# Development of Fragility Curves for Piping and Slope Stability of River Levees

^{*}

## Abstract

**:**

## 1. Introduction

_{f}and equivalent reliability indices for three consequence levels, based on random finite-element analyses.

## 2. Methodology for the Development of Fragility Curves

#### 2.1. Slope Stability Evaluation

#### 2.2. Internal Erosion (Piping) Evaluation

## 3. Case Study Example: River Drava Levee

#### 3.1. Conducted Investigation Works

#### 3.2. Probabilistic Characterization of Soil Parameters

_{r}) has been obtained via correlation with an SPT test.

## 4. The Probabilistic Analyses Background

## 5. Results and Discussion

#### 5.1. Fragility Curves for Levee Slope Stability

#### 5.2. Fragility Curves for Internal Erosion (Piping)

#### 5.3. Discussion on Calculation Assumptions and Recommendations for Future Work

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Levee failure mechanisms analysed in the study: slope instability (

**a**) and internal erosion (

**b**).

**Figure 5.**Flow regimes during overflow of a dam, redrawn from [65].

**Figure 7.**Fragility curves for landside slope stability with respect to varying hydraulic conductivities.

Material | $\mathsf{\gamma}\left[\mathsf{k}\mathsf{N}/{\mathsf{m}}^{3}\right]$ | $\mathsf{\phi}[\xb0]$ | $\mathsf{c}\left[\mathsf{k}\mathsf{P}\mathsf{a}\right]$ | ${\mathsf{k}}_{\mathsf{x}}\left[\mathsf{m}/\mathsf{s}\right]\left(\mathbf{Mean}\right)$ | ${k}_{y}/{k}_{x}[-]$ | |||
---|---|---|---|---|---|---|---|---|

$\mathsf{\mu}\left[\mathsf{k}\mathsf{P}\mathsf{a}\right]$ | $\mathsf{C}\mathsf{o}\mathsf{V}[-]$ | $\mathsf{\mu}\left[\mathsf{k}\mathsf{P}\mathsf{a}\right]$ | $\mathsf{C}\mathsf{o}\mathsf{V}[-]$ | SDC1 | SDC2 | |||

Levee body | 18 | 26 | 0.15 | 2 | 0.30 | 1 × 10^{−8} | 1 × 10^{−8} | 0.5 |

Crown and berm | 20 | 30 | 0.12 | 1 | 0.30 | 1 × 10^{−4} | 1 × 10^{−8} | 0.5 |

Foundation soil | 19 | 36 | - | 0 | - | 1 × 10^{−5} | 0.5 | |

Distribution | constant | normal | log-normal | constant | constant |

Material | ${\mathsf{k}}_{\mathsf{x}}\left[\mathsf{m}/\mathsf{s}\right]$ | ${D}_{r}[\%]$ | ${k}_{y}/{k}_{x}[-]$ | |
---|---|---|---|---|

$\mathbf{Median}\left[\mathsf{m}/\mathsf{s}\right]$ | $\mathsf{C}\mathsf{o}\mathsf{V}[-]$ | |||

Foundation soil | PDC1 | 80 | 0.5 | |

1 × 10^{−5} | 32.5 | |||

PDC2 | ||||

3 × 10^{−5} | 5.0 | |||

Distribution | log-normal | constant | constant |

**Table 3.**Deterministic safety factors for the case study levee, exposed to various design situations.

Design Situation | Safety Factor | |||
---|---|---|---|---|

Low water | Riverside | Static | Drained | 1.4 |

Seismic (475-year RP) | Undrained | 1.1 | ||

Landside | Static | Drained | 1.4 | |

Seismic (475-year RP) | Undrained | 1.1 | ||

High water | Riverside | Static | Drained | 1.6 |

Seismic (475-year RP) | Undrained | 1.6 | ||

Landside | Static | Drained | 1.3 | |

Seismic (475-year RP) | Undrained | 1.1 | ||

Rapid drawdown | Drained | 1.2 |

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**MDPI and ACS Style**

Rossi, N.; Bačić, M.; Kovačević, M.S.; Librić, L.
Development of Fragility Curves for Piping and Slope Stability of River Levees. *Water* **2021**, *13*, 738.
https://doi.org/10.3390/w13050738

**AMA Style**

Rossi N, Bačić M, Kovačević MS, Librić L.
Development of Fragility Curves for Piping and Slope Stability of River Levees. *Water*. 2021; 13(5):738.
https://doi.org/10.3390/w13050738

**Chicago/Turabian Style**

Rossi, Nicola, Mario Bačić, Meho Saša Kovačević, and Lovorka Librić.
2021. "Development of Fragility Curves for Piping and Slope Stability of River Levees" *Water* 13, no. 5: 738.
https://doi.org/10.3390/w13050738