Prediction of soil water characteristic curves based on low suction section and inflection point Open Access

The soil water characteristic curve (SWCC) characterizes the relationship between soil suction and soil water content (saturation, mass water content, volume water content) (Chen et al. 2015; Pham et al. 2019; Zhao et al. 2020a), which is the basis of studying soil water movement and solute transport (Fu et al. 2011; Xing et al. 2016). Therefore, researchers have developed many methods for the determination of SWCC (Ishimwe et al. 2014; Haghverdi et al. 2018), among which the centrifugal method is the most widely used. Although the operation is simple, the density change and centrifugal time in the centrifugal process have certain effects on measurement results, so measured parameters often have low accuracy (Sun et al. 2019; Wang et al. 2019a). Wang et al. (2020) compared and evaluated the van Genuchten model, Brooks-Corey model, lognormal distribution model and the residual film SWCC estimation model based on improved pore size distribution. Therefore, a method of minimizing the centrifugal speed and suction without losing important information has important research value.

The direct determination of a SWCC has the disadvantages of high cost and complex steps and is time-consuming. In addition, the spatial variation of soil also limits the application of SWCCs in practice (Qin & Fan 2020). Indirect methods are based on the basic properties of soil, and use some empirical or semi-empirical relationship to establish an SWCC prediction method, the main three being: pedotransfer function (Wang et al. 2019b); physical empirical method (Zeiliguer et al. 2000); and the fractal method (Perfect 1999). Wang et al. (2017, 2019a) explored the effects of ammoniated straw and inorganic changes on SWCCs and soil water holding capacity. Stoof et al. (2010) evaluated the effect of the addition of ash on soil water retention. Various methods have been used to combine empirical models for SWCCs in low-suction sections with Campbell and Shiozawa models to describe the full range of SWCCs. (Khlosi et al. 2006; An et al. 2019). Peng et al. (2012) combined the Hyprop system with rapid centrifugation to determine SWCCs in the full range of suction. The inflection point is an important characteristic for determining SWCCs. Chen et al. (2014) proposed a method to estimate SWCCs for high-suction sections by assuming that the sections were the tangents of the low-suction sections at a water potential of −15,000 cm. Niu et al. (2020) reported that pores corresponding to the peak point were the dominant pores, corresponding to the inflection points of SWCCs. Pan et al. (2020) found that determining the inflection point played an important role in obtaining the tangent equation of the transition zone. Few reports have predicted SWCCs using low-suction sections and inflection points.

Residual saturation and residual suction are basic parameters of SWCCs. The accurate determination of these parameters is the basis for the study of unsaturated soil strength, permeability, and constitutive relationships (Gao et al. 2017). Brooks & Corey (1964) believed that the soil-water content when the matric suction reached infinity was the residual water content. Fredlund & Xing (1994) used traditional mapping to obtain the air-entry value of SWCCs. These traditional methods, however, are prone to large errors due to subjective uncertainties (Soltani et al. 2019). Chai & Gao (2021) predicted that there was no test data available for SWCCs in the study area by using the saturated permeability (ks), plasticity index (PI) and grain size distribution (GSD) curves of soil. Throughout the current research, there are few reports on the prediction of SWCCs by using low suction section and inflection point.

Therefore, to reduce the influence of centrifugal force and subjective factors on the determination results of SWCCs, taking Lanzhou collapsible loess as an example, the SWCC with the best low suction section symmetrical about the inflection point was determined, and the calculation formula for the intake suction value of soil characteristic parameters was deduced. This is expected to provide a simple method for the prediction of SWCCs in this region and give guidance for soil moisture management in the loess area.

Soil samples were collected from the Pengjiaping Campus of Lanzhou University of Technology, Gansu Province, China (Figure 1) at an altitude of 1,628 m, latitude 36 °03′58″N, and longitude 103 °41′44″E. It is a transitional area from the Qinghai-Tibet Plateau to the Loess Plateau. This area has typical loessial landforms and the thickest loessial deposits in China. Annual average sunshine hours are 2,446 hours, with an average frost-free period of 180 days. The annual average temperature is between 6.4 and 11.2 °C, and the annual precipitation is between 276 and 494 mm. The precipitation is mainly concentrated from June to September. The main soil types are calcareous, chestnut, and cinnamon soils.

The study area was 80 × 80 m, and soil samples were collected mechanically. The tilled soil layer of 0–30 cm was excavated at the central point and every 20 m. (Figure 2). The soil particles in the study area were measured by a Mastersizer 2000 laser particle size analyzer. The test results were classified according to the soil texture classification standard of the United States Department of Agriculture (Table 1), and the tested soil was silty clay loam. Bulk density was measured using the ring knife method due to the wide distribution of soil samples and the convenience of centralized management. Bulk density ranged from 1.38 to 1.58 g/cm³. Accordingly, artificial loading was carried out with three different bulk densities of 1.38, 1.48 and 1.58 g/cm³. All samples were air-dried, sieved through a 2-mm mesh, and layered in a 100-cm³ ring knife. SWCCs were determined using a Nissan CR21G II high-speed refrigerated centrifuge maintained at 4 °C. The samples were centrifuged at a suction range of 0–7,000 cm.

A number of assumptions are made in the inverse inflection point symmetry method:

Soil saturation under various pressures is presented in Table 2. The spatial CV of soil saturation increased with the suction in each pressure section. The variation of saturation with bulk density was associated with the volumetric water content. As the suction increased, more soil pores were drained, soil-water content decreased and the CV of saturation increased. Bulk density was weakly and moderately spatially variable when suction was <800 and ≥800 cm, respectively.

The curve of soil saturation CV versus pressure for each bulk density is shown in Figure 3. At the same suction, the spatial variabilities of saturation and volumetric water content increased with bulk density. When the suction increased, the CV of each bulk density decreased as saturation decreased, indicating high spatial variability. This relationship was important for the determination of the SWCCs: when the suction is low, the spatial variability is low, and the number of samples can be reduced, and when the suction is high, the number of samples should be increased.

In order to further determine the relationship between different bulk densities and soil saturation, this paper analyzed the correlation between different bulk densities at 1.38 g/cm³, 1.48 g/cm³ and 1.58 g/cm³, respectively. The results are shown in Table 3. Each bulk density was significantly positively correlated with saturation, with coefficients for adjacent soil layers >0.9932. This result indicated that the SWCC for soil with a specific bulk density could be estimated using other bulk densities, which could substantially reduce manpower and material resources in future studies.

SWCCs of continuously graded or single graded soils show an S-shaped unimodal shape and have symmetrical geometric characteristics. The curve is sigmoidal (Figure 4). Two inflection points, A and C, divided the curve into three parts. Points A and C are usually determined using the tangent method (Zhou et al. 2010). Inflection point B is an important point in SWCCs. Assuming that the curve is symmetrical around point B, the curve can use part of the suction value to determine the complete SWCC by using the partial suction value and triangle equivalence theorem.

This paper refers to the inflection point, using Equation (1) to find a point where the second derivative equals 0, and using the measured data of different suction sections to predict SWCC symmetrically. The study showed that when the suction of each soil layer was less than 800 cm, the soil saturation showed weak variability, and the correlation of SWCC determined by the data of 0–800 cm suction was high. It can be seen that this method can not only reduce the time-consuming and laborious problem but also reduce the experimental error of spatial variability caused by the increase of suction.

For 48 groups of measured saturation data, Origin software fitting was used to determine the SWCC parameters a and n, and Equation (7) combined with a statistical method was then used to obtain the average bulk-density inflection point at 1.58 g/cm³ as (2.6626, 0.5066). The SWCCs for the 0–300, 0–500, 0–800 and 0–1,000 cm measured data were symmetrically determined, and the prediction-fitting equation of each data point was obtained using Equation (1). The relative values for suctions of 100, 300, 500, 800, 1,000, 3,000, 5,000 and 7,000 cm were entered into the above prediction-fitting equation, and the saturation predicted by this method was calculated. The measured and predicted values were statistically analyzed using least squares (Table 4). The maximum correlation coefficient between the measured value and the measured data for 0–800 cm suctions was 0.9941, indicating that the assumption of the symmetry method of the reverse bending point is feasible. Future determinations of SWCC will thus only need centrifugation to suction of 800 cm, which will reduce the problem of increasing spatial variability due to the increase in suction, greatly shortening the centrifugal time and reducing the workload.

The measured data from published SWCCs (Aubertin et al. 1998; Miao et al. 2006; Pan et al. 2020) were used to verify the proposed method. The published basic soil properties are presented in Table 5. The predicted and measured values were statistically analyzed using Equations (3) and (4). MAE and RMSE were close to 0, indicating that the predicted and measured values agreed well and that the proposed method for determining SWCCs using measured data for suctions of 0–800 cm on the inflection point was accurate.

Equation (1) was symmetrically determined using the inflection point (2.6626, 0.5066) of 0–800 cm suction measured data for bulk densities of 1.38 and 1.48 g/cm³, and the predicted saturation under different suctions was then calculated using it. The relationship between the predicted and measured values at different bulk densities was determined. The saturation dispersion points for each bulk density were distributed on both sides of the 1:1 line, with the small deviations and strong correlations (Figure 5). The correlations between the bulk densities for the same texture were strong, and the SWCCs could be symmetrically determined using the same inflection point.

Basic SWCC parameters include residual saturation and residual suction. The accurate determination of the basic parameters is the basis for the study of the strength and permeability of unsaturated soil. Zhou et al. (2010) used a graphical method to determine the actual measured values of the basic parameters of the traditional SWCC fitting method. The prediction value of residual saturation was determined by SWCC combined with the tangent method in this paper, and the prediction value of suction at intake point was determined by Equation (10). The statistical analysis of the characteristic soil parameters (Table 6) indicated that the absolute value of the relative error between the measured and the predicted values of the parameters was <0.0469, and the CV for each parameter tended to decrease as the bulk density increased.

In order to explore the spatial distribution characteristics of the basic parameters of SWCCs more intuitively, a spatial distribution map of soil characteristic parameters was drawn using Surfer's statistical Kriging interpolation method and taking 1.58 g/cm³ bulk density as an example (Figure 6). Each parameter had a ‘bump and uneven’ distribution. Each parameter diffused and migrated in the same direction, from high to low, under the action of the matrix potential gradient. The method for predicting SWCC with low suction and inflection points guaranteed accurate curve fitting and characteristic soil parameters, and the predicted values could effectively predict the spatial distribution of the characteristic soil parameters throughout the study area. This provides a new idea to guide other regions to use this method for determining SWCCs, which is important for current and future research.

The centrifuge method has the advantages of simple measurement and wide range of application for determining SWCCs. Increasing the speed of centrifugation, however, increases soil suction, the gradual discharge of water and air from the soil and bulk density, and decreases soil volume, leading to high variability. Studying the prediction of SWCCs using data from the low-suction section and inflection points therefore has practical importance. Shao et al. (1985) reported that the bulk density of Wugong heavy loam could be increased from 1.3 to 2.0 g/cm³ under suction of 0–204 m, and Lu et al. (2004) found that the bulk density of clayey loam increased by 0.6 g/cm³ during the determination of SWCCs, which had a great influence on soil water conductivity. Xing et al. (2015) reported that changes in bulk density could not be ignored when determining SWCCs by centrifugation, consistent with the conclusion that increasing suction and bulk density increases variability.

The characteristic parameters of soil water are very important in strength and seepage theories of unsaturated soil. Many studies have directly used water content corresponding to 1,500 or 3,000 kPa as the residual water content. This method is currently popular but is purely empirical (Genuchten & Th 1980; Sillers & Fredlund 2011; Tao et al. 2018). Niu et al. (2020) found that the corresponding air-entry value of pores between compact samples was about 73 kPa, and the corresponding residual value of pores between compact samples was about 600 kPa. The accuracy of SWCCs due to the accurate determination of the basic parameters of SWCC, however, has rarely been studied, so accuracy is difficult to guarantee. The predicted residual saturation was therefore determined using SWCCs combined with the tangent method, and the predicted suction at the intake point was determined using Equation (9). SWCC data for different textures and bulk densities were used to verify the method for predicting SWCCs at low-suction sections of 0–800 cm and inflection points. Both statistical indicators MAE and RMSE were close to 0, and the correlation coefficient was >0.9915. This method thus had high prediction accuracy, which is convenient for the determination of SWCCs and reduces the experimental error of spatial variability caused by an increase in suction.

In this paper, the low suction inflection point is used to predict SWCCs, which effectively reduces the problem of deviation caused by the increase of variability caused by high centrifugal force, and makes predicted value estimates close to the measured values, improves prediction accuracy and saves a lot of manpower and material resources. It is expected to provide a simple method for the prediction of SWCCs in this region and guidance for soil moisture management in the loess area.

SWCC is a very important parameter in the strength theory and seepage theory of unsaturated soil. To obtain these parameters conveniently and accurately, taking Lanzhou collapsible loess (silty clay loam) as the research object, SWCCs were predicted by using a low suction section and inflection point.

The spatial CV for bulk-density saturation increased with suction within the range of 0–7,000 cm. Soil saturation was weakly and moderately spatially variable at suctions <800 and ≥800 cm, respectively. Saturation CVs increased with bulk density under the same suction.

The optimal coordinates of the inflection point were determined by statistical method (2.6626, 0.5066). Taking the bulk density of 1.58 g/cm³ as an example, VG saturation prediction equations determined symmetrically by the measured data of different suction sections at 0–300, 0–500, 0–800 and 0–1,000 cm with respect to the inflection point were compared. The logarithm values of different suctions were brought into the above prediction equations to calculate the soil saturation. It was found that the predicted soil saturation determined by the symmetry of the suction section of 0–800 cm with respect to the inflection point was in the highest agreement with the measured value.

The predicted value of residual soil saturation was determined using graphical and mathematical methods. The results indicated that the correlation coefficients between the measured and predicted values were >0.6724. The method for predicting SWCCs with low suction and inflection points had high fitting accuracy and accurately predicted SWCC parameters. The method can be used for the determination of SWCCs and provides guidance for managing soil water and restoring vegetation in loessial areas.

This research was supported by the National Natural Science Foundation of China (51869010), the Guidance Program for Industrial Support of Colleges and Universities in Gansu Province (2019C-13) and the Lanzhou University of Technology Hongliu first-class discipline funding.

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