ThermalHydraulicMechanical (THM) Coupling Behaviour of Fractured Rock Masses
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Yongjun Song, Yongxin Che, Leitao Zhang, Jianxi Ren, Shaojie Chen, Mengling Hu, "Triaxial Creep Behavior of Red Sandstone in FreezeThaw Environments", Geofluids, vol. 2020, Article ID 6641377, 20 pages, 2020. https://doi.org/10.1155/2020/6641377
Triaxial Creep Behavior of Red Sandstone in FreezeThaw Environments
Abstract
To investigate the timedependent mechanical properties of rock masses in cold regions under the effects of freezethaw cycling and longterm loading, triaxial multilevel loading and unloading creep tests were performed on saturated red sandstone samples subjected to different numbers of freezethaw cycles. The effects of freezethaw cycles and confining pressure on the creep properties, longterm strength, and creep failure mode of the rock were analyzed. The effect of freezethaw cycles on the microstructure of the rock was analyzed using scanning electron microscopy. The results showed that as the number of freezethaw cycles increased, the rock particle boundaries became more distinct, and more pores formed. The effect of freezethaw cycles on the creep deformation of red sandstone was related to the loading stress level. At low stress levels, the rock viscoelastic strain increased gradually and almost linearly with an increasing number of freezethaw cycles; in contrast, at high stress levels, the rock viscoelastic strain increased nonlinearly. The viscoplastic strain increased almost linearly with increasing freezethaw cycles. The fourth loading stress level (70% ) corresponded to the transition of the creep deformation of the red sandstone. When the confining pressure was low, a higher stress level caused the confining pressure to have a more significant effect on the creep strain. However, as the confining pressure continued to increase, the effect of the confining pressure on the creep strain eventually disappeared. The longterm strength of the red sandstone decreased approximately linearly with an increase in the number of freezethaw cycles. When the number of freezethaw cycles and the confining pressure were high, the rock samples formed a transverse shear plane and were more fragmented than those without a transverse shear plane. These results provide a reference for construction in rock mass engineering and longterm stability analysis in cold regions.
1. Introduction
In cold regions, rock masses are subjected to the combined effects of freezethaw cycles and external loads. When investigating freezethaw disasters, it is also necessary to examine the creep behavior and strength reduction caused by longterm external loads. Therefore, the study of rock creep behavior in a freezethaw environment is crucial for rock mass engineering in cold regions. With increased human activity, largescale rock mass construction projects, such as cold area tunnels, highways, and slope engineering projects, have commenced in cold regions. However, tunnels, roadbeds, and slopes in cold regions experience varying degrees of frostheave cracking, freezethaw slumping, supporting structure instability, leakage, and freezing damage owing to longterm seasonal changes and significant daynight temperature variations because of the complex geographical environment and climatic conditions, such as seasonal frozen soil in plateau alpine regions.
In recent years, several scholars have conducted studies on the mechanical properties of rocks and the damage induced within them under freezethaw conditions. Yamabe and Neaupane [1] performed uniaxial compression tests on a rock sample after subjecting it to freezethaw cycling and found that its uniaxial compressive strength increased with decreasing temperature but decreased with an increasing number of freezethaw cycles. Chen et al. [2] conducted freezethaw cycle tests on tuff with varying water content and reported that freezethaw cycling had a minimal effect on the rock strength when the water content was below 60% but that the rock strength significantly decreased due to freezethaw cycling when the water content exceeded 70%. Yavuz et al. [3] carried out experimental tests to determine the freezethaw damage evolution of 12 types of carbonate rocks and observed that the wave velocity, hardness, and compressive strength of the rock samples after being subjected to freezethaw cycles decreased to varying degrees. Zhang and Yang [4] considered the coupling effect of freezethaw cycling and loading; proposed the concepts of freezethaw damage, loaded damage, and total damage; and established a freezethaw loading damage model of rocks. Bayram [5] investigated the strength development of nine types of limestone from Turkey subjected to varying numbers of freezethaw cycles. Khanlari et al. [6] and Momeni et al. [7] performed freezethaw cycle and uniaxial compression tests on different types of rocks and determined the effects of freezethaw cycles on P wave velocity, strength, and porosity. Liping et al. [8] determined the physical parameters and triaxialcompression mechanical properties of coarse and fine sandstones subjected to different numbers of freezethaw cycles. Their results showed that intact hard rocks exhibited significant attenuation effects under freezethaw conditions. Seyed Mousavi et al. [9] and Zhao et al. [10] conducted compression tests on rocks after subjecting them to freezethaw cycles, investigated the effects of freezethaw cycles on the rock compressive strength, and analyzed the effects of freezethaw conditions on rock microstructures using scanning electron microscopy (SEM). Lu et al. [11] carried out freezethaw cycle tests and triaxial compression tests on four cases of flawed sandstone to analyze the influence of freezethaw cycling on the mechanical properties of the rocks and propose an equation to describe the loadinginduced damage evolution of sandstone that previously underwent freezethaw cycling. Some researchers placed sandstone samples in different chemical solutions when performing freezethaw cycle tests to analyze the effects of these chemical solutions on the freezethaw damage relationships and mechanical properties of the sandstone [12–16].
The studies mentioned above investigated the mechanical properties and damage mechanism of rocks subjected to freezethaw conditions and reported various research results. However, under actual conditions, rock masses are often subjected to longterm effects of the surrounding rock pressure and other loads, and the creep behavior of rocks under longterm loading is a critical factor that affects their longterm stability and can cause rock damage [17–21]. Therefore, it is necessary to study the creep behavior of rocks in freezethaw environments. Currently, several scholars have investigated the creep characteristics and damage mechanisms of rocks under longterm loading [22–28]; however, the creep behavior of rocks in a freezethaw environment has not been studied in detail. Chen et al. [29] conducted creep tests on sandstone for different numbers of freezethaw cycles and analyzed the relationships between the creep deformation, creep rate, and longterm strength of the rock. Yang et al. [30] performed creep tests on quartzite under different freezethaw conditions (and different chemical solutions) and examined the effects of different chemical and freezethaw environments on the creep properties and microstructure of rocks. Li et al. [31] carried out creep tests on sandstone after exposure to freezethaw conditions and investigated the effect of freezethaw cycles on the creep deformation and pore structure of sandstone.
The creep characteristics of rocks under freezethaw conditions have been investigated to varying degrees. However, in terms of the effects of freezethaw cycles and confining pressure on rock creep behavior, detailed investigations have not been conducted, and few experimental data have been reported. Based on this research gap, multilevel loading and unloading triaxial creep tests under different numbers of freezethaw cycles and confining pressure conditions were carried out in this study using saturated red sandstone as the research object. The coupled effects of freezethaw cycles and confining pressure on the creep properties, longterm strength, and creep failure mode of red sandstone were determined, and the effect of freezethaw cycles on rock microstructure was analyzed using SEM. This study provides theoretical guidance for the longterm stability evaluation of rocks in cold regions.
2. Materials and Methods
2.1. Specimen Preparation
The red sandstone specimens in this study were collected from the Dafosi Coal Mine, which is located in the midwest zone of the Binchang Mining Area, Jurassic Coalfield, Huanglong, Shaanxi Province, China. The location of the Dafosi Coal Mine is shown in the map in Figure 1. The shaft of the Dafosi Coal Mine was constructed using the freezing method. The rock formations consisted of mostly thick, weak medium to finegrained sandstones. The sampled rock layer was light brownishred fine to mediumgrained feldspar quartz sandstone, mainly composed of quartz, plagioclase, potash feldspar, and calcite. Drilling and coring operations were performed to retrieve the red sandstone block from the site. All the rock samples used in this study were obtained from the same red sandstone block to reduce the influence of variation in the rock samples on the test results. Additionally, the drilling direction was consistent with the rock deposition direction. Following the methods recommended by the International Society for Rock Mechanics [32], the core removed from the drill hole was cut and polished into a standard rock sample with a diameter of 50 mm, a height of 100 mm, and an end surface unevenness that did not exceed 0.02 mm, as shown in Figure 2.
First, the rock samples that were visually different were removed, and the remaining rock samples were placed in an oven and dried at 105°C for 24 h. After drying, an ultrasonic tester was used to measure the wave velocity of each dried rock sample. Their mass was also measured to determine their dry density. By grouping samples with similar longitudinal wave velocity and dry density results, the rock samples were categorized into five groups, with eight samples in each group, for a total of 40 samples (there are 20 conventional tests and 20 creep tests each). All the rock samples were saturated through vacuum pumping, and a constant pumping pressure of 0.1 MPa was maintained. After pumping for 4 h, the rock samples were stored under atmospheric pressure for 6 h. After saturation, the mass of each saturated rock sample was measured to obtain their saturated density, saturated water content, and porosity. The average values of the physical properties of all the rock samples are listed in Table 1.

2.2. Testing Procedure
The prepared saturated red sandstone samples were placed in a freezethaw cycle test box for freezethaw cycle testing. The temperature and the duration of freezing and thawing were set based on the differences in temperature during the day and night in cold areas. In this study, the ambient temperatures during freezing and thawing were −20 and 20°C, respectively. The freezing and thawing durations were 12 h each; thus, a freezethaw cycle lasted 24 h. The temperature curve of a cycle is shown in Figure 3. Before implementing the freezing and thawing cycles, an initial test was performed on the rock samples. By observing the degree of particle shedding on the surface of the rock samples, it was determined that the different groups of rock samples would undergo 0, 1, 5, 9, or 13 freezethaw cycles.
Conventional triaxial compression tests and multilevel loading and unloading triaxial creep tests were carried out using a TAW1000 rock triaxial creep testing machine (Figure 4). The temperature of the test chamber was maintained at a constant value of 25°C. The testing machine consisted of four main units: conventional triaxial, servo loading, deformation monitoring, and data acquisition units. The maximum axial load that could be applied using the testing machine was 1000 kN, and the maximum confining pressure was 100 MPa.
(a)
(b)
(c)
Conventional triaxial compression tests were performed at confining pressures of 0, 2, 4, and 6 MPa on the red sandstone samples after they were subjected to a varying number of freezethaw cycles. The triaxial compressive strength of each rock sample was determined, as listed in Table 2 The loading applied in the conventional triaxial compression tests was controlled by the stress, and the rate at which the load was applied was 0.01 MPa/s.

Multilevel loading and unloading triaxial creep tests were performed on each group of rock samples at confining pressures of 0, 2, 4, and 6 MPa. Based on the triaxial compressive strengths listed in Table 2, the magnitude of deviatoric stress of each rock sample was determined at various stress levels. The loading stress of the first level was 40% of the triaxial compressive strength, and the subsequent loading stress was increased by 10% of the triaxial compressive strength until rock sample failure occurred. Table 3 shows the deviatoric stress magnitudes of the rock samples for different numbers of freezethaw cycles and confining pressures. During the loading period, the axial load was increased at a rate of 0.01 MPa/s to reach the targeted deviatoric stress level, and then a constant load was maintained. During the unloading period, the axial load was decreased at a rate of 0.03 MPa/s to reach a deviatoric stress of zero and then was removed. After a loadingunloading cycle was completed, the next stage was started following the same sequence. For each deviatoric stress level, the loading process lasted 48 h, and the unloading process lasted 24 h, except for the last level, in which there was no unloading. The specific loading method is shown in Figure 5.

2.3. Effect of FreezeThaw Cycles on the Microstructure of the Red Sandstone
Xray diffraction was conducted to analyze the composition of red sandstone after 0 and 13 freezethaw cycles, as shown in Table 4. The rock was mainly composed of quartz, plagioclase, potash feldspar, and calcite. After 13 freezethaw cycles, the proportions of plagioclase, calcite, and analcite in the rock decreased. This decrease occurred because the minerals that could easily react with water (such as plagioclase, calcite, and cristobalite) gradually dissolved under the action of the freezethaw cycles, resulting in a decrease in their mineral contents.

The red sandstone samples were observed using SEM after they were subjected to varying numbers of freezethaw cycles. An image archiving and communication system was used to process the SEM images to obtain binary images and rock parameters, such as the average length and area of the pores. Figure 6 shows SEM and binary images of red sandstone after different numbers of freezethaw cycles. The black part of a binary image (shown on the right side of the figure) represents the pores and microcracks encountered in the slice during scanning. The skeletal structure of the rock particles not subjected to freezingthawing was relatively tight, the surface was relatively flat, and no noticeable pores were observed. Larger rock particles appeared on the surface of the slice, and relatively scattered pores existed between the particles in the slice. As the number of freezethaw cycles increased, the mineral components of the rock dissolved, forming large pores. With increasing number of freezethaw cycles, the grain boundaries gradually became more noticeable, and the cohesion between the rock particles decreased significantly.
(a) 0 freezethaw cycle
(b) 1 freezethaw cycle
(c) 5 freezethaw cycles
(d) 9 freezethaw cycles
(e) 13 freezethaw cycles
3. Experimental Results
3.1. Results of the Conventional Triaxial Compression Tests
Owing to the influence of the variation in the rock samples on the creep tests, creep data at a confining pressure of 2 MPa after 9 freezethaw cycles were analyzed. The results of the conventional triaxial compression test at a confining pressure of 2 MPa after 9 freezethaw cycles were analyzed (Figure 7) to establish the relationship between the conventional mechanical properties and longterm mechanical properties of red sandstone. Table 2 and Figure 7 show that the number of freezethaw cycles and confining pressure had a significant effect on the triaxial compressive strength and elastic modulus of the rock.
(a) Curves of strain of red sandstone versus deviatoric stress at 2 MPa confining pressure
(b) Curves of strain of red sandstone versus deviatoric stress under 9 freezethaw cycles
At a confining pressure of 2 MPa, the triaxial compressive strength of the rock sample that was not subjected to any freezethaw cycle was 20.67 MPa. After 1 freezethaw cycle, the triaxial compressive strength was 19.13 MPa, which corresponded to a reduction of 7.45% compared to the strength of the sample subjected to zero freezethaw cycles. After 5 freezethaw cycles, the triaxial compressive strength was 17.79 MPa, which was 7.00% less than that after 1 freezethaw cycle. As the number of freezethaw cycles increased, after 9 and 13 cycles, the triaxial compressive strength values decreased by 5.23% and 1.86% compared to the strength of the sample subjected to 5 freezethaw cycles, to 16.86 and 16.51 MPa, respectively. The triaxial compressive strength of the rock gradually decreased with an increase in the number of freezethaw cycles, and the rate of decrease decreased continuously. The relationship between the triaxial compressive strength of the tested red sandstone and the number of freezethaw cycles under different confining pressure conditions was fitted (Figure 8). The coefficients of determination () of the fitted curves were all higher than 0.95. The fitting results are expressed in Equation (1). The triaxial compressive strength of the rock decreased exponentially with an increase in the number of freezethaw cycles under different confining pressures. where , , and represent the triaxial compressive strength, confining pressure, and number of freezethaw cycles, respectively.
Table 2 shows that the elastic modulus of the rock gradually increases with the confining pressure under the same freezethaw cycle conditions, while it gradually decreases with the number of freezethaw cycles under the same confining pressure. The relationship between the elastic modulus and the number of freezethaw cycles under different confining pressure conditions was fitted (Figure 9). The coefficients of determination () of the fitted curves exceeded 0.95 except at a confining pressure of 0 MPa. The fitting results are expressed in Equation (2). The elastic modulus decreased exponentially with an increase in the number of freezethaw cycles under different confining pressures, which was similar to the variation trend of the triaxial compressive strength. where , , and represent the triaxial compressive strength, confining pressure, and number of freezethaw cycles, respectively.
3.2. Results of the Multilevel Loading and Unloading Triaxial Creep Tests
Figure 10 shows the multilevel loading and unloading creep curves for the tested red sandstone under different freezethaw and confining pressure conditions. The red sandstone creep curves corresponding to 2 MPa of confining pressure and 0, 1, 5, and 9 freezethaw cycles all exhibited three stages: the reduced creep rate (initial creep), constant creep rate (steadystate creep), and increased creep rate (accelerated creep) states. After 13 freezethaw cycles, the rock damage caused by freezingthawing was relatively significant, considering the variation in the rock samples. One rock sample was destroyed during loading of the fifth stress level (80% ) and failed to reach the accelerated creep stage. Except for the rock samples under 1 and 13 freezethaw cycles, the other rock samples reached the accelerated creep stage at the sixth stress level (90% ), which was consistent with the test results obtained by [33, 34]. At the same confining pressure, the instantaneous deformation and creep deformation of the tested red sandstone increased with the applied stress until the rock sample failed. The freezethaw cycle had a significant effect on the rock deformation. The deformation of the rock samples gradually increased with the number of freezethaw cycles, and the effect of the freezethaw cycles on the rock deformation became more significant with the increase in the stress level.
(a) Multilevel loading and unloading creep curves of red sandstone under 2 MPa confining pressure
(b) Multilevel loading and unloading creep curves of red sandstone under 9 freezethaw cycles
Under the same number of freezethaw cycles, the creep deformation of the rock samples gradually increased with the confining pressure, which was different from previous research results in which the creep deformation of rocks decreased with the increase in confining pressure at a similar stress level [35, 36]. This difference arose because different magnitudes of loading stress were adopted in this study and previous studies to reach the same stress level. In previous studies, a certain deviatoric stress was taken as the loading stress under different confining pressures to reach the same stress level. However, in this study, the loading stress was a percentage of the triaxial compressive strength under this condition. Therefore, for the same stress level, when the confining pressure was different, the value of the loading stress was also different. For example, after 9 freezethaw cycles, the loading stress of the third level was 60% which was equal to 10.12 MPa at a confining pressure of 2 MPa but 13.91 MPa at a confining pressure of 4 MPa. Hence, the test results were different from those of previous studies. The red sandstones experienced the three abovementioned stages of creep under different confining pressure conditions. At the same loading stress level, the instantaneous deformation and creep deformation of the rock samples increased with the confining pressure. The confining pressure had a significant effect on both the instantaneous and creep deformations of the red sandstone. With the increase in the stress level, the effect of the confining pressure on the deformation of the red sandstone became more significant.
3.3. Effect of FreezeThaw Cycles on the Creep Characteristics of the Red Sandstone
The relationship between the instantaneous strain and the number of freezethaw cycles at various stress levels under 2 MPa of confining pressure is shown in Figure 11. At the same stress level, the instantaneous strain of the rock samples increased with the number of freezethaw cycles. At a stress level of 60% , the instantaneous strain of the rock sample that underwent 0 freezethaw cycles was . After 1 freezethaw cycle, the instantaneous strain increased by 31.21%, corresponding to a value of . As the number of freezethaw cycles increased, after 5, 9, and 13 freezethaw cycles, the instantaneous strains of the rock samples were , , and , respectively, signifying a corresponding increase of 23.09%, 5.57%, and 6.57%. The instantaneous strain increased with the number of freezethaw cycles, but the rate of increase gradually decreased with the increase in the number of cycles and tended to stabilize.
Based on the data processing method of the multilevel loading and unloading creep tests, the instantaneous strains of the rock at various stress levels comprised the instantaneous elastic strain and instantaneous plastic strain, considering the loading history [37, 38]. Figure 12 shows the instantaneous elastic and plastic strains versus the number of freezethaw cycles at various stress levels under 2 MPa of confining pressure. The instantaneous elastic strain gradually increased with the number of freezethaw cycles at the same stress level, and its rate of increase was similar to that of the total instantaneous strain. The instantaneous plastic strain increased almost linearly with the number of freezethaw cycles, and the rates of increase were similar at various stress levels.
(a) Instantaneous elasticity strain
(b) Instantaneous plastic strain
Figure 13 plots the creep strain against the number of freezethaw cycles for various stress levels before the rock samples entered the accelerated creep stage. The creep strain gradually increased with the number of freezethaw cycles at the same stress level. When the stress level was low (less than 60% ), the creep strain increased almost linearly with the number of freezethaw cycles, and the rate of increase was low. When the stress level was high (above 60% ), the creep strain increased nonlinearly with the number of freezethaw cycles, and the rate of increase was high. For example, at the 50% stress level, the creep strains after 1 and 9 freezethaw cycles were and , respectively, indicating an increase of 16.10%. At the 70% stress level, the creep strains after 1 and 9 freezethaw cycles were and , respectively, representing an increase of 40.21%. The freezethaw cycles had a significant effect on the creep deformation of the rock samples, and the freezethaw cycle effect was more significant when the stress level of the creep load was higher.
Depending on the data processing method used for analyzing the multilevel loading and unloading creep, the creep strain can be classified into the viscoelastic strain and the viscoplastic strain. Figure 14 shows the relationship between the viscoelastic and viscoplastic strains at various stress levels and the number of freezethaw cycles under 2 MPa of confining pressure. The viscoelastic strain of the red sandstone showed a gradual increase with the number of freezethaw cycles at the same stress level, and the variation in the viscoelastic strain with the increase in the number of freezethaw cycles was similar to that of the creep strain. The viscoplastic strain showed a relatively stable increase with the number of freezethaw cycles at various stress levels, and the viscoplastic strain did not significantly nonlinearly increase with the stress level.
(a) Viscoelastic strain
(b) Viscoplastic strain
Figure 15 shows the steadystate creep rate of the rock samples under the fourth loading stress level after being subjected to different numbers of freezethaw cycles at a confining pressure of 2 MPa. The steadystate creep rate increased nonlinearly with the number of freezethaw cycles under similar confining pressures and at the same stress level. The increase in the steadystate creep rate was significant when the number of freezethaw cycles was small. The steadystate creep rate was for 0 freezethaw cycles but was after 1 freezethaw cycle, representing an increase of 13.72%. As the number of freezethaw cycles increased, the rate of increase in the steadystate creep rate gradually decreased. After 9 freezethaw cycles, the steadystate creep rate was , and after 13 freezethaw cycles, the value was , signifying an increase of 6.79%. The freezethaw cycles had a considerable effect on the steadystate creep rate of this rock. The test results were fitted to quantitatively describe the relationship between the steadystate creep rate of the tested rock and the number of freezethaw cycles, as depicted in Figure 15. The fitting results are expressed in where and represent the creep rate and the number of freezethaw cycles, respectively. The resulting coefficient of determination () was 0.9865.
As indicated by Figure 15, the exponential expression can be used to describe the relationship between the steadystate creep rate of the rocks and the number of freezethaw cycles.
3.4. Effect of Confining Pressure on the Creep Characteristics of the Red Sandstone
After 9 freezethaw cycles, the relationship between the instantaneous strain of the rock samples and the confining pressure was determined at various stress levels (Figure 16). The instantaneous strain steadily increased with the confining pressure at the same stress level. The confining pressure had a significant effect on the instantaneous deformation of the rock samples, and this effect was more noticeable as the confining pressure increased. The instantaneous deformation of the tested red sandstone increased nearly linearly with the confining pressure at a low stress level. As the stress level increased, the instantaneous strain increased nonlinearly with the confining pressure. When the stress loading level was 80% , the instantaneous strain increased almost parabolically with the confining pressure, and the nonlinearity was significant.
Figure 17 shows curves of the creep strain versus the confining pressure after 9 freezethaw cycles for various stress levels. When the stress level was low, the creep strain of the rock increased almost linearly with the confining pressure. The increase in the creep strain was nonlinear when the stress level was high, and the increase in the confining pressure caused the creep strain to increase rapidly. As the confining pressure increased, the rate of increase in the creep strain decreased and then became stable. When the confining pressure was low, a higher stress level caused the confining pressure to have a more significant effect on the creep strain. However, as the confining pressure continued to increase, the effect of the confining pressure on the creep strain eventually disappeared.
The relationship between the confining pressure and the steadystate creep rate of the rock samples under the fourth loading stress level after 9 freezethaw cycles was plotted in Figure 18. The confining pressure had a significant effect on the steadystate creep rate. The relationship between the confining pressure and steadystate creep rate of the red sandstone was fitted. The resulting coefficient of determination () was 0.9967, and the fitting relationship is expressed in where and denote the creep rate and the confining pressure, respectively.
The steadystate creep rate increased linearly with the confining pressure, and its rate of increase was linear and unaffected by the confining pressure (Figure 18). The reason was that the increase in the confining pressure increased the triaxial compressive strength of the rock. At the same stress level, the higher the confining pressure, the higher the deviatoric stress value; hence, the creep rate of the rock was also higher.
3.5. LongTerm Strength of the Red Sandstone after FreezingThawing
The longterm strength of rock is the critical stress at the transition from stable creep to unsteady creep. When the stress in the rock is lower than this critical stress value, the rock will creep stably, and no matter how long this stress state is maintained, the rock will not experience failure. However, when the stress exceeds the longterm strength, the rock will experience unstable creep until creep failure occurs [39–41].
Currently, the isochronous stressstrain curve cluster, transition creep, and steadystate creep rate methods are the three most widely used methods of determining the longterm strength of rocks. The steadystate creep rate method and the transition creep method have a similar basic principle; the longterm strength of the rock is determined by the change in the creep rate. During creep, the steadystate creep rate of the rock increases with the loading stress level. When the stress level is lower than the longterm strength, the steadystate creep rate of the rock gradually decreases to zero with increasing time, yet the rock will not experience failure. When the stress level exceeds the longterm strength, the creep rate will increase after a period of steadystate creep, and the rock will enter the accelerated creep stage before ultimately failing.
Based on the above description, an improved steadystate creep rate method was used in this study to determine the longterm strength of the rock [42]. The relationship between the steadystate creep rate and the partial stress at various stress levels was analyzed. The results showed that the steadystate creep rate increased with the deviatoric stress before reaching the critical inflection point, but the rate of increase was small. However, the rock entered the unsteady creep stage when the curve suddenly increased beyond the critical inflection point. The relationship between the steadystate creep rate and the deviatoric stress data was fitted to plot the relationship curve. Before the critical inflection point, the fitted curve is almost parallel to the horizontal axis, and the rock is in the steadystate creep stage. The black straight line in the figure is the tangent line where the steadystate creep growth rate is “0,” and the black diagonal line is the tangent line at the critical inflection point. The two tangents of the curve before the critical point were also drawn, and the deviatoric stress value at the intersection of these two tangents represented the longterm strength of the rock. The relationship between the steadystate creep rate of the tested red sandstone and the applied deviatoric stress at a confining pressure of 2 MPa after different numbers of freezethaw cycles was analyzed to determine the longterm strength of the red sandstone, as shown in Figure 19.
(a) 0 freezethaw cycle
(b) 1 freezethaw cycle
(c) 5 freezethaw cycles
(d) 9 freezethaw cycles
(e) 13 freezethaw cycles
When the confining pressure was 2 MPa, the longterm strength of red sandstone that did not undergo freezethaw cycles was 17.33 MPa, and after 1 freezethaw cycle, the longterm strength was 17.18 MPa, which was 0.92% lower than that for 0 freezethaw cycles. As the number of freezethaw cycles increased, the longterm strength results of the red sandstone were 14.69, 13.83, and 12.36 MPa after 5, 9, and 13 freezethaw cycles, respectively, which were 15.23%, 20.19%, and 28.68% lower than that for 0 freezethaw cycles, respectively. The freezethaw cycle significantly influenced the longterm strength of the red sandstone. The relationship between the number of freezethaw cycles and the longterm strength of the red sandstone was determined to evaluate the effect of freezethaw cycles on the longterm strength of this red sandstone (Figure 19). The coefficient of determination () was 0.9511, and the fitting equation is expressed in where represents the creep rate and represents the number of freezethaw cycles.
Figure 20 shows that the longterm strength of the tested red sandstone linearly decreased with an increase in the number of freezethaw cycles. This trend was different from previous results, in which the conventional triaxial compressive strength decreased exponentially as the number of freezethaw cycles increased. The reason for this difference may be related to the creep damage generated during rock creep. The longterm strength ratio of rock λ was proposed to investigate the relationships between the longterm strength and triaxial compressive strength and the effect of the number of freezethaw cycles on the longterm strength and triaxial compressive strength. The longterm strength ratio of rock λ is defined as the ratio of the longterm strength to the triaxial compressive strength, as expressed in
The longterm strength ratios of the red sandstone under 2 MPa of confining pressure are shown in Figure 21 for different numbers of freezethaw cycles according to the longterm strength and triaxial compressive strength results. The longterm strength ratio increased firstly and then decreased. After 1 freezethaw cycle and 13 freezethaw cycles, the longterm strength ratios were 0.9 and 0.75, respectively, and the variations for 1 freezethaw cycle and 13 cycles were higher than those for 0, 5, and 9 cycles. This result was attributed to the significant effect of the variation in the rock samples on the longterm strength. Thus, the samples subjected to different freezethaw conditions did not experience failure at the same stress level, which remarkably influenced the longterm strength ratio. For example, the rock sample exposed to 1 freezethaw cycle failed at the seventh stress level, but the rock sample exposed to 13 freezethaw cycles failed at the fifth stress level.
3.6. Red Sandstone Failure Mode after Multilevel Loading and Unloading Creep
Figure 22 shows the creep failure morphology and corresponding sketch of the red sandstone fractures under different confining pressures and freezethaw conditions. The confining pressure significantly influenced the creep failure mode of the rock under the same freezethaw conditions. The rock exhibited a typical singleshear failure mode and splitting failure mode under confining pressures of 0 and 2 MPa, respectively. When the confining pressure was high (4 and 6 MPa), two or more shear planes formed in the rock, signifying a typical doubleshear failure or multipleshear failure mode. Different degrees of secondary cracking occurred around the rock sample fracture surfaces, mainly when the confining pressure and the number of freezethaw cycles were high. At a confining pressure of 6 MPa, the rock sample subjected to 0 freezethaw cycles was divided into several fragments by multiple oblique shear planes, and the integrity of the rock was disturbed. This tendency to fragment was driven by the continual development and expansion of the structural defects and microcracks inside the rocks, causing damage under repeated loading and unloading and longterm loading during the multilevel loading and unloading creep tests. Multiple cracks were generated at the same time as the main fracture surface was formed. The freezethaw cycle had a significant effect on the rock failure mode. When the number of freezethaw cycles was high, the rock samples under high confining pressures developed transverse shear planes. The rock fragmented into several pieces by this transverse shear plane and multiple oblique shear planes. The rock samples fragmented more significantly under higher confining pressures and numbers of freezethaw cycles, and the integrity of the samples declined sharply.
(a) 0 MPa, 0 freezethaw cycles
(b) 2 MPa, 0 freezethaw cycles
(c) 4 MPa, 0 freezethaw cycles
(d) 6 MPa, 0 freezethaw cycles
(e) 4 MPa, 1 freezethaw cycle
(f) 4 MPa, 5 freezethaw cycles
(g) 4 MPa, 9 freezethaw cycles
(h) 4 MPa, 13 freezethaw cycles
4. Conclusion
In this study, triaxial multilevel loading and unloading creep tests and SEM were performed on red sandstone under different freezethaw and confining pressure conditions. The main conclusions are as follows:
The SEM and binarized images show that as the number of freezethaw cycles increased, the boundaries of the rock particles became more distinct, and more pores formed.
The effect of freezethaw cycles on the creep deformation of red sandstone was related to the stress loading level. At low stress levels, the total creep strain of the rock increased slowly and almost linearly with the number of freezethaw cycles; however, at high stress levels, the total creep strain increased nonlinearly. The fourth loading stress level (70% ) corresponded to the transition point of the creep deformation of the tested red sandstone. The change in the viscoelastic strain with the number of freezethaw cycles was similar to that of the total creep. However, the viscoplastic strain increased almost linearly with the number of freezethaw cycles.
The instantaneous strain increased almost parabolically with the confining pressure. When the confining pressure was low, a higher stress level caused the confining pressure to have a more significant effect on the creep strain. However, as the confining pressure continued to increase, the effect of the confining pressure on the creep strain eventually disappeared.
The steadystate creep rate of the tested rock was significantly influenced by the number of freezethaw cycles and confining pressure. The steadystate creep rate of this red sandstone increased exponentially with the number of freezethaw cycles at the same confining pressure, but it increased linearly with the increase in confining pressure under similar freezethaw conditions.
The longterm strength of the red sandstone decreased nearly linearly with the increase in the number of freezethaw cycles. The longterm strength ratio λ of the red sandstone was defined. The longterm strength ratio increased firstly and then decreased under different numbers of freezethaw cycles.
The creep failure mode of the red sandstone was significantly influenced by the number of freezethaw cycles and the confining pressure. At low confining pressures, the failure mode of the rock was mainly singleshear failure, whereas at high confining pressures, failure mode was mainly doubleshear failure. Repeated loading and unloading and longterm loading resulted in the development of secondary cracks around the rock fracture surfaces. The rock samples formed a transverse shear plane when the number of freezethaw cycles and the confining pressure were high, and those rock samples were more fragmented than the rock samples without a transverse shear plane.
5. Discussion
In this paper, the concept of longterm strength ratio is put forward, but there was no consistent variation through the change of experimental data. So, if the relationship between the longterm strength ratio and the number of freezethaw cycles can be established, then the longterm strength of the rock can be indirectly deduced from the conventional triaxial compressive strength in the freezethaw environment. This has significant reference value for construction in rock mass engineering and longterm stability analysis in cold regions. Therefore, the trends of the longterm strength ratios in different freezethaw environments need to be investigated further.
Data Availability
The data supporting the results of our study are included within the manuscript.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This study was supported by the National Natural Science Foundation of China (Nos. 11972283, 41702346 and 11872299) and the Natural Science Foundation of Shaanxi Province of China (No. 2017JM1039). The authors are grateful for the generous support.
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Copyright © 2020 Yongjun Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.