Experimental studies on the pore structure and mechanical properties of anhydrite rock under freeze-thaw cycles

Cho Hou, Xiogung Jin,b,c,*, Jie He, Hnlin Li

a School of Civil Engineering, Chongqing University, Chongqing, 400045, China

b Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education, Chongqing University, Chongqing, 400045, China

c State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400045, China

Keywords:Anhydrite rock Freeze-thaw cycles Physico-mechanical characteristics Microstructure evolution Deterioration mechanisms

A B S T R A C T

1. Introduction

In the natural environment,rocks are formed by mineral grains,pores, microcracks, and cementing substances (Zhang et al., 2020;Zhao et al., 2022). Moreover, the properties of the rock are easily affected by the external environments (Grossi et al., 2007; Li and Liu, 2021). Cyclic freeze-thaw is deemed one of the most essential efflorescence processes that significantly affect the properties of rock (Zappia et al., 1998; Topal and Sözmen, 2003). Freeze-thaw cycles usually occur in the frigid area, causing damage to rock engineering such as tunnels, dams, and buildings (Lai et al., 2012;Freire-Lista et al.,2015).When the temperature is lower than 0°C,the water in the pores and microcracks of rock condenses into ice.The water volume expands by 9.08%, which leads to the concentration of tensile stress and the destruction of the rock’s internal structure. When the ice thaws, water flows along pores and microcracks, further aggravating the rock’s damage (Hori and Morihiro, 1998; Sousa et al., 2005). The decay of rock caused by the freeze-thaw cycles is related to many factors,such as lithology,temperature,water content,and in situ stress(Everett,1965;Chen et al., 2004; Takarli et al., 2008).

Various researchers have investigated the effects of freeze-thaw cycles on the physical and mechanical characteristics of rocks(Fang et al., 2018; Fan et al., 2020; Han et al., 2020). Tan et al. (2011)conducted a freeze-thaw experiment to investigate the deterioration characteristics of granite. They showed that the compressive strength, elastic modulus, and cohesion drop exponentially as the cycles increase. Han et al. (2016) adopted an experiment to determine the deterioration mechanisms of sandstone under combined influences of chemical solutions and freeze-thaw cycles. They indicated that chemical solutions and freeze-thaw cycles aggravate the damage of rock. Mousavi et al. (2019) performed 1200 m of drilling in the mine to study the triaxial compressive strength evolutions of calcareous schist rock under the influences of freezethaw cycles. They proved that the number of cycles leads to a decline in mechanical strength.

The microstructure of rock can distinctly affect its mechanical characteristics(Park et al.,2015;Liu et al.,2020a;Shen et al.,2020;Sun et al., 2020). To investigate the changes of rock’s microstructure with freeze-thaw cycles, Liu et al. (2020b) analyzed the influences of freeze-thaw cycles on granite. They acquired that as the number of cycles increases, the amount of macropores increases,but the dynamic flexural tensile strength decreases.Wang et al. (2020a) employed three-dimensional (3D) computed tomography (CT) technology to reveal the fracture evolutions of granite treated with different freeze-thaw cycles. They pointed out that a simple crack network is formed after the samples experience severe freeze-thaw fatigue damage.Zhou et al.(2020)studied the influences of microstructure evolution on sandstone permeability under freeze-thaw cycles. They found that as the number of cycles increases, the percentage of nano-sized throats decreases,while the percentage of sub-micron-and micron-sized throats increases.

For the sake of evaluating the durability of the rock engineering projects in a frigid area, various damage constitutive models were established by researchers (Liu et al., 2019; Huang et al., 2020;Lövqvist et al.,2020).Fatih (2012) developed a statistical model to determine the uniaxial compressive strength (UCS) of limestone after freeze-thaw cycles without destructive tests. Huang et al.(2018) derived a constitutive damage equation under freeze-thaw cycles for rock. This model was validated, and the results show that the constitutive model is suitable to describe the mechanical properties of rock under cyclic freeze-thaw,with high accuracy and practicability. Ke et al. (2018) proposed a model to determine the reduction of dynamic strength of rock after repeated freeze-thaw cycles. Although the tests were only carried out on sandstone, the proposed model is suitable for other rocks when subjected to the same or similar failure mechanisms during freeze-thaw cycles.

The above literature reviews show that the deterioration of rock caused by the freeze-thaw cycles was investigated by experiments and theoretical analysis.In the meantime,previous research mainly concentrated on sandstone, granite, limestone, etc. However, little work has been conducted on the deterioration mechanisms of anhydrite rock. The anhydrite rock is mainly formed by highly concentrated marine sediments. Anhydrite transforms into dihydrate gypsum (CaSO4∙2H2O) after absorbing water, resulting in a series of adverse geological phenomena such as softening and expansion(Serafeimidis and Anagnostou,2015).As an evaporative sedimentary rock, anhydrite rock masses are commonly encountered in engineering projects (Hemme and van Berk, 2017;Kaufmann and Romanov,2017;Wang et al.,2020b).Anhydrite rock engineering located in cold regions is affected by the freeze-thaw cycles, which endanger the stability of engineering. The freezethaw damage mechanisms of anhydrite rock are different from other rocks due to their water softening and expansion properties.Therefore, it is essential to investigate the deterioration mechanisms of anhydrite rock under freeze-thaw cycles.

In the current study,the variations in mass,porosity,mechanical properties, and microstructure of anhydrite samples were investigated by a series of laboratory tests under freeze-thaw cycles.Also,the deterioration mechanisms of anhydrite samples under cyclic freeze-thaw were obtained from macro and micro perspectives.The paper is organized as follows. After the Introduction, the experimental materials and methods are illustrated in Section 2,and the experimental results and analysis are implemented in Section 3. Section 4 presents the decay function model for mechanical parameters. Section 5 discusses the deterioration mechanisms of anhydrite rock under cyclic freeze-thaw. Finally,conclusions are drawn in Section 6.

2. Materials and methods

2.1. Sample preparation

The anhydrite rock tested in the experiments was sourced from Donghuishe Town, Hebei Province, China (Geographical coordinates: 114.1°E, 38.26°N). The anhydrite strata were located in the Middle Ordovician Fengfeng Formation, and its mineralization period was about 485-444 million years ago.The anhydrite strata were not continuously distributed in layers. Its production was controlled by the regional paleo-sedimentary environment and the fault structure. In the distribution area of anhydrite formations,anhydrite strata were usually produced in fault depressions, presenting a saline diapir structure(Guo et al.,2009).According to the integrated system for macro-scale anhydrite classification proposed by Forkner(2010),the rock studied in this work was diapiric layered anhydrite rock.

Forty-three cylindrical samples with a standard size of φ 50 mm×100 mm were drilled from the same block for the mass variation,nuclear magnetic resonance (NMR), and uniaxial and triaxial compression tests.In addition,three cuboid samples with a size of 10 (length) × 10 (width) × 5 mm (height) were made for the scanning electron microscope (SEM) tests. According to the International Soceity for Rock Mechanics (ISRM) (Kim et al.,1999) suggested specification,all cylindrical samples were polished to make the surface roughness less than 0.02 mm, and the end surfaces perpendicular to its axis with a tolerance less than 0.001 radians.The anhydrite samples used in the tests are depicted in Fig.1. The fundamental physical properties of the samples were measured through laboratory tests. The mean dry density of the samples is 2.931 g/cm3, and the natural moisture content is 0.037%. The mineral composition of the samples is shown in Table 1.

Table 1 The mineral composition (%) of the anhydrite samples investigated.

Fig.1. The samples used in the tests: (a) Cylindrical and (b) cuboid samples.

2.2. Test schemes and test instruments

All samples were thoroughly saturated with water before cyclic freeze-thaw treatment. The lowest temperature in winter at the sampling site can reach around -20°C. Thus, combined with the Chinese code DL/T 5368-2007 (2007), the freeze-thaw temperature used in this work was set at -20°C to 20°C. Meanwhile, the number of freeze-thaw cycles were set to 0,30,60,90,and 120.The schematic of the tests and the number of samples used in each test are presented in Fig.2.The main instruments used in the tests are illustrated in Fig. 3.

Fig.3. Main instruments used in the tests:(a)Freeze-thaw test machine;(b)WDAJ-600 rock shear rheological testing machine;(c)Rock 600-50 triaxial tester for rock mechanics;(d) Non-destructive NMR system for rock core imaging and analysis; and (e) SEM.

The freeze-thaw treatment was determined as follows: the saturated samples were frozen in a freeze-thaw test machine(Fig. 3a) with a temperature of -20°C for 4 h and then thawed in 20°C water for 4 h.The temperature range of the freeze-thaw test machine is -40°C to 100°C, with an accuracy of ± 2°C, and the temperature fluctuation range is within ± 0.5°C.

Fig. 2. Schematic of the tests.

2.3. Mass variation tests

Five cylindrical samples were selected in this work, numbered M1, M2, M3, M4, and M5, to carry out mass variation tests. The samples with the corresponding number of cycles(0,30,60,90,and 120) were put in an environment of 25°C and relative humidity(RH)of 70%for air-drying until their mass reached constant values.Subsequently, the mass of five cylindrical samples was measured through a balance with an accuracy of 0.01 g.Meanwhile,the mass variation (%) can be calculated as

wherem0is the initial mass of the samples,andmNis the mass of the samples afterNfreeze-thaw cycles.

2.4. Mechanical resistance tests

The uniaxial and triaxial compression tests were performed at room temperature.The uniaxial compression tests were carried out using the WDAJ-600 rock shear rheological machine (Fig. 3b). The maximum axial test force of the equipment is 600 kN, and the maximum axial displacement is 30 mm. A total of 15 cylindrical samples were used for the uniaxial compression tests. These samples were divided into five groups,with three samples in each group. Meanwhile, the displacement-controlled loading method was adopted in the uniaxial compression tests,and the loading rate was 0.1 mm/min.

The triaxial compression tests were carried out using the Rock 600-50 triaxial tester for rock mechanics (Fig. 3c). The maximum axial load of the equipment is 1000 kN, the maximum confining pressure is 60 MPa, and the sensor accuracy is within ±0.1%.Twenty cylindrical samples were divided into five groups for the triaxial compression tests. The triaxial compression tests adopted two confining pressures of 3 MPa and 5 MPa. The triaxial experiment’s loading procedure was first to load the confining pressure to a predetermined value using the stress-controlled loading method,with a loading rate of 0.5 MPa/min. Then, the displacementcontrolled loading method was used to load axial stress at a constant rate of 0.1 mm/min. Both uniaxial and triaxial compression tests were loaded until the samples reached failure. Then the mechanical parameters of samples under various freeze-thaw cycles were obtained.

2.5. Non-destructive tests

2.5.1. NMR tests

In order to reveal the pore structure evolution characteristics of the studied rock caused by the effects of the freeze-thaw cycles,three cylindrical samples numbered N1,N2and N3were employed to perform the NMR tests. At the 0, 30, 60, 90 and 120 cycles, the three samples were taken out from the freeze-thaw test machine and transformed to the State Key Laboratory of Coal Mine Disaster Dynamics and Control,Chongqing University,China,for NMR tests through a non-destructive NMR system for rock core imaging and analysis (Fig. 3d). The system’s cell chamber size is φ25.4 mm ×60 mm, the magnetic field of the system is 0.3 T ± 0.5 T, and the testing temperature is 32°C.

2.5.2. SEM tests

Three cuboid samples numbered S1,S2,and S3were used for the SEM tests.The SEM tests were performed through a field emission transmission electron microscope (Fig. 3e) developed by the Analysis and Test Center of Chongqing University. The mains voltage of the equipment is 230 V alternating current (AC), the mains frequency is 50/60 Hz,and the maximum resolution is 1 μm.To carry out the SEM tests, the samples that had reached the set number of cycles need to be dried in an oven at 50°C for 12 h first.Additionally, the samples should be sprayed with gold on the surface for 60 s. Then, the SEM tests were carried out at room temperature, and the samples were in a vacuum environment during the tests.

3. Experimental results and analysis

3.1. Mass variation and pore structure evolutions

Mass variation is regarded as a crucial parameter for evaluating the degradation characteristics of rocks caused by freeze-thaw cycle effects. The mass variation of anhydrite samples calculated by Eq. (1) is shown in Fig. 4. The mass variation increases with the number of freeze-thaw cycles,revealing that rock mass is declining.When the number of freeze-thaw cycles was 30,the mass variation of M1, M2, M3, M4and M5is 0.28%, 0.31%, 0.16%, 0.23% and 0.33%,respectively.After treated with 120 cycles,the mass variation of the five samples becomes 1.14%, 1.4%, 0.68%, 0.47% and 0.86%,respectively.

Fig. 4. Mass variation of anhydrite samples under various freeze-thaw cycles.

During the freeze-thaw tests, some white powders and small flake minerals were observed in the freezing water. Thus, we can speculate that the decrease of the rock mass was mainly due to some minerals dissolved in water or the exfoliation of rock surface under freeze-thaw cycles.It is worth noting that the mass variation of the M2sample changes abruptly at 120 cycles,which is due to the surface spalling of the M2sample.

The sample N1was selected to present the NMR test results.The pore size distribution of the N1sample after being treated with various cycles is presented in Fig. 5. There are three peaks in pore size distribution curves,and the pore size is mainly concentrated in the range of 0.001-10 μm. Based on the suggestions of previous studies (Li et al., 2018; Zhang et al., 2019), the pores of anhydrite samples were divided into three categories: micropores(r< 0.1 μm), mesopores (0.1 1 μm).To better understand the evolutions of various pores,the areas of the three categories of pores in the pore size distribution curves were calculated, as depicted in Fig. 6. It is concluded from Fig. 6 that as the number of freeze-thaw cycles increases, the proportion of macropores and mesopores increases, while the proportion of micropores decreases. This phenomenon indicates that the micropores gradually coalesced and formed the macropores and mesopores during the freeze-thaw cycles. Meanwhile, the porosity of the sample under different freeze-thaw cycles was also measured by the NMR tests,as listed in Table 2.The porosity of the sample increases with freeze-thaw cycles. After 120 cycles, the porosity increases by 75%.

Fig. 5. Pore size distribution curves of anhydrite rock under various cycles.

Fig. 6. Curve areas of various pores.

3.2. Deterioration of mechanical properties

The UCS-strain curves of the anhydrite samples under various freeze-thaw cycles are shown in Fig. 7. The naming rule of the samples was as follows: Taking "0-30-1" as an instance, "0" indicates that the confining pressure is 0 MPa,"30"indicates that the samples has experienced 30 cycles, and "1" represents the sample number in the group. The experimental results of the uniaxial compression tests are shown in Table 3.From Fig.7 and Table 3,the relationships between the sample compressive strength and elastic modulus with the freeze-thaw cycles can be obtained,as shown in Fig. 8.

As depicted in Fig.8,the UCS and elastic modulus decrease with the freeze-thaw cycles. The average UCS decreases by 13.88%,27.23%, 41.18%, and 46.54%, and the average elastic modulus decreases by 25.14%, 38.65%, 52.66%, and 60.16%, respectively, after the samples were dealt with 30, 60, 90 and 120 cycles.Finally, the variations of the UCS and elastic modulus are calculated as follows:

where σNandENare the UCS and elastic modulus of samples afterNfreeze-thaw cycles, respectively.

To present the effects of freeze-thaw cycles on the stress-strain curves of anhydrite samples more clearly, a representative sample was selected in each group, and their stress-strain curves are depicted in Fig. 9.

Fig. 9 shows that the UCS-axial strain curves of the anhydrite samples under different freeze-thaw cycles can be divided into four stages:

(1) Compaction stage(OA).In this stage,the stress-strain curve is concave, and the pores and microcracks in the anhydrite samples were compacted. As the number of freeze-thaw cycles increases, the length of the compaction stage increases, which indicates that the freeze-thaw cycles expanded the pores and microcracks in the rock.

(2) Elastic stage (AB). In this stage, the stress-strain curve is approximately a straight line,and the slope of theABsection is the elastic modulus. As the number of freeze-thaw cycles increases, the slope of the AB section gradually decreases,which reveals the decline of the resistance to deformation.

(3) Yield stage(BC).In this stage,the UCS of the samples reaches the maximum value, and pointCis the peak point. At the same time, the compressive strength decreases with the increase of freeze-thaw cycles.

(4) Failure stage (CD). In this stage, the microcracks in the rock were interconnected to form macrocracks,which caused the rock to be unstable and the stress to drop sharply. As the number of freeze-thaw cycles increases, the strain at the peak point increases, revealing that the plasticity characteristics of samples increase.There are 9.6%,24.1%,33.73%,and 37.35% relative growths of the strain at the peak point after the samples were dealt with 30, 60, 90, and 120 cycles,respectively.

The triaxial compressive stress-strain relationships of anhydrite samples with various freeze-thaw cycles are shown in Fig s.10 and 11. The triaxial compressive results of each sample can be obtained from Figs.10 and 11, as shown in Tables 4 and 5.

Table 2 Porosity of sample N1 under different numbers of freeze-thaw cycles.

Figs.12 and 13 more intuitively show the relationships between the compressive strength and elastic modulus and freeze-thaw cycles. It can be seen that as the number of cycles increases, the triaxial compressive strength and the elastic modulus decrease.For example, at the 3 MPa confining pressure, the average triaxial compressive strength decreases by 15.92%, 25.39%, 30.84%, and 35.72%, respectively, after the samples were dealt with 30, 60, 90,and 120 cycles.At the 5 MPa confining pressure,the average triaxial compressive strength decreases by 10.61%, 17.31%, 23.39%, and 28.24%, respectively, after the samples were dealt with 30, 60, 90,and 120 cycles.

Based on Figs.12 and 13,exponential functions were established to quantitatively describe the triaxial compressive strength and elastic modulus relations with freeze-thaw cycles:

where σN1and σN2are the triaxial compressive strength of samples afterNfreeze-thaw cycles under the confining pressures of 3 MPa and 5 MPa,respectively;andEN1andEN2are the elastic moduli of samples afterNfreeze-thaw cycles under the confining pressure of 3 MPa and 5 MPa,respectively.

To more clearly show the effects of the freeze-thaw cycles on the triaxial compressive stress-strain curves of anhydrite samples, a representative sample was selected in each group,and the stressstrain curves are depicted in Fig.14.

Fig.14. Evolutions of triaxial compressive stress-strain curves: (a) σ3 = 3 MPa; and (b) σ3 = 5 MPa.

As presented in Fig.14,due to the compaction effect of confining pressure, the stress-strain curves of anhydrite samples have no prominent compaction stage.They show good linear characteristics before the peak point. The stress of the untreated samples drops rapidly after reaching the peak strength, showing obvious brittleness. As the number of freeze-thaw cycles increases, the samples’brittleness characteristics decrease, and the plasticity characteristics increase.For example,when the confining pressure was 3 MPa,there are 15.85%, 21.95%, 37.8%, and 51.22% relative growths of the strain at the peak point after the samples were dealt with 30,60,90,and 120 cycles.When the confining pressure was 5 MPa,there are 27.16%, 35.8%, 48.15%, and 54.32% relative growths of the strain at the peak point after the samples were dealt with 30,60,90,and 120 cycles.

The Mohr-Coulomb criterion was used to determine the cohesioncand internal friction angle φ of anhydrite samples under various freeze-thaw cycles.The relationship curves of the principal stresses (σ1and σ3) are plotted in Fig. 15. The maximum and minimum principal stresses conform to the linear fitting relationship. Combining the fitted linear lines in Fig.15, the cohesion and internal friction angle of rock can be calculated by the following equations:

Fig. 7. UCS-strain curves of the anhydrite samples: (a) 0 cycle; (b) 30 cycles; (c) 60 cycles; (d) 90 cycles; and (e) 120 cycles.

Fig. 8. Evolutions of the (a) UCS and (b) elastic modulus of samples with the freeze-thaw cycles.

Fig. 9. Representative stress-strain curves of the uniaxial compression tests.

Fig.15. Evolution curves of principal stresses (σ1 and σ3): (a) 0 cycle; (b) 30 cycles; (c) 60 cycles; (d) 90 cycles; and (e) 120 cycles.

wheremis the slope of the fitted line,andbis the intercept of the fitted line on the longitudinal axis.

The cohesion and internal friction angle of samples calculated by Eqs. (8) and (9), respectively, are shown in Table 6. As can be seen,the cohesion decreases with the increase of cycles.There are 12.99%, 33.61%, 47.31%, and 52.48% relative reductions of the cohesion after the samples were dealt with 30, 60, 90, and 120 cycles. The change range of the internal friction angle is within 4.04°. It implies that the internal friction angle is basically unchanged under various freeze-thaw cycles. This finding is consistent with previous studies of sandstone (Wang et al., 2019) and granite (Tan et al., 2011) subjected to freeze-thaw cycles. The internal friction angle mainly reflects the friction characteristics between loose particles.Consequently,it is concluded that the freezethaw cycles have little influence on the internal friction angle of hard rocks.

Table 3 Experimental results of uniaxial compression tests.

Table 4 Results of the triaxial compression tests under various freeze-thaw cycles (σ3 = 3 MPa).

Table 5 Results of the triaxial compressive tests under various freeze-thaw cycles (σ3 = 5 MPa).

The relation between the cohesion and freeze-thaw cycles is plotted in Fig. 16. It can be seen that the cohesion decreases exponentially with the increase of cycles.The evolution of cohesion can be expressed as

Fig.16. Reduction of the cohesion.

wherecNis the cohesion of the samples afterNfreeze-thaw cycles.

3.3. Sample failure modes

To explain the failure modes of samples, some typical images are presented in Fig. 17. As illustrated in Fig. 17a, the failure modes of the samples under uniaxial compression conditions show single or multiple macrocracks that develop along the axial direction, presenting an obvious tensile failure mode. This is because the tensile strength of the sample is low, and the macrocrack bond was formed by tension. Some samples show tension-shear failure mode, and the friction trace on the shear surface is obvious with fine white powders. Some samples were seriously broken and divided into many parts by macrocracks,revealing that the samples show obvious brittleness under uniaxial compression conditions. As illustrated in Fig.17b, the failure modes of samples are single slope shear failure under triaxial compressive conditions. The shear cracks initiate at the edge of the sample’s end face, and the failure modes conform to the Mohr-Coulomb strength criterion.

Fig.17. Typical failure modes of samples: (a) Uniaxial and (b) triaxial compression tests.

Fig. 18 shows the microcracks characteristics on the fracture surface of tested anhydrite samples.As shown in Fig.18a,there exist many intragranular microcracks in the anhydrite rock. In order to more clearly describe the influences of crystal distribution on the growth of microcracks, a concept graph is depicted in Fig. 18b.Microcracks are most likely to initiate between crystals due to the relatively weak connection force,forming intergranular microcracks.The continuous development and convergence of intergranular microcracks will cause stress concentration at the microcracks tip.At this time,when the microcracks meet crystals,they can pass through crystals to form transgranular microcracks.In the damage zone,the intragranular and transgranular microcracks continuously cross and converge and finally form macrocracks, resulting in the failure of anhydrite samples.

Fig.10. Stress-strain curves of the triaxial compression tests (σ3 = 3 MPa): (a) 0 cycle; (b) 30 cycles; (c) 60 cycles: (d) 90 cycles; and (e) 120 cycles.

Fig.11. Stress-strain curves of the triaxial compression tests (σ3 = 5 MPa): (a) 0 cycle; (b) 30 cycles; (c) 60 cycles: (d) 90 cycles; and (e) 120 cycles.

4. Decay function model for mechanical parameters

A descriptive-behavioral model was raised by Mutlutürk et al.(2004) to measure the integrity loss in rocks caused by the recurrent freeze-thaw weakening effect as follows:

where dI/dNis the rate of deterioration;minus sign illustrates that the integrity of rock is decreasing; λ is the decay constant, which indicates the average relative loss of integrity under freeze-thaw cycles; andIis the integrity of rock.

Fig.12. Evolutions of the (a) triaxial compressive strength and (b) elastic modulus of samples (σ3 = 3 MPa).

A logarithmic form equation can be acquired by integrating Eq.(11) betweenI0andIN:

whereI0is the original integrity of the rock,andINis the integrity of the rock afterNfreeze-thaw cycles.

Eq. (12) is expressed in an exponential form as follows:

where e-λNis a decay factor, which reveals the proportion of integrity afterNcycles, i.eIN/I0.

Based on Eq.(13),Mutlutürk et al.(2004)defined the number of cycles required to reduce rock’s integrity by half as the half-life(N1/2). The half-life value is an essential parameter to measure the durability of rock,which has an inverse relationship with the decay constant λ.ReplacingINin Eq.(13)withI0/2,the half-life(N1/2)can be obtained:

This model is a descriptive model rather than a causative model.It describes rock’s behavior under cyclic worsening action but does not reveal why they behave that way.This model’s parameters can effectively evaluate the reliability of rock under cyclic worsening action and guide engineering decision-making.

The integrity of rock refers to the integrity of rock structure. It includes the physical and mechanical properties of rock, such as strength,hardness,etc.Many parameters can be used to represent the integrity of rock. In this paper, three parameters, i.e. compressive strength, elastic modulus, and cohesion, were selected to measure the integrity of rock. The decay constant (λ) and half-life(N1/2) value of the three mechanical parameters with different confining pressures were calculated by Eqs.(13)and(14),as shown in Table 7. It is noted that the decay constant (λ) values were obtained by the exponential fitting. The goodness of fit (R2) is high(>0.9), which indicates that the model can characterize the mechanical degradation of rock under any freeze-thaw cycles.

As shown in Table 7, the disintegration rates of the compressive strength and the elastic modulus decrease with the confining pressure. The disintegration rate of compressive strength with the confining pressure of 0 MPa (0.548%, i.e.λ = -0:00548) is 1.96 times that of compressive strength with the confining pressure of 5 MPa (0.278%, i.e. λ = - 0:00278). The disintegration rate of elastic modulus with the confining pressure of 0 MPa (0.795%, i.e. λ = -0:00795) is 1.45 times that of the elastic modulus with the confining pressure of 5 MPa (0.546%, i.e.λ = - 0:00546). The half-life values of compressive strength and elastic modulus increase with the confining pressure. The half-life value of compressive strength under the confining pressure of 5 MPa is about 249 cycles, which is 1.98 times that of compressive strength under the confining pressure of 0 MPa (126 cycles).The half-life value of elastic modulus under the confining pressure of 5 MPa is about 127 cycles, which is 1.46 times that of the elastic modulus under the confining pressure of 0 MPa (87 cycles). The compressive strength’s half-value is longer than that of the elastic modulus under the same confining pressure. It is revealed that the higher the confining pressure, the greater the ability of the samples to resist the damage induced by freezethaw cycles.

Table 6 Cohesion and internal frictional angle under different freeze-thaw cycles.

Table 7 Decay constant and half-life of mechanical parameters under different confining pressures.

Fig.13. Evolutions of the (a) triaxial compressive strength and (b) elastic modulus of samples (σ3 = 5 MPa).

5. Deterioration mechanisms of anhydrite rock under cyclic freeze-thaw

As discussed above, freeze-thaw cycles can cause irreversible damages to anhydrite samples. Fig.19 depicts the damage appearances during the freeze-thaw experiments.As shown in Fig.19,two obvious macrocracks appear in the sample after 70 cycles.With the progress of the experiment, the width and number of macrocracks on the sample surface increase gradually. At 105 cycles, the macrocracks expand obviously,and the sample reaches the failure state.

Generally, the rock damage caused by freeze-thaw cycles contains various mechanisms, such as volume expansion mechanism,hydrostatic pressure mechanism, capillary mechanism, and crystallization pressure mechanism(Zhou et al.,2020).It implies that when the freeze-thaw rate is high,the volume expansion mechanism and hydrostatic pressure mechanism play critical roles in the freezethaw damage to the rock. The mechanism of volume expansion is that during the freezing process, the water in the rock freezes into ice, resulting in a 9.08% volume expansion. However, due to the limited pore space,the volume expansion of ice is limited,resulting in expansion force. When the expansion force exceeds the bearing capacity of rock,new cracks will initiate(Berto and Lazzarin,2009).As for the mechanism of hydrostatic pressure, it is characteristic in the thawing process, and the ice thaws into the water, which produces seepage force in the rock mass(Yang et al.,2018).

Anhydrite samples are easy to expand and soften when they meet water (Serafeimidis and Anagnostou, 2015). Apart from the damage mechanisms for rock caused by freeze-thaw cycles mentioned above, there exist water expansion mechanism and water softening mechanism in the freeze-thaw damage to anhydrite samples, as shown in Fig. 20. As mentioned in Section 3.1,some white powders and small flake minerals were observed in the freezing water during the test process. Thus, we can deduce that the water softening mechanism plays a critical role in freeze-thaw damage to anhydrite samples. Additionally, the softening of anhydrite samples in water can be divided into physical and chemical softening. The water physical softening is mainly due to the water entering into the pores and microcracks of rock and adhering to the surface of minerals to produce lubrication, which reduces the friction between minerals. The water chemical softening of anhydrite samples is characterized by combining CaSO4and water to produce CaSO4∙2H2O. Meanwhile, CaSO4∙2H2O is slightly soluble in water. The crystal bond at the tip of the microcrack is hydrolyzed,which weakens the bonding force between minerals.The chemical dissolution and precipitation reactions of gypsum and anhydrite are

Fig. 20. Freeze-thaw damage mechanisms to anhydrite rock.

Fig. 21. Relations between the damage variable and cycles.

Simultaneously, the absorbed water enters into CaSO4crystal layers to form a hydration film interlayer,leading to the lattice and volume expansion of samples.

Another essential concern is to understand the influences of freeze-thaw cycles on anhydrite rock from the macro and micro aspects.As for the macro aspect,the relations between the damage variable and the compressive strength were studied. The damage variable can be calculated based on the changes in the elastic modulus of the samples (Lemaitre and Desmorat, 2005):

whereDis the damage variable,E0is the elastic modulus of the samples at the initial state,andENis the elastic modulus of samples afterNfreeze-thaw cycles.

Fig.18. Microcracks characteristics of anhydrite samples: (a) SEM image; and (b) Concept graph.

Fig.19. Damage phenomenon during the freeze-thaw tests.

The damage variable calculated by Eq. (18) is shown in Fig. 21.The figure depicts that as the number of freeze-thaw cycles increases, the damage variable increases progressively. Generally speaking, the damage variable decreases with the confining pressure. It is revealed that the confining pressure has a specific inhibitory effect on the damage. However, when the number of cycles was 60,the damage variable under 3 MPa confining pressure is slightly larger than that under 0 MPa confining pressure. This may be due to the heterogeneity of rock.The relation between the compressive strength and the damage variable of samples under different confining pressures is depicted in Fig.22.The compressive strength deteriorates exponentially with the damage variable,revealing that with the increase of cycles,the damage accumulates,resulting in the decline of rock’s mechanical properties.

As for the micro aspect,the evolutions of the S1sample’s texture detected by the SEM tests are shown in Fig.23.As depicted in Fig.23,as the number of freeze-thaw cycles increases,the surface roughness and the sample’s pore area increase gradually.When the number of freeze-thaw cycles was 30,many pores were formed on the surface of the anhydrite rock.After 120 freeze-thaw cycles,honeycomb and pitted surface appeared on the surface of the sample.As mentioned above, the water softening mechanism plays a critical role in the freeze-thaw damage to anhydrite samples, especially the water chemical softening mechanism. Due to the water softening mechanism, the minerals of anhydride rock are more likely to dissolve and peel off during the freeze-thaw weathering process.Thus, it can be concluded that the freeze-thaw cycles significantly influence the microstructure of anhydrite samples.

Fig. 22. Relations between the compressive strength and the damage variable of samples: (a) σ3 = 0 MPa; (b) σ3 = 3 MPa; and (c) σ3 = 5 MPa.

Fig. 23. Evolutions of the S1 sample’s texture during the freeze-thaw tests.

Fig. 24. Relations between the compressive strength and the porosity of samples.

Then, the relations between the compressive strength and the porosity of anhydrite samples are plotted in Fig.24.As the porosity increases, the average compressive strength under different confining pressures decreases exponentially. It is concluded that during the freeze-thaw cycles, the expansion of pores and microcracks leads to the degradation of rock’s physical and mechanical characteristics.The variations of the average compressive strength with the porosity of the samples can be expressed by

where σ01, σ31, and σ51are the compressive strengths under the confining pressures of 0 MPa,3 MPa,and 5 MPa,respectively;andpis the porosity of the anhydrite rock.

6. Conclusions

The following conclusions can be drawn from the analysis above:

(1) The mass variation and porosity of anhydrite samples increase with the number of freeze-thaw cycles, for example,the average mass variation and porosity change from 0.26%(N= 30) to 0.91% (N= 120) and 0.64% (N= 0) to 1.12%(N= 120), respectively. The pore size of anhydrite rock is mainly concentrated in the range of 0.001-10 μm. As the number of freeze-thaw cycles increases,there is a growth in the proportion of macropores and mesopores. In contrast,the proportion of micropores shows a declining trend.

(2) As the number of freeze-thaw cycles increases,the plasticity characteristics of anhydrite samples increase. At the same time, the UCS, triaxial compressive strength, cohesion, and elastic modulus decrease exponentially. Meanwhile, the internal friction angle is basically unchanged under various freeze-thaw cycles.

(3) With the increase of confining pressure, the disintegration rates of the compressive strength and the elastic modulus decrease,and the corresponding half-life values increase.For example, the disintegration rate and half-life value of the compressive strength change from 0.55% (σ3= 0 MPa) to 0.28% (σ3= 5 MPa) and from 126 cycles (σ3= 0 MPa) to 249 cycles(σ3= 5 MPa),respectively.It is revealed that the greater the confining pressure, the greater the ability of the anhydrite samples to resist the damage induced by freezethaw cycles.

(4) It is revealed that the water chemical softening mechanism plays an essential role in the damage induced by freeze-thaw cycles to the anhydrite rock. Furthermore, the compressive strength of anhydrite samples decreases exponentially with the porosity and the damage variable expressed by the elastic modulus.Additionally,it is concluded that the freezethaw cycles significantly impact the macroscopic and microscopic damage of anhydrite rock.

However, these experimental results were acquired from the water fully saturated anhydrite samples at -20°C to 20°C.Meanwhile, the freeze-thaw effects on the water expansion properties of anhydrite samples were not investigated. In the future,other test conditions (different temperature and saturation degrees) and the expansion properties of anhydrite samples under freeze-thaw cycles should be studied.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors would like to thank the Civil Engineering Testing Center of Chongqing University and the State Key Laboratory of Coal Mine Disaster Dynamics and Control,Chongqing University,China,for their experiment supports. The authors also like to thank the National Natural Science Foundation of China for financial support(Grant No.51578091).