In this paper, the transient pulse test is used to study the permeability and hydromechanical coupling effect of the fractured limestone. The permeability parameters (permeability,

Fractured rock mass, which is potentially dangerous, is widely existing in nature. The seepage instability of fractured rock mass is an important reason for rock engineering destruction and even large-scale geological disasters. Therefore, the hydraulic coupling and seepage characteristics of fractured rock masses are generally concerned [

The rock permeability is usually studied by the steady-state method or the transient method. Miao et al. used steady-state method to test the seepage performance of broken sandstone under different porosity conditions [

It is found that, under the condition of low water pressure, the coarse fractured rock mass has Darcy flow characteristics, and under the condition of high hydraulic pressure, the seepage of rock mass has Darcy flow characteristics, and the hydraulic pressure plays an important role in the development of rock fracture [

It can be seen from overview of the references that although there are many researches on the seepage of fractured rock mass, these researches mainly focus on the use of steady-state and transient methods to study the factors affecting the seepage of rock, the extraction of non-Darcy flow permeability coefficient mainly focuses on permeability, and the research on the extraction of acceleration coefficient and non-Darcy flow

In this paper, Maokou limestone from Ningxiang coal mine of Hunan Province was used to make a sample of Φ 50 × 100 mm. The limestone in Maokou is very dense, so it is necessary to induce some fractures artificially for seepage experiment. The artificial fractures were obtained by Brazil splitting method. Firstly, the standard rock sample of Φ 50 × 100 mm with no damage on the edge and smooth end face was selected. Then a layer of glue on the outer surface of the rock sample was evenly applied, and a layer of thermoplastic tube with the same height as the rock sample was covered. Next the heat gun was used to close the thermoplastic tube from top to bottom. Finally, the Brazilian splitting method was used to conduct the splitting test on the rock sample. In order to prevent the instant brittle failure of the test sample, which leads to the failure of rock sample production, the loading rate of the test is strictly controlled to 10 N/s until the rock fracture occurs; the test is stopped immediately.

Figure

The induced fracture diagram of the Brazil splitting method.

Fracture end face photo and fracture path sketch of the test piece.

The sample fracture was marked with a pen at different parts, especially at the places where the gap width is obviously different, so that the measured value can represent the gap width of the fracture more accurately. The fracture of the end face of the rock sample at the serial number was measured with a fracture microscope, each reading was recorded, and the average value of all the measured values is the gap width of the fracture. Table

Initial crack width of the rock sample terminal face.

Specimen number (mm) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Average value |
---|---|---|---|---|---|---|---|---|

M07 | 0.28 | 0.18 | 0.17 | 0.26 | 0.18 | 0.22 | 0.48 | 0.25 |

The test is carried out on MTS815 rock mechanics multifunctional testing machine, which is produced by MTS company of the United States and is specially used for testing rock and concrete and other materials. It has four independent control systems, which are axial force, confining pressure, hydraulic pressure, and temperature, and it is at international leading level in testing rock and concrete materials. It is mainly used for various dynamic tests and static tests of rock and concrete materials, including uniaxial compression test, uniaxial tensile test, fracture strength, triaxial pressure, osmotic pressure, hydraulic pressure, temperature simulation, and other rock-related physical property analysis applications, which provides the test means for the research and analysis of dynamic characteristics of these materials and structures. It is the most advanced indoor rock mechanics test equipment (Figure

The MTS815 testing system.

The seepage test of rock fracture under cyclic loading and unloading was carried out in the triaxial pressure chamber of MTS815. During the test, when the stress reaches the preset value, the hydraulic pressure loading system is used to apply the same pressure on both ends of the rock sample and then reduce the hydraulic pressure at one end. At this way, the hydraulic pressure difference between the two ends of the rock sample is formed, collecting the series of the hydraulic pressure difference of the fracture varying with time and calculating the permeability characteristics. Table

Test stresses and hydraulic pressure environment.

Axial pressure/MPa | Confining pressure/MPa | Hydraulic pressure at the upper end of the specimen | Hydraulic pressure at the bottom of the specimen | Initial hydraulic pressure difference ΔP = |
---|---|---|---|---|

6 | 4 | 3.0 | 1.0 | 2.0 |

6 | ||||

8 | ||||

10 | ||||

12 | ||||

14 |

Flowchart of seepage test of fractured rock under cyclic loading and unloading.

There are two methods to determine the permeability of rock samples: steady-state method and transient method. The transient method is to record the change value of the hydraulic pressure gradient with time in the process of rock seepage and calculate the change rate of the hydraulic pressure gradient. The permeability characteristics of rock can be obtained through the fitting curve of the hydraulic pressure gradient and its rate of change.

Figure

Principle of the transient permeation test system.

In (

According to the formulas

From (

For Darcy flow, the permeability velocity and pressure gradient follow the following formula:

In the experiment, sampling at equal interval

Equation (

The experimental study shows that, in many cases, the seepage flow of rock sample is non-Darcy flow, and its seepage law satisfies the Forchimer relation; that is,

From (

It is assumed that the time series of fracture hydraulic pressure difference collected by equal time interval

From (

Constructive functional is as follows:

The extremum conditions of the functional are as follows:

By combining (

Sometimes, the single time series of permeability velocity

The transient pulse penetration test was carried out on Maokou limestone. The percolation liquid was distilled water, its mass density is 1000 kg/m^{3}, its dynamic viscosity is 1.01 × 10–3 Pa·s, and its compression coefficient is 0.556 × 10^{–9} Pa^{−1}. The volume of two chambers in MTS hydraulic pressure system is 0.336 × 10^{–6} m^{3}.

Figure

Hydraulic pressure decay-time data and the corresponding fitting curves for M07 specimen at a confining pressure of (a) 4 MPa; (b) 6 MPa; (c) 8 MPa; (d) 10 MPa; (e) 12 MPa; and (f) 14 MPa.

The hydraulic pressure difference decay-time curve can be fitted by the quartic polynomial, and the fitting has a very high fitting precision. Table

The quartic polynomial fitting equations of hydraulic pressure difference varying with time of M07 under different confining pressures.

Axial pressure | Confining pressure | Volume pressure | Quartic polynomial fitting curve of hydraulic pressure difference varying with time | Correlation coefficient R^{2} |
---|---|---|---|---|

6 | 4 | 14 | 0.998 | |

6 | 18 | 0.997 | ||

8 | 22 | 0.996 | ||

10 | 26 | 0.995 | ||

12 | 30 | 0.998 | ||

14 | 34 | 0.997 |

This shows that the flow of fractured rock is a non-Darcy flow, which is time-varying. With the increase of confining pressure, the non-Darcy seepage effect of fractured rock is more obvious. The non-Darcy effect of fractured rock seepage is affected by confining pressure. When the confining pressure is low, the seepage of rock fracture is close to Darcy flow, and the seepage of rock fracture under high confining pressure is significant non-Darcy flow.

The volume pressure can be expressed as

The fitting equation under axial pressure of 6 MPa and confining pressure of 8 MPa is

Hydraulic pressure gradient can be expressed as

The seepage velocity yields

According to the fitting equation, there is no linear relationship between the hydraulic pressure gradient and the seepage velocity, indicating that the seepage of Maokou limestone does not obey Darcy flow.

According to the data collected from the experiment, the permeability characteristic parameters of non-Darcy flow are calculated.

From Figure

The curve of permeability versus volume stress.

The

The curve of

Acceleration coefficient _{a} is an index reflecting the seepage inertia. The greater the acceleration coefficient is, the more difficult it is to change the flow state. The process of crack and fracture expansion and porosity increase is the process of inertia weakening, that is, the process of acceleration coefficient decreasing, as well as the process of transformation from steady flow to unsteady flow. From Figure

The curve of acceleration coefficient _{a} versus volume stress.

By analyzing the test data of non-Darcy flow obtained from the seepage test of fractured rock, the fitting relationship between the permeability coefficient of fractured rock, volume stress, and hydraulic pressure difference can be obtained based on the transient pulse method

Equation (

The curve of permeability coefficient versus volume stress.

From the analysis of the test data, we can draw the conclusions that, under the same axial pressure, the permeability coefficient of rock sample decreases continuously with the volume stress increases. Under the action of low volume stress, the permeability coefficient change is more sensitive, and under the action of high volume stress, the permeability coefficient change is slow. This is because, at the initial stage of confining pressure loading, the rock fracture has closed to a large extent, which has great resistance to the seepage of water and reduces the permeability coefficient. With the increase of confining pressure, the rock fracture is further closed. When the fracture opening is close to the residual gap width, further increase of confining pressure will maintain the residual gap width rather than close the rock fracture further, resulting in the fact that the permeability coefficient of rock fracture has little correlation with stress under high volume stress.

The transient seepage test of fractured Maokou limestone is carried out based on MTS815 rock mechanics test system. The non-Darcy seepage characteristics of fractured rock under confining pressure are extracted by a single time series of hydraulic pressure difference to analyze the relationship among seepage characteristics, stress. Through the experimental study, the main conclusions of this paper are as follows:

Under the action of confining pressure, the hydraulic pressure difference of fractured rock is not in accordance with the specific exponential decay law. There is a significant difference between fractured rock seepage and Darcy flow. In the process of fractured rock transient pulse seepage test, the hydraulic pressure gradient and seepage velocity meet the Forchimer relationship rather than Darcy law. The equation of hydraulic pressure difference varying with time can be fitted by quartic polynomial.

With the confining pressure increase, the non-Darcy seepage effect of rock fracture seepage is more obvious. And the seepage of rock fracture which under high confining pressure is a kind of highly nonlinear time-varying seepage.

The permeability coefficient of fractured rock is affected by volume stress; the permeability coefficient decreases with the increase of volume stress. The relationship between permeability coefficient and stress is more sensitive while being under the action of low volume stress and it is not significant while being under the action of high volume stress.

During the process of volume stress increasing, the

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 research was supported by the National Natural Science Foundation of China (nos. 51774131, 51274097, and 51434006), the CRSRI Open Research Program (CKWV2017508/KY), and the Open Projects of State Key Laboratory of Coal Resources and Safe Mining, CUMT (no. SKLCRSM16KF12).