synthesis report - posiva · evaluated in order to check if the final saturated density...

POSIVA 2012-47

August 2013

POSIVA OY

Olki luoto

FI-27160 EURAJOKI, F INLAND

Phone (02) 8372 31 (nat. ) , (+358-2-) 8372 31 ( int. )

Fax (02) 8372 3809 (nat. ) , (+358-2-) 8372 3809 ( int. )

Erdem Toprak

Nadia Mokni

Sebastia Ol ivel la

Universitat Pol i tècnica de Catalunya

Xavier Pintado

B+Tech Oy

Thermo-Hydro-Mechanical Modelling of BufferSynthesis Report

ISBN 978-951-652-229-9ISSN 1239-3096

Tekijä(t) – Author(s)

Erdem Toprak, Nadia Mokni, Sebastia OlivellaUniversitat Politècnica de Catalunya Xavier Pintado, B+Tech Oy

Toimeksiantaja(t) – Commissioned by

Posiva Oy

Nimeke – Title

THERMO-HYDRO-MECHANICAL MODELLING OF BUFFER, SYNTHESIS REPORT

Tiivistelmä – Abstract

This study addresses analyses of coupled thermo-hydro-mechanical (THM) processes in a scheme considered for the spent nuclear fuel repository in Olkiluoto (Finland). The finite element code CODE_BRIGHT is used to perform modelling calculations. The objective of the THM modelling was to study some fundamental design parameters.

The time required to reach full saturation, the maximum temperature reached in the canister, the deformations in the buffer–backfill interface, the stress–deformation balance between the buffer and the backfill, the swelling pressure developed and the homogenization process development are critical variables.

Because of the complexity of the THM processes developed, only a single deposition hole has been modelled with realistic boundary conditions which take into account the entire repository. A thermal calculation has been performed to adopt appropriate boundary conditions for a reduced domain.

The modelling has been done under axisymmetric conditions. As a material model for the buffer bentonite and backfill soil, the Barcelona Basic Model (BBM) has been used. Simulation of laboratory tests conducted at B+Tech under supervision of Posiva has been carried out in order to determine the fundamental mechanical parameters for modelling the behaviour of MX-80 bentonite using the BBM model.

The modelling process of the buffer–backfill interface is an essential part of tunnel backfill design. The calculations will aim to determine deformations in this intersection, the behaviour of which is important for the buffer swelling.

The homogenization process is a key issue as well. Porosity evolution during the saturation process is evaluated in order to check if the final saturated density accomplishes the homogenization requirements.

This report also describes the effect of the existence of an air-filled gap located between the canister and the bentonite block rings in thermo-hydro-mechanical behaviour of the future spent nuclear fuel repository in Olkiluoto. The presence of the 10 mm air gap has an influence on the thermal, hydraulic and mechanical response of the buffer. The closure of the gap is controlled by the swelling deformation developed as the bentonite buffer saturates. Under unsaturated conditions, the buffer will not transfer heat efficiently, and that may disturb heat dissipation and lead to somewhat higher canister temperature. This is more evident when the hydration of the buffer takes place more slowly because the gap remains open during heating. The kinetics of water supply is affected by the hydraulic conductivity of the different elements and in particular by the hydraulic conductivity of the host rock formation.

Avainsanat - Keywords

Repository, spent fuel, thermal modelling, hydraulic modelling, mechanical modelling, thermo-hydro-mechanical. ISBN

ISBN 978-951-652-229-9 ISSN

ISSN 1239-3096 Sivumäärä – Number of pages

108 Kieli – Language

English

Posiva-raportti – Posiva Report Posiva Oy Olkiluoto FI-27160 EURAJOKI, FINLAND Puh. 02-8372 (31) – Int. Tel. +358 2 8372 (31)

Raportin tunnus – Report code

POSIVA 2012-47

Julkaisuaika – Date

August 2013

Tekijä(t) – Author(s)

Erdem Toprak, Nadia Mokni, Sebastia OlivellaUniversitat Politècnica de Catalunya Xavier Pintado, B+Tech Oy

Toimeksiantaja(t) – Commissioned by

Posiva Oy

Nimeke – Title

PUSKURIN TERMO-HYDRO-MEKAANINEN MALLINNUS.

Tiivistelmä – Abstract

Tässä työssä keskitytään analysoimaan kytkettyjä thermo-hydro-mekaanisia (THM) prosesseja liittyen bentoniittimateriaaleihin Olkiluodon käytetyn ydinpolttoaineen loppusijoituslaitoksessa. Mallinnus toteutettiin CODE_BRIGHT-mallinnusohjelmalla, joka perustuu elementtimenetel-mään. THM-mallinnuksen tavoitteena oli tutkia bentoniittipuskurin suunnittelun lähtökohtina käytettäviä materiaaliparametrejä. Tärkeimmät muuttujat mallinnustyössä olivat kestoaika täyteen saturaatioon, ydinjätekapselin saavuttama maksimilämpötila, puskuri-tunnelitäyttörajapinnan mekaaniset deformaatiot, rasitus-deformaatiotasapaino puskurin ja täytön välillä, paisuntapaineen kehittyminen sekä homogeni-saatioprosessin eteneminen. Mallinnus toteutettiin aksiaalisymmetrisellä geometrialla ja puskuri- ja täyttömateriaalin mekaa-nista käyttäytymistä kuvattiin nk. Barcelona Basic Model -materiaalimallilla (BBM). Keskeiset materiaaliparametrit kalibroitiin simuloimalla B+Techin laboratoriossa tehtyjä kokeita MX-80-materiaalille. Homogenisaatioprosessin tärkeyden vuoksi materiaalin huokoisuuden kehitystä saturaatioprosessin aikana arvioitiin pyrkimyksenä selvittää, täyttääkö lopullinen saturoitunut tiheys homogenisaatiolle asetetut vaatimukset. Tässä raportissa kuvataan myös kapselin ja bentoniittipuskurin välisen ilmaraon vaikutusta pus-kurin THM-käyttäytymiseen, ja tutkimuksissa havaittiin 10 mm raolla olevan vaikutuksia puskurin termiseen, hydrauliseen ja mekaaniseen vasteeseen. Saturoituneessa tilassa puskuri ei siirrä lämpöä riittävän tehokkaasti pois kanisterin luota, ja tämä voi vaikuttaa lämmön poistumiseen johtaen kapselin lämpötilan nousuun. Jos vettymisprosessi on hidas, ilmarako pysyy auki pidempään ja johtaa suurempaan lämpövaikutukseen kanisterin kohdalla.

Avainsanat - Keywords

Loppusijoitustila, käytetty ydinpolttoaine, terminen mallinnus, hydraulinen mallinnus, mekaaninen mallinnus, termohydromekaaninen mallinnus, saturoituminen, puskuri, täyttöaine, kallioperä, halkeama, elementtimallinnus, CODE_BRIGHT. ISBN

ISBN 978-951-652-229-9 ISSN

ISSN 1239-3096 Sivumäärä – Number of pages

108 Kieli – Language

Englanti

Posiva-raportti – Posiva Report Posiva Oy Olkiluoto FI-27160 EURAJOKI, FINLAND Puh. 02-8372 (31) – Int. Tel. +358 2 8372 (31)

Raportin tunnus – Report code

POSIVA 2012-47

Julkaisuaika – Date

Elokuu 2013

1

TABLE OF CONTENTS

ABSTRACT

TIIVISTELMÄ

1 INTRODUCTION .................................................................................................... 3

2 GEOMETRICAL AND PHYSICAL PROPERTIES OF THE PROBLEM ................. 5

2.1 Material properties ............................................................................................ 5

2.2 Gap properties .................................................................................................. 9

3 INITIAL AND BOUNDARY CONDITIONS ............................................................ 13

4 THM ANALYSES SIMULATING DISPOSAL IN A VERTICAL BOREHOLE ......... 17

4.1 Results for the Base Case .............................................................................. 19

4.2 Sensitivity analyses and comparison ............................................................. 27

5 THM ANALYSES SIMULATING A GAP BETWEEN THE BENTONITE–BUFFER AND THE CANISTER ........................................................................................... 33

5.1 Case I ............................................................................................................. 34

5.2 Case II ............................................................................................................ 40

5.3 Case II NOGAP .............................................................................................. 46

5.4 Case III ........................................................................................................... 49

5.5 Comparison of results .................................................................................... 59

6 DISCUSSION........................................................................................................ 65

7 CONCLUSIONS AND RECOMMENDATIONS ..................................................... 67

REFERENCES ............................................................................................................. 69

APPENDIX 1. DESCRIPTION OF THE BASIC THM FORMULATION ........................ 71

APPENDIX 2. MODELLING EXPERIMENTS ............................................................... 79

3

1 INTRODUCTION

This report contains a work that has been done at the Polytechnic University of Catalonia (UPC) in order to study the THM evolution in a spent nuclear fuel repository based on crystalline rock and containing a clay buffer among other elements since emplacement of the canisters till target state.

The repository will consist of a series of deposition holes in the bedrock. Bentonite buffer rings will surround the copper canisters containing spent fuel. As a protecting and isolating barrier between the waste canisters and the surrounding host rock, MX-80 (Kiviranta and Kumpulainen 2011; Karnland et al. 2006) bentonite will be used as buffer material (Juvankoski et al. 2012). Friedland clay is considered one of the candidates to be used as drift backfill material to meet the long-term performance requirements set for backfilling of a disposal tunnel in the repository (Autio et al. 2012, Börgesson et al. 2009). Figure 1.1 shows a cross section of the spent nuclear final disposal facility. There are two alternative disposal conditions of the spent fuel. The first alternative envisages the vertical emplacement of the canisters in vertical boreholes excavated in horizontal tunnels (KBS-3V). The second alternative envisages that the canisters will be disposed horizontally in the horizontal tunnels (KBS-3H). Figure 1.1 shows a schematic representation of the two disposal possibilities.

Figure 1.1. Alternative realizations of the KBS-3 spent fuel disposal method (In this study, the vertical deposition hole has been modelled). Figure Posiva Oy.

4

This report is a final report and includes the description of the work presented in two previous contributions, namely:

THM modelling of ONKALO Project, preliminary modelling study (E. Toprak, N. Mokni, S. Olivella, November 2011). In addition to various analyses investigating the response of an idealized scheme under THM conditions, this first report also included an appendix devoted to thermal calculations to identify appropriate boundary conditions and another appendix dedicated to modelling laboratory experiments to calibrate material parameters for the buffer. The time required for reaching full saturation, maximum temperature reached in the canister, deformations in the buffer–backfill interface and the stress–deformation balance in this interaction were the main issues addressed.

THM modelling of ONKALO Project, Gap Effect (E. Toprak, N. Mokni, S. Olivella, July 2012). This second report presents calculations in which the effect of the gap between the canister and the buffer is considered. Various cases are considered and compared.

A fundamental issue in the modelling was to determine relevant thermal boundary conditions so that the details of THM-behaviour could be captured by defining proper near-field thermal boundaries. The thermal boundary conditions fixed for the THM modelling have been calculated by solving the thermal problem for the entire repository using numerical methods and comparing with an analytical solution (Ikonen, 2005). Of particular interest was the analysis of the response of the buffer–backfill interface as it is an important part of the tunnel backfill design. Deformations in this intersection, whose behaviour is important for the buffer swelling, were observed in detail.

Before undertaking the THM calculations, it was necessary to investigate the hydro-mechanical behaviour of MX-80 bentonite which is the buffer material. A series of laboratory tests have been proposed by Posiva and carried out at B+Tech laboratory (Pintado et al. 2012). Two types of tests have been performed: oedometer tests and infiltration tests. These tests have been modelled using the same finite element program CODE_BRIGHT (Olivella et al., 1996) in order to calibrate the material parameters of the Barcelona Basic Model (BBM) (Alonso et al. 1990) and the required hydraulic parameters. The equations implemented in CODE_BRIGHT are presented in Appendix 1. The results of these model calibration calculations are included in Appendix 2. Calibrations of thermal and hydraulic properties are presented in Pintado and Rautioaho (2012).

Finally, thermo-hydro-mechanical calculations were performed regarding the presence of a 10 mm air-filled gap between canister and the buffer ring according to reference design (Juvankoski et al. 2012). The closure of the gap depends on the bentonite buffer saturation and swelling. If the saturation of buffer is delayed, the gap will not close and will disturb the heat dissipation causing higher canister temperatures. The main objective in this case was to see the influence of the presence of the air-filled gap on the THM behaviour of the engineered barrier. Several cases were considered in order to see the influence of the hydraulic conductivity of the rock on gap closure. The base case without gaps was also included in order to make the comparison easier.

5

2 GEOMETRICAL AND PHYSICAL PROPERTIES OF THE PROBLEM

2.1 Material properties

The concept for storage considered in this study is based on parallel vertical boreholes excavated in horizontal tunnels (KBS-3V concept, see Figure 2.1 for the deposition holes 1-2 from Loviisa and deposition holes 1-2 and 3 from Olkiluoto).

Figure 2.1. Loviisa 1 and 2, Olkiluoto 1 and 2 and Olkiluoto 3 tunnel and deposition hole geometries. Dimensions in mm.

The reference geometry chosen has been from Olkiluoto 1 and 2 deposition hole (see Figure 2.2). The gap between the canister and the ring blocks is 10 mm and the gap between the blocks and the rock is 50 mm (Juvankoski et al. 2012).

The canister placed in each borehole will be surrounded by the buffer, made with MX-80 bentonite. Bentonite disk blocks will be on and under the canister. The canister will be surrounded by ring blocks. The gap between the blocks and the rock will be filled with MX-80 pillow pellets. More details about the buffer design can be found in Juvankoski et al. (2012). According to the reference design, a 10 mm air-filled gap exists between the canister and the buffer rings. The hydro-mechanical behaviour of the bentonite buffer is of great importance. In fact, the closure of the gap is controlled by the swelling deformation developed as the bentonite buffer saturates. The HM behaviour of MX-80 bentonite has been extensively investigated (Pintado et al. 2012, Kiviranta and Kumpulainen 2011, Karnland et al. 2006, Tang 2005). The elasto-plastic properties of this material have been determined by calibration of the experimental tests

6

as it is explained in THM modelling of ONKALO Project, preliminary modelling study (see Appendix 2). The parameters obtained are presented in Table 2.1.

As an example of the laboratory tests and their corresponding simulation, Figure 2.3 shows the simulation of an oedometer test.

Figure 2.2. Olkiluoto 1 and 2 deposition hole geometry. Dimensions in mm.

Figure 2.3. Oedometer test set-up and stress–strain responses for experiment 100212c (Pintado et al., 2012) hydrated and loaded/unloaded under oedometric conditions. The sample of MX-80 is first inundated to reach full saturation, which produced a volumetric expansion higher than 30 %, and then compressed and finally unloaded.

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

100 1000 10000

Axial_stress (kPa)

Str

ain

Test

Model

Swelling due to sample inundation

7

Table 2.1. Parameters for elasto-plastic constitutive model (MX-80 bentonite).

Parameters Symbols Units Values

Poisson’s ratio υ - 0.35

Parameters for elastic volumetric compressibility against mean stress change

i0 - 0.05

i - -0.003

Parameters for elastic volumetric compressibility

against suction change

s0

- 0.25

sp

- -0.145

Elasto-plastic volumetric compressibility (0) - 0.15

Parameters to define LC yield curve

r 0.8

MPa -1 0.02

Reference stress pc MPa 0.01

Initial porosity 0 0.375

Preconsolidations mean effective stress

Po* MPa 0.75

Strength parameter M - 1.07

Infiltration tests under constant volume conditions were carried out also on MX-80 and simulated in order to compare the development of the stresses, i.e. the swelling pressure developed. Figure 2.4 shows the evolution of the volume of water inflow to the sample and the stress developed. The stress development of the MX-80 material is of the order of 10 MPa.

Friedland clay is envisaged as one of the backfill material options for the disposal tunnel (Autio et al. 2012, Börgesson et al. 2009).

According to Posiva (Design Basis report), the deposition tunnel backfill and the plug have the following safety functions:

To contribute to favourable and predictable mechanical, geochemical and hydrogeological conditions for the buffer and canisters,

To limit and retard radionuclide releases in the possible event of canister failure, and

To contribute to the mechanical stability of the rock adjacent to the deposition tunnels.

8

The material parameters for Friedland clay are presented in Table 2.2.

Figure 2.4. Water inflow and swelling stress under constant volume conditions (Pintado et al. 2012).

Table 2.2. Parameters for the elasto-plastic constitutive model (Friedland Clay).




i0 - 0.05

i - -0.003

Parameters for elastic volumetric compressibility

against suction change

s0

- 0.025

sp

- -0.145

Elasto-plastic volumetric compressibility (0) - 0.3


r 0.8

MPa -1 0.02


Initial porosity 0 - 0.38

Preconsolidations mean effective stress

Po* MPa 1.5

Strength parameter M - 1

0

5000

10000

15000

20000

25000

30000

35000

0 10 20 30 40 50 60 70Time (d)

Vol

ume

Inflo

w (

mm

3)

Test

Model

0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60 70

Time (d)

Str

esse

s (k

Pa)

Stress LC1 kPa

Stress LC2 kPa

Stress LC3 kPa

Stress LC4 kPa

Axial middle

Radial middle

Radial bottom

Radial top

Model

Experiment

9

According to the current disposal option, 74 % of the total volume of the deposition tunnel will be backfilled with pre-compacted blocks (Friedland clay) and the remaining space will be backfilled with bentonite pellets (17.6 %) and the foundation layer (8.4 %). The foundation layer is a foundation element prepared for the installation of the blocks.

Table 2.3 shows various properties of the different materials, such as density, porosity and intrinsic permeability. The permeability given in Table 2.3 corresponds to the porosity given in the table. Variations of porosity produce variations of permeability according to Kozeny’s law given in Appendix 1.

Table 2.3. Material properties.

Materials Dry density (kg/m³) Porosity Intrinsic permeability (m²)

Bentonite Rings 1752* 0.370 5.59x10-21 Bentonite discs 1701* 0.388 5.59x10-21

Pellets 919* 0.669 5.59x10-21 Backfill 1758** 0.367 10-18

*Juvankoski et al. 2012 **Autio et al. 2012

The dry density of the backfill is the mean considering the homogenization of the backfill components (foundation layer, blocks and pellets).

The relative permeability for these materials is considered to be equal to krl = (Sl)3

(Brooks and Corey, 1964), while gas relative permeability is calculated as: krg = 1 krl. Van Genuchten (1980) water retention curve has been used and the parameters are discussed in Pintado and Rautioaho (2012). For thermal conductivity, the value corresponding to dry conditions is taken to be 0.3 while for fully saturated conditions the value considered is 1.3 W/mK (Pintado and Rautioaho 2012). These values are weighted respectively with the degree of saturation of the gas phase and the degree of saturation of the liquid phase and added to obtain the thermal conductivity under unsaturated conditions.

2.2 Gap properties

In this report, some of the presented models contain a gap between the ring blocks and the canister. This gap is modelled as a material with very high porosity and permeability (several orders of magnitude larger than the other materials, see Table 2.4). Intrinsic permeability is assumed to be a function of porosity as in a porous material but with appropriate parameters. The retention curve is also considered but with a very low value of the reference air entry capillary pressure Po (Po = 0.001 MPa), as the gap corresponds to big pores (Table 2.4). This implies that saturation takes place sharply as capillary pressure vanishes. Porosity functions for permeability and air entry capillary pressures are available in CODE_BRIGHT. The use of a porosity equal to 1 in the gap is not convenient because this implies that the terms (1 ) are equal to zero and therefore the

10

variations of porosity are zero in any circumstances because d/dt = (1 ) dv/dt. What has been decided is to use a large porosity value (0.8) which will lead to porosity reduction as the volumetric deformation reduces. Since porosity reduces, intrinsic permeability also reduces and the retention curve tends towards a similar shape as the curve for the blocks.

The mechanical response of the gap is achieved using two different stiffness values depending on the opening. When the gap is open, the elastic modulus is 1 MPa (i.e. very low stiffness). On the contrary, when the gap is closed, the elastic modulus is 1000 MPa (i.e. high stiffness, see Table 2.4 and Figure 2.5). In this way relative displacement of the air gap boundaries (nodes) stops when closure takes place because closure leads to stiffness increase.

Heat transfer across the gaps will take place by conduction, radiation and convection. For a gap with a thickness d, subjected to a temperature gradient, the radiant heat flux (qr) can be calculated as follows (Ikonen, 2005):

41

42

2221

21 TTeeee

eeqr

(1)

Where e1 and e2 are surface emissivity of both sides of the gap, T1 and T2 are temperature on both sides of the gap and σ is the Stefan-Boltzmann constant. The emissivity of the canister surface is difficult to estimate because the status of the copper surface may, potentially, vary from “polished” (e = 0.023) to “calorized“ (e = 0.26), “oxidized” (e =0.6) to “new” (e = 0.63). For the other surfaces (bentonite, rough steel and rock) the emissivity is about 0.8 or larger according to all sources (Hökmark and Fälth 2003).

For the conductive flux the Fourier law is used. In this study the combined effects of conduction and radiation are included in the conductive flux using an equivalent conductivity. Thermal conductivity changes with saturation between two extreme values. When the gap is full of gas, a thermal conductivity of 0.045 W/mK (gas mixture of air and vapour) is considered, while when it is full of water a value of 0.6 W/mK (water thermal conductivity) is considered. These values correspond to the gap when it is open. The effect of closure comes from the dependency of the water retention curve on porosity, as indicated above.

11

Table 2.4. Gap Parameters.

Thermal parameters

λdry (W/(mK)*) 0.045

λsat (W/(mK)) 0.6

Hydraulic parameters

k0 intrinsic permeability (m2) 10-16

o porosity (-) 0.8

λ parameter for van Genuchten model (-) 0.5

-aPP ooo exp , P0 (MPa) 0.001

a parameter for van Genuchten model (-) 10

Mechanical Properties **

Ec (MPa) 1000

Eo (MPa) 1.0

v limit (-) 0.95

(-) 0.3

*This effective conductivity is chosen according to SKB technical report TR-0-09. ** When the gap is closed, a linear elastic model is used with the parameters and Ec.

Figure 2.5. Gap Model. Relationship between the volumetric strains and stress. Before the volumetric strains reach a value of v limit, the gap is considered open and it is quite soft (it is void), so the E0 is low. When the gap is filled, the volumetric strain reaches v

limit and it becomes rigid (Ec is high).

v

E0

Ec

13

3 INITIAL AND BOUNDARY CONDITIONS

The analysis has been assumed under axisymmetric conditions with a radius of 8.3 m, which corresponds to a spacing of 16.6 m if the boreholes were situated in a squared net. This value corresponds to the geometric average of 11 m and 25 m which is the spacing, respectively, for the boreholes and tunnels, i.e. boreholes situated in a rectangular net. In other words, the distance from borehole to symmetry planes is 5.5 m and 12.5 m in reality (parallel or perpendicular to tunnel direction). Since the model is axisymmetric, only one distance to the symmetry plane can be considered. Therefore the

radius has been taken to be the geometric mean of these two values ( 5.125.53.8 ).

Figure 3.1 shows the mechanical boundary conditions applied. An initial confining stress of 10.63 MPa has been considered for the host rock. This stress corresponds approximately to the gravity weight of the rock mass at 400 m depth (Posiva, 2009). The horizontal stress can vary as it is a function of the orientation and it is higher than the vertical stress. Posiva (2009) shows values of 27 and 16 MPa for the maximum and minimum horizontal stresses at 450 m depth. Because of the simplicity of the axisymmetric analysis and the fact that the rock is modelled as elastic, this effect is not taken into account and therefore the same value as that of the vertical stress has been chosen. This confining pressure has been used as an initial condition. The excavation has also been modelled. The initial water pressure for all the material in the deposition hole is 41 MPa and the initial temperature is 10.5 oC throughout the domain modelled. The initial porosities are indicated in Figure 3.1.

A fundamental issue in the modelling was to determine relevant thermal boundary conditions so that the details of THM-behaviour could be captured by defining proper near-field thermal boundaries. This implies that appropriate boundary conditions for thermal dissipation are considered for the top and bottom boundary conditions. The heat power considered in the modelling of the first series of calculations is as described in Table 3.1. The heat power has been calculated with the decay-coefficients for SKB reference fuel (Lönnqvist and Hökmark 2008).

14

Figure 3.1. Geometry and initial and boundary conditions. From left to right: Initial pressure and temperature, mechanical boundary conditions, prescribed pressure and initial porosity.

37 m

8.3 m

7.8 m

4.4 m

0.875 m

15

Table 3.1. Parameters for power described with an exponentially decaying function for 4 intervals.

Intervals (years) Source Heat flow (J/s) Decay of heat flow (1/s)

0–60 1698 4.4x10-10

60–100 1155 2.45x10-10

100–200 825 1.5x10-10

200–1000 420 4.51x10-11

Figure 3.2 shows the power of the canister calculated with two different approximations. The approximation by means of a combination of exponentially decaying functions defined in four intervals is convenient for model calculations, as this is a general source term in CODE_BRIGHT.

Figure 3.2. Canister power as a function of time using different approximations (SKB data from Lönnqvist and Hökmark 2008).

Figure 3.3 shows the evolution of temperature for various models having different vertical length. As the THM calculations are to be performed on a domain with close boundaries, the temperature boundary condition is not considered constant on the top and bottom boundaries. Instead, a variable temperature is considered which permits to improve the temperature evolution in the near field. Essentially, the temperature decreases more slowly when compared with the case with constant temperature at the close boundary. The variable temperature evolution on the closer boundary is the calculated temperature at the appropriate distance taken from the model with a boundary at a large distance.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1 10 100 1000

Time (y)

Po

wer

(W

)

Sum of various exponential terms(based on SKB data)

Approximated with one exponentialfunction (4 intervals)

16

Figure 3.3. Temperature evolution for different models. Reference case (37 m), factor 10 (370 m) and factor 20 (740 m) calculated with constant temperature on top and bottom boundaries of the domain (10.5 oC). The proposed model (37 m) is calculated with variable temperature on the top and bottom of the domain, calculated from the large model, to improve the simulated temperatures in the near field while maintaining a reduced domain.

Reference case

262.2 m262.2 m

Factor 10

512.2 m512.2 m

Factor 20

37.2 m37.2 m

8.3 m

37.2 m

512.2 m

37.2 m

512.2 m

200 years after disposal

37.2 m37.2 m

8.3 m

Proposed Model

Factor 20

0

10

20

30

40

50

60

70

80

90

0.01 0.1 1 10 100 1000

Tem

per

atu

re (

ºC

)

Time (y)

Reference Case

Factor 10

Factor 20

0

10

20

30

40

50

60

70

80

90

0.01 0.1 1 10 100 1000

Tem

per

atu

re (

ºC

)

Time (y)

Reference Model (boundary with constanttemperature)

Proposed Model (boundary with variabletemperature)

17

4 THM ANALYSES SIMULATING DISPOSAL IN A VERTICAL BOREHOLE

This section contains the description of the results obtained for various models based on the geometry described above and considering different aspects. Table 4.1 contains a description of the calculated models. The models are divided into a 1st and a 2nd series. There are different aspects that are investigated. The way to proceed has been to develop a base case from which variations have been considered. The different models cover variations of rock hydraulic conductivity, variations of the relative permeability of the buffer, variations of vapour diffusivity (via the variation of the coefficient of tortuosity), variations of the backfill preconsolidation pressure, and the presence of the gap.

Table 4.1. Models for comparative study.

Cases

Rock Intrinsic Permeab

ility (k, m2)

Power in the relative

permeability law

(n in krl = Sln)*

Coefficient of

tortuosity** ()

Backfill Pre-consolidation

pressure (p0*, MPa)***

1st s

erie

s

Base 10-17 3 0.4 0.5

A 10-17 6 0.4 0.5

B 10-18 3 0.4 0.5

C 10-17 3 0.8 0.5

D 10-18 6 0.8 0.5

E 10-17 3 0.4 2

2nd

seri

es GAP-I 10-18 3 0.4 2

GAP-II 10-19 3 0.4 2

NOGAP-II 10-19 3 0.4 2

GAP-III 1.5x10-20 3 0.4 2 * Brooks and Corey 1964 ** Pollock 1986 *** Alonso et al. 1990

In this chapter, the results of the cases grouped as the 1st series are briefly described. Another chapter (Chapter 5) is devoted to explaining the cases investigating the effect of the gap between the canister and the buffer and other geometry improvements (the 2nd series).

Figure 4.1 shows the mesh considered in the first series of calculations. As can be seen, the mesh is quite simple and only four materials are considered, namely: rock, backfill, buffer and canister. The mesh is composed of quadrilateral elements with 4 nodes. For the model used here, the number of nodes is 847 and the number of elements is 784.

18

The excavation process has been taken into account. Firstly, the stress redistribution before installation of buffer and backfill takes place. Secondly, the thermo-hydraulic boundary condition at the rock wall, which will be in contact with the buffer and backfill at a later stage, is maintained at atmospheric pressure and constant temperature before the installation of these materials. Due to the hydraulic boundary conditions before buffer installation, the hydraulic field corresponds to a saturated steady-state flow into the borehole from the far field where the pressure is hydrostatic and dictated by depth. Thirdly, the atmospheric pressure and constant temperature boundary condition on the excavation wall is removed as the different materials (buffer, canister and backfill) are installed. At this point fluxes of water take place to equilibrate the atmospheric pressure prevailing at the rock wall and the initial suction prevailing in the constructed materials.

For the purposes of plotting the THM analyses, five selected points have been considered according to essential functional requirements of the deposition tunnel (see Figure 4.1).

Figure 4.1. Axisymmetric domain, mesh and materials considered; and the approximate position of points at which results are calculated and compared.

Backfill

Backfill-buffer intersection

Buffer

Canister-buffer intersection

Buffer-rock intersection

19

4.1 Results for the Base Case

The typical distribution of temperature in the buffer and backfill is shown in Figure 4.2 together with the evolution of temperature calculated at different points. The power imposed in the canister (design value decaying with time) leads to an evolution of temperature with a peak value in time and space. A design condition is that the maximum temperature should not exceed the value +100 oC in order to guarantee that also the buffer remains below this value and the response of the clay material is as expected. Due to uncertainties and natural variation in thermal parameters, the allowable calculated maximum canister temperature (reference temperature) is set to 90 oC causing a safety margin of 10 oC (Ikonen, 2003). This is one of the fundamental parameters for planning, dimensioning and operation of the repository. This allowable temperature is controlled mainly by canister power at disposal and the cooling time period before disposal. In addition, the adjacent tunnel and canister spacing play a vital role as well.

From Figure 4.2 it can be seen that the maximum temperature is reached at the buffer–canister interface and is 80 ºC after 30 years. After 1000 years the model reaches conditions at which both materials have the same temperature of about 42 ºC, and the temperature is still decreasing towards the initial temperature.

Liquid pressure variations are influenced by heating. On account of canister heating and the resulting evaporation of water, the liquid pressure decreases strongly near the canister. Figure 4.3 indicates that full saturation of the filling components is nearly achieved after 10 years. The liquid pressure evolutions in Figure 4.3 show the drying of buffer near the canister when heat generation takes places. The point closer to the canister has a higher suction compared to the other locations. On the interface between the buffer and the canister, the liquid pressure drops to -50 MPa in 1 year and the evolution at this point has a different trend. In the backfill material, liquid pressure increases with time and reaches its steady-state condition quite early. This suction behaviour near the canister has an important effect on the time required for full saturation of these two materials because drying produces a decrease in permeability.

20

30 years 60 years 200 years 1000 years

Figure 4.2. Temperature distribution in buffer and backfill materials and time evolution of temperature at selected points.

0

10

20

30

40

50

60

70

80

90

0.01 0.1 1 10 100 1000

Time ( y)

Tem

pera

ture

( º

C )

Backfill

Buffer_Backfill

Buffer_Rock_Intersection

Buffer_Canister_Intersection

Buffer

21

Figure 4.3. Liquid pressure evolution for 5 representative points.

A consequence of hydration is swelling. The swelling under highly confined conditions produces stress increase. Figure 4.4 shows the distribution of mean stress in the backfill and buffer. The higher stresses in the buffer, as compared to the backfill, are induced by the fact that the buffer has a much higher swelling capacity than the backfill. It has to be taken into account that the mean stress includes the mean bentonite swelling pressure plus the liquid pressure.

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0.01 0.1 1 10 100

Time ( y )

Liqu

id P

ress

ure

( M

Pa)

BackfillBuffer_Backfill_IntersectionBuffer_Rock_IntersectionBuffer_Canister_IntersectionBuffer

22

1 year 5 years 10 years 1000 years

Figure 4.4. Total mean stress history in buffer and backfill materials.

The total stress development is not only responding to swelling of the clay-based materials but also to pore pressure. In other words, a non-swelling material such as sand when subjected to pore pressure increase under constant volume would develop a total stress equal to the pore pressure. To see the effect of swelling the effective stress should be calculated. The effective stress increase is the important variable from the point of view of sealing capacity of the buffer material in a repository.

Figure 4.5 shows the evolution of total mean stress and the evolution of mean effective stress at the buffer–canister interface and at the buffer–backfill interface. The contact with the canister gives a high value as this is a highly confined zone, while the contact with the backfill gives an idea of the transmission of stress/deformation from the buffer to the backfill. Note that the total stress reaches a value slightly above 10 MPa at the the buffer–canister interface while the effective stress stabilizes at around 7 MPa. Obviously the swelling pressure determined in the laboratory is higher than this value because the confinement is higher in the laboratory than in situ. According to the scheme, the backfill permits some buffer expansion.

23

Figure 4.5. Total and effective stress evolution for 2 representative points in the buffer.

Actually, the backfill should keep the buffer in place and prevent it from swelling upwards so that the buffer will not lose too much of its density. The final bulk density has to be 2000 kg/m3±50 kg/m3, as this is a design requirement (Juvankoski et al. 2012). As the backfill has a lower swelling pressure than the buffer and a higher compressibility, some upwards swelling will be expected.

The bearing load of the buffer and so the rate at which a canister will settle through the buffer to the base of the deposition hole is a mechanical case that should be assessed. In other words, the resistance to canister sinking is one of the requirements to be assessed for the buffer. This is beyond of the scope of the present study.

As the buffer bentonite expands due to hydration, the backfill reduces its volume due to compression (see Figure 4.7). Swelling of the buffer in a real repository causes the filling up of the voids in the bentonite. Hence, the performance of the buffer is critically

0

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al M

ean

Str

ess

(MP

a)

Buffer_Backfill_Intersection


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24

affected by the degree and speed at which bentonite will swell. Hydraulic conductivity controls swelling of buffer. One of the important reasons for using bentonite as a buffer material in a repository is its low hydraulic conductivity (Juvankoski et al. 2012). The low hydraulic conductivity limits the water flow and, consequently, the movement of radionuclides.

As can be seen in Figure 4.6, the movement of the interface between the buffer and the backfill is vertical and at maximum of the order of 11 cm according to model calculations. According to these deformations and movements, density decreases in the buffer and increases in the backfill.

As buffer drying takes place at the beginning, the buffer–backfill contact moves down somewhat due to shrinkage of the buffer. When swelling takes place induced by water inflow, the buffer starts moving upward and compresses the backfill in the tunnel. The final vertical displacement on the buffer–canister interface is about 8 cm for the selected point indicated in the contact zone. The maximum vertical displacement is 11 cm at the deposition hole axis (Figure 4.6).

When the canister is placed in the deposition hole, drying takes place in the buffer space close to the canister. As a result of the heating process, evaporation induces a porosity reduction close to the canister. Along the rock wall, hydration occurs and porosity increases in this area. The high density of buffer creates a high swelling pressure and makes bentonite relatively stiff. One of the important requirements for the deposition tunnel is that backfill should be sufficiently stiff to minimize its compression even when the buffer swells. Figure 4.7 displays porosity variations during hydration and swelling and also includes the evolution of dry density at different points (dry density and porosity can be related as: nsoliddry 1 ).

According to model calculations, the buffer space between the rock wall and the canister will be saturated within 4 or 5 years after the deposition of the canister. As the maximum buffer temperature is reached in 30 years, this implies that according to this model full saturation takes place before the maximum temperature is achieved. This is probably due to the relatively high permeability considered for the host rock in this model calculation.

25

1 year 5 years 10 years 1000 years

Figure 4.6. Vertical displacement history in buffer and backfill materials.

-4

-2

0

2

4

6

8

10

0.01 0.1 1 10 100 1

Ver

tica

l Dis

pla

cem

ent

(cm

)

Time (y)



26

1 year 10 years 1000 years

Figure 4.7. Dry density history in buffer and backfill materials and evolution of density at selected points.

1600

1650

1700

1750

1800

1850

1900

0.01 0.1 1 10 100

Time ( y )

Dry

den

sity

(kN

/m³)

BackfillBufferBuffer_Backfill_IntersectionBuffer_Canister_IntersectionBuffer_Rock_Intersection

Porosity

Dry

density

(kg/m3)

Saturated

density

(kg/m3)

0.44 1557 1997

0.42111 1609 2030

0.40222 1662 2064

0.38333 1714 2098

0.36444 1767 2131

0.34556 1819 2165

0.32667 1872 2199

0.30778 1924 2232

0.28889 1977 2266

0.27 2029 2299

27

4.2 Sensitivity analyses and comparison

A series of sensitivity calculations were carried out to understand the effect of different parameters on the model performance. The time required for full saturation of the bentonite buffer mainly depends on the hydrological conditions around deposition holes but it is also related to the bentonite material model. In these sensitivity analyses, the hydraulic parameters of the bentonite buffer have been varied to better understand the process of buffer hydration inside the deposition hole. Secondly, as a mechanical aspect, backfill preconsolidation pressure is increased to assume stiffer conditions due to better compaction, with the aim of finding out its effect on the obtained results. More results concerning the sensitivity analysis are presented in Pintado and Rautioaho (2012).

The flux of liquid and the flux of vapour dominate the saturation of the buffer. Therefore, the main parameters used in these formulations have been chosen to perform these comparative studies. The intrinsic permeability of rock, power in the relative permeability law (λ) and coefficient of tortuosity () corresponding to the buffer material and the preconsolidation pressure corresponding to the backfill (p0*) have been considered for sensitivity analyses (see Table 4.2).

Table 4.2. Parameters varied for the sensitivity exercise.

Models

Parameters Intrinsic

Permeability of Rock (k)


permeability law (λ)

Coefficient of tortuosity for

molecular diffusion ()

Pre-consolidation pressure of

backfill (p0*) Base Case 1e-17 m2 3 0.4 0.5 MPa Case A 1e-17 m2 6 0.4 0.5 MPa Case B 1e-18 m2 3 0.4 0.5 MPa Case C 1e-17 m2 3 0.8 0.5 MPa Case D 1e-18 m2 6 0.8 0.5 MPa Case E 1e-17 m2 3 0.4 2 MPa

The maximum temperature reached and the temperature behaviour do not differ much between the Base Case and the other models. The hottest point in the buffer which touches the canister has a temperature of 80 ºC. The maximum buffer temperature is not affected by the initial incomplete buffer saturation.

What is significantly different is the evolution of liquid pressure along the 6 cases analysed because water pressure is controlled by the hydraulic parameters varied in the different cases. Figure 4.8 compares the evolution of pressures for these cases. Case A shows more drying than the Base Case because of the lower relative permeability of the buffer considered in Case A. Case C shows more drying than the Base Case because the higher vapour diffusivity than in the Base Case permits more evaporation. The cases with lower permeability of the rock show somewhat higher drying, but more uniformly along the buffer.

28

Figure 4.9 shows the evolution of total mean stress. It can be seen that stress development shows a delay for cases B and D which have lower permeability of the rock and therefore a slower hydration rate. The stress developed at long-term conditions are practically the same in all cases. As indicated above, the total stress in the buffer material can be considered as the sum of the swelling stress developed as a consequence of the expansion under confined conditions (with some expansion permitted) and of the pore pressure developed which is controlled by the hydrostatic conditions. The value of 11 MPa is the maximum value reached by the total stress.

Base Case Case A

Case B Case C

Case D Case E

Figure 4.8. Pressure evolution at selected points for the various cases analysed.

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0.01 0.1 1 10 100 1000

Time ( y )

Liqu

id P

ress

ure

( M

Pa)


-80

-70

-60

-50

-40

-30

-20

-10

0

10

0.01 0.1 1 10 100 1000

Time ( y )

Liqu

id P

ress

ure

( M

Pa)


-80

-70

-60

-50

-40

-30

-20

-10

0

10

0.01 0.1 1 10 100 1000

Time ( y )

Liq

uid

Pre

ssu

re (

MP

a)


-80

-70

-60

-50

-40

-30

-20

-10

0

10

0.01 0.1 1 10 100 1000

Time ( y )

Liqu

id P

ress

ure

( M

Pa)


-80

-70

-60

-50

-40

-30

-20

-10

0

10

0.01 0.1 1 10 100 1000

Time ( y )

Liqu

id P

ress

ure

( M

Pa)


-80

-70

-60

-50

-40

-30

-20

-10

0

10

0.01 0.1 1 10 100 1000

Time ( y )

Liqu

id P

ress

ure

( M

Pa)


29

Base Case Case A

Case B Case C

Case D Case E

Figure 4.9. Total stress evolution at selected points for the various cases analysed.

Although some differences can be observed between cases regarding to effective mean stresses, they reach almost the same value. The maximum value is close to 7 MPa. The difference between the total stress and the effective stress gives the pore pressure which for long-term conditions reaches a value of 4 MPa in the buffer according to the boundary conditions applied on the top of the model.

It is known that stress and displacement balance in the buffer zone depends on the saturation degree of either the buffer or the backfill. As intrinsic permeability and vapour diffusion change, there is an effect on the saturation, but the trend of the effective mean stress differs slightly between cases (see Figure 4.10).

0

2

4

6

8

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12

14

0.01 0.1 1 10 100 1000Time (y)

To

tal M

ean

Str

ess

(M

Pa)



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0.01 0.1 1 10 100 1000Time (y)

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(MP

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ean

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ess

(M

Pa

)Buffer_Backfill_Intersection


0

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0.01 0.1 1 10 100 1000Time (y)

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tal M

ean

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ess

(M

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0.01 0.1 1 10 100 1000Time (y)

Tot

al M

ean

Str

ess

(MP

a)



30

Base Case Case A

Case B Case C

Case D Case E

Figure 4.10. Effective stress evolution at selected points for the various cases analysed.

As a consequence of the different parameters considered, the hydration takes place in a different way. Since hydration and swelling are strongly connected, porosity variations are affected by changes in the hydraulic parameters. For instance, if hydration takes place faster because the permeability of the rock is higher, then some zones may develop higher swelling because the hydration is not uniform within the buffer (see Figure 4.11).

0

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ean

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(MP

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0.01 0.1 1 10 100 1000

Time (y)

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ectiv

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ean

Str

ess

(MP

a)



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6

7

8

0.01 0.1 1 10 100 1000

Time (y)

Eff

ectiv

e M

ean

Str

ess

(MP

a)



31

Base Case Case A

Case B Case C

Case D Case E

Figure 4.11. Porosity evolution at selected points for the various cases analysed.

As a final conclusion, it can be said that for the range of parameters considered in this section, the results are not significantly different. The main features of the results are summarised in Table 4.3.

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.01 0.1 1 10 100 1000

Time ( y )

Por

osity


0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.01 0.1 1 10 100 1000

Time ( y )

Po

rosi

ty


0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.01 0.1 1 10 100 1000

Time ( y )

Po

rosi

ty


0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.01 0.1 1 10 100 1000

Time ( y )

Por

osity


0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.01 0.1 1 10 100 1000

Time ( y )

Por

osi

ty


0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.01 0.1 1 10 100 1000

Time ( y )

Por

osi

ty


32

Table 4.3. Summary of results from the 1st series of calculations.

Maximum temperature in the buffer 80 oC

Time for maximum temperature 30 years

Maximum suction in the buffer 50 to 70 MPa

Time for maximum suction in the buffer 0.1 to 0.3 years

Time for full saturation (depending on the zone) 2–10 years

Maximum total stress 11 MPa

Maximum effective stress 7 MPa

33

5 THM ANALYSES SIMULATING A GAP BETWEEN THE BENTONITE–BUFFER AND THE CANISTER

An important issue to consider in the THM calculations is the presence of gaps. In order to make the installation of the different elements in a repository feasible, it is necessary to foresee some spaces. These spaces will permit for instance to manufacture bentonite blocks which are later installed in the vertical drifts. Installation of these blocks will produce a gap between them and the wall of the excavated borehole. The space between the blocks and the rock wall will be backfilled with pellets (Juvankoski et al. 2012). Once the clay blocks are installed in the borehole, the internal space available for the future installation of the canister should be sufficient, i.e. have an extended size so the canister does not get stuck when it is emplaced. The gap between the bentonite blocks and the canister is expected to close as the buffer material swells.

As indicated above, the closure of the gap is controlled by the swelling deformations that develop as the bentonite buffer saturates. Since the intrinsic permeability of the rock plays an important role in determining the saturation time of the backfill material and thus in the closing of the gap, four cases have been analysed (Table 5.1).

Table 5.1. Models for comparative study.

Cases

Rock Intrinsic

Permeability (k, m2)


permeability law (λ)

Coefficient of tortuosity

()

Backfill Preconsolidation

pressure (p0*, MPa)

Case I 10-18 3 0.4 2

Case II 10-19 3 0.4 2

Case II NOGAP 10-19 3 0.4 2

Case III (*) 1.5x10-20 3 0.4 2

(*) Case with a slightly different geometry and mesh

In the analyses discussed in this chapter, i.e. cases I, II and III, a 10 mm gap has been considered between the bentonite–buffer and the canister. The properties of the gap have been described in Chapter 2. This gap closes due to clay swelling and tends to saturate. The gap has been simulated by means of appropriate properties to represent its THM response. The gap is able to close completely as the bentonite swells. The presence of this air gap has effects on the thermal, hydraulic and mechanical issues. The geometry and mesh, along with nodes at which results have been calculated, are presented in Figure 5.1.

34

Figure 5.1. Details of the geometry and mesh and representative nodes for representation of results.

5.1 Case I

The design criteria for the repository establish that the maximum allowed temperature for bentonite buffer is 90 ºC (Ikonen 2003). According to the model predictions of the model that is based on an adopted disposition of canisters, the maximum temperature is reached after about 30 years and it is about 80 ºC.

Figure 5.2 shows the effect on temperature of the existing air gap between the canister and the bentonite buffer. At both sides of the gap, temperature is not the same until a certain time is reached. As the gap closes, its thermal conductivity increases. Actually, the contact between the two sides of the gap will in reality produce a high effective conduction (but this is not accounted for by the model). It is observed that as the gap closes and saturates, the temperature differences vanish.

Materials Point considered

Backfill 818

Bentonite disc 697

Gap canister side 481

Gap bentonite ring side 480

Bentonite ring 478

Pellets 472

697

818

481 480 478 472

35

Figure 5.2. Evolution of temperature.

30 years

The insulating capacity of the gap produces an increase of temperature in the canister at early times. Since the temperature increase takes place before the temperature peak, the maximum temperature reached during all the calculation is practically not altered by the presence of the gap (a comparison of cases is carried out later).

Figure 5.3 shows the evolution of liquid pressure at representative points of the disposal materials. High suction values (i.e. low water pressure) are observed close to the canister resulting from the temperature increment induced by the heat generation of the canister. The temperature increase produces higher vapour content in the gas phase which leads to vapour diffusion from hotter to colder regions. In fact, the representative point for the air gap at the side of the canister reaches a suction value of 95 MPa. The reached value highly depends not only on temperature but also on the rock hydraulic conductivity, and in general on the thermo-hydrological conditions.

0

10

20

30

40

50

60

70

80

90

0.01 0.1 1 10 100 1000

Tem

per

atu

re (

ºC)

Time (y)

Pellets

bentonite ring

Gap wall bentonite side

Gap wall canister side

36

Figure 5.3. Evolution of liquid pressure.

3 years

At early times, a large difference in liquid pressure is observed between the two sides of the air gap. After a certain time, when the gap reaches fully saturated conditions (Figure 5.4), the two sides tend to have the same value of liquid pressure. Full saturation of all materials takes about 10 years (Figure 5.4). The strong heat generation from the canister causes the initial desaturation of the bentonite buffer (Figure 5.4). The effect of the air gap is considerable during the first year until full saturation of the bentonite is achieved. The gap acts as a capillary barrier that allows very high values of suction to develop close to the canister. This is because the high porosity of the gap induces very low values of the degree of saturation and, hence, very low values of relative permeability. This in turn slows down hydration of the area next to the canister until the gap starts to close (and the degree of saturation and relative permeability start to increase accordingly). In other words, the presence of the gap permits a much higher drying of the vicinity of the canister during heating. As the gap closes it also saturates.

-100

-90

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-50

-40

-30

-20

-10

0

0.01 0.1 1 10 100 1000

Liq

uid

Pre

ssu

re (

MP

a)

Time (y)

Pellets

bentonite ring



37

Figure 5.4. Evolution of degree of saturation.

3 years

Figure 5.5 displays the evolution of volumetric deformation in bentonite and backfill materials. At the beginning, the bentonite buffer and the backfill experience some compression which is attributed to the early swelling of bentonite near the hydration boundary. When water coming from the host rock reaches the buffer to a larger extend, the bentonite starts swelling globally. Swelling of the bentonite buffer results in compression of the backfill material (upward displacement). The maximum volumetric deformation reached is equal to 0.12. One of the requirements for the backfill material is to have a low compressibility in order to limit the upward movement; otherwise the swelling of the bentonite could be excessive.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.01 0.1 1 10 100 1000

Deg

ree

of

Sat

ura

tio

n

Time (y)

Pellets

bentonite ring



Bentonite disc

Backfill

38

Figure 5.5. Evolution of volumetric deformation.

10 years

Figure 5.6 shows the evolution of mean effective stress in the materials. The maximum effective stress reached in the bentonite buffer is equal to 9 MPa and tends towards the swelling pressure of this material.

Some stress peaks are observed after saturation. This can be explained by the expansion induced by hydration taking place at some point while other points still remain unsaturated and therefore stiff. After water redistribution, all zones tend to be more deformable, thus leading to stress reduction at some points.

The presence of the 10 mm air gap has an effect on the thermal, hydraulic and mechanical response of the disposal site. This effect diminishes as the bentonite buffer saturates, expands and causes the closure of the gap.

Figure 5.7 and Figure 5.8 show the evolution of the gap closure. In 4 years, horizontal displacement reaches a value of 10 mm and this implies that the gap can be considered totally closed. The closure time strongly depends on the swelling of the buffer as it saturates. The kinetics of water supply will basically be controlled by the hydraulic conductivity of the host formation. Hence, the hydraulic conductivity of rock has an important role to play in determining gap closure time.

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.01 0.1 1 10 100 1000

Vo

lum

etri

c D

efo

rmat

ion

Time (y)

Bentonite

Backfill

39

Figure 5.6. Evolution of mean effective stress. 10 years

Figure 5.7. Horizontal displacements in the air gap element. 3 years

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0.01 0.1 1 10 100 1000

Mea

n E

ffec

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a)

Time (y)

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bentonite ring

Gap wall bentonitesideGap wall canistersideBentonite disc

Backfill

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0.01 0.1 1 10 100 1000

Dis

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cem

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X d

irec

tio

n (

mm

)

Time (y)



40

Figure 5.8. Illustration of gap closure. It is worth remarking that the amplification factor for displacement in this figure is equal to 1.

The model described in this section considers a host rock intrinsic permeability of 10-18 m2. In the following section, the same case is considered but the permeability of the host rock is decreased by one order of magnitude. This must imply a slower saturation rate.

5.2 Case II

In this case, the rock hydraulic conductivity is reduced 10 times as compared to case A. The rest of the conditions and material parameters are kept the same as in Case I.

Figure 5.9 shows the effect on temperature of the existing air gap between the canister and the bentonite buffer. The maximum temperature is reached in the buffer bentonite and it is less than 80 ºC. No significant temperature variations are observed. This is normal as the thermal problem received small influence of the hydraulic one. The main couplings are heat advection and thermal properties varying with water content. Heat advection is small in this problem as the materials have, in general, low hydraulic conductivity. The thermal conductivity variations with water content may induce some differences as the hydration process is delayed. However, thermal conductivity variations of a porous material with respect to water content are very moderate.

CanisterAir gap

Bentonite Ring 2.13 years 3.13 years

41


30 years

The evolution of liquid pressure at representative points of the disposal materials is shown in Figure 5.10. High suction values are observed close to the canister. Suction reaches a maximum value of about 100 MPa after 1 year of the deposition of the canister. At early times, a large difference in liquid pressure is observed between the two sides of the air gap. In fact, suction at the selected point of the gap element close to the bentonite ring is lower compared to other side close to the canister.

0

10

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0.01 0.1 1 10 100 1000

Tem

per

atu

re (

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Time (y)

Pellets

bentonite ring

Gap bentonite side

Gap canister side

42


3 years

In this Case II, as the rock is less permeable than in Case I, the water supply from the rock requires more time. Hence, saturation of bentonite is delayed (Figure 5.11). Saturation of the bentonite buffer causes the material to swell and as a result, the backfill material compresses (Figure 5.12).

-100

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-10

0

10

0.01 0.1 1 10 100 1000

Liq

uid

pre

ssu

re (

MP

a)

Time (y)

Pellets

bentonite ring

Gap bentonite side

Gap canister side

43

Figure 5.11. Evolution of the degree of saturation.

3 years

Figure 5.12. Evolution of volumetric deformations.

10 years

0

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ree

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Gap canister side

Bentonite disc

Backfill

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-0.04

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c d

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rmat

ion

Time (y)

Bentonite ring

Backfill

44

Figure 5.13 shows the evolution of mean effective stress in the materials. The maximum mean effective stresses reached in the bentonite ring are in the range of 9–10 MPa.

Figure 5.13. Evolution of mean effective stresses.

10 years

As for the previous case, the presence of the 10 mm air gap has an effect on the thermal, hydraulic and mechanical response of the disposal site. This effect diminishes as the bentonite buffer saturates, expands and causes the closure of the gap. Figures 5.14 and 5.15 show the evolution of the closure of the gap. It can be seen that the gap is totally closed after 5 years, that is, 1 year later than for the previous case (Case I). This is a direct consequence of the lower permeability of the host rock considered in this case.

0

1

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9

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0.01 0.1 1 10 100 1000

Mea

n E

ffec

tive

Str

ess

(MP

a)

Time (y)

Pellets

bentonite ring

Gap bentonitesideGap canistersideBentonite disc

Backfill

45

Figure 5.14. Evolution of horizontal displacements.

5 years

3 years 5 years

Figure 5.15. Simulation of gap closing.

0

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4

5

6

7

8

9

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0.01 0.1 1 10 100 1000

Dis

pla

cem

ent

X d

irec

tio

n (

mm

)

Time (y)

Gap bentonite side

Gap canister side

CanisterAir gap

Bentonite Ring

46

5.3 Case II NOGAP

It has been indicated in the preceding sections that the gap had an effect on the thermo-hydro-mechanical processes. In this section, a quantification is done by calculation of Case II NOGAP, which is equal to Case II except for the air gap which is not considered now. In practice, the gap elements have been changed in order to have the same properties of the bentonite blocks. Figure 5.16 shows the evolution of temperature for the different materials. The maximum temperature in the bentonite buffer is reached after 30 years and is less than 80 ºC. As there is no air gap, the selected points on both sides of the gap element evolve in the same way. The temperature in the canister shows the effect of the saturation of the buffer and the associated change in thermal conductivity. The water saturation of a porous material implies an increase in thermal conductivity because water is more conductive than air.


30 years

Figure 5.17 shows the evolution of liquid pressure with time. The maximum suction is obtained close to the canister and reaches a value of 50 MPa. Although the desaturation of the bentonite buffer takes place due to heat generation, there is no significant difference at the selected nodes in comparison to Case I and Case II (Figures 5.18, 5.19 and 5.20).

0

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0.01 0.1 1 10 100 1000

Tem

per

atu

re (

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Time (y)

Pellets

bentonite ring

Canister wall

47


3 years


3 years

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Liq

uid

Pre

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bentonite ring

Canister wall

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ree

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ura

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bentonite ring

Canister wall

Bentonite disc

Backfill

48

As for the previous cases, saturation of the bentonite buffer causes the material to swell and as a result, the backfill material compresses (Figure 5.19). In fact, no significant differences are observed in terms of volumetric deformations of the bentonite disc and the buffer between this model and the one that has an air gap.

Figure 5.19. Evolution of volumetric deformations.

10 years

Figure 5.20 shows the evolution of mean effective stress in the materials. The maximum mean effective stress reached after 10 years is around 9 MPa.

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.01 0.1 1 10 100 1000

Vo

lum

etri

c D

efo

rmat

ion

Time (y)

Bentonite

Backfill

49


10 years

5.4 Case III

In this case, a coupled THM analysis of a somewhat more refined disposal geometry site including the gap element has been performed by considering an updated geometry and a more refined mesh (Figure 5.21). The same properties of the different materials are used except for rock permeability, as indicated in Table 5.1. Table 5.2 summarizes some basic properties of the bentonite buffer and the backfill.

0

1

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9

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Mea

n E

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Str

ess

(MP

a)

Time (y)

Pellets

bentonite ring

Canister wall

Bentonite disc

Backfill

50

Figure 5.21. Mesh, geometry and materials of the model.

Table 5.2. Initial density and porosity of buffer and backfill.

Materials Solid density (kg/m3) Initial porosity Initial dry density (kg/m3)

Buffer bentonite 2779 0.388 1700

Backfill 2781 0.368 1757

Once again, axisymmetric conditions have been assumed in the analysis. An initial suction of 5 MPa is imposed along the rock boundaries to simulate that the drift and the deposition hole walls undergo certain drying after excavation. Figure 5.22 shows the different representative points considered for comparison of the results.

51

Figure 5.22. Representative nodes for the materials.

Figure 5.23 shows the evolution of temperature for the different materials. The maximum temperature remains under 90 ºC as in the preceding cases I and II. However, the increase of temperature due to the presence of the gap takes place later because hydration evolves more slowly than in the other cases, as the rock permeability is lower. This implies that the maximum temperature increases somewhat, yet still remaining under the prescribed value of 90 oC.

727 725 721 716

Materials Point considered

Backfill 1233

Bentonite disc 1033

Gap canister side 727

Gap bentonite ring side 725

Bentonite ring 721

Pellets 716

1233

1033

52


30 years

Figure 5.24 shows the evolution of the liquid pressure with time. The maximum suction is obtained close to the canister and reaches a value almost of 150 MPa. A large difference is observed at the selected nodes on both sides of the gap element. Due to the lower permeability of the rock, the hydration progresses more slowly and this implies that less water is available when the heating takes place. As a consequence, the drying is more important, which implies that a higher suction develops near the heat source.

0

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Tem

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atu

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bentonite ring



53


30 years

The evolution of dry density of both the backfill and the buffer are shown in Figure 5.25. The minimum saturated density requirement for the buffer is 1950 kg/m3 according to Juvankoski et al. (2012). The plots show that neither the saturated density of the buffer nor the backfill exceeds this reference value. The points considered in Figure 5.25 are considered representative as they are chosen near the interface between the buffer and the backfill, where the clay can expand to a large extend as the backfill permits relatively large movements.

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-90

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0

10

0.01 0.1 1 10 100 1000

Liq

uid

pre

ssu

re (

MP

a)

Time (y)

Pellets

bentonite ring



54

Figure 5.25. Evolution of dry density. 30 years

As for the previous cases, the saturation of the bentonite buffer causes the material to swell and as a result the backfill material compresses (Figure 5.26). Three points have been considered on the interface between the buffer and the backfill. A vertical displacement of 16 cm has been calculated in the central zone of the contact (near the symmetry axis).

1600

1650

1700

1750

1800

1850

1900

1950

2000

1 10 100 1000

Dry

Den

sity

kg

/m³

Time (y)

Backfill

bentonite ring

Porosity

Dry

density

(kg/m3)

Saturated

density

(kg/m3)

0.44 1557 1997

0.42111 1609 2030

0.40222 1662 2064

0.38333 1714 2098

0.36444 1767 2131

0.34556 1819 2165

0.32667 1872 2199

0.30778 1924 2232

0.28889 1977 2266

0.27 2029 2299

55

Figure 5.26. Evolution of vertical displacements at 3 points at the contact between buffer and backfill.

Figure 5.27 shows the evolution of mean effective stress at the selected points. The maximum mean effective stress reached is around 9.2 MPa. Stresses increase during the hydration process and then remain stable as the material is fully saturated. At stabilization, the mean effective stress tends to the reference value of 8 MPa at points with maximum confinement.

30 years

0

2

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12

14

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18

1 10 100 1000

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tica

l D

isp

lace

men

t (c

m)

Time (y)

Buffer_Backfill_Interaction_1



Node 1114 : Interaction point 1

Node 1163: Interaction point 2

Node 1213: Interaction point 3

56


30 years

Figure 5.28 shows desaturation of points close to canister. The effect of the air gap can be seen as well. A sharp desaturation is observed at the point of the gap element close to the canister. In this case, achieving full saturation of all buffer components takes about 50 years. This time is larger than in the previous cases since for this model the rock permeability is lower.

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n E

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Backfill

57


30 years

Figure 5.29 shows the evolution of the closure of the gap. It is observed that 20 years are required for the gap to close completely. When the gap closes, horizontal displacements do not vary anymore and effective horizontal stresses keep increasing after closure of the gap (Figure 5.30).

0

0.1

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1

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Deg

ree

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Sat

ura

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bentonite ring



Bentonite disc

Backfill

58

Figure 5.29. Horizontal displacements in the air gap element.

30 years

Figure 5.30. Horizontal effective stress – horizontal displacement relation in the air gap.

0

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8

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0.01 0.1 1 10 100 1000

Dis

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Time (y)



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9

0 2 4 6 8 10

Eff

ecti

ve S

tres

s (X

) (M

Pa)

Displacement (mm)

59

5.5 Comparison of results

In this section, a comparison of the 4 cases presented for the THM study with the gap is conducted. The permeability of the rock considered in the different models is included in Table 5.3 together with the estimated time for gap closure.

Table 5.3. Summary of models for comparative study.

Models I II III II NOGAP

Rock Permeability 10-18 m2 10-19 m2 1.5x10-20 m2 10-19 m2

Gap Closing time (approx.) 2 years 4 years 20–30 years No air gap

Figures 5.31, 5.32 and 5.33 show the comparison of temperature, liquid pressure and the degree of saturation evolutions for the 4 calculated models.

60

CASE I CASE II

CASE III CASE II NO GAP

Figure 5.31. Evolution of temperature for the different models.

The temperature evolution is not significantly different for the points in the buffer and pellets. However, the temperature in the canister shows a different response depending on the presence of the gap and the value of the rock permeability. The maximum temperature is not significantly influenced in general but the evolution at early times is different, with a local maximum which is caused by the gap.

0

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40

50

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80

90

0.01 0.1 1 10 100 1000

Tem

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atu

re (

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Time (y)

Pellets

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Krock=1e‐18with gap

Krock=1e‐18 m2

with gap

0

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30

40

50

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70

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90

0.01 0.1 1 10 100 1000

Tem

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atu

re (

ºC)

Time (y)

Pellets

bentonite ring

Gap bentonite side

Gap canister side


Krock=1e‐19 m2

with gap

0

10

20

30

40

50

60

70

80

90

0.01 0.1 1 10 100 1000

Tem

pera

ture

(ºC

)

Time (y)

Pellets

bentonite ring



Krock=1e‐19 m2

without gap

Krock = 1.5e-20 m2 with gap

61

CASE I CASE II


Figure 5.32. Evolution of liquid pressure for the different models.

Regarding water pressure, the most important differences occur near the canister. The permeability of the rock affects the time evolution of pressure, at least for the values of permeability considered here. The time is actually controlled by the combination of rock, buffer and backfill permeabilities. For higher permeabilities of the rock, the time control will be dominated by the lower permeability of the buffer.

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Liq

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Krock=1e‐18with gapKrock=1e‐18 m

2

with gap

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-90

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Liq

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Gap bentonite side

Gap canister side

Krock=1e‐19 with gapKrock=1e‐19 m

2

with gap

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-90

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0.01 0.1 1 10 100 1000

Liq

uid

pre

ssu

re (

MP

a)

Time (y)

Pellets

bentonite ring



Krock=1e‐19 m2 without

gap


62

CASE I CASE II


Figure 5.33. Evolution of the degree of saturation for the different models.

The effective stress evolution shown in Figure 5.34 is controlled by the evolution of water pressure. Therefore, the earlier hydration that takes place when the rock permeability is higher induces a faster effective stress increase. However, the maximum effective stress is not significantly different. The different distribution of suction in the buffer and backfill induces a somewhat different strain and stress spatial distribution and temporal evolution.

0

0.1

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ree

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ura

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n

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bentonite ring



Bentonite disc

Backfill

0

0.1

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ree

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Sat

ura

tio

n

Time (y)

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bentonite ring

Gap bentonite side

Gap canister side

Bentonite disc

Backfill

0

0.1

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Deg

ree

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ura

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Time (y)

Pellets

bentonite ring



Bentonite disc

Backfill

0

0.1

0.2

0.3

0.4

0.5

0.6

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0.8

0.9

1

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Deg

ree

of

Sa

tura

tio

n

Time (y)

Pellets

bentonite ring

Canister wall

Bentonite disc

Backfill


Krock = 1e-18 m2 with gap

Krock = 1e-19 m2 with gap

Krock = 1e-18 m2 without gap

63

CASE I CASE II


Figure 5.34. Evolution of mean effective stress for the different models.

Table 5.4 contains a summary of the results obtained in the cases I, II and III. The effect of the gap on the maximum temperature is significant only in Case III due to the low permeability of the rock considered. As can be seen, the time for full saturation increases as the permeability of the rock decreases. The maximum suction achieved is also higher, the lower the rock permeability is. The presence of the gap leads to stronger drying near the canister because the gap has lower retention capacity.

0

1

2

3

4

5

6

7

8

9

10

0.01 0.1 1 10 100 1000

Mea

n E

ffec

tive

Str

ess

(MP

a)

Time (y)


Krock=1e‐18

m2 with gap

Krock=1e‐19 m2 with gap

0

1

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3

4

5

6

7

8

9

10

0.01 0.1 1 10 100 1000

Mea

n E

ffec

tive

Str

ess

(MP

a)

Time (y)

Pellets

bentonite ring


Backfill

Krock=1e‐19

m2 without

gap


64

Table 5.4. Summary of results from the 2nd series of calculations.

Case I Case II Case III

Case II NOGAP

Maximum temperature in the buffer

80 oC 80 oC 85 oC 80 oC

Time for maximum temperature 30 years 30 years 10 years 30 years

Maximum suction in the buffer 95 MPa 100 MPa 150 MPa 50 MPa

Time for maximum suction in the buffer

0.2 year 1 year 2 year 1 year

Time for full saturation (for the selected points)

5 years 15 years 35 years 10 years

Maximum effective stress 8.5 MPa 8.5 MPa 8.5 MPa 8.5 MPa

65

6 DISCUSSION

In this work, various thermo-hydro-mechanical aspects involved in nuclear waste disposal in a rock repository are investigated. Firstly, the BBM parameters for the buffer, which were determined by modelling laboratory experiments, are summarized (see Appendix 2). Since a gap is considered in some models, this feature is explained in detail.

Regarding the importance of hydraulic conductivity, the power parameter in the relative permeability law, the tortuosity factor in the molecular diffusivity law and the preconsolidation stress of the backfill have been examined as parameters in sensitivity analyses. These parameters affect the liquid pressure evolution and thereby the desaturation close to canister. It has been observed that maximum buffer temperature is not affected by the initial incomplete buffer saturation. The maximum temperature was reached in about 30 years and it was 80 ºC on the canister–buffer interface, which fulfils the design criterion for the canister for the equivalent spacing of 16.6 m, which is based on 11 m of borehole separation and 25 m of tunnel separation.

The functional requirement of the density of the buffer around the canister depends on the stress–displacement balance on the buffer surface. According to model results, vertical displacement in the buffer–backfill averages around 7 – 8 cm (with a maximum of 11 cm at the center). At the beginning of the deposition of the canister, as a result of the drying of the buffer, the backfill moves down. As soon as swelling takes place, backfill starts moving up and vertical displacements reach 8 cm on average.

In the KBS-3V concept, the plan is to include initial gaps between the canister and the buffer and between the buffer and the rock. The outer gap will be filled with bentonite pellets. Except for the gap between the canister and the ring blocks, the properties of the materials have been considered the same for the models that contain the gap elements.

The model results show that rock permeability has an effect on gap closing time, which is explained by the different hydration rate. Gap closure takes place in the model when the displacement of the buffer wall towards the canister is observed to reach the maximum 10 mm which is the initial gap aperture.

Higher suction values close to the buffer are observed for the models that contain an air gap. The reason is that the gap has low retention capacity. This high suction does not imply significant changes in the evolution of pressures in the clay buffer and backfill, as was shown when the model with a gap was compared to the model without a gap. The evolution of stresses induced by swelling was similar as well. With regard to temperature, the gap induces an temperature increase in the canister which, depending on the time evolution of hydration, may produce an increase of the maximum temperature calculated in the canister. If the saturation evolves rapidly, the gap-induced temperature increase occurs well before the maximum; otherwise the gap may raise the maximum temperature to some degree, but the allowed maximum of 90 oC will still not be exceeded according to the model calculations presented in this report. Therefore, it can be concluded that the presence of the gap does not significantly affect the buffer and backfill and only induces an increase in canister temperature of less than 10 oC.

66

In other words, the desaturation of the buffer can be said to take place as a result of the heating but the effect of the gap on the desaturation of the buffer is small. Although the gap largely desaturates, the overall effect is not significant because the total volume of the gap is small compared to the volume of the barrier. Therefore even undergoing large desaturation, the gap resaturates easily as its volume is small and the large suction that has developed induces an efficient gradient that attracts water. The closure reduces its volume even further and leads to negligible differences.

The total stress increases as the buffer hydrates. The effective stress also increases. It tends towards the swelling pressure value corresponding to the parameters considered, but the swelling pressure is not achieved since the buffer can expand as the backfill is compressed. As the buffer swells, the buffer–backfill interface moves upwards. The total stress is the sum of the swelling pressure and the water pressure. For this reason, the calculated total stress is higher than the swelling pressure, and it can be understood as the sum of the effective stress developed by swelling (7 MPa) and the pore pressure developed by the hydrostatic water column (4 MPa).

The swelling of the buffer leads to density variations. From an initial value of 1700 kg/m3, the dry density decreases to a value of 1600 kg/m3. This value corresponds to a saturated density of 2000 kg/m3. On the other hand, some zones suffer contraction leading to a dry density of the order of 1750 kg/m3 that corresponds to a saturated density of the order of 2100 kg/m3, but this happens only at some limited zones near the canister where drying is more important.

67

7 CONCLUSIONS AND RECOMMENDATIONS

For the models considered in this study, the maximum temperature does not reach the maximum allowed design temperature of 90 ºC in any of the cases presented, including when the effect of the gap is taken into account. This means that the design is satisfactory with regard to what is required to prevent overly high temperatures in the buffer.

The buffer space between the canister and the rock wall is fully saturated in less than 10 years for the first series of models which consider rock permeability equal to 10-18 and 10-17 m2. In the second series, this time increases up to 50 years, as the permeability of the rock has been considered as low as 10-20 m2. Liquid pressure variations are influenced by heating. Liquid pressure decreases significantly near the canister on account of the heating and the resulting evaporation of water. When the heating process starts, evaporation induces a porosity reduction near the canister and a porosity increase along the contact interface between the backfill and the rock wall.

The total stress increases as the buffer hydrates. If pore pressure becomes positive, total stress increases accordingly. The effective stress also increases. The maximum effective stress achieved is of the order of 7 MPa, somewhat lower than the swelling pressure which has been measured to be of the order of 10 MPa. The lower value obtained in the model is justified by the fact that the buffer can expand as the backfill is compressed.

Except for the zone in the buffer that is near the backfill, the variations of porosity or dry density in the bentonite are relatively small. Porosity varies between 35 and 45 %, which corresponds to a variation of saturated density between 1995 and 2150 kg/m3, although the high density is limited to small zones near the canister.

The backfill parameters have been selected according to what is required from a design point of view (hydraulic conductivity) or from proposed values (in the case of mechanical parameters, such parameters were selected that give lower swelling pressure than the buffer). Some oedometer tests have been carried out at the B+Tech laboratory and the analysis of the tests can give more realistic values for the behaviour of the buffer–backfill interface. Different mock-up tests have been considered that could help to better understand this part of the repository. These tests could be simulated and the model capacity for reproducing the behaviour of similar repository geometry could then be evaluated.

The mechanical parameters of the pellets have been the same as those of the bentonite blocks. Oedometer tests and water retention curve tests in reference pillow pellets are recommended in order to employ more realistic parameters in this part of the buffer.

The water could flow from the fracture network instead of the larger rock mass. Simulations in which the water flows through a fracture could be of interest in assessing the differences in the saturation process resulting from changes in local hydrogeological conditions. Detailed knowledge of groundwater flow is crucial in determining the saturation time and swelling pressure development of the filling components.

69

REFERENCES

Alonso E.E., Gens, A., Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique, 40(3): 405–430.

Autio, J., Hassan, Md. M., Karttunen, P., Keto, P. (2012). Backfill design 2012. Posiva report 2012-15. Eurajoki. Finland.

Brooks, R. H., Corey, A.T. (1964). Hydraulic properties of porous media. Hydrologic Paper 3, Colorado State University, Fort Collins, USA.

Börgesson, L., Dixon, D., Gunnarsson, D., Hansen, J., Jonsson, E., Keto, P. (2009). Assessment of backfill design for KBS-3V repository. Posiva Working report 2009-115. Eurajoki. Finland.

Hökmark, H., Fälth, B. (2003). Thermal dimensioning of the deep repository. SKB Technical report TR-03-09. Stockholm, Sweden.

Ikonen, K. (2003). Thermal analysis of spent nuclear fuel repository. Posiva Working report 2003-04. Eurajoki. Finland.

Ikonen, K. (2005). Thermal Analysis of Repository for Spent EPR-type fuel. Posiva Working report 2005-06. Eurajoki. Finland.

Juvankoski, M., Jalonen, T., Ikonen, K. (2012). Buffer Production Line 2012 - Design, production and initial state of the buffer. Posiva Report 2012-17. Eurajoki. Finland.

Karnland, O., Olsson, S., Nilsson, U. (2006). Mineralogy and sealing properties of various bentonites and smectite-rich clay materials. SKB TR-06-30. Stockholm, Sweden.

Kiviranta, L., Kumpulainen, S. (2011). Quality Control and Characterization of Bentonite Materials. Posiva Working report 2011-84. Eurajoki. Finland.

Lönnqvist, M., Hökmark, H. (2008). Thermo-mechanical analysis of a KBS-3H deposition drift at Olkiluoto site. SKB Report R-08-30. Stockholm, Sweden.

Olivella, S., Gens, A., Carrera, J., Alonso, E.E., (1996). Numerical formulation for a simulator (CODE-BRIGHT) for the coupled analysis of saline media. Eng. Comput. 1: 87–112. CODE_BRIGHT (www.etcg.upc.edu/recerca/code_bright)

Pintado, X., Hassan, Md. M., Martikainen, J. (2012). Thermo-hydro-mechanical tests of buffer material. Posiva Report 2012-49. Eurajoki. Finland.

Pintado, X., Rautioaho, E. (2012). Thermo-hydraulic modelling of buffer and backfill. Posiva Report 2012-48. Eurajoki. Finland.

Pollock, D. W. (1986). Simulation of fluid flow and energy transport processes associated with high-level radioactive waste disposal in unsaturated alluvium. Water Resour. Res. 22 (5), 765–775.

70

Posiva (2009). Olkiluoto site description 2008. Posiva Report 2009-01. Eurajoki. Finland.

Tang, A-M. (2005). Effet de la temperature sur le comportement des barrières de confinement. PhD dissertation. École Nationale des Ponts et Chaussées. Paris, France.

Toprak, E., Mokni, N., Olivella, S. (2011). THM modelling of ONKALO project. Preliminary modelling study. UPC Report.

Toprak, E., Mokni, N., Olivella, S.(2012). THM modelling of ONKALO Project, Gap Effect. UPC Report.

van Genuchten, R. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society American Journal, 44: 892–898.

71

APPENDIX 1. DESCRIPTION OF THE BASIC THM FORMULATION

A brief description of CODE_BRIGHT is included here. The reader may find more details in the references given below.

A1.1 General features of the computer code

Name of code: CODE_BRIGHT

Method used: FEM

Dimensionality: 1D, 2D & 3D

Processes: Coupled THM

Previous application cases: CATSIUS CLAY, BAMBUS I and II, FEBEX I and II, RESEAL I and II, HE-B, EBS, NF-PRO, Prototype, TBT, DECOVALEX-III, THERESA

A1.2 Some features important in THM modelling of repositories

The code has options that allow solving uncoupled or coupled problems, for instance, M, H, T, HM, TM, TH, and THM. The types of analyses can be 1D (uniaxial confined strain and axisymmetric), 2D (plane strain and axisymmetric) and fully 3D. The constitutive laws are defined by a set of parameters with alternative types of relations for different application cases.

The types of boundary conditions are:

- Mechanical problem: forces and displacement rate in any spatial direction. - Hydraulic problem: mass flow rate of water and air prescribed and liquid/gas

pressure prescribed. - Thermal problem: heat flow rate prescribed and temperature prescribed.

The convergence criteria are defined by tolerances for absolute and relative error independent for each unknown, and a tolerance for residual convergence of each problem (mechanical, hydraulic, etc.).

The output options include spatial distribution of variables at user-defined time points, and time evolution of variables at user-defined space points.

A1.3 Mathematical representation of mechanical processes

More detailed descriptions of the mathematical formulation can be found in Alonso et al. (1990), Olivella et al. (1994, 1996), Brooks and Corey (1964), Pollock (1986) and van Genuchten (1980).

72

A1.3.1 Equations of motion

The equation of equilibrium of stresses, the mass balance of water and air and the energy balance are:

b 0

w w w w wl l l g g g l gS S f

t

j j

a a a a al l l g g g l gS S f

t

j j

1 ( ) Qs s l l l g g g c Es El EgE E S E S f

t

i j j j

(A1)

where:

(Note: Bold non-italic symbols refer to a vector or a tensor)

A1.3.2 Mechanical Constitutive models

The viscoplasticity for unsaturated soils based on the Basic Barcelona Model is assumed for bentonite, and linear elasticity behaviour is assumed for other materials.

The strain terms are defined as:

e VP ε ε ε ; 1; e stress thermal suction stress ε ε ε ε ε D σ

σ

εG

FVP )( (Perzyna model)

(A2)

: porosity b: body forces, : density : mass fraction, j: total mass flux : mass content per unit volume of

phase, i: non-advective mass flux E: specific internal energy q: advective flux ic: conductive heat flux u: solid displacements jE: energy fluxes due to mass motion : stress tensor Sl, Sg: degree of saturation of liquid and gas phases i.e., fraction of

pore volume occupied by each phase. Superscripts w and a refer to water and air, respectively Subscripts s, l and g refer to solid, liquid and gas phase, respectively.

73

where eε is the elastic strain tensor (with stress, temperature and suction terms), D is

the elasticity tensor, vpε is the viscoplastic strain rate tensor, is the viscoplastic

parameter, F is the plastic flow function, F is the yield surface, and G is the

plastic potential function. 0

NF F F , where F0 is a reference stress to

normalise F, N is a parameter of the model, and the Macaulay brackets are used.

The model uses effective stress and suction as state variables. The effective stress is

defined as: ' max ,g lP P , which is a modification of the usual effective stress

considered for saturated soils. This function can be referred to also as net stress (in the case of unsaturated conditions) and effective stress (in the case of saturated conditions).

The thermal expansion of materials is considered. The parameters of the constitutive

laws change with temperature and suction. The elastic terms in Equation (A2) related to

temperature and suction are represented by a nonlinear function as in the BBM.

Integration of (A2) gives the stress increments as a function of the strain increments, temperature increments and suction increments.

The triaxial yield surface and plastic potential functions to be used in (A2) are given by:

0,, 22 pspsppMqsqpF os (A4)

0,, 22 pspsppMqsqpG os (A5)

where p is the net average stress, q is the deviatoric stress, s is the matrix suction, M is the slope of critical state shear strength, is the parameter that defines the non-associativity of the plastic potential (with = 1.0 indicating an associated flow rule),

sksp ss )( , and sk is the material parameter that controls the increase in cohesion

with suction, respectively. Parameter p0 representing the loading–collapse curve (LC) is given by

)(

)0(* s

c

ocop

ppsp (A6)

where cp is the reference stress of the loading–collapse curve, *op is the initial yield mean net stress, and )0( is the virgin compressibility for saturated conditions, with )0( being the slope of the virgin elastic compressibility for saturated conditions

and the slope of the unload–reload line. The parameter (s) is the volumetric compressibility index, written as

74

rsrs exp10 (A7)

where r is the parameter that establishes the minimum value of the compressibility index for high values of suction, and is the parameter that controls the rate of increase in stiffness with suction.

The hardening law is given by

pv

oo d

pedp

0

1 ** (A8)

where e is the void ratio, and pvd is the plastic volumetric strain increment.

A1.4 Mathematical representation of fluid flow processes

The fluid flow is governed by Darcy´s law, given by

gk

q

P

kr(A9)

3

2

2

3 )1(

)1( o

oo

kk (A10)

where q is the flux vector along porous media, k is the intrinsic permeability tensor

at porosity , ok is the intrinsic permeability at porosity o , rk is the phase relative

permeability, r is the viscosity of the fluid, P is the pressure of the fluid, and is

the density of the fluid. Gravity is represented by the vector g. Parameters o and are

defined as before.

The fluid density changes with temperature and with pressure. The intrinsic permeability changes with porosity. The hydraulic conductivity is affected by fluid viscosity that changes with temperature. The density of water is calculated as:

0 0 0exp l lP P T T where is the fluid compressibility, is a

volumetric expansion coefficient; and the viscosity is calculated as:

exp / 273.15l A B T where A=2.1x10-2 MPa and B=1808.5 K-1. For the gas

phase, the ideal gases law is used.

Relative permeability is considered with the van Genuchten function or a power of

degree of saturation: 2

1/1 1 ;n

r l l r lk S S k S

. A coupling of flow and

deformations is achieved by Kozeny’s equation (A10) and the thermal coupling is

75

achieved by considering the changes of fluid properties with temperature. However, primary couplings appear from balance equations.

Advection of water and air in gas and liquid phases is calculated by means of Darcy’s law. Non-advective fluxes include diffusion and dispersion (see below).

A1.5 Mathematical representation of heat transfer processes.

The heat transfer process is governed by Fourier´s law, given by the heat flux vector:

Tc i (A11)

with

ldrylsat SS 1 (A12)

or

ll SdrySsat 1)()( (A13)

where ci is the conductive flux vector of heat, T is the temperature, is the thermal

conductivity, sat is the thermal conductivity of the water-saturated porous medium,

dry is the thermal conductivity of the dry porous medium, and Sl is the degree of

saturation.

The heat is transported by liquid or gas flow and by vapour diffusion (advection). The thermal conductivity is modified by liquid and gas flows that change the degree of saturation Sl in Equations (A12) and (A13). The thermal conductivity changes with porosity that affects the saturation degree Sl as well.

Conduction is one of the heat transfer processes considered in Equation (A1), the others are advection due to mass movements.

A1.6 Other features of the code

A1.6.1 Retention curve

For bentonite and rock interfaces, the hydraulic conductivity of the materials considered depends on their degree of saturation. The retention curve (van Genuchten model) is

)1/(1

1P

PP

SS

SSS lg

rlls

rlle (A14)

0

oo

TP P

T

(A15)

76

where Se is the effective degree of saturation of porous media, Sl is the degree of saturation of liquid, Srl is the residual degree of saturation, Sls is the maximum degree of saturation, Pg is the gas pressure, Pl is the liquid pressure, is the shape function coefficient for the retention curve, Po is the pressure of air entrance at a reference temperature, and o is the surface tension at a temperature at which Po was measured. is the surface tension at a temperature T.

A1.6.2 Molecular Diffusion

The molecular diffusion is governed by Fick’s law:

iii DS Ii (A16)

where ii is the non-advective mass flux vector, is the porosity of porous media,

is the density of the phase , S is the degree of saturation of the phase , iD is the

diffusion coefficient, and i is the mass fraction(i), respectively. I is the identity tensor.

The superindex i refers to species and the subindex refers to phases.

The diffusion coefficient of vapour is given by:

273.15n

vapor vg

g

TD D

P

(A17)

where is the tortuosity and vD is the coefficient of diffusion, where Dv = 5.9x10-6

m2/s/K-nPa. The typical value for n is 2.3.

The diffusion coefficients of dissolved salt and air are given by:

exp(273.15 )

air or solutel

QD D

R T

(A18)

where R is the ideal gas constant, D = 1.1x10-4 m2/s, and Q =24530 J/mol are model parameters.

For bentonite and rock interfaces, the vapour pressure depends on temperature, and liquid and gas flow through suction changes (psychrometric law).

Mass fractions and densities of the gas phase are calculated using ideal gases law. Vapour pressure as a function of temperature and suction is obtained as:

, ,v c v cP T P P T F P T

5239.7136075exp

273vP TT

, exp273

c wc

l

P MF P T

R T

(A19)

77

where Pc is the capillary pressure, Mw (0.018 kg/mol) is the molar mass of water, T is the temperature absolute and R is the gas constant (8.31 J/mol/K).

A1.6.3 Mechanical Dispersion

The mechanical dispersion is governed by Fick’s law, given by

'i i i D (A20)

where ii is the non-advective mass flux vector, with superindex i refers to species and

the subindex refers to phase, is the density of phase , 'D is the mechanical

dispersion tensor and i is the mass fraction, respectively.

Note that diffusion and dispersion have similar mathematical form (based on Fick’s law) and can be added up together in a single non-advective flux vector (Equations A16 and A20).

A1.7 References

Alonso, E.E., Gens, A., Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique, 40(3), 405–430.

Brooks, R.H., Corey, A.T. (1964). Hydraulic properties of porous Media. Hydrologic Paper 3, Colorado State University, Fort Collins, USA.

Olivella, S., Carrera, J., Gens, A., Alonso, E.E. (1994). Nonisothermal multiphase flow of brine and gas through saline media. Transport in Porous Media, 15: 271–293.

Olivella, S., Gens, A., Carrera, J., Alonso, E.E. (1996). Numerical formulation for a simulator (CODE_BRIGHT) for the coupled analysis of saline media. Engineering Computations. 13(7): 87–112.

Pollock, D.W. (1986). Simulation of fluid flow and energy transport processes associated with high-level radioactive waste disposal in unsaturated alluvium. Water Resour. Res. 22 (5), 765–775.

van Genuchten, R. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society American Journal, 44: 892–898.

79

APPENDIX 2. MODELLING EXPERIMENTS

Bentonites of various types have been investigated in many countries as buffer materials in high-level radioactive waste disposal concepts. In Finland, MX-80 bentonite is considered one of the best candidates to be used as buffer material, for the construction of the multiple barrier disposal site for spent nuclear fuel repository. In order to investigate the hydro-mechanical behaviour of MX-80 bentonite, a series of laboratory tests have been started up by POSIVA. Two types of tests have been performed: oedometer tests and infiltration tests. These tests have been modelled using the finite element code Code_Bright. The Barcelona Basic Model (BBM) (Alonso et al., 1990) has been used to model the mechanical constitutive behaviour of the material.

A2.1 Introduction

The multiple barrier concept is envisaged in most of the proposed schemes for underground disposal of radioactive wastes. The concept invokes a series of barriers, both engineered and natural, between the canister of high-level radioactive waste and the surface. In almost all countries with a high-level radioactive waste management program, bentonite, in the form of dry compacted blocks, will be used as a buffer material.

In Finland, Olkiluoto was chosen as the final disposal site of spent nuclear fuel. One element of the site investigations conducted at Olkiluoto is the excavation of the underground rock characterization facility (ONKALO) that will be extended to the final disposal depth. One of the methods that are studied for the final placement of the radioactive waste considers the vertical deposition of the copper canisters in holes lined with bentonite clay. The tunnel will then be sealed with compressed clay blocks and pellets. Figure A2.1 shows a schematic representation of the deposition holes.

The long-term performance of the repository as a whole (canister, buffer, host rock, backfill, pellets and gaps) and, in particular, that of the bentonite buffer is of great importance. MX-80 bentonite is considered one of the best candidates to be used as buffer material due to its physical and chemical properties, i.e. large specific area, high cation-exchange capacity, and strong adsorptive affinity for organic and inorganic ions. The most important function of bentonite is to restrict groundwater flow and protect the canister.

80

Figure A2.1. Scheme of the repository.

Understanding the thermo-hydro-mechanical behaviour of the bentonite buffer (MX-80 bentonite) is one of the objectives in this project. An experimental program has been set up to gain insight into the material behaviour. The set of tests that have been performed consists of oedometer and infiltration tests.

In order to analyse the hydro-mechanical behaviour of MX-80 bentonite, the above-mentioned tests are modelled using the finite element code Code_Bright. The Barcelona Basic Model (BBM) (Alonso et al., 1990) has been used to model the mechanical constitutive behaviour of the material. The purpose of this work is to determine and calibrate BBM parameters of MX-80 bentonite clay according to the available tests data.

A2.2 Oedometer tests

As mentioned above, two types of tests have been performed on compacted samples: (i) oedometer tests under humidity controlled conditions and (ii) an infiltration test.

In this section, the experimental and modelling results of the oedometer tests performed on three samples of MX-80 bentonite will be described.

A2.2.1 Experimental results

In order to characterize the effect of suction on the compressibility of MX-80 bentonite, three oedometer tests under controlled humidity conditions, considering different stress paths, have been carried out. The experimental set-up is shown in Figure A2.2.

1-The backfill of the tunnel

2-The buffer made of bentonite

3-The canister

4-Bedrock

81

Figure A2.2. Oedometer test cell.

The samples (50 mm diameter and 19.05 mm high) were compacted at a dry density of around16 kN/m3 and at constant water content of around 6%. Table A2.1 completes the information of the initial conditions of the three tested samples.

Table A2.1. Initial properties of MX-80 bentonite sample (Oedometer tests).

100212c_oedometer

(Test/Sample A)

101222a_oedometer

(Test/Sample B)

100212a_oedometer

(Test/Sample C)

d (kN/m3) 16 15.9 16

w (%) 6.04 5.98 6.04

0.375 0.375 0.375

Initial suction (MPa)

153 219 153

A, B and C is a notation for this report.

The tested samples were subjected to different suction and stress paths. Once compacted the samples were placed in the oedometer cell and the following steps were followed

For samples A and B (100212c_oedometer and 101222a_oedometer):

Wetting path at a low vertical stress: the specimens were inundated to reach saturated conditions, that is, zero suction. For both cases the swelling deformation was measured.

82

Loading–unloading at constant suction s=0 MPa (saturated conditions). The pre- and post-yield compressibility parameters for changes in vertical stress, as well as the yield stress, were determined for each test at different initial suction.

For sample C (100212a_oedometer):

Loading–unloading at constant suction s=153 MPa (dry conditions).

Different constant loading steps were applied on the samples. Each loading step was applied instantaneously and maintained for some time. For each test different loading–unloading steps were considered. The vertical displacement for each loading step was recorded as a function of time. However, consolidation effects are not simulated and therefore the time evolution of deformations is not discussed here. Table A2.2 summarizes the different suction conditions and loading/unloading steps for each test.

Table A2.2. Suction and loading–unloading conditions in the tests.

100212c_oedometer

(Test A)

101222a_oedometer

(Test B)

100212a_oedometer

(Test C)

Vertical load (MPa)

Suction

(MPa)

0.23 153

0.23 0

0.39 0

0.95 0

2.63 0

4.88 0

2.63 0

0.95 0

Vertical load (MPa)

Suction (MPa)

0.196 219

0.196 0

0.476 0

1.877 0

3.559 0

5.240 0

1.597 0

0.476 0

0.196 0

1.877 0

4.119 0

1.877 0

Vertical load (MPa)

Suction

(MPa)

0.392 153

0.73 153

1.6 153

3.2 153

6.6 153

3.2 153

1.6 153

0.84 153

83

The coupled hydro-mechanical response of the MX-80 bentonite samples subjected to the hydraulic and stress paths described previously are displayed in Figures A2.3 to A2.6. Figure A2.3 shows the measured vertical stress–strain relationship for the three tested specimens. As mentioned previously, samples A and B (100212c_oedometer and 101222a_oedometer) were initially inundated and allowed to swell at a constant axial stress. For sample A (100212c_oedometer) hydrated under σv = 0.23 MPa, a swelling deformation of around 0.4 is measured. Afterwards, the sample was subjected to a loading up to 4.88 MPa followed by unloading up to 0.95 MPa. Sample B, hydrated under σv =0.196 MPa shows lower swelling (0.2) as compared to sample A. In this case after loading up to 5.24 MPa, the sample was unloaded up to 0.196 MPa and then subjected to an additional loading/unloading cycle in which the maximum vertical stress reached 4.119 MPa.

The post-yield compressibility parameter v

es ln for the case of sample A

and for the case of sample B is rather similar. The elastic compressibility parameter

v

es ln is also similar between samples A and B.

Figure A2.3. Axial stress–strain relationship for the three tested samples.

Sample C (100212a_oedometer) tested under dry conditions (s=153 MPa) shows quite different behaviour. In this case the sample was loaded up to 4.88 MPa. In spite of this high vertical stress, the sample showed little deformation (0.009). The slope s of the

normal compression line showed a significant drop when suction was reduced to zero. The normal compression line for zero suction (saturated conditions) fell considerably below the normal compression line for s=153 MPa. This variation of s is consistent

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

100 1000 10000

Str

ain

Axial_stress (kPa)

100212a_oedometer

100212c_oedometer

101222a_oedometer

A

B

C

84

with the proposals of Alonso et al. (1990) who proposed a monotonic decrease of swith increasing suction so that the normal compression line for different values of suction diverged with increasing vertical net stress.

Plots of the conventional stress path in the p:q and σv: σh planes are depicted in Figures A2.4 and A2.5. In Figure A2.4 the mean effective stress (p) is calculated as

32 31 p and the deviatoric stress (q) is calculated as 31 q where 1 and

3 are principal stresses. The results of the oedometer tests in terms of radial stress

versus axial stress are displayed in Figure A2.5. When suction is reduced under constant axial stress (samples A and B) the material experiences a swelling tendency resulting in a sharp increase of the radial stresses.

Figure A2.4. Plots in the conventional stress path p:q.

Radial stress is given as increments. Another important parameter that can be deduced from the oedometer tests results is the lateral earth pressure coefficient K0 calculated as

vhK ''0 . Figure A2.6 shows the data plotted in form of K0 against σv for the three

tested samples. For samples A and B (100222a_oedometer and 100212c_oedometer) swelling under constant axial stress provokes a sharp increase of the horizontal stresses causing an increase of lateral earth pressure coefficient (K0>1). Therefore by the end of the hydration phase both samples were over-consolidated. During unloading, axial stress decreases faster than horizontal stress and consequently an increase of K0 is observed. For samples A and C (100212c_oedometer and 100212a_oedometer) K0 at the end of the test reaches a value of 0.8 and 0.65 respectively.

0

1000

2000

3000

4000

5000

6000

0 500 1000 1500 2000 2500 3000 3500 4000

Mean Effective Stress(kPa)

Dev

iato

ric S

tres

s (k

Pa) 100212a_oedometer

100212c_oedometer

101222a_oedometer

A

B

C

85

Figure A2.5. Axial stress–radial stress relationship for the three tested samples.

Figure A2.6. Comparison of test results represented in terms of lateral earth pressure coefficient versus axial stress.

0

500

1000

1500

2000

2500

3000

100 1000 10000

Axial Stress (kPa)

Rad

ial s

tres

s (k

Pa)

100212a_oedometer

100212c_oedometer

101222a_oedometer

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1000 2000 3000 4000 5000 6000 7000

Axial Stress (kPa)

Late

ral e

arth

pre

ssur

e co

effic

ient

100212a_oedometer

100212c_oedometer

101222a_oedometer

A

B

C

A B

C

86

A2.2.2 Modelling results

Model geometry

In order to analyse the hydro-mechanical behaviour of MX-80 bentonite, the above-mentioned tests are modelled using the finite element code Code_Bright. Figure A2.7 shows the model geometry together with the applied boundary conditions. Along the vertical boundaries of the domain, horizontal displacements are restricted to represent the oedometric conditions. Along the horizontal upper boundary, a constant axial stress is imposed. Several time intervals were considered in the simulation and for each one the imposed vertical stress was varied to simulate the loading/unloading steps followed in the experiments. As mentioned in the previous section, the oedometer tests were performed under controlled humidity conditions. For two tests (100212c_oedometer and 101222a_oedometer) the samples were hydrated to reach zero suction and for one test (100212a_oedometer) the suction was maintained constant (s=153 MPa). To simulate this, hydraulic boundary conditions were imposed on the top andbottom boundaries.

The Barcelona Basic Model (BBM) (Alonso et al., 1990) has been used to model the mechanical constitutive behaviour of the material. A brief description of the model equations and parameters is included in Appendix 1.

Figure A2.7. Model geometry and boundary conditions.

87

Modelling results of tests 100212c_oedometer and 101222a_oedometer (Tests A and B)

Table A2.3 shows the parameters of the BBM model for MX-80 bentonite used for the calibration of the two tests (100212c_oedometer and 101222a_oedometer). The table includes the values of non-linear elasticity and elasto-plasticity parameters. The parameters have been calibrated to simulate the experiment performed with sample A (100212c_oedometer) (see Table A2.2 for suction and stress paths). The same parameters were used to simulate the experimental results of sample B (101222a_oedometer).

Table A2.3. Material parameters for tests 100212c_oedometer and 01222a_oedometer.




i0 - 0.05

i - -0.003

Parameters for elastic volumetric compressibility against suction change

s0 - 0.25

sp - -0.145

Elasto-plastic volumetric compressibility - 0.15


R 0.8

MPa -1 0.02



Preconsolidations stress po* MPa 0.75


Figures A2.8(a) and A2.8(b) display the vertical stress–strain relationships for 100212c_oedometer and 101222a_oedometer tests respectively. The plots show comparisons between the experimental data and the numerical simulations. For both tests, the modelled results fit quite well with the experimental data (taking into account that the model parameters have been calibrated with 100212c_oedometer). The model predicts well the swelling deformations that occur during the wetting phase. The

88

calculated swelling deformations for 100212c_oedometer (0.3) are in the same order of magnitude as the measured value (0.4). For experiment 101222a_oedometer, the swelling is over-predicted by the model. The sharp increase of the lateral stresses observed during swelling under constant axial stress is also quite well captured by the model (Figure A2.9). Some discrepancies are observed, however, between the experimental and model results. The model does not predict very well the variation of the lateral stresses that occurs during the loading/unloading phase (Figure A2.9). These discrepancies could be attributed to uncertainties that occurred during the experiment, as it is difficult to measure lateral stresses in an oedometer.

Figure A2.10 shows test 100212c_oedometer plotted in the form of the lateral earth pressure coefficient K0 against axial stress σv. The plots show that swelling under constant axial stress causes an increase of the lateral earth pressure coefficient (K0>1). Therefore by the end of the hydration phase the sample was over-consolidated. During unloading, axial stress decreases faster than horizontal stress and consequently an increase of K0 is observed. But the response is quite reversible as the loading and unloading process begins with a high lateral stress imposed by the initial inundation.

Modelling results of test 100212a_oedometer

As described in Section A2.2.1, in this test the sample were tested under nearly dry conditions. In fact, suction was maintained constant and equal to 153 MPa during the loading/unloading phase. Sample C (100212a_oedometer) tested under dry conditions (s=153 MPa) shows quite different behaviour. In this case the sample was loaded up to 4.88 MPa. In spite of this high vertical stress, the sample showed little deformation (0.009). Table A2.4 shows the parameters of the BBM model used for the calibration of this test (100212a_oedometer). In this case, the calibrated elastic parameters were 10 times lower than those obtained for calibration of tests 100212c_oedometer and 101222a_oedometer. For the properties considered, the model reproduced quite well the experimental results in terms loading/unloading induced deformations (Figure A2.11).

89

(a)

(b)

Figure A2.8. Modelling and experimental results. (a) Axial stress–strain relationship for 100212c_oedometer. (b) Axial stress–strain relationship for 101222a_oedometer.

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

100 1000 10000

Axial_stress (kPa)

Str

ain

Test

Model

Swelling due to sample inundation

-0.2

-0.1

0

0.1

0.2

0.3

0.4

100 1000 10000

Axial_stress (kPa)

Str

ain

Test

model

101222a_oedometer

100212c_oedometer

A

B

90

Figure A2.9. Axial stress–radial stress relationship for (a) 100212c_oedometer and (b) 101222a_oedometer.

0

500

1000

1500

2000

2500

3000

3500

4000

100 1000 10000

Axial Stress (kPa)

Rad

ial s

tres

s (k

Pa)

Test

Model

Stress increases during inundation at oedometer conditions

0

500

1000

1500

2000

2500

3000

3500

4000

100 1000 10000

Axial Stress (kPa)

Rad

ial s

tres

s (k

Pa)

Test

Model

100212c_oedometer

(a)

(b)

101222a_oedometer

A

B

91

Figure A2.10. 100212c_oedometer represented in terms of lateral earth pressure coefficient versus axial stress.

Figure A2.11. Calculated and measured strain during the loading/unloading phase (100212a_oedometer).

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 1000 2000 3000 4000 5000 6000

Axial Stress (kPa)

Late

ral E

arth

Pre

ssur

e C

oeffi

cien

t

Model

-0.018

-0.016

-0.014

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

100 1000 10000

Axial_stress (kPa)

Str

ain

Test

Model

Suction =153 MPa

100212c_oedometer

A

C

92

Table A2.4. Material parameters for test 100212a_oedometer.




i0 - 0.005

i - -0.003

Parameters for elastic volumetric compressibility against suction change

s0 - 0.025

sp - -0.145

Elasto-plastic volumetric compressibility - 0.02


r 0.7

MPa -1 0.02



Preconsolidation stress Po* MPa 0.75


Figure A2.12 shows the modelling results in term of K0 versus σv. In Figure A2.13 the stress path in the p:q plane is shown. Some differences are observed between the model and the experimental results.

93

Figure A2.12. Model lateral earth pressure coefficient versus axial stress (100212a_oedometer).

Figure A2.13. Mean effective stress versus deviatoric stress. Experimental and modelling results (100212a_oedometer).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1000 2000 3000 4000 5000 6000 7000

Axial Stress (kPa)

Late

ral E

arth

Pre

ssur

e C

oeffi

cien

t

Model

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000

Mean Effective Stress (kPa)

Dev

iato

ric S

tres

s (k

Pa)

Test

Model

C

C

94

A2.3 Infiltration test

In order to explore the behaviour of the bentonite buffer upon hydration under confined conditions, an infiltration test was performed on MX-80 bentonite. The samples were compacted at a dry density d=17 kN/m3 and at a constant water content w=5.33%. Table A2.5 completes the information of the initial conditions of the tested sample.

Table A2.5. Initial properties of MX-80 bentonite sample (Infiltration test).

d (kN/m3) 17

w (%) 5.33

Sr (%) 23.34

0.375

k m 5.59x10-21

Initial suction (MPa) 243

A schematic drawing of the infiltration test cell is presented in Figure A2.14. The lower face of the sample is maintained in contact with a porous stone. The hydration inlets are connected to a standard pressure/volume controller which is a water pressure source and a volume change gauge. Water is then collected into a reservoir.

95

Figure A2.14. Scheme of infiltration test device.

A2.3.1 Modelling results

Model geometry

The infiltration test is modelled using the finite element code Code_Bright. Figure A2.15 shows the model geometry together with the applied boundary conditions. The test is performed under confined conditions. Along the vertical and horizontal boundaries of the domain, displacements are restricted. Water inflow is allowed at the lower boundary of the domain.

The Barcelona Basic Model (BBM) (Alonso et al., 1990) has been used to model the mechanical constitutive behaviour of the material. The same model parameters as for the simulation of tests 100212c_oedometer and 101222a_oedometer were used (Table A2.3) except for the preconsolidation pressure which was set to 12 MPa (a value corresponding to the fabrication pressure).

Radial stress

GDS pump

Sample

Load Cell

Weight the water

Radial stress

GDS pump

Sample

Load Cell

Sample

Load Cell

Weight the water

96

Figure A2.15. Model geometry and boundary conditions.

Modelling Results: comparison between experimental and calculation results

Figure A2.17 shows the time evolution of water pressure within the simulated sample. As mentioned previously, the initial suction the sample is s=243 MPa. Water is then driven by advection into the sample because of the gradient of suction existing between the partially water-filled soil and the external reservoir (Figure A2.16). As a consequence, there is dissipation of the negative pore pressure prevailing initially in the pores of the sample (Figure A2.17).

The inflow of water into the sample induces the swelling of the material. Since the infiltration test is performed under confined conditions (constant volume), an increase of the total stresses in the sample is observed. Figure A2.18 shows the evolution with time of the calculated and measured stresses in three representative points (at the top, base and at the centre of the sample). The modelling results are in the range of the measurements.

97

Figure A2.16. Comparison of volume inflow.

Figure A2.17. Liquid pressure evolution (centre of the sample).

0

5000

10000

15000

20000

25000

30000

35000

0 10 20 30 40 50 60 70Time (d)

Vo

lum

e In

flow

(m

m3)

Test

Model

-250

-200

-150

-100

-50

0

0 10 20 30 40 50 60 70

Time (d)

Liqu

id P

ress

ure(

MP

a)

98

Figure A2.18. Comparison of stresses.

Figure A2.19 shows the evolution of porosity at two selected points. At the bottom of the sample the inflow of water causes the wetted layers to swell. As a result, porosity increases in the layers close to the hydration surface. Simultaneously, since the test is performed under constant volume conditions, there is compression of the upper layers inducing a decrease of porosity at this zone.

0

2000

4000

6000

8000

10000

12000

14000

0 10 20 30 40 50 60 70

Time (d)

Str

esse

s (k

Pa)

Stress LC1 kPa

Stress LC2 kPa

Stress LC3 kPa

Stress LC4 kPa

Axial middle

Radial middle

Radial bottom

Radial top

99

Figure A2.19. Porosity evolution at different points in the sample.

The porosity profiles obtained after 0.1, 1, 10, and 100 days are displayed in Figure A2.20. The maximum porosity is obtained near the hydration surface. The maximum peak is followed by a continuous and pronounced decrease in porosity when progressing upwards along the sample (upper layers). Permeability k has been considered as a function of porosity. Profiles of k after 0.1, 1, 10, and 100 days are presented in Figure A2.21. The plots show that permeability increases and reaches a maximum close to the hydration surface. After 100 days, porosity increases and reaches a maximum value of 0.48 at the bottom layers and decreases to a value of 0.34 at the upper layers (Figure A2.20). For the same period, the permeability varies between 5×10–21 m² and ~1×10–21 m² when progressing deeper into the sample (Figure A2.21).

0.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

0 20 40 60 80 100Time (d)

Por

osity Top Part

Bottom Part

100

Figure A2.20. Profiles of porosity.

As for all unsaturated materials, hydraulic conductivity is also strongly dependent on the degree of saturation. The relative permeability of the liquid phase (krl) is given by

lrls

rlleerl SS

SSSASk

; (A21)

Where A is a constant, λ is a power for the relative permeability function, and Se is the effective degree of saturation.

Profiles of relative permeability at several times are shown in Figure A2.22. Initially water is driven into the sample to dissipate the gradient of suction existing between the sample and the external reservoir. As a consequence, the degree of saturation of the hydrated layers starts increasing. At early times, a small increase of krl takes place at the outermost layers. As the hydration front progresses, the degree of saturation increases resulting in an increase of krl.

0.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

00.01

0.020.03

0.040.05

0.060.07

Distance (m

)

Porosity

0.1 day

1 day

10 days

100 days

101

Figure A2.21. Profiles of intrinsic permeability.

0

1E-21

2E-21

3E-21

4E-21

5E-21

6E-21

00.01

0.020.03

0.040.05

0.060.07

Distance (m

)

Intrinsic permeability (m2)

0.1 day

1 day

10 days

100 days

102

Figure A2.22. Profiles of relative permeability.

Figure A2.23 shows some variables of the simulation at the end of the test period. As it is shown, the mean effective stress reaches 10 MPa at the moment the sample is fully saturated. The radial and axial stresses reach 10 MPa as well, so the stress state is nearly isotropic. Overall, it can be said that the entrance of water provokes an increase in porosity and a decrease in dry density in the sections closer to the hydration surface due to the swelling of the clay. In contrast, the sections far from the hydration point undergo compression.

It is clear that the modelling tasks for the infiltration test are achieved by using the calibrated BBM parameters. The obtained results from the model have a strong analogy with the test results.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

00.0

10.0

20.0

30

.04

0.0

50.0

6

Dista

nce

(m)

Relative permeability (-)

0.1

da

y

1 d

ay

10 d

ays

100 d

ays

103

Figure A2.23. Situation of some vital variables at the end of the test.

A2.4 Concluding remarks

This report presents experimental and numerical results on the hydro-mechanical behaviour of MX-80 bentonite. Three oedometer tests and an infiltration test have been performed by POSIVA. These tests have been modelled using the finite element code

104

Code_Bright. The Barcelona Basic Model (BBM) has been used to model the mechanical constitutive behaviour of the material. The parameters have been calibrated according to data from the 100212c_oedometer test. The same parameters were used for the simulation of the 101222a_oedometer test and the infiltration test. Reasonably good estimates of the evolution of deformation for the two oedometer tests as well as of the evolution of stresses in the infiltration test (constant volume) have been obtained. Table A2.6 summarizes the parameters of the BBM model for MX-80 bentonite. The table compares the calibrated parameters and the BBM parameters for MX-80 and FEBEX found in the literature.

Table A2.6. Calibrated elastic and elastoplastic parameters of MX-80 bentonite. Comparison to BBM parameters of FEBEX bentonite.

Parameters Symbols Units MX80 (this report)

MX80 (*)

FEBEX(**)

Poisson’s ratio υ - 0.35 0.2 0.4

Parameters for elastic compressibility against

mean stress change

i0 - 0.05 0.06 0.05

i - -0.003 - -0.003

Parameters for elastic volumetric

compressibility against suction change

s0 - 0.25 0.3 0.25

sp - -0.145 - -0.161

ss 0 - 0

pref MPa 0.01 0.01 0.01Elasto-plastic

volumetric compressibility

- 0.15 0.15 0.9


r 0.8 0.925 0.75

MPa -1 0.02 0.05 0.03 Reference stress pc MPa 0.01 0.2 0.5

Slope of critical state M - 1.07 1 1 Parameter for the plastic

potential - 0.53 1 0.53

Initial preconsolidation stress for saturated

conditions po* MPa 12 3 12

Initial void ratio e0 - 0.6 0.579 0.63 These parameters will be used to perform thermo-hydro-mechanical modelling of the in situ repository disposal site. (*) MX-80 “Mechanical modelling of MX-80 – Quick tools for BBM parameter analysis” O. Kristenson, M. Akesson. Clay Technology. (**) FEBEX “2010 Code_Bright Course Tutorial_VII_THM_Mockup_test”

105

Mechanical constitutive model

In this section the elastic part of mechanical constitutive model based on the BBM model implemented in Code_Bright is described.

Elastic part of BBM (isothermal):

where:

For a3 = 0, the model (ITYCL=1) coincides with the elastic part of BBM for constant coefficients:

For a3 different from zero, the equation ( ITYCL=1) can be expanded in the following way:

Depending on the values of the parameters, negative compressibility can be obtained. This can be limited with the Kmin indicated above.

For a3 and a4 different from zero, the equation (ITYCL=5) can be transformed in the following way:

( ) ( ', )'

1 ' 1 0.1e i sv

s p sdp dsd

e p e s

( ) 1i io is s ( ', ) 1 ln ' exps so sp ref s sp s p p s

0 01 2

0.1 0.1ln ' ln ln ' ln

1 0.1 1 1 0.1i se s s

a p a pe e e

1 2 3

1 3 2 3

3 31 2

1 2

0.1 0.1ln ' ln ln ' ln

1 0.1 0.1

0.1 0.1ln ln ' ln ' ln

0.1 0.1

0.1 0.11 ln ln ' 1 ln ' ln

0.1 0.

e s sa p a a p

e

s sa a p a a p

a as sa p a p

a a

1

1 2 3 4

1 4 2 3

341 2

1 2

0.1 0.1ln ' ln ln '/ ln ln '

1 0.1 0.1

0.1ln ' ln ' ln

0.1

0.11 ln ' 1 ln '/ ln

0.1

ref

ref

e s sa p a a p p a s p

e

sa a s p a a p

aa sa s p a p p

a a

106

This analogy was used in all tests for modelling the elastic part.

Viscoplasticity for unsaturated soils based on BBM

Viscoplasticity (the general model for unsaturated soils based on the Desai and Perzyna theory):

where the yield function is defined as:

with the following additional functions:

The viscoplastic potential is defined similarly as:

where b is a non-associativity parameter. Hardening is described with the following function:

which is equivalent to the BBM model. Suction and net stress are defined as:

And the invariants are:

0 01 2 4 1 3 2

1 1i s

i spa a a a a ae e

( ) ( )'

N

o

d G FF F

dt F

21 2 3 2, , ,D D D b sF J J J s aJ F F

2 20 01 2 4 1 1 4 1 1 4 3 1

n n

bF J s k s k J k s k J k s k k sJ s

3/ 2

3 2

271

2m

s s D DF S S J J

21 2 3 2, , ,D D D b sG J J J s aJ b F F

(0)0* ( )

0 011 1( ) 3 ( ) ( ) / 3

3

sc

oc

JJ s p p s J s

p

0 1 exps r s r

max ,0g ls P P max( , )totaln n g lP P

107

Hardening depends on viscoplastic volumetric strains according to:

which is equivalent to the BBM model as shown.

Note that:

(using k1=3k, k2=3k, k3=0, k4=0, and Fs=1)

In the same way the viscoplastic potential is described as:

which incorporates a parameter to allow for non-associativity conditions. Strength can be considered also a function of suction in the following way:

A2.5 References

Alonso E.E., Gens A., Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique, 40(3): 405–430.

Kristensson, O., Åkesson, M. (2008). Mechanical modelling of MX-80 – Quick tools for BBM parameter analysis. Physics and Chemistry of the Earth 33 (2008): S508–S515.

Code_Bright Course Tutorial_VII_THM_Mockup_test (2010). Departamento de Ingeniería del Terreno. E.T.S. Ingenieros de Caminos, Canales y Puertos de Barcelona. Universidad Politécnica de Cataluña, Barcelona, Spain.

1

22

1' ' ' ' max( , ) / 3 max( , )

31 1

( : ) = ' '2 3

x y z g l g l

D

p p p p J p p

J trace q p

s s s I

*

0* * * *1 1 *

1 1 1

00 0o vp vp vpo

v o o v vo

dpe e edJ J d dp p d d

p

2 2 2 2 21( , , ) 3 ( ( ) ) ( ) ( )

3n n

oF q p s a q p s ks p ks p ks

2 2 2 2 21( , , ) 3 ( ( ) ) ( ) ( )

3n n

oG q p s a q b p s ks p ks p ks

s

satdry dry sat sat dry

dry

s

LIST OF REPORTS

POSIVA-REPORTS 2012

_______________________________________________________________________________________

POSIVA 2012-01 Monitoring at Olkiluoto – a Programme for the Period Before Repository Operation Posiva Oy ISBN 978-951-652-182-7 POSIVA 2012-02 Microstructure, Porosity and Mineralogy Around Fractures in Olkiluoto

Bedrock Jukka Kuva (ed.), Markko Myllys, Jussi Timonen, University of Jyväskylä Maarit Kelokaski, Marja Siitari-Kauppi, Jussi Ikonen, University of Helsinki Antero Lindberg, Geological Survey of Finland Ismo Aaltonen, Posiva Oy ISBN 978-951-652-183-4

POSIVA 2012-03 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Design Basis 2012 Posiva Oy ISBN 978-951-652-184-1 POSIVA 2012-04 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Performance Assessment 2012 Posiva Oy ISBN 978-951-652-185-8 POSIVA 2012-05 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Description of the Disposal System 2012 Posiva Oy ISBN 978-951-652-186-5 POSIVA 2012-06 Olkiluoto Biosphere Description 2012 Posiva Oy ISBN 978-951-652-187-2 POSIVA 2012-07 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Features, Events and Processes 2012 Posiva Oy ISBN 978-951-652-188-9 POSIVA 2012-08 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Formulation of Radionuclide Release Scenarios 2012 Posiva Oy ISBN 978-951-652-189-6

POSIVA 2012-09 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Assessment of Radionuclide Release Scenarios for the Repository System 2012 Posiva Oy ISBN 978-951-652-190-2 POSIVA 2012-10 Safety case for the Spent Nuclear Fuel Disposal at Olkiluoto - Biosphere Assessment BSA-2012 Posiva Oy ISBN 978-951-652-191-9 POSIVA 2012-11 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Complementary Considerations 2012 Posiva Oy ISBN 978-951-652-192-6 POSIVA 2012-12 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Synthesis 2012 Posiva Oy ISBN 978-951-652-193-3 POSIVA 2012-13 Canister Design 2012 Heikki Raiko, VTT ISBN 978-951-652-194-0 POSIVA 2012-14 Buffer Design 2012 Markku Juvankoski, VTT ISBN 978-951-652-195-7 POSIVA 2012-15 Backfill Design 2012 Posiva Oy ISBN 978-951-652-196-4 POSIVA 2012-16 Canister Production Line 2012 – Design, Production and Initial State of the Canister Heikki Raiko (ed.), VTT Barbara Pastina, Saanio & Riekkola Oy Tiina Jalonen, Leena Nolvi, Jorma Pitkänen & Timo Salonen, Posiva Oy ISBN 978-951-652-197-1 POSIVA 2012-17 Buffer Production Line 2012 – Design, Production, and Initial State of the Buffer Markku Juvankoski, Kari Ikonen, VTT Tiina Jalonen, Posiva Oy ISBN 978-951-652-198-8

POSIVA 2012-18 Backfill Production Line 2012 - Design, Production and Initial State of the Deposition Tunnel Backfill and Plug Paula Keto (ed.), Md. Mamunul Hassan, Petriikka Karttunen, Leena Kiviranta, Sirpa Kumpulainen, B+Tech Oy Leena Korkiala-Tanttu, Aalto University Ville Koskinen, Fortum Oyj Tiina Jalonen, Petri Koho, Posiva Oy Ursula Sievänen, Saanio & Riekkola Oy ISBN 978-951-652-199-5 POSIVA 2012-19 Closure Production Line 2012 - Design, Production and Initial State of Underground Disposal Facility Closure Ursula Sievänen, Taina H. Karvonen, Saanio & Riekkola Oy David Dixon, AECL Johanna Hansen, Tiina Jalonen, Posiva Oy ISBN 978-951-652-200-8 POSIVA 2012-20 Representing Solute Transport Through the Multi-Barrier Disposal System by Simplified Concepts Antti Poteri. Henrik Nordman, Veli-Matti Pulkkanen, VTT Aimo Hautojärvi, Posiva Oy Pekka Kekäläinen, University of Jyväskylä, Deparment of Physics ISBN 978-951-652-201-5 POSIVA 2012-21 Layout Determining Features, their Influence Zones and Respect Distances at the Olkiluoto Site Tuomas Pere (ed.), Susanna Aro, Jussi Mattila, Posiva Oy Henry Ahokas & Tiina Vaittinen, Pöyry Finland Oy Liisa Wikström, Svensk Kärnbränslehantering AB ISBN 978-951-652-202-2 POSIVA 2012-22 Underground Openings Production Line 2012 – Design, Production and Initial State of the Underground Openings Posiva Oy ISBN 978-951-652-203-9 POSIVA 2012-23 Site Engineering Report ISBN 978-951-652-204-6 POSIVA 2012-24 Rock Suitability Classification, RSC-2012 Tim McEwen (ed.), McEwen Consulting Susanna Aro, Paula Kosunen, Jussi Mattila, Tuomas Pere, Posiva Oy Asko Käpyaho, Geological Survey of Finland Pirjo Hellä, Saanio & Riekkola Oy ISBN 978-951-652-205-3 POSIVA 2012-25 2D and 3D Finite Element Analysis of Buffer-Backfill Interaction Martino Leoni, Wesi Geotecnica Srl ISBN 978-951-652-206-0

POSIVA 2012-26 Climate and Sea Level Scenarios for Olkiluoto for the Next 10,000 Years Natalia Pimenoff, Ari Venäläinen & Heikki Järvinen, Ilmatieteen laitos ISBN 978-951-652-207-7 POSIVA 2012-27 Geological Discrete Fracture Network Model for the Olkiluoto Site, Eurajoki, Finland: version 2.0 Aaron Fox, Kim Forchhammer, Anders Pettersson, Golder Associates AB Paul La Pointe, Doo-Hyun Lim, Golder Associates Inc. ISBN 978-951-652-208-4 POSIVA 2012-28 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Data Basis for the Biosphere Assessment BSA-2012 Posiva Oy ISBN 978-951-652-209-1 POSIVA 2012-29 Safety Case For The Disposal of Spent Nuclear Fuel at Olkiluoto - Terrain and Ecosystems Development Modelling in the Biosphere Assessment BSA-2012 Posiva Oy ISBN 978-951-652-210-7 POSIVA 2012-30 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Surface and Near-surface Hydrological Modelling in the Biosphere Assessment BSA-2012 Posiva Oy ISBN 978-951-652-211-4 POSIVA 2012-31 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Radionuclide Transport and Dose Assessment for Humans in the Biosphere Assessment BSA-2012 Posiva Oy ISBN 978-951-652-212-1 POSIVA 2012-32 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto - Dose Assessment for the Plants and Animals in the Biosphere Assessment BSA-2012 Posiva Oy ISBN 978-951-652-213-8 POSIVA 2012-33 Underground Openings Line Demonstrations Stage 1, 2012 ISBN 978-951-652-214-5 POSIVA 2012-34 Seismic Activity Parameters of the Olkiluoto Site Jouni Saari, ÅF-Consult Oy ISBN 978-951-652-215-2 POSIVA 2012-35 Inspection of Disposal Canisters Components Jorma Pitkänen, Posiva Oy ISBN 978-951-652-216-9

POSIVA 2012-36 Analyses of Disposal Canister Falling Accidents Juha Kuutti, Ilkka Hakola, Stephania Fortino, VTT ISBN 978-951-652-217-6 POSIVA 2012-37 Long-Term Safety of the Maintenance and Decommissioning Waste of the Encapsulation Plant Olli Nummi, Jarkko Kyllönen, Tapani Eurajoki, Fortum Power and Heat ISBN 978-951-652-224-4 POSIVA 2012-38 Human Factors in NDT of the EB-Weld ISBN 978-951-652-225-1 POSIVA 2012-39 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto: Radionuclide Solubility Limits and Migration Parameters for the Canister and the Buffer Wersin, P., Kiczka, M. & Rosch, D.. ISBN 978-951-652-219-0 POSIVA 2012-40 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto: Radionuclide Solubility Limits and Migration Parameters for the Backfill. Wersin, P., Kiczka, M., Rosch, D., Ochs, M., Trudel, D., ISBN 978-951-652-220-6 POSIVA 2012-41 Safety Case for the Disposal of Spent Nuclear Fuel at Olkiluoto: Radionuclide Migration Parameters for the Geosphere. Martti Hakanen, Heini Ervanne, Esa Puukko, ISBN 978-951-652-221-3 POSIVA 2012-42 Summary Report. Microbiology of Olkiluoto and ONKALO Groundwater Karsten Pedersen, Microbial Analytics Sweden Ab Malin Bomberg and Merja Itävaara, VTT ISBN 978-951-652-222-0 POSIVA 2012-43 In Situ Stress Measurement with LVDT-cell – Method Description and Verification. Matti Hakala, KMS Hakala Oy Topias Siren & Kimmo Kemppainen, Posiva Oy Rolf Christiansson, SKB Derek Martin, University Of Alberta ISBN 978-951-652-223-7 POSIVA 2012-44 Buffer Erosion in Dilute Groundwater Timothy Schatz, Noora Kanerva, Jari Martikainen & Petri Sane B+Tech Oy Markus Olin, Anniina Seppälä, VTT Kari Koskinen, Posiva Oy ISBN 978-951-652-226-8

POSIVA 2012-45 Current Status of Mechanical Erosion Studies of Bentonite Buffer Petri Sane (ed.) & Teemu Laurila, B+Tech Oy Markus Olin, VTT Kari Koskinen, Posiva Oy ISBN 978-951-652-227-5 POSIVA 2012-46 2D and 3D Finite Element Analysis Of Buffer-Backfill Interaction Martino Leoni, Wesi Geotecnica Srl ISBN 978-951-652-228-2 (published as POSIVA 2012-25) POSIVA 2012-47 Thermo-Hydro-Mechanical Modelling of Buffer. Synthesis Report Erdem Toprak, Nadia Mokni, Sebastia Olivella, Universitat Politècnica de Catalunya

Xavier Pintado, B+Tech Oy ISBN 978-951-652-229-9

synthesis report - posiva · evaluated in order to check if the final saturated density...

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