Coupled T–H–M issues relating to radioactive waste repository design and performance

International Journal of Rock Mechanics & Mining Sciences 38 (2001) 143–161

Coupled T–H–M issues relating to radioactive waste repository design and performance J.A. Hudsona,*, O. Stephanssonb, J. Anderssonc, C.-F. Tsangd, L. Jingb a

Rock Engineering Consultants and Imperial College, 7 The Quadrangle, Welwyn Garden City, Herts AL8 6SG, UK b Royal Institute of Technology, Stockholm, Sweden c JA Streamflow AB, Sweden d Lawrence Berkeley National Laboratory, California, USA Accepted 24 August 2000

Abstract In this paper, coupled thermo-hydro-mechanical (THM) issues relating to nuclear waste repository design and performance are reviewed. Concise statements, that were developed from DECOVALEX discussions, on the current state-of-knowledge are presented. Section 1 describes the THM background and the interface with performance assessment (PA). The role of THM issues in the overall repository design context is amplified in Section 2, which includes a review of the processes in terms of repository excavation, operation and post-closure stages. It is important to understand the overall context, the detailed THM issues, the associated modelling and how these issues will be resolved in the wider framework. Also, because uncoupled and coupled numerical codes have been used for this subject, there is discussion in Section 3 on the nature of the codes and how the content of the codes can be audited. To what extent does a particular code capture the essence of the problem in hand? Consideration is also given to the associated question of code selection and the future of numerical codes. The state-of-knowledge statements are presented in Section 4 under 11 headings which follow the repository design sequence. The overview conclusion is that ‘‘A predictive THM capability is required to support repository design because precedent practice information is insufficient. Many aspects of THM processes and modelling are now well understood and there is a variety of numerical codes available to provide solutions for different host rock and repository conditions. However, modelling all the THM mechanisms in space and time is extremely complex and simplifications will have to be made } if only because it is not possible to obtain all the necessary detailed supporting information. Therefore, an important step is to clarify the THM modelling requirement within the PA context. This will help to indicate the complexity of THM modelling required and hence the models, mechanisms, type of computing, supporting data, laboratory and in situ testing, etc. required. An associated transparent and open audit trail should be developed.’’ We also include comments from reviewers and highlight four outstanding issues which are currently being studied in the DECOVALEX III programme. # 2001 Elsevier Science Ltd. All rights reserved.

1. Introduction This paper summarizes the state-of-knowledge concerning thermo-hydro-mechanical (THM) coupled processes in the context of their role in providing a predictive capability for radioactive waste disposal, specifically for repository design and radionuclide migration modelling. The role of coupled THM issues in the repository design context is described in Section 1.1, and the link with performance assessment in terms of radionuclide *Corresponding author. Tel.: +44-1707-322819; fax: +44-1707375912. E-mail address: [email protected] (J.A. Hudson).

isolation and migration calculations is described in Section 1.2. The structure and content of the paper are described in Section 1.3. 1.1. The role of coupled THM issues In order to provide a context for THM state-ofknowledge statements, it is necessary to understand the role of the coupled THM processes in repository design and performance assessment. The process of designing a repository to contain spent nuclear fuel and other radioactive waste is unique in rock engineering terms for a combination of four main reasons:

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unlike the location of a civil engineering project or the location of an orebody for mining, there is wider flexibility (in principle) in choosing the location of the repository, i.e. the location may not be predetermined; in comparison to the functional objectives of other rock engineering schemes, the objective of the repository is that very little should happen, with only an acceptably low level of radionuclide migration; the design life of the scheme, being in the order of tens of thousands of years and up to a million years, is well beyond that of any other rock engineering project; and a high degree of design confidence is required because there is no opportunity to observe how the facility performs in the long term, nor can any necessary remedial action be easily implemented.

Because of the long design life resulting from the halflives of the radioactive materials, the repository cannot be designed by precedent practice. Optimal site selection criteria have not yet been established from an engineering perspective. So, there has to be a systematic consideration of all thermal, hydrological and mechanical effects that could prejudice the integritry of the repository and its man-made and natural barriers in the short and long terms. Then an adequate model for the radionuclide migration can be developed. As mentioned in the Preface to the book by Stephansson et al. [1] reporting on the DECOVALEX I experience, THM effects occur over a variety of space and time scales, with additional complexity when the effects are coupled. Furthermore, the parameters associated with the THM processes and their significance will be site specific. In order to design the repository to meet the performance and safety requirements, it is necessary to be able to adequately assess the role of THM processes and determine how they affect the performance and hence the safety case. Thus, THM processes have to be identified and modelled. It has been found through the DECOVALEX I experience that some of the THM processes can be adequately modelled already, e.g. aspects of the TM component, but that the fully coupled THM modelling is currently intractable. However, it is anticipated that it will not be necessary to include all aspects of the fully coupled processes } and so the identification of the key components is crucial. Also, most of the work to date has concentrated on construction and operational phases, but the safety assessment is based on the postclosure aspects; so the THM issues relate with different emphases to the operational and post-closure phases. The link between the performance assessment and the safety assessment is discussed in the article by Dewiere et al. [2] in which the question of the uncertainties involved is addressed. In that article it is stated that

‘‘. . .the role of safety assessment is to determine the area of acceptability, while performance assessment is to determine the limits of possibilities and ranges of uncertainties in predictions. . .’’. Somewhat different definitions are given in the OECD/NEA literature [3]. A key aspect of studying the THM processes is to identify the associated uncertainties. By focussing on THM processes, fundamental laws, numerical codes, etc., THM aspects in the context of the repository design and performance will be clarified. Naturally, the analyses should consider the balance between all the factors, and more details of the processes occurring during the evolution of the repository are presented in Section 2.2. Hence, the role of the THM processes within the context of repository design and performance assessment must be assessed and our current knowledge base established. The Task 4 work of DECOVALEX II which is being reported in this paper has provided a series of consensus statements on the state-of-knowledge in this area. 1.2. The interface with performance assessment The role of the THM issues in performance assessment (PA) is covered, for example, in the SKI SITE-94 Report 95:26 [4] which notes that ‘‘The idea, common to all versions of PA, is to describe the repository and its surrounding environment as an integrated system so as to evaluate the circumstances under which radionuclides disposed in the repository may be released and transported to the environment and to people. The problem is complicated by the fact that the state of the system, as well as its future evolution is subject to uncertainty.’’ In the systems approach adopted by SKI and SKB there is the listing of features, events and processes (FEPs) that potentially may influence the process system. However, there is system uncertainty in the sense that the extent and the content of the process system are not fully known. The THM mechanisms operating in and around the repository play a large part in the total system but are not fully amenable to experiment and are not supported by complete models. Also, the uncertainties governing the understanding, specification and modelling of the THM mechanisms are issues relevant to performance assessment and the safety evaluations. When considering the THM mechanisms, it is important to show that a given process has relevance to the repository performance, or that increasing the complexity of characterization and modelling is actually required. Given that there are first- second- and thirdorder THM processes, the modelling has to be developed to a useable practical scheme which captures the essence of the required processes. Some THM couplings will be concept, site and waste-type specific, e.g. whether high-, medium- or low-level waste is being considered.

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1.3. Structure and content of the paper The paper has been structured to present the consensus opinions on the state-of-knowledge of various issues relating to coupled THM processes. Section 2 explains the THM processes in the contexts of the repository stages: the excavation, operation, and postclosure stages. Discussion on heterogeneity, site characterization, modelling phases and scaling is also included. Other subjects not included here that will need addressing in due course are natural THM processes in the far field, e.g. ice loading, thermal gradients, seismic activity. A variety of numerical codes have been developed that are relevant to repository design and others have been developed specifically for disposal performance assessment. It is essential to be able to audit these codes in the context of the THM processes to establish whether they are capable of capturing the essence of the THM issues in hand. This refers initially not to whether the codes are internally correct, but whether the variables and mechanisms that they represent are appropriate to a given analysis objective and associated system or sub-system. This auditing of numerical codes is explained in Section 3 together with a discussion on the future of the codes. A summary of the specific state-of-knowledge statements on THM issues is given in Section 4. The summary statements have been arranged in categories } ordered according to the repository design process. A listing of the original consensus statements is given in [5]. The original report [5] on which this paper is based was reviewed by seven ‘PA reviewers’; they made additional contributory comments which have been summarized in Section 5. Readers who wish to read about the THM issues in further depth, are referred to the original report [5] which also contains an appendix on the need and methodology for technical auditing of models and codes to ensure that they do indeed capture the essence of the problem as defined, with a demonstaration case example included as Supplementary Report 1. Also, Supplementary Report 2 included in [5] contains a review of the use of THM processes in some safety assessments and highlights the necessity to understand the processes and that the optimal way forward may well be achieved by a simplification, rather than complication, of the THM modelling.

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how the design process is being approached, i.e. the total system and the sub-systems, so that the role of the coupled mechanisms and the associated issues can be put in context. Moreover, the THM issues will be different for the operational and post-closure evaluations.

2.1. The overall repository design consideration The objective of constructing a radioactive waste repository is to be able to safely dispose of spent nuclear fuel and other nuclear waste according to appropriate safety and environmental requirements. Thus, there will be a series of objectives related to safe and economical repository construction, safe waste transport and emplacement, acceptable environmental impact, criteria associated with radionuclide migration and the corresponding dosage back to man, etc. Thus, to establish whether a particular coupled THM mechanism is important or not requires an appreciation of the role of the particular mechanism in each and all of the overall design criteria and assessments. A mechanism may have a strong effect on, for example, the extent of the excavation disturbed zone (EDZ), but if the EDZ does not affect any of the construction, and design and performance and safety assessment criteria, then the coupled mechanism may be of limited significance in the overall repository performance, depending on the repository concept and site. Hence, there has to be some method for quantifying the effect of the coupled mechanism and evaluating the effect on the repository sub-systems and then on the whole system. Moreover, there also has to be a method of identifying and structuring all the THM coupled mechanisms. A simple mechanism links two variables. A force applied to an elastic spring causes a displacement. This is an M mechanism linking the variable ‘force’ with the variable ‘displacement’ using the parameter governing the mechanism, the ‘spring stiffness’. In the case of heatgenerating radioactive wastes, it is possible to envisage a range of individual and coupled T, H and M processes that can operate. This is illustrated schematically in Fig. 1, which reinforces the point that there are many different

2. THM issues in the repository system context As explained in the Introduction, the purpose of the work described in this paper was to provide statements on the coupled THM issues related to nuclear waste repository design and performance assessment. In order to prepare such statements, it is important to understand

Fig. 1. Examples of thermo-hydro-mechanical (THM) couplings, from [6].

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Fig. 2. THM coupling illustrated using an interaction matrix: (a) represents the same network as that shown in Fig. 1; (b) shows that THM coupling can be a specific pathway, such as T ! TH ! H ! HM ! M; (c) shows the coupling as T ! TM ! M ! MH ! H, or TMH. Note that, for full coupling, all the links in Fig. 1 or 2(a) are relevant and that all pathways are potentially possible.

types of coupling. Hence, there can be a variety of fully coupled THM issues, which need attention at the conceptual, physical and modelling levels. It is also possible to represent the THM couplings shown in Fig. 1 using the interaction matrices of the rock engineering systems (RES) methodology [7] as illustrated in Fig. 2. Here the separate thermal, hydrological and mechanical variables are placed along the leading diagonal of the matrix with the binary links as the off-diagonal terms, as in Fig. 2(a). Note that the interaction matrix in Fig. 2(a) is not symmetrical in the sense that TH, i.e. T ! H, is not the same as HT, i.e. H ! T. Taking the sequence into account, the T ! H ! M coupling is represented by a pathway through the interaction matrix as shown in Fig. 2(b) using the linking interactions of TH and HM. However, the three subjects can also be coupled as T ! M ! H, illustrated by the pathway in Fig. 2(c) using the interactions TM and MH. In fact, the shorthand ‘THM’ used in the title of this document means the combination of the three processes } which includes all THM permutations, and indeed all possible partial couplings and different pathways linking the three processes. This is an important aspect of THM modelling since the result will depend on the particular pathway used to incorporate all the interactions. Thus, a full THM coupling } if required } should invoke all the links represented by the network in Fig. 1, which are the same as all the binary interactions in the off-diagonal terms of Fig. 2(a). Considering now the whole disposal scheme, a systematic approach is required to categorize all the mechanisms potentially relevant to the repository design and disposal systems and hence to be able to identify the relevant THM issues. In Fig. 3, we show the five subsystems defined by SKB [8]. Other radwaste agencies follow a similar classification. In Fig. 3, the shaded squares along the leading diagonal of each interaction matrix are the variables used to characterize each sub-system. The binary or pairwise interactions between all pairs of variables are

Fig. 3. The repository system and the sub-systems studied by SKB [8]. Highlighted off-diagonal terms (illustrated here schematically) are the mechanisms identified by SKB as the components of the process system. Some of these mechanisms will be THM mechanisms; some will be other types, e.g. chemical mechanisms.

found as the off-diagonal terms. These are larger matrices than those shown in Fig. 2 because more variables are needed. Each off-diagonal term can be assessed in terms of whether the interaction is significant for the operation of the sub-system, as diagramatically illustrated by the shaded off-diagonal terms in Fig. 3. This is the RES method of structuring the information and hence studying the THM mechanisms and processes within the overall disposal context. A mechanism involving three or more variables is represented by a pathway through the matrix. The other method is to use influence diagrams which are representations of the connections between relevant features, events and processes. Influence diagrams are discussed, for example in [10–12]. The preparation and auditing of the FEP list, together with the method of building process influence diagrams is particularly well explained in [10]. The report also shows how the process influence diagrams are used in performance assessment.

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Fig. 4. A section of the SITE-94 Process Influence Diagram, showing features, events and processes (FEPs) and influences, from [9].

An example of an influence diagram is shown in Fig. 4. The three main areas within which the THM studies have been focussed are conceptual studies, experimental studies and numerical studies. The context for these studies is discussed in the next section. 2.2. Review of THM processes associated with nuclear waste repositories1 The following discussion of the THM processes associated with radioactive waste geological repositories is based on a review of a number of reports and books including the proceedings of an EC conference [13], a literature review by USNRC [14], an edited book [1], a special issue of the International Journal of Rock Mechanics and Mining Sciences [15],

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The content of Section 2.2. has previously been published in issue 37(1–2), pp. 397–402, of this journal, but has also been included here for completeness of this article on coupled THM issues } the subject having been a specific component of the DECOVALEX II research work.

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as well as a number of individual papers and articles [6,16–20].

A review of how several radioactive waste management agencies treat the issues of coupled THM processes has been prepared by Andersson and is presented as a supplement in [5]. 2.2.1. Introduction It is useful to group the THM processes into several time periods, rather than according to the spatial distance from the near field to the far field of the repository. The US NRC [14] defined three temporal stages according to the US regulation 10CFR760: (1) the operation stage (up to permanent closure); (2) the containment stage (from permanent closure to 300–1000 years, probably after the heat pulse has peaked); and (3) the isolation stage (for long-term isolation up to the nominal 10,000+years). The AEC of Japan [21] defined the stages as (1) construction stage, covering coupled effects during excavation;

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(2) operation stage, covering period of emplacement of an engineered barrier system; (3) enclosure stage, covering backfilling and closing of the repository; and (4) post-closure stage. However, for our consideration of coupled THM processes, we emphasize the earlier time periods, which are when the most significant initial effects of the processes occur (although later processes may be just as significant for the safety assessment, see [5].) Thus, in the following discussion, we group the processes according to (1) excavation stage, (2) operation stage and (3) post-closure stage. This is similar to the AECJ definition, except that the third stage of the enclosure period is combined with the second stage of the operation period } since the THM processes are similar during these two stages. 2.2.2. Excavation stage During the excavation stage, no radioactive waste is yet emplaced to provide thermal input, and the thermal effects of normal geothermal gradients and tunnel ventilation are expected to be small. Then a number of coupled MH processes are expected to occur. Here we have used MH, rather than HM } indicating that the direction of coupling at this stage is mostly from mechanical to hydrologic effects. They are briefly described as follows. (A) The excavation of the repository causes a major perturbation of the rock formation by the creation of a large cavity. The impact depends on the initial stress field around the system, the nature of the excavation method and the repository design, plus the nature of the ground, e.g. clay or fractured rock. It is not easy to determine the in situ stress field of a region, especially in the presence of fracture sets forming a network, which could well be anisotropic. The excavation will concentrate stress changes around the cavity, which in turn will change the local fracture apertures and permeability. In general, the question is how to determine the nature and extent of anisotropic change in hydraulic conductivity around the repository cavity. Since a repository will probably be excavated in stages, then how does the first stage change the stress field and how do we calculate the MH effect of excavation at a later stage, which is conducted in a different stress field environment? (B) The excavation also represents a relatively sudden event and hence the normal and shear stress across nearby fractures may change in a short time, producing sudden aperture changes. This may cause the pore pressure to rise quickly before the water has a chance to move and equilibrate. This has been noticed as a result in calculations, but no experiment has yet been designed to detect it. Such a transient coupled MH effect may cause local failures, as well as local hydraulic conductivity changes.

(C) The cavity at this early stage will be ventilated. This means that water will be taken out of the system and the pore pressure near the repository will be much reduced from the original condition, which may induce fracture closure because of the increase of effective stress (an HM coupling). (D) Reduction of pore pressure near the repository cavity may also result in degassing of the pore water. Gases that were in solution in water under pressure will be released. Thus, the flow in the rock surrounding the cavity will be two-phase flow (i.e. both water and gas are present), so that water permeability is much reduced due to gas interference represented by the relative permeability function. There is precedence from other excavations that can be called upon to study this phase of the repository. 2.2.3. Operational stage During the operational stage, the nuclear waste and buffer/backfill or liner materials have been emplaced. Thus, at this stage, there is thermal input and a series of THM processes occur. (A) The thermal output from the nuclear waste will heat up the buffer/backfill and the rock. This will occur over several decades in the different repository rooms as they are successively filled with the waste. Thermalinduced stresses will be created around the repository, which may change the hydraulic conductivity. The TM effects have been relatively well studied and much experience has been gained in their modelling and observation. (B) What is interesting here is the heating up of the multiple media system, the waste canister, backfill materials (e.g. bentonite), and then the surrounding rock. These all have different expansion coefficients. How they move and compress each other and how the interfaces between them behave may cause a significant change in the hydraulic properties of these interfaces. (C) Since water and rock have different thermal expansivity, thermal input may also cause significant pore pressure changes. This is particularly the case for repositories in clay where the original hydraulic conductivity is low and much of the water is in closed pores. The thermal input will then cause changes in effective stress, possibly giving rise to local failures and hence increased local hydraulic conductivity. (D) For bentonite backfill, the incoming water from the rock will increase its saturation and cause it to swell. The imposition of the swelling pressure and the capability of the bentonite to fill in gaps and fractures will change the local hydrologic properties and hence the water flow paths. (E) It is not obvious how to assess the behaviour of the gases, which could be either air from the open cavity migrating into the rock, or gas from degassing of the water during the first stage, or due to phase changes

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(steam). The gases will move into the system under buoyancy or temperature gradients, and then may redissolve into water or form gas pockets that expand with temperature and interfere with the groundwater pathways. The presence of gases will change significantly the local permeability to water flow, as represented by the relative permeability function. (F) The heat will induce convective flow in the rock, and, as in the case of the Yucca Mountain site in the US, the local temperature near a waste canister may be high, and significant vaporization will occur. The water vapour will move away from the repository and condense at cooler regions of the rock. This process forms a complex hydrologic system that requires a fully multiphase code for its analysis. How this system will affect the effective stress field and thus the mechanical condition is an open question. (G) During this period, the repository may be kept open to allow for the option of retrievability. Thus, the system is ventilated and heat/moisture taken out of it. This, coupled with thermal evaporation, will cause a dehydration in the near field. 2.2.4. Post-closure stage This is the stage after permanent closure of the repository. The repository is now sealed and thus there is no ventilation or escape of moisture. The repository cavity is then resaturated (if below the water table) and repressurized to its original hydrostatic pressure corresponding to its depth. During this stage, a number of important changes take place. (A) Thermally, the temperature builds up to a certain level and then decreases. The temperature peak of the heating–cooling cycle is reached after 15–100 years near the waste canister, but may take 200–1000 years to attain in the far field. The exact temporal and spatial distribution of the heating cycle depends on the waste inventory and repository design. (B) This is also the period when the hydraulic pressure is rebuilt in the backfilled and sealed repository opening. Thermally induced flow or convection (TH) depends on thermal energy imparted to the water, which will last much longer than the temperature pulse. The convective velocity could peak at around 10,000 years. (C) In the same way, the TM effect is also dependent on thermal energy imparted to the rock and is not directly dependent on temperature. Thus coupled TM processes will also last up to 10,000 years. One example is that the thermal expansion distribution may open fractures below the repository and close fractures above it, thus creating an under-pressure region below. The possible occurrence of this coupled TMH effect should be evaluated by modelling and be detected and studied by a repository monitoring programme. In general, mechanical deformation during the resaturation and repressurization is an irreversible

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coupled THM process. It is not expected that the system will return to pre-excavation conditions because of mechanical hysteresis. Similarly, the thermal strain during the cycle of temperature build-up and decrease may also be an irreversible process. The role of gases during this stage, in terms of their flow and dissolution in water, is also an open question. Yet, hopefully, any effect at this later stage would be moderate in magnitude and in time rate. Other coupled processes have been envisaged away from this ‘base case scenario’. These include links involving chemical effects, seismically induced HM, glacially induced THM, erosion, asteroid/meteorite induced THM. 2.2.5. Remarks on heterogeneity Along with the above discussions of coupled THM processes, two important and difficult scientific problems need to be considered. These are discussed in this and the next sub-sections. The first is the question of heterogeneity. Though much research has been done on this subject in recent years, it is still a wide open question. We do not yet know clearly and definitely how to characterize heterogeneity at a potential repository site, or how to design and perform a reasonable set of field measurements to obtain the basic heterogeneity parameters. Because of this, heterogeneity is a critical uncertainty that pervades all modelling input, the modelling sensitivities and output, and may well be one of the factors limiting the confidence level of THM predictions. The subject is important in the sense that THM models may be required to support a PA safety case for regulatory approval. A special class of heterogeneity is the fracture network in the rock. This is well known in crystalline rocks. There is a suggestion that there are also fractures in clay formations (unless the clay is very plastic) and that fractures may be induced during dehydration of clay as well [18]. All the coupled THM processes mentioned above will be present in fractured porous systems. In other words, both fractures (with their high permeability and low stiffness) and the porous block need to be considered. In hydrothermal coupling it is now well known that it is the presence of both fractures and porous matrix that promotes the heat pipe effect. In THM, similar special effects may occur. Furthermore, there can be strong heterogeneity even in the porous medium itself, and it is not extraordinary to find, for example, variations of hydraulic conductivity of one or two orders of magnitude or more in the porous medium. In the general case, heterogeneity means different THM properties at different points in space and time. Modelling the THM processes in a heterogeneous system is still very much an unsolved problem. At one extreme, the fractal scaling laws associated with some

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fracture types preclude the concept of an equivalent volume. At the other extreme, fractures on all scales may need to be characterized differently. Work is being conducted in at least three directions for the case of fractured rock. *

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The first is the development of an effective continuum model by homogenization of the fracture network [22,23]. In this approach, the effects of the fractures in a calculational element are approximated by the behaviour of an effective anisotropic continuum block. As shown in [23], the results are quite inaccurate when tested against detailed numerical results. The second is the approach being taken by Noorishad and Tsang [24] who are developing a 3-D heterogeneous model of ubiquitous joints, allowing preferred elastic/plastic directions for the elements. The basis for both of these approaches is not yet established; in other words, one may question whether such an equivalence exists. Perhaps, the equivalent continuum blocks are valid for a limited range of fracture parameters and for a limited set of stress and hydraulic conditions. The third direction is to employ a detailed fracture network model and let each network fracture deform (change in aperture) according to variations in the local pore pressures, gradient, and in situ stress conditions. The difficulties with this approach include both the need for neglecting the role of the matrix between fractures in coupled processes and for neglecting the interference between nearby fractures, particularly the way in which the presence and behaviour of one fracture affects the local in situ stress field seen by a neighbouring fracture.

We anticipate that, as this field matures, additional methods will be developed to model coupled effects in heterogeneous rocks. It may be found that a completely different approach is needed to deal with heterogeneity for performance assessment of a nuclear waste repository. 2.2.6. Remarks on multiple-stage data needs Data needs for each stage of the repository development and assessment should be built up from the previous stage. It is useful to note that each stage of repository development represents a major perturbation of the hydromechanical conditions of the rock formation. Responses to these perturbations can be utilized to characterize the system, and hence they need to be monitored in detail, both spatially and temporally. Before the excavation starts, information is needed on the geologic structures and stress distributions. The former include the geometry of faults and joints, and the presence of geologic domains, as well as effective boundaries of the region to be studied. The stress distributions may require borehole measurements such

as hydrofracturing and profiling. Water injection and withdrawal pressure transient tests also need to be done. Of particular importance are the hydraulic and mechanical conditions at the chosen boundaries. In general, many of these data and information details are not easy to obtain. Some may have to be left as uncertain and estimated later through calibration. The Nirex work at Sellafield that was conducted in preparation for the RCF Shaft sinking is an example of this kind of effort [25]. It is to be noted that the period of the actual excavation of the repository represents an opportunity to obtain data at the scale of the repository and at the magnitude of its mechanical impact. After the excavation stage, the impact of the excavation on rock hydromechanical behaviour is very useful to further characterize and understand the site. Deformations of the cavity profile, especially near fractures that intercept the cavity, are useful for estimating the mechanical condition near those locations. Distribution of water emergence in the freshly excavated surfaces and changes in pore pressure distribution also will give information on major flow paths and how they are affected by mechanical changes because of the excavation. Some efforts along these lines have been made, for example, in the Kamaishi experiment [26]. However, that study was on a smaller scale, with the test pit being 1.7 m in diameter and 5 m in depth. Careful monitoring design needs to be made prior to the excavation. Afterwards, the circumstances may be changed because any installation of rock support systems will alter local EDZ conditions. During the operation stage, assuming that the physical and chemical properties of the backfill materials are known from laboratory testing, monitoring of rock changes and hydromechanical conditions at the rock–backfill interface may be made at a number of representative locations. The objective of this monitoring programme is to understand the rock responses with thermal input from the waste and under the swelling pressure of the material backfill (e.g. bentonite). The swelling is in general non-uniform at an early stage of deposition. An example of this kind of effort is the ENRESA FEBEX experiment [27]. During the post-closure stage, we do not expect drastic or abrupt changes in THM conditions but significant changes involving a temperature rise-and-fall cycle, as well as TH and TM cycles with a much longer duration, occur. Certain types of remote geophysical monitoring of these changes may still be possible. One school of thought is that we should abandon the site after establishing monuments to warn future generations not to disturb the underground system. However, an alternative view is that monitoring should still be continued to detect these changes, and to ensure they are within model expectation ranges. Moreover, many

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countries are incorporating ‘retrievability’ into the design considerations. 2.2.7. Comments on modelling phases and scaling Three modelling phases should be carried out, corresponding to the three stages of repository development and based on data collected before the start of each stage. As the data and information build up for successive stages, so does the degree of sophistication of the model for successive phases. Each modelling phase should include: (1) model selection; (2) data evaluation and calibration of model structure/ parameters; (3) modelling studies, including sensitivity study and uncertainty evaluation, with feedback to repository design and PA; and (4) predictive modelling of the next stage. To evaluate and understand the field observations and monitoring data at each stage, it is necessary to compare with predictive results of the models from the previous phase. Further, calibrations are particularly important to prevent within-phase errors and cumulative errors developing with successive phases of the modelling exercise. The degree of success with which this can be done depends on the design and execution of the monitoring and testing programme at each repository stage. It is important to think carefully about how to design a data-gathering strategy for that period and set it in place. The repository may otherwise be excavated without adequate preparation, and consequently proper data are not obtained for THM evaluation: if the unique opportunity to obtain large-scale THM responses is overlooked, it will be difficult to gain it again. 2.3. Modelling the THM processes Considering the overall repository design considerations outlined in Section 2.1 and the issues presented in Section 2.2, how are the THM processes modelled and in what context should the THM issues be considered? The series of steps below indicates one method by which this could be achieved. Modelling THM processes for repository design and performance assessment (noting that quantitative modelling may not be necessary, and that the modelling will be disposal concept- and site-specific) Step 1: Model conceptualization Step 2: Identification, definition and specification of THM mechanisms/processes in the model. Step 3: Selection of those items identified in Step 2 which are considered to be important for the process system and hence performance assessment.

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Step 4: Listing of analytical solutions and numerical codes able to simulate the selected THM processes. Step 5: Auditing of codes to establish their capability to model sub-systems as defined by the performance assessment strategy. Step 6: Choice of codes for numerical calculations. Step 7: Obtaining all necessary supporting data for analysis. Step 8: Conduct modelling and obtain results Step 9: Application of results for repository design and performance assessment. This sequence of steps is a ‘top-down’ or analytic approach. To date, the modelling of the THM processes has been more of a ‘bottom up’ or synthetic approach } for the practical reason that the modelling has evolved by incrementally improving the numerical codes to include more and more components of the THM coupling, and by acquiring laboratory data on simple systems. However, if the THM modelling is to reflect the nature of the THM coupling within the repository design and performance assessment contexts, the modelling must be tailored to the specific THM mechanisms and couplings required, as defined by the process system. Therefore, in the future it will become increasingly necessary to ‘modularize’ the numerical codes so that the necessary code components can be linked according to the anticipated sequence of engineering perturbations at the site and hence the sequence of THM links that require modelling. It may also involve the ability to link the matrices in Fig. 3 by ensuring that the modelling output of one matrix can provide the modelling input of another } so that the THM aspects can be followed through the necessary space and time ranges. Also, the auditing of the code components and the composite code will be necessary in order to facilitate the provision of an audit trail demonstrating that the modelling does indeed capture the THM essence of the problem, both in the structural components and in operational sequence. These requirements are discussed further in Section 3.

3. Numerical codes The necessary modelling of the THM processes may be conducted qualitatively or quantitatively. In the event that numerical codes with THM coupled components are to be used for performance assessment purposes, the question of the level of complexity has to be addressed. Is a simple representation of the system adequate? Is it necessary to attempt to use fully coupled THM codes? Which stage of the disposal is being supported by the modelling: operational or post-closure? It should also be noted that part of the use of the modelling and codes is

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to compare the results with the site information in the validation context. In this way, the numerical models and site data are complementary However, given that experiments cannot be conducted over the long time scales of interest, there is probably only one acceptable method of including the combined THM couplings for predictive purposes } the use of numerical codes containing algorithms for evaluating the coupling equations. Thus, it is important that the advantages and limitations of numerical codes are understood. Analytical or closed-form solutions do exist for some problems. By using ‘equivalent’ rock properties, the power of the analytical solutions can be extended considerably [1] and these extended analytical solutions may provide sufficient characterization of the problem for the performance assessment and safety assessments in hand. In Sections 3.1 and 3.2, the nature and THM coupling of numerical codes are discussed. This is followed in Section 3.3 by an explanation of how numerical codes can be audited, to see *

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whether they can capture the essence of the problem in hand, and whether they are indeed adequate models of reality.

In Section 3.4, the future of numerical codes is considered in terms of whether they will continue to exponentially increase in complexity or will there be a shift in the modelling paradigm. The content of Supplementary Report 2 in [5] on the THM issues in the PA context is also relevant to the subject of this work. 3.1. The nature of numerical codes Numerical codes have been applied widely in rock engineering for analysis of mechanical, hydraulic, thermal and coupled problems. They are commonly used for obtaining stress and displacement distributions, fluid inflow, fluid pressure distribution and temperature distribution in a rock structure for certain geometries and given boundary conditions. Numerical codes have been developed to a high level and are able to include complex geometries and some degree of coupled mechanical, hydraulic and thermal processes. There are many numerical codes that can be supplied ready for purchase and use. The question naturally arising then is ‘Which numerical code should be used for the particular rock engineering problem in hand?’ In the waste disposal context, the question is ‘Which codes can be used for which aspects of the problem?’, noting that there are no off-the-shelf codes encompassing the whole problem. Referring to the sub-systems in Fig. 3, which codes can be used for which aspects of the sub-systems? Moreover, because a transparent audit trail is required, follow-on questions are ‘What is the formal procedure

by which a particular code is chosen for use in this project?’ and ‘Has the code been adequately verified and validated?’ However, for the coupled mechanical–hydraulic– thermal rock engineering and performance assessment problem with complex rock geometry, the information involved is diverse and complicated. Many assumptions are made in numerical codes to simplify the information for the code’s use. As a result, the outputs resulting from the use of different codes may be different due to the different ways in which the information is used and simplifications assumed. Because it is not immediately clear what information is relevant, it is not apparent which codes should be used. 3.2. Uncoupled and coupled codes One of the important decisions will be to decide whether to use uncoupled or coupled codes, i.e. whether to use a set of codes each dealing with one aspect of the problem or codes which have algorithms representing the THM processes. Referring to Figs. 1 and 2, there are codes that have been developed to study uncoupled problems, i.e. they solve problems in only one subject } thermal or hydraulic or mechanical processes. There are also codes that have been developed to study coupled problems, i.e. incorporating one or more of the network links in Fig. 1or the off-diagonal interactions in Fig. 2. But can uncoupled codes capture sufficient essence of the problem for engineering purposes, which is a similar question to whether a continuum solution can be a sufficient approximation for a jointed rock mass? The coupled codes have extra levels of complexity above uncoupled codes. Firstly, a coupled code has to contain more processes than a single-subject code. Secondly, the full THM coupling introduces two-way links between the separate T, H and M algorithms (cf. the pathways in Fig. 2(b) and (c)). This is illustrated by the studies in DECOVALEX I [6]. However, we will never be able to characterize all the details of all the couplings with the characterizing parameters, so work should be directed towards the optimal level of approximation. 3.3. Technical auditing of numerical codes It is immediately clear from the DECOVALEX 1 examples [6] and when considering more complicated cases that one key aspect of the subject is being able to match a particular code’s analysis capability with the problem in hand. Does the code capture the essence of the problem? Is this code the best one to use? Do we need to develop new codes? The main issues associated with the application of numerical codes to the radioactive waste disposal

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problem are * * *

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defining the problem to be solved, considering codes that could be used, establishing that the codes can capture the essence of the problem, checking that the code is internally correct, and ensuring that the code is an adequate representation of reality.

In the performance assessment context, there are wider issues. Can a simpler representation of the system

be shown to be conservative and hence be used in place of a full THM model? Work is still required in defining the problem. The work illustrated by Fig. 3 is well developed in that the structure of the problem has been established and the important processes have been identified, i.e. the components of the interaction matrices which are the components of the process system and can be linked to the FEPs via a database, e.g. [28]. In choosing the codes to use, there is a limited resource of codes that can deal with the THM processes, as evidenced by the DECOVALEX 1 studies. A long time is required to develop new codes } so the numerical code resources will not change quickly. A formal method is needed to check that the codes do capture the essence of the problem. A method for establishing such an audit trail procedure is discussed in the next section and explained further in [5]. In the context of checking that the code is internally correct, there has to be some form of guarantee that the operations of the code are indeed internally correct. Methods, which have been developed in the nuclear and aerospace industries to approve numerical codes, will need to be applied to the codes used for modelling THM processes so that the audit trail is complete. Finally, for checking that the code does model the real conditions acceptably well, fully coupled in situ tests will be required and adequate ‘‘acceptance’’ tests defined to demonstrate the code’s adequacy. 3.3.1. Capturing the essence of the problem In order to establish whether a code can capture the essence of the problem in hand, it is necessary to define the analysis capability of the code and compare this with the analysis requirements of the problem.

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Continued work around the world on the FEPs, the process system, performance assessment and safety studies will enable the components of the problem to be identified, but how can the analysis capability of a code be specified? One method using an interaction matrix is described below. Other presentational methods are also possible. For example, we could start by compiling a table with the physical THM processes relating to the rock mass, rock joints and codes } using the template below.

Also, this information and the information used in any numerical code can be presented by a binary interaction matrix (BIM) similar to those presented in Figs. 2 and 3. The state variables are those known to be required by the physics of the problem, and listed along the leading diagonal of the matrix. The mechanisms linking the state variables form the off-diagonal components. The components of the binary interaction matrix necessary to model the problem are established first in order to provide the reference requirements. The content of this reference interaction matrix in principle contains all the information required to solve the problem. For a specific code being considered, the binary interaction matrix is also used to present the specific capability of the code in utilizing information, i.e. a statement of the specific links between the state variables which are actually in the code. An example of the type of interactions which one might like to have in a THM code is shown in Fig. 5 and the components that might be in a code are shown in Fig. 6. A comparison of the two diagrams will immediately indicate if the necessary code content is there. It is not sufficient, however, to only compare the content: it is also necessary to consider the code algorithms connecting the variables and mechanisms } because one missing algorithmic connection or an inappropriate coupling sequence could have a significant effect. In numerical codes, the values of some variables can be directly obtained by solving the sets of equations with respect to certain boundary conditions. Examples are displacement in a mechanical equilibrium problem and fluid pressure (hydraulic head) in a fluid flow problem. In addition, some variables’ values are obtained by physical laws. For example, stress can be directly obtained from strain (which can be directly obtained

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Fig. 5. Using an interaction matrix to define the variables and interactions required to solve a THM problem (this matrix is illustrative of the technique and is not necessarily the one which would be used).

by differentiating displacement) via the stress–strain constitutive law. Fluid flow can be directly derived from hydraulic head via Darcy’s law. The first step in assessing the capability of the numerical codes is to determine the state variables that could be or are actually used in the codes. For example, the coupled THM problem will require a certain number of variables for a complete description of the problem, say n variables, and an associated number of binary relations, n2 ÿ n, included in the numerical codes to represent the maximal capability of utilizing the information (this is the input information), see Fig. 5. So, for a specific code in use, an information audit can be conducted directly by using the interaction matrix representation to compare the required variables (the leading diagaonal components in the interaction matrix) and the required mechanisms (the off-diagonal components in the interaction matrix). Why is a particular box empty? Is it important? How does the coupled performance of this code compare to an optimal code? Answering these questions leads to the concept of assessing and auditing the analysis capability of numerical codes. Thus, it is possible to develop audit sheets for formalizing this aspect of the THM modelling and hence to provide a way-marked audit trail that

emphasizes the rigour and transparancy of the numerical modelling work. 3.3.2. Validation The term ‘validation’ means ensuring that the code with input conditions and parameters does adequately represent the real conditions (although validation in general does not have to include numerical codes). The only way that this can be done is by comparing the effects of a perturbation to fully coupled site conditions. There will be a hierarchy of models } from a single interaction connecting two state variables of the system, to the behaviour of a sub-system, to the fully coupled total response. Thus, the experimental work will be preceded by verification studies for models with different components. At this stage, the experimental work can involve: * *

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single interactions between two variables; behaviour of well-defined sub-systems (such as TC1 in DECOVALEX 1 [6]); and fully coupled site studies.

The way in which the validation of the total system can be developed from validation of sub-systems is a subject ripe for research and one that will have to be established in due course. One adverse aspect of this subject is that increased study of coupled models simply increases the number of

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Fig. 6. Presenting the physical variables and mechanisms that are actually included in a specific numerical code and how these are connected by the code’s algorithms. (The content of this interaction matrix is then compared with the required code content as defined via Fig. 5.)

unsolved problems relating to their compilation and use } making an eventual solution more distant. Moreover, it will be difficult to validate complex numerical models. Both these features indicate the desirability of simpler models, if at all possible, if only so that validation is more practical. Additionally, as the codes become more complex and more mechanisms are included, the rock characterization problem becomes intense, increasing the data uncertainty problem highlighted in Section 2. 3.4. The future of numerical codes A characteristic of numerical codes is that they have increased in complexity with time, as is illustrated by the conceptual diagram in Fig. 7. Despite the possible preference for a simpler model for PA validation, it is anticipated that this increasing model and code complexity will continue. It is prudent to consider the ways in which the process system for radioactive waste disposal might be modelled in the future, given the inability for the increasing use of information illustrated in Fig. 7 to be sustained. Are numerical codes the way to process the information and hence establish the repository design? It is likely that computers will be involved, but perhaps neural networks

Fig. 7. Conceptual diagram illustrating the increasing complexity of numerical codes with time and the likelihood of a modelling paradigm shift when the amount of information required to support the codes becomes excessive.

will be used rather than numerical codes per se. Perhaps computers using neural networks will enable us to have a ‘perception’ of the THM processes and the performance assessment } and indicate the way ahead themselves. Also, many people consider that the repository design problem should be solved by a procedure involving simplification rather than complication } for which the neural networks and related techniques are ideally suited. Or maybe other techniques will be required.

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Perhaps in situ work will be the dominant method of assessing the rock response to repository construction, although the results from this approach cannot predict the repository behaviour over the full design life.

rock type. Also, those factors relevant to the PA and repository need to be identified. All this requires a transparent and open audit trail. Also, related analog systems should be identified for supporting information. 4.3. Structuring the relevant factors

4. State-of-knowledge statements on THM issues The specific state-of-knowledge statements were elicited from the DECOVALEX participants, discussed and agreed upon, and subsequently included as ‘raw data’ in [5]. These were used for the summary statements presented in this section. The statements were obtained in 10 categories, with an 11th for any statements which did not fall into the first 10 categories. The categories are as follows: 4.1. Characterizing the problem. 4.2. Identification of the relevant factors. 4.3. Structuring the relevant factors. 4.4. The operation of the repository system. 4.5. Matching numerical codes to the system. 4.6. Obtaining the information for modelling. 4.7. The role of site experimentation. 4.8. Scenarios and long-term extrapolation. 4.9. Variability, uncertainties and unknowns. 4.10. The ways ahead. 4.11. Statements not fitting in previous categories. The thrusts of the set of statements in each category are presented below as an editorialized summary for each category. These summaries are followed by an overall ‘summary of summaries’ of all the state-ofknowledge statements. 4.1. Characterizing the problem The process of characterizing the problem needs more study, especially how the THM processes should be included in the design of the repository system and subsystems, given that these are concept and site specific. The modelling can be simple initially, with an initial range of parameters. Then the sequence of modelling should be linked to the spatial and temporal phases of the operational sequence. For example, the heat aspects are well defined and important, but may not be required before the emplacement modelling stage. Then the complexity of the modelling can be matched to the requirements. 4.2. Identification of the relevant factors Expert judgement will be needed to develop the methodology for linking the existing FEP database information, the THM processes and the associated modelling, perhaps within the context of a particular

The inventory of factors, characteristics and initial conditions needs to be structured and matched to the repository type and operational sequence. For this purpose, related literature reviews are important. Many aspects of the uncoupled processes are understood; however, further work is required in coupled areas, such as the effect of heat on rock structure and the link between the THM processes and radionuclide migration. 4.4. The operation of the repository system The range of models available to study the THM outcome, during and after repository construction, emplacement and closure has to be considered. Data are available on fracture systems but other aspects are less well known. For example, the material properties may change with time, the THM processes can be a function of scale, and the processes may not be reversible. It is anticipated that the EDZ will be important. Thus, monitoring and feedback are important in the design loop, although full-scale testing may not be possible for all aspects. Consideration should also be made of process and system reversibility. 4.5. Matching numerical codes to the system Although many codes are available, there is a need to improve the matching of numerical codes to the disposal sub-systems under consideration. A literature review, including codes in other areas, and cross-comparison may be required. This should include an evaluation of the capability of closed-form solutions. In addition, there is a need to predict ahead because of the code development times, acceptability procedures, and changing requirements. In some cases, alternatives to complex codes should be considered, e.g. analytical solutions. Also, the development needs to be matched to the relevance of the couplings and the need for the model. 4.6. Obtaining the information for modelling The required site parameters will be governed by the type and sequence of modelling, which in turn is governed by the disposal objectives and implementation progamme. The data can change with time, location and scale. A combination of laboratory and field tests will be required. The uncertainty associated with incomplete

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supporting information will need to be assessed, taking into account the contributions from back analysis and natural analogs. This will assist in establishing when enough information has been obtained. Of course, the data requirements will depend on the modelling, which may have been simplified so that some information is then not required.

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4.11. Statements not fitting in previous categories It is important to establish the influence of the THM processes in the PA and the method for evaluating this influence, taking into account any previous work and budgetary requirements. This will clarify such aspects as the role of laboratory experiments and the acceptance– monitoring connection for particular schemes.

4.7. The role of site experimentation The role and needs of in situ work for site investigation and validation should be clarified. Site work may provide the most important input for model validation. 4.8. Scenarios and long-term extrapolation Because there is little precedent practice, some form of long-term predictive THM capability is required. Information on the initial processes can give confidence in the methodology } and any monitored data should be archived. Long-term predictions will need to be simpler and include a study of the propagation of errors. Factors such as glaciation and earthquakes will have to be included. Relevant natural and engineered analogs should be studied. 4.9. Variability, uncertainty and unknowns Because there are many uncertainties of different kinds associated with the THM modelling and codes, the approach and further model development should be driven by their importance to safety. This includes the qualitative understanding of the system and the range of model simplifications bearing in mind the couplings that need to be included. It will not be possible to obtain ‘perfect’ information on all aspects of the system. 4.10. The ways ahead Bearing in mind the complexity discussed in previous sub-sections, the need for THM support for PA has to be clarified first, including the significance of the THM processes in PA. The methods of incorporating the THM couplings as appropriate and the mathematical aspects of numerical analysis, e.g. solution algorithms and algorithm robustness, need to be considered. Other factors requiring clarification are mechanisms related to chemistry and transport in the context of performance assessment, constitutive relations at different scales, and possible computer paradigm shifts in the years ahead. The latter will naturally include the interfaces between different models and using the full power of computing methods. Computer code development should incorporate flexibility to allow for the inclusion of new phenomena and new couplings, or alternatively for the models to become simpler.

4.12. Overall ‘summary of summaries’ of the THM modelling state-of-knowledge statements A predictive THM capability is required to support repository design because precedent practice information is insufficient. Many aspects of THM processes and modelling are now well understood and there is a variety of numerical codes available to provide solutions for different host rock and repository conditions. However, modelling all the THM mechanisms in space and time is extremely complex and simplifications will have to be made } if only because it is not possible to obtain all the necessary detailed supporting information. Therefore, an important step is to clarify the THM modelling requirement within the PA context, and to ensure that the relation between THM modelling and the PA and design context is interactive and two-way. This will help to indicate the complexity of THM modelling required and hence the models, mechanisms, type of computing, supporting data, laboratory and in situ testing, etc. required. An associated transparent and open audit trail should be developed.

5. Summary of reviewing comments Many individuals from a variety of organizations have reviewed and commented on earlier drafts of the report on which this paper is based [5]. Also, the penultimate version of [5] received the benefit of careful ‘performance assessment’ review from a number of distinguished individuals with expertise in the PA area, as listed in the Acknowledgements section. Amendments have been made to address all these comments. However, there remain a large number of insightful remarks that cannot be incorporated simply and could be important in further THM studies for radioactive waste disposal and other rock engineering projects with THM coupled components. In this section, we compile and summarize these remarks in outline form. The remarks are listed and briefly discussed below } in no special order. *

In PA, frequently, modelling does not need to be quantitative, rather bounding calculations may be sufficient. This is particularly so for such complex models as the coupled processes models. Then the

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important PA issue is how to test the validity and applicability of such bounding models and how to evaluate the uncertainties associated with them. It is useful to note that the importance of different coupled processes depends on the repository concept under consideration. General statements may not be possible and one should discuss them on a conceptby-concept basis. There is a balance between complexity and uncertainty. A complex model may have less uncertainty, but it may be hard to use it for PA. A simplified model that is more amenable for PA would have a higher uncertainty level. How to evaluate this balance for PA purposes is an important issue. By the same token, it is still an open question whether simple models can be shown to be really conservative and useful to represent complex systems. For PA, we are more concerned with post-closure coupled processes. Earlier stages are relatively less interesting because we can make direct observation of what is happening. The current report is concerned more with THM processes in repository design and operation, rather than post-closure PA. The implications of coupled processes on PA using current codes/models have not been fully explored, and this should be actively pursued. (Supplementary Report 2 was produced to fill this gap.) In discussing coupled processes in PA, one needs to state the status of solutions, not just the list of problems. It would be useful to provide concrete examples of coupled THM processes in PA. Possibly it is more tractable to perform a series of bounding THM calculations than comprehensive fully coupled calculations. For example, it may be enough to incorporate only the important binary couplings (e.g. HM and MH) and there is no need for full THM. Can this statement be reformulated on a better scientific basis for a given repository concept? For the inclusion of coupled processes in PA, there is a need for emphasis on data and methods to obtain data, i.e. what are the right ways to make experiments and to derive relevant parameters. Perhaps one can develop an ‘auditing’ procedure for experiments. (Supplementary Report 1 in [5] was provided to explain how this can be done.) There is also the need to validate users’ interpretations of experiment results. From the experience of benchmark test cases in DECOVALEX I, it was found that participants using the same code to evaluate the same raw data obtained significantly different conclusions. Can we establish an auditing procedure also to ensure we understand the divergence of interpretations from different participants? (Supplementary Report 1 in [5] explains the need for Comparison Protocols and back analysis Discriminator Protocols.)

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It would be useful to conduct benchmark exercises. By this we do not mean code comparison exercises. For the latter, the input is ensured to be the same, and the outputs of codes are compared with each other for the same well-defined conditions. On the other hand, participants for benchmark tests are given the experimental conditions and raw data; they have to develop their separate inputs for their own codes. This requires reasoning and judgment, which should be properly documented. (In Supplementary Report 1 in [5], it is explained that this may be premature, given the complexity of THM processes, and that consensus work on modelling is required first.) What can we say about the scale effects of coupled processes? The choice of scaling description probably depends on the nature of results to be derived. The importance of a given coupled mechanism may depend also on the scales in time and space of interest. Criteria need to be developed and defined for the validity of models and acceptability of results. How to handle data variability? Some of the impacts may be non-linear. In these cases, how to find conservative modelling methods or bounding calculation approaches? How to characterize the natural system so that the evaluation of coupled THM processes can be done in situ with minimum ambiguity? We need the state-of-knowledge on the development of FEPs (features, events and processes) involving coupled THM processes. We need the state-of-knowledge on methods for deriving the optimal repository design with respect to coupled THM processes. How to mitigate the negative impact of THM by an adequate repository design? We also need the state-of-knowledge on methods for assessing PA impact of coupled THM processes for a well-designed repository during the post-closure stage. (Supplementary Report 2 in [5] touches on these issues.) We need statements on our qualitative understanding of coupled THM processes in conceptualization, data acquisition, data interpretation and modelling as related to performance. It is useful to demonstrate the importance of some of the FEPs with coupled THM, by model calculations or experiences in underground structures. It is necessary to differentiate the evaluations of the importance of coupled THM processes in three different contexts: (a) in field experiments to obtain in situ parameter values needed to conduct coupled THM processes for PA; (b) in achieving optimal design of the repository, and (c) in postclosure PA.

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The reviewers also made additional comments of a more technical nature and asked a number of technical questions related to coupled processes. These need to be addressed in future studies of coupled THM processes. They are outlined below: * *

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How to measure heterogeneity? How to make in situ observations of coupled THM processes? Mechanical and thermal behaviour of dehydrating clays need to be evaluated. Coupling is of two types:

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Methods need to be defined to check that a code is internally correct. It is useful to note that though it may take 1000 years for the temperature around a repository to peak, it could take 10,000 years for the velocity to peak, because the buoyancy flow velocity depends not on temperature but on the thermal energy. Consideration of coupled processes needs to include movements of gas and vapor, gas production due to corrosion, and desaturation/resaturation. It would be useful to consider the presence of the repository as a perturbation to THM behaviour of the system, and this perturbation may be of three types: (a) limited-duration type; (b) irreversible type; and (c) self-healing type. It may also be useful to consider a step-wise approach to repository development in evaluating coupled THM processes:

(a) desk studies; (b) regional investigation and surface site characterization; (c) shaft and URL (underground research laboratory); (e) construction and operation; (f) closure. The above are interesting and important points, and many of these should be accounted for in evaluating coupled THM processes for PA.

6. Conclusions The description of the work in Section 1.1, plus the discussion on THM issues and the interface with PA in Sections 1.2 and 1.3, highlight the need for understanding and modelling the THM processes in sufficient detail. Both the THM coupled processes themselves and

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the sub-systems of the repository are complex and require a structured approach. The outline review of work conducted to date, as presented in Section 2.2 and within the context of the excavation, operation, and containment and isolation stages, emphasizes the need for the structured approach and provided further background. Also, the fact, that the THM issues have to be considered in terms of those THM processes which contribute to the performance assessment, was highlighted in Section 2.3. Similarly, it was noted that the capabilities of specific numerical codes have to be matched with the analysis requirements of the problem in hand. In Section 3.3, a methodology for auditing the capability of numerical codes is described and the possibility of a future paradigm shift in numerical modelling is considered at the end of Section 3. The information and discussion in this paper, together with the presented state-of-knowledge statements elicited during the DECOVALEX II work and presented in Section 4, indicate that indeed the THM issues are important } but that they are poorly understood. The overall summary statement, i.e. the ‘summary of summaries’, is as follows. ‘‘A predictive THM capability is required to support repository design because precedent practice information is insufficient. Many aspects of THM processes and modelling are now well understood and there is a variety of numerical codes available to provide solutions for different host rock and repository conditions. However, modelling all the THM mechanisms in space and time is extremely complex and simplifications will have to be made } if only because it is not possible to obtain all the necessary detailed supporting information. Therefore, an important step is to clarify the THM modelling requirement within the PA and design context. This will help to indicate the complexity of THM modelling required and hence the models, mechanisms, type of computing, supporting data, laboratory and in situ testing, etc. required. An associated transparent and open audit trail should be developed.’’ This statement is amplified by the comments of seven eminent ‘performance assessment’ reviewers of this paper whose comments have been included in Section 5. As a result of (a) the elicitation and compilation of the state-ofknowledge statements, and (b) the subsequent extensive internal and external reviews of [5], outstanding issues were identified. Four of the most important are as follows: Clarifying the role of THM processes for PA: Although the need to consider the THM processes for

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PA is understood, it is evident from the information collected that further work is required to identify the type of THM information that is necessary for PA studies (see also Supplementary Report 2 in [5]). The PA model may well contain overall simplifications of the detailed THM processes and it is not clear how the THM processes should be presented and described. Demonstration analysis of disposal system stability: One of the most important aspects of the study of repository design and performance is to ensure that the presence of destabilizing positive feedbacks does not cause the disposal system to become unstable. For example, a natural disturbance to a major rock fracture could enhance the water flow through the fracture which in turn causes further disturbance and more water to flow. Thus, the long-term effects of perturbations and time should be studied in the system context. Study of the scale-dependent properties relevant to repository design and performance: The importance of this subject is that the parameters and constitutive relations for rock masses are known to be scale dependent. This is a crucial factor for modelling THM processes for repository design and performance. Moreover, the modelling itself may depend on the scale, e.g. discontinuum for the small scale and continuum for the large scale. There is currently no coherent approach to this subject, nor a survey of current understanding of the topic } yet it could well be critical in deciding on the THM modelling strategy. Technical auditing demonstration of the overall modelling and a specific numerical code: Many points arose during the elicitation of state-of-knowledge statements and during the subsequent extensive internal and external reviewing of [5]. A common theme running through many of the comments was to establish which THM processes are actually required in the modelling and whether analysis does capture these processes. For example, does the code include chemical processes? Is two-way coupling included in the code or not? Are gas processes and multiphase flow included? Further demonstration examples should be developed using the formal methodology for assessing the inclusion of variables and mechanisms in general modelling and as analysed by a specific code. All of these four highlighted issues are being studied, inter alia, in the DECOVALEX III work currently underway. Acknowledgements We are grateful to all the Funding Organizations and Research Teams of DECOVALEX II for their support and expertise. The following expert ‘performance assessment reviewers’ provided invaluable helpful criticisms and comments: Johan Andersson, Golders Sweden (for SKB) } now also a co-author of this paper;

Antonio Gens, Spain (for ENRESA); Bruce Goodwin, Canada (for OH); Aimo Hautoja¨rvi/Timo Vieno, Finland (for STUK); Ghislain de Marsily, Ecole de Mines, France (for the project); Alain Millard,CEN/SACLAY France (for IPSN); Piet Zuidema, NAGRA, Switzerland (for the project). We are grateful to them and have included amendments directly in response to their comments, especially in Section 5.

References [1] Stephansson O, Jing L, Tsang CF. Coupled thermo-hydromechanical processes of fractured media, Developments in geotechnical engineering, vol. 79. Amsterdam: Elsevier, 1996. [2] Dewiere L, Plas F, Tsang C-F. Lessons learned from DECOVALEX I. In: Stephansson O, Jing L, Tsang C-F, editors. Mathematical and experimental studies of coupled thermohydro-mechanical processes of fractured media. Amsterdam: Elsevier Science, 1997. p. 495–504. [3] NEA. Lessons learnt from ten performance assessment studies. NEA-OECD Report, 1997. [4] Chapman NA, Andersson J, Robinson P, Skagius K, Wene C-O, Wiborgh M, Wingefors S. SITE-94: systems analysis, scenario construction and consequence analysis definition for SITE-94. SKI Report 95:26, 1995. 102pp. [5] Stephansson O, Hudson JA, Tsang C-F, Jing L, Anderson J. DECOVALEX II Project: coupled THM issues related to repository design and performance } Task 4. SKI Report 99:7, March 1999. [6] Jing L, Tsang C-F, Stephansson O. DECOVALEX } an international co-operative research project on mathematical models of coupled THM processes for safety analysis of radioactive waste repositories. (special issue on THM coupling in rock mechanics). Int J Rock Mech Min Sci, 1995;32(5):387–98. [7] Hudson JA. Rock engineering systems: theory and practice. Chichester: Ellis-Horwood, 1992. [8] SKB. SR 95 Template for safety reports with descriptive examples. SKB Technical Report 96-05, 1996. p. 263. [9] SKI. SKI site-94: deep repository performance assessment project } summary. SKI Report 97:5, 1997. 90pp. [10] SKI. Systems analysis, scenario construction and consequence analysis definition for SITE-94. SKI Report 95:26, 1995. [11] SKI. SKI site 94: deep repository performance assessment project } vols. I & II. SKI Report 96:36, 1996. 660pp. [12] Eng T, Hudson JA, Stephansson O, Skagius K, Wiborgh M. Scenario development methodologies. SKB Technical Report 9428, 1994. 71pp. [13] Haijtink B, editor. Testing and modelling of thermal, mechanical and hydrogeological properties of host rocks for deep geological disposal of radioactive waste. In: Proceedings of Brussels Workshop, European Commission Report EUR 16219, 1995. 298pp. [14] Manteufel RD, Ahola MP, Turner DR, Chowdhury AH. A Literature review of coupled thermal–hydrologic–mechanical– chemical processes pertinent to the proposed high-level nuclear waste repository at Yucca Mountain. U.S. Nuclear Regulatory Commission Report NUREG/CR-6021, Center for Nuclear Waste Regulatory Analyses Report CNWRA 92-011, July, 1993. [15] IJRMMS. Special issue: thermo-hydro-mechanical coupling in rock mechanics (guest editor, Stephansson O). Int J Rock Mech Min Sci 1995;32(5):387–535. [16] Tsang CF, editor. Coupled processes associated with nuclear waste repositories. San Diego: Academic Press, 1987. [17] Tsang CF. Coupled hydromechanical–thermochemical processes in rock fractures. Rev Geophys, 1991;29(4):537–51.

J.A. Hudson et al. / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 143–161 [18] Gera F. Radioactive waste disposal in clays, A review of site characterization, thermo-hydro-mechanical effects and repository design. In: Haijtink B, editor. Proceedings of Workshop on Testing and Modelling of Thermal, Mechanical and Hydrogeological Properties of Host Rocks for Deep Geological Disposal of Radioactive Waste, European Commission Report EUR 16219 EN, 1995. [19] Come B. A review of thermal, mechanical and hydrogeological properties of hard, fractured rocks. In: Haijtink B, editor. Proceedings of Workshop on Testing and Modelling of Thermal, Mechanical and Hydrogeological Properties of Host Rocks for Deep Geological Disposal of Radioactive Waste, European Commission Report EUR 16219 EN, 1995. [20] Langer M. Review of R&D requirements on THM properties of salt. In: Haijtink B, editor. Proceedings of Workshop on Testing and Modelling of Thermal, Mechanical and Hydrogeological Properties of Host Rocks for Deep Geological Disposal of Radioactive Waste, European Commission Report EUR 16219 EN, 1995. [21] AECJ. Guidelines on research and development relating to geological disposal of high-level radioactive waste in Japan. Advisory Committee on Nuclear Fuel Cycle Backend Policy, Atomic Energy Commission of Japan, November 1996. [22] Oda M. An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses. Water Resour Res 1996;22:1845–56. [23] Stietel A, Millard A, Treille E, Vuillod E, Thoravel A, Ababon R. Continuum representation of coupled hydromechanic processes of fractured media. In: Stephansson O, Jing L, Tsang CF, editors. Coupled thermal-hydro-mechanical processes of fractured medium, Developments in geological engineering, vol. 79. Amsterdam: Elsevier, 1996. [24] Noorishad J, Tsang C-F. Coupled thermohydroelasticity phenomena in variably saturated fractured porous rocks } formulation and numerical solution. In: Stephansson O, Jing L, Tsang CF, editors. Coupled thermal-hydro-mechanical processes of fractured medium, Developments in geological engineering, vol. 79. Amsterdam: Elsevier, 1996. p. 93–104.

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[25] Nirex. DECOVALEX II Project, definition for test case 1, Sellafield. DECOVALEX Secretariat, Royal Institute of Technology, Stockholm, 1997. [26] PNC. DECOVALEX II Project, definition for test case 2, Kamaishi. DECOVALEX Secretariat, Royal Institute of Technology, Stockholm, 1997. [27] ENRESA. Test plan for FEBEX experiment. Empresa Nacional de Residuos Radiactivos, SA, Spain, 1996. [28] Skagius K, Strom A, Wiborgh M. The use of interaction matrices for identification, structuring and ranking of FEPs in a repository system: application on the far-field of a deep geological repository for spent fuel. SKB Technical Report 95-22, 1995. 219pp.

Further reading AECL. Summary of the environmental impact statement on the concept for disposal of Canada’s nuclear fuel waste. Atomic Energy of Canada Ltd., Report AECL-10721, COG-93-11, 1994. Andersson J, King-Clayton L. Evaluation of the practical applicability of PID and RES scenario approaches for performance and safety assessments in the Finnish nuclear spent fuel disposal programme. Posiva Report TURVA-96-02, 1996. 63pp. ENRESA. Repository study for granite: directory of features, events and processes of importance to the performance of a repository for spent fuel in crystalline rock. Appendix to ‘‘General safety aspects } a background document’’, 1991. 74pp. Jiao Y, Hudson J. The fully-coupled model for rock engineering systems. Int J Rock Mech Min Sci 1995;32(5):491–512 (special issue (Stephansson O. editor) on THM coupling in rock mechanics). SKB. General siting study 95: siting of a deep repository for spent nuclear fuel. SKB Technical Report 95-34, 1995. 141pp. SKB. RD&D } Programme 95: treatment and final disposal of nuclear waste, 1995. 235pp. SKI. SKI’s evaluation of SKB’s RD&D Programme 95. SKI Report 96:56, 1996. 26pp.