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Disposal of high-level radioactive waste (HLW) deep underground is one of the most challenging research subjects in rock engineering. In China, Beishan granite is usually chosen as host rock for the construction of the HLW repository. In this study, mechanical tests are conducted on Beishan granite and the stress-strain state during the complete failure process is analyzed by numerical simulation. The results show that the tensile strength and uniaxial compressive strength of Beishan granite are 8.66 and 162.9 MPa, respectively. Dilatancy appears when the stress reaches about 81% of the peak strength. Heterogeneity is introduced by Weibull distribution in numerical simulation. With the increase of homogenization degree, the degraded elements are more easily to concentrate locally. Based on experimental and numerical simulation results, it is noticeable that the sample volume is basically in the state of compaction before reaching the peak strength. The elements are more likely to show expansion, and the splitting failure dominates the destroy mode when the confining pressure is relatively low. With increasing confining pressure, more and more degraded elements are concentrated in the shear band, which develops from the surface to the interior of the sample during loading. Therefore, the granite shows ductile mechanical response characteristics when the confining pressure is relatively high. The results are instructive for the construction of the repository.

High-level radioactive waste (HLW) is one of the most harmful pollutants in the world. Currently, the most feasible way to isolate the HLW from the biosphere is to seal them in a geological disposal repository underground for 500–1000 m. Granite, characterized by low permeability and high strength, is a potential host rock for HLW. It is reported that Beishan granite is chosen as the host rock of a HLW repository in China [

As a natural material, rocks contain microcracks. It has been widely recognized that the growth of microcracks associated with crack propagation and coalescence can ultimately cause crystalline rock failure [

From another view, the variation of rock volume is closely related to the propagation of microcracks. As a result, rocks will show the most direct performance of compaction or expansion [

In order to solve the problems mentioned above, numerical simulation is extensively used to study the deformation behavior and fracturing process during loading. Besides, the heterogeneity of rock can be studied by using numerical simulation. Tang et al. conducted a numerical analysis to evaluate the effect of heterogeneity on the fracture processes and strength characterization of brittle materials [

Therefore, in this study, experimental tests are conducted to study the basic properties of Beishan granite. Parameters used in the numerical simulation are determined. In addition, the Weibull distribution is introduced to characterize the heterogeneity of rock in numerical simulation. Afterwards, a heterogeneous model of Beishan granite is built to study the deformation behavior and fracturing evolution during the complete failure process.

The granite cores were taken from the Beishan area, Gansu Province, China. And it is mainly composed of approximately 33.7% ± 5.8% plagioclase, 30.7% ± 6.1% K-feldspar, 28.6% ± 8.0% quartz, and 7.1% ± 4.8% biotite [

As shown in Figure

Rock mechanics experimental system of MTS815.

For the direct tensile test, the two ends of the specimen are bonded with the instrument with strong glue. During the loading process, the axial displacement was increased with a constant displacement rate of 0.005 mm/min until the failure of the specimen.

For the uniaxial compression test, the axial stress was increased with a constant loading rate of 30 kN/min until the failure of the specimen.

For CTC tests, the confining pressures were set to 5, 10, 15, 20, and 30 MPa, respectively. First, to fix the position of the specimen, a vertical load of about 2 kN was applied. Then, a constant loading rate of 0.05 MPa/s was applied to reach the designated confining pressure. Afterwards, the axial stress was increased with a constant loading rate of 30 kN/min. Lateral deformation control was used when the axial stress approached the peak strength.

As shown in Figure

Stress-strain curves of Beishan granite for direct tensile test.

Direct tensile test results of Beishan granite samples.

Sample no. | Tensile strength (MPa) | Average value (MPa) |

T-1 | 12.66 | 8.66 |

T-2 | 7.17 | |

T-3 | 7.14 | |

T-4 | 9.11 | |

T-5 | 7.20 |

As shown in Figure

Stress-strain curves of Beishan granite for uniaxial compression test.

Uniaxial compressive test results of Beishan granite samples.

Sample no. | Peak strength (MPa) | Young’s modulus (GPa) | Poisson’s ratio |
---|---|---|---|

UCT-1 | 160.5 | 30.1 | 0.123 |

UCT-2 | 163.1 | 27.7 | 0.123 |

UCT-3 | 165.2 | 27.9 | 0.120 |

Average | 162.9 | 28.6 | 0.122 |

Figure

Stress-strain curves and failure patterns under different confining pressures.

Triaxial compressive test results of Beishan granite samples.

Sample no. | Confining pressure (MPa) | Peak strength (MPa) | Cohesion (MPa) | Friction (°) |
---|---|---|---|---|

CTC -1 | 5 | 207.1 | 35.4 | 52.4 |

CTC -2 | 10 | 245.9 | ||

CTC-3 | 15 | 274.1 | ||

CTC-4 | 20 | 326.6 | ||

CTC-5 | 30 | 405.3 |

As an inhomogeneous material, rock is composed of different mineral particles. Besides, micropores and cracks are distributed randomly inside rocks. These individual components behave in different mechanical responses, leading to different deformation behaviors. Therefore, the stress and strain states can be dominated by the spatial distribution of these individual components during loading [

The Weibull distribution is a continuous probability distribution. The general expression of Weibull probability density function can be written as

The mean and variance of a Weibull random variable can be expressed as

The relationship between the scaled mathematical expectation ^{2}, and shape parameter

Scaled mathematical expectation (a) and dispersion (b) of the Weibull distribution with different shape parameters.

In the numerical simulation, mechanical parameters, such as the elastic modulus

The inverse function is

Based on equation (

A cylindrical model (see Figure ^{3D} to study the stress-strain state and fracture development inside the specimen during the complete failure process. The strain-softening model is chosen to simulate the mechanical response. The constant compressive displacement rate is set to 5e-8 m/step, which will be applied on end faces of the model in the following simulation. Based on the tests in Section

Schematic diagram of Beishan granite model [

Mechanical parameters of Beishan granite.

Elastic modulus/GPa | Poisson’s ratio | Dilation (°) | Density (kg/m^{3}) | Cohesion (MPa) | Friction (°) | Tension (MPa) | |||
---|---|---|---|---|---|---|---|---|---|

Initial | Residual | Initial | Residual | Initial | Residual | ||||

28.6 | 0.122 | 17 | 2700 | 29.74 | 21.24 | 51 | 31.44 | 7.66 | 0 |

First, the homogeneity index ^{3D}. For instance, the cohesion distribution with different homogeneity index

Cohesion distribution in models of Beishan granite with different homogeneity index

The cohesion distribution after failure is shown in Figure

Cohesion distribution in models after failure with different homogeneity

Simulated stress-strain relations for models with different homogeneity

Figure

Simulated stress-strain curves for different confining pressures.

The comparison between simulated strength and experimental strength.

Confining pressure (MPa) | Simulated strength (MPa) | Experimental strength (MPa) | Error (%) |
---|---|---|---|

5 | 237.0 | 207.1 | 12.62 |

10 | 268.8 | 245.9 | 9.31 |

15 | 298.6 | 274.1 | 8.94 |

20 | 326.9 | 326.6 | 0.09 |

30 | 384.6 | 405.3 | −5.11 |

Simulated axial stress-strain curve under confining pressure of 20 MPa.

Volumetric strain evolvement at different stress level in simulated triaxial compression test under confining pressure of 20 MPa.

Shear strain evolvement at different stress level in simulated triaxial compression test under confining pressure of 20 MPa.

Minimum principal stress (Pa) evolvement at different stress level in simulated triaxial compression test under confining pressure of 20 MPa.

Displacement evolvement at different stress level in simulated triaxial compression test under confining pressure of 20 MPa.

Some conclusions can be drawn based on the simulation results. During the pre-peak period from point

At the peak stress (point

In the stress drop stage from point

In the residual stage from point

Figures

Volumetric strain (

Shear strain (

In this research, the strength and deformation processes of Beishan granite are obtained by experimental tests. The stress-strain state during the complete failure process is analyzed by numerical simulation. Based on the results, the following conclusions can be drawn.

The tensile strength and uniaxial compressive strength of Beishan granite are 8.66 and 162.9 MPa, respectively. Under triaxial compression, the dilatancy of Beishan granite appears when the stress reaches about 81% of the peak stress.

The heterogeneity of rock can be well introduced by Weibull distribution. With the increase of homogenization degree in numerical simulation, the degraded elements are more easily to concentrate locally.

The splitting failure dominates the destroy mode when the confining pressure is relatively low. With increasing confining pressure, more and more degraded elements are concentrated in the shear band, which develops from the surface to the interior of the sample during loading. Hence, the granite shows ductile mechanical response characteristics when the confining pressure is relatively high.

For the safety of HLW repository, more tests are needed for further investigating mechanical properties and fracturing characteristics of Beishan granite subjected to different conditions.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no competing financial interests or personal relationships that could have influenced the work reported in this paper.

This work was supported by the National Natural Science Foundation of China (52074168 and 51874190), Major Program of Shandong Province Science and Technology Innovation Foundation (2019SDZY02), and China-APEC Cooperative Foundation in 2020, Major Program of Shandong Province Natural Science Foundation (ZR2018ZA0603).