What Scientists Don't
About Geological Disposal
Verbatim Quotes From:
Techniques for Determining Probabilities
of Geologic Events and
International Association for Mathematical Geology
Studies in Mathematical Geology No. 4
edited by Regina L. Hunter and C. John Mann
Oxford University Press 1992
New York ~ Oxford
The U.S. Environmental Protection Agency (EPA) has set a probabilistic standard for the performance of geologic repositories for the disposal of radioactive waste . . . .
Chapter 1 ~ Introduction
Chapter 2 ~ Thermomechanical Effects
Chapter 3 ~ Tunneling and Mining Engineering
Chapter 4 ~ Hydrology
Chapter 5 ~ Climatology
Chapter 6 ~ Tectonics and Seismicity
Chapter 7 ~ Seismic Hazard Assessment
Chapter 9 ~ Geochemistry
Chapter 11 ~ Conclusions
In preparing this volume, experts in various geologic and closely
related fields were asked to compile techniques in use in their fields for
probabilistic predictions and to evaluate the state of the art. The evaluations do not constitute endorsements; it is too early in the overall task to endorse one technique over another.
Chapter 1 ~ Introduction
Regina L. Hunter, C. John Mann, W. Jay Conover, and Robert J.
Methods used by waste-management scientists have differed widely....
These methods have ranged from informed but unsupported guesses to elaborate calculations that may represent the best approximations that can be made today with available data. Methods commonly have contained a significant subjective component representing an individual's experience, judgment, or assumptions; this component may or may not be explicitly described. Few applications have involved adequate data bases, and therefore their results must remain suspect.
Thus ground-water flow within some aquifers and basins also can be
predicted, although the accuracy of the prediction depends on data that may not be readily obtained. Generally speaking, hydrologic data from sites currently being considered for waste repositories are sparse. Inadequacies in the data make uncertainty and sensitivity analysis of the predicted flow necessary.
Methods for determining probabilities can be divided into axiomatic
approaches, frequentist approaches, modeling approaches, and expert
The axiomatic approach assumes that the system is well understood;
few geologic systems are simple enough or well enough understood to make an axiomatic approach practical.....
Frequentist approaches depend on the analysis of existing data. Rather
than determining what outcomes are possible in a system, frequentist
approaches examine what outcomes have been recorded. The nature of the
system need not be well understood if data are numerous enough to
represent all possible outcomes. Unfortunately, 'numerous enough' depends
on the system; because the frequentist approach does not require any fundamental understanding of the system, an analyst can never know that one more trial will not produce a new outcome.....
Modeling approaches, often called Monte Carlo approaches, entail
developing a model of the system, allowing the system itself to be subjected to
numerous trials by proxy.....
The use of an axiomatic, frequentist or modeling approach implicitly
assumes [emphasis in original] that some part of an event or process under
consideration is random. Geologic events and processes for the most part are not random phenomena. They differ from truly random occurrences in two major ways. First, geologic phenomena rarely occur repeatedly under identical conditions. Therefore, geologic phenomena rarely, if ever, can constitute an infinitely long sequence from which theoretically correct probabilities could be determined..... Second, most scientists would agree that many geologic events and processes actually are deterministic phenomena and could be treated as such if they were understood adequately and enough information existed to calculate these deterministic relationships.....
Expert opinion in assigning probabilities is more subjective and uncertain than axiomatic, frequentist, or modeling approaches ..... A disadvantage of all subjective probability determinations, which must be recognized, is that they are subject to manipulation or bias, either deliberately or unknowingly, because each holds varying amounts of individual judgment.
Chapter 2 ~ Thermomechanical Effects
Krishan K. Wahl
Consideration of deep geologic disposal of nuclear waste has created the
need for a better understanding of thermomechanical processes in geologic
media. Thermomechanical effects on underground structures or systems
have not been considered probabilistically in the past. Unlike volcanic eruptions or earthquakes, thermomechanical processes are continuous and the probability of the process occurring in a high-level waste repository is 1.
Deleterious effects resulting from thermomechanical response are uncertain
and must be addressed probabilistically in the context of repository
performance. For example, what is the likelihood that thermoelastic uplift of the rock mass will fracture an overlaying aquitard and connect the aquifer to the host rock? How reliable is the predicted magnitude of thermoelastic uplift, given the uncertainties in the material properties and the simplifying assumptions of model calculations?
Three important questions (Donath and Cranwell, 1981) related to the potential
for deleterious effects resulting from thermomechanical effects are
- what is the probability of an undetected fault;
- what is the probability of new
fault development or of movement along an existing fault for a given state of stress
and the rock properties; and
- what are the consequences for a repository system if a fault is present or
Perturbation of the in-situ stress field can cause movement along a
fault that otherwise might have remained inactive. Stress perturbations can
result from natural or man-made causes, such as the construction of a
repository. Heat generated by emplaced waste introduces thermal stresses that are in addition to stress changes caused by excavation. Depending on the magnitude of these stress changes, development of new faults or fractures is also conceivable.
Although substantial experience exists in mining and design of underground
openings, unique complexities are introduced by heat generated by the emplaced waste. The thermomechanical response of the rock mass could significantly affect the overall performance of the repository system during the regulatory period.....
The rock-mass response to thermomechanical stresses and strains could activate processes that enhance permeability or create new connections to adjacent aquifers.
Intact rock does not contain joints, fractures, faults, shear zones, or other discrete discontinuities. A rock mass, in contrast, typically contains joints and fractures. A rock mass is essentially composed of pieces of intact rock with interspersed discontinuities. Soft rocks, such as salt, are more likely to contain larger volumes of intact rock than are hard rocks. Even in soft
rocks, the rock mass is significantly weaker than intact rock. Laboratory-sized
specimens tend to provide properties and characteristics of intact rock rather
than those of the rock mass. Although the linear elastic behavior of intact
rock is well understood and can be expressed analytically, rock masses in
general exhibit more complex behavior. Numerical methods are available to
describe thermal, mechanical, and thermomechanical responses of
underground structures with material and geometric nonlinearities.
Wang et al. (1983) evaluated the thermal impact of waste emplacement
in geologic media in analyses performed before 1983 and found that most modeling studies were based on thermoelastic calculations that neglected the effect of discontinuities. In identifying research needs, they stated that thermoelastic analyses could not predict the behavior of nonelastic, fractured rock masses and that rock failure conditions should be evaluated with
Many couplings among thermal, mechanical, hydrological, and chemical processes are conceivable. Not all couplings are equally significant, and different couplings may dominate at different times during the life of a repository. Thermomechanical, thermohydrological, thermohydromechanical, and thermochemical couplings are thought to be more important than others. A panel report (Tsang and Mangold, 1984) discussed 11 potential couplings and attached levels of significance to subprocesses within a given coupling. One dominant coupling during both preclosure and postclosure phases is between thermal and
Most analyses performed to date have not considered couplings other than thermomechanical or thermohydrological. Two primary reasons for the absence of such analyses are the relative lack of models and techniques to handle three- or four-way couplings and the general lack of appropriate input data (e.g. how does fracture permeability vary with normal stress?).
However, discontinuous behavior is difficult to characterize mathematically and difficult to measure in the field and laboratory. Unfortunately, most rock masses contain discontinuities, and the mechanical behavior is typically dominated by discontinuities. The state of knowledge and data bases for developing the constitutive relations for such rock masses are too limited at this time to be reliable. Application of models is possible and desirable, but uncertainties in the predicted behavior are large, especially when models have not been validated. The occasional claim by some analysts that thermoelastic calculations (numerical or analytical) are a
conservative estimate of the thermomechanical response must be viewed
Frequently, the effect of existing fractures is indirectly accounted for through the use of rock-mass properties that inherently represent a weaker rock compared with intact rock. This may be adequate for scoping, far-field calculations but may not provide the information needed to calculate stability of openings or onset of progressive failure.
Wahi et al. (1978) calculated the thermomechanical response of three hypothetical repositories in bedded salt.... Vertical displacement histories for a surface point on the axis of symmetry (i.e., point of maximum uplift)
differed considerably for spent fuel and high-level-waste repositories.
The amount of heat accumulated in the rock mass during the operational period is relatively small, but temperatures and temperature gradients in the vicinity of rooms and waste packages are large. Moreover, thermomechanical stresses local to openings are also large, causing
convergence of the openings. If rock support is not adequate, the openings may collapse; ultimate damage could either be local or extend into the rock mass by progressive failure. Over longer times, the total heat in the rock mass will be large, but maximum temperatures and stresses will be less.
After openings have been backfilled and the fill material consolidates, the net movement of rock is likely to result in an uplift followed by subsidence as cooling occurs. Several mechanisms could be triggered by changing stress and temperature fields. Fracture apertures might be reduced due to larger compressive stresses, new fractures could form and propagate, and movement along faults or shear zones could be initiated by the accumulated strain energy.
Identifying mechanisms that can affect long-term repository performance is speculative. Yet a cause-and-effect relationship is thought to exist such that a random treatment could not be justified. Numerical models do exist that can be used to perform deterministic thermomechanical analyses of a given repository design for a given geologic setting. To account for
uncertainties in material properties, model accuracy, model validity, and site
stratigraphy, Monte Carlo simulations using deterministic models are
pg. 44-45 -- Chapter Summary
Rock as a material cannot be characterized with great certainty.
Heterogeneities, local anomalies, joints, fractures, and interbeds all introduce uncertainties in rock behavior. These uncertainties extend into models and mathematical idealizations of thermomechanical response of a rock system.
The data base on site-specific rock properties and their dependence on
temperature is just starting to emerge. The state of the art in thermomechanical modeling permits nonlinear behavior (e.g. creep), discrete discontinuities (e.g., joints, faults), and coupled effects (e.g., thermohydromechanical) to be included. Such models have not been adequately validated and tend to be expensive to use, although limited validation has been achieved for some aspects of thermomechanical response. Not surprisingly, thermal-response validation has been considerably more successful than mechanical or thermomechanical validation.....
In general, however, the ability to assign probabilities to the potential disruption of the repository system or one of its components as a direct or indirect result of thermomechanical effects needs to be developed. Until
appropriate methods are developed, these probabilities will likely be assigned
on the basis of expert judgment.
Chapter 3 ~ Tunneling and Mining Engineering
Herbert H. Einstein and Gregory B. Braecher
Discontinuity-element, direct boundary-element.... and distinct-
element.... methods open an unlimited number of possibilities to represent discontinuities and interfaces.
Although numerical methods make it possible to analyze
underground openings, there is a surprising lack of supporting field validation of them. The number of methods and theoretical parametric studies far exceeds the number of field or even laboratory validations.
Temporal effects can be predicted to some extent with empirical methods (e.g., Myer et al., 1981) and can be included in analytical or numerical methods (e.g., Semple et al., 1973, 1974; Carter and Booker, 1983a, 1983b; Ladanyi and Gill, 1984; Liedtke and Bleich, 1985). Validation is scarce, however.....
A special time-dependent effect, swelling, has received considerable attention, and a number of empirical, analytical, and numerical methods exist for the prediction of swelling effects on tunnel supports.... These methods are notoriously weak in relating time to the predicted swell phenomena.
Although time-dependent performance seems to be difficult to predict,
disturbing evidence suggests that time-dependent effects may be severe.
Many old railroad tunnels show considerable decay. Tests on intact rock
reveal that stress at the start of crack propagation and long-term strength are
similar; both may be considerably smaller than 'intact strength.'.... Temporal effects clearly introduce major uncertainty, but little basis for estimating the magnitude of this uncertainty is recognized.
A difficulty with the early studies has been the ambition to comprehensively model a physical system as large, complex, and poorly defined as a repository, and to include both mid-term physical processes (e.g. thermomechanics, rock-mass behavior) and long-term geologic events (e.g. historic changes) in the analysis. This has led to large bushy fault or event trees and a lack of assurance that important chains of events have been adequately represented.
Unlike a power plant, aircraft, or electronic circuit, a repository is an open
system. Boundaries of the system are ill-defined for purposes of analysis. Even
within the near field, not all components of the system may be recognized or
identified. Thus, representational and completeness issues cloud the results of
comprehensive PRAs [probabilistic risk assessments] for geologic repositories. Current approaches to PRA for repositories, as evidenced by Golder Associates (1985) and others, are focused on narrower classes of repository performance, and thus may provide more concrete results.
pg. 74 - Chapter Summary
Detailed consideration of PRA techniques for underground
construction suggests that certain questions must be answered and additional
developments made before probabilistic methods can be applied to the
tunneling aspects of radioactive waste repositories. First, tunneling is a
complex geotechnical problem area, characterized by the interaction of many
physical mechanisms. Identifying relevant mechanisms in a particular case and modeling combinations of mechanisms are not satisfactorily resolved, particularly if long-term effects are important. Such model uncertainty has yet to be incorporated into tunnel-performance predictions.
Allin L. Gutjahr
If complete data were available for a model, no probabilistic component would be necessary, although all parameters at all locations would need to be known. [emphasis in original] Such a complete data set cannot realistically be expected. In consequence, the probabilistic approach can be envisioned as a way to model both the uncertainty inherent in nature and the lack of information about ground-water flow and dispersion. As more data become
available, the probabilistic model can be 'conditioned' by the data and the uncertainty in predictions reduced.
Models with single discrete fractures .... are probably the simplest, but even these yield complex results. These studies examined flow and dispersion mechanisms that are controlling in single fractures. In addition, they indicate that matrix diffusion and sorption are important.
Sudicky and Frind (1984) examined transport of a radionuclide within a single fracture, including molecular diffusion into the porous matrix and adsorption both on the rock face and in the porous medium. They derived an analytical solution for two-member chains and showed that the parent nuclide must be included even if it is short-lived. In addition, the daughter may advance ahead of the parent even if the parent's half-life is longer.
Schwartz and Donath (1982) looked at effects of a single fracture in a
nuclear-waste facility design. The effects of such a fracture are complex; small changes in geologic conditions result in large differences in the pattern of contaminant transport.
Long et al. (1982) studied fracture domains with finite fracture lengths,
random orientation, and random apertures. The primary focus was on two-
dimensional flow, and their intent was to see whether an equivalent-porous-
medium approach could be applied. Using Monte Carlo methods, their
results show that the samples do not have a symmetric conductivity tensor
and that large variations exist in conductivity from sample to sample. Thus, for moderate fracture density, the medium cannot be modeled as an equivalent porous medium.
Schwartz et al. (1983) studied two perpendicular discrete fracture sets
with the flow gradient arbitrarily oriented in the domain, using a two-
dimensional Monte Carlo study.... They observed significant longitudinal
dispersion and transverse dispersion that was relatively independent of
longitudinal dispersion. They concluded that classical dispersion models did
not apply to the medium. The concentration distributions were strongly
skewed, with long tails, and considerable variation existed between realizations.
Results from fracture flow models tend to be confusing; there is no unanimity as to which factors are important. Unsaturated or partially saturated flow models require added study. More experimental work would be useful in both cases.
Fractured-media models are not nearly as well validated experimentally nor as well accepted as the porous-media models. Fractured-media models can be segregated into deterministic parameter-variation models and stochastic-process models.
Deterministic parameter-variation models require a large number of
parameters for reasonably realistic zoned values. Even then, how
correlations between different zones or fluctuations from mean values
(which are important for transport and dispersion) could be incorporated is
not always clear. For any particular site, the application of deterministic
models would require many data points and perhaps a large number of zones;
such a complex numerical model still may not represent the site adequately.
Fractured media require more study before model results can be applied confidently. From a practical point of view, the stochastic approach would be more amenable for realistic applications. Location of all specific fractures and their exact parameters would be formidable, if not impossible. Results obtained regarding equivalent porous media and scales as well as results of the type given by Brown (1984) again are useful from a generic viewpoint. Almost all fracture models are two-dimensional. Full three-dimensional models now under development could yield significantly different results.
Probability estimates based on Monte Carlo methods, on the other hand, may require too many runs for reasonably accurate estimates. As DeMarsily (1983) pointed out, estimating events that have probability 0.001 would require 10 000 runs, unless one assumes a form for the probability law (e.g. lognormal) for the output.
Koplick et al. (1982) suggested that subjective probabilities assigned by experts may simply obscure the role of judgment; however, judgment seemingly cannot be avoided. Any subjective procedure used should be
explicitly stated and explained with justification. The use of methods like the Delphi method is also suspect, and a more straightforward, informed
approach may be preferable.
A more crucial need for waste-disposal problems would seem to be in
the area of unsaturated fractured media, because fractured media in general pose many unresolved problems. Although development is proceeding rapidly, predictive efforts are still in their infancy.
Chapter 5 ~ Climatology
Patrick J. Bartlein, Thompson Webb III and Steven Hostetler
An important consideration in comparing models is their relative
performance (Schlesinger, 1984). A standard benchmark used is how well a
model fits the data with which it is calibrated, or how well it reproduces a
particular feature of the paleoclimatic record. In the case of climatic prediction, the issue is how well a model will perform given substantially
different input than that with which it was calibrated....
The danger will always exist, even in the case of a model with elaborate physics, that it will be tuned to work well with the modern climate at the expense of its overall performance through time.
Chapter 6 ~ Tectonics and Seismicity
Jonathan F. Callender
The short instrumental record and society-dependent historic earthquake record can be an inadequate statistical base.... For example, whether earthquake processes are episodic on the scale of 105 years is important (cf. Allen, 1975). If they are, seismic analysis based on the historic record may be meaningless for long-term assessments, and an understanding of the relationship between seismic and tectonic events is more tenuous than assumed.
One critical view of earthquake prediction is that great earthquakes are
not random occurrences, that the historic record generally provides an
inadequate data base for proper statistical and probabilistic analysis, and thus
that deterministic models may be more useful. A second view suggests that
earthquake risk cannot be expressed in deterministic terms because of the
enormous uncertainties about the nature and location of future earthquakes.
The most significant problem with earthquake prediction is probably the lack of acceptable models that explain why precursors work.
At present, no tectonic or seismologic method is completely adequate to quantitatively assess, with a good degree of certainty, the probability of tectonic activity at a repository site during the long periods for which
performance must be predicted.
Chapter 7 ~ Seismic Hazard Assessment
C. Allin Cornell and Gabriel Toro
Earthquake-induced shaking may affect the performance of repositories during the period of waste emplacement and after closure. Mechanisms of damage during the emplacement would be similar to those experienced in a deep mining operation: damage to above-ground facilities or the vertical conveyance system, rock spalling, and collapse of tunnels. These mechanisms may lead to releases of radioactivity from waste temporarily stored above ground, in transit, or in permanent storage. The mechanisms of damage after backfilling and closure of the repository may compromise the integrity of the rock mass in the vicinity of the opening, the tunnel liner, the closure system (backfill and plugs), or the waste package.
In summary, given the limitations in the available data, empirical methods, although perhaps adequate for conventional surface facilities, are not well suited for predicting ground shaking in underground repositories.
Current estimates of the probability of new faulting near a repository vary widely. For instance, Wight (1979) suggested that the probability be taken as unity, whereas Trask (1982) suggested a small probability.
Chapter 9 ~ Geochemistry
Malcolm D. Siegel, Heinrich D. Holland and Carolyn Feakes
Data describing the chemical speciation and reaction mechanisms of radionuclides are lacking for most environmental systems of concern. Therefore, in transport models, complex mass transfer mechanisms are lumped together into a single constant describing the distribution of the solute between the aqueous and solid phases (cf. Chapter 4, this volume). When sorption is the dominant chemical interaction, a distribution constant (Kd) is used to describe the intensity of the solute-rock interaction as
moles of radionuclide per gram of sorbent rock
Kd = ----------------------------------------------
moles of radionuclide per milliliter of water
Retardation factors describe the capacity of the rock matrix or fracture lining
to adsorb the radionuclides. They depend on the solution/solid ratio of the
aquifer and take the general form
moles of radionuclide per gram or sq.cm. of sorbent rock in unit volume
R = 1 + -----------------------------------------------------------------------
moles of radionuclide per milliliter of water in unit volume
The mathematical form of the retardation factor depends on the nature of the
transmissive media: porous matrix, fractured impermeable rock, or fractured
porous matrix .... The use of retardation factors in solute transport models has been widely criticized in recent years. The nature of these criticisms and the implications for the inclusion of geochemical phenomena in a probabilistic risk assessment model is discussed in a later section.
The Environmental Transport Model represents radionuclide movement by a box model. Radionuclides in an area under consideration are divided into a number of compartments, and radionuclide movement between compartments is represented by a system of linear differential equations.
Because of the diversity of solutions, minerals, and radionuclides that
will be present at potential repository sites, a large body of empirical radionuclide sorption data has been generated. These data are at best valid for specific experimental conditions and cannot be extrapolated to other
The frequency distribution of open fractures of sufficient width to permit free flow of solutions from the repository would be difficult to estimate confidently using currently available geostatistical methods. A small number of these fractures might be sufficient to affect the safety of a repository.
Kerrisk (1984) and Siegel et al (1989) have shown that a number of elements in nuclear wastes are apt to be released into ground water at a
sufficiently rapid rate that their presence in ground water will exceed EPA
release limits, unless they are retarded or removed en route to the surface.
The efficiency of most removal mechanisms is difficult to predict.
Chapter 11 ~ Conclusions
C. John Mann and Regina L. Hunter
... subjectivity is inherent in all human activity through the decisions or selections that must be made in all we do. Examples in scientific activity include parameter values that are selected for use in analyses; number of samples that are collected to determine a data value; the data base used;
method of analysis employed; accuracy of measurements; care taken to eliminate gross errors, bias, and systematic errors; and even the philosophy and experience of the individual.... Subjectivity is present regardless of the type of analysis, accuracy of the computer, or validity of the operational concept; each of these, in turn, will be supplying additional variations that also enter the final results as a probabilistic component.
Rare events, extreme values, or those values contained in the tails of probability density functions are important in all risk assessments, because they commonly will present the greatest hazard and most extreme cases that
may be encountered. They also are the least common and least likely to be recognized or recorded in empirical data. Furthermore, they are most sensitive to errors in fitting a prediction curve to empirical data that will be necessary if they are to be used in risk assessment. No completely satisfactory method exists for addressing this problem.
Thermomechanical theory, which is well advanced and understood, has dealt only with intact rock that contains no discontinuities, such as bedding, joints, fractures and faults. Much less is known about how
discontinuities modify thermomechanical predictions.... Accurate and realistic predictions for rock masses will depend largely on successful modeling of the discontinuities revealed through field exploration data....
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