# A Study on Infiltration Characteristics and One-Dimensional Algebraic Model Simulation in Reclaimed Soil with Biochar

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Test Soil and Biochar Preparation

^{−3}, the soil available nitrogen content was 32.08 mg·kg

^{−1}, the soil organic matter content was 7.20 g·kg

^{−1}, the saturated water content was 38.05%, and the saturated hydraulic conductivity was 8.07 × 10

^{−4}cm·s

^{−1}. Two types of biochar were bought from Henan Lize Environmental Protection Technology Co. LTD, which originated from corn straw and rice husk, respectively, and were pyrolyzed at 600 °C for 12 h; the characteristics of the two kinds of biochar are listed in Table 1.

#### 2.2. Experimental Design

#### 2.3. Infiltration Experiment

^{−3}. As biochar is usually applied at the surface soil layer in the field [15], biochar was added to a depth of 0–250 mm of the soil column, and the rest of the column was filled with only the soil. The column was filled layer by layer in 50 mm intervals; each layer of mixture (biochar and soil samples) or soil was calculated and weighed separately, then mixed evenly, and loaded into the soil column. The soil was disturbed between layers to prevent stratification during infiltration. The top of the soil was covered with a filter paper to prevent erosion.

#### 2.4. Model Simulation

^{b}, where F is the wetting front migration distance (mm), t is the infiltration time, min, and a and b are the dimensionless empirical constants. The a value indicates the wetting front migration distance within the first unit of time, and the b value indicates the attenuation of the wetting front’s advance process [16].

^{0.5}+ At

^{n′}

^{−0.5}; A is the steady infiltration rate, mm·min

^{−1}; and t is the infiltration time, min; K > 0 and 0 < n′ < 1 are dimensionless empirical constants.

^{3}·cm

^{−3}), θ

_{s}is the saturated water content (cm

^{3}·cm

^{−3}), θ

_{r}is the residual water content (cm

^{3}·cm

^{−3}), hd is the air entry suction (cm), h is the soil water suction corresponding to the water content θ, and N is a parameter. The Richards equation has been used widely to describe soil water movement. For one-dimensional vertical infiltration into soil, the governing equation and the initial and boundary conditions are as follows:

_{i}is the initial soil water content (cm

^{3}·cm

^{−3}), t is time, and z is the vertical coordinate, positive downward. The rest of the symbols are the same as above.

_{f}is the generalized wetting front depth (cm); and parameter α is the comprehensive shape coefficient of the soil water content distribution in terms of Equations (5) and (6). The rest of the symbols are the same as above.

_{r}= θ

_{i}; then, Equations (5) and (6) become as follows:

_{f}is obtained via an experiment, α may be determined based on Equation (7), and then the soil water content at any vertical coordinate z can be obtained using Equation (8).

_{i}is the predicted soil water content (cm

^{3}·cm

^{−3}), O

_{i}is the measured ones, $\overline{O}$ is mean value of the measured ones, and n is sample size. RMSE is used to evaluate the deviation between the simulated values and the measured ones. The closer the RMSE is to 0, the more accurate the model simulation is. The coincidence index (D) is between 0 and 1; the higher the value, the more accurate the simulated values, and the better the model prediction.

#### 2.5. Data Analysis

## 3. Results

#### 3.1. Effects of Biochar Addition on Soil Water Infiltration

^{2}all exceeded 0.99, and reached an extremely significant level (p < 0.01), indicating a perfect fitting performance. The a value decreased with a raise of maize straw biochar, while initially decreasing and then increasing with an increase in rice husk biochar addition. Compared to CK, rice husk biochar promoted wetting front migration, while maize straw biochar limited it within the first unit of time (30 s). By taking the first derivative of that function, the value of a × b can roughly describe the migration rate of the wetting front. It can be found that except B2 and B8, the values of a × b were all lower than that under CK, which indicates that the wetting front migrated slowly with increasing rates of biochar. Additionally, it migrated more slowly with increasing rates of maize straw biochar than that with rice husk biochar.

#### 3.2. The Relationship between Cumulative Infiltration and Wetting Front Migration

_{f}) was quantified as CI = n″Z

_{f}, with n″ being the shape coefficient. The fitting results are listed in Table 3. The value of n″ reflects the variation of cumulative infiltration with unit wetting front migration distance. The determination coefficient R

^{2}of the regression was over 0.99, which indicating a good linear relationship between them. The n″ value ranged from 0.3229 to 0.3629, as shown in Table 3. Compared to CK, the n″ value varied, declining at first and then increasing with an increased addition rate of both kinds of biochar. The n″ value was highest under A8 and lowest under B4, which revealed that over the course of a unit wetting front migration distance, the cumulative infiltration was greatest with 8% maize straw biochar, while it was lowest with 4% rice husk biochar.

#### 3.3. The Simulation of the Infiltration Process

^{2}of the regression was over 0.995, indicating that the Philip model accurately simulated the water infiltration of reclaimed soil with different biochar types and their application.

^{2}of the regression was over 0.997, indicating a satisfying simulation performance. According to the fitting results, the K values of the biochar treatments were lower than that of CK, and reached a significant level (p < 0.05) except for the case of B8, indicating that the biochar addition was beneficial for inhibiting initial soil water infiltration. As the addition rate of biochar increased, the K values first increased and then decreased in corn straw biochar, while an inverse tendency was observed with the addition of rice husk biochar, indicating that the soil water infiltration will be differently affected by different biochar types, and the suitable addition rate threshold for each kind of biochar is different.

#### 3.4. The Simulation of Moisture in the Soil Profile

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**A**) The cumulative infiltration dynamics under different biochar varieties and addition rates. (

**B**) The specific cumulative infiltration at different infiltration times. Notes: The different lowercase letters on each set of columns indicate significant differences at this time (p < 0.05).

**Figure 3.**The simulated moisture and measured values in the soil profile under different treatments.

Variety | The Origin Material | Appearance | Size (mm) | pH | Water Content (%) | Ash Content (%) | Organic Carbon (%) |
---|---|---|---|---|---|---|---|

Corn straw biochar | Corn straw | Black powder | 0.15 | 9 | 3 | 10 | 40 |

Rice husk biochar | Rice husk | Black filamentous powder | 1 | 8 | 8 | 10 | 50 |

Treatment | a | b | a × b | R^{2} |
---|---|---|---|---|

CK | 22.994 | 0.471 | 10.830 | 0.999 |

A2 | 20.278 | 0.462 | 9.368 | 0.993 |

A4 | 18.279 | 0.482 | 8.810 | 0.999 |

A8 | 15.971 | 0.489 | 7.810 | 0.999 |

B2 | 27.289 | 0.442 | 12.062 | 0.997 |

B4 | 24.191 | 0.431 | 10.426 | 0.994 |

B8 | 25.373 | 0.450 | 11.418 | 0.997 |

**Table 3.**Fitting coefficient of the relationship between cumulative infiltration and wetting front migration distance.

Item | CK | A2 | A4 | A8 | B2 | B4 | B8 |
---|---|---|---|---|---|---|---|

Coefficient n″ | 0.3364 | 0.3284 | 0.3233 | 0.3629 | 0.3317 | 0.3229 | 0.3288 |

Determination coefficient R^{2} | 0.9930 | 0.9981 | 0.9954 | 0.9998 | 0.9993 | 0.9982 | 0.9991 |

Treatment | Sorptivity S/(mm·min ^{−0.5}) | Stable Infiltration Rate A/(mm·min ^{−1}) | Determination Coefficient R ^{2} |
---|---|---|---|

CK | 6.282 a | 0.066 ab | 0.995 |

A2 | 4.690 c | 0.010 e | 0.998 |

A4 | 4.856 c | 0.018 d | 0.998 |

A8 | 3.980 d | 0.031 c | 0.999 |

B2 | 5.548 b | 0.009 e | 0.996 |

B4 | 4.756 c | 0.016 d | 0.999 |

B8 | 6.197 a | 0.076 a | 0.999 |

Treatment | K | n′ | Determination Coefficient R^{2} |
---|---|---|---|

CK | 7.393 a | 0.439 c | 0.997 |

A2 | 4.958 c | 0.483 b | 0.998 |

A4 | 5.303 b | 0.473 b | 0.999 |

A8 | 3.612 d | 0.539 a | 0.999 |

B2 | 5.927 b | 0.482 b | 0.999 |

B4 | 5.055 c | 0.479 b | 0.999 |

B8 | 7.153 a | 0.438 c | 0.999 |

Coefficient | CK | A2 | A4 | A8 | B2 | B4 | B8 |
---|---|---|---|---|---|---|---|

RMSE/% | 0.1737 | 0.4519 | 0.5213 | 0.3907 | 0.4132 | 0.3516 | 0.7668 |

D | 0.6688 | 0.6589 | 0.6156 | 0.7258 | 0.5430 | 0.7125 | 0.5765 |

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**MDPI and ACS Style**

Wang, J.; Shi, D.; Li, Y.; Chen, A.; Feng, S.; Liu, C.
A Study on Infiltration Characteristics and One-Dimensional Algebraic Model Simulation in Reclaimed Soil with Biochar. *Water* **2023**, *15*, 2985.
https://doi.org/10.3390/w15162985

**AMA Style**

Wang J, Shi D, Li Y, Chen A, Feng S, Liu C.
A Study on Infiltration Characteristics and One-Dimensional Algebraic Model Simulation in Reclaimed Soil with Biochar. *Water*. 2023; 15(16):2985.
https://doi.org/10.3390/w15162985

**Chicago/Turabian Style**

Wang, Juan, Danyi Shi, Yan Li, Anquan Chen, Shaoyuan Feng, and Chuncheng Liu.
2023. "A Study on Infiltration Characteristics and One-Dimensional Algebraic Model Simulation in Reclaimed Soil with Biochar" *Water* 15, no. 16: 2985.
https://doi.org/10.3390/w15162985