3.1 Weathered debris particle size composition and particle size parameter change
3.1.1 Particle size composition
Under different temperatures, the particle size fractions of weathered debris produced by different particle sizes of grey-green slate significantly differed (significance level up to 0.05, Fig. 1). As seen in the figure, the weathered debris of each treatment combination contained relatively more clay, fine silt, and fine sand, and the lowest amount of very fine sand and coarse silt (less than 10%). The clay content of weathered debris in the A4B1, A4B2, A4B3, and A4B4 treatments was higher than that in the remaining treatments, while the silt content in the four treatments was less than that in the remaining treatments. Thus, a smaller particle size of grey-green slate indicates more clay content of weathered debris in the process of freeze-thaw and dry-wet cycles; the possibility of weathering into clay loam is more unusual. On the other hand, grey-green slate can somewhat increase the clay content of the soil, which helps improve the physical and chemical properties of soil and plant growth (Shi et al., 2020) alleviate desertification. In all treatments except for A4B1, A4B2, A4B3, and A4B4, the clay, sand, and silt (very fine silt, fine silt, medium silt, and coarse silt) in the weathered debris were all greater than 30%. During the freeze-thaw and dry-wet cycles, slate with smaller particle sizes had a more uniform particle size distribution of weathered debris.
Temperature has a reduced effect on particle size composition variations of grey-green slate debris under freeze-thaw and dry-wet cycles. The particle size relationship between the particle size fraction of grey-green slate and temperature is as follows: when the particle size is 10–5 mm, the content of fine sand and medium sand gradually increases as temperature increase; the content of clay and very fine sand increases and then decreases as temperature increases; and the content of fine sand and very fine sand decreases and then increases with a temperature increase. When the particle size is 5–2 mm, the content of medium silt, coarse silt, and very fine sand first increases and then decreases with a temperature increase. When the particle size is 2–1 mm, the content of fine sand increases gradually as temperature increases, and the content of clay and very fine silt first increases and then decreases with a temperature increase. When the particle size is 1–0.5 mm, the content of clay, very fine silt, and fine silt decreases and then increases with a temperature increase, and the range of very fine sand and medium coarse sand increases and then decreases as temperature increases.
The cumulative content percentage of the particle size value was used to determine the particle size cumulative frequency distribution curve. The points on the curve represent the probability cumulative percentage sum before the particle size. The particle size distribution range, particle size (coarse or refined), and beneficial or detrimental sorting characteristics can be analyzed using the particle size range on the angle and the steepness of the curve (Dai., 2020). Figure 2 depicts the frequency distribution curves of the particle size accumulation for various particle sizes of grey-green slate under different temperatures. According to the graph, the frequency distribution curves of the particle size accumulation for each treatment had similar shapes and trends. In the 0.5–30.75 µm range, the angle is steeper, where the slopes of the cumulative curve under the A4B2, A4B3, and A4B4 treatments are nearly vertical, indicating that the sorting is better in the 0.5–30.75 µm range under these treatments. The curve is flatter for 30.7–102.4 µm and the slope is almost zero, indicating poor sortability across treatments in this particle size range. The curve shows a steep increase for 102.4–413 µm, indicating a higher sand content and better sorting under each treatment.
3.1.2 Variation of particle size parameters
According to Table 2 and Eq. (1), the particle size parameter calculation formula was derived from the particle size parameters of weathered grey-green slate debris under different temperatures and particle size treatments (Fig. 3). As seen from the figure, the average particle size of the weathered debris of grey-green slate under each treatment was 5.52 Ф (silt grain class 4 Ф-8 Ф). At 44°C and 36°C, the average particle size of weathered debris increased, decreased, and then increased as the particle size of the grey-green slate became smaller. At 28°C and 20°C, the average particle size of weathered debris increased, then decreased with a decrease in the particle size of grey-green slate. The average particle size was largest in the A4B4 treatment and decreased as follows: A4B4 > A4B3 > A4B1 > A4B2 > A3B3 > A2B1 > A1B3 > A1B4 > A1B1 > A3B4 > A2B2 > A3B2 > A2B3 > A3B1 > A1B2 > A2B4.
The median particle size distribution of the weathered debris in each treatment ranged from 4 Ф to 7 Ф, with the silt grade of 4 Ф–8 Ф. Under any temperature treatment, the median particle size of weathered debris with the particle size of grey-green slate was consistent with the average particle size.
Weathering debris skewness varied from 0.7 to 0.95. Overall, the debris had highly positive skewness without symmetry, with an average value of 0.85. The maximum skewness value occurred in the A4B4 treatment, and the minimum skewness value occurred in the A1B1 treatment. Overall, the size of weathered debris in each treatment was concentrated in the coarse range. Weathered debris had a standard deviation of -3.5 to -2.5, with a fluctuation of 1 and a mean value of -2.84. The kurtosis variation of weathered debris ranged from 0.65 to 0.85, with a mean value of 0.75. The low kurtosis values of the curves for the 16 treatments indicate that the particle size frequency distribution curves are mostly broad- or multi-peaked. The kurtosis of the weathering debris frequency curves of 1–0.5 mm and 5–2 mm grain sizes gradually decreased with increasing temperature. 44°C, 36°C, and 28°C showed a trend of increasing and then decreasing weathering debris kurtosis with a decrease in the grey-green slate grain size.
In general, the fractal dimension can categorize the distribution and homogeneity of soil particle size as well as reflect soil fertility. A greater fractal dimension corresponds to more fine particles in the soil (Li et al., 2017; Zhao et al., 2013). The mean value of the weathered debris fractal dimension was 2.41, which is distributed between 2.35 and 2.46. The most significant values of the weathered debris fractal dimension occurred in A2B1 and A3B3, indicating that the two treatments had a higher content of fine particles. The cumulative content of clay, very fine silt, fine silt, medium silt, and coarse silt in the two treatments was greater than 72%, which was higher than that in the remaining treatments.
3.2 Relationship between fractal dimension and particle size composition of weathered debris
The fractal dimension of weathered debris for different treatments was regressed against the particle size composition (Fig. 4). The figure shows that the fractal dimension of weathered debris is linearly related to the particle size composition in the first order. The fractal dimension was significantly positively correlated (P < 0.05) with the content of very fine sand (correlation coefficient of 0.85441) and highly negatively correlated (P < 0.05) with the content of fine and medium coarse sand (correlation coefficients of -0.72692 and − 0.81473, respectively). The fractal dimension was positively correlated with the content of clay, fine silt and medium silt, and it was negatively correlated with the content of coarsesilt and very fine sand. The correlation between the fractal dimension of weathered debris and the content of clay, very fine silt, fine sand, and medium-coarse sand is roughly the same as that found by other scholars (Gao et al., 2014) studying the correlation between soil fractal dimension and particle size composition. Specifically, the fractal dimension had a positive correlation with clay and very fine sand and a negative correlation with fine sand and medium-coarse sand. There is a correlation between the fractal dimension and each particle size composition of weathered debris, which shows that the fractal dimension can characterize the soil's particle size composition.
3.3 Relationship between fractal dimension and mineral elements
The weathering debris formed during the freeze-thaw dry-wet cycle of grey-green slate is partly due to the formation of rock surface fragmentation and leaching, i.e., the element content affects the particle size composition of the weathering debris to an extent. Partial least squares regression (PLSR) was used to screen the mineral element factors affecting the fractal dimension of weathered debris to clarify the influence of each mineral element on the particle size composition of weathered debris.
PLSR is a new multivariate regression analysis method that combines the benefits of multiple linear regression analysis, typical correlation analysis, and principal component analysis. The method can represent the explanation of the dependent variable by the independent variable (Yu et al., 2015). The projection importance (VIP) of each mineral element content on the fractal dimension of weathered debris was calculated using B, Mn, Fe, Ni, Cu, Zn, Ca, Mg, P, K, S, Si, Na, Mo, N, and Cl mineral element content as independent variables and weathered debris fractal dimension as dependent variables. The stepwise screening of the respective variables was carried out based on the size of the VIP value of the full PLSR model. A VIP value greater than 0.8 usually indicates that the independent variable has a greater influence on the dependent variable. A VIP value greater than 1 indicates that the independent variable has a large influence on the dependent variable. The mineral element factors influencing the fractal dimension of weathered debris are screened based on VIP values greater than 1.
Figure 5 depicts the stepwise screening of the mineral element factor. The screening was terminated when the VIP values of all independent variables were greater than 1. There were four screenings in total. The VIP values of Ni, Zn, Ca, P, S, Si, Na, N, and Cl in the first screening step were more significant than 1, which indicates that these elements among the 16 mineral elements had a greater influence on the fractal dimension of weathered debris. Mineral elements with VIP values more significant than 1 were screened again, and the results indicate that the VIP values of Ni, Ca, P and Na were more critical than 1. The third screening step showed that the VIP values of Ni and P were higher (1.180 and 1.181, respectively). After screening, the Ni and P VIP values were more significant than 1. At this time, the screening was stopped, and the primary mineral elements affecting the fractal dimension of weathered debris were extracted (i.e., P and Ni).
Combining the VIP values of each mineral element, the magnitudes of the influence of 16 mineral elements on the fractal dimension of weathered debris were largest to smallest as follows: P, Ni, Na, Ca, N, Si, Zn, Cl, S, Mg, Mn, Mo, Cu, B, Fe, and K.
3.4 Analysis of potential environmental factors affecting the fractal dimension of weathered debris
Principal component analysis (PCA) analyzed the potential environmental factors affecting the fractal dimension of weathered debris (Fig. 6). The variance contribution of the first central component (PC1) was 44.7%, and the variance contribution of the second principal component (PC2) was 25.5%, resulting in a representative cumulative variance contribution of 70.2%. The fractal dimension vector of weathered debris forms an acute angle with the electrical conductivity (EC) and elemental leaching vectors, as shown in Fig. 5. The direction is consistent, indicating a positive relationship between fractal dimension, EC, and elemental leaching. The relationship between fractal dimension and EC is more robust than the relationship between elemental leaching. The fractal dimension correlated negatively and weakly with particle size, temperature, and pH. Weathered debris formation is generally influenced by EC, elemental leaching, temperature, grain size, and pH.