^{1}

^{2}

^{1}

^{2}

^{3}

^{1}

^{2}

^{4}

^{1}

^{2}

^{3}

^{4}

In the deep geological repository of nuclear waste, the corrosion of waste generates gas, which increases the storage pressure, changes the properties of the rock strata, and affects the stability of nuclear waste repository. Therefore, it is of great importance to understand the gas migration in the engineering barrier and the potential impact on its integrity for the safety assessment of nuclear waste repository. A hydro-mechanical-damage model for analyzing gas migration in sedimentary rocks is established in this paper. On the basis of which, a set of coupled formulas for the coupling of gas migration in rock mass is established. The model considers the characteristics of gas migration in sedimentary rock, especially the microcracks caused by the degradation of elastic modulus and damage, and the coupling between the rock deformation and failure of fractures. The numerical simulation of gas injection test is beneficial to understand the mechanism of gas migration process in sedimentary rock.

Nuclear waste contains strong radioactivity, large calorific value, high toxicity, and long half-life nuclides, which should be isolated from the environment for human residence in a reliable way. In a large number of disposal schemes, the deep geological disposal of nuclear waste is a widely accepted and feasible disposal scheme at present [

The generated gas tends to migrate through underground barrier. The increase in pressure caused by the generated gas induces the formation of factures and the expansion of the pore of the barrier. This affects the long-term function of waste repository and causes the risk to ecological environment, as shown in Figure

Effects of gas generation in a repository [

For all major international waste separation schemes, the study of gas migration and its effect on the rock has become a key goal. Horseman et al. 1999 carried out the gas injection test of the precompacted bentonite and suggested that the gas entry and breakthrough were accompanied by the development of the propagation path of clay. The initial saturated bentonite is impermeable without the absence of pressure-induced gas channels. Davy et al. [

The objective of this paper is to establish a hydro-mechanical-damage model to predict the gas migration in the sedimentary rock. The model considering the characteristics of gas migration, especially the microcracks caused by the degradation of elastic modulus and damage, the effect of damage on permeability, and the relationship between the damage and the rock deformation and failure of fractures. Based on this model, we can simulate the gas migration process and study the mechanism of gas flow and its influence on rock stability in sedimentary rocks.

In order to establish the governing equation, we have made the following main assumptions:

The rock stratum is continuous and uniform.

The gas flow process in rock stratum is pseudostatic.

Gas viscosity does not change.

In terms of mechanical response, the deformation is small and the strain is infinitely small.

Isothermal condition is considered.

According to the theory of porous elasticity, the unit of rock satisfies the following equilibrium equation:

The rock is regarded as a porous medium, and the rock element satisfies the constitutive equation. It can be expressed by stress, strain, and pore pressure as follows:

According to the continuous deformation condition, the following geometric equations are obtained:

After the rock adsorbs gas, the adsorption expansion strain can be expressed

The stress equilibrium equation can be expressed by displacement, pore pressure, and adsorption expansion.

Darcy flow is widely employed in the gas migration process. The Darcy velocity of gas is expressed as

The seepage of gas follows the law of conservation of mass.

Because of the compressibility of the gas, the relation between the gas density and the pressure is

The continuity equation of gas seepage can be obtained as

The basic skeleton of rock is deformed under the affection of gas pressure, which changes the porosity of rock and affects the seepage of gas in rock. The rock is subjected to the double action between external stress and pore pressure. The following equation can be obtained:

The rock body is regarded as the porous medium. The volume of the rock

The permeability of the rock body is related to the porosity, which can be expressed as cubic law.

The permeability of rock can be expressed as

The following equation can be obtained after finishing transposition:

In order to describe the heterogeneity of rock materials, it is assumed that rock consists of a large number of microscopic elements. Assuming that the mechanical properties of these units obey Weibull distribution, the distribution can be defined according to the following density distribution function:

The greater the parameter

The maximum tensile stress criterion is used to determine the tensile damage of rock, and the Mohr-Coulomb criterion is adopted to determine the shear damage of rock [

The constitutive law of rock.

Based on the strain, the damage variable of rock units can be expressed using the following expression:

The elastic modulus of rock under damage state can be expressed as follows:

When the rock is damaged, the effect of the rock damage on the permeability can be described as

The coupled hydro-mechanical-damage model for rock is proposed and COMSOL Multiphysics and MATLAB are employed to achieve the coupled solution of solid field, fluid field, and damage field.

The in situ gas injection test was carried out at the Mont Terri underground laboratory in the Ru La mountains, northwest of Switzerland [

Location of rock laboratory and field gas injection test.

Geological section of the Mont Terri Underground Rock Laboratory [

Schematic presentation of field gas injection test [

Based on the engineering geological characteristics, a calculation model is established. The size of the numerical model is 10m×10m, and the diameter of the borehole is 0.1m. Figure

Parameters in the calculation.

Parameter | Value | Unit |
---|---|---|

Elastic modulus, | 2.7 | GPa |

Elastic modulus of rock grains, | 8.1 | GPa |

Poisson’s ratio, | 0.22 | - |

Initial porosity, | 0.008 | - |

Initial permeability, | 1×10^{−17} | m^{2} |

Klinkenberg effect, | 1.44×10^{5} | Pa |

Langmuir pressure constant, | 7.2 | MPa |

Langmuir volume constant, | 0.015 | m^{3}/kg |

Langmuir volumetric strain constant, | 0.013 | - |

Density of rock, | 1,250 | kg/m^{3} |

Homogeneity index, | 2 | - |

Uniaxial compressive strength, | 9 | MPa |

Uniaxial tensional strength, | 2 | MPa |

Internal friction angle, | 30 | ° |

Gas viscosity, | 1.84×10^{−5} | Pa·s |

Density of gas, | 0.717 | kg/m^{3} |

Damage-permeability effect coefficient, | 4.5 | - |

Numerical model of gas seepage process of borehole surrounding rock.

The seepage distribution and the damage distribution of the rock around the borehole can be obtained through the analytical solution in previous literature [

Because the excavation damage zone (EDZ) is mostly concentrated near the excavation wall, we mainly focus on the area of 0.5m×0.5m around the borehole. It can be seen in Figure

Damage distribution of borehole surrounding rock.

Comparison between numerical results and analytical results of damage.

Figure

Elastic modulus distribution of rock.

The permeability distribution of surrounding rock after drilling is shown in Figure ^{2}, which increases by two orders of magnitude compared with the initial permeability of rock. The permeability in the red area is high, and the damage degree is high, which is a high permeability area. After the drill is excavated, the gas can quickly pass through the high permeable area, and the high permeability area also improves the gas migration efficiency. With the increase of distance to the borehole wall, the permeability gradually decreases. Although the damage degree is small, the damage still improves the permeability of rock and accelerates the seepage of gas in the rock. Figure

Permeability distribution of borehole surrounding rock.

Comparison between numerical results and analytical results of permeability.

Figure

Gas pressure distribution of borehole surrounding rock.

The damage distribution characteristics and gas seepage characteristics of rock under the condition of equal horizontal stress and vertical stress are analyzed in the above section; that is, the lateral pressure coefficient is equal to 1. However, under some geological conditions, the rock stratum is not in the hydrostatic pressure state and the influence of the lateral pressure coefficient should be considered. Figure

Damage distribution of surrounding rock under lateral pressure coefficient

Permeability distribution of surrounding rock under lateral pressure coefficient

Figures

Damage distribution under lateral pressure coefficient

Permeability distribution under lateral pressure coefficient

In practical engineering of underground nuclear waste storage, the damage will appear around the excavation cavity, which will seriously affect the strength and seepage characteristics of the rock mass. The permeability of rock in excavation damage zone normally increases by 2-3 orders of magnitude compared to the initial value. The gas will quickly flow through the excavation zone, while the flow will be relatively slow in the undamaged zone. Although a lot of scholars have done research on the gas seepage process [

The coupled hydro-mechanical-damage model is established to predict and analyze the gas migration in rocks, which involves the coupling process, the microcrack or damage caused by elastic degradation, the control of the fluid flow, the rock failure and rock deformation, and porosity change with stress. In addition, the model also takes into account the change of gas pressure caused by the change of pore structure of sedimentary rocks. Tensile and compression damage in the rock is also considered.

Based on the hydro-mechanical-damage coupling model of rock mass, the damage and fracture characteristics of surrounding rock and seepage characteristics in rock mass are analyzed, and the numerical solution results are compared with the analytical solution results to verify the validity of the model. In addition, the influence of the lateral pressure coefficient on the damage and the permeability of rock are also considered. The results indicate that a circular excavation damage zone appears in the surrounding rock after drilling, and the damage degree of rock is higher within the range of 40 mm from the borehole wall. The closer to the borehole wall, the higher the damage degree of the rock. When the lateral pressure coefficient

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This study is sponsored by the National Natural Science Foundation of China (no. 51679199), the Natural Science Foundation of Jiangsu Province (no. BK20170457), the China Postdoctoral Science Foundation (no. 2018M633549), and the Initiation Fund of Doctor’s Research (no. 107-451117008).