1 Introduction

The extraction and use of mineral resources over the last few decades have generated an enormous amount of mine waste, especially in China, one of the world's largest developing economies (Zhang et al. 2001). By 2018, the annual production of tailings in large and medium-sized cities in China reached 880 billion tons, accounting for 27.4% of general solid waste production (Palmer 2019). Mine waste comprises two main waste types: relatively fine-grained tailings and coarse-grained waste rock. The disposal of mine waste is one of the most challenging tasks in the mining industry (Sun et al. 2010).

A tailings dam is a mining facility that contains an enormous amount of sand and water. Once a failure occurs, it will cause incalculable damages to production, people's lives, and property safety. China has 8000 tailings ponds, ranking first in the world (Hou et al. 2021). As a result, China has a great potential to face tailings dam failure hazards.

Among the various contributing tailings dams failure factors, rainfall is the most important factor (Rico et al. 2008), accounting for 24% of the instability of tailings ponds (Rahardjo et al. 2005). On September 21, 2010, the tailings dam at the Yinyan Tin mine in Guangdong Province collapsed because of heavy rainfall. 22 people died, 523 houses collapsed and direct damages amounted to $19 million (Zhou 2013). On October 4, 2010, a catastrophic collapse of the Ajka red mud reservoir failure in Hungary occurred because of unusual rainfall, a disaster that injured 286 people, damaged 367 properties, and affected 1017 hectares of land (Turi et al. 2013).

Many scholars have performed numerous experiments to study the hazards of rainfall on the stability of tailings dams (Aditian et al. 2017; Assouline et al. 2006; Liu et al. 2018; Pan et al. 2009; Zhao et al. 2015). Ma (2019) showed that rainfall influences the tailings' water content at different depths. Since the destabilization of tailings dams starts by losing the shear strength of the tailings at a certain height and then slowly resulting in the destruction of the entire dam, the change of tailings dam properties needs to be considered by height. Tailings dams have various particle size gradation characteristics during the dam construction process. The distribution of tailings particles close to the initial dam and the sub-dam is disparate than the particles near the tail (Yin et al. 2011). Therefore, an in-depth study of rainfall coupled depth is necessary.

In practical applications, it is important to study the physical and mechanical behavior of the three main tailings types, sand, silt, and clay (Albers 2011). Many pieces of literature (Iwasaki et al. 2008; Wichtmann et al. 2009, 2010; Afzali et al. 2017) have shown that the size distribution has a profound effect on the tailings' shear modulus. According to Pete (2006), it can be observed that during the shearing of the tailings, the particles rearrange and exchange energy, which changes the density. Lu (2021) shows that shear strength and deformation modulus increase significantly with increasing dry density and consolidation envelope pressure. Zhang (2019) showed the tailings water content and the tailings particle size distribution at the sampled dams varied with location along with the dam and tailings depth. At present, the research (Hasan et al. 2016; Proskin et al. 2010; Wang et al. 2017; Wei et al. 2009; Yin et al. 2008) on tailings mainly focuses on the physical and mechanical properties of tailings, the seepage characteristics, stability of the dam, etc. Many scholars (Wu et al. 2022; Adiguzel et al. 2019; Long et al. 2017; Wang et al. 2022) have studied rainfall, tailings particle gradation, tailings cohesion, friction angle, etc., however, there is a lack of study to consider these factors together and analyzed the interrelationships among them. Considering all these factors, and their effect on the stability of tailings dams can provide a better vision into the process of tailings dam failure.

This study aims to investigate the variation of the tailings' physical parameters including tailings particle size gradation and water content in different areas of a modeled tailings dam under various rainfall intensities and their influence on the mechanical properties of the tailings. Besides, the mechanism of action and correlation among these parameters are explored.

2 Materials and testing procedure

2.1 Dam model experiment

2.1.1 Test materials

The test materials were obtained from the Luomukeng tailings pond in Jiangxi Province, China. The tailings pond is in a narrow valley, with geographic coordinates of 114° 21′ 16″ E and 25° 23′ 08″ N. It is placed in the northern part of the valley (Fig. 1). The initial dam is in the valley's north and is a tailing clay core wall weathering material dam with a height of 22 m, and a downstream slope ratio of 1:2.5. The stacking dam was constructed by the upstream stacking dam method, and the stacking side slope ratio is 1:5. The designed stacking dam height is 368 m. The total dam height is 106 m, and the total storage capacity of the dam is 1.55 × 107 \({m}^{3}\). According to Safety regulations for tailing ponds (GB39496-2020), the tailing pond is classified as a second-class pond. The tailings pond is located in a warm and humid climate with an average annual precipitation of 1563 mm, maximum annual rainfall intensity of 61.7 mm/h, and maximum daily rainfall of 121 mm.

Fig. 1
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Geographical position and terrain map of Luomukeng Tailing Pond

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The physical dam model experiments were used to deduce the accumulation process of the tailings dam and to get a tailings dam model similar to the actual situation on site. Based on the stacked dam model experiments, a special rainfall simulation device was employed to simulate the rainfall process on the tailings dam. The effect of rainfall intensity on the particle gradation of the tailings, water content, and strength parameters (cohesion and friction angle) in different areas was investigated. Besides, the changes in structural characteristics of the tailings dam under rainfall, the erosion mechanism of rainfall on the surface of the dam, and the seepage damage law of rainwater were analyzed.

Scanning electron micrographs of the tailings at 2000 and 10,000 magnifications was conducted and the result shows that the tailings particles are flaky and have a relatively smooth surface (Fig. 2).

Fig. 2
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Micromorphology of tailings

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The particle gradation curve of the tailings in the initial state is illustrated in Fig. 3. \({d}_{50}\) indicates size on the particle size distribution curve where the mass of particles smaller than this size accounts for 50% total mass, also called the average particle size. Cu and Cc are Coefficient of Uniformity and curvature coefficient respectively which describe the uniformity and the overall shape of the curve. The flat curve has a better grading and it means that the pores of coarse intergranular particles are filled by the fine particles. From the Fig. 3 the tailing in this study is classified as poorly graded.

Fig. 3
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Tailing particle distribution curve of dam initially material

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2.1.2 Heap dam model test

The experimental system of the tailings dam model in this study comprises four principal parts: the mountain model, mine release system, drainage system, and rainfall system (Fig. 4). The model length scale was determined as 1:100 according to the tailings dam site in Table 1. Because gravity plays a major role in the deposition process of tailings, other similar scales were determined according to the gravity similarity criterion. To simulate the tailings deposition process, the tailings were mixed with water in a large plastic bucket according to the actual tailings slurry solid–liquid ratio. During the damming process, the tailings were injected into the tailings reservoir using a PVC pipe of 8 cm diameter, placed at the bottom of the plastic bucket. The rainfall system consisted of 6 groups of 1 mm diameter rotating downward spraying cutting nozzles (each group had 6 nozzles). The height of the nozzles from the slope was 2 m, and the effective rainfall area was 4 × 9 m. The continuous variation range of rainfall intensity was 0–100 mm/h and the rainfall uniformity coefficient was over 0.86. The control range of raindrop size was 1.7–2.8 mm, and the rainfall intensity change accuracy was 7 mm/h.

Fig. 4
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The experimental system of the tailings dam model

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Table 1 Similar factors used for the model
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The rainfall test procedure is as shown in Fig. 5. Each rainfall duration was 10 min. The rainfall amounts were 8 mm/h, 15 mm/h, 20 mm/h, 25 mm/h, 30 mm/h, 35 mm/h, and the groups were divided into G1-G6 according to the size of rainfall. To ensure the accuracy of the experiment, some extra tailings were subjected to rainfall together with the modeled dam to fill the holes caused by subsequent sampling. After closing the rainfall facility, to avoid sampling errors, 12 samples were taken at three different locations on the surface of each sub-dam level, with sampling heights of 0.6 m, 1 m, 1.4 m, and 1.8 m. The samples were placed in plastic bags for subsequent particle gradation and shear strength experiments (Fig. 6). After sampling, the holes resulting from the sampling were filled with the same tailings that received rainfall. The tailings dam was left to stand for a while and then moved to the next rainfall pattern. The above steps were repeated until all six sets of rainfall tests were completed. The total number of samples taken in the six sets of rainfall tests was 72.

Fig. 5
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Flow chart of rainfall experiment

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Fig. 6
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On-site samples

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2.2 Physical and mechanical property testing

The tests conducted on the obtained tailings samples comprised three parts: moisture content test, particle gradation test, and shear strength test.

(1) Moisture content and density test

The water content of tailings was determined according to State Standard of the People's Republic of China for soil method (GB/T50123-2019). 500 g of tailings were weighted and dried at 105 °C for 12 h at a constant temperature, then cooled in the drying oven for 1 h, and then weighted again. The water content was obtained using Eq. (1).

$$\omega =\frac{m-{m}_{s}}{{m}_{s}}\times 100$$
(1)

In the formula, ω is water content (%), m is Mass of wet soil (g), \({m}_{s}\) is mass of dry soil (g).

In addition, the density of tailings was measured according to GB/T50123-2019 using the ring knife method.

(2) Particle gradation test

Particle analysis tests were carried out on the test tailings to determine the particle size distribution of the tailings, and the tests were divided into hydrometer test and sieve analysis method. According to Standard for soil method (GB/T50123-2019) for hydrometer test, 0.5 kg sample was washed by water through a 0.075 mm sieve plate and was immersed in water for about 24 h. Then it was dried in an oven at 105℃ and weighed for the experiment. The experimental instrument was TM85 hydrometer. Then the sieving experiment was carried out. According to Standard for soil method (GB/T50123-2019), the remaining tailings were sieved on a vibrating screen, and the soil particles that remained on each screen were weighed and the percentage of material passing on each screen plate was calculated. The experimental device was a GZS-1 high-frequency vibrating screen.

(3) Shear strength test

The shear box test was employed to test the shear strength of the samples. The shear box test and sample preparation were based on the specification Standard for soil method (GB/T50123-2019), and the equipment used was ZJ strain-controlled straight shear instrument. The samples were unsaturated specimens samples size were 30 cm2 × 2 and the shearing method was fast shear. The vertical pressures applied in the straight shear test were 50 kPa, 100 kPa, and 200 kPa, the shear rate was 0.8 mm/min. The cohesive force and friction angle were obtained by plotting the Mohr strength criterion (Xiao et al. 2010).

2.3 Correlation analysis

Correlation analysis can measure the strength of correlation between variables. Spearman's correlation coefficient is a nonparametric measure of the dependence of two variables, as a measure of the strength of monotonic association between variables. For a sample of sample size n, n raw data are converted into rank data, and the correlation coefficient is given by Eq. (2)

$$\gamma =\frac{{\sum }_{i=0}^{n}{ (x}_{i}-\overline{x}) ({y}_{i}-\overline{y})}{\sqrt{{\sum }_{i=0}^{n}{ \left({x}_{i}-\overline{x}\right)}^{2}{\sum }_{i=0}^{n}{ \left({y}_{i}-\overline{y}\right)}^{2}}}$$
(2)

In the formula, \(\gamma\) is sample correlation coefficient, \(\overline{x}\) and \(\overline{y}\) is sample mean.

In this study, Spearman correlation analysis (Cavallo 2020) was used to explore the correlation between parameters with unique attributes of tailings samples, and the correlation coefficient r shows the degree of relationship, as shown in Table 2.

Table 2 Correlation coefficient level
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3 Experimental results and analysis

3.1 Particle gradation analysis

Erosion of the dam surface and seepage within the dam structure can lead to particle migration. To investigate the effect of rainfall on the tailings particle gradation, mean values were calculated for three samples from each stage of the dam, and the mean values of particle composition and \({C}_{c}\) and \({C}_{u}\) were obtained for different locations of the dam at different rainfall levels. The particle gradation curves of the four sub-dams were plotted for each group of rainfall intensity as shown in Fig. 7.

Fig. 7
figure 7figure 7figure 7

Particle gradation curve under different rainfall intensity

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(1) From Fig. 7, it can be seen that the particle size of 0.002–0.6 mm (the area marked by the red thick line in the figure) is the most significant variation in particle content in these four levels of dams. According to the Tailings Pond Safety Regulations (GB39496-2020), which is the State Standard of the People's Republic of China, the silt particle size is less than 0.074 mm. The sand particle size is 0.074–2 mm, and the gravel particle size is greater than 2 mm. The difference is obvious in the composition of the particles are silt and sand particles, indicating that fine particles were more susceptible to migration by rainfall. (2) In each rainfall test, the particle gradation curve of the first-stage dam (i.e. G1-1, G2-1, G3-1, G4-1, G5-1, and G6-1) is at the top of the other curves, indicating that its particle size was the smallest. In contrast, the curve related to the sample taken from the fourth-stage dam (G1-4, G2-4, G3-4, G4-4, G5-4, and G6-4) is placed at the bottom, indicating its particle size was the largest among the others. From Fig. 7a, b, it can be seen that the gradation curves of the fourth-stage dam differ significantly from those of the other three stages, while the gradation curves of the other three stages are extremely overlapped, indicating that the particle sizes of the first two stages were similar. With the increase in rainfall, the particle content of each sub-dam varies widely in the particle size range of 0.002–0.6 mm, which indicates that the larger the rainfall, the larger the proportion of fines below the dam body and the smaller the proportion above, and the more obvious the change of particle size. (3) The distribution of the particle size curves is in the order of primary dam (i.e., G1-1, G2-1, G3-1, G4-1, G5-1, and G 6-1), secondary dam (i.e., G1-2, G2-2, G3-2, G4-2, G5-2, and G6-2), tertiary dam (i.e., G1-3, G2-3, G3-3, G4-3, G5-3, and G6-3), and quaternary dam (i.e., G1-4, G2-4, G3-4, G4-4, G5-4, and G6-4). It can be seen that the change of particle size in the dam was not sudden, and particles gradually became smaller as the height decreases.

There are significant fluctuations in \({C}_{u}\) and \({C}_{c}\) for all samples compared to the initial sample. The gradation at the bottom of the dam (quaternary dam) was the most heterogeneous. The rainfall erosion causing small particles to move downward from the top of the dam and fill the pores formed by the larger particles, resulting in the reduction of uniformity at the bottom.

3.2 Height as the independent variable

The variation of different particles at different heights was studied, as shown in Fig. 8. The percentage of all three particles changed, indicating that the particles migrated under the combined effect of rain and gravity. Among the three types of particles, the percentage of fine particles varied mostly. The percentage of fine particles increased along the downward side of the dam, indicating that under the erosion of rainfall, the fine particles above the dam were washed to the foot of the dam, and the fine particles accumulated below the dam. The percentage of sand particles fluctuated slightly, while the percentage of gravel particles decreased. Under the same rainfall conditions, the displacement of fine grains was larger than that of coarse grains, indicating that fine grains were more susceptible to rainfall.

Fig. 8
figure 8

Relationship between the particle gradation and height

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The analysis of the variation of physical parameters of tailings with external influences has a crucial impact on the subsequent study of their mechanical properties. Thus, the variation of physical parameters including Cu, Cc, \({d}_{50}\), and density of tailings at different heights is plotted as Fig. 9.

Fig. 9
figure 9

Relationship between physical properties and height: the six curves (G1, G2, G3, G4, G5, G6) respectively represent different rainfall intensities (8 mm/h, 15 mm/h, 20 mm/h, 25 mm/h,30 mm/h,35 mm/h)

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It can be observed in Fig. 9 that \({C}_{c}\) decreases with increasing height, which is due to the migration of fine particles to the bottom the dam due to rainfall. As a result, the tailings lack a certain size of soil particles in the range of 30% of the sieving weight and 60% of the sieving weight.

The variation of \({C}_{u}\) at different heights is plotted as shown in Fig. 9. \({C}_{u}\) decreases with increasing height, i.e., the percentage difference between coarse and fine particles below the dam body is much larger than that above the dam body. This indicates that more fine particles filled the voids between the coarse particles at the bottom of the dam in comparison to the top. From the perspective of \({C}_{u}\), it proves that rainfall causes particle displacement and the fine particles are washed below the dam body by rainwater. As the height is lower, the dispersion of the \({C}_{u}\) values are more significant, indicating that the \({C}_{u}\) values below the dam body are more influenced by the rainfall.

The figure shows \({d}_{50}\) increases with height, indicating that the average particle size below the dam was smaller than that above the dam. The absence of fine particles above the dam body is positively correlated with the amount of rainfall, therefore the higher the location of the tailings, the faster the \({d}_{50}\) growth rate of the large rainfall group. Thence, with the increase of height, the \({d}_{50}\) curves of G3–G6 grow faster than G1–G2. Below the dam body, the \({d}_{50}\) values of G1, G2 are slightly larger, and the \({d}_{50}\) curves of G1–G6 meet at a height of about 1.2 m. This area is the turning point of dam body. Below this height, the higher the rainfall, the smaller the \({d}_{50}\). And above it, the higher the rainfall, the larger the \({d}_{50}\). The rainfall intensity of G3 is 20 mm/h, which is the turning point, and at this point the gradient of the \({d}_{50}\) of the dam increases significantly.

The bulk density of tailings samples against the height for different rainfall intensities is given in Fig. 9. It can be obtained that generally during the rainfall the density decreased and the tailings became looser as the height increased. The ratio of density reduction is higher at the bottom of the dam and it reduces gradually as the height increases at low rainfall intensities (i.e., G1 and G2). However, at higher rainfall intensities the reduction ratio is almost the same for the whole dam body. It can be concluded that the rainfall intensity and the position of the samples are factors affecting the density of tailings.

The water content of tailings samples at different heights is illustrated in Fig. 10. From the graph, it can be seen that there is a similarity on the water content variation of the G1, G2, G3 groups related to the height. In these groups, the water content increases as the height rise from 0.6 to 1.4 m, and then suddenly drops at 1.4 m to 1.8 m. A parallel behavior on the water content variation of G4, G5, G6 is also observed, which is the water content increases with height. There could be two reasons for this behavior. First, the loss of fine particles at high places increased the void ratio, and as a result, much more water could fill the pores and the water content increased. Second, the value of \({d}_{50}\) at 1.8 m is larger, the pores between particles are larger and permeability is high. Therefore, under low rainfall intensity (i.e., 8–15 mm/h), the water could more freely penetrate down the dam body, with a ratio greater than rainfall intensity. Therefore, the water content dropped at the top of the dam. With the further increase of rainfall, the ratio of rainfall intensity became greater than water penetration and caused an increase in the water content at 1.8 m.

Fig. 10
figure 10

Relationship between water content and height: the six curves (G1, G2, G3, G4, G5, G6) respectively represent different rainfall intensities (8 mm/h, 15 mm/h, 20 mm/h, 25 mm/h,30 mm/h,35 mm/h)

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The ultimate strength of soil against shear sliding under external forces is called shear strength, which can be considered being composed of the internal frictional resistance between particles and the cohesive force caused by the molecular gravitational force of the cement and the bound water film. The variation of cohesion and friction angle of tailings samples at different heights is plotted in Fig. 11.

Fig. 11
figure 11

Relationship between cohesion, friction angle, and height: the six curves (G1, G2, G3, G4, G5, G6) respectively represent different rainfall intensities (8 mm/h, 15 mm/h, 20 mm/h, 25 mm/h,30 mm/h,35 mm/h)

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The figure indicates the cohesive force drops and becomes smaller with the increase of height. This behavior could be due to three reasons. First, the cohesive force includes the original cohesive force and the curing cohesive force (Anthony 2012). The closer the distance between the particles, the more contact points of soil particles per unit area, the greater the original cohesion. The gradation of the tailings below the dam is not uniform, the \({d}_{50}\) is smaller, and the density is larger, which means the distance between the particles is closer, the water film is thinner, and the original cohesion is greater. Second, cured cohesion is the cohesion of the soil due to cementation, and when the natural structure of the soil is destroyed, the cured cohesion is then lost. Compared with the lower part of the dam body, the upper part of the dam body was destructured by rainfall, which caused the particles to migrate, the gradation became uniform, and the density became smaller. Third, the water content above the dam body was greater, and the surface of the tailing particles was thickened with a water film, which reduced the hydraulic cementation force.

On other hand, Fig. 11 shows that the friction angle generally increases with the increase in height. After the rainfall, compared with the lower part of the dam, \({d}_{50}\) and the percentage of coarse particles in the particle gradation above the dam body was greater. These particles have an irregular shape. The larger the tailings particles, the more irregular the shape. The greater the sliding friction generated by sliding between particles, and the greater friction angle. Due to the absence of fine particles at top of the dam, the proportion of gravel grains increased and caused the friction angle to grow. Experimental research shows that while the value of internal friction angle of sandy soil in a dry state and the internal friction angle value in a saturated state are very close (only 1–2° difference), the water content has no significant effect on the friction angle of sandy soil (Xian et al. 2017). The reason the internal friction angle increased at the top of the dam while the density decreased is compared to the density, the particle size gradation, and particle shape have more influence on the friction angle.

3.3 Rainfall intensity as the independent variable

The variation of different particles at different heights was studied (Fig. 12). The percentage of all three particles changed, indicating that the particles migrated under the combined effect of rain and gravity. Among the three types of particles, the percentage of fine particles varied mostly. The percentage of fine particles increased along the downward side of the dam, indicating that under the erosion of rainfall, the fine particles above the dam were washed to the foot of the dam, and the fine particles accumulated below the dam. The percentage of sand particles fluctuated slightly, while the percentage of gravel particles decreased. Under the same rainfall conditions, the displacement of fine grains was larger than that of coarse grains, indicating that fine grains were more susceptible to rainfall.

Fig. 12
figure 12

Relationship between the particle gradation and rainfall intensity

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The variation of physical parameters of tailings with rainfall intensity is plotted as shown in Fig. 13.

Fig. 13
figure 13

Relationship between physical properties and rainfall intensity

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The values of \({C}_{c}\) and \({C}_{u}\) below the dam are greater than above. The \({C}_{c}\) and \({C}_{u}\) values show an M-shape behavior with the increase of rainfall, and the lower the location the greater the change of \({C}_{u}\) values. The \({C}_{c}\) and \({C}_{u}\) values of the whole dam body are abnormal when the rainfall is 20 mm/h, and their values reach a tough at the point. From the above analysis, it can be concluded that the rainfall of 20 mm/h is the critical point for the change of physical properties of tailings to accelerate, and the preliminary analysis of \({C}_{c}\) and \({C}_{u}\) abnormalities at this point are related to this.

The changes in \({d}_{50}\) were analyzed for different rainfall amounts as illustrated in Fig. 13. At 0.6 m and 1 m, \({d}_{50}\) decreased with increasing rainfall. And at 1.4 and 1.8 m, \({d}_{50}\) increased with increasing rainfall. As the rainfall intensity increased the variation ratio of \({d}_{50}\) increased at the above dam body and decreases at the bellow of the dam body. Above the dam body (i.e., 1.4 and 1.8 m), fine particles moved and left the pores formed by coarse particles. And with the increase of rainfall, the rate of particle loss was further accelerated, which accelerated the destabilization of the dam body.

The variation of density at various positions of the dam with rainfall intensity is given in Fig. 13. As the height is lower, the density is higher. At 0.6 m the density increased with the rising of rainfall. At 1 m the density first increased and then leveled off with the increase of rainfall. At 1.4 m the density increased as the rainfall increased from 8 to 20 mm/h, and then with further increase of rainfall the density dropped. Finally, at 1.8 m the density diminished with the expansion of rainfall. It can be concluded that rainfall had different effects on different areas of the dam body in terms of density and the greater the rainfall, the more significant effect.

The variation of water content under different rainfall amounts is plotted in Fig. 14. It can be observed that the water content at 1.4 m was greater than that at 1.8 m when the rainfall was 5–20 mm/h. With the increase of rainfall, the water content at 1.8 m exceeded that at 1.4 m. The water content at 1 m was always higher than that at 0.6 m. From this, it can be concluded that as rainfall intensity increased the water content raised which is a typical behavior of tailings materials.

Fig. 14
figure 14

Relationship between water content and rainfall intensity

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The variation of cohesion and friction angle of tailings is plotted for different rainfall amounts in Fig. 15. The cohesive force below the dam body was greater than that above the dam body. The cohesive force at 0.6 m increased with the increase of rainfall, which was resulted from the continuous accumulation of fine particles above the dam body to the bottom. At 1 m height, the cohesion increased at rainfall intensity of 8-15 mm/h, and then dropped as the rainfall increases. When the rainfall was small, the fine particles moved from above to this position. With the increase in rainfall, the fine particles at 1 m were washed away and transferred to the bottom of the dam resulting reduction in the cohesive force. Besides, at 1.4 m and 1.8 m the fine particles were lost significantly causes a lowering in the cohesive force. With the increase in rainfall, the friction angle fluctuated slightly, and the friction angle above the dam body was greater than that below the dam body. The friction angle at 1.4 m and 1.8 m increased and decreased in opposite directions when the rainfall was 8–25 mm/h. The friction angle at 1 m increased abruptly when the rainfall was 20 mm/h, and then changed in the same way as at the high place, while the friction angle at 0.6 m was almost unchanged. Therefore, when the rainfall was small, the friction angle at different locations of the dam body showed different change patterns. And with the increase of rainfall, the changing trend tended constantly.

Fig. 15
figure 15

Relationship between cohesion and friction angle with rainfall intensity

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3.4 Comprehensive analysis of multiple factors

The nine parameters (rainfall intensity, dam height, \({d}_{50}\) \({C}_{u}\), \({C}_{c}\), water content, density, internal friction angle and cohesion) were classified into three levels. The primary parameters are external influences: rainfall intensity, and dam height; the secondary parameters are physical parameters: particle gradation parameters (\({d}_{50}\), \({C}_{u}\), \({C}_{c}\)), water content and density; and the tertiary parameters are mechanical: internal friction angle, and cohesion. The degree of influence between the parameters of different grades was analyzed.

Spearman correlation analysis was used to investigate the effect of dam height in the primary parameters on the five secondary parameters. Table 3 shows that the height has a highly negative correlation with \({C}_{u}\), \({C}_{c}\) and density, a highly positive correlation with \({d}_{50}\), a moderate positive correlation with water content. For the whole dam, the higher the location, the more homogeneous the size of the tailings. The larger the particles, the higher the water content, and the lower the density.

Table 3 Correlations between height and physical parameters
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The effect of rainfall on the secondary parameters of each level of the dam was studied in blocks according to height using Spearman correlation analysis. The effect of rainfall on \({C}_{u}\) and \({C}_{c}\) of first sub-dam was weak, with a significant negative correlation with \({d}_{50}\) and significant positive correlation with water content and density (in Table 4). Rainfall had a low negative correlation with \({C}_{u}\) and \({C}_{c}\), a significant negative correlation with \({d}_{50}\), a significant positive correlation with water content, and a moderate positive correlation with density for the second sub-dam as shown in Table 5. Rainfall was negatively correlated with low \({C}_{u}\), significantly negatively correlated with \({C}_{c}\), significantly positively correlated with \({d}_{50}\), highly positive with water content, and negatively correlated with low density for the third sub-dam in Table 6. Rainfall was moderately positively correlated with \({C}_{u}\), moderately negatively correlated with \({C}_{c}\), significantly positively correlated with \({d}_{50}\) and water content, and significantly negatively correlated with density for the fourth sub-dam in Table 7. Therefore, it can be concluded that, the effect of rainfall on the nature of tailings at different heights had different patterns. As the intensity of rainfall increases, the difference between the size of tailings particles in the middle and lower part of the dam body becomes larger, and the difference between coarse and fine particles above the dam body becomes smaller. The water content increased with increasing rainfall intensity at different heights. Rainfall increased the density below the dam body and decreased the density above the dam body.

Table 4 Correlations between rainfall intensity and physical parameters at first sub-dam
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Table 5 Correlations between rainfall intensity and physical parameters at second sub-dam
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Table 6 Correlations between rainfall intensity and physical parameters at third sub-dam
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Table 7 Correlations between rainfall intensity and physical parameters at fourth sub-dam
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The effects of five secondary parameters on the cohesion and friction angle were analyzed. From the results, \({C}_{u}\) and \({C}_{c}\) were highly positively correlated with cohesion, while \({d}_{50}\) moisture content and density were highly negatively correlated with cohesion in Table 8. Among the five secondary parameters, \({C}_{u}\) had the strongest effect on cohesion, similar observations about \({C}_{u}\) were obtained in the studies (Cao et al. 2019). \({C}_{u}\), \({C}_{c}\) and density were highly negatively correlated with the friction angle, \({d}_{50}\) was moderate positively correlated with the friction angle, and water content was highly positively correlated with the friction angle. Among the five secondary parameters, water content had the strongest effect on the friction angle.

Table 8 Correlations between physical parameters and mechanical parameters
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The primary parameters affect the secondary parameters and thus the tertiary parameters. The effect of dam height on all five secondary parameters is moderately strong, with the strongest effect on \({d}_{50}\). The effect of rainfall on the secondary parameters varies among the primary parameters at different heights. For the whole dam body, rainfall has the strongest effect on water content, and the physical parameters at the top of the dam are more influenced by rainfall compared to the middle and lower parts. The movement of fine particles above the dam body downward by rainfall changes the particle distribution and density of the tailings at different locations, and the spatial distribution of the cohesion and friction angle of the tailings consequently changes, which affects the stability of the dam body and causes the upper part of the dam body to be more susceptible to destabilization. This explains why in rainfall-induced landslides of tailings dams, the upper part of the tailings dam is generally the first location where damage occurs.

4 Discussion

In this study, a tailings dam model similar to the actual situation on site was built, which is a large outdoor model compared to other model experiments (Li et al. 2023; Zhang et al. 2022), the model length scale was determined as 1:100 according to the tailings dam site, it can be analyzed more clearly and comprehensively that the variation of the tailings' physical parameters including tailings particle size gradation and water content in different areas of a modeled tailings dam under various rainfall intensities and their influence on the mechanical properties of the tailings. Besides, Spearman's correlation analysis was used to explore the correlation among the physical parameters such as particle grading parameters (\({d}_{50}\), \({C}_{u}\),\({C}_{c}\)), water content, and density. It filled the research gap of consider these factors together and analyzed the interrelationships among them, provided a better vision into the process of tailings dam failure and lays a foundation for future generations to study the monitoring and warning methods of tailings pond.

From a microscopic point of view, tailings are a broken granular material, and the tailings particles themselves are difficult to be destroyed, but the contact interfaces between them are fragile and easily displaced. Therefore, the interaction force between the particles determines the strength of the tailings. This leads to the dominant form of tailings damage is shear damage, and the shear strength of tailings is expressed as cohesion and friction. The tailings in the initial state of the size particles are relatively closely arranged, as shown in Fig. 16a. When the rainfall is small, water enters the tailings skeleton and destroys the original stable state between the tailings particles. Fine particles float due to the buoyancy of the water, and the arrangement of particles within the soil unit becomes loose, and the cohesion and friction angle of the tailings change. Next, the water is absorbed by the tailings, the water content increases, and the weight of the tailings increases accordingly in Fig. 16b. As a result, the tailings unit needs to bear greater pressure from other tailings units and its state is more unstable. As the intensity of rainfall increases, finer particles move out of the pores formed by the coarse particles under the action of seepage water in Fig. 16c. Subsequently, the porosity of the tailings continues to increase, and the percolation rate continues to increase. The coarse particles are carried away by the water one after another. As the above scouring process continues to develop, permeable seepage channels will form within the tailings, causing tailings collapse or other types of damage.

Fig. 16
figure 16

Three state of tailings unit

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From a macroscopic point of view, the fine particles are more susceptible to the impact of rainwater and move greatly from the top to the bottom of the dam. Therefore, the homogeneity of the tailings above the dam body increases and the water content increases. The density decreases, leading to a decrease in cohesion. Although the friction angle increases slightly, the shear strength of the tailings decreases because of its slight variation and the tangential influence of the Coulomb shear strength formula. On the contrary, at the foot of the dam, the fine particles fill the pores formed by the coarse particles, the inhomogeneity of the tailings decreases, the density increases, and the shear strength increases. For the whole dam body, the physical parameters vary from region to region and their mechanical parameters vary as well. Therefore, the damage of the tailings dam occurs in a way that the shear strength of the tailings is first reached above the dam body, where the tailings are in a state of instability. With further growth of rainfall, the physical properties of the tailings further change, and their mechanical properties also change. The tailings are more likely to become unstable. More and more tailings are in the destabilized state until a through sliding damage surface is formed and the tailings fall off in pieces and the dam could be damaged.

5 Conclusions

To study the spatial variation of rainfall on the physical and mechanical properties of tailings in tailings dams and the correlation between the parameters, rainfall experiments were carried out on a physical model with the Luomukeng tailings pond as the prototype, and the following conclusions were obtained.

  1. 1.

    Rainwater transferred the tailings particles from the top of the dam body to the bottom. However, due to the irregular shape of coarse particles and a rougher surface in comparison to the fine particles, they were more stable. The number of fine particles which transferred and the range of relocation were greater. Additionally, as the rainfall intensity increased the erosion was more significant and caused an impressive change in the particle size distribution of tailings which could lead to instability of the dam structure.

  2. 2.

    Changes in the physical properties of the tailings resulted in changes in their mechanical properties. As rainfall amount increased, the mechanical properties of the tailings changed significantly in different areas, and the spatial distribution of the mechanical properties became uneven. It made the tailings dam more susceptible to instability, especially at the upper part of the dam.

  3. 3.

    From Spearman's correlation analysis, it can be concluded that the effect of dam height on all five secondary parameters is moderately strong, with the strongest effect on \({d}_{50}\), rainfall has the strongest effect on water content, and the physical parameters at the top of the dam are more influenced by rainfall compared to the middle and lower parts, among the physical parameters such as particle grading parameters (\({d}_{50}\), \({C}_{u}\), \({C}_{c}\)), water content, and density, the variation of \({C}_{u}\) had the strongest effect on cohesion and the variation of the water content had the strongest effect on friction angle.