Effect of Freeze–Thaw Cycles on Shear Strength of Tailings and Prediction by Grey Model

: Tailings dams in the seasonal frozen regions experience freeze–thaw cycles with the change in natural geography and climatic conditions, which may have a strong influence on the mechanical properties of the tailings. In this paper, the effects of freeze–thaw cycles on the mechanical properties and pore structure of tailings were investigated. Triaxial tests were carried out on tailings with different moisture contents (5%, 10%, 15%, 20%) under different confining pressures (50 kPa, 100 kPa, 200 kPa, 300 kPa) after different freeze–thaw cycles (10, 20, 30, 40, 50). The pore structures of tailings were quantitatively analyzed as well. Furthermore, grey system theory was applied to develop a shear strength prediction model for tailings in cold regions. The results showed that the optimal moisture content of tailings fell 10%–15%. The shear strength of the tailings increased under higher confining pressures, while it decreased after more freeze–thaw cycles. Irrecoverable large pore deformation between particles within the tailings was found after 40 freeze–thaw cycles. After 50 freeze–thaw cycles, the proportion of pores larger than 100 μ m increased from 22.76% to 48.45%. Predictions based on the Grey Model were found to be consistent with the test results and the shear strength test law. The residual error and class ratio dispersion of the model were less than 0.2, indicating that the Grey Model has high prediction accuracy and thus can be used for the prediction of the shear strength of tailings.


Introduction
Tailings dam failures not only endanger the lives and property of people downstream but can also cause significant damage to the environment [1][2][3][4].According to statistics, many factors contribute to the failure of tailings dams, the majority of which are weather-related (e.g., irregular and periodic rainfall, snowfall) [5].The temperature within the tailings dam body in the seasonally frozen region varies periodically with the change of seasons.Continuous water-ice transition in the tailings dam will lead to changes in the structure, water field, solute field, and stress field of the tailings, especially in the frozen zone where the moisture in the tailings exists in the form of ice crystals.Tailings dams with poor bonding quality are more prone to damage.Therefore, it is urgent to study the mechanical properties of tailings in cold regions so as to provide a guiding basis for the stability evaluation of tailings dams in cold regions.
Numerous researchers [6][7][8][9] have investigated the effect of freeze-thaw cycles on the mechanical properties of tailings through a vast number of experimental and theoretical studies.Yang proposed stress-strain curves for seasonal and permafrost soils for various influencing parameters using indoor uniaxial compression tests.The results indicated that temperature was the most influential factor in frozen soil [10].Using triaxial testing, Yang [11] investigated the compression-thawing phenomenon of permafrost, analyzed the strength change law of permafrost, and presented a damage criterion for permafrost  strength.Based on static and dynamic triaxial testing, Cui explored the macro-micro mechanical properties of pulverized clay and provided the intrinsic structural relationship of the melting soil [12].Yang [13] examined the mechanical properties of artificially frozen soil in terms of strength and stress-strain at various envelope pressures and moisture contents and suggested a nonlinear Mohr-Coulomb criterion.With the advent of particle flow theory, researchers have begun to study the nature of the discontinuous structure of frozen soil and link the macroscopic mechanical performance to the microstructure [14,15].Liu [16] conducted triaxial tests and microscopic analysis of tailings subjected to varying numbers of freeze-thaw cycles and then proposed a fractional-order intrinsic constitutive model.Geng [17] investigated the settlement deformation and fine structure of tailings subjected to continuous loading.He discovered that the tailings having the optimal moisture content present the greatest compressive strength.In order to study the strength properties of the weak soil reinforced by fibers, Kravchenko [18] conducted a series of unconsolidated undrained triaxial compression tests of fine-grained soil subjected to freeze-thaw cycles.Ahmadi studied the strength properties of natural and reinforced samples under freeze-thaw conditions via a series of unconfined compression and direct shear tests [19].A series of unconfined compression and ultrasonic pulse velocity tests were carried out by Boz [20], and it was found that the unconfined compression strength and ultrasonic pulse velocity of each specimen decreased with the increase of freeze-thaw cycles.Ahmadi [21] used scanning electron microscopy (SEM) and Brunauer-Emmett-Teller (BET) tests to assess the microstructure of soil affected by freeze and thaw periods.Changizi [22] observed, by SEM images, that the freeze-thaw cycle changed the soil particle sorting.After nine freeze-thaw cycles, the soil structure reached a stable state.However, further research on the mechanical properties and pore structure of tailings in seasonal frozen regions is required.In this paper, triaxial tests and microscopic tests were carried out on tailings samples with different moisture contents, confining pressures, and freeze-thaw cycles, aiming to explore the internal relationship between the macroscopic mechanical properties and pore structure changes of tailings under freezethaw cycles.Finally, the Grey Model was used to predict the shear strength of the tailings and the residual error and class ratio deviations of the predicted values.This paper provides a theoretical reference for the stability analysis of tailings dams in seasonal regions.

Materials
In this paper, a tailings dam located in the seasonally frozen region in Fuxin City, Liaoning Province, China, was used as the study target, and the samples were taken from this tailings dam.The tailings were dried in a drying box, and the natural moisture content was determined to be 11.3%.Tailings sand was screened according to the standard for geotechnical test methods (GB/T 50123-2019) [23].The fine particles passing through a 2 mm sieve were obtained for testing as the coarse tailings.The dry density of the tailings was 1.79 g/cm 3, and the porosity was 0.863.The optimum water content of tailings was measured by compaction testing as 14.8%.The particle size distribution curve is shown in Figure 1.The main compositions of the tailings are listed in Table 1.The water used in this paper was tap water.The main ions in water were Ca 2+ (43.7 ppm), Mg 2+ (2.35 ppm), and Na + (3.10 ppm) and the pH value was ca.7.25.

Sample Preparation
Cylindrical samples with an inner diameter of 38.1 mm and a height of 8 cm were prepared for the triaxial test [24].The test barrel was made of acrylic because it had the characteristics of high strength, high toughness, low heat transfer, light weight of the mold, and high light transmission, which allows for observing the pores around the samples.Before mixing, the tailings samples were dried in a drying box at 105 °C for 8 h, and the dried particles were sealed and stored for 4 h until their temperature was the same as room temperature.The tailings particles were then mixed with water using a machine to form mixtures with a moisture content of 5%, 10%, 15%, and 20%.The mixtures were loaded into a circular mold, and the cylindrical sample was prepared using a layer-bylayer (5 layers in total) compaction.The prepared samples were packaged in fresh bags and placed in a freeze-thaw cycle box for 10, 20, 30, 40, and 50 freeze-thaw cycles.The freezing temperature of the box was −20 ± 0.5 °C, the thawing temperature was 20 ± 0.5 °C, and the freezing and thawing times were both 12 h [9].

Test Scheme
In this study, triaxial tests consisting of 80 sets of tests with a total of 160 test pieces were used to examine the effect of various freeze-thaw cycle periods, moisture levels, and confining pressures on the shear strength of the samples.The mesoscopic test was carried out for samples after 10, 20, 30, 40, and 50 freeze-thaw cycles.Two samples were used for each group, and a total of ten samples were used for mesoscopic analysis.The moisture content was 15%.The test results are the average data of two tailings specimens in each group.The test scheme is shown in Table 2.The shear stress of four kinds of moisture content of tailings specimens is affected by confining pressure and freeze-thaw times; the moisture content of 15% is closer to the optimal moisture content of tailings specimens.Therefore, this manuscript discusses the tailings specimens with 15% moisture content.The triaxial test was performed on a permafrost triaxial testing machine.The main technical specifications were as follows: the maximum axial force was 10 kN, minimum measurement value was 0.001 kN, frequency range was 0.001-5 Hz, maximum displacement was 90 mm, minimum measurement value was 0.0001 mm, maximum confining pressure was 1 MPa, and 1.5 MPa back pressure control value.The test machine is shown in Figure 2.After freeze-thaw cycles (10,20,30,40,50), the shear strengths of tailings samples with different moisture contents (5%, 10%, 15%, 20%) were measured according to the Chinese standard GB/T 17671-1999.The confining pressures were 50 kPa, 100 kPa, 200 kPa, and 300 kPa, respectively, and the shear rate was set to 1%/min.

Mesoscopic Test
The tailings samples were subjected to a mesoscopic test after freeze-thaw cycles.The samples were ruptured to expose the fresh section, and the unbonded particles on the section surface were blown away.Samples of tailings were vacuum-dried prior to testing.The tests were carried out using an AO-HD206 video microscope in combination with Image-Pro Plus 6.0 to obtain relevant parameters such as pore size, pore area, and other parameters.

Influential Factors on Shear Strength of Tailings
Through triaxial tests, the effects of freeze-thaw cycle times, moisture content, and confining pressures on the shear strength of tailings were studied.The following is a detailed discussion based on the test results.

The Effect of Freeze-Thaw Cycle Times
Figure 3 shows a histogram of the average shear strength of the tailings after different times of freeze-thaw cycles.It can be seen that the shear strength of tailings tends to decrease with the increase in the number of freeze-thaw cycles when the moisture content and the confining pressure remain constant, which is consistent with the conclusions of studies on fine-grained soil [25,26].At a moisture content of 20% and confining pressure of 300 kPa, the shear strength of tailings samples subjected to 50 freeze-thaw cycles decreased by 36.5% compared to that of samples after 10 freeze-thaw cycles.The shear strength of tailings samples showed a slight decay after 20 freeze-thaw cycles, while after 40 freeze-thaw cycles, the shear strength of tailings samples decreases significantly and then remains stable after more freeze-thaw cycles.During the freeze-thaw cycles, the internal moisture continuously undergoes phase transition, leading to continuous expansion and contraction of tailings samples.This may cause damage to the skeletal structure formed by the internal particles.The tailings can resist this phase transition within a certain range; therefore, the shear strength of tailings declines slightly after 20 freeze-thaw cycles.After more freeze-thaw cycles, however, the pore structure of tailings samples reaches the limit of shrinkage and expansion, and irreversible structural collapse occurs, resulting in instability of the overall structure and a significant decrease in shear strength.In addition, after 40 freeze-thaw cycles, the collapsed particles are in a state of irregular accumulation and cannot be restored to their original skeletal structure, and therefore the shear strength becomes stable [27].

The Effect of Confining Pressure
Figure 4 shows the shear strengths of the tailings at different confining pressures with a moisture content of 15%.When the moisture content and the number of freeze-thaw cycles are constant, the shear strength of tailings samples increases with the increase of confining pressure [11].After 10 freeze-thaw cycles, the shear strength of the tailings sample with a confining pressure of 300 kPa is 684.89 kPa, while the shear strength of the sample with a confining pressure of 50 kPa is only 161.40 kPa.The reason is that the micropores and micro-fractures within the tailings are gradually closed under higher confining pressure, the distance between the particles is gradually reduced, and the tailings become more compact.As the confining pressure increases, the sliding and displacement between grains in the tailings increases, which reduces the strain recovery ability and improves the plastic deformation of the tailings.After certain freeze-thaw cycles, the confining pressure increases the contact points of the particles in the tailings, the micro-cracks and micropores in the tailings are gradually closed or compacted, the compactness becomes larger, and the bearing capacity is enhanced.The increase in confining pressure also improves the contact state of the particles of the tailings, increasing the resistance of the tailings to damage and the shear strength as well.

The Effect of Moisture Content
Figure 5 shows the shear strength curves of tailings samples with different moisture contents.It is clear that at 300 kPa, the shear strengths of tailings first increase and then decrease with the increase of initial moisture content.The maximum shear strength was achieved when the moisture content of the sample was between 10% and 15% [24].The tailing sample was not water-saturated when the moisture content was low.During the freezing process, the volume of the pore water expanded and filled the internal pores of the tailings.After the ice melted, the water diffused evenly.Therefore, increasing the moisture appropriately improves the freezing shear strength of the tailings.When the moisture content of the tailings sample was beyond 15%, more water molecules were trapped in the pore volumes of tailings, and the volume expansion due to water-ice transition induced great stress, cracking the pore structure.After the ice melted, the large pores were unable to resist the water pressure, resulting in secondary damage to tailings samples.Therefore, the shear strength of tailings decreases significantly.

Mesoscopic Characterization of Tailings under Freeze-Thaw Cycles
Studies by many scholars have shown that in a freeze-thaw cycle, the tailings structure transforms from an unstable state to a dynamically-stable state gradually, and repeated freeze-thaw cycles will give the tailings a new dynamic and stable equilibrium state [28][29][30][31][32].In this paper, the tailings sample with 15% moisture content was used as an example to study the microstructure evolution of tailings after different times of freezethaw cycles, as shown in Figure 6.In this case, Figure 6a shows the results of the microscopic pore structure of the tailings sample that have not undergone freeze-thaw cycles.It can be seen that the pores are evenly distributed in the tailings, and only small pores are observed.The particles in tailings make contact with each other via point-topoint connections, forming a relatively loose structure with poor bonding quality.With the increase in the number of freeze-thaw cycles, the porosity of the tailings gradually increases.Under the periodic action of freezing and thawing, the water molecules inside the tailings experience water-ice transition cycles.As a result, the internal cracks in the tailings gradually expanded, changing the arrangement of the soil particles.Meanwhile, the porosity increased, which was reflected in the tailings specimens after 10 freeze-thaw cycles.Compared with the unfrozen tailings specimens, the porosity increased by 0.775%, as shown in Figure 6b.Under the action of the first 20 freeze-thaw cycles, the pores and small deformations are generated during the freezing process, but these defects are recovered in the thawing stage [19].Compared with the unfrozen tailings specimens, the porosity increased by 1.949%, as shown in Figure 6c.After 30 freeze-thaw cycles, the bond between the particles in the tailings is destroyed and large pores are formed.These defects cannot be recovered in the thawing stage.Compared with the unfrozen tailings specimens, the porosity increased by 4.247%, as shown in Figure 6d.However, after 40 freeze-thaw cycles, due to the frequent extrusion between tailings particles, the edges of tailings particles were continuously smoothed and the particles gradually became rounded, which also increases the pores between tailings particles.Compared with the unfrozen tailings specimens, the porosity increased by 5.653%, as shown in Figure 6e.After 50 freeze-thaw cycles, the internal structure of the tailings sample was destroyed, the internal particles became smoother, the pore diameters became larger, and the internal structure became looser.Therefore, the shear strength of the tailings samples was reduced.
Compared with the unfrozen tailings specimens, the porosity increased by 6.918%, as shown in Figure 6f.This is a clear indication that the freeze-thaw cycle effect causes changes in the micro-structure of the tailings, and frost heaving stress is the main reason for the sharp drop in the shear strength of tailings.Table 3 gives the pore parameters of tailings after different freeze-thaw cycles.It can be seen that with the increase in the number of freeze-thaw cycles, the maximum pore size and pore area also increase.During the freezing process, the transition of water in the tailings to ice causes volume expansion.When the expansion force is less than the pore pressure, the pore structure may be maintained.In the thawing process, water can again perfectly fill into the pore volumes between tailings particles.This is why the shear strength decreases slowly before 20 freeze-thaw cycles [33].However, with the further increase of freeze-thaw cycles, the water-ice transitions will eventually lead to partial collapse of pore structures.As a result, the average pore size increased significantly to 378 μm and the maximum pore size increased to 586.416 μm after 40 freeze-thaw cycles.After 50 freeze-thaw cycles, the total orifice area and average pore size increased slightly, indicating that further increasing the freeze-thaw cycles contributes little to pore structure deterioration.

Grey Model Operation
As a cutting-edge mathematical modeling method, Grey Systems Theory can effectively explore the intrinsic laws of uncertain systems and solve system problems with a small sampling of data.The main feature of the model is that it uses not the original data series, but the generated data series.The core of the system is the Grey Model, where an approximate exponential pattern is established by adding up (or otherwise) the raw data and then modeling it.The Grey Model can use differential equations to fully explore the essence of the system and input results with high precision.It can generate irregular raw data to obtain a more regular generation sequence.The model is easy to operate and test.Furthermore, the model can ignore the distribution law and change trends.As such, the Grey Model is suitable for short-and medium-term forecasting and has been widely used by scholars in the engineering field [34][35][36].
To explore the effect of freeze-thaw cycles on the shear strength of tailings samples, this paper employs the Grey Model to predict the shear strength of tailings.The tailings samples with a confining pressure of 200kPa under different moisture contents were selected for prediction.The shear strength corresponding to each freeze-thaw cycle was selected as the reference sequences  = ( (1),  (2), ⋯ ,  ()).The smoothness test was performed on the reference sequence.If the smoothness condition is met and the quasi-exponential law is satisfied, the reference sequence meets the basic conditions for modeling and the Grey Model can be utilized.
The model background value  ( ) is set as the immediate neighboring mean generating sequence of  ( ) :  ( ) = ( ( ) (1),  ( ) (2), ⋯ ,  ( ) ()), the model background values can be expressed as:  ( ) = 0.5 *  ( ) () + 0.5 *  ( ) ( − 1) = 2,3, ⋯ , Let Y and B be the data matrix and data vector respectively,  = , and let  = [, ] ; Through the least square method, the estimated value of u that makes () = ( − ) ( − ) reach the minimum value is determined as: The Grey Model prediction equation is as follows: Finally, the reduction process is performed to obtain the corresponding predicted values of each original data  ( ) : Figure 7 shows the original and predicted values of shear strength of tailings samples after different freeze-thaw cycles.With the increase in the number of freeze-thaw cycles, the shear strength of tailings showed a decreasing trend.In addition, the shear strength decreased more significantly when the tailings sample had higher moisture content.When the moisture content was 10%, the predicted value of the shear strength after 100 freezethaw cycles was the largest, 283.31 kPa.However, for tailings samples with 20% moisture content, the predicted shear strength dropped to the smallest value, 219.02 kPa, after 100 freeze-thaw cycles.This is consistent with the results mentioned in the previous section.

Predicted Value Test
Residual error and class ratio dispersion tests were performed on the predicted values obtained.
First, the class ratio () is calculated from the data  ( ) ( − 1) , and the development coefficient a is used to find the class ratio dispersion (): () = 1 − ( . .)() (7) If () < 0.2, it is considered to meet the standard; if () < 0.1, it is considered to meet the high standard.
According to Formulas ( 6) and ( 7), the residual error and the class ratio dispersion were both less than 0.2, as shown in Figure 8.The relative error of each data set was solved, where the maximum value was 8.87%, indicating a high similarity between the predicted data and the original data.The prediction model can be used to predict the shear strength of tailings samples under freeze-thaw cycles.This model can give the predicted value according to the practical engineering conditions.

Conclusions
In this paper, the effect of the number of freeze-thaw cycles, moisture content, and confining pressure on the shear strength and pore structure of tailings in a seasonally frozen region was investigated.The shear strength of the tailings was predicted by the Grey Model.The following conclusions can be drawn from the above study: 1.With the increase in freeze-thaw cycle times, the shear strength of tailings generally shows a decreasing trend.When the number of freeze-thaw cycle is less than 20 times, the shear strength of tailings does not decrease significantly.After 20 freeze-thaw cycles, the shear strength of the tailings decreases significantly, but further increasing the cycles does not significantly impair the shear strength of tailing samples.2. The shear strength of the tailings increases with increasing confining pressure applied in the triaxial test.The shear strength of the tailings increases first, and then decreases

Figure 1 .
Figure 1.Frequency distribution curve of laser particle size of tailings.

Figure 4 .
Figure 4. Shear strength of tailings under different confining pressures.

Figure 5 .
Figure 5. Shear strength of tailings under different moisture content.

Figure 7 .
Figure 7. Actual and predicted values of peak tailings stress.

Figure 8 .
Figure 8. Residual error and class ratio dispersion for each prediction formula.

Table 1 .
Chemical composition of tailings.

Table 3 .
Pore parameters of tailings under different freeze-thaw cycles.