Hypothetical Nuclear Waste Repository Research Articles

Numerical Simulation of Cracking Process in Rock Mass Under the Coupled Thermo-Mechanical Condition

To investigate crack initiation and propagation of rock mass under coupled thermo-mechanical (TM) condition, a two-dimensional coupled TM model based on the numerical manifold method (NMM) is proposed, considering the effect of thermal damage on the rock physical properties and stress on the heat conductivity. Then, the NMM, using empirical strength criteria as the crack propagation critical criterion and physical cover as the minimum failure element, was extended for cracking process simulation. Furthermore, a high-order cover function was used to improve the calculation accuracy of stress. Therefore, the proposed method consists of three parts and has a high accuracy for simulating the cracking process in the rock mass under the coupled TM condition. The ability of the proposed model for high accuracy stress, crack propagation, and thermally-induced cracking simulation was verified by three examples. Finally, the proposed method was applied to simulate the stability of a hypothetical nuclear waste repository. Based on the outcome of this study, the application of NMM can be extended to study rock failure induced by multi-field coupling effect in geo-materials.

A comparative study of discrete fracture network and equivalent continuum models for simulating flow and transport in the far field of a hypothetical nuclear waste repository in crystalline host rock

One of the major challenges of simulating flow and transport in the far field of a geologic repository in crystalline host rock is related to reproducing the properties of the fracture network over the large volume of rock with sparse fracture characterization data. Various approaches have been developed to simulate flow and transport through the fractured rock. The approaches can be broadly divided into Discrete Fracture Network (DFN) and Equivalent Continuum Model (ECM). The DFN explicitly represents individual fractures, while the ECM uses fracture properties to determine equivalent continuum parameters. We compare DFN and ECM in terms of upscaled observed transport properties through generic fracture networks. The major effort was directed on making the DFN and ECM approaches similar in their conceptual representations. This allows for separating differences related to the interpretation of the test conditions and parameters from the differences between the DFN and ECM approaches. The two models are compared using a benchmark test problem that is constructed to represent the far field (1×1×1km3) of a hypothetical repository in fractured crystalline rock. The test problem setting uses generic fracture properties that can be expected in crystalline rocks. The models are compared in terms of the: 1) effective permeability of the domain, and 2) nonreactive solute breakthrough curves through the domain. The principal differences between the models are mesh size, network connectivity, matrix diffusion and anisotropy. We demonstrate how these differences affect the flow and transport. We identify the factors that should be taken in consideration when selecting an approach most suitable for the site-specific conditions.

FEM analysis for influences of a fault on coupled t-h-m-m process in dual-porosity rock mass

For the case in which a large geological structure like fault existing within the surrounding rock mass in the near field of a repository for high-level radioactive nuclear waste, one kind of coupled thermo-hydro-mechanical-migratory model of dual-porosity medium for saturated-unsaturated ubiquitous-joint rock mass was established. In the present model, the seepage field and the concentration field are double, but the stress field and the temperature field are single, and the influences of sets, spaces, angles, continuity ratios, stiffness of fractures on the constitutive relationship of the medium can be considered. At the same time, a two-dimensional program of finite element method was developed. Taking a hypothetical nuclear waste repository located at a rock mass being unsaturated dual-porosity medium as a calculation example, the FEM analysis for thermo-hydro-mechanical-migratory coupling were carried out under the condition of radioactive nuclide leaking for the cases with and without a fault, and the temperatures, pore pressures, flow velocities, nuclide concentrations and principal stresses in the rock mass were investigated. The results show that the fracture water in the fault flows is basically along the fault direction, and its flow velocity is almost three orders of magnitude higher than that of fracture water in rock mass; the nuclide concentration in the fault is also much higher than that without fault, and the nuclides move along the fault faster; moreover, the fault has obvious influences on the pore pressures and the principal stresses in the rock mass.

FEM analyses for influences of pressure solution on thermo-hydro-mechanical coupling in porous rock mass

The model of pressure solution for granular aggregate was introduced into the FEM code for analysis of thermo-hydro-mechanical (T-H-M) coupling in porous medium. Aiming at a hypothetical nuclear waste repository in an unsaturated quartz rock mass, two computation conditions were designed: 1) the porosity and the permeability of rock mass are functions of pressure solution; 2) the porosity and the permeability are constants. Then the corresponding numerical simulations for a disposal period of 4 a were carried out, and the states of temperatures, porosities and permeabilities, pore pressures, flow velocities and stresses in the rock mass were investigated. The results show that at the end of the calculation in Case 1, pressure solution makes the porosities and the permeabilities decrease to 10%–45% and 0.05%-1.4% of their initial values, respectively. Under the action of the release heat of nuclear waste, the negative pore pressures both in Case 1 and Case 2 are 1.2–1.4 and 1.01–1.06 times of the initial values, respectively. So, the former represents an obvious effect of pressure solution. The magnitudes and distributions of stresses within the rock mass in the two calculation cases are the same.

FEM analyses for influences of stress-chemical solution on THM coupling in dual-porosity rock mass

The models of stress corrosion, pressure solution and free-face dissolution/precipitation were introduced. Taking a hypothetical nuclear waste repository in an unsaturated dual-porosity rock mass as the calculation objective, four cases were designed: 1) the fracture aperture is a function of stress corrosion, pressure solution and free-face dissolution/precipitation; 2) the fracture aperture changes with stress corrosion and pressure solution; 3) the fracture aperture changes with pressure solution and free-face dissolution/precipitation; 4) the fracture aperture is only a function of pressure solution, and the matrix porosity is also a function of stress in these four cases. Then, the corresponding two-dimensional FEM analyses for the coupled thermo-hydro-mechanical processes were carried out. The results show that the effects of stress corrosion are more prominent than those of pressure solution and free-face dissolution/precipitation, and the fracture aperture and relevant permeability caused by the stress corrosion are only about 1/5 and 1/1000 of the corresponding values created by the pressure solution and free-face dissolution/precipitation, respectively. Under the action of temperature field from released heat, the negative pore and fracture pressures in the computation domain rise continuously, and are inversely proportional to the sealing of fracture aperture. The vector fields of flow velocity of fracture water in the cases with and without considering stress corrosion are obviously different. The differences between the magnitudes and distributions of stresses within the rock mass are very small in all cases.

Coupled thermo-hydro-mechanical-migratory model for dual-porosity medium and numerical analysis

A coupled thermo-hydro-mechanical-migratory model of dual-porosity medium for saturated-unsaturated ubiquitous-joint rockmass was established, in which the stress field and the temperature field were single, but the seepage field and the concentration field were double, and the influences of sets, spaces, angles, continuity ratios, stiffnesses of fractures on the constitutive relationship of the medium were considered. Also, the relative two-dimensional program of finite element method was developed. Taking a hypothetical nuclear waste repository as a calculation example, the case in which the rockmass was unsaturated dual-porosity medium and radioactive nuclide leak was simulated numerically, and the temperatures, negative pore pressures, saturations, flow velocities, nuclide concentrations and principal stresses in the rockmass were investigated. The results show that the negative pore pressures and nuclide concentrations in the porosity and fracture present different changes and distributions. Even though the saturation degree in porosity is only about 1/10 that in fracture, the flow velocity of underground water in fracture is about three times that in porosity because the permeability coefficient of fracture is almost four orders higher than that of porosity. The value of nuclide concentration in fracture is close to that in porosity.

FEM analyses for influences of stress corrosion and pressure solution on THM coupling in dual-porosity rock mass

With the models of stress corrosion and pressure solution, by Yasuhara et al., two computation conditions were designed for a hypothetical nuclear waste repository in an unsaturated dual-porosity rock mass: (i) the fracture apertures are changed with the stress corrosion and pressure solution (the porosity of rock matrix is also a function of stress); (ii) the fracture apertures and the porosity of rock matrix are constants. Then the corresponding two-dimensional FEM analyses for the coupled thermo- hydro-mechanical processes were carried out, and the states of temperatures, rates and magnitudes of aperture closure, pore pressures, flow velocities and stresses in the rock mass were investigated. The results show the followings: The aperture closure rates caused by stress corrosion are almost six orders higher than those caused by pressure solution, and the two kinds of closure rates climb up, then decline, furthermore tend towards stability; the fracture apertures decrease from the original value and tend towards the residual value, and the contact-area ratios of asperities increase also from the original value and tend towards the nominal value; when the effects of stress corrosion and pressure solution are considered, the negative fracture pressures in near field rise very highly; the differences between the magnitudes and distributions of stresses within the rock mass in two calculation cases are very small.

3D thermo-hydro-mechanical-migratory coupling model and FEM analyses for dual-porosity medium

One kind of 3D coupled thermo-hydro-mechanical-migratory model for saturated-unsaturated dual-porosity medium was established, in which the stress field and the temperature field are single, but the seepage field and the concentration field are double, and the influences of sets, spaces, angles, continuity ratios, stiffness of fractures on the constitutive relationship of the medium can be considered. The relative three-dimensional program of finite element method was also developed. By comparing with the existing computation example, reliability of the model and the program were verified. Taking a hypothetical nuclear waste repository as a calculation example, the radioactive nuclide leak was simulated numerically with both the rock mass and the buffer being unsaturated media, and the temperatures, negative pore pressures, flow velocities, nuclide concentrations and normal stresses in the rock mass were investigated. The results showed that the temperatures, negative pore pressures and nuclide concentrations in the buffer all present nonlinear changes and distributions that even though the saturation degree in porosity is only about 1/9 of that in fracture, the flow velocity of underground water in fracture is about 6 times of that in porosity because the permeability coefficient of fracture is almost four orders higher than that of porosity, and that the regions of stress concentration occur at the vicinity of two sides of the boundary between buffer and disposal pit wall.

2D FEM analysis for coupled thermo-hydro-mechanical-migratory processes in near field of hypothetical nuclear waste repository

In order to consider the influence of temperature and stress fields on the migration of radioactive nuclide with underground water movement, an elastoplastic model and a 2D FEM code for analysis of coupled thermo-hydro-mechanical (THM) processes in saturated and unsaturated porous media were extended and improved through introducing the percolation and migration equation, so that the code can be used for solving the temperature field, flow field, stress field and nuclide concentration field simultaneously. The states of temperatures, pore pressures and nuclide concentrations in the near field of a hypothetical nuclear waste repository were investigated. The influence of the half life of the radioactive nuclide on the temporal change of nuclide concentration was analyzed considering the thermo-hydro-mechanical-migratory coupling. The results show that, at the boundary of the vitrified waste, the concentration of radioactive nuclide with a half life of 10 a falls after a period of rising, with the maximum value of 0.182 mol/m3 and the minimum value of 0.181 mol/m3 at the end of computation. For a half life of 1 000 a, the concentration of radioactive nuclide always increases with the increase of the time during the computation period; and the maximum value is 1.686 mol/m3 at the end of the computation. Therefore, under the condition of THM coupling, the concentration of radioactive nuclide with a shorter half life will decrease more quickly with water flow; but for the radioactive nuclide with a longer half life, its concentration will keep at a higher level for a longer time in the migration process.

Numerical study of the THM effects on the near-field safety of a hypothetical nuclear waste repository—BMT1 of the DECOVALEX III project. Part 1: Conceptualization and characterization of the problems and summary of results

Geological disposal of the spent nuclear fuel often uses the concept of multiple barrier systems. In order to predict the performance of these barriers, mathematical models have been developed, verified and validated against analytical solutions, laboratory tests and field experiments within the international DECOVALEX III project. These models in general consider the full coupling of thermal (T), hydraulic (H) and mechanical (M) processes that would prevail in the geological media around the repository. For Bench Mark Test no. 1 (BMT1) of the DECOVALEX III project, seven multinational research teams studied the implications of coupled THM processes on the safety of a hypothetical nuclear waste repository at the near-field and are presented in three accompanying papers in this issue. This paper is the first of the three companion papers, which provides the conceptualization and characterization of the BMT1 as well as some general conclusions based on the findings of the numerical studies. It also shows the process of building confidence in the mathematical models by calibration with a reference T–H–M experiment with realistic rock mass conditions and bentonite properties and measured outputs of thermal, hydraulic and mechanical variables.

Thermally induced mechanical and permeability changes around a nuclear waste repository—a far-field study based on equivalent properties determined by a discrete approach

Abstract A numerical investigation is conducted on the impacts of the thermal loading history on the evolution of mechanical response and permeability field of a fractured rock mass containing a hypothetical nuclear waste repository. The geological data are extracted from the site investigation results at Sellafield, England. A combined methodology of discrete and continuum approaches is presented. The results of a series of simulations based on the DFN–DEM (discrete fracture network–distinct element method) approach provide the mechanical and hydraulic properties of fractured rock masses, and their stress-dependencies. These properties are calculated on a representative scale that depends on fracture network characteristics and constitutive models of intact rock and fractures. In the present study, data indicate that the large scale domain can be divided into four regions with different property sets corresponding to the depth. The results derived by the DFN–DEM approach are then passed on to a large-scale analysis of the far-field problem for the equivalent continuum analysis. The large-scale far-field analysis is conducted using a FEM code, ROCMAS for coupled thermo-mechanical process. The results show that the thermal stresses of fractured rock masses vary significantly with mechanical properties determined at the representative scale. Vertical heaving and horizontal tensile displacement are observed above the repository. Observed stress and displacement fields also shows significant dependency on how the mechanical properties are characterized. The permeability changes induced by the thermal loading show that it generally decreases close to the repository. However, change of permeability is small, i.e., a factor of two, and thermally induced dilation of fracture was not observed. Note that the repository excavation effects were not considered in the study. The work presented in this paper is the result of efforts on a benchmark test (BMT2) within the international co-operative projects DECOVALEX III and BENCHPAR.

A Thurstonian comparison of the analytic hierarchy process and probabilistic multidimensional scaling through application to the nuclear waste site selection decision

Monte-Carlo simulation and subjective evaluations are used to compare the Analytic Hierarchy Process (AHP) and probabilistic multidimensional scaling (PROSCAL) in the context of selecting the United States' first high-level nuclear waste repository. The simulation assumes a Thurstonian judgment framework as a means of evaluating the perofrmance of AHP/PROSCAL estimation procedures. Simulated factors include the amount of Thurstonian uncertainty and number of decision-makers. The subjective evaluations of the two methods are given by individuals who make both AHP and PROSCAL judgments in a hypothetical nuclear waste repository decision. Various strengths and weaknesses of the two methods are identified.

Uncertainty and Sensitivity Analyses of Groundwater Travel Time in a Two-Dimensional Variably-Saturated Fractured Geologic Medium

ABSTRACTThis paper presents a method for sensitivity and uncertainty analyses of a hypothetical nuclear waste repository located in a layered and fractured unconfined aquifer. Groundwater travel time (GWTlT) has been selected as the performance measure. The repository is located in the unsaturated zone, and the source of aquifer recharge is due solely to steady infiltration impinging uniformly over the surface area that is to be modeled. The equivalent porous media concept is adopted to model the fractured zone in the flow field. The evaluation of pathlines and travel time of water particles in the flow domain is performed based on a Lagrangian concept. The Bubnov-Galerkin finite-element method is employed to solve the primary flow problem (non-linear), the equation of motion, and the adjoint sensitivity equations. The matrix equations are solved with a Gaussian elimination technique using sparse matrix solvers. The sensitivity measure corresponds to the first derivative of the performance measure (GWTT) with respect to the parameters of the system. The uncertainty in the computed GWTT is quantified by using the first-order second-moment (FOSM) approach, a probabilistic method that relies on the mean and variance of the system parameters and the sensitivity of the performance measure with respect to these parameters. A test case corresponding to a layered and fractured, unconfined aquifer is then presented to illustrate the various features of the method.