer porosity (\(\phi\)) and modified porosity of smectite in the hydrous state at \(\alpha 1\) and \(\alpha 2\) (where \(\alpha 1>\alpha 2\), \(\phi>\phi_{\alpha 2}>\phi_{\alpha 1}\)) are as follows. The term \(\phi\) is measured by vaporizing the interlayer water, and thus overestimates the buffer void volume and yields the largest porosity. A higher hydrous state of smectite refers to the presence of interlayer water of greater void volume and smaller porosity, and vice versa. Thus, the difference in porosity (\(\Delta\phi\)) between the hydrous states \(\alpha 1\) and \(\alpha 2\) of smectite is:  
\[\Delta\phi=\phi_{\alpha 2}-\phi_{\alpha 1} \tag{14}\]  
The interlayer water transforms into pore water because of smectite dehydration, which could cause temporary overpressure within the buffer material. Thus, the dissipation of excess pore pressure could cause bentonite consolidation and induce compression of the buffer. By contrast, smectite rehydration occurs because of lower buffer temperatures. Swelling pressure during rehydration could cause the expansion recovery of smectite volume. Thus, buffer volume (V\({}_{\text{buf}}\)) caused by dehydration/rehydration can be defined as the difference in porosity (\(\Delta\phi\)) multiplied by the earlier volume (V\({}_{\text{ear}}\)):  
\[\text{V}_{\text{buf}}=\Delta\phi\times\text{V}_{\text{ear}} \tag{15}\]  
Initially, the buffer is not saturated. The bentonite buffer is in contact with groundwater when the repository operation begins, which causes complete wetting of the smectite clay in the bentonite buffer. The basal spacings of the smectite hydration state are assumed to be approximately 15.7 A (two layers of water molecules) in repository operations of the subsurface hydrogeological environment. However, [PERSON] et al. [41] asserted that at 30 \({}^{\circ}\)C, the largest number of layers occurs in a two-layer state.