creep behaviour of a buffer material for nuclear fuel waste vault
TRANSCRIPT
Creep behaviour of a buffer material for nuclear fuel waste vault
RAYMOND N. YONG, PRAPOTE BOONSINSUK, AND DEMOS YIOTIS Geotechnical Research Centre, McGill University, 817 Sherbrooke Street West, Montreal, P .Q. , Canada H3A 2K6
Received December 10, 1984 Accepted May 22, 1985
In the Canadian nuclear fuel waste disposal concept currently under study, one of the prime candidate procedures is the borehole emplacement technique. Each fuel waste container will be placed in a 1.1 m diameter hole in the floor of a disposal vault in deep plutonic rock. The container will be surrounded by buffer material consisting of a mixture of clay and sand. This study examines the creep behaviour of the buffer material in the borehole during interaction with the waste container and the host rock. It simulated the buffer - container - host rock interaction through a small-scale physical model using the loading pressures anticipated in the full-size system. The results from the model tests were compared with those predicted by a finite element analytical model. The creep behaviour of the full-size system was then predicted using the analytical model.
From the results, it is evident that the creep behaviour of the buffer material depends significantly on interaction within the container- buffer - host rock system, overburden pressure, and water uptake. At relatively low overburden pressures, the waste container might settle, causing a separation between the buffer material and the container top. However, this could be alleviated by the swelling properties of the buffer material. The secondary creep rates are negligible, and creep in the buffer material is primarily governed by the primary creep stage.
Key words: creep, model test, swelling soil, soil deformation, unsaturated soil, finite element analysis.
Dans le concept canadien d'entreposage des rCsidus de combustible nuclCaire, une des principales prockdures considCrCe est la technique d'un emplacement de forages. Chaque contenant de rCsidus sera placC dans un trou de 1 , l m de diamktre for6 dans le plancher d'une voiite d'entreposage creusCe dans une roche plutonique profonde. Le contenant sera entour6 d'un matCriau tampon constituC d'un mClange d'argile et de sable. La prCsente Ctude examine le comportement en fluage du matCriau tampon dans le forage au cours de l'interaction avec le contenant et la roche ambiante. La technique utilisCe a simulC I'interaction tampon-contenant-roche au moyen d'un modble physique ?i petite Cchelle utilisant les pressions de chargement anticip6es dans le systkme ?i I'Cchelle naturelle. Les rCsultats des essais sur modkle sont cornparks avec ceux prCdits au moyen d'un modkle analysC en ClCments finis. Le comportement en fluage du systbme i 1'Cchelle naturelle a par la suite kt6 prCdit en utilisant le modkle analytique.
D'aprks les rCsultats, il est Cvident que le comportement en fluage du matCriel tampon dCpend de f a ~ o n significative de I'interaction entre le systbme contenant-tampon-roche, la pression des terres susjacentes et I'eau ascendante. A des pressions susjacentes relativement faibles, le contenant peut s'affaisser causant une skparation entre le matCriau tampon et le dessus du contenant. Cependant, ce phknomkne peut Stre attCnuC par les propriCtCs de gonflement du matCriau tampon. Les vitesses de fluage secondaire Ctant nkgligeables, la quantitC de fluage dans le matCriau tampon est principalement rCgie par 1'6tape de fluage primaire.
Mots cles: fluage, essai sur modble, sol gonflant, dCformation du sol, sol non saturk, analyse en ClCments finis. [Traduit par la revue]
Can. Geotech. J . 22,541-550 (1985)
Introduction In the Canadian program on the disposal of nuclear fuel waste
currently being investigated by Atomic Energy of Canada Limited (AECL) (Lopez et al. 1984), one candidate procedure is the borehole emplacement technique (Fig. l), where an 8000 kg waste container will be placed permanently in a 1.1 m diameter hole in the floor of the disposal vault installed in plutonic rock at a depth of 500-1000m below the ground surface. The waste container will be surrounded by buffer material, the main functions of which are (1) to minimize access of groundwater to the surface of the container and to control groundwater chemistry to minimize container corrosion; (2) to retard the migration of radionuclides from the failed containers, through the buffer to the backfill or surrounding rock; (3) to dissipate the heat generated by radionuclide decay; and (4) to support the containers to avoid significant deformation. The details of the borehole emplacement procedure have been described by Lopez et al . (1984).
This study addresses the creep' behaviour of the buffer material under the anticipated loading conditions within the underground nuclear fuel waste vault. The two main parameters
'Creep is defined herein as the long-term movement of soil under the constant applied loading exerted by a rigid waste container and (or) an overburden pressure.
studied were (1) stress levels induced by the overburden backfill or stress transfer in the rock formation and (2) water uptake by the buffer material from the surrounding rock or backfill. At the present time, a candidate for the buffer material is a mixture of granular material and swelling clay. Other parameters that were beyond the scope of this study include temperature, composi- tionldensity of the buffer material, and placement process. The primary objective of this study was to develop a better understanding of the deformation characteristics of the buffer material in the designed configuration of the borehole emplace- ment concept.
Experimental procedure Buffer material
The buffer material selected for this investigation was a laboratory-prepared mixture of sodium bentonite (Avonseal) and graded Indusmin silica sand at a proportion of 50150 by dry weight. A detailed compositional study of the bentonite has been reported by Quigley (1984). The mixing solution used was a "reference" synthetic granitic groundwater (GGW) with a composition, as given by Abry et al. (1982), of mainly MgS04.7H20, MgC12-6H20, and NaHC03. The liquid limit of the Avonseal clay was 284.0% and the plastic limit was 40.7%. The grain-size distribution of the Avonseal clay was 3% sand, 12% silt, and 85% clay. The specific proportions of the
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backfilled I
FIG. 1. Details of borehole emplacement concept (after AECL).
mixtures were chosen because of their potentially attractive physical, chemical, and mechanical properties for the required performance criterion (Lopez 1984). A buffer material of dry density of 1.57 Mg/m3 at the moisture content of 23.5% was used owing to its compactability and workability. The swelling pressure of the buffer material was measured to be 47 kPa, and the free swell was 10.7%. Each test specimen used (63.5 mm in diameter and 20 mm in height) was trimmed from a soil sample compacted at the same dry density and moisture content, after which it was assembled in the consolidation apparatus. For free-swell measurement a hydraulic head of 100 mm (granitic groundwater) was applied at the bottom, and the specimen was allowed to swell freely without surcharge until it reached the maximum value. The 100 mm hydraulic head was also applied for the swelling pressure measurement without permitting any volume change.
Physical model To appreciate the creep characteristics of the buffer material
as installed in a disposal borehole, a small-scale physical model was used (Fig. 2). Since the deformation of the buffer material was the primary focus of this study, the "glass-box" technique was adopted to allow visual monitoring of the overall movement of the buffer material. The half-section model of the emplace- ment borehole (Fig. 1) was constructed using a scale of approximately 1:8 as illustrated schematically in Fig. 2. The model consisted of a concrete block cast with a semicylindrical space to accommodate a half section of a waste container and the buffer material. The model waste container was made of aluminum and the buffer material was compacted to achieve a dry density of 1.57 Mg/m3 at a moisture content of 23.5%. The two components were covered with a thick, lubricated Plexiglas plate after a network of grid lines was inscribed onto the buffer material. This arrangement permitted photographic recording of the movement of grid lines (i.e. the soil deformation) at various periods during the test sequence. From the displacement fields obtained, additional information could be derived in terms of soil particle velocity, strain rate, and stress distribution using
- loading rod
reference points - t o p plate
- Plexiglas plate
-buffer material (50150 sandlciay)
- aluminum container
grid network
steel base plate
lubricated wire
granitic groundwater
(bottom entry)
FIG. 2. Schematic diagram for the physical model of the container - buffer - host rock system.
the visioplasticity method described previously by Yong and Windisch (1970).
In addition to scaling of the full-size container and borehole dimensions, the pressure exerted by the waste container onto the supporting buffer material was similar in both the model and the full-size system (i.e. 277.4 kPa). In the model (Fig. 2), the required pressure was applied by pulling the aluminum semi- cylinder downwards with dead weights, through a small lubricated and sleeved wire passing through the buffer material. The simulated overburden pressure in the model was varied by changing the top surcharge weights applied through the loading rod. Different water-entry positions were provided at the top, bottom, and sides of the concrete block, as shown in Fig. 2 for the bottom position only. The test program conducted in the glass-box model simulation is summarized in Table 1.
Test results and discussion The two main variables investigated were the overburden
pressure and water intake of the buffer material (Table 1). During the operating phase of an underground disposal vault (Fig. 1) one possible scenario being considered is that, after emplacement of the waste container in the borehole, the tunnel space above the borehole will not be backfilled immediately. Tests 1 and 2 in Table 1 simulate such a situation by imposing no overburden pressure. The other tests consider a range of backfill surcharge-from 36 kPa (representing partial backfilling and (or) live load prior to full backfilling) to full backfill height where an overburden pressure of about 120 kPa is anticipated. Water intake was simulated by allowing granitic groundwater to enter the buffer material at various applied overburden pres- sures. The deformation of the entire exposed face of the buffer material was monitored during the imposed loading conditions. The results obtained directly from the experiment will be discussed prior to the analytical treatment using the finite element method.
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TABLE 1. Summary of test conditions
Overburden Granitic Creep duration* Creep duration Test pressure, groundwater Initial creep* under constant during water No. kPa intake (before water intake) axial load, days intake, days Remarks
1 0 No -
2 0 Yes at bottom Yes 3 36 No - 4 36 Yes at bottom Yes 5 36 Yes at bottom No 6 120 No - 7 120 Yes at bottom Yes
-
15 - Reference 15 15 18 - 24 24
24 18 - About full backfill height 24 24 About full backfill height
*Prior to inducing water intake, the container-buffer system was allowed to reach its equilibrium state (i.e. no further creep after installation).
Soil particle movement-without water intake The movement of the buffer material around the waste
container as observed in the model tests will be presented with reference to Fig. 3. Specific reference points (e.g. A1 , B 1, etc.) were selected for detailed monitoring. The control point B2 is located on the centre line of the waste container, which is considered to be incompressible.
The displacment-time relationships of the reference points in Fig. 3 are depicted in Fig. 4. The relationships depict "typical" soil particle movement behaviour without the influence of water intake. The cumulative displacement patterns of the buffer material in the disposal hole are shown in an exaggerated scale in Fig. 5 for various overburden pressures. It should be mentioned that both the overburden pressure and the container pressure were applied simultaneously, after which the deforma- tion patterns of the buffer material were recorded. From these results (Fig. 4), the following observations can be made:
1. Upon loading, the buffer material undergoes immediate deformation, and continues to increase with time (i.e. primary creep) until it reaches its peak value-normally in about 10-20 days as shown in Fig. 4. The secondary creep observed (where the rate is constant, after passing the primary stage) appears to be, in general, insignificant. The experiment was terminated when the buffer material reached the secondary creep stage.
2. Within the buffer mass, maximum displacement is experi- enced by the container and the supporting material immediately underneath it (i.e. points B2 and C2). The displacements at other points of interest are dependent on their locations relative to the boundary conditions.
3. Not all the soil movements are downward under the am plied vertical pressures. The zones located close to the container side boundaries exhibit upward movements when no overbur- den pressure is imposed (i.e. points A l , A3, B1, and B3), despite the fact that the corresponding central points move in the opposite direction. This kind of behaviour could be due to the influence of confinement of the buffer material between the container and the dis~osal hole. Once the container moves downward, the buffer Aaterial located at the bottom edges of the container is squeezed upward as a result of the interaction of the entire system. Unlike the material underneath the container, which is compressed by the container, the material along the container side is not directly under any compression, and is therefore more susceptible to volume change.
4. For the buffer material located within the vicinitv of the container, the soil particles on the same horizontal plank do not necessarily exhibit the same displacement characteristics. Thus
overburden pressure
t z 140 m m 4
76.4mm
FIG. 3. Schematic diagram of the borehole system (used as refer- ence for presentation).
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Time (day81 Time (days)
Overburden Pressure
o 0 kPa (test 1) A A 36 kPa (test 3) o e 120 kPa (test 8)
Time (days) Time (days)
positive values denote downward movement
FIG. 4. Soil deformation vs. time relationship (at constant moisture content).
FIG. 5. Soil particle movement pattern (at constant moisture container top due to the cohesive nature of the material. Higher content). overburden pressure reduces this separation.
overburden pressure the central point A2, for example, undergoes higher magnitudes o kPa 38 kPa 120 kPa of deformation than the corresponding points A1 and A3. For
15 days
C C C 4 C 4 < C C C C
120 kPa. Such a trend is followed by the buffer material located above the bottom of the container. The effect of overburden pressure is diminished in the zone located well below the container bottom (e.g. points Dl-D3). In addition, the upward movement of the soil noticed in sections a-a and b-b without
b L d i overburden pressure appears to be suppressed when the over-
P '- 4 4 burden pressure is applied at the top of the buffer material. i l b I The applied overburden pressure is transferred downward to the
C C b 6 bottom part of the container, below which the effect of I 4 overburden pressure is negligible.
6. At the two low overburden pressures (0 and 36 kPa) the i b + 1 4 b r a t ) j 4 b b b I i + L b t J container settles more than does the buffer material located 1 , l i , l l l l
amm I' =imm 1- dmm 1 immediately above the container (i.e. comparing points B2 and
exaggerated scale for soil deformation A2). For zero overburden pressure, point B2 moves downward by 1.43 mm while point A2 settles 0.99 mm. This results in a
(the number of days shown indicates the elapsed time of observation) noticeable se~aration between the buffer material and the
18 days
( C ( I I L b 4 6 L b
18 days
i \ 4 b 4 L L L b i J
the zones beyond the influence of the rigid container, the displacement patterns are normally uniform-particularly for the buffer material located well above the container.
5. The overburden pressure obviously affects both the container and the buffer material movements. The container displacement as indicated by point B2 increases with increasing overburden pressure, from 1.43 mm at 0 kPa to 1.70 mm at
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I test 2 water intake started
0 20 40 60 80
Time (days)
3 .o B 2 B 2 B 1 , 8 3 0 1 , B 3
1.5
0.0 tests 4 8 7
V L, I test 2 water intake started
0 20 40 60 80
Time (days)
Overburden Pressure o 0 kPa A 36 kPa o 120 kPa (test 2) (test 4) (test 7 )
h - 3.0 3.0 E E V Y
C C C C P)
a 1.5 E 1.5 E 0) 0 0 (0
Q - - P n
0 0.0 5 0.0
- water Intake started - 0 0
0 water intake started
v - - C
C
$ -1.5 & 1.5 > 0 20 40 60 80 > 0 20 40 60 80
Time (days) Time (days)
Granitic groundwater was used throughout
Positive values denote downward movement
FIG. 6. Vertical displacement vs. time relationship (granitic groundwater intake at the bottom)
7. Comparing the deformation of the buffer material on both sides of the central line of the disposal hole (i.e. points A1 vs. A3, B1 vs. B3, etc. in Figs. 3 and 4), one observes that the movements of the soil particles are not necessarily symmetrical. This should be due to nonuniformity in the buffer material properties developed during placement, and possible slight misalignment of the container - buffer - host rock system. It is possible, therefore, that a slight tilting of the container might occur during long-term creep.
From the foregoing discussion, it is evident that the creep behaviour of the buffer material in the disposal hole is governed by the interaction between the container - buffer - host rock. Such a complex situation renders it difficult to predict the movement of the buffer material unless the disposal system is properly modelled in the analytical formulation.
Soil particle movement-with water intake The possibility of water intake by the buffer material was
simulated by providing water entry at the bottom of the buffer material under a pressure of 103 kPa. Granitic groundwater was allowed to enter the soil only after the end of primary creep, subsequent to applying the container and overburden pressures (i.e. test Nos. 2, 4, and 7 in Table 1).
The results obtained are illustrated in Fig. 6 in terms of vertical displacement - time relationships, from which the following observations can be made:
1. Prior to water ktake, the displacement patterns in the buffer material were similar to those observed earlier in test
Nos. 1 , 3, and 6 , including the upward movement at zero overburden pressure. Thus the creep behaviour of the buffer material in the disposal hole simulated by the model testing is reproducible.
2. Upon introduction of water at the bottom of the buffer material, the material deformation together with the container settlement increases considerably. For the first few days after water intake, an increase in settlement is experienced in all regions of the buffer material-from the top (points A 1-A3) to the bottom (points Dl-D3).
3. The ability of the buffer material to swell upon water uptake only appears after it undergoes substantial settlement. The swelling of the buffer is evident where the overburden pressure is low or zero, e.g., points C1 and C3 at no overburden pressure (after 25-30 days). The fact that the buffer material in the lower part of the container (i.e. sections c-c and d-d in Fig. 3) has not shown any sign of upward movement when creeping at constant moisture content (test 2-the first 20 days) confirms the swelling of the material due to water intake.
4. The influence of the overburden pressure on the buffer deformation is evident. Without any overburden pressure imposed, the buffer material undergoes the highest settlement during the first 5 days of water intake, after which it either increases slightly or decreases because of the development of swelling forces. Higher overburden pressure normally leads to higher settlement in the buffer material during water intake. For comparison, an additional increase in settlement of 2 mm (maximum) occurs, in the case of no overburden pressure, due
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,- top surface
70.2 mm
FIG. 7. Mesh layout for the model.
O h one-dimensional compression test
Stress (kPa)
FIG. 8. Load-deformation relationship for buffer material (50150).
loOO consolidated - undrained triaxial test
(without saturation and pore pressure measurement)
800 1 9 .+ Confining Pressure
0 4 8 12 16 20
Axlal Strain (46)
FIG. 9. Stress-strain relationship for buffer material (50/50).
process and (2) prediction of the buffer creep characteristics in a full-size borehole based on the results of the model test. The finite element method adopted is described below.
Mesh arrangement and boundary conditions The borehole disposal configuration used in the model test
(Figs. 1 and 3) was idealized by the finite element mesh arrangement for half of the section as shown in Fig. 7, taking advantage of axial symmetry. A total of 122 elements and 90 nodes was used. All the boundaries except the top buffer space were placed on rollers,. allowing buffer material movement only in one direction owing to boundary and symmetrical con- straints. All the boundaries of the model container were placed on rollers for sim~licitv. In effect, it is assumed that the different . . contacting surfaces-buffer/concrete and buffer/aluminum
to water intake as to a Of mm at container-are smooth. This assumption is considered permis- constant moisture 'Ontent (point D2)' As a of high sible since all these surfaces were lubricated to reduce side settlement at the bottom part of the buffer material, the upper friction effects during the experiments. portion of the buffer material settles accordingly but to smaller In the finite element analysis, the input boundary conditions values. are prescribed using displacement-time relationships obtained
In the water intake of the buffer causes in the model tests (Fig. 4). The input displacements are imposed substantial additional displacement of the container and the on two boundaries that are externally loaded, i.e. the top buffer buffer material. The ability of the buffer material to swell is surface on which the overburden pressure is applied and the evident when the pressure is low. bottom of the model container where the container pressure is The time to reach a rate of creep (in the applied. The input displacements achieve the final values stage) appears to be longer than that observed without water through small increments. intake.
Constitutive relationships Analytical modelling Observations of soil response performance above the model
The objectives for formulating an analytical model were to container (Fig. 3) indicated that the soil deformed relatively provide a means for (1) evaluation of the buffer response uniformly (Fig. 5). This suggests that the material in this behaviour in terms of stress distribution during the loading particular zone behaved in a manner typical of one-dimensional
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Final ffy contour
vertical stress ($1 contour (kPa)
negative = compression
FIG. 10. Comparison of the vertical stress between the one-type and the two-type constitutive relationships.
compression. Thus the settlement (strain) - stress relationship (Fig. 8) obtained from the one-dimensional compression test appeared to be appropriate. For the region below the model container (Fig. 3), the material acted like the supporting foundation for the model container. Thus, the stress-strain relationships obtained from the consolidated-undrained triaxial tests (Fig. 9) should be applicable. For the buffer material located between the container wall and the interior wall of the concrete block (Figs. 2 and 3), the response behaviour of the material could not be readily identified, unlike the other two regions already mentioned. It was, nevertheless, decided to adopt the triaxial stress-strain curves (Fig. 9) for this zone, since some upward movements of soil particles were observed (Fig. 5).
Another approach that might be taken is to adopt a common single triaxial stress-strain relationship for the entire buffer (soil) mass. The results of both approaches are compared in Fig. 10 in terms of calculated vertical stress distribution. Based on the same input boundary displacements, the calculated stresses from the approach using two types of stress-strain curves are in better agreement with the imposed pressures than those calcu- lated using a common single stress-strain curve throughout the
Vertkal Wplacement Contour (mm )
38 kPa
18 days
120 kPe
18 days
from F.E. --- measured 0, 3 8 , 120 = overburden pressure 15, 18, 18 = creep period
(kPa) (days)
FIG. 11. Comparison of the vertical displacement contours between the measured and the calculated values.
soil. It should be emphasized that the analytical model is used to analyze the model test results as a first approximation. More sophisticated analyses can obviously be adopted. Continuing studies requiring further attempts at model scaling of physical experiments would be needed to provide input to the develop- ment of more sophisticated analytical models.
Both stress-strain relationships (Figs. 8 and 9) were directly described in numeric format for computational purposes. Owing to the nonlinearity of the stress-strain curves, the initial modulus of elasticity was taken as the initial tangent modulus of the stress-strain curve with the lowest confining pressure. Subsequently, a number of iterations were imposed to arrive at the appropriate values of elastic moduli.
Validation of analytical model developed The simplest means for evaluation of the applicability of the
developed analytical model is a comparison between measured and calculated buffer deformation distributions. Such a com- parison is illustrated in Fig. 11 for three different overburden pressures. It is evident that the vertical displacement patterns obtained in the finite element analysis agree relatively well with those visually measured in the model tests, particularly for high overburden pressures. Furthermore, neither discontinuity nor incompatibility, especially in the transition zone between the top of the container and the bottom part, can be readily distinguished. In essence, the analytical model formulated appears to be valid, although it is realized that better accuracy can be achieved, if warranted, by a more sophisticated analytical approach.
Analytical results The analytical model formulated is applied primarily to
evaluate the buffer behaviour under the overburden pressure imposed, first for the test model, and then extended for the
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Overburden Pressure
0 kPa 3 6 kPa 120 kPa
negative = compression
Final Stress ay (kPa)
Overburden Pressure
0 kPa 36 kPa 120 kPa
negative=compression
Final Stress ax (kPa)
FIG. 12. Vertical stress distribution from the finite element method. FIG. 13. Horizontal stress distribution from the finite element method.
full-size disposal borehole. The results are obtained in terms of distribution of stress, displacement, strain, particle velocity, the container and the host-rock walls are the result of compres- strain rate, etc. Only those that are of direct interest herein will sion by the upward movement of the buffer material around the be presented. It should be recalled that the displacement patterns container bottom comer, and the downward movement of of the buffer mass are illustrated in Fig. 11 for three different material from the container top due to the overburden pressure. overburden pressures at the end of primary creep. The analytical The stress distributions are obviously affected by the rigid results agree well with those measured, when the overburden container configuration, which eventually leads to the nonuni- pressure is applied. form stress distributions, especially around the corners of the
Stress distribution The stress distributions within the buffer mass under the
disposal hole configuration are presented in Fig. 12 for vertical stresses (a,,) and Fig. 13 for horizontal stresses (a,). The values of stresses shown correspond to the final displacements mea- sured in the model tests, which are used as input boundary conditions in the finite element analysis. For the vertical stresses, it is evident that the stresses developed in the buffer material at the buffer top surface are in good agreement with the overburden pressures imposed. The vertical stresses near the buffer surface are uniformly distributed in accordance with the uniformly loaded surface induced by the overburden pressure. At the bottom of the container, the contact stress distributions resemble those underneath a rigid unyielding foundation, which is the actual boundary condition of the model container. The relatively high stresses within the buffer mass confined between
container. The horizontal stresses (Fig. 13) exhibit behaviour similar to
that of the vertical stresses, i.e. uniform distribution within the top zone and nonuniform distribution around the container. The high horizontal stresses generated would significantly influence the interaction within the container - buffer - host rock system, particularly if the container and (or) host-rock walls are not sufficiently smooth to alleviate friction.
Prediction offull-size system response byjnite element method Having validated the analytical model developed, it is
possible to study the behaviour of the full-size system subjected to the same loading conditions as the test model using the finite element method. In this respect, the "full-size" dimensions are fully idealized by extending the finite element mesh for the model (Fig. 7). For simplicity, only the responses of the buffer material around the container bottom are investigated. The
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prototype prototype
model model
FIG. 14. Comparison of the stress distribution between the prototype and the model.
extended finite element model is subjected to the same boundary displacements as those used in the analysis of the physical model for direct comparison. The applied pressure (from the container) is maintained equal to the pressures exerted by the model container. Thus, the main difference is the dimensions: the full-size system is eight times larger than the test model.
Scaling between model and prototype, with respect to interpretation or extrapolation of results, cannot be readily applied via simple geometric or mass scaling laws, principally because the material properties are not scaled-even when the geometry of the problem is scaled. In this instance, whereas the model system is geometrically scaled as one-eighth, both buffer material properties and applied container loading pres- sures are not scaled. In the discussion to follow, the results are examined with a view to development of an empirical means for scaling from model to prototype, to permit reasonable predic- tion of prototype behaviour.
The results presented in Fig. 14, in terms of vertical and horizontal stress distributions around the bottom of the waste container, show that under the same amount of displacement at the container bottom, the stresses developed in the buffer material for a full-size system are much less than those found in the test model. It is likely that since the mass of buffer material being compressed in the full-size system is considerably larger, the boundary effects from the host rock are correspondingly reduced. In addition, identical displacements of individual points in the buffer material (between model and prototype) will produce less calculated strains in the prototype (because of the larger mass of material) than in the model. Thus, the calculated stresses in the full-size system will be less.
A comparison of the calculated displacements for the full-size system and the test model under the same container loading pressures, using the finite element method, shows that the nodal vertical displacements in the full-size system are generally higher than those in the model by an average factor of about 13.
The data show that other values, such as stresses, strains, and horizontal displacements in the buffer mass, are also different. Recognizing that the relationship between the prototype perfor- mance and model behaviour should be evaluated on the basis of similar loading boundary conditions, i.e. overburden pressure, surface conditions, etc., scale factors for transforming the corresponding characteristics of the physical model to the full-size system can then be evaluated by using the finite element model developed.
Effect of overburden pressure The overburden pressure acting on the top of the buffer
material for the borehole disposal method depends primarily on the backfill density, and the pressures developed by the surrounding host rock. To provide information regarding the settlement of the waste container due to various overburden pressures, the analysis simulates the physical situation by increasing overburden pressure from 120 to 950 kPa. Using the average scale factor of 13 (based on the average ratio of prototype/model strains), the model result can be transformed to the full-size situation. The results shown in Fig. 15 indicate that the container settlement increases exponentially with the increasing overburden pressure. Settlement starts to increase at an accelerating rate when the overburden pressure is higher than 600 kPa.
Effect of water uptake The influence of water uptake on the container and buffer
settlement can be simulated by the finite element model in a simplified approach. Considering the fact that it is the long-term settlement of the waste container that is of greatest importance, one can assume that all the buffer material will be saturated by the surrounding groundwater-sometime after commission. The simplest technique in applying the analytical model is to obtain the constitutive relationship of the buffer material under saturated conditions. However, such information is difficult to
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Calculated Results from Finite Element Method
0 300 600 900 1200
Overburden Pressure (kPa)
FIG. 15. Container settlement vs. overburden pressure relationship.
- - California Bearlng Ratio Test
- Buffer 50150
o no soaking -
1. The creep behaviour of the buffer material depends significantly on interaction within the container - buffer - host rock system, overburden pressure, and water uptake. An accurate prediction of the container settlement cannot be arrived at without accounting for these parameters. A simple approach using the finite element method, as formulated in this study, can provide some useful insight.
2. At relatively low overburden pressures, waste container settlements might be so large that a separation between the buffer material and the container top might occur. Such a situation would lead to loss of tight contact between the two materials, possibly reducing the effectiveness of the buffer material. However, intake of groundwater during the life span of the buffer material could alleviate this potential problem provided the buffer material is capable of swelling from water uptake.
3. The analytical model developed has been verified with the physical model test results. In effect, it can be used to analyze and (or) predict the behaviour of the buffer material around a full-size container in conjunction with the similarity principles of model tests.
4. It appears that creep in the buffer material is primarily governed by the primary creep period since the secondary creep rates are small and would produce negligible settlement over the lifetime of the waste containment.
0 4 8 12 16 20
Penetration (mm)
FIG. 16. Stress vs. penetration relationship.
obtain since the buffer material has a high swelling potential. With the knowledge that the buffer mass settles considerably during water uptake (Fig. 6), one method of simulation would be to lower the strength of the buffer material by a reasonable proportion. As a guide, the compressibility of the buffer material, due to the rigid waste container, under both constant moisture content and saturated conditions can be evaluated by a California bearing ratio test. The results shown in Fig. 16 suggest that for a container contact pressure of 277.4 kPa, the strength of the buffer material is reduced by more than 50% when it is saturated. Obviously, the swelling of the buffer material cannot counteract the softening effect, leading to high compressibility of the buffer material. Additional pressures at the bottom of the container, probably induced by the overburden pressure, will eventually cause much higher settlement upon water uptake.
Conclusions Based on the test methodology and analytical model used to
study the creep behaviour of the buffer material when placed in the borehole disposal configuration, the following conclusions can be made:
Acknowledgements This study was funded by Atomic Energy of Canada
Limited (AECL). The useful input and contributions given by R. S. Lopez of AECL are gratefully acknowledged. The permission given by AECL for publication of this paper is also acknowledged.
ABRY, D. R. M., ABRY, R. G. F., TICKNOR, K. V., and VANDER- GRAAF, T. T. 1982. Procedure to determine sorption coefficients of radionuclides on rock coupons under static conditions. Atomic Energy of Canada Limited, Chalk River, Ont., Technical Record, Report TR-189.
LOPEZ, R. S. 1984. Disposal vault seating. Proceedings of the Infor- mation Meeting of the Nuclear Fuel Waste Management Program, 1984 General Meeting. Atomic Energy of Canada Limited, Chalk River, Ont., AECL Technical Report TR 320.
LOPEZ, R. S . , CHEUNG, S. C. H., and DIXON, D. A. 1984. The Canadian program for sealing underground nuclear fuel waste vaults. Canadian Geotechnical Journal, 21(3), pp. 593-596.
QUIGLEY, R. M. 1984. Quantitative mineralogy and preliminary pore-water chemistry of candidate buffer and backfill materials for a nuclear fuel waste disposal vault. Atomic Energy of Canada Limited, Pinawa, Man., Report AECL-7827.
YONG, R. N., and WINDI~CH, E. 1970. Determination of wheel contact stresses from measured instantaneous soil deformations. Journal of Terramechanics, 7(3, 4), pp. 57-67.
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