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Beishan granite is a potential host rock for a high-level radioactive waste (HLW) repository in China. Understanding the hydromechanical (HM) behavior and permeability evolution of Beishan granite is important for the HLW repository safety. Therefore, the granite of Beishan in Gansu province was studied. HM coupled tests are carried out on Beishan granite under different pore pressures. The results show that the initial pressure difference has little influence on permeability measurement before dilatancy starts. However, after onset of dilatancy, the permeability increases with the increasing initial pressure difference. The initial permeability of Beishan granite is about

Disposal of high-level radioactive waste (HLW) deep underground is one of the most challenging research subjects in rock engineering. The biggest difficulty is the proof of safe and long-term isolation of the HLW from the biosphere. Granite, characterized by high strength and low permeability, is one of the preferred host rocks for geological disposal of HLW. China plans to build a HLW repository in the granite strata of Beishan, Gansu Province [

As a heterogeneous material, rock contains microcracks. The failure process of rock associated with crack propagation has been well studied [

On the other hand, important progress has been made in numerical simulation of HM coupled processes in rocks, especially in the DECOVALEX project [^{3D}—for analysis of coupled THM processes, in which the coupling module containing nonlinear stress versus permeability functions is taken into account. Tan and Konietzky [

This paper presents HM coupling tests carried out on Beishan granite under different pore pressures. The influence of initial pressure difference (

In most cases, permeability can be measured either by using the constant head method [

The test principle of transient pulse method is shown in Figure ^{2}), ^{-3} Pa·s), ^{2}), ^{3}), ^{3}),

Simplified schematic of the transient pulse method: (a) testing system and (b) measuring pressure decay over time.

The granite samples were taken from the Beishan area, Gansu Province, China. The specimens, with a diameter of 50 mm and length of 100 mm, were prepared according to ISRM recommendations [

The HM coupled tests were carried out with a MTS815 Flex Test GT (see Figure

Rock mechanics experimental system of MTS815 and installation of sample.

Four specimens were prepared for HM coupled testing. Before the tests, the specimens were immersed in water for 72 hours in the vacuum suction device to reach the saturated state [

In addition, in order to study the influence of initial pressure difference (

The permeability measured by different initial pressure differences under the same strain levels is shown in Tables

Permeability test results for specimen BSS-1 for three different initial pressure differences.

Axial strain (%) | Axial stress (MPa) | Permeability ( | ||
---|---|---|---|---|

3.4 MPa | 5.4 MPa | 7.4 MPa | ||

0 | 0 | 3.77 | 2.97 | 2.33 |

0.386 | 38.6 | 1.05 | 1.30 | 1.34 |

0.629 | 79.3 | 1.03 | 1.12 | 1.29 |

0.855 | 123.8 | 0.55 | 1.08 | 1.26 |

1.066 | 165.6 | 0.94 | 1.29 | 1.65 |

1.240 | 201.8 | 1.45 | 1.92 | 2.36 |

1.528 | 256.6 | 3.43 | 5.30 | 7.54 |

2.337 | 81.8 | 72.74 | 55.31 | 59.57 |

Permeability test results for specimen BSS-2 for three different initial pressure differences.

Axial strain (%) | Axial stress (MPa) | Permeability ( | ||
---|---|---|---|---|

3.4 MPa | 5.4 MPa | 7.4 MPa | ||

0 | 0 | 1.32 | 1.24 | 0.64 |

0.414 | 48.7 | 0.71 | 0.66 | 0.66 |

0.716 | 106.1 | 0.78 | 0.50 | 0.47 |

0.940 | 150.1 | 0.48 | 0.56 | 0.48 |

1.163 | 200.0 | 0.75 | 0.61 | 0.70 |

1.425 | 252.5 | 1.33 | 1.12 | 1.54 |

1.855 | 315.6 | 5.81 | 9.86 | 15.36 |

2.011 | 79.5 | 13.56 | 16.07 | 17.74 |

2.599 | 75.9 | 13.25 | 14.08 | 14.69 |

Permeability for different initial differential pressures (a) BSS-1 (b) BSS-2.

At the initial stage of loading, due to the closure of micro cracks, permeability decreases. Before onset of dilatancy, the permeability changes little. After onset of dilatancy, permeability is increasing. Also, the permeability increases with the increasing initial pressure difference. For instance, the permeability measured for sample BSS-2 under the initial pressure difference of 7.4 MPa (

Figure

Stress strain curves of Beishan granite under different pore pressures [

The permeability measured during HM coupled testing is shown in Table

Permeability evolution under different pore pressures.

Sample | Pore pressure (MPa) | Permeability/ | |||||||
---|---|---|---|---|---|---|---|---|---|

1st^{a} | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | ||

HM-1 | 2 | 5.8 | 2.78 | 4.91 | 6.5 | 20.29(p^{b}) | 22.71 | 22.89 | 25.49 |

HM-2 | 4 | 1.29 | 0.51 | 0.38 | 1.14(p) | 3.04 | 3.74 | 5.38 | — |

HM-3 | 6 | 0.95 | 0.29 | 0.48 | 1.3 | 2.46 | 5.85 | 10.7(p) | 32.78 |

HM-4 | 8 | 2.29 | 1.48 | 1.77 | 3.84 | 7.03 | 11.51 | 13.17(p) | 26.16 |

^{a}”1st” represents the first time to measure permeability. ^{b}”P” represents the permeability measured around peak stress.

Permeability evolution of Beishan granite during HM coupling. (a, b) Pore pressure of 2 MPa, (c, d) pore pressure of 4 MPa, (e, f) pore pressure of 6 MPa, and (g, h) pore pressure of 8 MPa.

Taking the pore pressure of 8 MPa as an example, combined with the volumetric strain development, the permeability evolution of Beishan granite under loading can be roughly divided into the following stages. In the first stage (i.e., the initial stage of loading), micro cracks begin to close, which leads to a decrease of sample volume and loss of some seepage channels. Therefore, the decrease of permeability is relatively large compared to the initial permeability (for instance, reduction by 40% under pore pressure of 4 MPa). In the second stage, as the axial stress continues to increase, the volume of the specimen decreases. But there is possibility that new micro cracks are generated. Thus, the permeability almost keeps constant. After the dilatancy point, micro cracks are reactivated gradually and interact with each other, which leads to crack coalescence and provides new seepage channels. The permeability increases gradually with increasing volumetric strain. It can be concluded from Figures

According to tests results, the permeability evolution of Beishan granite in respect to volumetric strain can be roughly divided into two stages before reaching the peak stress, as shown in Figure ^{2}) and

Simplified illustration of permeability evolution in HM coupling processes in Beishan granite.

In order to study the stress strain state inside the specimen, a heterogeneous cylindrical model with 50 mm in diameter and 100 mm in length is established in the explicit Finite Difference code FLAC^{3D} as shown in Figure

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 |

Hydraulic parameters of Beishan granite.

Fluid modulus (GPa) | Fluid density (kg/m^{3}) | Initial permeability (m^{2}) | Porosity (%) | Saturation |
---|---|---|---|---|

2.2 | 1000 | 2.58^{-18} | 0.02 | 1 |

According to Section ^{3D}. Therefore, the permeability is updated during the numerical simulation. However, the linear relationships cannot be applied to describe the permeability evolution of the elements directly. Therefore, the linear coefficients need to be calibrated by several numerical simulations [

First, simulation of the conventional triaxial compression (CTC) test under confining pressure of 20 MPa is conducted. A compressed numerical model (see Figure

Volumetric strain for confining pressure of 20 MPa: (a) compressed stage and (b) damaged stage.

Flow rates and corresponding coefficients: (a)

The proposed permeability evolution rule (Equation (^{3D}. The pore pressures correspond to the HM coupling tests. Figure

Simulated stress-strain curves for different pore pressures under 20 MPa confining pressure.

Simulated stress-strain curve for pore pressure of 8 MPa under confining pressure of 20 MPa.

Evolution of maximum stress tensor (Pa) for simulated HM coupled test: (a) initial compressed stage, (b) elastic stage, (c) peak stress point, (d) stress drop stage, and (e) residual stage.

Evolution of volumetric strain for simulated HM coupled test: (a) initial compressed stage, (b) elastic stage, (c) peak stress point, (d) stress drop stage, and (e) residual stage.

Evolution of permeability (

Evolution of discharge vectors (m/s) for simulated HM coupled test: (a) initial compressed stage, (b) elastic stage, (c) peak stress point, (d) stress drop stage, and (e) residual stage.

Some conclusions can be drawn from the numerical simulations. In the quasi elastic stage (points a and b), the stress state is nearly homogeneous; volumetric strain decreases with increasing axial stress, and all elements are compressed; permeability is decreasing and fluid flow is restricted. In brief, there is no damage at this stage. At the peak stress (point c), the stress distribution is no longer uniform; volumetric strain increases especially close to the model boundary; therefore, permeability and flow rate increase near the model boundary. During the stress drop (point e), local tensile stresses appear; volumetric strain increases rapidly and forms serval shear bands, which develop from the model boundary to the inside. And it provides several seepage channels with high permeability for fluid flow. In the residual stage (point e), the tensile stress area expands; the volumetric strain bands become wider and interact with each other.

The macroscopic fracture patterns for samples under different pore pressures are shown in Figure

Volumetric strain (

HM coupled tests are carried out on Beishan granite under different pore pressures. The permeability evolution is studied. And numerical simulations are conducted to study the stress state and deformation process. Based on the results, the following conclusions can be drawn.

Before dilatancy, the initial pressure difference (

The initial permeability of Beishan granite maintains at the order

The simulation results show that the damaged zone first appears close to the model boundary and then extends to the inside, forming local high volumetric strain areas. And it provides seepage channels for fluid flow. The macroscopic fracture patterns indicate that pore pressure accelerates rock degradation during HM coupling.

In the future, more tests are needed for further investigating permeability evolution and fracturing characteristics of Beishan granite subjected to different confining stresses and pore pressures.

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 Major Program of Shandong Province Natural Science Foundation (ZR2018ZA0603) and the National Natural Science Foundation of China (51674266).