# Study on Acoustic Emission and Damage Mechanical Properties of Freeze-Thaw Sandstone under Uniaxial Compression

Authors: Bo Liang; Gengshe Yang; Jinjie Yu
Journal: Geofluids
 (2022)

---

## Abstract

The damage strength of freeze-thaw rock provides an important reference for stability evaluations used during rock engineering in cold regions. In this paper, real-time acoustic emission tests of saturated sandstone are performed after various freeze-thaw cycles to study the uniaxial compressive strength and deformation characteristics of the resulting materials. The macro-meso damage evolution law of loaded sandstone is studied under the action of freeze-thaw cycles. The results show the following: (1) The saturated water absorption of sandstone increases, the peak strength and elastic modulus loss rates of sandstone increase linearly, and the frost resistance of the rock decreases with the number of freeze-thaw cycles. The sandstone failure mode gradually shifts from splitting failure to complex splitting shear failure of the failure surface. (2) If fewer than 10 freeze-thaw cycles are applied, the ring count signals at the compaction stage and after the peak strength is reached are extremely weak under a uniaxial compression load. With additional freeze-thaw cycles, damage inside the rock accumulates gradually, and the ring count signal appears during the rock compaction stage, fluctuates up and down, and continues until the peak strength is reached. When the compressive strength reaches its peak, the ring count intensity signal increases suddenly, and the frequency is high. After the strength reaches its peak, the acoustic emission signal shows that the rock sample still has some residual strength. As the number of freeze-thaw cycles increases, the cumulative ring count of sandstone gradually changes from the jumping stage to gradual growth. The acoustic emission characteristic parameters and ring count reflect damage to and expansion of freeze-thaw sandstone. (3) The cumulative extent of rock damage reaches the threshold value under loading and increases linearly until the rock is destroyed. When more freeze-thaw cycles are used, the time required for the rock to reach this threshold value is shorter, and the time required for sandstone damage is reduced gradually. These results provide a reference for the study of freeze-thaw damage and rock stability in cold regions.


---

## Body

## 1. Introduction

In cold regions, rocks are subject to seasonal freeze-thaw cycles. The temperature difference between day and night cycles has an important impact on rock mechanical properties and creates a series of geotechnical engineering problems. For example, rock slope collapses and landslides are caused by the effect of perennial freeze-thaw cycles. Frost heaving and cracking of rocks lead to tunnel instability, and frost heaving and thawing settlement appear at the subgrade and foundation. Therefore, real-time sandstone acoustic emission testing under freeze-thaw cycles and load can provide theoretical support for geotechnical engineering stability evaluations and support the prevention and control of freeze-thaw disasters in mines, water conservation areas, transportation systems, and other places in cold regions.Many scholars have studied rock mass mechanical properties and damage laws under the influence of freeze-thaw cycles [1–9]. Shi et al. [10] analyzed the effects of freeze-thaw cycles and confining pressures on the mechanical properties of red sandstone. Using freeze-thaw cycles and triaxial compression tests, full stress-strain curves were obtained for various freeze-thaw cycles and confining pressures. The extent of red sandstone degradation was considered quantitatively using various mechanical parameters such as the ultimate stress, elastic modulus, and Poisson’s ratio. Song et al. [11] investigated the time-dependent mechanical properties of rock masses in cold regions under the effects of freeze-thaw cycling and long-term loading. Triaxial multilevel loading and unloading creep tests were performed on saturated red sandstone samples that were subjected to various numbers of freeze-thaw cycles. The effects of freeze-thaw cycles and confining pressure on the creep properties, long-term strength, and creep failure mode of the rock were analyzed. Man et al. [12] used sandstone from the slope of the Baorixile open-pit mining area in Hulunbuir City, Inner Mongolia, to perform split Hopkinson pressure bar tests after various freeze-thaw cycles. The test results showed that the extent of sandstone crushing increases with the freeze-thaw cycle time and strain rate. Zhang et al. [13, 14] conducted freeze-thaw cycle compression tests on Shaanxi red sandstone and analyzed the effect of the number of freeze-thaw cycles on the rock mass deterioration law, density, wave velocity, and characteristic mechanical parameters. They also studied the influences of freeze-thaw cycles and confining pressure on the rock microstructure; physical and mechanical properties; and failure mode. Jia and Xing [15, 16] observed the pore structure of sandstone under the influence of freeze-thaw cycles using backscatter SEM (scanning electron microscope, SEM) and explored the mechanisms by which freeze-thaw cycles damage sandstone. Kiyoo Mogi [17] performed a large number of cyclic loading and unloading tests on rock and discussed the acoustic emission characteristics of rock under uniaxial compression. Su et al. [18] carried out experiments on the influence of freeze-thaw cycle on the acoustic emission characteristics of granite and characterized the influence of rock on the uniaxial damage failure process of rocks in the number of freeze-thaw cycles from acoustic emission ringing technology and energy characteristics. Li et al. [19] obtained the mechanical properties and acoustic emission parameters characteristics of uniaxial compression rock by synchronous acoustic emission testing. Liu et al. [20] studied the tensile splitting damage characteristics of freeze-thaw sandstone by acoustic emission technology. Based on acoustic emission, the evolution law of damage variable of freeze-thaw sandstone is studied according to the cumulative ringing count. Zhao et al. [21] conducted a freeze-thaw cycle test on the immersed rubble and analyzed the development of internal cracks in the specimen during the freeze-thaw process by using an acoustic emission instrument. The authors conducted an in-depth study on the degradation mechanism of rubble from a micro perspective, but did not consider the change of acoustic emission characteristics during external loading. Wu et al. [22] and Chen et al. [23] carried out the acoustic emission test of rock after freeze-thaw cycles under different loading conditions. The variation of some acoustic emission parameters with the number of freeze-thaw cycles is obtained. However, there are still some limitations in understanding the acoustic emission characteristics of rock failure under different environments and test conditions.Freeze-thaw rock damage caused by the long-term impact of a freeze-thaw environment has not only the obvious time effect, but also a substantial spatial effect due to the influence of original rock mass defects. Therefore, freeze-thaw rock damage identification and detection methods must be at different levels in order to reveal the freeze-thaw rock mass damage mechanism more effectively [24]. Internal rock damage expansion under an external load releases strain energy in the form of an elastic wave. This failure process is accompanied by the release of an acoustic emission signal. Therefore, the acoustic emission characteristic parameters contain precursor information regarding progressive damage [25–38]. This paper considers real-time acoustic emission tests of frozen-thawed sandstone under load. The dynamic frozen-thawed sandstone damage process can be analyzed via its characteristic acoustic emission parameters. In addition, correlations between macroscopic and microscopic frozen-thawed sandstone damage can be analyzed using an organic combination of macroscopic mechanical and acoustic emission characteristic parameters. This is of great significance for the prediction of rock engineering stability in cold regions and the study of freeze-thaw rock damage mechanisms.


## 2. Materials and Methods

### 2.1. Specimen Preparation

Rock samples were taken from red sandstone located in Dijiahe area, Baishui County, Shaanxi Province. The rock samples had good uniformity and integrity; high strength; and a stable structure. Field collection was used to obtain uniform rock samples from the same stratum as much as possible. The rock samples were marked above and below the stratum. Large, intact rock samples without obvious damage were selected and transported to the geotechnical laboratory of Xi’an University of Science and Technology. Large rock samples were processed via core drilling, cutting, and grinding to meet test requirements. Samples with good structure were selected for group numbering (Figure1). The experimental rock samples were 50 mm in diameter and 100 mm in height. They were cemented with sandy gravel and were argillaceous. The sample surfaces were brownish red with uniform texture, uniform color, small internal pores, and good compactness. The particle size was within 0.05~0.25 mm. During freeze-thaw cycles, all frozen rock samples were saturated in an open system.Figure 1
Grouping and numbering of sandstone specimens.The rock samples were divided into five groups: F-0, F-5, F-10, F-20, and F-30. Each group contained five rock samples. Later, 0, 5, 10, 20, and 30 freeze-thaw cycles were applied to the respective groups.The dried rock samples were saturated fully for 24 h using a vacuum pressure saturation instrument and weighed. Based on the characteristics of diurnal temperature differences in cold regions and research results from relevant scholars, it was determined that freezing at −20 °C for 12 h and thawing at +20 °C for 12 h represents a freeze-thaw cycle. In order to prevent water loss from the rock during the freeze-thaw cycles, the rock samples were soaked and saturated for 12 h at the end of each freezing-thaw cycle. Water was supplemented in a timely manner, and the rock sample saturation (mp) was recorded.Real-time uniaxial compression AE tests of the rock samples were performed in the geotechnical engineering laboratory of Xi’an University of Science and Technology. The laboratory included RTX-1500 electro-hydraulic servo-controlled triaxial test systems used to evaluate low-temperature, high-pressure rock, and soil from GCTS Company of the United States and an AE-8 full digital AE monitoring system produced by PAC Company of the United States. The test device is shown in Figure2. The AE-8 full digital acoustic emission monitoring system was composed mainly of a Micro-ll host, probe, and preamplifier. The acquisition and monitoring system had 24 channel signal input ports, a sampling frequency of 10 MSPS, an 18 bit converter to record data, a filtering broadband range of 10~1200 KHz, a maximum operating temperature of 150 °C, and a maximum pressure of 140 MPa. The preamplifier provided 40 dB of fixed gain. The threshold value of the test system was set to 40 dB after considering noise from the environment. The peak definition time was 50 μs, the shock definition time was 200 μs, and the shock locking time was 300 μs. In this experiment, 3- and 4-channel acoustic emission data were collected. The acquisition frequencies of the 3- and 4-channel probes were 51.76 KHz and 64.8 KHz, respectively. The sensor installation and data acquisition system are shown in Figure 3.Figure 2
The uniaxial compression and acoustic emission testing systems.Figure 3
Sensor installation and data acquisition.
(a)
Sensor installation(b)
Data collectionAfter the acoustic emission parameters were prepared, two transducer probes (No. 3 and No. 4) were arranged symmetrically in the middle of the rock sample. The angle between the two transducer probes was 180°, and the probes were arranged perpendicular to the middle of the rock sample. In order to ensure good coupling between the sensor and rock sample surfaces, a rubber sleeve was installed on the rock sample surface, and then petroleum jelly was smeared between the sensor and the rubber sleeve. Then, rubber reinforcement was fixed to ensure that the elastic wave propagation generated during sample failure was received by the sensor. During the test, the compression system operated synchronously with the acoustic emissions. The test loading system used displacement control loading, and the loading rate was 0.1 mm/min. The acoustic emission characteristic parameters of channel 3 and channel 4 were obtained synchronously. The basic physical properties of the rock samples are shown in Table1.Table 1
Changes in the physical parameters of red sandstone after freeze-thaw cycling.
Freeze-thaw cyclesQuality/gMass change rate/%Wave velocity/km·s-1Variation rate of wave velocity/%Open porosity/%Leeb hardness/HL0488.7103.83200.022427385487.20− 0.327734.13257.8418580380.0272373410486.11− 0.409674.2029.6555323590.02806728.620492.02− 0.471124.255511.051670150.0281675.830484.30− 0.479314.273511.521398750.0283571.6


## 2.1. Specimen Preparation

Rock samples were taken from red sandstone located in Dijiahe area, Baishui County, Shaanxi Province. The rock samples had good uniformity and integrity; high strength; and a stable structure. Field collection was used to obtain uniform rock samples from the same stratum as much as possible. The rock samples were marked above and below the stratum. Large, intact rock samples without obvious damage were selected and transported to the geotechnical laboratory of Xi’an University of Science and Technology. Large rock samples were processed via core drilling, cutting, and grinding to meet test requirements. Samples with good structure were selected for group numbering (Figure1). The experimental rock samples were 50 mm in diameter and 100 mm in height. They were cemented with sandy gravel and were argillaceous. The sample surfaces were brownish red with uniform texture, uniform color, small internal pores, and good compactness. The particle size was within 0.05~0.25 mm. During freeze-thaw cycles, all frozen rock samples were saturated in an open system.Figure 1
Grouping and numbering of sandstone specimens.The rock samples were divided into five groups: F-0, F-5, F-10, F-20, and F-30. Each group contained five rock samples. Later, 0, 5, 10, 20, and 30 freeze-thaw cycles were applied to the respective groups.The dried rock samples were saturated fully for 24 h using a vacuum pressure saturation instrument and weighed. Based on the characteristics of diurnal temperature differences in cold regions and research results from relevant scholars, it was determined that freezing at −20 °C for 12 h and thawing at +20 °C for 12 h represents a freeze-thaw cycle. In order to prevent water loss from the rock during the freeze-thaw cycles, the rock samples were soaked and saturated for 12 h at the end of each freezing-thaw cycle. Water was supplemented in a timely manner, and the rock sample saturation (mp) was recorded.Real-time uniaxial compression AE tests of the rock samples were performed in the geotechnical engineering laboratory of Xi’an University of Science and Technology. The laboratory included RTX-1500 electro-hydraulic servo-controlled triaxial test systems used to evaluate low-temperature, high-pressure rock, and soil from GCTS Company of the United States and an AE-8 full digital AE monitoring system produced by PAC Company of the United States. The test device is shown in Figure2. The AE-8 full digital acoustic emission monitoring system was composed mainly of a Micro-ll host, probe, and preamplifier. The acquisition and monitoring system had 24 channel signal input ports, a sampling frequency of 10 MSPS, an 18 bit converter to record data, a filtering broadband range of 10~1200 KHz, a maximum operating temperature of 150 °C, and a maximum pressure of 140 MPa. The preamplifier provided 40 dB of fixed gain. The threshold value of the test system was set to 40 dB after considering noise from the environment. The peak definition time was 50 μs, the shock definition time was 200 μs, and the shock locking time was 300 μs. In this experiment, 3- and 4-channel acoustic emission data were collected. The acquisition frequencies of the 3- and 4-channel probes were 51.76 KHz and 64.8 KHz, respectively. The sensor installation and data acquisition system are shown in Figure 3.Figure 2
The uniaxial compression and acoustic emission testing systems.Figure 3
Sensor installation and data acquisition.
(a)
Sensor installation(b)
Data collectionAfter the acoustic emission parameters were prepared, two transducer probes (No. 3 and No. 4) were arranged symmetrically in the middle of the rock sample. The angle between the two transducer probes was 180°, and the probes were arranged perpendicular to the middle of the rock sample. In order to ensure good coupling between the sensor and rock sample surfaces, a rubber sleeve was installed on the rock sample surface, and then petroleum jelly was smeared between the sensor and the rubber sleeve. Then, rubber reinforcement was fixed to ensure that the elastic wave propagation generated during sample failure was received by the sensor. During the test, the compression system operated synchronously with the acoustic emissions. The test loading system used displacement control loading, and the loading rate was 0.1 mm/min. The acoustic emission characteristic parameters of channel 3 and channel 4 were obtained synchronously. The basic physical properties of the rock samples are shown in Table1.Table 1
Changes in the physical parameters of red sandstone after freeze-thaw cycling.
Freeze-thaw cyclesQuality/gMass change rate/%Wave velocity/km·s-1Variation rate of wave velocity/%Open porosity/%Leeb hardness/HL0488.7103.83200.022427385487.20− 0.327734.13257.8418580380.0272373410486.11− 0.409674.2029.6555323590.02806728.620492.02− 0.471124.255511.051670150.0281675.830484.30− 0.479314.273511.521398750.0283571.6


## 3. Uniaxial Compression Damage Analysis of Freeze-Thaw-Exposed Sandstone

### 3.1. Saturated Water Absorption and Frost Resistance

The saturated water absorption of a rock sample indirectly reflects its index of internal pores. The denser the rock, the better its integrity and the smaller its saturated water absorption. The saturated water absorption of rock (ωsa) is the difference between the saturated (mp) and dry (ms) rock masses before freezing and thawing expressed as a percent of the dry rock mass (ms):
(1)ωsa=mp−msms×100%.The frost resistance coefficient (Kf) reflects the mechanical properties of rock under freezing and thawing conditions. The frost resistance of rock refers to the ratio of the average saturated uniaxial compressive strength of a rock sample before freezing and thawing (Rs¯) to that after freezing and thawing (Rf¯):
(2)Kf=Rf¯Rs¯.The saturated water absorption of a rock sample indirectly characterizes the change law that governs its internal pores during freeze-thaw cycles. The frost resistance coefficient of rock reflects the law that governs the deterioration of its mechanical properties. The relationship between saturated water absorption and the frost resistance coefficient of sandstone after various freeze-thaw cycles is shown in Figure4.Figure 4
The relationship between the saturated water absorption rate and the frost resistance coefficient of sandstone after various freeze-thaw cycles.In Figure4, the saturated water absorption of sandstone increases with the number of freeze- thaw cycles. The increase in the saturated water absorption gradually slows as the number of freeze-thaw cycles increases. The average frost resistance coefficient of sandstone decreases significantly due to the number of freeze-thaw cycles. The larger the saturated water absorption of a rock sample, the smaller its frost resistance coefficient. This is because, during a freeze-thaw cycle, the differences between the expansion coefficients of various minerals in sandstone cause local damage to the rock samples. As more freeze-thaw cycles occur, the pore structure inside the rock sample expands, resulting in an increase in its saturated water absorption. Second, as the saturated water absorption of sandstone increases, the water in the sandstone pores freezes at a lower temperature, the volume increases, and damage to the microstructure increases. As freeze-thaw cycles accumulate, the damage inside the rock gradually expands and increases, eventually leading to decreases in the rock frost resistance coefficient.


### 3.2. Analysis of Characteristic Mechanical Parameters

The peak strength and elastic modulus are important characteristic mechanical parameters of rock samples. The peak strengthα (Formula (3)) and elastic modulus β (Formula (4)) damage rates are defined to reflect the degradation law that governs the characteristic mechanical parameters of sandstone under freeze-thaw cycling:
(3)α=F0−FnF0×100%,(4)β=E0−EnE0×100%.where α is the peak strength loss rate; β is the elastic modulus loss rate; F0 is the peak strength at 0 freeze-thaw cycles; Fn is the peak strength at n freeze-thaw cycles; E0 is the elastic modulus at 0 freeze-thaw cycles; and En is the elastic modulus at n freeze-thaw cycles.Using uniaxial sandstone compression tests performed under after various freeze-thaw cycles, the relationships between the number of freeze-thaw cycles and the loss rates of characteristic mechanical parameters are plotted using the average peak strength and elastic modulus (Figure5).Figure 5
Relationships between freeze-thaw cycle counts and the loss rates of characteristic mechanical parameters.
(a)
Line graph(b)
Fitting curveFigure5 shows that the peak strength and elastic modulus loss rate of sandstone increase linearly with the number of freeze-thaw cycles. The peak strength loss rate reaches 47.27%, and the elastic modulus loss rate reaches 60.35% after 30 freeze-thaw cycles. This indicates that the number of freeze-thaw cycles has an obvious degradation effect on the peak strength and elastic modulus. The peak strength and elastic modulus loss rates increase quickly during the first 10 freeze-thaw cycles, but decrease after 10 freeze-thaw cycles.


### 3.3. Failure Mode Analysis of Freeze-Thaw Sandstone

Comparing and analyzing sandstone failure modes after various freeze-thaw cycles enables one to divide sandstone failure into splitting failure, shear failure, and splitting-shear mixed failure, as shown in Figure6.Figure 6
Uniaxial compression failure modes of freeze-thaw cycled sandstone.
(a)
Splitting failure(b)
Shear failure(c)
Splitting-shear mixed failureAccording to Griffith’s theory, a tiny crack tip in a rock sample produces stress concentration under the action of an external force. The crack begins to expand when the aggregation energy reaches a certain value. When the rock sample in the low freezing-thawing cycle is subject to an external load, the crack expands in a direction that is perpendicular to that of the maximum tensile stress, forming a typical splitting failure. In a freeze-thaw environment, the volume of mineral particles shrinks, the water phase in the pores becomes ice, and volume expansion causes non-coordinated shrinkage and expansion across the particle boundary as the rock sample temperature decreases. This produces a frost heaving force between mineral particles and within pores that destroys the connections between mineral particles with weak cementation strength and produces meso-structural damage. When the temperature rises, the pore ice melts, but the bond strengths between mineral particles and microstructural changes cannot be restored completely. This is accompanied by the release of freezing stress and the migration of water and results in accelerated microstructural damage. During additional freeze-thaw cycles, the freezing stress cycle alternately acts on the rock skeleton. The effect of external load promotes further slip and dislocation among mineral particles, the initiation and expansion of pores, and expansion of and gradual connections between damaged areas. This greatly changes the internal mesoscopic structure of the rock sample, resulting in a decrease in the rock bearing capacity. Under a uniaxial compression load, displacement and rotation of broken rock blocks occur with relative ease, resulting in changes in the principal stress direction. The more complex the failure surface formed in the rock sample, the more complex the failure surface formed in the rock. Each failure surface is interconnected and intersects with others to form a failure zone. The rock sample is thus into fragments, and its failure mode gradually changes to that of splitting shear mixed failure. The internal damage to the rock sample is most serious after 30 freeze-thaw cycles. The internal failure surfaces within the rock sample intersect other to form a failure zone, and the degree of rock fragmentation is high.


## 3.1. Saturated Water Absorption and Frost Resistance

The saturated water absorption of a rock sample indirectly reflects its index of internal pores. The denser the rock, the better its integrity and the smaller its saturated water absorption. The saturated water absorption of rock (ωsa) is the difference between the saturated (mp) and dry (ms) rock masses before freezing and thawing expressed as a percent of the dry rock mass (ms):
(1)ωsa=mp−msms×100%.The frost resistance coefficient (Kf) reflects the mechanical properties of rock under freezing and thawing conditions. The frost resistance of rock refers to the ratio of the average saturated uniaxial compressive strength of a rock sample before freezing and thawing (Rs¯) to that after freezing and thawing (Rf¯):
(2)Kf=Rf¯Rs¯.The saturated water absorption of a rock sample indirectly characterizes the change law that governs its internal pores during freeze-thaw cycles. The frost resistance coefficient of rock reflects the law that governs the deterioration of its mechanical properties. The relationship between saturated water absorption and the frost resistance coefficient of sandstone after various freeze-thaw cycles is shown in Figure4.Figure 4
The relationship between the saturated water absorption rate and the frost resistance coefficient of sandstone after various freeze-thaw cycles.In Figure4, the saturated water absorption of sandstone increases with the number of freeze- thaw cycles. The increase in the saturated water absorption gradually slows as the number of freeze-thaw cycles increases. The average frost resistance coefficient of sandstone decreases significantly due to the number of freeze-thaw cycles. The larger the saturated water absorption of a rock sample, the smaller its frost resistance coefficient. This is because, during a freeze-thaw cycle, the differences between the expansion coefficients of various minerals in sandstone cause local damage to the rock samples. As more freeze-thaw cycles occur, the pore structure inside the rock sample expands, resulting in an increase in its saturated water absorption. Second, as the saturated water absorption of sandstone increases, the water in the sandstone pores freezes at a lower temperature, the volume increases, and damage to the microstructure increases. As freeze-thaw cycles accumulate, the damage inside the rock gradually expands and increases, eventually leading to decreases in the rock frost resistance coefficient.


## 3.2. Analysis of Characteristic Mechanical Parameters

The peak strength and elastic modulus are important characteristic mechanical parameters of rock samples. The peak strengthα (Formula (3)) and elastic modulus β (Formula (4)) damage rates are defined to reflect the degradation law that governs the characteristic mechanical parameters of sandstone under freeze-thaw cycling:
(3)α=F0−FnF0×100%,(4)β=E0−EnE0×100%.where α is the peak strength loss rate; β is the elastic modulus loss rate; F0 is the peak strength at 0 freeze-thaw cycles; Fn is the peak strength at n freeze-thaw cycles; E0 is the elastic modulus at 0 freeze-thaw cycles; and En is the elastic modulus at n freeze-thaw cycles.Using uniaxial sandstone compression tests performed under after various freeze-thaw cycles, the relationships between the number of freeze-thaw cycles and the loss rates of characteristic mechanical parameters are plotted using the average peak strength and elastic modulus (Figure5).Figure 5
Relationships between freeze-thaw cycle counts and the loss rates of characteristic mechanical parameters.
(a)
Line graph(b)
Fitting curveFigure5 shows that the peak strength and elastic modulus loss rate of sandstone increase linearly with the number of freeze-thaw cycles. The peak strength loss rate reaches 47.27%, and the elastic modulus loss rate reaches 60.35% after 30 freeze-thaw cycles. This indicates that the number of freeze-thaw cycles has an obvious degradation effect on the peak strength and elastic modulus. The peak strength and elastic modulus loss rates increase quickly during the first 10 freeze-thaw cycles, but decrease after 10 freeze-thaw cycles.


## 3.3. Failure Mode Analysis of Freeze-Thaw Sandstone

Comparing and analyzing sandstone failure modes after various freeze-thaw cycles enables one to divide sandstone failure into splitting failure, shear failure, and splitting-shear mixed failure, as shown in Figure6.Figure 6
Uniaxial compression failure modes of freeze-thaw cycled sandstone.
(a)
Splitting failure(b)
Shear failure(c)
Splitting-shear mixed failureAccording to Griffith’s theory, a tiny crack tip in a rock sample produces stress concentration under the action of an external force. The crack begins to expand when the aggregation energy reaches a certain value. When the rock sample in the low freezing-thawing cycle is subject to an external load, the crack expands in a direction that is perpendicular to that of the maximum tensile stress, forming a typical splitting failure. In a freeze-thaw environment, the volume of mineral particles shrinks, the water phase in the pores becomes ice, and volume expansion causes non-coordinated shrinkage and expansion across the particle boundary as the rock sample temperature decreases. This produces a frost heaving force between mineral particles and within pores that destroys the connections between mineral particles with weak cementation strength and produces meso-structural damage. When the temperature rises, the pore ice melts, but the bond strengths between mineral particles and microstructural changes cannot be restored completely. This is accompanied by the release of freezing stress and the migration of water and results in accelerated microstructural damage. During additional freeze-thaw cycles, the freezing stress cycle alternately acts on the rock skeleton. The effect of external load promotes further slip and dislocation among mineral particles, the initiation and expansion of pores, and expansion of and gradual connections between damaged areas. This greatly changes the internal mesoscopic structure of the rock sample, resulting in a decrease in the rock bearing capacity. Under a uniaxial compression load, displacement and rotation of broken rock blocks occur with relative ease, resulting in changes in the principal stress direction. The more complex the failure surface formed in the rock sample, the more complex the failure surface formed in the rock. Each failure surface is interconnected and intersects with others to form a failure zone. The rock sample is thus into fragments, and its failure mode gradually changes to that of splitting shear mixed failure. The internal damage to the rock sample is most serious after 30 freeze-thaw cycles. The internal failure surfaces within the rock sample intersect other to form a failure zone, and the degree of rock fragmentation is high.


## 4. Damage Evolution of Freeze-Thaw Loaded Sandstone Based on Acoustic Emission Characteristic Parameters

### 4.1. Damage Characteristic Analysis Based on the Acoustic Emission Ring Count

According to the real-time acoustic emission test of the whole process of uniaxial compression of sandstone under different freeze-thaw cycles, the acoustic emission ring count and the change curve of sandstone stress with time can be extracted. The damage characteristics of sandstone during uniaxial compression can be compared and analyzed by ring count and sandstone stress-time curve. The relationship between stress and ring count of 0, 5, 10, 20, and 30 times with time in sandstone is shown in Figure7.Figure 7
The relationship between stress and the ring count in sandstone as a function of time. The statistical range of the ring count is0~200×103.
(a)
0 cycles(b)
5 cycles(c)
10 cycles(d)
20 cycles(e)
30 cyclesAs shown in Figures7(a) and 7(b), when fewer than 10 freeze-thaw cycles are used, the sandstone ring count is almost negligible before 1500 s. This initial uniaxial compression stage corresponds to the rock compaction stage and occurs mainly because the freeze-thaw cycle produces no obvious damage to the internal structure of the rock and the structural characteristics of the changes that occur within the rock are not obvious. The internal rock structure is uniform and has a certain bearing capacity. In this stage, the internal pores within the rock are compacted, and crystal dislocation is not obvious. Changes in the internal rock structure under load produce little signal frequency oscillation. Thus, there is little acoustic emission ringing. As time passes, the rock gradually enters the elastic stage under the action of a load. As internal damage within the rock accumulates gradually, the ring count gradually appears and fluctuates, indicating that the internal structure of the rock has changed significantly. The crystals inside the rock began to undergo obvious dislocation and microcrack initiation begins. At the same time, along with the acoustic emission signal, the number of oscillation of the signal over the threshold signal is more and more. Microcrack development instability leads to fluctuation of the ring count, and internal damage to the rock structure increases gradually. The plastic stage occurs from 2700 s to the peak strength of the rock. Stress growth within the rock slows mainly due to the gradual development and further expansion of microcracks in the rock. Microcracks gather to form a fracture surface gradually, internal damage deformation within the rock is large, and the acoustic emission signal decreases.During the failure stage, the rock stress reaches its maximum and the internal failure surface of the rock is penetrated and completely destroyed, releasing large acoustic emission signals with high strength and frequency. The ring count is concentrated in the sudden increase of peak strength. In the post-peak stage, the number of freeze-thaw cycles decreases, and the stress within the rock decreases linearly to 0 MPa. The rock is brittle, and there is no acoustic emission signal.Rock samples that have undergone 10 freeze-thaw cycles are shown in Figures7(c), 7(d), and 7(e). Unlike rock samples that have not undergone 10 freeze-thaw cycles, these samples exhibit obvious acoustic emission signals during the initial stage of loading (from compaction to the plastic stage). This indicates that internal rock damage is intensified after the freeze-thaw cycles and that the internal rock structure has changed significantly. As loading time passes and the external load increases gradually, rock damage intensifies gradually, the acoustic emission signal continues to release, and the ring count continues to fluctuate. During loading to the failure stage, the internal rock fracture surface releases a large acoustic signal, the ring count increases sharply, and concentrated in the peak. In the post-peak stage, brittleness weakens the rock sample after 20 freeze-thaw cycles, and the stress within of the rock is reduced, though not all the way to 0 MPa, after failure. Some residual bearing capacity remains and is accompanied by acoustic emission signals.


### 4.2. Damage Characteristic Analysis Based on Cumulative Acoustic Emission Ring Counts

The cumulative acoustic emission ring count is taken as logarithm, and a curve that relates the cumulative ring count from rock damage and failure to the corresponding rock stress is obtained (Figure8).Figure 8
Rock damage and destruction cumulative ring count curves.
(a)
0 cycles(b)
5 cycles(c)
10 cycles(d)
20 cycles(e)
30 cyclesFor samples that have not undergone 10 freeze-thaw cycles, the cumulative ring count curve is divided into three stages. During the first stage, i.e., the early loading stage, there is little internal damage to the rock, and there are no obvious acoustic emission characteristics. The ring count does not appear continuously, and thus the cumulative ring count either contains discontinuities or does not appear. When the stress within the rock reaches 30 MPa, it enters the second stage. Rock damage accumulates under a continuous load, and the cumulative rock ring count increases rapidly and linearly until the stress reaches about 50% of the peak stress. During the third stage, the cumulative ring count growth rate slows gradually, and the rock reaches its peak strength. When the rock reaches its peak strength, the cumulative ring count growth rate increases, but this increase is small.For samples that have undergone 10 freeze-thaw cycles, the shape of cumulative ring count curve of rock is nearly the same. It can be divided roughly into four stages. During the first stage, damage begins to appear inside the rock, and the ring count grows under the action of a load. The growth of the cumulative ring count slows gradually. This occurs mainly during the rock compaction stage. During the second stage, the internal pores within the rock gradually become compacted, and the rock enters the elastic stage. During this stage, the cumulative ring count increases slowly, and internal damage accumulates gradually within the rock. During the third stage, the rock enters the plastic stage from the elastic stage, and the cumulative ring count increases step-by-step until the peak is achieved. This indicates that internal damage within the rock continues to grow in an unstable manner. Before the peak, the cumulative ring count increases linearly until rock failure. The fourth stage is the post-peak stage, during which the cumulative ring count no longer increases and the rock loses all bearing capacity.


## 4.1. Damage Characteristic Analysis Based on the Acoustic Emission Ring Count

According to the real-time acoustic emission test of the whole process of uniaxial compression of sandstone under different freeze-thaw cycles, the acoustic emission ring count and the change curve of sandstone stress with time can be extracted. The damage characteristics of sandstone during uniaxial compression can be compared and analyzed by ring count and sandstone stress-time curve. The relationship between stress and ring count of 0, 5, 10, 20, and 30 times with time in sandstone is shown in Figure7.Figure 7
The relationship between stress and the ring count in sandstone as a function of time. The statistical range of the ring count is0~200×103.
(a)
0 cycles(b)
5 cycles(c)
10 cycles(d)
20 cycles(e)
30 cyclesAs shown in Figures7(a) and 7(b), when fewer than 10 freeze-thaw cycles are used, the sandstone ring count is almost negligible before 1500 s. This initial uniaxial compression stage corresponds to the rock compaction stage and occurs mainly because the freeze-thaw cycle produces no obvious damage to the internal structure of the rock and the structural characteristics of the changes that occur within the rock are not obvious. The internal rock structure is uniform and has a certain bearing capacity. In this stage, the internal pores within the rock are compacted, and crystal dislocation is not obvious. Changes in the internal rock structure under load produce little signal frequency oscillation. Thus, there is little acoustic emission ringing. As time passes, the rock gradually enters the elastic stage under the action of a load. As internal damage within the rock accumulates gradually, the ring count gradually appears and fluctuates, indicating that the internal structure of the rock has changed significantly. The crystals inside the rock began to undergo obvious dislocation and microcrack initiation begins. At the same time, along with the acoustic emission signal, the number of oscillation of the signal over the threshold signal is more and more. Microcrack development instability leads to fluctuation of the ring count, and internal damage to the rock structure increases gradually. The plastic stage occurs from 2700 s to the peak strength of the rock. Stress growth within the rock slows mainly due to the gradual development and further expansion of microcracks in the rock. Microcracks gather to form a fracture surface gradually, internal damage deformation within the rock is large, and the acoustic emission signal decreases.During the failure stage, the rock stress reaches its maximum and the internal failure surface of the rock is penetrated and completely destroyed, releasing large acoustic emission signals with high strength and frequency. The ring count is concentrated in the sudden increase of peak strength. In the post-peak stage, the number of freeze-thaw cycles decreases, and the stress within the rock decreases linearly to 0 MPa. The rock is brittle, and there is no acoustic emission signal.Rock samples that have undergone 10 freeze-thaw cycles are shown in Figures7(c), 7(d), and 7(e). Unlike rock samples that have not undergone 10 freeze-thaw cycles, these samples exhibit obvious acoustic emission signals during the initial stage of loading (from compaction to the plastic stage). This indicates that internal rock damage is intensified after the freeze-thaw cycles and that the internal rock structure has changed significantly. As loading time passes and the external load increases gradually, rock damage intensifies gradually, the acoustic emission signal continues to release, and the ring count continues to fluctuate. During loading to the failure stage, the internal rock fracture surface releases a large acoustic signal, the ring count increases sharply, and concentrated in the peak. In the post-peak stage, brittleness weakens the rock sample after 20 freeze-thaw cycles, and the stress within of the rock is reduced, though not all the way to 0 MPa, after failure. Some residual bearing capacity remains and is accompanied by acoustic emission signals.


## 4.2. Damage Characteristic Analysis Based on Cumulative Acoustic Emission Ring Counts

The cumulative acoustic emission ring count is taken as logarithm, and a curve that relates the cumulative ring count from rock damage and failure to the corresponding rock stress is obtained (Figure8).Figure 8
Rock damage and destruction cumulative ring count curves.
(a)
0 cycles(b)
5 cycles(c)
10 cycles(d)
20 cycles(e)
30 cyclesFor samples that have not undergone 10 freeze-thaw cycles, the cumulative ring count curve is divided into three stages. During the first stage, i.e., the early loading stage, there is little internal damage to the rock, and there are no obvious acoustic emission characteristics. The ring count does not appear continuously, and thus the cumulative ring count either contains discontinuities or does not appear. When the stress within the rock reaches 30 MPa, it enters the second stage. Rock damage accumulates under a continuous load, and the cumulative rock ring count increases rapidly and linearly until the stress reaches about 50% of the peak stress. During the third stage, the cumulative ring count growth rate slows gradually, and the rock reaches its peak strength. When the rock reaches its peak strength, the cumulative ring count growth rate increases, but this increase is small.For samples that have undergone 10 freeze-thaw cycles, the shape of cumulative ring count curve of rock is nearly the same. It can be divided roughly into four stages. During the first stage, damage begins to appear inside the rock, and the ring count grows under the action of a load. The growth of the cumulative ring count slows gradually. This occurs mainly during the rock compaction stage. During the second stage, the internal pores within the rock gradually become compacted, and the rock enters the elastic stage. During this stage, the cumulative ring count increases slowly, and internal damage accumulates gradually within the rock. During the third stage, the rock enters the plastic stage from the elastic stage, and the cumulative ring count increases step-by-step until the peak is achieved. This indicates that internal damage within the rock continues to grow in an unstable manner. Before the peak, the cumulative ring count increases linearly until rock failure. The fourth stage is the post-peak stage, during which the cumulative ring count no longer increases and the rock loses all bearing capacity.


## 5. Theoretical Analysis of Sandstone Damage Characteristics after Various Freeze-Thaw Cycles

According to the theory of rock mechanics and statistical principles, the strain increases gradually when the rock is loaded. When the stress exceeds the strengths of some of the elements, the elements whose strength is exceeded rupture successively. If these elements have linear elastic properties and the same elastic modulus, the system conforms to the compressive strain failure criterion. Using statistical theory [39, 40], if the strain is ε, the strength probability of the micro-element body is
(5)Fε=Pε≥0=∫0εϕxdxDerivation (5):(6)dFεdε=ϕεIn Equation (6), ϕε is the probability distribution density function of the microelement strength. If the cross-sectional area is A, the area of the failure element is
(7)AFε=AFε.The effective area is(8)A=EA−AF=A1−Fε.According to the basic theory of damage mechanics:(9)A=EA1−D.Comparison Formulas (8) and (9) are as follows:
(10)D=Fε.Formula (10) shows that the accumulation of microdamage leads to macroscopic deterioration of the rock sample. The damage variable D measures the degree of damage. The damage degree is the probability of micro-element damage. Therefore, from Formulas (6) and (10), the following relationship is obtained between the damage variable D and the micro-element damage probability density:
(11)dDdε=dFεdε=ϕε.If the micro-element follows the bivariate parameterized Weibull distribution, the distribution density function is(12)ϕε=mαεm−1exp−εαm.In Formula (12), α and m are the physical and mechanical parameters of the material, where α is the Weibull distribution parameter and m represents the non-uniformity of the distribution. Formulas (11) and (12) can produce
(13)D=∫0εϕεdx=mα∫0εxm−1exp−xαmdx=1−exp−εmαm.The damage variable expression of the Weibull distribution is thus derived. A rock damage model based on AE parameters is derived below.AE is the release of the elastic wave generated during rock damage. It reflects the degree of rock damage and is related to internal defects with the rock and the defect derivation process. Assuming that AE isnv when a unit area micro-element is damaged, AE accumulation when micro-element ΔA is damaged is
(14)Ω=nv⋅ΔAThe AE accumulationΩ in Equation (14) is a parameter that can be used to characterize rock AE characteristics.If the cross-sectional area of the entire specimen isA0, AE accumulation across the entire section is Ωf. Equation (14) can be written as
(15)Ω=ΩfA0⋅ΔA.According to the assumption of the strength distribution of the element, when the strain of the specimen increases byΔε, the failure section area increment is
(16)ΔA=A0⋅ϕε⋅Δε.We can replace Formula (15) with Formula (16) using
(17)Ω=Ωf⋅ϕε⋅Δε.Therefore, when the compressive strain of the rock sample increases toε, the AE accumulation is
(18)Ω=Ωf∫0εϕxdx.Replace Formula (12) with Formula (18) and integrate to produce
(19)ΩΩf=1−exp−εmαm.Comparison of Formulas (13) and (19) indicates that the rock damage variable can be written in terms of characteristic AE parameters:
(20)D=ΩΩf.The AE ring count characteristics reflect the frequency of micro-fracture events in the rock under load. Acoustic emission characteristic parameter ringing technology is selected to describe the uniaxial compression damage and failure process of sandstone after various freeze-thaw cycles using Formula (20). Based on AE characteristic parameter ringing technology, the curve of uniaxial sandstone compression damage under the freeze-thaw cycle is obtained and shown in Figure 9.Figure 9
Variation in sandstone uniaxial compression damage with the number of freeze-thaw cycles.
(a)
Damage description based on the ring count (logarithmic)(b)
Damage description based on the ring count (linear)Freeze-thaw cycles cause little damage to rock. To analyze the damage caused by the freeze-thaw cycle as part of the uniaxial rock compression process, the damage degree is taken as logarithmic, as shown in Figure9(a). The logarithmic curve of the uniaxial compression damage degree of sandstone after 0 or 5 freeze-thaw cycles is the same. Before 1700 s, there is no damage to the rock under the load. Between 1700 s and 2000 s, damage to the rock increases gradually, and the damage degree reaches 0.1. Under a continuous load, damage to the rock accumulates after 2000 s, and the damage degree increases rapidly until it reaches 1, and the rock loses its bearing capacity completely. After 10 freeze-thaw cycles, the logarithmic curve of rock damage degree is consistent. As the load increases gradually, initial damage appears inside the rock and increases gradually. When the damage degree increases to 0.001, rock damage enters the quiet zone. When the load increases further, the damage degree increases by a negligible amount. Later, the damage reaches the threshold damage value of approximately 0.1, rock damage increases rapidly, and bearing capacity is lost.For the uniaxial compression damage degree (linear) of sandstone under the action of freeze-thaw cycles, see Figure9(b). Under the action of a load, the damage degree (linear) of samples exposed to 0 and 5 freeze-thaw cycles increases linearly in a gradual manner. When these systems approach failure, the damage degree increases vertically until failure. For samples exposed to 10 freeze-thaw cycles, the damage degree accumulates until it reaches a certain threshold under load and then increases linearly until the rock is destroyed. Larger numbers of freeze-thaw cycles result in shorter times for the rock to reach this threshold and quicker uniaxial compression failure. This indicates that rock damage caused by freeze-thaw cycles reduces the threshold value for rock damage growth.


## 6. Conclusions

(1)
The saturated water absorption rate of sandstone increases with the number of freeze-thaw cycles, but the rate of increase slows gradually as the number of freeze-thaw cycles increases. When the saturated water absorption rate increases, the water in the rock pores freezes, and the associated volume increase causes more damage. The damage caused by the internal rock increases gradually, and the frost resistance of the rock is weakened(2)
Freeze-thaw cycles have a substantial effect on the peak strength and elastic modulus of sandstone. The peak strength and elastic modulus loss rates increase gradually and linearly. The peak strength and elastic modulus loss rates reach 47.27% and 60.35%, respectively, after 30 freeze-thaw cycles. After 10 freeze-thaw cycles, the peak strength and elastic modulus loss rates increase slowly(3)
Sandstone failure modes after various numbers of freeze-thaw cycles can be roughly divided into splitting failure, shear failure, and splitting-shear mixed failure. The fewer freeze-thaw cycles are applied, the more brittle the rock. With few cycles, rock failure occurs via splitting failure. As the number of freeze-thaw cycles increases, the failure surface formed inside the rock under the action of load becomes increasingly complex. Such samples fail primarily via split shear failure(4)
With fewer than 10 freeze-thaw cycles, there was almost no ring count after the compaction order and peak value of the rock. When more freeze-thaw cycles were used, damage accumulated inside the rock and the ring count appeared during the compaction stage and fluctuated until the peak was reached. When the peak rock was destroyed, the ring count intensity increased suddenly, and the frequency was high. After the peak was reached, the residual ringing strength of the rock appeared and was accompanied by acoustic emission signals(5)
With fewer than 10 freeze-thaw cycles, the cumulative ring count curve growth is divided into three stages. With more than 10 freeze-thaw cycles, the cumulative ring count curve growth is divided into four stages. As the number of freeze-thaw cycles increases, the brittleness of the sandstone decreases, and the cumulative ring count gradually transitions from the jumping stage to gradual growth(6)
The sandstone damage degree increases substantially under the action of a freeze-thaw cycle. Under load, the degree of rock damage increases until it reaches a certain threshold value and then increases linearly until the rock is destroyed. When the number of freeze-thaw cycles increases, the time required for the rock to reach this threshold value becomes shorter, and the time required for sandstone damage decreases gradually(7)
The mineral composition and structure of the rock and the natural physical environment (force fields, temperature fields, groundwater, etc.) exert important influences on the macroscopic mechanical and damage properties of the rock. Therefore, the experimental results in this paper provide a reference for the study of sandstone mechanical properties and damage in a freeze-thaw environment. More experiments should be performed using different lithologies to study the acoustic emission characteristics of rocks damaged via uniaxial compression in a freeze-thaw environment



---

*Source: 3961317-2022-07-30.xml*