# 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

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**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