Hydromechanical Coupling Characteristics of the Fractured Sandstone under Cyclic Loading-Unloading

The mechanical and hydraulic properties of rock mass play a crucial role in underground engineering. To study the e ﬀ ect of hydraulic pressure, con ﬁ ning pressure, and axial cyclic loading-unloading on variation of the deformation and permeability in fractured rock mass, the coupling triaxial experiment of sandstone was conducted. The concept of permeability recovery rate (PRR) and permeability enhancement reduction rate (PERR) was proposed to characterize the change in permeability. The results show that the permeability of fractured sandstone quadratically varies with the change of hydraulic pressure and con ﬁ ning stress. In detail, the permeability decreases with the decrease of hydraulic pressure and increases with the decrease of con ﬁ ning stress, respectively. Compared with the single-fracture permeability, the double-fracture permeability is more sensitive to the change of hydraulic pressure. Furthermore, the permeability of fractured sandstone is more dependent on the hydraulic pressure than the con ﬁ ning stress. With the performance of axial cyclic loading-unloading, the permeability spirals down, and both the axial and radial residual strains quadratically evolve. Following the ﬁ rst axial cyclic loading-unloading, an obvious deformation memory phenomenon characterized by a parallelogram shape in axial stress-strain curves was observed for the sandstone. The cumulative PRR of 85%-95% was maintained in double-fracture sandstone. On the contrary, a ﬂ uctuation of cumulative PRR characterized by “ V shape ” was observed for single-fracture sandstone. The enhancement e ﬀ ect of axial cyclic loading on the permeability was characterized by the decrease of PERR for double-fracture sandstone and increase of PERR with a greater gradient for single-fracture sandstone.


Introduction
Understanding the mechanical and hydraulic properties of rock mass is critical for the safety of underground engineering, such as deep tunnel engineering [1], geothermal extraction [2][3][4][5], radioactive waste treatment [6][7][8], CO 2 geological storage [9][10][11], deep coal mining [12,13], and underground reservoir [14]. The fluid flow mainly occurred in the strata comprised of plenty of natural and human activity-induced fractures and was easily influenced by the variable high stress [15]. To meet the widespread utilization of energy resources, underground mining has exploited into the deeper crust [16]. Therefore, recent research in geo-mechanical and hydromechanical mecha-nism of fractured rock mass extensively studied in the deep underground activity.
The hydraulic conductivity as a vital index for fractured rock mass with the hydromechanical coupling effect has been extensively investigated using theoretical analysis, field and laboratory measurements, and numerical simulation [17]. In fractured rock mass, the deformation in the rock matrix and fracture caused by the effect of hydromechanical coupling also significantly affect the seepage and diffusion of fluid. Due to the high strength of the rock matrix, the deformation of fracture is more sensitive than that of rock matrix for stress-dependent deformities [18]. The equivalent continuum and discrete element algorithms have been employed in the characterization of the response of fractured rock mass to changes in stress and hydraulic pressure [19][20][21]. Considerable efforts have been focused on the flow behaviors, including Darcy and non-Darcy flow, of fractured rock mass with the effect of hydromechanical coupling [22][23][24][25]. Furthermore, the study on the variation of permeability in deformable rough-walled fractures subjected to the change of fracture geometric is also performed [26,27].
The rock mass, consist of matrix and fractures, is often subjected to mining stresses (cyclic or dynamic loads) in deep coal mining. It is important to study the effect of cyclic mining stresses on rock stratum, which would be beneficial to predict dynamic hazards in coal mines. Hence, the mechanical and seepage properties of different rocks under complicated stress conditions, especially under cyclic loading and unloading, have received extensive attention [28,29]. For constant-amplitude cyclic loading-unloading, Chen et al. [30] investigated the deformation modulus of sandstone under different cyclic loading and found that the tangent modulus and Poisson ratio show a shape of asymmetric "X," and the mean of unloading modulus is larger than the loading modulus under the sine wave cycle load. Fuenkajorn and Phueakphum [31] experimentally studied the deformation parameters and uniaxial compressive strength of salt rock under the effect of cycle loading and unloading. Liu and He [32,33] researched the residual axial and volumetric strain characteristics with variable confining stress and frequency and described the degradation process of sandstone with damage variable under cycle loading-unloading. Liu et al. [34] experimentally investigated the permeability variation of fractured sandstone under confining stress cyclic loading. For cycle loading-unloading at different stress levels or tiered cyclic loading-unloading, Liu et al. [35] carried out the different stress level cyclic loading experiments to realize the damage evolution of salt rock and established a formula to describe the evolution of damage. Zhao et al. [36] studied the deformation and permeability of sandstone with cycle loading and unloading of different unloading rates. With the increase of cycle times, the shape of permeability curves is ∞ type. The relationship between the variation of axial strain, unloading rate, and loading stress can be described with a power function. Jiang et al. [37] experimentally studied the evolution of permeability, acoustic emission, and energy dissipation of gas-containing coal under tiered cyclic loading, described the relative process by defining permeability recovery rate, damping ratio, acoustic emission energy rate and ring count rate, and developing a coal damage variable equation. Duan et al. [38] carried out the hydromechanical experiments to analyze the inherent relationship between the residual strain, permeability, acoustic emission, and energy dissipation of gas-bearing coal under the confining stress cyclic unloading-loading. The existing studies are mainly focused on intact rock samples, while there are rare reports on the evolution of deformation and permeability of fractured rocks under cyclic loading-unloading.
In this study, the hydromechanical experiment of fractured sandstone comprised of single-fracture and doublefracture is carried out. The deformation and permeability of fractured sandstone subjected to the change of hydraulic pressure, confining stress, and axial cycle loading-unloading are investigated and quantitatively analyzed based on the permeability recovery rate (PRR) and permeability enhancement reduction rate (PERR).

Experiment Principle.
During the experiment process, we assume that (1) the permeable water is an incompressible fluid; (2) the steady seepage under constant pressure is regarded as continuous seepage; and (3) for low permeability fractured sandstone, the seepage obeys Darcy's law during experiment process. The permeability formula is expressed as follows: where k is the permeability (m 2 ); V is the inflow volume of the seepage fluid during the time Δ t (m 3 ); μ is the dynamic viscosity of water, μ = 1 × 10 −3 Pa•s (T = 20°C); L is the length of the rock sample (m); A is the cross-sectional area of the rock sample (m 2 ); Δ P is the hydraulic pressure difference (Pa); and Δ t is the increment of time (s).

Sample Preparation.
The experimental samples were prepared with a dimension of 50 mm × 100 mm (diameter × length). The physical property of density and porosity is 2350 kg/m 3 and 7.78%, respectively. The fractured rock mass with a single fracture of 100 degree inclined angle relative to the horizontal plane and two mutually perpendicular fracture of 100 degree inclined angle and 90 degree inclined angle relative to the horizontal plane were obtained through the Brazilian splitting test, as shown in Figure 1.
The specific mechanical property of the intact sandstone under different confining stress is shown in Table 1.
The hydromechanical tests were carried out by triaxial hydromechanical coupling experimental system, as shown in Figure 2. The triaxial hydromechanical coupling experimental system includes a triaxial cell and a fluid injection pump. The scope of confining stress, axial stress, and hydraulic pressure are 0-60 MPa, 0-600 MPa, and 0-30 MPa, respectively. The specific experimental process is presented in Figure 3.

Testing Scheme.
To investigate the evolution of deformation and fluid conductivity subjected to the change of hydraulic pressure, confining stress, and cycle loadingunloading, the fractured sandstones were loaded into the triaxial chamber subjected to a complicated triaxial loading path, which consists of three parts. In the first part, the axial and confining pressure were initially loaded to the hydrostatic pressure of 36 MPa with a rate of 0.1 MPa/s, and the water pressure was reduced from 4.3 to 0.4 MPa with a gradient of 0.86 MPa. In the second part, the axial and confining pressure decreased from 36 to 18.5 MPa with a gradient of 2.5 MPa, while maintaining the hydraulic pressure of 0.4 MPa. Finally, the axial cyclic loading-unloading stress was set to an increment of 21.6 MPa at each cycle. The specific loading path is shown in Figure 4.

Experimental Results and Discussion
3.1. Effect of Hydraulic Pressure and Confining Stress. The deformations in the experiment procedure of 1st and 2nd are small, which are not the focus of this study. Therefore, the deformations of 1st and 2nd parts in this research are not analyzed in detail in Section 3.1.

Relationship between Permeability and Hydraulic
Pressure. The relationship between permeability and hydraulic pressure is shown in Figure 5. The permeability of doublefracture sandstone is almost three times that of singlefracture sandstone under the initial stress condition. With the decrease of hydraulic pressure, the permeability of both single-and double-fracture sample gradually decreased as a      4 Geofluids fracture sandstone is larger than single-fracture sandstone, due to more fractures exiting in the double-fracture sandstone.

Relationship between Permeability and Confining
Stress. Figure 6 depicts the change of permeability of fractured sandstone subjected to the variation of confining stress at a constant hydraulic pressure. With the decrease of confining stress, the permeability of both single-and doublefracture sandstones increases slowly as a quadratic function.
And the permeability of double-fracture sandstone in each stage is 2.7 times that of single-fracture sandstone. It is indicating that the effect of confining stress for fractured sandstone is relatively limited.

Evolution Characteristics of the Deformation and
Permeability. Figure 7 shows the relationship of the axial strain, axial stress, and permeability of the fractured sandstones in the process of axial cyclic loading and unloading. For single-fracture sandstone, with axial cyclic loadingunloading, both axial and radial strains gradually increase, and the correlative permeability spiralled down quickly in the compaction stage and slowly in the elastic and plastic stage. However, for double-fracture sandstone, the permeability slightly changes with axial cyclic loading and unloading. Furthermore, the axial stress-strain curves of both singleand double-fracture sandstones approximately present a parallelogram shape after the first cycle, showing obvious deformation memory characteristics. The deformation and permeability characteristics of each cycle stage are presented in Figures 8 and 9. In the first cycle, the loading and unloading curves of both single-fracture sandstone and double-fracture sandstone did not form a closed loop, and a large amount of residual deformation was observed, resulting in nonlinear properties of rock materials and damages of artificial fractures [36]. The corresponding permeability decreased dramatically and did not completely recover with axial loading and unloading. For single-fracture sandstone, the crossing of permeability curves at the loading state and unloading state was observed at the second cycle, while it was not found in the double-fracture sandstone. This phenomenon indicates that fractures were majorly compressed in the second cycle. Consequently, the flow channels were narrowed, and permeability reduced step-wise. In the third cycle, the permeability curves of both single-fracture sandstone and double-fracture sandstone gradually decreased with the loading and unloading, indicating that the fractures and secondary cracks also compressed during the third cycle. After the third cycle, the reexpansion of existing fractures and the generation of secondary cracks dominated the loading and unloading process. The compressed flow channels were expanded under the action of hydraulic pressure. As a result, the corresponding permeability of single-and double-fracture sandstones gradually increased. Finally, the axial stress-strain and permeabilityaxial strain curves of both single-and double-fracture sandstone have similar trend at the fifth loading.

Relationship between Axial Residual Strain and Axial
Cycle Stress. To quantitatively analyze the irrecoverable deformation of fractured sandstone subjected to the axial cyclic loading-unloading, the cumulative residual strain, comprised axial, and radial residual strains are defined. And the cumulative residual strain ε j pi is expressed as [38]: where the superscripts j are 1 and 3 represent the axial and radial directions, respectively; ε i j is the strain at the ith cycle when the axial stress is 36 MPa, %; and ε 1 j is the strain for the initial axial stress of 36 MPa, %. Figure 10 reflects the relationship between the cumulative residual strain and the cycle loading increment of the axial stress. Along the axial and radial direction, the cumulative residual strains increase in form of quadratic function as the increase in the loading increment of the axial stress. For cumulative axial residual strain and radial residual strain of  5 Geofluids double-fracture sandstone, the increment of residual strain increases remarkably in the first cycle and then increases slowly. Conversely, when the increment of axial stress is small, the cumulative radial residual strain of singlefracture is small with a slight increase gradient. The radial residual strain increases sharply after the second cycle. Generally, the change of residual strains can be divided into two stages: the sharp increase stage and slow increase stage.

Evolution of Permeability Recovery Rates (PRR) and
Permeability Enhancement Reduction Rates (PERR). To quantitatively characterize the permeability change of fractured rock caused by the axial cyclic loading-unloading and cyclic loading enhancement at σ 1 =108 MPa, the concept of PRR and PERR was proposed, respectively. The PRR is defined as the ratio of the permeability in every cycle after unloading to the permeability at time of initial loading (cumulative PRR) or at the last cycle after unloading (relative PRR). Similarly, the PERR is defined as the ratio of the permeability in every cyclic loading at 108 MPa to the permeability at initial loading at 108 MPa (cumulative PERR) or at the last cyclic loading at 108 MPa (relative PERR). And the formulas for calculating the cumulative PPR (CPRR) and cumulative PERR (CPERR) λ j c and relative PRR (RPRR) and relative PERR (RPERR) λ j r are as follows:  where the superscripts j = 36 and 108 indicate the PPR and PERR, respectively, and k i is the permeability at the ith cyclic loading-unloading and loading when the axial stress is 36 MPa and 108 MPa, respectively, m 2 . k 1 is the correspond-ing permeability when the initial axial stress is 36 MPa and 108 MPa for the first time, respectively, m 2 . Figure 11 shows the relationship between PRR and axial cyclic loading and unloading. During the cyclic loading- 7 Geofluids unloading process, the CPRR of single-fracture sandstone gradually decreased. This change mainly caused by the continuous increment of load stress. With the continuously increasing of axial stress, the seepage channels, consisting of mainly compressed pores and fractures, were gradually narrowed. And the CPRR of double-fracture sandstone was stabled at 85%-95%, while the RPRR of both single-and double-fracture sandstones shows a certain fluctuation. This   Geofluids indicates that the stress sensitivity of permeability of doublefracture sandstone is lower than that of single-fracture sandstone, because it has more seepage channels. Figure 12 presents the relationship between PERR and axial cyclic loading at the axial stress of 108 MPa. As the axial cyclic loading, the CPERR and RPERR of double-fracture sandstone decreased synchronously, presenting the enhancement effect of cyclic loading. The sandstone pore-fracture system was further compressed with increased cycle times, and then, the flow channels were narrowed. In contrast, the CPERR of single-fracture sandstone increased gradually with the first three axial loadings in the elastic stage, and the increasing degree was greater (about 2.4 times), which is attributed to the dislocation of artificial fracture surface. With axial cyclic loading time increase, the dislocated spaces increase, combing with fracture swelling and developing, the flow channels increase, and the permeability increases dramatically. Mine water inrush is one of the main disasters that restrict the safe and efficient production of coal mines. Combining Figure 12, when mining above or below the deep confined aquifer, especially the effect of repeated mining, even if the aquifuge is not failure, the displacement of roof and floor should be controlled reasonably to prevent the dislocation of vertical fractures, the increase of permeability of rock stratum, and water inrush disaster.

Conclusions
Based on the hydromechanical experiments of triaxial loading, the change of the axial and radial strain and permeability subjected to the effect of the hydraulic pressure, confining stress, and cyclic loading-unloading was observed. And cumulative residual strain, PRR, and PERR were proposed to quantitatively analyze these changes. The main conclusions are as follows:  (1) The relative permeability of both single-and doublefracture sandstone varies as a quadratic function of hydraulic and confining stress. The permeability of fractured sandstone is positively related to the hydraulic pressure, and double-fracture sandstone is more sensitive to the hydraulic pressure than the single-fracture sandstone. The permeability of fractured sandstone is negatively related to the confining stress. However, the effect of confining stress on the strain is more obvious than the permeability (2) As the advance of axial cyclic loading-unloading, the axial and radial strains of fractured sandstone increase, and the permeability of single-fracture sandstone spirals down. However, for doublefracture sandstone, the permeability slightly changes with more seepage channels. Furthermore, the axial stress-strain curves approximately present a parallelogram shape after the first cycle, showing obvious deformation memory characteristics. The CPRR of single-fracture sandstone decreases first and then increases. The CPRR of double-fracture sandstone maintains 85%-95% with a fluctuated RPRR (3) With axial cycle enhancement loading, the PERR of double-fracture sandstone decreases gradually; in contrast, the PERR of single-fracture sandstone dramatically increases. For the single-fracture sandstone, the dislocation of fracture surface was presented and developed with the increase of the axial loading time, resulting in the increase of the seepage channels characterized by the increase of the permeability Nomenclature PRR: Permeability recovery rate PERR: Permeability enhancement reduction rate k: Permeability V: Inflow volume μ: Dynamic viscosity L: Height of the rock sample A: Cross-sectional area of the rock sample Δ P: Hydraulic pressure difference Δ t: Increment of time ε j pi : Cumulative residual strain CPRR: Cumulative permeability recovery rate RPRR: Relative permeability recovery rate CPERR: Cumulative permeability enhancement reduction rate RPERR: Relative permeability enhancement reduction rate.

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

Conflicts of Interest
The author declares no conflict of interest regarding the publication of this manuscript Single-fracture Double-fracture (b) Figure 12: The permeability enhancement reduction at different loading stages (at 108 MPa): (a) cumulative permeability enhancement reduction rate; (b) relative permeability enhancement reduction rate.