# Reversible and Irreversible Processes in Drying and Wetting of Soil

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## Abstract

**:**

## 1. Introduction

_{J}. The capillarity effect was neglected in the second region where the radius of the pore is larger than a capillary tube.

_{p}and the pore is filled 100%. After the entire pore is emptied (z = z

_{0}corresponding to 0%) and the level of the liquid increases, then the wetting process occurs. In fact, in field it is very difficult to remove all water from the soil as this can be done only in the laboratory. In Figure 2c, we show the dependence of the filling percentage of the pores (named usually θ) as a function of z on both drying and wetting processes which show a hysteretic behavior. From the theoretical point of view, it is important to say that the shape of this hysteresis loop can be controlled by the geometrical parameters characterizing the pore. Additionally, an important fact that we have to mention is that the hysteresis loop is far from having a rectangular shape, as it is required in the Classical Preisach Model (CPM). Essentially, this means that we have to add to the model a reversible component, which can account for the variations in the measured filling degree which are not due to irreversible processes. A simple analysis for the pore shape we have considered shows that the reversible component is dependent on the radii of the cylinders in the three distinct regions.

## 2. Classical and Generalized Preisach Models

## 3. Identification Techniques Based on FORC Diagram Method

## 4. Results of FORC Identification

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Irreversible rectangular hysteron associated to one point in the Preisach plane; (

**b**) reversible rectangular hysteron associated to one point in the Preisach plane.

**Figure 2.**Independent pore in (

**a**) wetting and (

**b**) drying processes. The hysteresis behavior of the independent pore (

**c**) with a tank in the middle and capillary tubes at the ends.

**Figure 3.**3D Preisach distribution in Generalized Preisach Model (

**a**) and the Preisach plane separation line (

**b**).

**Figure 4.**Simulation of the minor hysteresis loops when a small variation in the quantity of water occurs at one point on major hysteresis loop or First-Order Reversal Curve (FORC) (

**a**); water content from soil $\left(\theta \left(z,{\text{}z}_{r}\right)\right)\text{}$ when the water level reached height z on FORC curve after the pore was filled with water up to the reversal point ${z}_{r}$ (

**b**); and a set of FORC curves (

**c**) simulating the drying curves starting from different points of wetting branch till the empty state.

**Figure 5.**The distributions in FORC diagram have been performed for experimental data measured by Morrow and Harris [61]. Distribution ${P(z}_{r})$ was identified for the section of reversal points (line A) and $P\left(z\right)$ for the section of current water pore level (line B).

**Table 1.**The parameters value of irreversible and reversible distributions used in our simulation were.

- | S | P_{0} | A | σ | μ_{1} | k_{2} | μ_{2} | B | k_{3} | μ_{3} |
---|---|---|---|---|---|---|---|---|---|---|

P(z_{r}) | 0.65 | 0.0088 | 0.6625 | 29.0005 | 22.8078 | 0.2093 | 10.1015 | 0.4121 | 0.3054 | 26.6118 |

P(z) | 0.65 | 0.0557 | 1.3109 | 35.5867 | 33.7578 | 0.0772 | 33.4031 | −0.6025 | 0.2467 | 40.8232 |

- | (1−S) | P_{0_rev} | A_{rev} | σ_{rev} | μ_{rev} | - | - | - | - | - |

P_{rev}(z) | 0.35 | 0.0219 | 0.3621 | 2.3923 | 26.0625 | - | - | - | - | - |

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Bodale, I.; Stancu, A. Reversible and Irreversible Processes in Drying and Wetting of Soil. *Materials* **2020**, *13*, 135.
https://doi.org/10.3390/ma13010135

**AMA Style**

Bodale I, Stancu A. Reversible and Irreversible Processes in Drying and Wetting of Soil. *Materials*. 2020; 13(1):135.
https://doi.org/10.3390/ma13010135

**Chicago/Turabian Style**

Bodale, Ilie, and Alexandru Stancu. 2020. "Reversible and Irreversible Processes in Drying and Wetting of Soil" *Materials* 13, no. 1: 135.
https://doi.org/10.3390/ma13010135