# Effects of Temperature Change on the Soil Water Characteristic Curve and a Prediction Model for the Mu Us Bottomland, Northern China

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Soil-Water Characteristic Curve Model at Different Temperatures

^{2}) and the root mean square error (RMSE) are used to evaluate the model fit. The larger the correlation coefficient and the smaller the RMSE error, that greater the fitting accuracy.

^{lg}(N·m

^{−1}) is the surface tension of the liquid–gas interface; γ (°) is the contact angle; r (m) is the average radius of the liquid–gas interface.

_{0}, Grant and Salehzadeh [23,35] put forward the formula:

_{r}[K] are the reference and observed temperatures, respectively; θ is the volumetric water content (dimensionless); β

_{0}is a constant empirical coefficient associated with water content and the effect of temperature on capillary pressure.

^{3}·cm

^{−3}); θ

_{s}is the saturated volumetric water content (cm

^{3}·cm

^{−3}); θ

_{r}is the residual volumetric water content (cm

^{3}·cm

^{−3}); h(T) is the water pressure head of the linear function, list Equation (3) (cm); α[m

^{−1}] is an empirical fitting parameter related to the air entry value; m and n are curve shape parameters, m = 1 − 1/n or m = 1 − 1/2n.

#### 2.2. Sample Collection

#### 2.3. Experimental Setup

#### 2.3.1. Soil Column Experiment

#### 2.3.2. Ku-pF Experiment

## 3. Results and Discussion

#### 3.1. Results from the Two Devices without Any Temperature Effect

#### 3.2. Results of Soil Column Experiments at Different Temperatures

#### 3.3. Results of Ku-pF Experiments at Different Temperatures

_{s}and θ

_{r}are closely associated with the thermal properties of the liquid–solid interface. Parameter n, a shape parameter corresponding to the effect of the pore size distribution on the slope of the retention curve, increased as temperature rose, demonstrating the effect of temperature change on soil porosity [30,35]. (4) The influence of temperature on the SWCC of undisturbed soil is relatively small in the middle stage but is relatively large in the initial and residual stages. Similarly, Arnfin et al. [41] carried out experiments with a mixture of Calcigel calcium bentonite and quartz sand (50% each) and pure Calcigel calcium bentonite and found that when the water content is constant, the soil suction value is significantly lower at 80 °C than at 20 °C.

#### 3.4. Prediction Model for the Soil-Water Characteristic Curve (SWCC) at Different Temperatures and Error Analysis

_{0}, θ

_{s0}, θ

_{r0}, and α

_{0}are the main parameters for reference temperature T

_{r}; n, θ

_{s}, and θ

_{r}are the fitting parameters at a specific temperature, and α is an empirical function related to the air entry value.

_{s}, and θ

_{r}respectively, and Equation (10) can be used to obtain fit parameter β. Table 4 shows the relevant fitting parameters.

#### 3.5. Effect of Temperature on the Unsaturated Hydraulic Conductivity of Undisturbed Soil

^{2}), γ is the bulk weight of water (10

^{−3}kN·m

^{−3}); μ is the dynamic viscosity coefficient of water (10

^{−6}kPa·s

^{−1}); T is the soil temperature (°C), and K is the saturated hydraulic conductivity (m/d).

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**The schematic map of the experimental equipment. 1. Soil column; 2. top exhaust pipe; 3. upper water level control drain pipes; 4. water potential sensors; 5. temperature and volumetric water content sensors; 6. piezometer tube; 7. filter plate; 8. filter layer; 9. loading soil sample area; 10. upper filter material; 11. flange plate; 12. cavity; 13. water supply control ball valve; 14. drain control ball valve; 15. pedestal; 16. water meter (16-1), pressure pump (16-2); 17. constant temperature water supply box.

**Figure 7.**Fitting values for parameters n and θ

_{r}. (

**a**) shows the change of n with temperature, and (

**b**) shows the change of θ

_{r}with temperature.

**Table 1.**Fitting parameters of soil-water characteristic curves (SWCC) at different temperatures from the soil column experiment.

Temperature (°C) | θ_{r} | θ_{s} | α | n | R^{2} | RMSE |
---|---|---|---|---|---|---|

13 | 0.1097 | 0.3661 | 0.0313 | 10.65 | 0.9956 | 0.002493 |

18 | 0.1143 | 0.351 | 0.0307 | 10.72 | 0.998 | 0.002193 |

23 | 0.1077 | 0.3508 | 0.0311 | 9.31 | 0.9953 | 0.002364 |

27 | 0.1073 | 0.3437 | 0.0306 | 9.62 | 0.9962 | 0.002365 |

30 | 0.1012 | 0.3455 | 0.0312 | 8.189 | 0.9963 | 0.001904 |

**Table 2.**Fitting parameters of soil-water characteristic curve (SWCC) at different temperatures from Ku-pF experiments.

Temperature (°C) | θ_{r} | θ_{s} | α | n | R^{2} | RMSE |
---|---|---|---|---|---|---|

13 | 0.0739 | 0.3993 | 0.0409 | 3.798 | 0.9760 | 0.0139 |

18 | 0.0433 | 0.3585 | 0.0237 | 8.736 | 0.9143 | 0.0324 |

23 | 0.0219 | 0.4028 | 0.01656 | 5.739 | 0.9861 | 0.0128 |

**Table 3.**Fitting parameters of the soil-water characteristic curve (SWCC) from the soil column and Ku-pF experiments.

T (°C) | θ_{r} | θ_{s} | α | n | R^{2} | RMSE |
---|---|---|---|---|---|---|

13 | 0.07203 | 0.3919 | 0.03282 | 5.921 | 0.9755 | 0.006541 |

18 | 0.0418 | 0.3684 | 0.0287 | 5.815 | 0.9872 | 0.009596 |

23 | 0.02118 | 0.3642 | 0.01595 | 5.784 | 0.9829 | 0.01275 |

**Table 4.**Fitting parameters for an soil-water characteristic curve (SWCC) model based on the VG model.

Parameters | n_{0} | θ_{s0} | θ_{r0} | β | κ_{n} | λ_{s} | λ_{r} |
---|---|---|---|---|---|---|---|

13 °C | 5.921 | 0.3919 | 0.072 | 1.41286 | −0.01475 | −0.00307 | −0.00507 |

R^{2} | 0.8028 | 0.9597 | 0.9219 | 0.9999 |

T (°C) | 13 | 18 | 23 | 28 | Scaling Factor | |
---|---|---|---|---|---|---|

θ (%) | ||||||

0.1 | 0.03 | 0.17 | 0.33 | 0.52 | 0.228 | |

0.15 | 0.22 | 0.58 | 0.94 | 1.28 | 0.394 | |

0.2 | 1.62 | 2.98 | 3.68 | 4.05 | 0.559 | |

0.3 | 5.48 | 9.41 | 10.46 | 10.74 | 0.891 | |

0.35 | 10.34 | 15.16 | 17.07 | 17.82 | 1.057 |

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**MDPI and ACS Style**

Qiao, X.; Ma, S.; Pan, G.; Liu, G.
Effects of Temperature Change on the Soil Water Characteristic Curve and a Prediction Model for the Mu Us Bottomland, Northern China. *Water* **2019**, *11*, 1235.
https://doi.org/10.3390/w11061235

**AMA Style**

Qiao X, Ma S, Pan G, Liu G.
Effects of Temperature Change on the Soil Water Characteristic Curve and a Prediction Model for the Mu Us Bottomland, Northern China. *Water*. 2019; 11(6):1235.
https://doi.org/10.3390/w11061235

**Chicago/Turabian Style**

Qiao, Xiaoying, Shaoyang Ma, Guixing Pan, and Guanglu Liu.
2019. "Effects of Temperature Change on the Soil Water Characteristic Curve and a Prediction Model for the Mu Us Bottomland, Northern China" *Water* 11, no. 6: 1235.
https://doi.org/10.3390/w11061235