Evaluation of Deformation and Permeability Behavior of Amygdaloidal Basalt under a Triaxial Cyclic Loading Creep Test

Amygdaloidal basalt is a typical rock mass in the dam foundation of the Baihetan hydropower project in southwest China. With rising and drawdown of the reservoir water level, the permeability and creep deformation characteristics of the amygdaloidal basalt are much complicated in the long-term cyclic loading processes. A cyclic loading-unloading creep test on the amygdaloidal basalt was performed to evaluate its deformation and permeability behavior. The results showed that Poisson’s ratio and elastic modulus of the rock specimen varied significantly under different loading processes with a relatively large irreversible deformation. The permeability and strain rates of rock changed in two phases under lower deviatoric stresses, while there are three typical stages of strain growth with the final stress level of 121.8MPa. For axial stress of 128MPa, the creep deformation and creep rate in the axial direction are smaller than these in the lateral direction. Before the sample failure, the lateral deformation accelerates earlier than the axial deformation. The results also suggested that the permeability of the rock specimens decreases considerably during each loading process and then tends to be constant with time. No apparent change in steady permeability is observed with variation of stress. For 128MPa axial stress, the permeability first decreases, then tends to be in a stable value, and at last increases during the sample failure.


Introduction
Permeability and time-dependent mechanical behavior of rock are very important in rock engineering during its lifetimes, especially in powerhouse and dams, underground petroleum storage caverns, and tunnels [1][2][3][4][5]. The permeability of rock material is determined from laboratory experiments [6][7][8][9] and site experiments [10]. For measuring the permeability, the laboratory mainly relied on Darcy's law to measure permeability during steady-state seepage flow [11]. Some research scholars had mostly focused on the permeability measurement method, influencing factors of rock permeability, permeability under complex stress conditions, and the anisotropic permeability [12][13][14][15]. Other scholars have studied the evolution of rock permeability during creep loading [16,17]. For time-dependent mechanical behavior, the researchers have carried out extensive laboratory creep experiments [5,[17][18][19]. The experimental results show that the main factors affecting the creep characteristics of the rock are environmental conditions, stress condition (such as deviatoric stress level, confining pressure, and pore water pressure), and microfractures of a rock specimen [5,[19][20][21]. The exponential function can accurately describe the relationship between the steady-state creep rate and the deviatoric stress. Similarly, confining pressure has a significant impact on the creep rate with the increasing confining pressure creep rate being reduced under the constant stress. The environmental conditions (water presence, temperature) also affect the creep characteristics of the rock.
However, the permeability and mechanical properties of rock during cyclic loading creep are still unclear. This is very important for the seepage evolution and creep characteristics of high dam foundation rock mass in the process of reservoir water level fluctuation. This study introduces the results of the cyclic loading and unloading triaxial creep test, and then, the experimental results are analyzed and discussed in detail. The results have an important theoretical significance for the seepage characteristics and time-dependent mechanical behavior during the cyclic loading and unloading creep test, which also provides test results for the long-term stability and safety research of hydropower projects.

Experimental Method and Material
The focus of this paper is to study the permeability and deformation characteristics of the amygdaloidal basalt sample during the long-term cyclic loading process. The hydromechanical-creep coupling triaxial system was used in the experiment (see Figure 1). The development and design of the rock testing system are introduced in detail by Wang et al. [13]. The system consists of three high-precision pumps for providing pressures to control confining pressure (σ 2 = σ 3 ), axial pressure (σ 1 ), and fluid pressure (P).
The following testing detail and procedure were adopted for each of the steps: (1) The prepared specimen was vacuum saturated for a period of 24 hours. (2) Install the sample and adjust the setting of LVDT sensors. (3) The confining pressure is applied to the predetermined value through the oil pressure system and remains constant during the experiment. (4) After the confining pressure remains stable, the seepage pressure is applied. In this experiment, the predetermined value of the upstream end of the specimen is 2.0 MPa, and the downstream end is exposed to the atmospheric pressure. (5) To retain 24 hours under confining pressure of 6.0 MPa and seepage pressure of 2.0 MPa, the permeability of the sample remains essentially unchanged and the axial deviatoric stress was applied under stress control at a constant rate of 0.075 MPa/s. The rate of unloading is consistent with the loading process. The stress path was applied in the loading-unloading triaxial creep testing of the sample as illustrated in Figure 2.
The permeability of rock was measured by a steady-state method in cycle loading and unloading creep processes. The permeability of rock can be expressed by Equation (1), and the formula is based on Darcy's law and calculated the volume of water in the pump as it changes with time [14]: where K is the permeability of the rock specimen (m 2 ); V is the flow volume through the specimen during the experiment (m 3 ); ΔP is the pore pressure difference between the upper and lower ends of the sample (Pa); L (m) and A (m 2 ) are the length and cross-sectional area of the sample, respectively; μ is the dynamic viscosity of water at 20°C and μ = 10 −3 Pa•s; and Δt is the time interval (s). Amygdaloidal basalt is a typical dam foundation rock mass of the Baihetan hydropower station. The tested specimen was prepared according to the IRSM [22] recommendations, and the standard cylindrical specimen of 50 mm in diameter and 100 mm in height is shown in Figure 3(a).
The main reason of amygdaloidal basalt formation is the deposition of secondary minerals; during the cooling process, calcite and quartz trapped are in the interior of the rock. There are many cavities in the lava process, called amygdales, the color of which is usually white. When the cavities are filled with calcite and quartz, the structure is called amygdaloidal basalt.
Using scanning electron microscopy, the microscopic pore distribution of the amygdaloidal basalt sample enlarged 500 times and 2000 times are obtained as shown in Figures 3(c) and 3(d). The tested amygdaloidal basalt has classical granular structures, and the micropores, irregularly arranged mineral particles, and irregular lump in shape can be seen clearly in SEM photos. Compared to other basalt, amygdaloidal basalt has the characteristics of high porosity and low strength.

Experimental Results and Discussion
3.1. The Stress-Strain Curves during the Creep Test. Figure 4 shows stress-strain curves of the sample under σ 3 = 6 MPa and ΔP = 1:9 MPa. The stress-strain curves are described in detail in the following stages:

Geofluids
(1) Crack Closure (OA). This stage occurs only during the first loading process. Because of the preexisting microcracks into the specimen, the stress-strain curves present a nonlinear characteristic in the initial loading process, when the deviatoric stress applied to the specimen reaches 53 MPa (A point) and the microcracks and micropores in the rock are completely closed.
(2) Elastic Deformation (AB). The rock deformation enters this stage (starting from point A) and the stress-strain curves to exhibit linear elastic characteristics. At this stage, we can consider that the rock sample is still in an elastic state for both loading and unloading processes, and there is no new microscopic damage into the sample during this process. However, with the increasing deviatoric stresses, the time characteristics of the sample as well as its rheological properties under different stress levels were obvious. During the previous four loading processes, the deformation of the sample is still at the elastic stage. As general compaction, the axial strains (instantaneous and rheological) are greater than the lateral strain.

Geofluids
In the linear elastic phase of the stress-strain curves, Young's modulus and Poisson's ratio at different loading stages can be calculated. The elastic modulus of the specimen is about 28.61-29.61 GPa in the process of loading-unloading. In the first five loading-unloading cycles, Poisson's ratio ranges from 0.23 to 0.26, but in the last loading process, Poisson's ratio is 0.33.   (4) Unstable Crack Growth (CD). During the last loading to 104 MPa (85.4% of the failure stress), the volumetric strain appeared in the turning point (C) and entered the microcrack generation and expansion stage. In this stage, the sample volumetric strain is mainly caused by lateral strain.

Time-Dependent
Strain of the Sample. Figure 5 shows the curves of creep strain change with time. The creep deformation increased smoothly, which means that the creep strains of this sample have good continuity with time. For low deviatoric stresses, the curves have two stages (decelerated and steady creep stages). In this experiment, the last deviatoric stress level is 121.8 MPa, the sample has a typical threestage creep (decelerated stage, steady stage, and increasing creep stage) in this deviatoric stress level, and the failure of the sample occurs after the last loading for 6.5 h. The overall trend of volumetric strain and lateral strain are similar to that of the axial strain. Before failure, the initial creep and steady creep phenomenon of the sample is obvious, which has the same varying tendency under different deviatoric stresses. When the deviatoric stress of the specimen exceeds the capacity of the rock material, the rate of volumetric strain is obviously greater than the axial strain rate. With the increase in deviatoric stress, the original defects (micropores and microcracks) of the sample are compressed to the minimum. Thereafter, when the deviatoric stress reaches the fifth-order stress level (111.6 MPa), the deformation occurs mainly in the circumferential direction, and the lateral strain is more significant than the increase in the axial strain (in Figure 4).
By comparing the strain-time relationship at different deviatoric stress levels, we can see that the increase in deviatoric stress accelerates the occurrence of creep strain. When the deviatoric stress is unloaded to 30.6 MPa, a considerable part of irreversible deformation occurs because of rheological effects. With the increase in deviatoric stress, the residual deformation occurs also after unloading the stress to 30.6 MPa. Take the axial train as an example, the axial strain is 2.001 at the first loading to 30.6 MPa. After the five  Table 1). The increased amplitude of axial strain increases with the increasing loading cycles (at the 2nd to 5th unloading processes), which implied that with the increase in deviatoric stress and creep time, the viscoplastic strains present a nonlinear increasing trend.

Strain Rate
Analysis. The rock's creep rate is an important index in stability to evaluate long-term stability of rock engineering. Figure 6 shows that in the low deviatoric stress levels, the rock's creep rate also shows two stages: decelerated stage and steady creep stage. When the deviatoric stress loading was stopped, the creep rate quickly reduces with time and trends to be a constant value, which explains that the sample's creep is in a steady creep stage, but the deformation of rocks still grows during this stage. For the creep deformation for 10 hours after loading, the axial strain creep rate is less than 0:4 × 10 −5 /h under different deviatoric stresses. From Figures 7(a) and 7(b), it can be seen that in the final stress level (121.8 MPa), the volumetric and axial creep rates show different behaviors in comparison with those of the  The creep rate of volumetric strain is larger than the axial creep rate in the last stress level, and the main reason is that large deformation occurs in the radial direction of the sample. From Figure 7, each creep strain rate-time curve has an obvious inflection point (points A and B in Figure 7) which indicates that the creep stage changes from a steady creep stage to an increasing creep stage, and the rock sample tends to fail. Meanwhile, we can see that the time of the inflection point of the volumetric creep rate is earlier than that of the axial creep rate, which means that the lateral deformation acceleration of the specimen before the failure is earlier than that of axial deformation. Figure 8 shows the relationship between the seepage flow and the axial strain versus time. It can be found that there are two jumps in the cumulative seepage curve during the creep process, and there is no sudden change in the axial pressure and strains during the two jumps. This indicates that the jump is not the real permeability of the specimen. In the steady-state creep process, the magnitude of permeability is 10 -19 m 2 .

Permeability Evolution during the Creep Test.
During the transient loading stage, the preexisted microcracks and micropores are compressed and closed due to the increase in deviatoric stress, and the permeability of the testing sample decreases with the increase in stress (as shown in Figure 9). Before applying deviatoric stress, most of the microcracks and micropores of the porous material are not connected, and the seepage pattern is mainly pore flow; the initial permeability is 45: At the last level of the deviatoric stress, the microcracks in the sample are continuously expanding over time to form a macroscopic fracture, which led to rock sample failure under the cyclic loading process [23]; before the sample is completely destroyed, the permeability coefficient increases to 1:7 × 10 −19 m 2 (see Figure 10). Even after failure, the permeability did not increase significantly. Figure 3(b) shows the specimen after macroscopic failure. This explains that the macroscopic failure surface does not completely pass through the longitudinal axial direction of the specimen, but only half of it, so the permeability is maintained at a relatively low level even after macroscopic failure. Figure 11 shows the relationship between the seepage flow and creep strain during unloading (deviatoric stress from 111.6 MPa to 30.6 MPa) and loading (deviatoric stress from 30.6 MPa to 121.8 MPa). The seepage flow changed significantly in the moment when the deviatoric stress increases or decreases. When deviatoric stress decreases from 111.6 MPa to 30.6 MPa, the reason is that the decrease in deviatoric stress compresses the rock sample crack so that the seepage flow is increased. Conversely, some microcracks reclose with the increase in deviatoric stress, so we can see that the seepage flow is reduced. The slope of the seepage flow did not change significantly before and after the change of 7 Geofluids deviatoric stress (in Figure 11), there is no obvious change in permeability during the deviatoric stress change, and the permeability magnitude of the sample is 10 -19 m 2 . The main reason is that there are no obvious cracks in the rock sample before failure.

Conclusion
In this research, through the triaxial cyclic loading and unloading creep test, Young's modulus and Poisson's ratio of the amygdaloidal basalt sample at different loading stages can be obtained; these values are varied rather than a fixed value. The creep deformation and creep rate all demonstrate two stages (decreasing phase and steady phase) when the deviatoric stress is less than the yield stress. And a considerable part of irreversible deformation occurred during the loading creep processes. The permeability of amygdaloidal basalt undergoes an evident decrease during each loading process and then tends to be in a constant value during the steady creep phase. For the final deviatoric stress level, the permeability first decreases, then tends to be in a stable value, and at last increases during the sample failure. The permeability of the material is related not only to the porosity and microcrack distribution but also to the stress environment. When the deviatoric stress level is 121.8 MPa, a large deformation occurs in the radial direction and the lateral deformation accelerates earlier than the axial deformation before rock failure; the creep strain increases at an increasing rate until the rock sample failure. This research does not discuss more about the influence of confining pressure and permeable pressure on the permeability of this rock material under cyclic loading and unloading creep processes, and future work will be done on this part.

Data Availability
The data that support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that they have no conflicts of interest.