# Order Out of Chaos in Soil–Water Retention Curves

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## Abstract

**:**

## 1. Introduction

## 2. Physical Description

- The SWRC is not necessarily a bijective function relating porepressure to water content. It often presents a hysteresis loop, and it is coupled to the deformation of the solid skeleton. On the other hand, for simplicity, these complex issues are not considered in the present work and will be addressed in future works.
- It is assumed that air pressure inside the pores of the soil matrix is constant and equal to atmospheric pressure.
- Only unimodal soils are considered (unimodal poresize distributions). The literature indicates that some soils may present a multimodal behavior, but this type of behavior will not be considered in this paper [17,18,19]. One may refer to Turturro et al. [7] to assess enhanced experimental methods to properly quantify multimodality (bi- and trimodal poresize distributions).

**Statement**

**1.**

**Remark**

**1.**

**Statement**

**2.**

**Remark**

**2.**

## 3. ODE Description and Solution

## 4. Normalized Water Content Solution

## 5. Experimental Exploratory Validation Analysis

## 6. Numerical Approach

#### 6.1. Finite Difference Alternative

#### 6.2. Beyond the Numerical Approach: Logistic Map Attractor

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Analytical fitting for the fine Sand G.E. # 13 from Brooks and Corey [21].

**Figure 4.**Analytical fitting for the silty material from Aubertin et al. [22].

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**MDPI and ACS Style**

Borges, L.P.d.F.; Cavalcante, A.L.B.; Ozelim, L.C.d.S.M.
Order Out of Chaos in Soil–Water Retention Curves. *Water* **2022**, *14*, 2421.
https://doi.org/10.3390/w14152421

**AMA Style**

Borges LPdF, Cavalcante ALB, Ozelim LCdSM.
Order Out of Chaos in Soil–Water Retention Curves. *Water*. 2022; 14(15):2421.
https://doi.org/10.3390/w14152421

**Chicago/Turabian Style**

Borges, Lucas Parreira de Faria, André Luís Brasil Cavalcante, and Luan Carlos de Sena Monteiro Ozelim.
2022. "Order Out of Chaos in Soil–Water Retention Curves" *Water* 14, no. 15: 2421.
https://doi.org/10.3390/w14152421