# Bridge Pier Scour in Complex Environments: The Case of Chacao Channel in Chile

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Modelling Flow Fields

^{−2}), $\nu $ the fluid viscosity (=${10}^{-6}$ m

^{2}s

^{−1}) and ${\nu}_{t}$ the turbulent viscosity. This last parameter is a function of the turbulent kinetic energy of the flow k and the and turbulence specific dissipation rate $\omega $ [31] both of which are estimated from the $k-\omega $ SST turbulence closure model of an incompressible flow [30,31,32,33]:

^{2}and 1150 × 950 m

^{2}, respectively (Figure 3a). The boundaries and bathymetric regions of each domain were differentiated by mesh refinement levels (Figure 3b). Far from the towers, the seafloor and the mean sea level, the cell-size was set to 8 m in all directions. The grid was progressively refined toward the structures to properly include the bathymetric characteristics of the seafloor (Figure 3c). The grid adopted a cylindrical shape with a radius of 60 m just above the center of mass of CT and NT, with a cell-size of 2 m. Piles and its surroundings upto 1 m were modelled with cell-sizes of 0.25 m (Figure 3d). A cell-size of 2 m was also used within a band of 5 m centered vertically at the mean sea level. The choice of the grid and the cells size refinement, particularly near the walls of the numerical domain, was based on the own experience of designers fitting the critical deadlines of the project. Other CFD parameters adopted for these simulations are included in Table 1. Each simulation took around 12 to 18 h with nearly 120 parallel processors. These computations lead to simulation periods $\Delta T$ of around 370 s (≈6.2 min) up to 550 s (≈9.2 min), which were enough to observe a completely developed flow around the piles of each tower. The steady regime was reached once no significant variation of the hydraulic parameters of incoming flow (e.g., water depth, velocity) were observed. This usually occurred at the time ${t}^{*}<\Delta T$, varying between 350 s and 530 s. Once the steady regime was reached, a periodic vortex shedding phenomena was generated downstream each row of piles. The analysis of the most significant hydraulic variables of the flow (e.g., shear stress and velocity components) was undertaken considering this phenomenon into the steady regime (i.e., for $t\in [{t}^{*},\Delta T]$).

#### 2.2. Estimation of the Erosion Rate in Earth Materials

^{−1}, is estimated as:

#### 2.3. Erosion and Scour in Central Tower

#### 2.4. Erosion and Scour at North Tower Site

## 3. Results for North Tower

#### 3.1. Flow Field

#### 3.2. Shear Stress around Bridge Piers

#### 3.3. Erodibility and Scour Depth

## 4. Results for Central Tower

#### 4.1. Flow Field

#### 4.2. Erodibility and Scour Depth

^{−2}. This value can be compared with the available stream power ${P}_{A}$, estimated from Equation (14) as ${P}_{A}=\tau V$, where $\tau $ and V are representative scales for shear stress and velocity, respectively. For this study such velocity scale is given by the upstream flow velocity defined by Equation (20), whereas $\tau $ corresponds to ${\tau}_{\lambda min},{\tau}_{\lambda ave}$ and ${\tau}_{\lambda max}$. This choice is in agreement with recommendations proposed by Arneson et al. [48] who suggests the use of local variables for a better estimation of ${P}_{A}$, thus rock scour around bridges. Using data of Figure 13c,d and the velocities calculated with OpenFoam, the hydrodynamic available stream power ${P}_{A}$ was estimated for flood-tide and ebb-tide scenarios around each pile. These estimations led to minimum, average and maximum values of ${P}_{A}$. Figure 14a compares ${P}_{A}/P$ with the approximating velocity V of each pile, for both hydrodynamic scenarios. The ratio ${P}_{A}/P>$1 represents an estimate of the effective probability of rock erosion, otherwise not. The black line is a fit of average data, represented by the function:

## 5. Discussion

#### 5.1. About North Tower

#### 5.2. About Central Tower

#### 5.3. Design Value of Scour Depth

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Syngros, K.; Dobry, R.; Leventis, G.E. Chacao Channel Bridge–the Design Challenges. In Proceedings of the International Conference on Case Histories in Geotechnical Engineering—Sixth International Conference on Case Histories in Geotechnical Engineering, Arlington, VA, USA, 11–16 August 2008. [Google Scholar]
- Forsberg, T. The challenge of constructing a bridge over the Chacao channel. In Proceedings of the Fourth Symposium on Strait Crossings, Bergen, Norway, 2–5 September 2001; p. 345. [Google Scholar]
- Forsberg, T. Multi-span suspension bridges. Int. J. Steel Struct.
**2001**, 1, 63–73. [Google Scholar] - Valenzuela, M.A.; Márquez, M.A. Chacao Suspension Bridge: Tender and Technical Challenges. In Proceedings of the IABSE Symposium: Engineering for Progress, Nature and People, Madrid, Spain, 3–5 September 2014; pp. 2516–2523. [Google Scholar]
- Caceres, M.; Valle-Levinson, A.; Atkinson, L. Observations of cross-channel structure of flow in an energetic tidal channel. J. Geophys. Res. Ocean.
**2003**, 108, 968. [Google Scholar] [CrossRef] - Cuatro; Cowi, I. Final Report—Engineering Study—Volumes 1 through 9. Technical Report, Ingeneria Cuatro/Cowi. 2001; (not available online). [Google Scholar]
- Aiken, C.M. Barotropic tides of the Chilean Inland Sea and their sensitivity to basin geometry. J. Geophys. Res. Ocean.
**2008**, 113, 4593. [Google Scholar] [CrossRef] - Soto-Mardones, L.; Letelier, J.; Salinas, S.; Pinillas, E.; Belmar, J.P. Análisis de parámetros oceanográficos y atmosféricos del Seno de Reloncaví. Gayana (Concepción)
**2009**, 73, 141–155. [Google Scholar] [CrossRef] - Warren, R.; Larsen, J.; Svendsen, H. Chacao Channel, an Extreme Application of MIKE 21; COWI Consulting Engineers and Planners AS: Lyngby, Denmark, 2007. [Google Scholar]
- Marín, V.H.; Campuzano, F.J. Un modelo hidrodinámico barotrópico para los fiordos australes de Chile entre los 41
^{∘}S y los 46^{∘}S. Cienc. Tecnol. Del Mar**2008**, 31, 125–136. [Google Scholar] - Sepúlveda, I.; Winckler, P.; Cáceres, M. Hydrodynamic modeling of tidal currents and power extraction in Chacao Channel, Chile. In Proceedings of the 4th Annual Marine Renewable Energy Technical Conference, University of Massachusetts Dartmouth, North Dartmouth, MA, USA, 10 January 2013. [Google Scholar]
- De la Fuente, L.; Miguel, N.E. Hydrodynamic Modelling of Tidal Currents at Chacao Channel for a Preliminary Energy Resource Assessment. Master’s Thesis, Pontificia Universidad Católica de Chile, Escuela de Ingeniería, Santiago, Chile, 2012. [Google Scholar]
- Winckler, P.; Sepúlveda, I.; Aron, F.; Contreras-López, M. How do tides and tsunamis interact in a highly energetic channel? The case of canal Chacao, Chile. J. Geophys. Res. Ocean.
**2017**, 122, 9605–9624. [Google Scholar] [CrossRef] - Peña, Á.; Valenzuela, M.; Márquez, M.; Pinto, H. Requerimientos geotécnicos mínimos para el diseño de fundaciones de puentes tradicionales y singulares: Puente Colgante Chacao. Rev. Construcción
**2017**, 16, 498–505. [Google Scholar] [CrossRef] - Melville, B.W.; Coleman, S.E. Bridge Scour; Water Resources Publications LLC: Highlands Ranch, CO, USA, 2000. [Google Scholar]
- Ettema, R. Scour at Bridge Piers—Report No 216; Technical Report; University of Auckland: Auckland, New Zealand, 1980. [Google Scholar]
- Pizarro, A.; Manfreda, S.; Tubaldi, E. The science behind scour at bridge foundations: A review. Water
**2020**, 12, 374. [Google Scholar] [CrossRef] - Shen, H.W.; Schneider, V.R.; Karaki, S. Local scour around bridge piers. J. Hydraul. Div.
**1969**, 95, 1919–1940. [Google Scholar] [CrossRef] - Chiew, Y.M.; Melville, B.W. Local scour around bridge piers. J. Hydraul. Res.
**1987**, 25, 15–26. [Google Scholar] [CrossRef] - May, R.; Ackers, J.; Kirby, A. Manual on Scour at Bridges and Other Hydraulic Structures; Ciria: London, UK, 2002; Volume 551. [Google Scholar]
- Annandale, G.W.; Kirsten, H.A. On the erodibility of rock and other earth materials. In Proceedings of the Hydraulic Engineering, Buffalo, NY, USA, 1–5 August 1994; pp. 68–72. [Google Scholar]
- Annandale, G. Erodibility. J. Hydraul. Res.
**1995**, 33, 471–494. [Google Scholar] [CrossRef] - Annandale, G.W. Prediction of scour at bridge pier foundations founded on rock and other earth materials. Transp. Res. Rec.
**2000**, 1696, 67–70. [Google Scholar] [CrossRef] - Annandale, G.; Smith, S. Calculation of Bridge Pier Scour Using the Erodibility Index Method; Technical Report; Colorado Department of Transportation: Denver, CO, USA, 2001.
- Annandale, G. Scour Technology: Mechanics and Engineering Practice; McGraw Hill Professional: New York, NY, USA, 2005. [Google Scholar]
- Annandale, G. Current state-of-the-art Rock Scouring Technology. In Geotechnics of Soil Erosion; ASCE: Denver, CO, USA, 2007; pp. 1–12. [Google Scholar]
- Keaton, J.R.; Mishra, S.K.; Clopper, P.E. Scour at Bridge Foundations on Rock; Transportation Research Board: Washington, DC, USA, 2012; Volume 717.
- Bloomquist, D. Erosion of Cored Samples for the Chacao Channel Bridge Project Chile, South America. Interim Report; Technical Report; GeoHazards Co.: Gainesville, FL, USA, 2017. [Google Scholar]
- Marine, S. Proyecto Puente Chacao, Ingeniería Básica. Estudio de Socavación y Erosión, CHB-CPC-DGN-RPT-0282; Technical Report; Skyring Marine Ltd.: Valparaíso, Chile, 2017. [Google Scholar]
- The OpenFOAM Foundation. 2014. Available online: https://scholar.google.ca/scholar?hl=zh-TW&as_sdt=0%2C5&q=The+OpenFOAM+Foundation.+2014.&btnG= (accessed on 11 November 2022).
- Pope, S.B. Turbulent Flows; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Menter, F.R. Improved Two-Equation K-Omega Turbulence Models for Aerodynamic Flows—Technical Memorandum 103975; Technical Report; NASA Ames Research Center Moffett Field: Mountain View, CA, USA, 1992.
- Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J.
**1994**, 32, 1598–1605. [Google Scholar] [CrossRef] - Ahrens, J.; Geveci, B.; Law, C. Paraview: An End-user Tool for Large Data Visualization. 2005, Volume 717. Available online: https://datascience.dsscale.org/wp-content/uploads/2016/06/ParaView.pdf (accessed on 29 November 2022).
- Fluent, A. 12.0 User’s Guide; Ansys Inc.: Canonsburg, PA, USA, 2009; Volume 6, p. 552. [Google Scholar]
- Bloomquist, D.; Crowley, R. Enhancement of FDOT’s SERF Device and a Study of Erosion Rates of Rock, Sand, and Clay Mixtures Using FDOT’s RETA and SERF Equipment; Technical Report; Florida Department of Transportation: Tallahassee, FL, USA, 2010.
- Bloomquist, D.; Sheppard, D.M.; Schofield, S.; Crowley, R.W. The rotating erosion testing apparatus (RETA): A laboratory device for measuring erosion rates versus shear stresses of rock and cohesive materials. Geotech. Test. J.
**2012**, 35, 641–648. [Google Scholar] [CrossRef] - Crowley, R. Development of FDOT SERF and RETA Design Equations for Coastal Scour When a Single Vertical Pile Is Subjected To Wave Attack; Technical Report; Florida Department of Transportation: Tallahassee, FL, USA, 2021.
- Castillo, L.G.; Carrillo, J.M. Scour, velocities and pressures evaluations produced by spillway and outlets of dam. Water
**2016**, 8, 68. [Google Scholar] [CrossRef] - Bollaert, E.; Schleiss, A. Transient Water Pressures in Joints and Formation of Rock Scour Due to High-Velocity Jet Impact; Technical Report; Ecole Polytechnique Federale de Laussane, Platform of Hydraulic Constructions: Lausanne, Switzerland, 2002. [Google Scholar]
- Bollaert, E.; Schleiss, A. Scour of rock due to the impact of plunging high velocity jets Part I: A state-of-the-art review. J. Hydraul. Res.
**2003**, 41, 451–464. [Google Scholar] [CrossRef] - Bollaert, E.; Schleiss, A. Scour of rock due to the impact of plunging high velocity jets Part II: Experimental results of dynamic pressures at pool bottoms and in one-and two-dimensional closed end rock joints. J. Hydraul. Res.
**2003**, 41, 465–480. [Google Scholar] [CrossRef] - Jalili Kashtiban, Y.; Saeidi, A.; Farinas, M.I.; Quirion, M. A Review on Existing Methods to Assess Hydraulic Erodibility Downstream of Dam Spillways. Water
**2021**, 13, 3205. [Google Scholar] [CrossRef] - Moore, J. The characterization of rock for hydraulic erodibility. In Technical Release; USDA: Washington, DC, USA, 1991; Volume 78. [Google Scholar]
- Moore, J.S.; Temple, D.M.; Kirsten, H.A. Headcut advance threshold in earth spillways. Bull. Assoc. Eng. Geol. (United States)
**1994**, 31, 7231905. [Google Scholar] - Kirsten, H. A classification system for excavating in natural materials. Civ. Eng. Siviele Ingenieurswese
**1982**, 1982, 293–308. [Google Scholar] - Kirsten, H. Case histories of groundmass characterization for excavatability. In Rock Classification Systems for Engineering Purposes; ASTM International: West Conshohocken, PA, USA, 1988. [Google Scholar]
- Arneson, L.; Zevenbergen, L.; Lagasse, P.; Clopper, P. Evaluating Scour at Bridges; Technical Report; U.S. Department of Transportation, Federal Highway Administration: Washington, DC, USA, 2012.
- Deere, D. The rock quality designation (RQD) index in practice. In Rock Classification Systems for Engineering Purposes; ASTM International: West Conshohocken, PA, USA, 1988. [Google Scholar]
- Mandl, G. Rock Joints; Springer: Berlin/Heidelberg, Germnay, 2005. [Google Scholar]
- Barton, N. Rock mass classification and tunnel reinforcement selection using the Q-system. In Rock Classification Systems for Engineering Purposes; ASTM International: West Conshohocken, PA, USA, 1988. [Google Scholar]
- Yang, C.T. Incipient motion and sediment transport. J. Hydraul. Div.
**1973**, 99, 1679–1704. [Google Scholar] [CrossRef] - Chow, V. Open-Channel Hydraulics, Classical Textbook Reissue; Mc-Graw Hill: New York, NY, USA, 1988. [Google Scholar]
- Sumer, B.; Christiansen, N.; Fredsoe, J. Time scale of scour around a vertical pile. In Proceedings of the Second International Offshore and Polar Engineering Conference, San Francisco, CA, USA, 14–19 June 1992. [Google Scholar]
- Gazi, A.H.; Afzal, M.S.; Dey, S. Scour around piers under waves: Current status of research and its future prospect. Water
**2019**, 11, 2212. [Google Scholar] [CrossRef] - Briaud, J.L.; Ting, F.; Chen, H.; Cao, Y.; Han, S.; Kwak, K. Erosion function apparatus for scour rate predictions. J. Geotech. Geoenvironmental Eng.
**2001**, 127, 105–113. [Google Scholar] [CrossRef] - Briaud, J.; Chen, H.; Kwak, K.; Han, S.; Ting, F. Multiflood and multilayer method for scour rate prediction at bridge piers. J. Geotech. Geoenviron. Eng.
**2001**, 127, 114–125. [Google Scholar] [CrossRef] - Briaud, J.L. The Sricos-EFA Method. In Current Practices and Future Trends in Deep Foundations; American Society of Civil Engineers: Reston, VA, USA, 2004; pp. 348–360. [Google Scholar]
- Briaud, J.L.; Chen, H.C. SRICOS-erosion function apparatus method: An overview of its measurement of scour depth. In Proceedings of the 6th International Bridge Engineering Conference: Reliability, Security, and Sustainability in Bridge Engineering, Boston, MA, USA, 17–20 July 2005; pp. 525–529. [Google Scholar]
- Kwak, K.; Briaud, J.L.; Cao, Y.; Chung, M.; Hunt, B.; Davis, S. Pier scour at Woodrow Wilson Bridge and SRICOS method. In Proceedings of the First International Conference on Scour of Foundations, College Station, TX, USA, 17–20 November 2002; pp. 227–241. [Google Scholar]
- Kwak, K.S.; Briaud, J.L. Case study: An analysis of pier scour using the SRICOS method. KSCE J. Civ. Eng.
**2002**, 6, 243–253. [Google Scholar] [CrossRef] - Briaud, J.; Chen, H.C.; Li, Y.; Nurtjahyo, P.; Wang, J. SRICOS-EFA method for contraction scour in fine-grained soils. J. Geotech. Geoenviron. Eng.
**2005**, 131, 1283–1294. [Google Scholar] [CrossRef] - Briaud, J.L.; Ting, F.C.; Chen, H.; Gudavalli, R.; Perugu, S.; Wei, G. SRICOS: Prediction of scour rate in cohesive soils at bridge piers. J. Geotech. Geoenviron. Eng.
**1999**, 125, 237–246. [Google Scholar] [CrossRef] - Ting, F.C.K.; Jones, A.L.; Larsen, R.J. Evaluation of SRICOS Method on Cohesive Soils in South Dakota; Technical Report; Mountain-Plains Consortium: Brookings, SD, USA, 2010. [Google Scholar]
- Richardson, E.; Davis, S. Evaluating Scour at Bridges; Technical Report; Federal Highway Administration. Office of Bridge Technology: Washington, DC, USA, 2001.
- Shan, H.; Kilgore, R.; Shen, J.; Kerenyi, K. Updating HEC-18 Pier Scour Equations for Noncohesive Soils; Technical Report; United States. Federal Highway Administration. Office of Infrastructure Research and Development: Georgetown, TX, USA, 2016.
- Mondal, M.S. Local Scour at Complex Bridge Piers in Bangladesh Rivers: Reflections from a Large Study. Water
**2022**, 14, 2405. [Google Scholar] [CrossRef] - Comodromos, E.M.; Anagnostopoulos, C.T.; Georgiadis, M.K. Numerical assessment of axial pile group response based on load test. Comput. Geotech.
**2003**, 30, 505–515. [Google Scholar] [CrossRef] - Briaud, J.L.; Hunt, B. Bridge scour and the structural engineer. Structure
**2006**, 2006, 58–61. [Google Scholar]

**Figure 1.**(

**a**) Map showing Chacao Channel, Chiloé Island and the Chilean Inland Sea. (

**b**) Aerial view of the narrowest section of Chacao Channel during ebb tide. Remolinos Rock generates a turbulent wake (courtesy of Horacio Parrague). (

**c**) A frontal view of the bridge showing the position of Central and North towers. (

**d**) A close view of Remolinos rock. (

**e**) A current view of bridge piers being mounted over Remolinos rock site. (

**f**) A projected view of the bridge.

**Figure 2.**Top view geometry and dimensions, in m, of (

**a**) North Tower (NT) and (

**b**) Central Tower (CT) of Chacao bridge (adapted from [29]). NT is made up of two groups of piles, each having 9 cylindrical piles with diameters of $D=$ 2.5 m. CT is a larger structure made up of four groups of piles, each formed by 9 piles of the same diameter. NT and CT occupy areas of 50 × 21 m

^{2}and 59 × 51 m

^{2}, respectively. The distance between neighbouring piles is $s=$ 7.5 m, measured from their respective vertical axes. Dashed lines show profiles where speed and shear stress are estimated. Points in red (green): locations where the velocity $V\left(t\right)$ was estimated for flood (ebb) tide scenario. Points in black: locations for estimating $V\left(t\right)$ in both scenarios. (

**c**) Definition of a reference frame for the estimation of the approximating flow velocities $V\left(t\right)$ and the shear stress ${\tau}_{w}$ acting around the piles. (

**d**) Front view of CT site.

**Figure 3.**(

**a**) Definition of the modelling domain at the CT. (

**b**) Definition of boundaries of the numerical domain. (

**c**,

**d**) show a views of the refined mesh used for numerical modelling. Figures adapted from [29].

**Figure 4.**(

**a**) A front view of RETA apparatus [38]. (

**b**) A view of some of the samples and the involved dimensions. Taps at both extremes were also indicated (arrows in red). (

**c**,

**d**) Some samples of Remolinos rock after an erosion test. (

**e**) A view of a sample from NT after an erosion test (figures extracted from [28]).

**Figure 6.**Velocity fields at −6 m LAT in the North Tower site for the flood-tide scenario in the (

**a**) no-project condition and (

**b**), with the future assemble of 18 piles. Similar results for the ebb-tide scenario in the (

**c**) no-project condition and (

**d**) with the piles’ structure. Arrows show the local flow direction, black circles the location of each pile and black regions represent seafloor located above −6 m LAT.

**Figure 7.**Side views of velocity fields at a vertical plane (A) coinciding with the southern-most line of piles in the North Tower site for the flood-tide (

**a**,

**b**) and ebb tide- scenarios (

**c**,

**d**) in the no-project condition and with the structure, respectively. Similar results at a vertical plane (B) between the southern-most and the immediate interior lines of piles for the flood-tide (

**e**,

**f**) and ebb tide- scenarios (

**g**,

**h**) in the no-project condition and with the structure, respectively. Arrows show the local flow direction and black lines delineate the structure’s profile.

**Figure 8.**Iso-contours plots of shear stress $\tau $ (measured in Pa) around the piles of North Tower for (

**a**) flood-tide and (

**b**) ebb-tide scenarios. High intensity shear stress is shown in yellow, and low intensity in blue. For simplicity, only results for the front and rear rows of the tower were shown. Figures adapted from [29].

**Figure 9.**Frequency distribution of ${\tau}_{w}\left(t\right)$ for pile A1, obtained for $t>{t}^{*}$ (upper left pier in Figure 2a) of the NT for (

**a**) the flood-tide (

**b**) and the ebb-tide scenarios. The cumulative frequency curve (in red) is also included. Distribution of ${\tau}_{\lambda}$ versus the central angle $\theta $ (Figure 2c) for (

**c**) the flood-tide (

**d**) and the ebb-tide scenarios. Minimum, maximum and the average of this parameter are shown for reference. Figures adapted from [29].

**Figure 10.**(

**a**) Erosion curves $Z\left(t\right)$ obtained by considering different erosion rates, ${\dot{r}}_{min},{\dot{r}}_{ave},{\dot{r}}_{max}$, for one of the piles of NT (pile A6). The erosion depth ${Z}_{s}$ was indicated for reference. (

**b**) Parameter ${Z}_{max}$ involved in Equation (19) versus mean flow velocity $\parallel \overrightarrow{V}\parallel $ at each pile ($\overrightarrow{V}$ is the velocity obtained from OpenFoam). The fitting curve is given by Equation (21). (

**c**) Cumulated frequency distribution of ${Z}_{s}$ for its minimum and maximum range of values. Some referential points were included as a guide to the eye. Figures adapted from [29].

**Figure 11.**Velocity fields at −4 m LAT in the Central Tower site for (

**a**) the flood-tide scenario in the no-project condition and (

**b**), with the future assemble of 36 piles. Similar results for (

**c**) the ebb-tide scenario in the no-project condition and (

**d**) with the piles’ structure. Arrows show the local flow direction, black circles the location of each pile, black regions represent seafloor located above −4 m LAT and white regions areas where the water level is below −4 m LAT. Figures adapted from [29].

**Figure 12.**Side views of velocity fields at a vertical plane (A) coinciding with the southern-most line of piles in the CT site for the flood-tide (

**a**,

**b**) and ebb tide- scenarios (

**c**,

**d**) in the no-project condition and with the structure, respectively. Similar results at a vertical plane (B) between the southern-most and the immediate interior lines of piles for the flood-tide (

**e**,

**f**) and ebb tide- scenarios (

**g**,

**h**) in the no-project condition and with the structure, respectively. Arrows show the local flow direction and black lines delineate the structure’s profile. Figures adapted from [29].

**Figure 13.**Frequency distribution of ${\tau}_{w}\left(t\right)$ for pile A1, for $t\in [{t}^{*},\Delta T]$ for pile A1 (upper left pier in Figure 2b) of the CT site for (

**a**) the flood-tide scenario (

**b**) and the ebb-tide scenario. The cumulative frequency curve (in red) is also included. Distribution of ${\tau}_{\lambda}$ versus the central angle $\theta $ (Figure 2c) for for (

**c**) the flood-tide scenario (

**d**) and the ebb-tide scenario. Minimum, maximum and the average of this parameter are shown for reference. Figures adapted from [29].

**Figure 14.**Erodibility at CT site. (

**a**) Distribution of ${P}_{A}/P$ versus V obtained for minimum, maximum and average shear stress (${\tau}_{\lambda min},{\tau}_{\lambda ave},{\tau}_{\lambda max}$). The fit corresponds to Equation (21) for averaged data. A critical “scour” velocity ${V}_{c}=$6.6 m/s was included. (

**b**) Cumulated frequency distribution curves obtained for the ratio ${P}_{A}/P$ for the same conditions. The erosion risk region (${P}_{A}/P\ge 1$) was shown for reference (box in light green).

**Figure 15.**Distribution of parameter $\xi $ for flood-tide and ebb-tides acting at North Tower site, versus (

**a**) the mean Froude ($Fr$) number and (

**b**), the relative depth $h/D$, where h is the mean flow depth around each pier and D the diameter. The horizontal dashed line corresponds to $\xi =$1.

Description | Item | Central Tower (CT) | North Tower (NT) |
---|---|---|---|

Grid Stats | Mesh software | SnappyHexMesh | SnappyHexMesh |

# of Points | 2,020,283 | 2,171,168 | |

# of Faces | 5,109,534 | 5,447,175 | |

Internal | 4,722,233 | 4,977,149 | |

# of Cells | 1,565,737 | 1,656,988 | |

Skewness (max) | 3.72 | 4.13 | |

Solver/Numerics | Internal solver | InterFoam | InterFoam |

(incompressible/biphase) | (incompressible/biphase) | ||

Continuity link with pressure | PIMPLE algorithm | PIMPLE algorithm | |

Interpolation advection scheme (U) | Linear Upwind | Linear Upwind | |

Interpolation advection scheme ($\alpha $) | Van Leer | Van Leer | |

Linear solvers for Prgh | GAMG /PCG | GAMG /PCG | |

(w/preconditioner) | (w/preconditioner) | ||

Linear solvers for $U/k$ | SmoothSolver | SmoothSolver | |

GaussSeidel | GaussSeidel | ||

Turbulence Treatment | Primary aproximation | RANS | RANS |

Turbulence closure model | kOmegaSST | kOmegaSST | |

Boundary Conditions | Wave2Foam | Wave2Foam | |

w/relaxation zone | w/relaxation zone | ||

Initial Conditions | Velocity (U) | 0 | 0 |

Pressure (P) | Hydrostatic P. by sea lvl. | Hydrostatic P. by sea lvl. | |

$\alpha $ | Air-water by cell z coord. | Air-water by cell z coord. |

**Table 2.**Boundary conditions at NW and SE sides of the numerical domain of both sites obtained from a large-scale numerical model built in a Mike21, using the non-linear shallow water equations for extreme tidal ranges [29].

^{(1)}A negative value denotes a free surface under the sea level ($=0$ m.a.s.l.).

^{(2)}A negative value denotes a flow direction opposite to flood tide.

Velocity | Free Surface | ||||
---|---|---|---|---|---|

(m/s) | (m.a.s.l.) | ||||

Site | Scenario | NW | SE | NW | SE |

North Tower | Flood-Tide | 2.38 | 2.27 | −2.32 ^{(1)} | −2.32 |

North Tower | Ebb-Tide | −2.69 ^{(2)} | −2.66 | 1.60 | 1.63 |

Central Tower | Flood-Tide | 3.60 | 2.48 | −1.81 | −1.87 |

Central Tower | Ebb-Tide | −3.25 | −2.87 | 1.70 | 1.94 |

**Table 3.**Rate erosion $\dot{r}$ obtained from RETA tests for samples extracted from North Tower (samples: TN1, TN2 and TN3).

Sample | Run | T | $\Delta \mathit{t}$ | $\Delta \mathit{m}$ | $\mathit{\tau}$ | $\dot{\mathit{r}}$ |
---|---|---|---|---|---|---|

(N·mm) | (hr.) | (g) | (Pa) | (mm/year) | ||

TN1 | 1 | 15 | 13.2 | 1.49 | 20.88 | 18.10 |

2 | 15 | 35.5 | 2.17 | 20.88 | 9.80 | |

3 | 30 | 6.2 | 0.00 | 41.76 | 0.00 | |

4 | 30 | 19.3 | 0.68 | 41.76 | 5.60 | |

5 | 45 | 6.0 | 0.38 | 62.63 | 10.20 | |

6 | 60 | 6.0 | 0.38 | 83.51 | 10.20 | |

TN2 | 1 | 40 | 17.3 | 1.87 | 78.47 | 32.74 |

2 | 30 | 26.0 | 0.79 | 58.86 | 9.22 | |

3 | 20 | 34.0 | 0.58 | 39.24 | 5.18 | |

4 | 15 | 11.0 | 0.23 | 29.43 | 6.35 | |

5 | 50 | 22.0 | 1.11 | 98.09 | 15.31 | |

TN3 | 1 | 2 | 20.0 | 3.18 | 5.77 | 32.60 |

2 | 20 | 7.3 | 0.49 | 52.46 | 13.90 | |

3 | 30 | 8.0 | 0.62 | 78.69 | 15.90 | |

Min. | 6.0 | 5.77 | 0.00 | |||

Max. | 35.5 | 98.09 | 32.74 | |||

Average | 16.6 | 50.89 | 13.22 |

**Table 4.**Rate erosion $\dot{r}$ obtained from RETA tests for samples extracted from CT (samples: RR1, RR2, RR3, RR4 and RR5).

Sample | Run | T | $\Delta \mathit{t}$ | $\Delta \mathit{m}$ | $\mathit{\tau}$ | $\dot{\mathit{r}}$ |
---|---|---|---|---|---|---|

(N·mm) | (hr.) | (g) | (Pa) | (mm/year) | ||

RR1 | 1 | 15 | 30.0 | 0.00 | 21.01 | 0.00 |

2 | 25 | 66.5 | 0.00 | 35.02 | 0.00 | |

3 | 50 | 99.0 | 0.00 | 70.05 | 0.00 | |

RR2 | 1 | 40 | 14.0 | 2.16 | 113.52 | 402.97 |

2 | 20 | 21.0 | 0.25 | 56.76 | 46.64 | |

3 | 10 | 72.0 | 0.35 | 28.38 | 65.30 | |

4 | 30 | 48.0 | 0.46 | 85.14 | 85.82 | |

RR3 | 1 | 40 | 14.0 | 2.16 | 113.52 | 402.97 |

2 | 200 | 1.4 | 0.02 | 294.73 | 3.90 | |

3 | 250 | 1.1 | 0.01 | 368.41 | 1.90 | |

RR4 | 1 | 50 | 137.0 | 0.00 | 99.44 | 0.00 |

RR5 | 1 | 60 | 149.5 | 0.00 | 90.63 | 0.00 |

Min. | 1.1 | 21.0 | 0.00 | |||

Max. | 149.5 | 368.4 | 402.97 | |||

Average | 54.5 | 114.7 | 84.12 |

**Table 5.**Erodibility index K calculated for Remolinos rock. The parameters included in the table were already described in the text.

Symbol | Description | Value | Comment |
---|---|---|---|

${M}_{s}$ | Mass strength number | 8.39 | It considers information extracted |

from geotechnical test (in MPa) | |||

${K}_{b}$ | Particle size number | 19.04 | |

${J}_{x}$ | Average joint spacing (along x) | 1.00 | It considers a mean spacing |

=$D/2$, where $D=$ 6 m | |||

${J}_{y}$ | Average joint spacing (along y) | 1.00 | |

${J}_{z}$ | Average joint spacing (along z) | 1.00 | |

d | Mean diameter of blocs | 1.00 | Measured in (m) |

${J}_{c}$ | =$3(1+{\left({J}_{x}{J}_{y}{J}_{z}\right)}^{-0.33})$ | 6.00 | |

$RQD$ | Rock quality | 95.20 | This parameter usually ranges |

from 0 to 100 | |||

${J}_{n}$ | Joint set number | 5.00 | Considering very fractured |

rock, suggested by [25,27] | |||

${K}_{d}$ | Shear strength number | 0.10 | |

${J}_{r}$ | Joint roughness | 1.00 | It assumes that joints remain |

open during rock’s scour | |||

${J}_{a}$ | Joint alteration | 10.00 | It considers rock void spaces |

filled with strongly consolidated | |||

cohesive materials, with or without | |||

crushed rocks | |||

${J}_{s}$ | Ground structure number | 0.73 | Value suggested by [27] |

K | Erodibility index | 11.66 | |

P | Threshold Power $={K}^{0.75}$ | 6.31 | kWatt·m^{−2} |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Martinez, F.; Winckler, P.; Zamorano, L.; Landeta, F. Bridge Pier Scour in Complex Environments: The Case of Chacao Channel in Chile. *Water* **2023**, *15*, 296.
https://doi.org/10.3390/w15020296

**AMA Style**

Martinez F, Winckler P, Zamorano L, Landeta F. Bridge Pier Scour in Complex Environments: The Case of Chacao Channel in Chile. *Water*. 2023; 15(2):296.
https://doi.org/10.3390/w15020296

**Chicago/Turabian Style**

Martinez, Francisco, Patricio Winckler, Luis Zamorano, and Fernando Landeta. 2023. "Bridge Pier Scour in Complex Environments: The Case of Chacao Channel in Chile" *Water* 15, no. 2: 296.
https://doi.org/10.3390/w15020296