# Flood Vulnerability Study of a Roadway Bridge Subjected to Hydrodynamic Actions, Local Scour and Wood Debris Accumulation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Material Properties and Input Data

#### 2.1.1. Geometry and Materials

#### 2.1.2. Geotechnical Data

#### 2.1.3. Hydraulic Data

#### 2.2. Methodology and Modelling Approach

#### 2.2.1. Overview

#### 2.2.2. Structural Finite-Element Modelling

#### 2.2.3. Soil–Structure Interaction Modelling

#### 2.2.4. Loads Modelling

#### **Hydrodynamic** **Forces**

#### **Wood** **Debris Forces**

#### 2.2.5. Local Scour Modelling

#### **Effect** **of Local Scour on SSI and Flood Loading**

#### 2.2.6. Parameters’ Uncertainty

#### 2.2.7. Latin Hypercube Sampling

## 3. Results

#### 3.1. Model Validation

#### 3.2. Vulnerability Analysis

#### 3.2.1. Debris Accumulation Sizes

#### 3.2.2. Limit State Definition

- Bending and shear failure at the base of the piers;
- Shear failure of the bearing above the pier and the abutments;
- Bending failure of the deck around the weak axis at the section above the piers and the midspan of the bridge;
- Bearing failure of the foundation (vertical and bending capacity at the base);
- Failure due to local scour reaching the base of the foundation.

#### 3.2.3. Results for Serviceability Limit State

#### 3.2.4. Results for Ultimate Limit State

#### 3.3. Sensitivity Analysis

#### 3.3.1. Scour Depths

#### 3.3.2. Utilization Ratios for ULS

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## List of Symbols and Notations

$a$ | Pier width |

${a}_{d}^{\ast}$ | Equivalent pier width |

${A}_{d}$ | Projected wetted area in the direction of the flow |

${A}_{l}$ | Wetted area perpendicular to the flow |

${c}^{\prime}$ | Effective cohesion of the soil |

${C}_{d}$ | Drag coefficient |

${C}_{l}$ | Lift coefficient |

CPT | Cone Penetration Test |

$D$ | Diameter of a well foundation |

${D}_{E}$ | Embedment depth of the foundation |

${D}_{L}$ | Length of the deck |

${d}_{sp}$ | Wetted depth of the deck |

${d}_{ss}$ | Wetted depth of the solid superstructure |

${d}_{wgs}$ | Distance from the girder soffit to the flood water surface |

$E$ | Soil elastic modulus |

${E}_{s}$ | Steel elastic modulus |

${f}_{cm}$ | Concrete compressive strength |

${f}_{sy}$ | Steel yield strength |

${F}_{d}$ | Hydrodynamic drag force |

${F}_{l}$ | Hydrodynamic lift force |

${F}_{rL}$ | Debris Froude number |

${F}_{r}$ | Froude number |

$g$ | Gravitational acceleration |

$G$ | Shear modulus of the soil |

$H$ | Water height |

${H}_{d}$ | Height of wood debris accumulation |

IM | Intensity measure |

$in{d}_{LS}(j|H,v)$ | Index vector for each LS and each H-v |

$j$ | Index of j-th LHS simulation |

${K}_{1}$ | Correction factor for the pier nose shape |

${K}_{2}$ | Correction factor for the angle of attack flow |

${K}_{3}$ | Correction factor for the riverbed condition |

${K}_{d,1}{K}_{d,2}$ | Correction factors used in the calculation of the equivalent pier width depending on the shape of the debris raft |

${K}_{H}^{e}$ | Horizontal embedded stiffness of the well foundation |

${K}_{R}^{e}$ | Rocking embedded stiffness of the well foundation |

${K}_{V}^{e}$ | Vertical embedded stiffness of the well foundation |

${K}_{T}^{e}$ | Torsional embedded stiffness of the well foundation |

$L$ | Depth of the foundation |

${L}_{d}$ | Length of wood debris accumulation in the flow direction |

${L}_{L}$ | Key log length |

LHS | Latin Hypercube Sampling |

LS | Limit state |

${N}_{60}$ | Equivalent number of Standard Penetration Test (SPT) blows of the soil |

${N}_{LS}\left(H,v\right)$ | Number of simulations that leads to the exceedance of LS for a given H-v |

${N}_{sim}$ | Number of LHS simulations |

${N}_{var}$ | Number of random input variables |

$P(LS|H,v)$ | Probability of exceeding the designated LS for a given H-v |

PI | Prediction Intervals |

${P}_{r}$ | Proximity ratio |

$Q$ | Water discharge |

RC | Reinforced Concrete |

${R}_{f}$ | Foundation radius |

${S}_{L}$ | Span length of the bridge |

${S}_{r}$ | Relative submergence of the deck |

SLS | Serviceability Limit State |

SSI | Soil–Structure Interaction |

ULS | Ultimate Limit State |

$UR$ | Utilization ratio |

$v$ | Mean flow velocity |

${W}_{d}$ | Width of wood debris accumulation |

${y}_{gs}$ | Average vertical distance from the girder soffit to the riverbed |

${y}_{s}$ | Local scour depth |

${\phi}^{\prime}$ | Effective shear angle of the soil |

$\gamma $ | Soil unit weight |

$\nu $ | Poisson’s ratio |

$\theta $ | Angle of flow attack |

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**Figure 1.**Overview of the case-study bridge: (

**a**) side view, (

**b**) detailed view of the middle pier and well foundations, (

**c**) view below the bridge deck, and (

**d**) detailed view of the roller bearing at the abutment.

**Figure 2.**(

**a**) Cross-section of the case-study bridge; (

**b**) cross-section A-A at the base of the pier.

**Figure 3.**Results obtained from the numerical simulations of two flooding events. (

**a**) Relation between water height ($H$) and discharge ($Q$); (

**b**) relation between water velocity ($v$) and water height ($H$). The steady flow relationship and the 95% prediction interval curves are also represented.

**Figure 4.**Flowchart illustrating the procedure that is implemented for the flood vulnerability analysis of the bridge.

**Figure 7.**Relationship between (

**a**) the width, (

**b**) the height, (

**c**) the length of debris accumulation and the water height (H) for the two different debris modelling approaches. The results are represented for the steady flow condition and for the upper prediction bound of the regression curve of Figure 3.

**Figure 8.**(

**a**) Contour and (

**b**) 3-D surface plot of the flood vulnerability surface for the serviceability limit state (SLS) for the first scenario (no debris).

**Figure 9.**(

**a**) Contour and (

**b**) 3-D surface plot of the flood fragility surface for the serviceability limit state (SLS) for the second scenario (AS5100.2-2004 standard).

**Figure 10.**(

**a**) Contour and (

**b**) 3-D surface plot of the flood fragility surface for the serviceability limit state (SLS) for the third scenario (Panici and Almeida’s model [48]).

**Figure 11.**(

**a**) Contour and (

**b**) 3-D surface plot of the flood fragility surface for the ultimate limit state (ULS) for the first scenario (no debris).

**Figure 12.**(

**a**) Contour and (

**b**) 3-D surface plot of the flood fragility surface for the ultimate limit state (ULS) for the second scenario (AS5100.2-2004 standard).

**Figure 13.**(

**a**) Contour and (

**b**) 3-D surface plot of the flood fragility surface for the ultimate limit state (ULS) for the third scenario (Panici and Almeida’s model [48]).

**Figure 14.**Representation of the (

**a**) 5th percentile, (

**b**) 50th percentile and (

**c**) 95th percentile of scour depths (${y}_{s})$ against the water heights ($H$) for the three different scenarios and the upper prediction bound of the $H-v$ relationship.

**Figure 15.**Representation of the (

**a**) 5th, (

**b**) 50th, and (

**c**) 95th percentiles of the failure utilization ratios ($UR$) against the water heights ($H$) for the three different scenarios and for the upper prediction bound of the $H-v$ relationship.

**Figure 16.**Frequency of occurrence of two leading mechanisms (i.e., local scour and pier bearing failure) within LHS simulations for the (

**a**) first, (

**b**) second, and (

**c**) third debris scenario and the upper prediction bound of the $H-v$ relationship. Note that the frequencies between $H$ = 2 m and $H$ = 8 m are omitted, since, in this range, local scour is the leading mechanism.

**Table 1.**Soil characteristics used for modelling the soil–structure interaction at the central pier of the bridge.

Parameters | Value |
---|---|

$\mathrm{Effective}\mathrm{shear}\mathrm{angle}({\phi}^{\prime}$) | 40° |

$\mathrm{Effective}\mathrm{cohesion}({c}^{\prime}$) | 0 kPa |

$\mathrm{Soil}\mathrm{unit}\mathrm{weight}(\gamma $) | 19.8 kN/m^{3} |

$\mathrm{Poisson}\u2019\mathrm{s}\mathrm{ratio}(\mathsf{\nu}$) | 0.30 |

$\mathrm{Elastic}\mathrm{modulus}(E$) | 50 Mpa |

$\mathrm{Shear}\mathrm{modulus}(G$) | 19 Mpa |

$\mathrm{Equivalent}\mathrm{SPT}\mathrm{blows}({N}_{60}$) | 19 |

Wood Debris Accumulation Properties | ||||
---|---|---|---|---|

shape | ${\mathit{H}}_{\mathit{d}}$ | ${\mathit{W}}_{\mathit{d}}$ | ${\mathit{L}}_{\mathit{d}}$ | |

AS5100.2-2004 | rectangular | 1.2–3 m | Pier: ${W}_{d}=min\left\{\begin{array}{c}20m\\ \frac{1}{2}\sum {S}_{L}\end{array}\right.$ $\mathrm{Deck}:{W}_{d}={D}_{L}$ | not specified |

Panici and Almeida’s model [48] | half conical | $f\left(v,g,H,{L}_{L}\right)$ | $f\left(v,g,H,{L}_{L}\right)$ | $f\left(v,g,H,{L}_{L}\right)$ |

Parameters | Probabilistic Distributions | References |
---|---|---|

$\mathrm{Concrete}\mathrm{compressive}\mathrm{strength}(fcm$) | $\mathrm{Normal}(\mu =1,COV=0.20)$ | [55] |

$\mathrm{Steel}\mathrm{yield}\mathrm{strength}(fsy$) | $\mathrm{Log}-\mathrm{normal}(\tilde{m}=1,COV=0.07$) | [56] |

$\mathrm{Steel}\mathrm{elastic}\mathrm{modulus}({E}_{s}$) | $\mathrm{Log}-\mathrm{normal}(\tilde{m}=1,COV=0.03$) | [56] |

$\mathrm{Soil}\mathrm{shear}\mathrm{modulus}(G$) | $\mathrm{Log}-\mathrm{normal}(\tilde{m}=1,COV=0.30$) | [54,57] |

$\mathrm{Soil}\mathrm{effective}\mathrm{shear}\mathrm{angle}({\phi}^{\prime}$) | $\mathrm{Normal}(\mu =1,COV=0.12)$ | [54,57] |

Soil unit weight (γ) | $\mathrm{Normal}(\mu =1,COV=0.10)$ | [54] |

$\mathrm{Hydrodynamic}\mathrm{drag}\mathrm{forces}({F}_{d}$) | $\mathrm{Normal}(\mu =1,COV=0.10)$ | [24] |

$\mathrm{Local}\mathrm{scour}\mathrm{depth}({y}_{s}$) | $\mathrm{Log}-\mathrm{normal}(\tilde{m}=0.68,COV=0.16$) | [58] |

$\mathrm{Debris}\mathrm{width}({W}_{d}$) | $\mathrm{Normal}(\mu =1,COV=0.10)$ | [48] |

$\mathrm{Debris}\mathrm{height}({H}_{d}$) | $\mathrm{Normal}(\mu =1,COV=0.25)$ | [48] |

$\mathrm{Debris}\mathrm{length}({L}_{d}$) | $\mathrm{Normal}(\mu =1,COV=0.25)$ | [48] |

**Table 4.**Correlation matrix implemented for the soil characteristics taken from [54].

$G$ | ${\phi}^{\prime}$ | $\gamma $ | |

$G$ | 1.0 | 0.35 | 0.45 |

${\phi}^{\prime}$ | 0.35 | 1.0 | 0.30 |

$\gamma $ | 0.45 | 0.30 | 1.0 |

No. | Description | Period (s)—Calculated | Period (s)—Measured |
---|---|---|---|

1 | 1st vertical mode of the deck | 0.67 | 0.68 |

2 | Global longitudinal mode | 0.58 | ND |

3 | 2nd vertical mode of the deck | 0.41 | 0.43 |

4 | Global transverse mode | 0.36 | ND |

5 | Global vertical mode | 0.21 | ND |

6 | 1st transverse mode of the deck | 0.21 | 0.21 |

7 | 3rd vertical mode of the deck | 0.18 | 0.19 |

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## Share and Cite

**MDPI and ACS Style**

Kosič, M.; Anžlin, A.; Bau’, V. Flood Vulnerability Study of a Roadway Bridge Subjected to Hydrodynamic Actions, Local Scour and Wood Debris Accumulation. *Water* **2023**, *15*, 129.
https://doi.org/10.3390/w15010129

**AMA Style**

Kosič M, Anžlin A, Bau’ V. Flood Vulnerability Study of a Roadway Bridge Subjected to Hydrodynamic Actions, Local Scour and Wood Debris Accumulation. *Water*. 2023; 15(1):129.
https://doi.org/10.3390/w15010129

**Chicago/Turabian Style**

Kosič, Mirko, Andrej Anžlin, and Valentina Bau’. 2023. "Flood Vulnerability Study of a Roadway Bridge Subjected to Hydrodynamic Actions, Local Scour and Wood Debris Accumulation" *Water* 15, no. 1: 129.
https://doi.org/10.3390/w15010129