# Study on Water Vertical Infiltration Characteristics and Water Content Simulation of Sandstone Overlying Loess

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}/cm

^{3}), θs (0.2306–0.4786 cm

^{3}/cm

^{3}), α (0.01899–0.06071 cm

^{−1}), n (1.438–6.408), and Ks (1.96·10

^{−4}–0.0576 cm/s) were inverted and optimized for each 20 cm soil layer (total of 60 cm). The Van Genuchten model constructed using these parameters demonstrated high accuracy in the simulation of water content in the vertical infiltration process of sandstone covered by loess with the coefficient of determination R

^{2}> 0.849 and relative error RE < 5.311.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Design

^{3}), B represents the dry unit weight of soil mass (g/cm

^{3}), and W represents the water content of soil (%).

#### 2.2. Model Principle

_{x}, θ

_{s}

_{,}α, n, and K

_{s}were adjusted and optimized numerous times during parameter inversion optimization, thus improving the match between the hydraulic parameters and the physical properties under natural conditions.

^{3}/cm

^{3}); h is the matrix potential (cm); t is the infiltration time (d); K is the hydraulic conductivity (cm/d); z is the vertical coordinate axis with the ground surface as the origin, and the direction vertically downward is positive (cm); and S is the absorption and confluence term of plant roots (cm

^{3}/cm

^{−3}·day

^{−1}). In this study, the experimental soil designed was nonvegetated surface soil. Therefore, water absorption by roots did not exist. Thus, its value was set as 0.

_{x}, θ

_{s}

_{,}α, n, and K

_{s}. The key parameters of the model based on these five parameters were mainly derived from the soil water characteristic curve. Given that the soil in the study was unsaturated, the VG model was used to simulate the soil hydraulic parameters. The model is expressed as follows:

^{3}/cm

^{3}); h is the soil pressure head (cm); θx is the residual volumetric water content (cm

^{3}/cm

^{3}); θs is the saturated volumetric water content (cm

^{3}/cm

^{3}); θ is the volumetric water content (cm

^{3}/cm

^{3}); α, n, m and ι are empirical constants, where α is the reciprocal of the intake air value (cm

^{−1}), n is the pore distribution coefficient, ι is the connectivity coefficient of soil pores, usually taking the empirical value of 0.5; Ks is the saturated hydraulic conductivity of soil (m/d). K(h) is the unsaturated hydraulic conductivity of soil (m/d); Se is the effective water content of soil (cm

^{3}/cm

^{3}).

#### 2.3. Accuracy of the Verification Parameters

^{2}and relative error RE were used to verify the accuracy and rationality of the hydraulic parameters and initial conditions in the simulation [20,21]. The determination coefficient R

^{2}is used to reflect the deviation and coincidence degree of the curve between the measured and simulated values. Its value is generally between 0 and 1, and R

^{2}values close to 1 are indicative of the high degree of coincidence between simulated and measured values. The relative error RE can reflect the relative error between the total amount of measured and simulated values. Generally, if the RE is close to 0, then the fitting accuracy of the simulated and measured values is high. Its calculation formula is as follows:

_{i}represents the measured value, I(s)

_{i}represents the simulated value, and I(o) represents the average value of I(o)

_{i}(i = 1, 2, ..., n).

## 3. Results

#### 3.1. Characteristics of Water Infiltration in Loess–Sandstone Structures

#### 3.2. Simulation of Water Movement in Loess-Sandstone Structure

#### 3.2.1. Determination and Inversion of Hydraulic Parameter of Soil

#### 3.2.2. Establishment of Spatial and Temporal Information and Setting Boundary Conditions

#### 3.2.3. Simulation and Accuracy Verification of Moisture Transport in Loess-Overlaid Sandstone

_{x,}, θ

_{s}, α, n, and K

_{s}for each modeling scenario were introduced into the established model to acquire the simulation curves of soil moisture transport in each soil configuration then compared with the measured profile volume water content curves obtained in the one-dimensional vertical test (Figure 6).

^{2}between the measured and simulated values of soil moisture for each type of loess-overlaid sandstone ranged from 0.849 to 0.97. The relative error RE values were below 5.311% and were distributed between 0.423–5.311%. These results showed that the measured values of each type of loess-overlaid sandstone fit well with the simulated values. The validation accuracy of L–FS was lower than that of other loess-overlaid sandstones, indicating that the inversion parameters and the accuracy control of the test process in the model of this type of loess-overlaid sandstone need to be improved.

## 4. Discussion

#### 4.1. Influencing Factors of Water Infiltration in Loess-Overlaid Sandstone

#### 4.2. Role of Infiltration in Loess-Overlaid Sandstone in Hydraulic Erosion

## 5. Conclusions

_{x}(0.028–0.05795 cm

^{3}/cm

^{3}), θ

_{s}(0.2306–0.4786 cm

^{3}/cm

^{3}), α (0.01899–0.06071 cm

^{−1}), n (1.438–6.408), and Ks (1.96·10

^{−4}–0.0576 cm/s), were inverted and optimized for each 20 cm soil layer (total of 60 cm). The VG model constructed by applying these parameters exhibited high accuracy in simulating the vertical infiltration of moisture content in the loess-overlaid sandstone structures with the coefficient of determination R

^{2}> 0.849 and the relative error RE < 5.311. This work is important for the study of the hydrological and soil erosion processes in loess-overlaid sandstone slopes.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Morbidelli, R.; Corradini, C.; Saltalippi, C.; Flammini, A.; Dari, J.; Govindaraju, R.S. A New Conceptual Model for Slope-Infiltration. Water
**2019**, 11, 678. [Google Scholar] [CrossRef] - Shen, Z.; Liu, K.; Wu, Z.; Liu, J.; Qi, K.; Niu, X.; Wang, G.; Yao, W. Transformation of Raindrop characteristics (Nov 24, 2015) of natural rainfall of Yellow River basin. IOP Conf. Series: Earth Environ. Sci.
**2018**, 113, 012014. [Google Scholar] [CrossRef] - Guo, Y.; Liu, S.; Baetz, B.W. Probabilistic rainfall-runoff transformation considering both infiltration and saturation excess runoff generation processes. Water Resour. Res.
**2012**, 48. [Google Scholar] [CrossRef] - Shoaib, M.; Shamseldin, A.Y.; Melville, B.W. Comparative study of different wavelet based neural network models for rainfall–runoff modeling. J. Hydrol.
**2014**, 515, 47–58. [Google Scholar] [CrossRef] - Zongjie, L.; Zongxing, L.; Qi, F.; Xufeng, W.; Yanhu, M.; Huijuan, X.; Ling-Ling, S.; Juan, G.; Baijuan, Z.; Wende, G.; et al. Hydrological effects of multiphase water transformation in Three-River Headwaters Region, China. J. Hydrol.
**2021**, 601, 126662. [Google Scholar] [CrossRef] - Marquart, A.; Eldridge, D.J.; Geissler, K.; Lobas, C.; Blaum, N. Interconnected effects of shrubs, invertebrate-derived macropores and soil texture on water infiltration in a semi-arid savanna rangeland. Land Degrad Dev.
**2020**, 31, 2307–2318. [Google Scholar] [CrossRef] - Foley, J.; Loch, R.; Glanville, S.; Connolly, R. Effects of tillage, stubble and rainfall energy on infiltration. Soil Tillage Res.
**1991**, 20, 45–55. [Google Scholar] [CrossRef] - Sun, Z. Effect of Soft Rock Amendment on Soil Moisture and Water Storage in Mu Us Sandy Land. IOP Conf. Series: Mater. Sci. Eng.
**2018**, 381, 012044. [Google Scholar] [CrossRef] - Szejba, D.; Cymes, I.; Szatylowicz, J.; Szymczyk, S. An impact of drainage system on soil water conditions at Lidzbark Warminski experimental site. Biologia
**2009**, 64, 565–569. [Google Scholar] [CrossRef] - Ryzhenko, B.N.; Sidkina, E.S.; Cherkasova, E.V. Thermodynamic modeling of water-rock systems to evaluate their generative potential for hydrocarbons. Geochem. Int.
**2015**, 53, 825–837. [Google Scholar] [CrossRef] - Belyaeva, T.A.; Bobrov, P.P.; Kroshka, E.S.; Lapina, A.S.; Rodionova, O.V. The effect of very low water content on the complex dielectric permittivity of clays, sand-clay and sand rocks. Meas. Sci. Technol.
**2016**, 28, 014005. [Google Scholar] [CrossRef] - Yuan, L.H.; Fan, G.S. The Experiment Study on the Soil Infiltration Characteristics of Yumenkou Water Pumping Station Irrigation District of Regional Scale. Appl. Mech. Mater.
**2013**, 316, 661–664. [Google Scholar] [CrossRef] - Morel-Seytoux, H.J.; Meyer, P.; Nachabe, M.; Tourna, J.; van Genuchten, M.; Lenhard, R.J. Parameter Equivalence for the Brooks-Corey and Van Genuchten Soil Characteristics: Preserving the Effective Capillary Drive. Water Resour. Res.
**1996**, 32, 1251–1258. [Google Scholar] [CrossRef] - Mbagwu, J. Testing the goodness of fit of infiltration models for highly permeable soils under different tropical soil management systems. Soil Tillage Res.
**1995**, 34, 199–205. [Google Scholar] [CrossRef] - Al Maimuri, N.M.L. Applicability of Horton model and recharge evaluation in irrigated arid Mesopotamian soils of Hashimiya, Iraq. Arab. J. Geosci.
**2018**, 11, 610. [Google Scholar] [CrossRef] - Haowen, X.; Yawen, W.; Luping, W.; Weilin, L.; Wenqi, Z.; Hong, Z.; Yichen, Y.; Jun, L. Comparing simulations of green roof hydrological processes by SWMM and HYDRUS-1D. Water Supply
**2019**, 20, 130–139. [Google Scholar] [CrossRef] - Shelia, V.; Šimůnek, J.; Boote, K.; Hoogenbooom, G. Coupling DSSAT and HYDRUS-1D for simulations of soil water dynamics in the soil-plant-atmosphere system. J. Hydrol. Hydromechanics
**2018**, 66, 232–245. [Google Scholar] [CrossRef] - González, M.G.; Ramos, T.B.; Carlesso, R.; Paredes, P.; Petry, M.T.; Martins, J.D.; Aires, N.P.; Pereira, L.S. Modelling soil water dynamics of full and deficit drip irrigated maize cultivated under a rain shelter. Biosyst. Eng.
**2015**, 132, 1–18. [Google Scholar] [CrossRef] - Okamoto, K.; Sakai, K.; Nakamura, S.; Cho, H.; Nakandakari, T.; Ootani, S. Optimal Choice of Soil Hydraulic Parameters for Simulating the Unsaturated Flow: A Case Study on the Island of Miyakojima, Japan. Water
**2015**, 7, 5676–5688. [Google Scholar] [CrossRef] - Trafimow, D. The intelligibility of r or r2 as an effect size statistic: Dichotomous variables. Front. Psychol.
**2015**, 6, 294. [Google Scholar] [CrossRef] - Romero-Padilla, J.M.; Han, C.-P. Estimation of variance in bivariate normal distribution after the preliminary test of homogeneity. Commun. Stat. -Theory Methods
**2016**, 46, 1290–1305. [Google Scholar] [CrossRef] - Valdes-Abellan, J.; Pachepsky, Y.; Martinez, G. MATLAB algorithm to implement soil water data assimilation with the Ensemble Kalman Filter using HYDRUS. MethodsX
**2018**, 5, 184–203. [Google Scholar] [CrossRef] [PubMed] - Su, L.; Li, M.; Wang, Q.; Zhou, B.; Shan, Y.; Duan, M.; Sun, Y.; Ning, S. Algebraic model for one-dimensional horizontal water flow with arbitrary initial soil water content. Soil Res.
**2021**, 59, 511–524. [Google Scholar] [CrossRef] - Grant, S.A.; Jabro, J.D.; Fritton, D.D.; Baker, D.E. A stochastic model of infiltration which simulates “macropore” soil water flow. Water Resour. Res.
**1991**, 27, 1439–1446. [Google Scholar] [CrossRef] - Elshafei, Y.Z.; Aldarby, A.M. Bulk-Density in Relation to Infiltration Capacity of Loam Soils. Arab Gulf. J. Sci. Res.
**1991**, 9, 55–69. [Google Scholar] - Li, H.; Fan, G. The Quantitative Relation of Stable Infiltration Rates between the Pressured and Non-pressured Water Infiltration in Unsaturated Soils. J. Irrig. Drain.
**2010**, 29, 17–21. [Google Scholar] - Noborio, K.; Mclnnes, K.J.; Heilman, J.L. Measurements of cumulative infiltration and wetting front location by time domain reflectometry. Soil Sci.
**1996**, 161, 480–483. [Google Scholar] [CrossRef] - Zhao, L.; Wang, L.; Liang, X.; Wang, J.; Wu, F. Soil Surface Roughness Effects on Infiltration Process of a Cultivated Slopes on the Loess Plateau of China. Water Resour. Manag.
**2013**, 27, 4759–4771. [Google Scholar] [CrossRef] - Hardie, M.; Deurer, M.; Doyle, R.; Lisson, S.; Cotching, W.; Mattern, K. Development of Unstable Flow and Reduced Hydraulic Conductivity due to Water Repellence and Restricted Drainage. Vadose Zone J.
**2012**, 11, vzj2011.0099. [Google Scholar] [CrossRef] - Najm, M.R.A.; Stewart, R.D.; Di Prima, S.; Lassabatere, L. A Simple Correction Term to Model Infiltration in Water-Repellent Soils. Water Resour. Res.
**2021**, 57, 2. [Google Scholar] [CrossRef] - Sawhney, B.L.; Parlange, J.-Y. Two-Dimensional Water Infiltration from a Trench in Unsaturated Soil. Sci. Soc. Am. J.
**1974**, 38, 867. [Google Scholar] [CrossRef] - Dong, Q.G.; Han, J.C.; Zhang, Y.; Li, N.; Lei, N.; Sun, Z.H.; Du, Y.C.; He, J. Water Infiltration of Covering Slils With Different Textures and Bulk Densities in Gravel Mulched Areas. Appl. Ecol. Envrion. Res.
**2019**, 17, 14039–14052. [Google Scholar] - Chen, L.; Fei, L.; Liu, L.; Wang, Z.; Zhong, Y. Effects of Soil Initial Water Content on Transport Characteristics of Free Infiltration Water and Nitrogen Under Film Hole Irrigation with Muddy Water. J. Soil Water Conser.
**2018**, 32, 58–66. [Google Scholar] - He, J.; Bai, D.; Guo, L.; Wang, X. Study on influence factors of vertical tube emitter’s infiltration characteristics. J. Xi’an Univ. Technol.
**2017**, 32, 354–358. [Google Scholar] - Guo, S.; Shao, Y.; Zhang, T.; Zhu, D.Z.; Zhang, Y. Physical Modeling on Sand Erosion around Defective Sewer Pipes under the Influence of Groundwater. J. Hydraul. Eng.
**2013**, 139, 1247–1257. [Google Scholar] [CrossRef] - Grieve, I.C.; Davidson, D.A.; Bruneau, P.M. Effects of liming on void space and aggregation in an upland grassland soil. Geoderma
**2005**, 125, 39–48. [Google Scholar] [CrossRef] - Xu, Y.; Cui, G. Influence of spectral characteristics of the Earth’s surface radiation on the greenhouse effect: Principles and mechanisms. Atmospheric Environ.
**2020**, 244, 117908. [Google Scholar] [CrossRef] - Mingalev, I.V.; Fedotova, E.A.; Orlov, K.G. Parameterization of the Infrared Molecular Absorption in the Earth’s Lower and Middle Atmosphere. Atmospheric Ocean. Opt.
**2018**, 31, 582–589. [Google Scholar] [CrossRef] - Badro, J.; Aubert, J.; Hirose, K.; Nomura, R.; Blanchard, I.; Borensztajn, S.; Siebert, J. Magnesium Partitioning Between Earth’s Mantle and Core and its Potential to Drive an Early Exsolution Geodynamo. Geophys. Res. Lett.
**2018**, 45, 13240–13248. [Google Scholar] [CrossRef] - Bryan, R.; Rockwell, D. Water table control on rill initiation and implications for erosional response. Geomorphology
**1998**, 23, 151–169. [Google Scholar] [CrossRef] - Kinnell, P. Applying the RUSLE and the USLE-M on hillslopes where runoff production during an erosion event is spatially variable. J. Hydrol.
**2014**, 519, 3328–3337. [Google Scholar] [CrossRef] - Han, S.; Yang, Y.; Fan, T.; Xiao, D.; Moiwo, J.P. Precipitation-runoff processes in Shimen hillslope micro-catchment of Taihang Mountain, north China. Hydrol. Process.
**2011**, 26, 1332–1341. [Google Scholar] [CrossRef] - Chang, C.-M.; Yeh, H.-D. Spectral analysis of temporal non-stationary rainfall-runoff processes. J. Hydrol.
**2018**, 559, 84–88. [Google Scholar] [CrossRef] - O’Loughlin, G.; Huber, W.; Chocat, B. Rainfall-runoff processes and modelling. J. Hydraul. Res.
**1996**, 34, 733–751. [Google Scholar] [CrossRef] - Schertxer, D.; Tchiguirinskaia, I.; Lovejoy, S.; Hubert, P.; Bendjoudi, H.; Larcheveque, M. Discussion of “Evidence of chaos in the rainfall-runoff process” Which chaos in the rainfall-runoff process? Hydrol. Sci. J.
**2002**, 47, 139–148. [Google Scholar]

**Figure 2.**Schematic of the one-dimensional vertical infiltration test. (

**a**) Schematic of the types of soil-covered sandstone required for the test. (

**b**) Test device.

**Figure 4.**Vertical water infiltration volume and change of the wetting front. (

**a**) is the change in cumulative infiltration volume, and (

**b**) is the change in the wetting front.

**Figure 5.**Model discrete schematic diagram and monitoring point setting basis. (

**a**) is the schematic of profile simulation and boundary settings. (

**b**) is the initial moisture content of the loess and sandstone samples at the depths of 0–60 cm determined by analyzing ANOVA results.

**Figure 6.**Simulation of water vertical transport in different types of loess-overlaid sandstones. (

**a**) is the change process of the L–FS structure, (

**b**) is the change process of the L–AS structure, (

**c**) is the change process of the L–FS–AF structure, and (

**d**) is the change process of the L–AS–FS structure.

Type | Bulk Density (g·cm^{−3}) | Mechanical Composition Content (%) | Initial Moisture Content (cm^{3}·cm^{−3}) | Total Porosity (%) | ||
---|---|---|---|---|---|---|

Clay <0.002 mm | Powder 0.05~0.002 mm | Sand 0.050~2.00 mm | ||||

L | 1.36 ± 0.09 | 23.62 ± 2.54 | 29.06 ± 1.14 | 65.02 ± 5.55 | 0.25 ± 0.04 | 40.48 ± 2.11 |

FS | 1.68 ± 0.1 | 11.72 ± 1.36 | 5.88 ± 2.41 | 82.4 ± 7.12 | 0.27 ± 0.21 | 30.66 ± 3.45 |

AS | 1.54 ± 0.13 | 27.21 ± 2.21 | 13.89 ± 5.01 | 58.9 ± 4.31 | 0.31 ± 0.07 | 37.4 ± 0.98 |

**Table 2.**Characteristic parameters of vertical infiltration rate of water of different types of loess-sandstone structure.

Type | Initial Infiltration Rate (cm·min ^{−1}) | Stable Infiltration Rate (cm·min ^{−1}) |
---|---|---|

L–FS | 0.65 | 0.025 |

L–AS | 0.91 | 0.03 |

L–FS–AS | 0.47 | 0.01 |

L–AS–FS | 0.53 | 0.015 |

Type | Location of Interlayer Transition Plane | Time (min) | |
---|---|---|---|

Double layer structure | L–FS | 30 cm | 195 |

L–AS | 30 cm | 175 | |

Three layer structure | L–FS–AS | 20 cm | 120 |

40 cm | 420 | ||

L–AS–FS | 20 cm | 100 | |

40 cm | 330 |

Type | Depth (cm) | θ_{x} (cm^{3}·cm^{−3}) | θ_{s} (cm^{3}·cm^{−3}) | α (cm^{−1}) | n | K_{s} (cm/s) |
---|---|---|---|---|---|---|

L | 0–20 | 0.0362 | 0.2629 | 0.02528 | 1.329 | 0.00513 |

20–40 | 0.0311 | 0.24 | 0.04528 | 1.213 | 8.15 × 10^{−4} | |

40–60 | 0.0332 | 0.256 | 0.04525 | 1.229 | 1.15 × 10^{−4} | |

FS | 0–20 | 0.031 | 0.2626 | 0.0332 | 1.6508 | 0.00753 |

20–40 | 0.028 | 0.2724 | 0.02938 | 1.6508 | 0.00301 | |

40–60 | 0.031 | 0.1995 | 0.0332 | 1.4508 | 1.38 × 10^{−4} | |

AS | 0–20 | 0.068 | 0.3412 | 0.01166 | 1.243 | 2.07 × 10^{−4} |

20–40 | 0.038 | 0.2286 | 0.01416 | 1.257 | 2.35 × 10^{−4} | |

40–60 | 0.033 | 0.3122 | 0.02136 | 1.145 | 1.56 × 10^{−4} |

Type | Depth (cm ) | θ_{x} (cm^{3}·cm^{−3} ) | θ_{s} (cm^{3}·cm^{−3} ) | α (cm^{−1} ) | n | K_{s} (cm/s) |
---|---|---|---|---|---|---|

L–FS | 0–20 | 0.04795 | 0.3271 | 0.06071 | 1.438 | 0.00803 |

20–40 | 0.038 | 0.2808 | 0.05166 | 1.543 | 0.0576 | |

40–60 | 0.028 | 0.2799 | 0.05166 | 1.543 | 0.0221 | |

L–AS | 0–20 | 0.05795 | 0.2833 | 0.03528 | 1.696 | 0.00639 |

20–40 | 0.038 | 0.3562 | 0.0423 | 1.427 | 6.92 × 10^{−4} | |

40–60 | 0.035 | 0.4786 | 0.01899 | 6.408 | 4.49 × 10^{−4} | |

L–FS–AS | 0–20 | 0.05795 | 0.265 | 0.0922 | 1.929 | 0.00518 |

20–40 | 0.045 | 0.2724 | 0.02938 | 1.75 | 0.00301 | |

40–60 | 0.033 | 0.332 | 0.05155 | 1.584 | 0.005 | |

L–AS–FS | 0–20 | 0.05795 | 0.2824 | 0.03149 | 1.849 | 0.00538 |

20–40 | 0.038 | 0.2306 | 0.02863 | 4.31 | 2.91 × 10^{−4} | |

40–60 | 0.035 | 0.2802 | 0.03541 | 1.589 | 1.96 × 10^{−4} |

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**MDPI and ACS Style**

Dong, X.; Qin, F.; Li, L.; Yang, Z.; Li, Y.; Wu, Y. Study on Water Vertical Infiltration Characteristics and Water Content Simulation of Sandstone Overlying Loess. *Water* **2022**, *14*, 3716.
https://doi.org/10.3390/w14223716

**AMA Style**

Dong X, Qin F, Li L, Yang Z, Li Y, Wu Y. Study on Water Vertical Infiltration Characteristics and Water Content Simulation of Sandstone Overlying Loess. *Water*. 2022; 14(22):3716.
https://doi.org/10.3390/w14223716

**Chicago/Turabian Style**

Dong, Xiaoyu, Fucang Qin, Long Li, Zhenqi Yang, Yan Li, and Yihan Wu. 2022. "Study on Water Vertical Infiltration Characteristics and Water Content Simulation of Sandstone Overlying Loess" *Water* 14, no. 22: 3716.
https://doi.org/10.3390/w14223716