Spatiotemporal variability of soil-water characteristic curve model parameters of Lanzhou collapsible loess Open Access

Collapsible loess is widely distributed worldwide, accounting for about one-tenth of the global land area (Li et al. 2019; Ostad-Ali-Askari et al.,2018b). The sensitivity of the hydro-mechanical properties of loess deposits contributes to various problems including the differential settlement (Ostad-Ali-Askari et al. 2018a, 2018b; Derakhshannia et al. 2020), landslides (Yan & Wen 2013), which can in turn damage infrastructure and even cause casualties of the loess region areas of China (Zhang & Peng 2015; Haeri et al. 2019). Numerous studies were conducted to better understand the influence of collapsibility and the stability of slopes in loess deposits from the mechanism. Ng et al. (2017) studied the mechanism from the aspects of microstructure, mechanics and temperature. Xing et al. (2007) believed that the collapsibility of loess was mainly due to the reduction of soil strength and to structural damage from water absorption. Loess is mainly distributed among China in the northwest, where the climate is dry, rainfall is low and the loess is generally unsaturated. The study of the mechanism of collapse of loess based on the theory of unsaturated soil mechanics therefore has high theoretical and application value.

The soil-water characteristic curve (SWCC) defines the relationship between water content and matrix suction in unsaturated soil (saturation, Sr, mass water content, ω, or volumetric water content, θ) (Wang et al. 2017; Zhao et al. 2020), which is widely used in geotechnical, geo environmental, and agricultural engineering (Wang et al. 2017). SWCC is a fundamental element for characterizing the essential aspects of unsaturated soil behavior and it plays an important role in unsaturated soil mechanics. The estimation of the soil-water characteristic curve (SWCC) is currently the main method. Experts and scholars have developed several empirical formulas to represent SWCC, such as the Van Genuchten (VG) model (Lin & Xu 2018) and the Gardner model (Zhang et al. 2019). Among these, the VG model has been widely used because of its good fit with measured data (Liu et al. 2007). Therefore, this paper selects the VG model with good applicability, high precision, and clear physical meaning. Olyphant (2003) found that the VG model parameters of sand basically showed a steady-state change trend over time, but abnormal values appeared before the end of the monitoring period. Chen (2004) obtained an SWCC for slopes in a small watershed in the gully region of the Loess Plateau, which had some amount of spatial variability. Idrysy & Smedt (2007) better predicted the spatial variation of hydraulic conductivity by using hydraulic gradients and Kriging spatial interpolation.

Using SWCC to indirectly derive the permeability coefficient of unsaturated loess has great randomness (Wen et al. 2015). The concept of temporal stability; that is, the preservation of spatial patterns of SWC over time, was introduced by Vachaud et al. (1985). Zucco et al. (2014); Zhao et al. (2017) successfully identified representative sample points that remained stable over time and estimated the average SWC in the field. Coppola et al. (2011) found that the average water saturation affects the temporal stability of the spatial distribution of soil moisture in farmland. The spatiotemporal variability of SWCC has been well studied, but these studies have mainly focused on weak expansive soil, calcareous soil, weathered granite residual soil, gravel-mulched fields (Yun-Xue et al. 2019; Lv et al. 2021; Shen et al. 2021). Little is known about the validity of the concept for Collapsible Loess in northwestern China. The objective of the study is to analyze the temporal stability, spatial variation and determine the representative measurement points of SWCC parameters in collapsible loess using the mean relative differences (MRD), standard deviation (SDRD), index of temporal stability (ITS). A more descriptive understanding of the spatiotemporal patterns of SWCC can further be provided. The findings can be used as a simple method to predict SWCC and provide theoretical guidance for soil water management and soil collapse erosion monitoring in collapsible loess area…

The experimental soil samples were collected from the Peng jia ping campus of Lanzhou University of Technology in Lanzhou City, Gansu Province, China (35°50′–36°06′N and 103°36′–103°54′E) (Figure 1), located in the transitional area from the Qinghai-Tibet Plateau to the Loess Plateau, belonging to the Yellow River Basin. This area is a typical loess landform in China. The climate is temperate continental climate, with an average annual sunshine duration of 2,446 h and an average frost-free period of >180 days. The annual average temperature is between 6.4 and 11.2 °C, the annual precipitation is between 276.4 and 494.2 mm, and the rainfall is mainly concentrated in June to September. Grey cinnamon soil, lime calcite soil, and chestnut soil are the predominant soils in this area.

The temporal stability, spatial variation and the representative measurement points of SWCC parameters were analyzed using the Mean relative differences (MRD), standard deviation (SDRD), index of temporal stability (ITS) with Origin11.0, Surfer and other software.

Geostatistical methods

The SWCC model parameters of the soil in the 0–30 cm soil layers at each sampling point were counted. The statistical results showed that the coefficient of variation (CV) of parameter α (the scaling parameter that is inversely proportional to mean pore diameter) is greater than that of parameter θ_s (the saturated volumetric water content) and n (shape coefficients, the value of n determines the slope of the SWCC, when n is large, the slope is large, and when n is small, the slope is small), CV of α is between 10.19% and 22.36% which indicates moderate variation. The next most influential was n, which indicates low variation. The θ_s had the smallest influence and indicates low variation (Table 1). CV tended to decrease as mean θ_s increased for all layers, in accordance with most previous studies of θ_s spatial variability (Brocca et al. 2012). This is because higher surface θ_s may be the result of soil surface evaporation and plant root water absorption. At the same time, environmental factors such as rainfall and infiltration will make surface CV stronger than its lower layer. However, CV tended to increase as mean θ_s increased for all layers (Penna et al. 2013; Vanani et al. 2017). This is different from our results, which may have been due to study area, the topography or sand content.

The parameter α did not differ significantly between the layers, but the average fitting tended to decrease with depth. The size distribution of the soil particles was 12.88% gravel, 66.58% silt and 20.54% clay for the 0–10 cm layer, 11.03% gravel, 67.32% silt and 21.65% clay for the 10–20 cm layer and 9.59% gravel, 67.14% silt and 23.27% clay for the 20–30 cm layer. Clay content increased, the intake value of the characteristic curve increased and the fitting parameter α accordingly decreased with depth. θ_s was correlated strongly with the change of season. θ_s was low in November, but significantly higher in July, because the region receives more rainfall in July.

The authors used geostatistical Kriging interpolation (Oliver & Webster 2014) in Surfer to draw the spatial distribution maps of SWCC parameters to a depth of 30 cm (Figure 3) and to more intuitively explore the characteristics of the spatial distribution of the parameters at different depths. The soil-water suction measured using a centrifuge was processed by the flow-direction analysis tool in Surfer. The soil-water suction was used as the driving force of the SWCC parameters. The direction of flow obtained from the soil-water suction can approximately represent the prediction of the direction of migration of parameters; the longer the arrow, the stronger the driving force.

The distribution of the SWCC parameters was consistent in different space and time (Figure 3). This result indicated that the SWCC for a specific layer could be estimated using data from adjacent soils, thereby reducing the waste of human and financial resources. The θ_s increases with the increase of soil depth at 0–30 cm, with ranges of 0.4171–0.4510, 0.4205–0.4512 and 0.4208–0.4521 for the 0–10, 10–20, 20–30 cm layers, respectively. The predicted direction of migration of parameters was the same in each layer, indicating that the area was less affected by humans. Parameters migrated from high to low under the effect of the matrix potential gradient. Comparing the statistical results of July and November 2019, the range of the parameter θ_s on the 0–10 cm soil layer further proves that the sampling time is different and the model parameters are quite different.

The authors determined the correlations between the SWCC parameters and the 0–10, 10–20, and 20–30 layers (Table 2). α, n and θ_s were all strongly significantly correlated positively, with correlation coefficients of adjacent layers >0.749. Determining SWCC for the surface layer of the representative point helped the study of soil-water movement and solute transport (Mohammadi & Vanclooster 2010; Golian et al. 2020). SWCC plays an important role in estimating shear strength and the coefficients of unsaturated permeability, diffusion and adsorption.

The model parameters α, n, and θ_s at the 16 sampling points in 2019 are sorted by the mean relative difference (MRD) in order to represent the temporal stability of the SWCC parameters at a depth of 0–10 cm. The green points represent the mean relative difference (MRD). The black error line is the standard deviation of MRD (SDRD). The red points represent the index of temporal stability (ITS) of parameters (Figure 4). SDRD for α, n and θ_s was 0.0263–0.0845, 0.0126–0.0337 and 0.0040–0.0117, respectively. SDRD for θ_s for most measurement points was <10%, similar to the results reported by Liu et al. (2014). MRD for α, n and θ_s was −0.1749–0.2913, −0.1625–0.1013、and −0.0188–0.0319, respectively.

Determining one or a few sampling points where SWCC is the most temporally stable can decrease cost or increase sampling frequency and can be used to estimate the overall field SWCC. Several studies have successfully identified representative points and have estimated the conditions of SWC for study areas (Zucco et al. 2014; Zhao et al. 2017). The representative point with a mean relative difference closest to zero and with the lowest SD can be used to estimate the mean SWC of an experimental area (Bai & Shao 2011). The authors thus selected the point with the lowest ITS, which considers both the MRD and the SDRD, as the most representative point in our study (Figure 4). α, n and θ_s the observation points of the MRDs to 0 were 16, 16 and 12 respectively. However, the SDRDs for these points were not the lowest. α, n and θ_s the observation points of the lowest SDRDs were 2, 11 and 13 respectively. The authors had no observation points for the SWCC parameters, and both of the above conditions were met. So the authors introduced the ITS to assist in identifying the representative measurement points, thereby obtaining the lowest ITS values. The observation points were 16, 16 and 9.

The goodness of fit of the representative sample points identified by the above three methods was analyzed to obtain a statistical table for the VG fitting curve of the representative measuring points of the layers (Table 3). A comparison of the coefficients of determination (R²) and residual square for each layer indicated that R² was highest for measurement point 16, at 0.9718, 0.9662 and 0.9634, for the 0–10, 10–20 and 20–30 cm layers, respectively. The residual squared were lowest at 0.0529, 0.0608 and 0.0643 for the 0–10, 10–20 and 20–30 cm layers, respectively. SWCC and the measured values at measuring point 16 in the layers are shown in Figure 5. The measured points were evenly distributed on both sides of the curve. A single sampling point could thus be used to accurately estimate the field mean SWCC. The identification of representative measurement points of SWCC for collapsible loess because it can reduce the sample size while maintaining a high accuracy of prediction. So the prevention of loss of soil and water on the Loess Plateau provides a fast and efficient monitoring method.

In this study, the spatiotemporal variability and the representative measurement points of SWCC parameters in the collapsible loess region were analyzed using the mean relative differences (MRD), standard deviation (SDRD), and index of temporal stability (ITS). The SWCC parameter α was moderately variable, n and θ_s were weakly variable in the layers. The CVs gradually increased with depth. The analysis of the standard deviations indicated that α, n and θ_s did not differ significantly between the layers. α, n and θ_s were strongly significantly correlated positively in the layers, with correlation coefficients between adjacent layers >0.749. Point 16 was identified as the point most representative of the SWCC, with the lowest cumulated ITS. The representative point was quite reliable for estimating the SWCC, with the highest R² of 0.9718 and the residual squared of 0.0529.

This study has contributed to our understanding of SWCC spatiotemporal patterns in the collapsible loess area in northwestern China. The results can be effectively used to design sampling schemes for SWCC measurements and provide theoretical guidance for soil water management and other applications.

This study was supported by National Natural Science Foundation of China (51869010). Industry Support and Guidance Project for Colleges in Gansu Province (2019C-13).

All relevant data are included in the paper or its Supplementary Information.