# An Integrated Bayesian Risk Model for Coastal Flow Slides Using 3-D Hydrodynamic Transport and Monte Carlo Simulation

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. The Breaching Failure

## 3. Liquefaction Flow Slides

## 4. The New Hybrid Bayesian Risk Model

**a. The wind climate module**conducts long-term and extreme analyses of the wind data for the specified station. Moreover, this module analyses the data using ECMWF at each 0.1-degree horizontal grid spacing by 6 hourly time frames encompassing all Turkish coastal waterways between the years 2000 and 2022. It is possible to collect annual, seasonal, and monthly wind roses, all of which give information on the directional variation of wind speeds. The highest wind speeds and the directions in which they blow are examined, and then the prevailing wind direction for the area is analyzed and calculated. The statistical analysis of the yearly maximum wind speeds is performed using the Gumbel Probability distribution, and the most appropriate line is then fitted to the wind speeds presented in this study. Extrapolation to a greater value is thus feasible.

**b. The wave climate module**gives long-term significant wave statistics, annual and seasonal wave roses, and links among wave heights and periods [20]. In addition to this, it estimates the amplitude and duration of significant waves. The issue of coupled refraction and diffraction in the wave module is addressed by subjecting equations similar to the one provided by Ebersole (1985) to numerical analysis [21]. Three equations describing the wave phase function, wave amplitude, and wave approach angle make up the mild slope equation that computes the wave field resulting from the transformation of an incident, linear wave as they propagate over irregular bottom contours. The numerical model is quite effective when it comes to modeling wave propagation across wide coastal regions that are exposed to different wave conditions from a computational standpoint. It has been selected to make use of the sophisticated velocity potential $\mathsf{\Phi}$:

_{g}is group velocity; k is wave number, respectively. They are determined by the dispersion regards. The combined equations are determined for three wave parameters, wave height H, local wave angle θ and |∇s|:

**c. The current climate module**includes three-dimensional modeling of wind, tide, or density stratification-induced currents, changes in water surface elevations, and storm surges. The Hydrodynamic Turbulence Module includes a three-dimensional k-ε turbulence model for transport processes. In a Cartesian coordinate system with three dimensions, the equations that are used to regulate the system are as follows:

_{x}, ν

_{y,}and ν

_{z}, respectively. f: the coefficient of the Coriolis effect, (x, y, z, t): the water density at the current location, ρ

_{o}: the density used as a reference, g: gravitational acceleration, p = pressure.

_{T}) is a terminology used in oceanography to measure the density of seawater (σ

_{T}) at a given temperature.

_{T}is defined in terms of sea water density [ρ(S, T) − 1000 g/cm

^{3}], where ρ(S, T) is the density of seawater at a certain temperature T and salinity S at standard atmospheric pressure. For example, a water sample with a density of 1.027 g/cm

^{3}has a σ

_{T}value of 27. The relation between the two is:

^{3}. The density increases noticeably with depth due to the increased hydrostatic pressure. This compression does not affect buoyancy or stability because all water masses moved up and down are similarly compressed. Therefore, the convention has been adopted to reduce all densities to σ

_{t}(at 1 atm pressure) and to neglect compressibility in the equations of motion. The following formulae are used to calculate density $\rho $ as a function of salinity (S) and temperature (T):

#### Verification of Hydrodynamic Sub-Model

^{3}. At t = 0, the pump was started, so that the water began to flow in the intake, whereas the remaining part of the water body was assumed to be at rest, and the water surface was horizontal. Steady-state conditions were reached approximately 1.5 h after the start of pumping in the hydraulic model.

**d. The sediment transport module**is interrelated with the hydrodynamic transport and turbulence modules. The Boussinesq approximation, a commonly used method that assumes that the density change is minimal in comparison to the velocity, is employed to calculate the Navier–Stokes equations in the hydrodynamic model component. To find the solution, finite elements, and finite differences are employed, combining the strengths of both techniques. The vertical plane is modeled using finite element shape functions and the horizontal plane using finite difference approximations. In a Cartesian coordinate system, the equations that regulate the system are solved implicitly.

_{xx}and S

_{yy}are the components of the normal radiation stress that are acting, respectively, on the plane that is perpendicular to the x and y axes. The following are the sources from which radiation stress calculations are derived:

_{g}/C, E = $\rho $gH

^{2}/8 wave energy, $\rho $ = water density, θ = incident wave angle, C

_{g}= group velocity of waves, C = wave celerity and H = wave height.

**e. The climate change module**uses the Sea Level Rise Projections for the climate change scenario of RCP8.5 for the determination of extreme design water levels of the project area. CMIP6 (Coupled Model Intercomparison Project Phase 6) is the sixth phase of the standard experimental framework for studying the output of combined atmosphere-ocean general cycle models.

**f. The MCS module**presents the development of a statistical model for conducting failure analysis of Coastal Flow slides. The module simulates the stability failure function, to provide a comprehensive understanding of the various factors that could contribute to coastal flow slides system failure. The results of the simulation deliver statistical distributions of failure probabilities, which can be used to estimate the risk associated with CRB failures under various conditions.

**g. The Bayesian network module:**The traditional method for forecasting the probability of events involved representing the “joint distribution,” which stored one probability value for each possible combination of states. However, this approach could result in a large number of calculations, as the total number of states for each node was multiplied by the total number of states in the joint distribution. Bayesian networks offer a more efficient solution. They only connect nodes that are probabilistically related by dependent relationships, thus reducing the number of possible combinations that need to be considered. The flexibility of Bayesian networks has contributed to their widespread use and success. They can be applied to complex systems involving interrelated variables, such as active wall velocity, which plays a critical role in understanding sediment erosion in coastal flow slides. The Bayesian network can evaluate various parameters to calculate the active wall velocity, which reflects the rate at which a vertical underwater slope propagates horizontally due to coastal flow slides. This calculation allows for an estimation of the rate at which the underwater slope is propagating. It was described as the active wall velocity by underlying its physical principles [23].

_{0}represents the porosity of the sand measured in situ, ρ

_{s}represents the particle density, ${\rho}_{w}$ represents the water density, ${k}_{l}$ represents the permeability in the loose state, $\phi $ represents the angle of the internal friction, $\alpha $ represents the angle of the beach slope, and $\u2206$n represents the relative change in porosity.

_{z},

_{j}of a particle of size D

_{j}.

_{s}of a given size corresponds to the slip velocity ${v}_{s,j}$, which depends on the sediment concentration. The Shields parameter gives the relationship between grain size diameter and the dimensionless parameter to calculate the initiation of motion as given by Equation (29):

_{50}is the median particle size.

## 5. The Durap Sensitivity Index (DSI) of CFS Failure

_{BF}and k

_{L}, where k

_{BF}is the coefficient of breaching and k

_{L}is the liquefaction coefficient. The breaching coefficient k

_{BF}consists of the following variables: dredging rate, slope, packing type, and type of driving force. The liquefaction coefficient (k

_{L}) depends only on the dredging rate, slope, densely packed slope, and mass flow as driving forces.

_{L}, since they are the main reasons for the liquefaction type of failure of the slope, as given in Equation (35).

^{3}/h) and is intended for short-term risk assessment purposes. The dredging intensity levels range from no dredging to very high or heavy dredging, and each level corresponds to a specific approximate volume of material that is being dredged per hour. This table can be used as a reference for assessing the risk associated with different dredging intensity levels, especially in the short-term period.

## 6. Application of the Hybrid Risk Model to the Osman Gazi Bridge

#### 6.1. Application of Wind Climate Sub-Model

#### 6.2. Application of Wave Climate Sub-Model

_{s}= 1.5 m during the past 20 years.

#### 6.3. Application of Climate Change Sub-Model

#### 6.4. Application of Current Climate Sub-Model

#### 6.5. Application of the Sediment Transport Module

#### 6.6. Application of the MCS Module

^{3}) or pounds per gallon (lb/gal).

^{3}) or pounds per cubic foot (lb/ft

^{3}).

^{2}/s) or pounds per square foot per minute (lb/ft

^{2}/min).

#### 6.7. Application of the BN Module

^{2}and depth of −7.50 m was built and 70% of the construction works of the bridge caissons were carried out in this dry dock.

## 7. Discussion of Results

## 8. Conclusions

- very low: the parameter has little to no effect on the DSI;
- low: the parameter has a small effect on the DSI;
- moderate: the parameter has a moderate effect on the DSI;
- high: the parameter has a significant effect on the DSI;
- very high: The parameter has a very significant effect on the DSI.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Inskip Point coastal flow slides: when coastal flow slides occur below the waterline, the coastline loses its support, and a portion of it slips seaward, creating a hole, the edges of which regress toward the coast. ((

**a**): The Sunshine Coast Daily, 2015, (

**b**): SBS news, 2015).

**Figure 2.**Field investigation is being conducted in Walsoorden to study the cause of the coastal flow slide that occurred in the area [3].

**Figure 3.**Coastal Breaching Mechanism: Processes and Factors Involved in the Formation and Propagation of Breaching Flow Slides and Associated Turbidity Currents.

**Figure 7.**The comparison of float paths and velocity distributions at the surface layer as obtained from the mathematical model of HYDROTAM-3D with the physical (hydraulic) model when the morning glory is placed on the right-end corner of the marina.

**Figure 8.**The case study area of the Osman Gazi Bridge Footing (The concern point for this study is point 1).

**Figure 10.**Comparison of wind sources of ECMWF-OA with İzmit Meteorological Station (The red line is the linear regression of the data).

**Figure 14.**The average currents (V) of İzmit Bay (

**a**) surface (

**b**) sea bottom as obtained from wind prevailing from SE direction.

**Figure 15.**The pattern of the currents on the surface of the water at steady state with winds coming from the north-northwest at 10 m per second.

**Figure 16.**The sediment transport rates (m

^{3}/year) of the study area were obtained from the 3D hydrodynamic model.

**Figure 19.**Correlations between the critical slope angle and soil/fluid parameters obtained from the Hybrid Model.

**Figure 22.**Simulation of retrogressive breach failure by BN (critical angles vary (

**a**) = 20, (

**b**) = 15, (

**c**) = 13, (

**d**) = 10, (

**e**) = 9, and (

**f**) = 8, respectively. The blue lines show the critical angle slope).

**Figure 25.**Effects of parameters (dredging rate, beach slope, loosely sand packed, mass flow) on coefficient breaching.

**Figure 26.**Effects of parameters (dredging rate, beach slope, loosely sand packed, mass flow) on liquefaction coefficient and their percentage.

**Table 1.**The global summary of events, including attributes, dates, and links [3].

Location | Year and Date | Retrogression Length (m) | Hyperlink to Video |
---|---|---|---|

Amity Point, QL, Australia | 17 August 2014 | 210 | https://www.couriermail.com.au/questnews/sport/massive-sinkhole-reopens-at-amity-north-stradbroke-island/video/5e8d9a6d175c5929f0863c8e9b82ec0d (Accessed on 25 March 2023) |

Inskip Point, QL, Australia | 26 September 2015 | 22 | https://www.brisbanetimes.com.au/national/queensland/car-and-caravan-in-sinkhole-at-qld-beach-20150927-gjvq44.html (Accessed on 25 March 2023) |

Jumpinpin, NSW, Australia | 24 November 2016 | 20 | https://www.dailymail.co.uk/news/article-3334566/Huge-sinkhole-size-football-field-swallows-sand-Jumpinpin-beach-Queensland.html (Accessed on 25 March 2023) |

Ameland SW, Netherlands | 27 January 2019 | - | https://www.youtube.com/watch?v=vubgtLRbkho (Accessed on 25 March 2023) |

Fort Popham, MN, USA | 18 March 2011 | . | https://www.youtube.com/watch?v=BEN5SR0yXfU (Accessed on 25 March 2023) |

North Wildwood, NJ, USA | 19 September 2012 | . | https://www.youtube.com/watch?v=rKrtoLa3uJo (Accessed on 25 March 2023) |

DSI Parameters | Ranking of Sensitivity Index | |||||
---|---|---|---|---|---|---|

Very Low | Low | Moderate | High | Very High | ||

1 | 2 | 3 | 4 | 5 | ||

Dredging rate (P1) | No dredging activity | Low | Moderate | Higher | Heavy | |

Number of coastal structures (P2) | No structure | 1 | 2 | 3 | >4 | |

Slope (P3) | Flat | Gentle | Moderate | Steep | Very steep | |

Packing type | Loosely packed (P4) | Very low | Low | Moderate | High | Very high |

Densely packed (P5) | Very low | Low | Moderate | High | Very high | |

Driving force | Turbidity current (P6) | Intact | Stable | Unstable | High | Very high |

Mass Flow (P7) | Intact | Stable | Unstable | High | Very high |

Qualitative Term | Dredging Rate (P1) | Number of Coastal Structures (P2) | Slope (P3) | Packing Type—Loosely Packed (P4) | Packing Type—Densely Packed (P5) | Driving Force—Turbidity Current (P6) | Mass Flow (P7) |
---|---|---|---|---|---|---|---|

Very low | <100,000 m^{3}/year | No structure | Flat: <5 degrees | D_{50} > 5 mm and 1.8 ≤ packing density < 2 | D_{50} > 5 mm and 2.1 ≤ packing density < 2.4 | Turbidity current not affecting the area | Low sediment supply and no change in transport regime for LFS |

Low | 100,000–500,000 m^{3}/year | 1 | Gentle: 5–10 degrees | D_{50} < 5 mm and 2.1 ≤ packing density < 2.3 | D_{50} < 5 mm and 1.8 ≤ packing density < 2 | Turbidity current present but not causing CRBF | Moderate sediment supply and transport regime fluctuations for LFS |

Moderate | 500,000–1,000,000 m^{3}/year | 2 | Moderate: 10–20 degrees | D_{50} < 5 mm and 1.3 ≤ packing density < 1.6 | D_{50} < 5 mm and 2.1 ≤ packing density < 2.3 | Turbidity current causing occasional CRBF | High sediment supply and frequent transport regime changes for LFS |

High | 1,000,000–5,000,000 m^{3}/year | 3 | Steep: >20 degrees | D_{50} < 5 mm and packing density ≤ 1.3 | D_{50} < 5 mm and 1.6 ≤ packing density < 1.8 | Turbidity current causing frequent CRBF | Excessive sediment supply and significant transport regime changes for LFS |

Very high | >5,000,000 m^{3}/year | >4 | Very steep: >30 degrees | D_{50} < 1mm and 1.3 ≤ packing density < 1.6 | D_{50} < 1mm and 2 ≤ packing density < 2.5 | Turbidity current causing severe and continuous CRBF | Sudden and extreme sediment supply and transport regime changes for LFS |

Dredging Intensity Level | Approximate Volume (m^{3}/h) |
---|---|

No dredging | 0 |

Low | 50–200 |

Moderate | 200–500 |

High | 500–1000 |

Very High (Heavy) | >1000 |

Slope (P3) | Angle Range | Description |
---|---|---|

Flat | <5 degrees | Little to no incline, suitable for structures requiring stability and low LFS control |

Gentle | 5–10 degrees | Gradual incline, suitable for structures requiring moderate LFS control |

Moderate | 10–20 degrees | Moderate incline, requiring both LFS and CRBF control |

Steep | >20 degrees | Steep incline, requiring high CRBF control and slope stabilization (It is not recommended to construct coastal structures) |

Very steep | >30 degrees | Extremely steep incline often requires additional stabilization measures such as vegetation to prevent CRBF (It is not recommended to construct coastal structures) |

**Table 6.**Probability distributions describe the fluctuations of key design parameters in the simulations.

Parameters | Mean | Variation (%) | Distribution |
---|---|---|---|

Sediment density ($\rho $s) (kg/m^{3}) | 2650 | 10 | Normal Distribution |

In situ porosity (n_{0}) | 0.37 | 6.0 | Normal Distribution |

In situ permeability (k_{0}) (m/s) | 0.000004 | 50.0 | Normal Distribution |

Median particle size (D_{50}) (μm) | 140 | 15 | Normal Distribution |

Active wall height (H) (m) | 2 | 40 | Normal Distribution |

Water density ($\rho $w) (kg/m^{3}) | 1015 | 2.0 | Normal Distribution |

Slope (m/m) | $\frac{3}{20}$ | 50 | Normal Distribution |

Researchers | Focus | DSIP | Pertaining Parameters | Major Equation | Hybrid Model Results |
---|---|---|---|---|---|

S. Alhaddad et al., 2020 [30]. | CRBF | P1 P2 P3 P4 P5 P6 P7 | P1 = 1 P2 = 4 P3 = 1 P5 = 4 P6 = 4 | $\frac{{k}_{BF}\cdot P\left({V}_{\mathrm{breach}}\right)}{{k}_{L}\cdot P\left({V}_{\mathrm{liquefaction}}\right)}$ | CRBF |

G. A. van den Ham et al., 2023 [31] | CRBF | P1 P2 P3 P4 P5 P6 P7 | P1 = 4 P2 = 4 P3 = 1 P4 = 4 P5 = 4 | $\frac{{k}_{BF}\cdot P\left({V}_{\mathrm{breach}}\right)}{{k}_{L}\cdot P\left({V}_{\mathrm{liquefaction}}\right)}$ | CRBF |

LFS | P1 P2 P3 P4 P5 P6 P7 | P1 = 4 P2 = 2 P3 = 1 P4 = 4 P7 = 4 | $\frac{{k}_{L}\cdot P\left({V}_{\mathrm{liquefaction}}\right)}{{k}_{BF}\cdot P\left({V}_{\mathrm{breach}}\right)}$ | LFS | |

K. Beinssen et al., 2015 [1]. | CRBF | P1 P2 P3 P4 P5 P6 P7 | P1 = 1 P2 = 4 P3 = 1 P5 = 5 P6 = 4 | $\frac{{k}_{BF}\cdot P\left({V}_{\mathrm{breach}}\right)}{{k}_{L}\cdot P\left({V}_{\mathrm{liquefaction}}\right)}$ | CRBF |

M. B. De Groot et al., 2012 [32]. | LFS | P1 P2 P3 P4 P5 P6 P7 | P1 = 3 P2 = 2 P3 = 1 P4 = 4 P7 = 5 | $\frac{{k}_{L}\cdot P\left({V}_{\mathrm{liquefaction}}\right)}{{k}_{BF}\cdot P\left({V}_{\mathrm{breach}}\right)}$ | LFS |

**Table 8.**DSI ranking of parameters affecting coastal liquefaction for Osman Gazi Bridge: dredging rate, coastal structures, packing type, and driving force.

DSI Parameters | Value | Sensitivity Index Ranking |
---|---|---|

Dredging rate (P1) | 1 | Low |

Number of coastal structures (P2) | 3 | Moderate |

Packing type (P4) | 3 | Moderate |

Driving force (P7) | 4 | High |

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## Share and Cite

**MDPI and ACS Style**

Durap, A.; Balas, C.E.; Çokgör, Ş.; Balas, E.A.
An Integrated Bayesian Risk Model for Coastal Flow Slides Using 3-D Hydrodynamic Transport and Monte Carlo Simulation. *J. Mar. Sci. Eng.* **2023**, *11*, 943.
https://doi.org/10.3390/jmse11050943

**AMA Style**

Durap A, Balas CE, Çokgör Ş, Balas EA.
An Integrated Bayesian Risk Model for Coastal Flow Slides Using 3-D Hydrodynamic Transport and Monte Carlo Simulation. *Journal of Marine Science and Engineering*. 2023; 11(5):943.
https://doi.org/10.3390/jmse11050943

**Chicago/Turabian Style**

Durap, Ahmet, Can Elmar Balas, Şevket Çokgör, and Egemen Ander Balas.
2023. "An Integrated Bayesian Risk Model for Coastal Flow Slides Using 3-D Hydrodynamic Transport and Monte Carlo Simulation" *Journal of Marine Science and Engineering* 11, no. 5: 943.
https://doi.org/10.3390/jmse11050943