Discrete element modelling of conceptual deep ...

Arab J Geosci DOI 10.1007/s12517-014-1762-7

ORIGINAL PAPER

Discrete element modelling of conceptual deep geological repository for high-level nuclear waste disposal A. K. Verma & P. Gautam & T. N. Singh & R. K. Bajpai

Received: 1 April 2014 / Accepted: 19 December 2014 # Saudi Society for Geosciences 2015

Abstract The long-lived high-level spent nuclear has to be isolated from environment for the protection of ecosystem. One of the methods suggested to isolate the nuclear waste from ecosystem is its burial in deep underground repository. In this paper, discrete element method is used to disposal of spent fuel on stability of underground space and its surrounding rock strata. Effect of temperature increment on stressesstrains and temperature variation of surrounding rockmass due to heat generated by nuclear waste is studied and discussed. Simulation was performed on both strong and jointed granite rock in which tunnel is excavated. Bentonite is used as buffer because of its high sorptivity, longevity and low permeability. It has been found that both temperature and stresses at any point in the rock mass is below the design criteria which are 100 °C for temperature over a time period of 16 years. Keywords High-level waste . Discrete element . Granite . DGR

Introduction Nuclear power is an important and vast source of energy. The major technical drawback of nuclear power is that it produces A. K. Verma (*) : P. Gautam Department of Mining Engineering, Indian School of Mines, Dhanbad-04, Jharkhand, India e-mail: [email protected] T. N. Singh Department of Earth Science, Indian Institute of Technology, Powai, Mumbai-76, India R. K. Bajpai Scientific Officer F, Technology Development Division, Nuclear Recycle Group, BARC, Mumbai-76, India

high-level radioactive waste (HLW) which can be in gaseous, liquid, solid or a composite forms, and their radiation strength vary over a large scale (Giusti 2009). These are hazardous radiations which greatly affects its surrounding environment so there is need of its isolation from the ecosystem. Although radioactivity of waste depletes with time, however, it remains and hence is essential to be isolated from the living environment, until it has decayed to levels that cause no significant risk to health and contamination. Long-lived radioactive element are strontium (90Sr) and caesium (137Cs), found in nuclear waste whose half-lives are approximately of 30 years. Radioactive waste is generated by a wide range of industrial, medical and military activities, each having its own specific inventory of radio nuclides. There are various possible methods adopted for management of nuclear waste like recycling, transmutation (Chwaszczewski 2003; Vladimir et al. 2005), space disposal (Ehricke 1983), ocean disposal although comparatively unsafe, and ground burial (Kwon 2005; Verma et al. 2011, 2013; Verma and Singh 2010; Laredj et al. 2011; Sengun 2013; Mohammed and Sharaf 2011; Bo et al. (2014); Jonny et al. 2014). Whatever is the method of disposal, measurement and understanding of radiation effect on surrounding environment is of utter importance. Out of these methods, disposal of highly hazardous radioactive waste in deep underground repositories/tunnels has been chosen as solution by several developed and developing countries. In order to ground burial of spent fuels several factors must be taken into account concerning the safety of the site where a nuclear waste repository (NWR) construction is planned. Among them are the depth of the burial, the tectonic stability, the geohydrological properties of the host rock and the properties of the rock for proper radioactive attenuation. In the process of ground disposal, a suitable site is located which can able to tolerate the effect of radiation on it. The site is then excavated with required dimensions, and bore holes are created in it. In these bore holes, bentonite material is filled with

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canister, mainly made up of high strength, and noncorrosive metal is placed in it. Radioactive waste is sealed in the canister. The second layer of protection has been provided by bentonite. These layers will also provide protection not only migration of heat but also retard any kind of migration and contamination in surrounding medium. Applied and basic sciences of bentonite mineralogy have played a significant role in radioactive waste disposal practices. Bentonite material is used because its high sorptivity, longevity and low permeability, making it a promising candidate for retaining most natural and anthropogenic long-lived radionuclides within the contaminated and engineered disposal sites (Allard 2009). Most of the earlier analysis of thermomechanical processes in deep geological repositories was based on continuum method like finite element and finite difference (Guvanasen 1985; Ledesma and Chen 2003; Thomas et al. 2003; Rutqvist et al. 2001; Millarda and Barnichonb 2014; Hywel et al. 2014; Rutqvist et al. 2014). Continuum methods like finite element and finite difference methods treat all particles separately and average the physics across many particles, thereby treating the material as a continuum. In the case of solid-like granular behaviour as in rock mechanics, the continuum approach usually treats the material as elastic or elasto-plastic and models it with the finite element method or a mesh-free method. In the case of liquid-like or gas-like granular flow, the continuum approach may treat the material as a fluid and use computational fluid dynamics. The particle model have been used to understand element behaviour (in which conditions are “uniform”), and a continuum method used to solve real problems that involve complicated deformation patterns (with the element behaviour derived from the particle model tests). Hence, particle- or micromechanics-based method is more universal and widely applicable to rock mechanics. The aim of this paper is to study the temperature, stress and deformation of intact and jointed granitic rockmass during underground disposal of high-level nuclear wastes using micromechanics-based approach called bonded particle model (BPM). For this purpose, particle flow code (PFC) 2D developed by Itasca Consulting Group has been used. In this paper, an attempt has been made to use a new and generalised micromechanics-based modelling approach, i.e. BPM for a potential site of deep geological repository (DGR) in India. This paper is organised as follows: in the next section, petrographic analysis of pink granite has been done to study the shape and size of grains at microlevel. Laboratory tests on macrorock specimen have been done as per ISRM standard to determine the macroproperties of granite. Laboratory experiment have been carried out to determine stress-strain behaviour of pink granite, and the same experiment have been simulated in PFC2D to determine the microproperties of the pink granite by matching the stress-strain results with laboratory experiment. Once the microproperties of intact and jointed rockmass have been determined, actual DGR have been

modelled in PFC2D using these microproperties and thermal boundary conditions. The approach used in this paper is shown in a flowchart (Fig. 1).

Host rock: granite The host rock granite in this study is pink in colour, medium grain size of approximately 2.8 mm and epigranular. It is hypidiomorphic in texture and homogenous in structure. The mineralogical composition and mean grain size of pink colour granite is given in Table 1 and Fig. 2a. Figure 2b shows the view of fracture development after triaxial tests.

Discrete element method A physical problem that is concerned with the movement and interaction of circular particles may be modelled directly by PFC2D (Potyondy et al. 1996; Itasca Consulting Group 1999). It represents a material as an assembly of rigid disc particles with desired thickness that moves independently of one another and interacts only at the contact points. Complex rock mass behaviour can be modelled by allowing the particles to be bonded together at their contact points with some type of bond which develops tensile forces between particles. A process analogous to physical compaction is followed until the required porosity, and in situ stress is obtained. A further difficulty arises when it is required to match the behaviour of a simulated solid (composed of bonded particles) with a real solid tested in the laboratory because there is no complete theory that can predict macroscopic behaviour from microscopic properties and geometry. The equations of motion are satisfied for each ball. Calculation cycle consists of repeated application of the law of motion to each particle, a forcedisplacement law to each contact and a constant updating of wall positions. Contacts, which may exist between two balls or between a ball and a wall, altered automatically during the course of a simulation. Force-displacement law Contact forces arise due to both ball-ball and ball-wall contacts. These contact forces can be decomposed in normal and contact plane direction. Fc ¼ Fn þ Fs

where Fc denotes total contact force, Fn denotes normal component of contact force and Fs denotes shear component of contact force. For ball-wall contact, normal component (ni) is directed along the line defining the shortest distance between

Arab J Geosci

Start

Mineralogical composition and grain size analysis of Pink Granite

Discrete element biaxial test on numerical pink granite rock using Macro properties

Stress-Strain behavior of Experimental and Numerical Pink Granite at confining pressures of 0,10,20,46 MPa

Stress and Strain behavior of Experimental and Numerical jointed rocks with 60/30 block at confining pressures of 1.3, 3.4, 6.9, 13.8 MPa

Stress and Strain behavior of Experimental and Numerical jointed sandstone with single joint at 600 at confining pressures of 5.0, 2.5, 1.0 Mpa

Determination of Micro properties to be used in real DGR

Discrete element modelling for DGR in intact and jointed rock Fig. 1 Flowchart showing methodology used in the study

wall and ball, and for ball-ball contact, it is directed along the line joining their centres. The magnitude of the normal contact force is calculated by F n ¼ KnU n

incremental fashion. When the contact is formed, the total shear contact force is initialised to zero. Each subsequent relative shear-displacement increment results in an increment of elastic shear force that is added to the current value. The shear elastic force increment is calculated by ΔF s ¼ −k s ΔU s

n

where K is the normal stiffness [force/displacement] at the contact. The overlap, Un, defined as the relative contact displacement in the normal direction and is given by U n ¼ Ra þ Rb  d U n ¼ Ra  d

f or ball‐ball contact f or wall‐ball contact

ΔU s ¼ V s Δt

where R is the radius of balls and d is the distance between their centres. The shear contact force is computed in an Table 1

where ks is the shear stiffness [force/displacement] at the contact. The shear component of the contact displacement increment occurring over a time step of Δt is calculated by

where Vs is the relative shear velocity (which is defined as the shear velocity of ball B relative to ball A at the contact point

Mineralogical composition and grain size analysis of pink granite

Pink granite

Minerals

Quartz

K-feldspar

Plagioclase

Biotite

Amphibole

Mineralogical composition (%) Grain size (mm)

37.5 2.1

45 2.8

13 2.1

2.5 0.9

1 1.1

Arab J Geosci

54mm

b View of fracture developed in pink granite

a A microscopic view of pink granite

after triaxial loading Fig. 2 a A microscopic view of pink granite. b View of fracture developed in pink granite after triaxial loading

for ball-ball contact and is defined as the shear velocity of the wall relative to the ball at the contact point for ball-wall contact). It is defined as

F t ¼ mat

  V s ¼ vi ½Φ2 −vi ½Φ1 t i −ω½Φ2 xk ½c −xk ½Φ2 −ω½Φ1 xk ½c −xk ½Φ1

where F is total external force acting on mass m, and a is the acceleration of body. In this model, spin=0 so moment of body is not considered. This equation is integrated using a centred finite difference procedure involving a time step of Δt. The quantities V (translation velocity) is computed at the mid-intervals of t±nΔt/2, while the quantity F is computed at the primary intervals of t± nΔt. The following expression describes the translational accelerations at time, t, in terms of the velocity values at midintervals.   at ¼ 1 = Δ t vðtþnΔt=2Þ −vðt−nΔt=2Þ  

where vi[Φj] and ω[Φj] are the translational and rotational velocity, respectively, Φ1 for ball, Φ2 for ball or wall (whichever is the case), xk is the centre of rotation of the wall and ti ={−n2, n1}. Law of motion: the motion of a single rigid particle is determined by the resultant force and moment acting on it. Resultant force is related o translation motion by

σ1

¼

vðtþnΔt=2Þ v

t −nΔt=2

þ ð F t =mÞΔt

Using above equations, the position of particle centre is updated as

σ2

112mm

xðtþΔtÞ ¼ xðtÞ þ V ðtþΔt=2Þ Δt Table 2

56 mm Fig. 3 Schematic diagram of biaxial test on numerical pink granite rock

Macroproperties of rock used for validation

Parameters

Pink granite

Gypsum plaster

Density (kg/m3) Shear modulus (GPa) Bulk modulus (GPa) Friction angle (φ°) Dilatancy angle (ψ°)

2243 20.10 33.05 49 0.0

1568 4.50 5.20 30 0.0

Arab J Geosci Table 3

Input parameters for biaxial test

Parameter

Value

Confining pressure (MPa) Minimum particle radius (mm) Ratio of maximum to minimum particle radius Normal spring stiffness (MN/m) Ratio of shear to normal spring stiffness Friction coefficient Density of a particle (kg/m3)

0, 10, 20, 46 6.0 3.33 9×108 0.5 0.5 2000

Thermal analysis In thermal analysis, simulation of transient heat conduction and storage in materials consisting of particles can be done. The thermal material is represented as a network of heat reservoirs and contact bond as thermal pipes (active pipes) in which heat flows due to conduction. If thermal microproperties are specified, subsequent loading and unloading changes the number of active pipes and hence affects the heat conductivity of material directly.

The variables involved in heat conduction in a continuum are the temperature and the heat-flux vector. These variables are related by the continuity equation and Fourier’s law of heat conduction. q ¼ −k∂T =∂x where k is the thermal conductivity tensor [W/m °C]. And hence, the differential equation of heat conduction is derived which may be solved for particular geometries and properties, given specific boundary and initial conditions. −∂q=∂x þ qv ¼ ρC v ∂T =∂t where qi is the heat flux vector [W/m2], qv is the volumetric heat source intensity or power density [W/m3], ρ is the mass density [kg/m3], Cv is the specific heat at constant volume [J/kg °C] and T is the temperature [°C]. Starting with an initial temperature field, the power in each pipe is updated using Q=−ΔT/ηL Then, reservoir temperatures are updated (provided the temperature is not fixed) using the forward finite difference expression. T ðtþΔtÞ ¼ T ðtÞ þ Δt ðQ0 =m C v ÞðtÞ

Fig. 4 Stress and strain behaviour of experimental and numerical pink granite at a confining pressure of 0 MPa, b confining pressure of 10 MPa, c confining pressure of 20 MPa and d confining pressure of 46 MPa

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Fig. 5 Stress and strain behaviour of experimental and numerical jointed granite (Brown and Trollope 1970) with 60/30 block-jointed rocks at a confining pressure of 1.3 MPa and b confining pressure of 3.4 MPa, c confining pressure of 6.9 MPa and d confining pressure of 13.8 MPa

where ΔT is the temperature difference between the two reservoirs on each end of the pipe, L is the pipe length and Q′ is referred to as the out-of-balance power. Thermal strains are produced in the granular material by accounting for the thermal expansion of the particles and of the bonding material that joins them. For a temperature change of ΔT, change in particle radius, R, is given by ΔR ¼ α RΔT

where α is the coefficient of linear thermal expansion associated with the particle.

Validation For validation, numerical biaxial test were carried out for calibration to match the micromechanical properties of the numerical material with the macroscopic response of the physical material (Fig. 3). Results of discrete element model are

compared to the actual laboratory experiment results (Sitharam et al. 2007). Discrete element modelling have been carried out for three different types of rocks with different number and orientation of joints namely intact pink granite, jointed gypsum plaster with 30°/60° joints and sandstone with single joint at 60°. Discrete model of NX size pink granite core rock sample as per ISRM standard were tested in biaxial c o nd i t i o n b o t h n u m er i c a l l y a n d e x p e r i m e n t a l l y. Macroproperties of the tested numerical rock are shown in Tables 2 and 3, respectively. Comparison result of stress-strain response for experimental and numerical pink granite is shown in Fig. 4a–d under different confining pressure. The stress increase with strain, reaches the peak value and then decrease with increase in strain. The strain softening gradually decrease with increase in confining pressure and a transition from brittle to ductile behaviour in pink granite have been captured in at higher confining pressure (σ3 =46 MPa). To simulate highly jointed rock mass using PFC2D, the experimental work carried out by Brown and Trollope (1970) on gypsum plaster having dimension 4×4×8 in. has been used. Block-jointed samples were made up of assemblies

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Fig. 6 Comparison of stress and strain behaviour of experimental and numerical jointed sandstone with single joint at 60° at a confining pressure of 5 MPa, b confining pressure of 2.5 MPa and c confining pressure of 1 MPa

of small cubes cast in a steel mould. As explained by Brown and Trollope (1970), the assemblies of small cubes are cured for a few days and the cubes were stacked in a special fashion such that of the three sets of mutually perpendicular planes so formed, two are inclined at angles of 0 and 90, 15 and 75, 30 and 60, and 45 and 45 to the sample axes, with a third set remaining vertical in each case. The joint properties are taken, i.e. normal stiffness (Kn) is 100 times the stiffness of the adjacent elements and shear stiffness (Ks) is 0.1 times the Kn (Sitharam et al. 2007). Comparative results of laboratory and numerical simulation of block-jointed tests, having 30°/60° joints and for confining pressures of 1.4, 3.4, 6.9 and 13.8 MPa have been shown in Fig. 5a–d. To validate discrete element simulation of single joined rock, a comparison of stress and strain behaviour of experimental and numerical jointed sandstone with single joint at 60° has been done, as shown in Fig. 6a–c at confining pressures of 1.0, 2.5 and 5 MPa. Microproperties of the pink granite were determined through a series of parameter analysis to match the macroproperties of the pink granite. Discrete element model simulates the mechanical behaviour (both static and dynamic) of a material by representing it as an assembly of circular particles that can be bonded to one

another. Contact-bonded material is used for simulation of rock mass. To obtain desired microproperties which can match the laboratory results of rock, there is a need for inverse modelling which can simulate laboratory tests. For this purpose, built-in Fish functions for biaxial tests are used. Microproperties obtained by this procedure are listed in Table 4. The macroproperties and microproperties of canister and bentonite used in the model are given in Table 5. After careful validation studies and based on composition of pink granite, a numerical pink granite rock is prepared with different groups of balls having different radii. For example, quartz is represented by 9840 number of balls with radii varying from 2.0 to 2.2 mm (Table 6). Case study Two models each for intact and jointed rock consists of 26, 242 particles or balls having radii ranging from 0.7 to 2.0 mm are generated by radius expansion method (Table 6). In each case, contact-bonded assembly in square shape of dimension 25×25 m is generated. To create a model of jointed granite, three joints sets were incorporated at different angles shown in Fig. 7b. In situ stress is applied to these models to create the in situ stress environment. These

Arab J Geosci Table 4 Parameters that define a contact-bonded material (intact and jointed granite) Parameters

Intact granite

Jointed granite

Height (m) Width (m) Minimum ball radius (m) Ball size ratio, uniform distribution Wall normal stiffness multiplier Ball density (kg/m3) Ball-ball contact modulus (GPa) Ball stiffness ratio Ball friction coefficient

25 25 0.006 1.66 1.1 2660.0 88.0 1.0 0.50

25 25 0.006 1.66 1.1 2660.0 10.0 1.0 0.50

Contact bond normal strength mean (MPa) Contact bond normal strength standard deviation (MPa) Contact bond shear strength mean (MPa) Contact bond shear strength standard deviation (MPa) Specific heat (J/kg K) Thermal expansion coefficient Conductivity (W/mK) Fracture spacing joint normal stiffness shear

200 50

20 0.5

200 50

20 0.5

1576 1576 1.92×10−5 1.92×10−5 2.523 2.523 – 1.5 m

stresses are applied using built-in FISH function. Horizontal in situ stresses proposed by Sheorey et al. (2001) have been used in both the models. σv ¼ 0:025 H ðMPaÞ σh ¼ 2:1 þ 0:01 H ðMPaÞ

The whole assembly is solved to reach the state of equilibrium. After equilibrium, a horseshoe-shaped tunnel is excavated in the square domain and properties of buffer (bentonite) and canister are modelled (Fig. 7a, b). In this model, canisters having dimension of 2.05×0.35 (length×diameter) are used. Displacements, stresses and temperature of three vulnerable positions were recorded at an interval of five steps.

Table 5 Parameters

Parameters that define bentonite and canister material Bentonite

Canister

2670 3500 Ball density (kg/m3) Contact bond normal strength mean (MPa) 250 2500 Contact bond shear strength mean (MPa) 250 2500 Specific heat (J/kg K) 888 424 Thermal expansion coefficient 3.1×10−4 1.2×10−5 Conductivity (W/mK) 1.74 43

Table 6

Composition of numerical pink granite

Mineral

No. of balls

Range of radii (mm)

Quartz K-feldspar Plagioclase Biotite Amphibole

9840 1008 3411 656 263

2.0–2.2 2.5–2.9 1.9–2.3 0.7–0.9 0.8–1.4

Initial and boundary conditions Applying heat flux A constant heat flux of 500 W/m2 is applied to the all canisters. Hence, canisters behave as a source of heat. Initial temperature of the model is taken as 21 °C. In these models, constant heat flux is applied to canisters to analyse the thermal effect for 1 year. Effect of heat flux generated by nuclear waste can also be analysed for hundreds years by varying heat flux with time, but it takes much computational time so effect of constant heat flux for 1 year is analysed to understand the behaviour of heat migration and subsequent effect in surrounding rockmass. Models are solved by coupled thermomechanical mode to study the both thermal and mechanical effects with time. Due to thermal expansion of particles, stresses and strains will develop in the system. So, all three stress components, displacement in x and y directions, velocity in x and y directions and temperature at ten different vulnerable locations were recorded at every five steps. Strain energy, frictional work and kinetic energy of the whole model were also calculated at an interval of five steps. There two types of boundary conditions which have been applied to the model: (1) mechanical and (2) thermal. Roller boundary conditions have been applied to the left and right boundary, bottom is fixed and the nodes at the upper boundary are free in x, y and z directions. Similarly, adiabatic boundary conditions were used for all sides of the model: the initial and boundary conditions for the mechanical and thermal. A vertical stress of 3.99 MPa has been applied to the top surface of the model to simulate the effect of 147.5 m of pink granitic overburden (Fig. 8). Where Ft T t k Z σ0x, σ0z H,F(t0)

Thermal flux Temperature Time Coefficient of earth pressure Z coordinate Normal stresses deconst-Constant

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25m Granite Rock

Canister

Bentonite

5.0m

5.0 m

25m

1.35m

2.05 m

4.05m

Canister Bentonite Interface .35m

Granite Rock

Bentonite Rock Interface

Fig. 7 Mechanically stable model of excavated tunnel in a hard granite rockmass and b jointed granite rockmass, and disposal holes with canisters

Fig. 8 Boundary and initial conditions of the model

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a Temperature variation of DGR without joint at different monitoring points

b Temperature variation of DGR with joint at different monitoring points

Fig. 9 a Temperature variation of DGR without joint at different monitoring points. b Temperature variation of DGR with joint at different monitoring points

Results and discussion Three points have been chosen at different interfaces to monitor the evolution of stresses and temperature with respect to time (Fig. 7). Temperature evolution Initial temperature of each particle is kept at ambient temperature of 21 °C. Temperature is maximum at canister buffer interface after 9 years of heating and minimum of granite rock. It is observed that temperature increment is minimum at the roof of the tunnel (10 °C) and is maximum in the floor of tunnel because floor particles experience combined effect of thermal heat radiation of all the three canisters while in the roof, particles are affected by individual canisters only. Figure 9a, b compares the predicted temperature evolution, during heating period (up to 9 years) and cooling (up to 8 years) at three monitoring points that is canister-bentonite interface,

a Minimum principle effective stress variation of DGR without joint at different monitoring points

bentonite-rock interface and granite rock. As shown in Fig. 9a, during heating, the temperature increase and reaches a peak of 92 °C in the near-field after about 9 years with developing a temperature gradient of an average 1.8 °C/cm in the buffer zone. The elevated temperature causes the heater and rock to expand, which strains the softer buffer (bentonite). Local material inhomogeneity affects the displacements and strain due to thermal expansion. However, expansion was observed to move the rock upwards and moving into the cavern causing the drift floor to heave about 0.46 mm. After 9 years of heating, the heating power decays and the temperature declines back to approximately ambient temperature within 8 years of decaying heat which is accompanied with cooling shrinkage and corresponding fracture response. Stress evolution It is found that principle effective stresses are most important factor in determining the state of failure of the rock walls of the

b Minimum principle effective stress variation of DGR with joint at different monitoring points

Fig. 10 a Minimum principle effective stress variation of DGR without joint at different monitoring points. b Minimum principle effective stress variation of DGR with joint at different monitoring points

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a Displacement of particles in the tunnel in hard granite after nine years

b Falling of particles in tunnel in jointed granite rock mass after nine years

Fig. 11 a Displacement of particles in the tunnel in hard granite after 9 years. b Falling of particles in tunnel in jointed granite rock mass after 9 years

disposal tunnel (Rutqvist et al. 2001), and we have plotted only the evolution of minimum principle effective stresses over a period of 16 years. Minimum principle effective stresses have a maximum value of 12 MPa at bentonite-rock interface after 11 years, and then, it decays to 6 MPa after 19 years of heating and cooling cycle. The minimum principle effective stresses have dramatically reduced to almost half of the value in case of three sets of jointed pink granitic rockmass. The stresses in the bentonite-rock interface have reached the peak value earlier in both the cases as compared to canister-bentonite interface. Among all selected three monitoring points, stresses are accumulated mostly in the location near to the canisters. Stresses acting on particles increase with increase in temperature (Fig. 10a, b). This may be due to the increment in temperature resulted from thermal expansion of particles and also due to the increased contact forces between particles. Stress accumulation is maximum at the centre of the floor of the tunnel and decreases with distance from centre point. At the roof of tunnel, there is very little variation in temperature, so change in stresses is very less.

Fig. 12 Stress path for a point in granite rock (as shown in Fig. 7) located in rock for intact and jointed pink granite

Deformation evolution Displacement of particles near to the tunnel floor, sides and buffer is maximum (0.46 mm) due to more thermal expansion which is consequently caused by increment in temperature (Fig. 11a). At the roof of the tunnel, displacement of particles is negligible because there is very small increment in the temperature. Figure 11b shows the falling of particles from the boundary. Effective principle stresses for both the intact and jointed pink granite rockmass have been compared in Fig. 12. Intact rock due to its low permeability as compared to high permeability of jointed granite have higher possibility of failure. The reason can be attributed to delay in resaturation in buffer region in intact rock which consequently delays the development of compressive stress in the buffer to hold the canister.

Conclusion In this paper, a numerical simulation based on discrete element method is used to predict the variation of temperature, stresses and deformation during disposal of the nuclear waste in DGR. Numerical models of a tunnel in intact and jointed granitic rock mass with disposal hole densely filled with buffer (bentonite) and canisters (containing nuclear waste) at the centre of tunnel floor and sides were prepared. Change in stress, strain and temperature was studied at the selected locations. It was observed that displacement of particles is maximum near the canisters. Buffer experiences compression and canister is in tension zone. Temperature increment at the centre of floor is maximum and minimum at roof. Maximum temperature increment over 16 years time is observed 94 and 90 °C in intact and jointed granitic rockmass, respectively.

Arab J Geosci

There are some rockmass failures in case of jointed granite rockmass which suggest that spent fuel should be disposed in tunnel with high strength and least fractured rock strata, but on the contrary, the delay in resaturation due to intact rock pose a serious problem for design of DGR in intact rock condition. Hence, it can be concluded that the design should be a tradeoff between DGR in intact granite and fractures granitic rockmass.

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