1. Introduction
With the development of intelligent automation, the production efficiency of large-scale mines in China is increasing, producing more tailings. Many scholars have studied the problems of tailings disposal. At present, the most important form of tailings storage facility in the world is still the tailings pond [
1].
About 70% of China’s land area comprises permafrost and seasonally frozen ground, while about 91.4% of tailings piles are located in frozen-ground areas. Tailings are a discrete material with specific pores between constituent particles, and water, air, and solid particles of tailings inside the pores constitute a complex fine-scale three-phase structure. In permafrost and seasonally frozen-ground regions, F-T cycling directly affects changes in the mechanical properties of the tailings and also leads to changes in the pore pressure and other indicators within the tailings dam body, which in turn has an impact on the stability of the tailings dam [
2,
3].
Moreover, tailings ponds are large-scale and prone to safety hazards. The collapse of a tailings dam can cause a serious risk to people’s lives and properties downstream and in the surrounding environment. Therefore, it is necessary to investigate tailings under cyclic freeze–thaw conditions to maintain the safety and stability of tailings ponds in cold regions [
1].
The current research on freeze–thaw cycling mainly comprises laboratory studies on granites and other geotechnical bodies. Many scholars have investigated the effects of freeze–thaw on the strength, anisotropy, and other properties of rocks, and found that the strength of these rocks decreases after freeze–thaw cycles. Few of these studies have dealt with tailings as a material, and few have used numerical simulations as a method of study [
4,
5,
6,
7,
8,
9,
10]. Some scholars also studied the effects of freeze–thaw processes on the leaching of metals from waste rock and the oxidation of sulfides [
6].
Some researchers also studied the properties of clay materials after cyclic freeze–thaw. Their work revealed that the water content, elastic modulus, and cohesion of clay decreased with the number of freeze–thaw actions; however, the internal friction angle increased [
11].
Some researchers have also conducted laboratory experiments using artificial permafrost and permafrost from laboratory tests and found the effect of freeze–thaw cycle numbers is more remarkable. In contrast, the freeze–thaw temperature has a minor impact on the mechanical properties [
12]. Some scholars have also studied permeability, strain rate, strain energy, temperature, surrounding pressure, water content, and soil particle size of permafrost soils [
13,
14,
15,
16,
17].
So far, there have been many studies on tailings’ mechanical properties under freeze–thaw cycles. Many researchers have also investigated water content, porosity, mineral composition, fine structure, strength, and deformation characteristics through laboratory tests [
18,
19] and the effect of ice lensing and freeze swelling during freeze–thaw cycles [
20]. It has been suggested that temperature gradients lead to water transport during freeze–thaw processes, which changes the structure of geological bodies (sands and tailings) with discrete types [
21]. Therefore, for tailings materials, the freeze–thaw cycling effect may lead to inhomogeneity of the particle structure, leading to the deterioration of mechanical properties at the macroscopic level.
For the impact of cyclic freeze–thaw on pore water transport of discrete geological bodies, the influence of freeze–thaw temperature, pore water pressure, and pore characteristics on water transport have been comparatively studied by scanning electron microscopy (SEM)-acquired fine view images. It is believed that after the cyclic freeze–thaw action, soil pores show a new alignment trend, while the pore water pressure gradually decreases. The particles become more aggregated [
10]. The study of the effect of water content on the mechanical properties of soil and rock materials, such as tailings under freeze–thaw cycle conditions also has a specific basis. Some scholars have conducted impact compression experiments on granite specimens with different water contents and degrees of freezing using separated Hopkinson rods. The effect of water on the dynamic modulus of elasticity was more significant than the effect of freeze–thaw temperature [
22]. Some scholars also investigated the shear strength of specimens with different water contents after freezing and thawing using fine-grained sand from the drainage field and found that the samples’ shear strength decreased the most after a single freeze–thaw action, and the specimens’ cohesion and internal friction angles decreased according to water content with the increasing numbers of freeze–thaw cycles.
In contrast, the cohesion of samples with the same water content was more obviously influenced by the effects of the freeze–thaw process [
23]. The effect of seepage on the refined mechanics of tailings has also been studied. It was found that seepage significantly affects the particle diameter distribution of tailings particles at different depths [
24].
The primary method for studying the physical and mechanical properties of tailings in the freeze–thaw zone is laboratory testing. Laboratory experiments with many freeze–thaw cycles are difficult to realize due to the high time cost and specimen loss. The capacity of freeze–thaw equipment limits them, and the low number of specimens available for experiments and reproducibility means that it is challenging to meet the experimental requirements. The errors in the testing results are challenging to reduce. At present, many scholars have researched numerical simulation and obtained results consistent with laboratory tests [
25,
26,
27,
28], so it is feasible to conduct examinations through numerical simulation.
The first objective of the study was to explore the effects of dry density, average particle size, and number of freeze–thaw cycles on the mechanical properties of tailings. The numerical simulation of freezing–thawing cycles is a thermo-stress coupling problem, which has many precedents [
29,
30,
31], but is rarely applied in the study of tailings. The second objective of this study was to verify the feasibility of this method in the study of tailings. Therefore, in this paper, we first designed orthogonal tests using SPSS software, and analyzed the numerical simulation results of pre-experiments by mathematical methods. On this basis, freeze–thaw cycles and uniaxial compression numerical simulations were carried out using PFC2D software. In accordance with the results, the mechanism and law of the changes in the mechanical properties of tailings caused by different factors were studied to provide a basis and reference for the stability study of tailings dams under the effects of freeze–thaw cycles.
3. Numerical Simulation Mechanism and Numerical Specimen Preparation
3.1. Numerical Simulation Mechanism
The numerical simulation software PFC2D was used in this simulation, and the numerical simulation code used was divided into three main parts. (1) The model generation part. This part was used to generate the model and assign values to the model’s modulus of elasticity, dimensions, and other parameters. (2) The thermal treatment part. In this part, the model particles were first given thermodynamic parameters, such as heat transfer coefficients, and then the model as a whole was given an initial temperature and a freeze–thaw cycle by customizing the temperature increments. This part enabled the transfer of temperature in the model, the change in temperature, and the resulting change in parameters, such as porosity. (3) The loading part. This part implemented the loading process of the model by applying velocities to the walls at the top and bottom of the model. The changes in particle displacements, stresses, and other parameters could be monitored in real time during the loading process. The initial overlap between the particles was balanced within the model by loading the surrounding pressure between the different parts to avoid errors in the final results, due to the initial contact force or initial velocity that the particles had in the subsequent run.
The model particles could apply velocity and force; the walls could only apply rate directly. Therefore, when loading the model in the loading section, if the wall was to be used to exert pressure on the particles, it could only be carried out in a converted way: by converting the pressure to the velocity of the wall. When monitoring parameters, such as stress and strain, the stress magnitude of the wall could not be monitored directly; rather, the stress value was obtained by scanning the combined external force on the wall and dividing it by its contact area. In the model, the time step between each calculation was small enough to make the value of the contact area change negligible.
3.2. Thermodynamic Temperature Module
The thermodynamic module of PFC can run independently for simulating the heat transfer of the medium; it can also run coupled with other modules and can be used to analyze the deformation and damage of the medium caused by the interaction of heat and force, which is the application in this simulation.
In this module, the thermodynamic parameters of the different components of the particles needed to be customized, including the specific heat capacity and the coefficient of thermal expansion. According to the tests, the coefficient of thermal expansion mainly controlled the differences in the mechanical properties of the model after the temperature treatment. At the same time, the variation in the specific heat capacity did not significantly influence the mechanical properties curve of the model.
3.3. Preparation of Numerical Simulation Model
One of the main elements impacting the calculation time of numerical simulation is the number of model particles. To improve the efficiency of the simulation, the number of model particles should be reduced as much as possible without affecting the simulation results when simulating indoor geotechnical tests. There are two ways to achieve this goal: (1) increasing the particle radius; (2) reducing the specimen size. To enhance the simulation results’ reliability, reduction of the number of particles has certain limitations. Richard P. Jessen [
32] et al. studied this problem. Their results showed that when the ratio of the specimen diameter D to the average particle diameter d is greater than 30–40, the number of particles will not significantly affect the simulation results. Liu Hong [
33] proposed that for sandy soils, of which the particle size is smaller and the difference between the maximum and minimum particle diameter is significant, the number of particles can be reduced by taking the weighted average of the particle radius in the indoor test and enlarging it by a certain number of times. This provides an idea for the reduction of particle numbers in this simulation.
3.4. Model Properties
The size of the model in this simulation was set as a standard cylindrical specimen of 50 mm*100 mm. The average tailings particle size according to the measured tailings particle sizes of different gradations processed by the methods mentioned above and guidelines after amplification is shown in
Table 1. The dry density is listed in
Table 2.
3.5. Parameter Calibration and Model Reliability
The type of modeling was the contact bonding model. The characteristics of this model were that it provided a minimal linear elastic behavior for contact forces, could only carry friction when the contact interface was not bonded, and could not carry friction when the contact interface was bonded. The size of the domain was set to 500 mm * 500 mm, which was sufficient to fully contain the whole model. The initial temperature was set to the usual room temperature of 25 °C, the temperature increment during freezing was set to −45 °C, and the temperature increment during thawing was set to 40 °C.
The initial reliable model was obtained by repeatedly adjusting each parameter through a trial-and-error method to make the numerical model curve characteristics close to the indoor test curve. The final calibrated partial mechanical parameters are listed in
Table 3.
As shown in
Figure 1, the initial numerical model curve was close to the laboratory test curve based on the peak stress and strain and the curve change trend, which proved the reliability of the numerical model. The subsequent cyclic freeze–thaw numerical simulations were based on this, and the corresponding results were obtained by adjusting the values of each factor and analyzing them.