Simulated rainfall experiments were conducted in the State Key Laboratory of Eco-Hydraulic Engineering at Xi’ an University of Technology in China in April 2015. The simulated rainfall system used in this study consisted of more than 1300 hypodermic needles attached to a 0.9 m (length) and 0.45 m (width) bottom plate (Fig.1) that could produce raindrops being quite similar to the naturally-occurred raindrops. The soil-testing bin was 0.9 m long and 0.45 m wide.

Fig.1

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	Fig.1 Schematic diagram of the simulated rainfall system: the overall structure of the system (a); the structural relationship among raindrop, soil flume and overland flow collector (b); the details of raindrop generator(c)

First, a 2-cm-thick layer of field-collected loamy sand was laid in the bottom of the bin to keep the soil drainage conditions similar to those of the natural slope. Next, the upper part was filled with loess of 10-cm thick. The slope of the flume was adjustable with a fixed slope of 15° . The moisture of the testing bin (i.e., loess) was controlled at about 15% and the dry soil bulk density was maintained at 1.25 g/cm³ (Table 1).

Table 1

Table 1

Table 1 Observed rainfall intensity, soil bulk density and porosity under freeze-thaw slopes (FTS)and under control slopes (CS) Treatment Mean rainfall intensity (mm/min) Mean soil bulk density (g/cm3) Soil porosity (%) CS 1.03± 0.005 1.25± 0.006 52.70± 0.33 FTS 1.01± 0.002 1.21± 0.003 53.10± 0.19 Note: All data are means± standard deviation.

Table 1 Observed rainfall intensity, soil bulk density and porosity under freeze-thaw slopes (FTS)and under control slopes (CS)

A rainfall intensity of 1 mm/min was maintained by controlling the flow discharge in the pipe using a flow controller (Ran et al., 2012). A runoff collection device was installed at the bottom of the bin to collect runoff and sediment (Fig. 1). Runoff and sediment samples were collected in pails of known volume at 3-min intervals for each treatment (FTS or CS).Rainfall intensity was measured for each replicate and never deviated from the target intensity by more than 5%. Simulated rainfall was applied for 60 min to both the FTS and CStreatments and three replicates were conducted for all experiments. Splash particles were collected on plastic boards (1.0 m× 0.3 m) and covered with filter paper. Two splash boards were set on both side of the soil flume, intersecting at a 10° -20° angle. The splash particles were collected immediately before runoff appearance and at 10-min intervals after runoff appearance. The FTS was constructed as follows: the flume filled with soil was first wrapped with heat-insulating material to maintain the needed freezing from the top to the bottom. Next, the soil-filled flume was packed in an ultra-low-temperature freezer at a 15° slope. The soil was completely frozenat a temperature of -20.0° C for 24h and then thawed at room temperature for 24h. The room temperature during the experiments was maintained between 18.0° C to 20.0° C.

The soil particle size was measured by laser diffraction using a Mastersizer 2000 particle-size analyzer (Malvern Instruments, Malvern, England; Xu et al., 2013). The ring method was used to measure the soil bulk density, and the soil water content was measured by the gravimetric method. The original soil particle sizes are listed in Table2.

Table 2

Table 2

Table 2 Mechanical composition of the original soil Clay Silt Sand Mean value (%) 1.13 92.87 6.00 Standard error 0.12 0.34 0.24

Table 2 Mechanical composition of the original soil

In this research, soil erodibility was obtained from rainfall simulation experiments conducted in the laboratory. The soil erodibility factor K can be calculated as follows (Yu et al., 2006; Wang et al., 2014):

$K=A/(R\times LS)$.(1)

WhereK(kg• h/(MJ• mm)) is the soil erodibility; A (kg/m²), the amount of soil loss; R(MJ• mm/(m²• h)), the rainfall erosivity factor; and LS, the slope length (i.e., gradient factor). It should be noted that the management practice factors (C and P) of theUSLE were set to 1.

The size distribution of the eroded material was expressed as the mean weight diameter (MWD), which can becalculated using the equation below (Le Bissonnais, 1996):

$MWD=\frac{\sum\limits_{1}^{7}{\overline{{{\chi }_{i}}}}{{\omega }_{i}}}{100}$. (2)

Where$\overline{{{\chi }_{i}}}$ (mm) is the mean diameter of the isize class andω _i(%) is the percentage of particles of thei size class. A total of seven size classes were used (< 0.005, 0.005-0.1, 0.1-0.2, 0.2-0.5, 0.5-1, 1-2and > 2mm).

The soil porosity was calculatedas follows (Hunt et al., 1991):

$P=\left( 1-\frac{{{d}_{i}}}{\rho } \right)\times 100%$.(3)

WhereP (%) is the soil porosity; d_i(g/cm³), the soil bulk density; ρ (g/cm³), the soil density and the commonly-usedvalue is 2.65 g/cm³.

${{V}_{d}}=v\times 10/(c\times t)$.(4)

${{i}_{d}}=i\times \cos \alpha -10\times v/(c\times t)$.(5)

WhereV_d(mm/min) is the runoff rate; v(mL), the runoff volume; c(m²), the simulation area; t(min), the runoff time; i_d(mm/min), the infiltration rate; i(mm/min), the rainfall intensity; andα (° ), the slope gradient.

Statistical analyses were performed with SPSS 16.0 for Windows. An analysis of variance (ANOVA) test was performed to determine the treatment effects on the measured variables. The data were generated using the OriginPro8.5 and CAD 2010.

The runoff rates increased rather rapidly during the initial stage of runoff productionand increased rather slowly after about 15 min underboth treatments (FTS and CS) for the same conditions (Fig. 2a): rainfall intensity, rainfall duration, initial soil water content (before freezing) and slope gradient. The runoff rate of the CS ranged from 0.13 to 0.50 mm/min with a mean value of 0.44 mm/min and the runoff rate of the FTS from 0.12 to 0.46 mm/minwith a mean value of 0.40 mm/min, with the runoff rate of the CS being systematically higher than that of the FTS.

Fig. 2

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	Fig. 2 Temporalvariations in runoff rate (a), infiltration rate (b), sediment yield rate (c) and sediment concentration (d) underfreeze-thaw slopes (FTS) and control slopes (CS).Barsindicate standard errors.

The infiltration rateswere almost identicalunder both treatments (FTS and CS) and declined rapidly during the initial stage of runoff production (Fig. 2b). And, the ratesunderboth treatments declined rather slowly after about 10 min. The infiltration rate under CS ranged from 0.47 to 0.83 mm/minwith a mean value of 0.53 mm/min and the infiltration rate of the FTSfrom 0.51 to 0.85 mm/minwith a mean value of 0.56 mm/min, with the rate under CS being systematically lower than that under FTS.

Sediment yield rate is another important parameter for describing the slope erosion processes. The sediment yield rateswererapidly rising during the initial stage of runoff production and gradually declined after about 10 min under both treatments (FTS and CS; Fig. 2c). The sediment yield rate ranged from 2.76 to 7.98 g/(m²• min)with a mean of 6.74g/(m²• min) under CS and from 2.91 to 8.99 g/(m²• min)with a mean of 7.44 g/(m²• min) under FTS, with the rate under FTS being systematically higher than that under CS. It should be particularly noted that the difference of sediment yield rates between FTS and CS became larger and larger during the initial stage of runoff production (approximately from 3 to 15 min), remained to be rather large during the middle stage (approximately from 15 to 30 min), and maintained at an intermediate level during the final stage (approximately from 30 to 60 min).

The sediment concentrations underboth FTS and CS exhibited gradual declining trends from the runoff initiation onward and the concentration under FTS was systematically higher than that under CS (Fig. 2d). The sediment concentration ranged from 0.021 to 0.012 g/mLwith a mean of 0.016g/mLunder CS and the concentration from 0.024 to 0.014 g/mLwith a mean of 0.018 g/mLunder FTS.

The relationship between cumulative runoff and sediment yield can be fitted by the power function S=aW^b, where S(g/m²)is the cumulative sediment yield, W(L/m²) is the cumulative runoff, and aandb are regression coefficients (Table 3).

Table3

Table3

Table3 Regression analysis of the cumulative runoff (W) and cumulative sediment yield (S) underFTSand under CS Treatment Mean rainfall intensity (mmmin) Regression equation Samples R2 CS 1.03 S=21.201W0.9185 20 0.998* * FTS 1.01 S=24.513W0.9323 20 0.998* * Note: * * , P< 0.01.

Table3 Regression analysis of the cumulative runoff (W) and cumulative sediment yield (S) underFTSand under CS

All fitting equations were significant at P< 0.01 (Table 3), and the absolute value of a for the FTS was 1.15 times greater than that for the CS. For both FTS and CS treatments, the sediment yield increased with increasing runoff with the cumulative sediment yield under FTS being 1.10times greater than that under CS(Fig. 3). Under the same rainfall-intensity conditions, the a and bcoefficients of the power function were significantly larger for the FTS than for the CS, indicating that the dependency of sediment yield on runoff was stronger for the FTS than for the CS.

Fig. 3

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	Fig. 3 Relationship between cumulative runoff and cumulativesediment yield under FTS and under CS

The mean weight diameter (MWD) measurements of washed and splashed sedimentsunder FTS and under CS are illustrated in Figure 4 and the relevant statistical parameters are listed in Table 4. The MWD of splashed sediment ranged from 45.68 to 51.15 µ m and that of washed sediment from39.49 to 47.88 µ m under CS. The MWD of splashed sediment ranged from46.81 to 54.02 µ m and that of washed sediment from40.92 to 51.61 µ m under FTS. The mean values of MWD of splashed sedimentsunder CS and under FTS were 48.00 and 49.83 µ m, respectively. The mean values of MWD of washed sedimentsunder CS and under FTS were 43.17 and 44.68 µ m, respectively, suggesting that there were significant differences in the sizes of particlesbetween splash-detached and wash-detached sediments and betweenCS treatment and FTS treatment.

Table 4

Table 4

Table 4 Mean weight diameter (MWD) values for splashed and washed sediments under FTS and underCS MWD value (µ m) CS FTS Splash Wash Splash Wash Minimum 45.68 39.49 46.81 40.92 Maximum 51.15 47.88 54.02 51.61 Mean 48.00 43.17 49.83 44.68

Table 4 Mean weight diameter (MWD) values for splashed and washed sediments under FTS and underCS

Fig. 4

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	Fig. 4 Mean weight diameter (MWD) of original unerodedsoils, splashed sediments, and washedsediments under CS (a)and under FTS (b)

The MWD values for both splash-detached and wash-detached sedimentsvaried with rain duration (or rain time). The MWD values of splashed sediments were stably higher than the values of washed sedimentsand also than the values of the original uneroded soils (i.e., approximately 46.8 µ m) under both FTS and CS treatments. Three additional notes need mentioning here. First, the MWD values of splashed sediments were more significantly higher than the values of uneroded soils and the MWD values of washed sediments were more significantly higher under FTS than under CS. Second, the MWD values of splashed sediments were significantly higher than those in other two cases (i.e., uneroded soils and washed sediments) only in the middle of the rain time (around 35 min) under CS treatment. Third, the MWD values of splashed sediments were significantly higher than those in other two cases (i.e., uneroded soils and washed sediments) at three time intervals (i.e., around 15 min, around 45 min, and around 70 min) under FTS treatment.

The soil bulk density and porosity decreased by 2.93% and 2.30%, respectively, under FTS compared with those under CS (Table1). These differences between FTS and CS treatments can definitely affect the erosion-relatedsoil physical properties because soil erodibility is directly related to the soil physical properties (Wischmeier et al., 1971). The soil erodibility factor Kin this study was calculated from the rainfall simulation experiments (Table 5). The soil erodibility under FTS treatment was approximately 1.10times greater than that under CS treatment.

Table 5

Table 5

Table 5 Soil erodibility factor (K) calculated from rainfall simulation experiments under FTS and underCS Treatment A (kg/m2) MA (kg/m2) R (MJ• mm/(m2• h)) LS R× LS (MJ• mm/(m2• h)) K (kg• h/(MJ• mm)) 0.40 0.40 0.11 0.78 CS 0.38 0.11 0.78 0.09 4.58 0.43 0.11 0.78 0.47 0.45 0.12 0.78 FTS 0.43 0.11 0.78 0.09 4.99 0.44 0.11 0.78 Note: A, amount of soil loss; MA, mean amount of soil loss; R, rainfall erosivity; LS, slope length-gradient factor; K, soil erodibility.

Table 5 Soil erodibility factor (K) calculated from rainfall simulation experiments under FTS and underCS

As shown in Figure 2a, the FTS soil had a lower runoff rate than theCSsoildid simply because the FTS soil had a lower bulk density and thus a higher porosity, resulting in a greater infiltration rate (Fig. 2b). This finding is consistent with that by Li et al. (2009) and further confirms the significant effects of FT on runoff and on infiltration. As shown in Figure 2c, the FTS soil had a larger sediment yield rate than the CS soil did although the former (FTS soil) had a lower runoff rate. Our result is in contradiction with previous studies (Gimé nez andGovers, 2008; Cao et al., 2015; Zhang et al., 2015). The previous studies indicated that alarger runoff rate could carry a greater amount of sediments. This contradiction or difference might be relatedto the higher erodibility resulted from FTS treatment. Our finding is consistent with that by Wischmeier et al.(1978) and suggests that freeze-thaw (FT) processes can effectively decrease the runoff production and increasethe sediment yield. Also as shown in Figure 2c, the sediment yield rate under FTS was significantly larger than those under CS during the middle stage (approximately from 15 to 30 min) of the rain time and the significantly high rate of sediment rate under FTS may be attributable to potential high erodibility during the middle stage of rain time.As shown in Figure 3, the sediment yield increased with increasing runoff under both FTS and CS, being rather consistent with the data observed in bare field plots (Flanagan et al., 2002; Benik et al., 2003; Zhao et al., 2013). The power-function relationships between cumulative runoff and sediment yield both under FTS and CS presented in this study lend a further support to the early reported relationships (Wang et al., 2010; Xiao et al., 2011; Xu et al., 2015).

The MWD of splashed sediments was larger than that of washed sediments and also larger than that of uneroded soil both under FTS and CS, being supportive to some previous studies showing that the splash-detached particles are coarser thanwash-detached particles (Sutherland et al., 1996; Wan and El-Swaify, 1998). However, our results differ from other previous studies. For example, Issaet al.(2006) demonstrated that the size of splash-detached particles was similar to that of wash-detached particles. A reconcilable explanation for the differences between our results and those of Issaet al. (2006) is that the rainfall intensity can affect sediment yieldmore effectively through runoff generation than throughraindrop splashing (Meyer, 1981). That is, the high rainfall intensity in the case of Issaet al.(2006) first splash-detached the particles and then wash-transported the detached particles, thus resulting in the observed similar sizes between splash and wash. Under similar rainfall conditions, the values of the runoff rate under CS (0.13 to 0.5 mm/min) were not significantly different from those under FTS (0.12 to 0.46 mm/min). However, the MWD values of wash-detached particles under FTS were significantly larger than thoseunder CS in the case of interrill erosion. This indicated that runoff was not the main factor affecting particle selectivity in our experiment. The differences in MWD values between the two treatments (FTS and CS) in the case of interrill erosionmay be resulted from the changes in the soil propertiescaused by FT processes.

This study showed that the soil erodibility under FTS was larger (by approximately 1.10 times) than that under CS (Table 4). The difference in soil erodibility between FTS and CS treatments was primarily resulted from the different soil texture caused by these two different treatments. That is, seasonal FT cycles caused by seasonal and even diurnal changes in soil temperature and moisture can definitely change the soil physical properties and the changes include the decrease in soil bulk density and the increase in soil porosity(Zhu and Zhu, 1991). Specifically, the water (liquid or vapor) within the soil pores can forms a variety of ice intrusions when the soil is frozen, leading to an expansion in the soil volume. The expanded soil starts to thaw and develops a larger porosity when the temperature rises, resulting in an increase in the soil erodibility (Gatto, 2000). This study used the value of K to assess the soil erodibility under FTS and CS treatments. The relationships between runoff and sediment yield have often been used to assess the soil erodibility and the absolute value of the regression coefficient awas also advocated to assess the soil erodibility (Pan and Shangguan, 2006; Wanget al., 2014). The ratio of the absolute values of Kbetween the FTS and the CS was 1.10 and the ratio of the absolute avaluesbetween FTS and CS was 1.15. This suggests that both Kratio andaratio can be used to evaluate the soil erodibility.However, it should be noted that the ratio of the absolute value of a is not equivalent to the soil erodibility factor K. Instead, the value of K only reflects the average conditions of a certain soil, while the value of a may reflect changes in the cumulative amount of sediment eroded under different treatments (FTS andCS).Therefore, the absolute value of a could be used to evaluate soil erodibility to predict the amount of lostsoil more accurately.