# Effect of Biochar on Soil-Water Characteristics of Soils: A Pore-Scale Study

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Measurements

_{0}has two components in two directions, namely the longitudinal component M

_{z}and the transverse component M

_{t}. Their time derivative is:

_{z}is 0 and its transverse component M

_{t}is the maximum M

_{tmax}, the integral of Equations (1) and (2) can be obtained:

_{1}is the spin-lattice relaxation time (the longitudinal relaxation time) and T

_{2}is the spin–spin relaxation time (the transverse relaxation time), which are the dimensions of time [43,44]. Generally, T

_{2}is always less than or equal to T

_{1}.

_{2}, is controlled by three superposition relaxation processes and can be expressed as:

_{b}is bulk relaxation time, which greatly depends on fluid properties such as ionic type [45], T

_{s}is surface relaxation time, and T

_{d}is diffusion relaxation time, which is induced by the diffusion within the magnetic field gradient [46]. Jaeger et al. [41] assumed that the condition for the fast-diffusion regime is satisfied and T

_{d}can be neglected. Since bulk relaxation time is much longer than surface relaxation time [47,48], Equation (5) can be expressed as:

_{2}is the transverse surface relaxation coefficient, which is related to soil surface properties, S is the pore surface area, V is the pore volume, R is the pore radius, and α is the pore shape factor, corresponding to planar, cylindrical, and spherical pore geometry when a = 1, 2, or 3, respectively [49]. Then, the Carr-Purcell-Meiboom-Gill (CPMG) sequence can be utilized to measure the transverse relaxation time.

_{2}value, and the intensity of the T

_{2}transverse relaxation signal is directly proportional to the content at the hydrogen core(

^{1}H). The higher the content at the hydrogen core (

^{1}H), the stronger the signal intensity. Therefore, the porous media sample can be fully saturated initially, and its void is filled with water. The resulting T

_{2}spectrum obtained by inversion can reflect the pore size distribution curve of the porous media.

_{2}and the pore radius, R, and α is related to the pore shape, which is assumed to be spherical pore in this paper (α = 3). Then, we obtain:

_{2}is the transverse surface relaxation coefficient, which is related to soil surface properties, R is the pore radius, T

_{2}is the transverse relaxation time.

_{2}can be estimated by making reference to the approximate soil type. According to the research by Matteson et al. [50], the ρ

_{2}value of clay mineral kaolin is ρ

_{2}= 1.8 μm/s, while that of quartz sand is ρ

_{2}= 2.4 μm/s. Given the composition of the soil in this test, compared with the above minerals, the value is ρ

_{2}= 2.1 μm/s for the fine-grained remolded soil, ρ

_{2}= 2.2 μm/s for the medium-grained remolded soil, and ρ

_{2}= 2.3 μm/s for the coarse-grained remolded soil.

^{2}) is the surface tension of water, α (°) is the contact angle between the water–air interface and soil particle surface, and $\psi $ is the matric suction. Then, the saturation corresponding to different suction can be obtained by accumulating the proportion of pore size distribution.

#### 2.2. Materials

#### 2.3. Methods

#### 2.4. Preparation and Procedures

^{3}to 1.9 g/cm

^{3}.

_{2}spectral distribution; ➄ repeating the test of all samples in this experiment. The test procedures of SWRC for the filter paper method refer to ASTM, as shown in Figure 1c,d. The steps include ➀ determining the moisture content gradient; ➁ preparing samples with different moisture content; ➂ estimating the density of soil samples with different moisture content under the saturation to be achieved; ➃ cutting and drying the filter paper; ➄ preparing ring cutter sample and static sample; ➅ measuring the moisture content of the filter paper; ⑦ data processing and matrix suction calculation.

## 3. Results and Discussions

#### 3.1. NMR Results and Analysis

#### 3.1.1. Test Results of NMR

_{2}-signal spectrums of three types of soil with different biochar contents. The x-coordinate T

_{2}represents the pore size and the y-coordinate signal strength represents the pore content corresponding to the pore size. Therefore, NMR T

_{2}-signal spectrums of soil samples can be transformed into pore size distribution curves (PSDCs) by Equation (8), as shown in Figure 2d–f.

#### 3.1.2. Pore Size Distribution

#### 3.2. Soil Water Retention Curve

#### 3.2.1. SWRC from PSD

^{5}kPa. In the case of medium-grained remolded soil (Figure 4b), the saturation of B1~B3 is smaller than B0 for suction states where ψ < 600 kPa. Figure 4c shows that the saturation of C3 and C4 is greater than C0 for suctions less than 2000 kPa, displaying lower saturation levels. Furthermore, C4 exhibits higher saturation levels than other samples at the same suction state.

#### 3.2.2. SWRC from Filter Paper Method

#### 3.3. Analysis of Possible Errors in the Test

_{2}for remolded soils in this experiment can be influenced by different mineral types in the samples, leading to variations in ρ

_{2}and some certain errors in the pore size distribution curve calculated by NMR; ② the SWRCs calculated using the NMR technique do not take into account the impact of pore throat and closed pore, resulting in higher water content of samples under low matrix suction conditions.

#### 3.4. Biochar Size, Soil Particle Size, and Soil Texture Classification

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Process of the NMR test and SWRC test of the filter paper method, including: (

**a**) sample preparation; (

**b**) saturated samples; (

**c**) filter paper method; (

**d**) weighing the filter paper.

**Figure 2.**NMR T2 signal spectra of the fine- (

**a**), medium- (

**b**), and coarse- (

**c**) grained remolded soil and pore size distribution of the fine- (

**d**), medium- (

**e**), and coarse- (

**f**) grained remolded soil. (Abbreviations: MP, main peak; LP1, the first peak on the left; LP2, the second peak on the left; RP1, the first peak on the right; RP2, the second peak on the right).

**Figure 5.**The SWRC based on the filter paper method. (

**a**–

**c**) Shows the raw data of the samples and (

**d**–

**f**) shows the SWRC fitted by the EMFX model.

Agrotype | Ingredient | No. | ||
---|---|---|---|---|

Calcined Kaolin | Standard Sand | Biochar | ||

Fine-grained remolded soil | 60% | 40% | 0% | A0 |

2% | A1 | |||

4% | A2 | |||

6% | A3 | |||

8% | A4 | |||

Medium-grained remolded soil | 40% | 60% | 0% | B0 |

2% | B1 | |||

4% | B2 | |||

6% | B3 | |||

8% | B4 | |||

Coarse-grained remolded soil | 20% | 80% | 0% | C0 |

2% | C1 | |||

4% | C2 | |||

6% | C3 | |||

8% | C4 |

No. | NMR | Filter Paper Method | |||||
---|---|---|---|---|---|---|---|

α (1/cm) | m | n | α (1/cm) | m | n | RMSE | |

A0 | 0.0020 | 1.1777 | 3.4409 | 2.9 × 10^{−7} | 86.7163 | 0.3634 | 0.0242 |

A1 | 0.0017 | 1.2240 | 3.5792 | 0.0005 | 7.2429 | 0.3720 | 0.0189 |

A2 | 0.0016 | 1.1269 | 3.3615 | 1.8 × 10^{−7} | 69.1308 | 0.3281 | 0.0162 |

A3 | 0.0015 | 1.0796 | 3.1761 | 6.5 × 10^{−6} | 19.3970 | 0.3045 | 0.0241 |

A4 | 0.0014 | 1.1796 | 2.5773 | 0.0073 | 2.9026 | 0.4937 | 0.0274 |

B0 | 0.0021 | 1.0195 | 3.0437 | 0.0019 | 4.1706 | 0.4299 | 0.0159 |

B1 | 0.0020 | 1.3243 | 2.3058 | 0.0120 | 2.1993 | 0.5695 | 0.0222 |

B2 | 0.0021 | 1.5868 | 1.8142 | 0.0373 | 1.7347 | 0.4893 | 0.0252 |

B3 | 0.0019 | 1.5481 | 1.5213 | 0.0104 | 2.6010 | 0.3867 | 0.0310 |

B4 | 0.0014 | 1.5256 | 2.2244 | 0.0590 | 1.8891 | 0.5154 | 0.0321 |

C0 | 0.0018 | 2.6085 | 1.1413 | 0.7915 | 0.9594 | 0.9559 | 0.0627 |

C1 | 0.0025 | 2.6031 | 1.1365 | 0.8710 | 1.0438 | 0.7856 | 0.0526 |

C2 | 0.0022 | 2.2283 | 1.4129 | 0.7886 | 1.0209 | 0.7547 | 0.0632 |

C3 | 0.0001 | 25.2130 | 0.9797 | 0.7486 | 0.9886 | 0.9726 | 0.0520 |

C4 | 0.0005 | 6.0681 | 1.1931 | 0.9563 | 0.8931 | 1.1157 | 0.0454 |

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**MDPI and ACS Style**

Chen, X.; Li, L.; Li, X.; Kang, J.; Xiang, X.; Shi, H.; Ren, X.
Effect of Biochar on Soil-Water Characteristics of Soils: A Pore-Scale Study. *Water* **2023**, *15*, 1909.
https://doi.org/10.3390/w15101909

**AMA Style**

Chen X, Li L, Li X, Kang J, Xiang X, Shi H, Ren X.
Effect of Biochar on Soil-Water Characteristics of Soils: A Pore-Scale Study. *Water*. 2023; 15(10):1909.
https://doi.org/10.3390/w15101909

**Chicago/Turabian Style**

Chen, Xin, Linfei Li, Xiaofeng Li, Jianyu Kang, Xiang Xiang, Honglian Shi, and Xingwei Ren.
2023. "Effect of Biochar on Soil-Water Characteristics of Soils: A Pore-Scale Study" *Water* 15, no. 10: 1909.
https://doi.org/10.3390/w15101909