Abstract

In order to evaluate the long-term behaviour of the engineered barriers in geological disposal sites for transuranic element-bearing (TRU) waste, an evaluation by numerical analysis is required. Although chemical and hydraulic/mechanical analyses have been conducted independently until now, essentially both type of phenomena occur simultaneously and produce synergistic effects. Therefore, we focused attention on the buffer (bentonite) engineered barrier and conducted a study of which involved incorporating hydraulic/mechanical phenomena into the chemical analysis of bentonite alteration. The simulations employed weakly-coupled chemical and hydraulic/mechanical effects to study the behaviour in one dimension.

The results showed that the dissolution of the montmorillonite is suppressed in the buffer section nearest the cement material. Moreover, in order to achieve a fully coupled analysis in future, the present study also identifies issues that need to be resolved.

In order to carry out long-term safety evaluation of an artificial barrier for a transuranic element-bearing (TRU) waste repository, we have examined analysis methods to reduce uncertainties in safety evaluations. We analysed the chemical alteration of the bentonite engineered barrier material in a previous study, but did not consider the hydraulic/mechanical modeling of the materials. The bentonite in a geological repository must maintain very low hydraulic conductivity by swelling, and the mechanical and hydraulic properties of bentonite swelling may affect the evaluation of chemical alteration. In current research, the coupled analysis of hydraulic, mechanical and chemical (HMC) properties or thermal, hydraulic, mechanical and chemical (THMC) properties intended for the compacted bentonite have been examined (Xie et al., 2006; Zheng et al., 2010). However, there are few published papers concerning chemical analysis that have considered the mechanical effects on the alteration of the bentonite by the influence of hyperalkaline cement over a long term.

Therefore, in this paper, we add the effects of mechanical and hydraulics properties to the safety evaluation of conventional chemical alteration. In particular, we consider the effect of weak coupling by use of a coupled geochemical reaction/mass-transport code and a hydraulic/mechanical code.

The performance properties of bentonite relate to each other and there are many kinds of links. We consider part of these in this study and Fig. 1 shows the scope of our study. We considered four factors that are common parameters in the mechanical and chemical analysis among these links (upper part of figure). The lower part of the figure shows properties not considered in this study and show scope for the future studies. The model which we are using is straightforward and preliminary. However, we believe that we can identify potential problems by using this model.

Coupled Analysis Method

Normally, changes in the mechanical properties and the chemical alteration of bentonite take place simultaneously. However, a fully coupled analysis method is very difficult to solve accurately and quickly. In a coupled analysis, the governing equations are non-linear and a solution cannot be guaranteed. Moreover, even if equations can be solved, the calculation convergence time may be very long.

Therefore, for this study, we used a weakly-coupled analysis in order to allow the following: (1) shortened simulation time, despite the lower accuracy of the solution, and (2) development of analytical tools identifying separate chemical and hydraulic/mechanical model behaviours. The geochemical code used here was PHREEQC-TRANS (2005) and the hydraulic/mechanical code was DACSAR-MP (Kanazawa, 2010). The coupled analysis method for the hydraulics, mechanics, and chemistry is shown in Fig. 2.

It is necessary to select an appropriate technique because there are various methods for coupled analysis which range from weak coupling to strong coupling. A weakly-coupled method shortens the computation period but with less accuracy in the solution. Also, both tools for the chemical and hydraulic/mechanical analyses can be developed individually. On the other hand, a strongly coupled analysis provides no guarantee of obtaining a solution because non-linearity is expected to appear at the rule equation level. Even if a solution can be obtained, the strong non-linearity means that the time for solution convergence will be very long. One merit of this approach is that the solution is rigorous. However, if the convergent calculations are not completed, increasing the frequency at which data is exchanged in a weakly coupled analysis may attain a higher accuracy than that using a fully-coupled analysis. We therefore devised three methods that are shown in a schematic diagram of the coupled analysis used in the present study (Fig. 2). Iteration A addresses the re-distribution of stress that occurs during hydraulic disequilibrium caused by chemical alteration. Iteration B computes the re-distribution of stress, and then the chemical analysis is conducted when the calculation attains a dynamic equilibrium. Finally, Iteration C is an analysis in which the hydraulic and chemical analyses are not conducted during the convergent calculation for computing the re-distribution of stress, but are conducted after dynamic equilibrium is attained. All methods, Iterations A, B and C, are classified as weakly coupled analyses. Iteration A is the strongest coupled analysis among these three methods and appears to take a longer computation period. It is necessary, therefore, to examine the differences in the numerical solutions by the respective differences in the coupled analytical approaches and to attempt to increase the accuracy and optimize the analytical period.

In this study, we evaluate the long-term behavior of the alteration of the engineered barriers predicted by use of Iteration C.

Analysis Parameters and a Model

In this study we selected four common parameters: (1) content of montmorillonite, (2) Ca exchange rate, (3) void ratio, and (4) dry density as shown in Table 1. The considered each parameter is described in the analysis as follows.

Content of montmorillonite

The time change of the content of the montmorillonite in each mesh was calculated by a chemical analysis including the mass-transport, in consideration of the solution velocity. Because the relation between the swelling pressure and the density changes depends on the content of the montmorillonite (Kobayashi et al., 2011), the results of the chemical analysis are reflected in the hydraulic/mechanical analysis.

Ca exchange rate

The interlayer cation of Na-montmorillonite is exchanged from Na to Ca by Ca2+ eluted from the cement. The changes in relation between consolidation stress and void ratio which were used in the hydraulic/mechanical analysis was calculated based on the ratio of Ca-montmorillonite. The change in the hydraulic/mechanical characteristic according to the ratio of Ca-montmorillonite was estimated following Kobayashi et al. (2011).

Void ratio

In the hydraulic/mechanical analysis, the density was redistributed with the change in the mechanical characteristic, taking into account the content of montmorillonite and the Ca exchange ratio. Both had been obtained from the result of the chemical analysis. This hydraulic/mechanical analysis suggested that the density (i.e. void ratio) distribution in this result was assumed to result from the chemical analysis. We further restarted the chemical analysis. The void ratio in response to the dry density was calculated by the following equation:  
Void ratio:e=ρsρd1
(1)
where ρs: the density of soil particle, ρd: the dry density.  
e=ε(1ε)
(2)
where ε: porosity (-).

Dry density

The density (i.e. void ratio) distribution that had been obtained by this hydraulic/mechanical analysis result was reflected in that of a chemical analysis in the following way.

In the chemical analysis of bentonite alteration, the dry density changed with dissolution and precipitation of minerals in the bentonite. However, the change in the amount of the solid phases cannot be observed in the hydraulic/mechanical analysis. Therefore we reset the dry density in the chemical analysis. We fixed the whole quantity of the solid-phase to reproduce the distribution of the dry density. There are two parts of the buffer material, the upper and the lower, in our conceptual model of the analytical system. The upper part is decompressed and the lower one is compressed. In order to reflect this phenomenon, each part should be allotted appropriately. The specific amount of the lower buffer material is shown in Tables 2 and 3. Table 2 shows the result of the hydraulic/mechanical analysis of the lower buffer material over 1,000 years. The value used for a chemical analysis was calculated based on this dry density distribution by the following equations:  
ρMb=AMbx=1mLbx
(3) [in Table 2.1]
 
ρCb=ACbx=1mLbx
(4) [in Table 3.2]
 
ρCb=ρCb×ACbACb
(5) [in Table 3.3]
 
ρCbx=RρMbx×ρCb
(6) [in Table 3.4]
where

AMb=x=1mρMbx×Lbx; weight of lower part in hydraulic/mechanical analysis

AMu=y=1nρMuy×Luy; weight of upper part in hydraulic/mechanical analysis

ACb=x=1mρCbx×Lbx; weight of lower part in chemical analysis

ACu=y=1nρCuy×Luy; weight of upper part in chemical analysis

ACb=(ACu+ACb)×AMbAMu+AMb; weight that considers hydraulic/mechanical analysis

RρMbx=ρMbxρMb; ratio of dry densities of individual mesh

Conceptual model of the analytical system

We considered a one-dimensional horizontal cross-section of the repository for the conceptual model of the analysis system as shown in Fig. 3.

Figure 4 shows the process by which the bentonite is changed through chemical alteration and undergoes a dynamic change in its properties. First, the alkaline components such as Ca2+ and OH- ions infiltrate from the cementitious material into the bentonite. Then, montmorillonite dissolution, precipitation of secondary minerals, and the production of Ca-type montmorillonite occur in the bentonite (C).

Re-equilibrium of pressure occurs in the bentonite because the production of Ca-type montmorillonite causes a change in the degree of swelling (H/M). Because the ions are moved by mass transfer, Ca2+ and OH- ions infiltrate further into the bentonite. These steps are then repeated by iteration.

Results and Discussion

We first performed a hydraulic/mechanical analysis from unsaturated moisture conditions to saturation. The hydraulic/mechanical analysis that was conducted until re-saturation showed that dry density had a heterogeneous distribution at the saturation point. We set this distribution as the initial condition for the chemical analysis. As a reference case, we also conducted another analysis that set a homogeneous distribution for the initial conditions.

The solid phase composition distribution is shown in Fig. 5 (initial) as the changes in analysis results after 2000 (Fig. 6) and 5000 (Fig. 7) years. In each figure the results for the case of only chemical analysis (the reference case) in the left-hand column are presented; the results for the case of weakly coupled analysis are in the right-hand column.. The simulation period for these two analyses was set to 10,000 years, and data were applied to the chemical analysis and hydraulic/mechanical analysis at 1000, 2000, 3000 and 5000 years. The amount of Na-type montmorillonite in the buffer decreases at the surface in contact with the cementitious material, whereas the amount of Ca-type montmorillonite increases. A comparison of both cases shows few differences.

The hydraulic conductivity of the buffer material was calculated by using the amount of montmorillonite, the ratio of Na-type montmorillonite, and the composition of the interstitial water included in the bentonite. The calculation is expressed as follows:  
Hydraulic conductivity of bentoniteK=101.30Ciesme3.48CiK0However,Ci101.49ESP1.0K101.63esme0.24K0andK10105K0=(0.911.57ESP+2.00ESP2)×1013×esme7.445.69ESP:esme7.0K0=(0.911.57ESP+2.00ESP2)×1013×7.07.445.69ESP(esme7.0)11.4:7.0<esmeHowever,K0ESP=1K0105

Ci: Equivalent ion concentration of pore water ESP: Exchangeable Na proportion in bentonite esme: Smectite void ratio

Figure 8 shows the change in hydraulic conductivity over time, as calculated by this expression. In the case of the non-coupled analysis (the reference case), the distribution of hydraulic conductivity shows a gradual increase after about 3500 years at a location near the boundary with the cementitious material. On the other hand, in the case of the weakly coupled analysis, hydraulic conductivity remained small compared with the values from the reference case.

Figure 9 shows how the hydraulic conductivity changes over time for meshes that range from mesh 1 on the rock side to mesh 8 on the waste side. Mesh number 8 on the waste side had the largest value, and the hydraulic conductivity grew in the areas where it came into contact with the cementitious material. Also, the hydraulic conductivity increased smoothly in the case of chemical analysis only. In the other case in which mechanical behavior was also considered, the hydraulic conductivity shows inflection points because data are being passed into the model.

When performance as a buffer material is evaluated, the equivalent hydraulic conductivity is generally considered as an index. The equivalent hydraulic conductivity coefficient was calculated by the formula in Fig. 10. Figure 11 shows its evolution with time. The data represented by the dotted line in Fig. 11 were obtained from the case of chemical analysis only, and those represented by the solid line were obtained from the weakly coupled analysis. The two sets of data show no significant differences.

The Realization of a Fully Coupled Approach

The evaluation of hydraulic/mechanical effects produced by chemical alteration of bentonite in the one-dimensional model presented in this study was small as stated above. However, it is necessary to examine the behaviour by using models in two or more dimensions in order to evaluate the uncertainty. Moreover, some problems were identified in this study, such as:

The basis for calculating the hydraulic conductivity differs between the chemical and hydraulic/mechanical models;

In the present hydraulic/mechanical analysis, it has not been considered that the soil grain density and the water density change when the montmorillonite alters;

Unsaturated conditions have not been considered in the chemical analysis;

For simulations in two dimensions, the speed of calculation in the chemical model is insufficient.

It would be necessary to solve the above problems in order to make advances in the coupled analysis of chemical and hydraulic/mechanical processes. The first problem can be solved by setting a common coefficient. However, the effects will need to be examined. Addressing the second problem requires the types of mechanical changes be reviewed through a theoretical examination. The third and fourth problems are those that concern the details of the chemical model. New numerical approaches must be introduced or developed in order to solve these problems, although these do not appear to be achievable in the short-term.

Thus, to evaluate the performance of the engineered barrier in the long-term, it is generally recognized that more attention needs to be given to the synergistic effects of the chemical and hydraulic/mechanical processes. However, some difficult problems need to be solved in order to realize a fully-coupled simulation. It is therefore necessary to ascertain these effects using a more effective approach.

This research is a part of “Development of the technique for the evaluation of long-term performance of EBS (FY2007-2011)” under a grant from the Agency of Natural Resources and Energy, the Ministry of Economy Trade and Industry of Japan (METI).