# Analysis of Water Infiltration under Impermeable Dams by Analytical and Boundary Element Methods in Complex

## Abstract

**:**

## 1. Introduction

## 2. Analytical Methods for Water Infiltration under an Impermeable Dam

#### 2.1. Semicircular Water Infiltration Zone

#### 2.2. The Lower Half Plane Water Infiltration Zone

## 3. BEM in Complex Analysis

_{1}leads to

#### Semicircular Water Infiltration Zone

## 4. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Boundary $\mathsf{\Gamma}$ | Nodes ${\mathit{z}}_{\mathit{j}}$ | Unknowns | Conditions |
---|---|---|---|

$AB$: waterproof bed | $j=1,\dots ,n$ | ${\phi}_{j}$ | ${\psi}_{j}=q$ |

$BC$: feeding surface | $j=n+1,\dots ,n+m$ | ${\psi}_{j}$ | ${\phi}_{j}=0$ |

$CD$: bottom dam | $j=n+m+1,\dots ,2n+m$ | ${\phi}_{j}$ | ${\psi}_{j}=0$ |

$DA$: feeding surface | $j=2n+m+1,\dots ,2n+2m$ | ${\psi}_{j}$ | ${\phi}_{j}=-kH$ |

Boundary $\mathsf{\Gamma}$ | Nodes ${\mathit{z}}_{\mathit{j}}$ | Nodes Values |
---|---|---|

$AB$ | $j=1,\dots ,n$ | ${z}_{j}={R}_{2}exp(-i(n+1-j)\pi /n)$ |

$BC$ | $j=n+1,\dots ,n+m$ | $z}_{j}={R}_{2}-\frac{\left({R}_{2}-{R}_{1}\right)(j-n-1)}{m$ |

$CD$ | $j=n+m+1,\dots ,2n+m$ | ${z}_{j}={R}_{1}exp(-i(j-n-m-1)\pi /n)$ |

$DA$ | $j=2n+m+1,\dots ,2n+2m$ | $z}_{j}=-{R}_{1}-\frac{\left({R}_{2}-{R}_{1}\right)(j-2n-m-1)}{m$ |

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**MDPI and ACS Style**

Cipu, E.C.
Analysis of Water Infiltration under Impermeable Dams by Analytical and Boundary Element Methods in Complex. *Axioms* **2023**, *12*, 654.
https://doi.org/10.3390/axioms12070654

**AMA Style**

Cipu EC.
Analysis of Water Infiltration under Impermeable Dams by Analytical and Boundary Element Methods in Complex. *Axioms*. 2023; 12(7):654.
https://doi.org/10.3390/axioms12070654

**Chicago/Turabian Style**

Cipu, Elena Corina.
2023. "Analysis of Water Infiltration under Impermeable Dams by Analytical and Boundary Element Methods in Complex" *Axioms* 12, no. 7: 654.
https://doi.org/10.3390/axioms12070654