# Aquifer Response to Stream-Stage Fluctuations: Field Tests and Analytical Solution for a Case Study of the Yangtze River in Wuhan, China

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Field Hydrological Monitoring Tests

#### 2.1. Hydrological Monitoring Area

^{2}, as shown in Figure 1a. The geomorphological unit in the working area is mainly the first and second terrace accumulation plains of the Yangtze River. The first terrace is mainly located along the Yangtze River, with elevations of 18 to 22 m. The second terrace is mainly located around the third annular urban road, with elevations of 22 m to 26 m. The bedrock in the study area is deeply buried, and the upper overburden layer is composed of quaternary sediment. Due to the potential flow heterogeneity, the overburden layer presents a typical “binary structure”, with the stratigraphic characteristics being fine at the top and coarse at the bottom [43]. The stratum of the site from top to bottom is a mixture of backfill (Q

^{ml}), clay (Q

_{4}

^{al}), silty sand (Q

_{4}

^{al}), medium–coarse sand (Q

_{4}

^{al}), strong weathering mudstone, and medium weathering mudstone (S). Figure 2 showed the typical geological engineering profile of the study area.

#### 2.2. Hydrological Monitoring Plan

#### 2.3. Hydrological Monitoring Results

## 3. Yangtze River Water Level Fluctuation Model

^{2}= 0.889, and T = 2π/ω = 359 days. The period was consistent with the length of a hydrological year in the observation data, which indicated that the fitting result of the function is reliable.

## 4. Prediction of Confined Water Head

#### 4.1. Analytical Derivation of Stream–Aquifer Interactions: Solution of the Ground Water Flow Equations

^{2}/h); S is a dimensionless coefficient representing water storage.

^{2}/h).

#### 4.2. Calculation and Validation

_{0}for $x=600\mathrm{m},800\mathrm{m},\mathrm{and}1700\mathrm{m}$ are 15 m, 14.5 m, and 13 m, respectively. The blue line represents the results calculated by the classical Equation (10), and the red line represents the results calculated by the proposed Equation (14). As can be seen in Figure 9, the results computed by Equation (14) match better with the monitoring data than those computed by Equation (10). The relative errors (calculated value minus monitored value, the result is taken as absolute value and divided by monitored value) of Equation (14) for $x=600\mathrm{m},800\mathrm{m},\mathrm{and}1700\mathrm{m}$ are 8.88%, 8.71%, and 6.14%, which are much smaller than those of Equation (10), which are 19.15%, 17.67%, and 41.33%, respectively. The prediction error has been greatly reduced (by about 18%) from 26% to 8%. This indicates that the proposed Equation (14) is valid for predicting the response of the groundwater head of the confined aquifer to stream-stage fluctuation.

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Diagram of the working groundwater monitoring area (

**a**) and a distribution map of the groundwater monitoring wells (

**b**).

**Figure 2.**Typical engineering geological profile (Profile 1 in Figure 1).

**Figure 4.**Diagram of the Profile 1 (

**a**) and Profile 2 (

**b**) river level and confined water level fluctuations.

**Figure 5.**Comparison of calculation results and observed data of the water level of the Yangtze River.

**Figure 6.**Different values of the parameters in Equation (1): (

**a**) a = 1, a = 5, and a = 10; (

**b**) b = 1, b = 5, and b = 10; (

**c**) ω = 1, ω = 5, and ω = 10; and (

**d**) c = 1, c = 5, and c = 10.

**Figure 7.**Generalized hydrogeological model of the riverine area on the Hankou first terrace: (

**a**) actual situation; (

**b**) idealized assumption.

**Figure 9.**The comparison of calculation results and observed data (monitoring data in (

**a**–

**c**) are respectively obtained from SW063, SW016, and SW025).

Profile | Monitoring Well |
---|---|

Profile 1 | SW023- SW029- SW027- SW025- SW017- SW016- SW063- Yangtze River |

Profile 2 | SW005- SW003- SW002- SW008- SW006- Yangtze River |

Profile 3 | SW013- SW046- SW015- SW014- Yangtze River |

Profile 4 | SW022- SW031- SW026- SW024- Yangtze River |

Profile 5 | SW021- SW020- SW053- SW018- Yangtze River |

Monitoring Wells | |||||||
---|---|---|---|---|---|---|---|

Profile 1 | SW063 | SW016 | SW017 | SW025 | SW027 | SW029 | SW023 |

Distance/km | 0.6 | 0.8 | 0.9 | 1.7 | 2.2 | 3.8 | 4.8 |

Profile 2 | SW06 | SW08 | SW02 | SW03 | SW05 | ||

Distance/km | 2.6 | 4.1 | 5.5 | 7.2 | 8.0 |

Parameter | Value | Unit |
---|---|---|

T | 30 | m^{2}/d |

S | 0.005 | Dimensionless |

D | 6000 | m^{2}/d |

K | 1 | m/d |

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Liu, Y.; Wang, H.; Wu, Y.; Zhao, Y.; Ren, X. Aquifer Response to Stream-Stage Fluctuations: Field Tests and Analytical Solution for a Case Study of the Yangtze River in Wuhan, China. *Water* **2021**, *13*, 2388.
https://doi.org/10.3390/w13172388

**AMA Style**

Liu Y, Wang H, Wu Y, Zhao Y, Ren X. Aquifer Response to Stream-Stage Fluctuations: Field Tests and Analytical Solution for a Case Study of the Yangtze River in Wuhan, China. *Water*. 2021; 13(17):2388.
https://doi.org/10.3390/w13172388

**Chicago/Turabian Style**

Liu, Yanmin, Hao Wang, Yungang Wu, Yuan Zhao, and Xingwei Ren. 2021. "Aquifer Response to Stream-Stage Fluctuations: Field Tests and Analytical Solution for a Case Study of the Yangtze River in Wuhan, China" *Water* 13, no. 17: 2388.
https://doi.org/10.3390/w13172388