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MODELAGEM MATEMÁTICA QUANTO À INFLUÊNCIA DOS EFEITOS DE MARÉ E

DOS VENTOS, RELACIONADO AO COMPORTAMENTO HIDRODINÂMICO DA

BAÍA DE SEPETIBA.

De acordo com o estabelecido na INSTRUÇÃO TÉCNICA PARA ELABORAÇÃO DE

ESTUDO DE IMPACTO AMBIENTAL - EIA E SEU RESPECTIVO RELATÓRIO DE

IMPACTO AMBIENTAL - RIMA PARA AS OBRAS DE IMPLANTAÇÃO DO TERMINAL

PORTUÁRIO, RETROÁREA E PÍER NO PORTO DE ITAGUAÍ, DE

RESPONSABILIDADE DA USINAS SIDERÚRGICAS DE MINAS GERAIS S/A,

LOCALIZADO NO MUNICÍPIO DE ITAGUAÍ, RIO DE JANEIRO (Instrução Técnica

CEAM No 03/2010 - Notificação No CEAMNOT/00010114), emitida pelo INEA, faz parte

do escopo dos trabalhos a apresentação de uma modelagem matemática para a

verificação da influência das marés e ventos em relação às instalações portuárias do

empreendimento.

Para desenvolver o referido estudo, foram contratados os serviços da renomada

instituição norte-americana Battelle, que apresentou como primeiro produto um relatório

preliminar, apresentado a seguir, com os primeiros resultados da análise.

Neste relatório, que ainda está sendo traduzido, são apresentados os resultados

obtidos dos seguintes esforços: desenvolver uma modelagem numérica da Baía de

Sepetiba, baseado em mecanismos de maré, vento e descargas de água doce (rios e

canais), utilizar o modelo para estimativas conservadoras de movimentação de

sedimentos de fundo causados pela hidrodinâmica da Baía e estimar os efeitos de

marés e ventos.

Os trabalhos continuarão em desenvolvimento, sendo que as etapas atualmente em

elaboração são:

Avaliar eventos extremos de vento/ondas (ventos de 16 m/s e 26.1 m/s para ondas)

Avaliar a sensibilidade dos resultados para parâmetros imprevisíveis.

Atualizar a base de dados com novas informações geradas pelo projeto

Preparar modelos em escalas mais detalhadas para as áreas de maior interesse, com ênfase nos locais previstos para a disposição de sedimentos dragados.



DRAFT SUMMARY OF NUMERICAL MODELING OF BOTTOM SHEAR STRESSES IN

SEPETIBA BAY DUE TO TIDES, WINDS, AND WIND-WAVES, PERFORMED FOR

USIMINAS AT THE FORMER INGÁ FACILITY, SEPETIBA BAY, RIO DE JANEIRO

Usiminas, one of Brazil’s largest producers of steel, is planning to construct a terminal to export 25 to 50

million tons of iron ore and import 5 to 10 million tons of coal annually. Prior to constructing the

infrastructure necessary to accomplish this objective, contaminated soil and sediment present at the site

must be characterized and treated/removed. The soil and sediment is contaminated with a variety of

heavy metals including cadmium, lead, zinc (and possibly others), which resulted from operations of the

now bankrupt Ingá metallurgical plant.

Usiminas has requested that HAZTEC perform an environmental impact assessment for the construction

and operation of a terminal to export iron ore and import coal in the vicinity of the former Ingá

metallurgical plant. HAZTEC has requested that Battelle perform modeling of the hydrodynamic

behavior of the aquifer in the vicinity of the former Ingá facility and the hydrodynamic behavior of the

Sepetiba Bay itself, with emphasis given to the generation of potential bottom shear stresses that could

impact sediment stability. Key findings pertaining to the hydrodynamic behavior of the aquifer were

summarized in a letter to Haztec entitled “Summary of Hydrodynamic Modeling Performed for Usiminas

at the Former Ingá Facility, Sepetiba Bay, Rio de Janeiro.” The results of the numerical modeling

performed in Sepetiba Bay are described in this progress report.

This draft progress report describes the datasets and methods that were used to develop bed shear stress

estimates for Sepetiba Bay for a baseline environmental scenario. The data used in the analysis and the

methods used to develop the numerical model for Sepetiba Bay and the result of the circulation model

analysis are described. The estimation of the wind-generated waves and the associated bed shear stresses

due to the waves and circulation are discussed.



Summary

Battelle conducted a modeling analysis to characterize tidal and wind-driven circulation, wind-generated

waves, and the associated bed shear stress within the bay using best available data. Specific study

objectives were to 1) develop a numerical model of Sepetiba Bay based on tidal, wind and freshwater

discharge forcing mechanisms; 2) apply the model for conservative estimation bed stresses due to

circulations; and 3) to conservatively estimate wind-wave generated bed-stresses.

Battelle found that maximum bed stress due to circulation in the project area were estimated to be 0.5 Pa

southeast of Ilha de Madeira and that conservative estimated wind-waves provided maximum bed shear

stress less than 0.2 Pa. The circulation and wind-wave bed shear stress can be added to provide a

conservative estimate of the total maximum bed stress (a maximum of 0.7 Pa) expected in the bay. In the

future, these stresses can be used to evaluate the stability of the dredged sediment within a confined

aquatic disposal facility, which is proposed to be designed and installed in the Sepetiba Bay.

Additional work is needed to complete the analysis, which includes:

Perform review and quality assurance of digital bathymetry survey data recently received from Haztec that covers the entirety of the bay

Evaluate the large wind-wave cases (16 m/s and 26.1 m/s wind waves),

Evaluate the sensitivity of the results to uncertain parameters,

Compare results to observational data that may be provided by Usiminas,

Report more detailed model results for specific areas of the bay at which the sediment will be disposed

The results of the work performed to date are described in the remainder of this letter.

Numerical Modeling of Circulation

Delft3d-FLOW (Deltares, 2009) was used to analyze the tidal and wind-driven flows in the bay. Delft3d-

FLOW is based on horizontally discretizing an aquatic area into an orthogonal curvi-linear mesh and

vertically into σ-layers. These layers have a variable thickness but are a prescribed fraction of the local

water depth. These features allow for meshes to reasonably conform to shoreline features and

bathymetry. The model allows for areas to “wet” and “dry” as tidal conditions change. The modeling

software accounts for tides, meteorological forcing (winds and heat fluxes), density driven flow, bed

stresses, river discharges, Coriolis forces and bathymetric steering of flow. Computational meshes can be

cast in either Cartesian or spherical (geographic) coordinate systems. Key assumptions in the model are

that horizontal circulation dominates over vertical motions (hydrostatic assumption), a quadratic drag law

is appropriate for bottom-stress estimation, fluid stresses are appropriately treated as Reynolds stresses

and a k-ξ turbulence model is appropriate for estimating the sub-grid scale dissipation of momentum.

These are common assumptions used for applied coastal circulation studies. Further details about

Delft3d-FLOW are described by Deltares (2009).



In order to develop a numerical model capable of estimating the circulation near the project area, the

entirety of Sepetiba Bay was treated as the model domain so that the model’s estimation of tidal and

wind driven flow could be estimated at sufficient distance from where the model’s open boundary

conditions were applied. The model mesh used is shown in Figure 1.

Bathymetry. The study used publicly available bathymetric data obtained from Brazil’s Department of

Hydrography and Navigation ( https://www.mar.mil.br/dhn/chm/cartas/cartas.html ). Chart Number 1622

covers the Sepetiba Bay area. The shoreline and soundings contained on the chart were digitized. The

chart is shown for reference in each report figure. The digitized sounding and shoreline information was

stored in a format readily used by the Delft3D-FLOW modeling software utilities. The model domain

and bathymetry are shown in Figures 1 and 2, respectively. The depths in the project area range from 3 to

11 m above mean lower low water elevation. Detailed digital bathymetry survey data were not available

in a dataset that covered the entirety of the bay at the time the model was developed for this study. These

data can be updated in the future.

Tides. Tidal forces are incorporated into the model as an open boundary condition. For the Sepetiba Bay

model, this open boundary condition is the bay mouth, which runs north to south along the western edge

of the bay (Figure 1). The tidal harmonics near Sepetiba Bay are reported in the literature (Nunes da

Rosa, 2009); these are presented in Table 1. These harmonics were used to set the water surface

elevations at either end of the boundary of the model, which linearly vary along the boundary and drives

the tidal flow in the bay.

Table 1. Tidal Harmonics near Sepetiba Bay Mouth

Harmonic Manharatiba Ponta Leste Ilha Grande

Amplitude (cm) Phase (degrees) Amplitude (cm) Phase (degrees)

Q1 3.5 61 4.9 114

O1 10.7 83 8.8 96

M1 1.9 186 4.3 235

P1 1.7 132 0.1 67

K1 5.3 136 0.3 65

N2 3.9 114 4.1 90

M2 32.6 77 24.7 62

S2 17.8 85 20.1 84

K2 4.8 85 5.5 86

M3 1 220 1.9 253

M4 7.5 66 3.4 38

Freshwater Discharges. Most of the freshwater discharges into Sepetiba Bay are from locations along

the northeastern shore of the bay (Cunha et al., 2006). These are presented in Table 2 (after Cunha et al.,

2006). The long-term average flow is reported to be 106 m3/s (Molisani et al., 2003). Cunha et al. (2006)

https://www.mar.mil.br/dhn/chm/cartas/cartas.html



report that there is little seasonal variation in these discharges and report smaller estimates for Sao

Francisco Canal (89 m3/s) than reported by Molisani et al. (2003).

Winds. Winds speeds were summarized for the period from 2003 to 2008 that were collected from the

Marambaia Weather Station, located at the eastern end of Sepetiba Bay. These wind speeds were

referenced to 10.0 meters aboveground which is a standard reference height. The average winds speed

was about 3 m/s and the maximum wind speed was 16 m/s. The 100-year wind speed was reported to be

26.1 m/s.



Table 2. Average Freshwater Discharge to Sepetiba Bay (Cunha et al., 2006)

Source Discharge (m3/s)

Guarda River 6.8

Sao Francisco Canal 89.0

Guandu Canal 8.8

Ita Canal 3.3

Saco do Engenho River 0.5

Piraque River 2.5

Cacao River 1.1

Table 3. Estacao da Marambaia Wind Speed (2003-2008) at 10 meters Above Ground

Month

Average Wind

(m/s)

Maximum

Wind (m/s)

1 3.0 11.9

2 3.2 10.8

3 3.1 10.5

4 3.1 13.4

5 3.1 13.5

6 3.2 14.3

7 3.3 14.3

8 3.5 14.5

9 3.7 14.9

10 3.7 16.0

11 3.6 14.8

12 3.6 15.9

Model Mesh. Delft3d-FLOW numerical model applications are based on orthogonal curvilinear finite

difference mesh like that shown in Figure 2. The mesh used for this study has 327 cells in the west to east

direction and 137 cells in the north to south direction with some land areas including islands. Note that

the land areas were removed from the computational mesh. While the size of the cells can be variable,

they are nearly uniformly sized at 125 by 125 meters in this application. The model has five vertical

layers; each layer has a thickness that is 20 percent of the local depth. Estimates of Bed Stress due to Tides, Freshwater Discharges and Winds. The digitized shore line and bathymetric data were used to configure the model domain in terms of shape and depth. Tides were



applied to the western boundary of the bay with tidal harmonics specified as described above. A steady

106 m3/s freshwater discharging into the bay was applied based on the reports described above. Steady



16 m/s winds were applied representing the maximum reported monthly mean. Two cases of wind

direction were simulated: winds coming from the northeast and winds coming from the southwest. For

this progress report the cases where the winds come from the northeast are discussed.

With the tides, winds and freshwater discharges applied, the model of the bay develops a flow that

quickly responds to the tide. Figures 3 and 4 depict representative bottom layer circulations for flood and

slack tide conditions. The area shown in these figures corresponds to the inset depicted in Figures 1 and

2. Note that only 1 percent of the flow vectors are shown to increase clarity of the figures. Bottom

currents in the project area are estimated to be 20 to 40 cm/s; higher currents are estimated in the

constricted and shallower areas. While observed bottom currents at this location and at these conditions

are not available, the model appears to be reasonable. Note that Molisani et al. (2003) reported maximum

current speeds of 50 to 75 cm/s at the bay entrance. The currents reported here are smaller but occur in

the less constricted project location and therefore are expected to be smaller than found at the bay

entrance.

The bed shear stress is a model output. Because the bed shear stress varies spatially and over time due to

changes in circulation of the surface water, these results are archived at sub-tidal time scales (every 30

minutes) over a simulated month. Results are shown as maps at a single instant in time for both low and

high tides. The bottom velocity (Ub) and water density (ρ), a drag coefficient, (Cd) and gravity, g are used

to estimate the circulation-induced bed shear stress, (τc) using the formulation given in Deltares (2009)

and shown below:

The bed roughness (Chezy) parameter value was set to 65, which is the default value and is used to

estimate the drag coefficient, Cd. Details are provided in Deltares (2009). The bottom velocities and

water density are computed by the model and g is set to 9.81 m/s2. Velocity profile measurements, bed

form and sediment properties are needed in the area of interest to verify the velocity structure and the

roughness characteristics.

The maximum circulation-induced bed shear stress estimated for the conditions described are shown in

Figure 5. This figure shows the local maximum that occurred during the modeled period as opposed to

the estimated value at a particular instant in time. Note that the maxima predicted may not have occurred

in unison. Bed stresses in the modeled area are predicted to range from about 0.2 to 0.5 Pa and tend to be

higher to the west of the project area. This result is consistent with what would be expected given the

estimated currents shown in Figures 3 and 4.

These bed shear stress estimates can be compared to critical shear stress associated with native sediments

and design capping materials to assess material mobility in the absence of additional stresses due to wind-

waves. Additional simulations will be performed to assess 100-year wind-driven circulation and to

evaluate parameter uncertainty. In addition, more detailed examination of model output, which will

include the maximum stress conditions and the time history of bed sheer, will be performed at proposed

sediment disposal locations.



Numerical Modeling of Wind-Waves Induced Stresses

Winds that pass over Sepetiba Bay will generate a spectrum of waves with a range of heights, periods and

directions. The spectrum of waves when integrated over a range o frequencies and heights represents the

total wave energy. A single monochromatic wave possessing the same total wave energy is termed the

significant wave. The significant wave will grow in size as it passes over unobstructed lengths of open

water, which results from the additional momentum to the water body that is imparted by the wind. This

distance is referred to as fetch. For winds that pass over Sepetiba Bay, in a northeast to southwest or

southwest to northeast direction, the fetch is about 15 km.

The combination of fetch (15 km), average depth (6.0 m) and the higher observed and 100-year wind

speeds (16.0 and 26.1 m/s) were used to estimate the wind-generated wave conditions, which for the

purpose of the model, was applied uniformly throughout the bay. The approach described for this

analysis does not take into account wave refraction, diffraction or energy dissipation due to wave

breaking. The analysis, aside from potential fetch limitation, does not reduce wind effects due to land

sheltering. The analysis also does not include wave-current interactions and conservatively assumes that

near-bottom wave motion is aligned with currents giving the greatest combined bottom stress.

Using an average wind speed of 3.0 m/s (measured 10 m above ground surface), a fetch of 15 km, and

water depth, (h) of 6.0 m, a nominal wind wave height (H) and period (T) of 0.14 m and 1.58 s were

estimated based on linear wave theory and provided by the SEDX package available at United State

Geological Survey (http://woodshole.er.usgs.gov/staffpages/csherwood/sedx_equations/sedxinfo.html ).

This code is based on Shore Protection Manual (Coastal Engineering Research Center, 1984).

The bottom orbital velocity associated with wind waves, Uw, was estimated using the approach and an

adaptation of the code described by Wiberg and Sherwood (2008).

The wave, k, is found iteratively through the wave dispersion relation:

The bottom orbital velocity, Uw, was used to estimate the bed shear stress associated with wind waves,

(τw) based on a typical formulation reported by many investigators and recently by Brand et al. (2010) and

Newgard and Hay (2007). This is based on the water density and a wave friction factor (fw):

A detailed field investigation should be performed to validate the choice for the wave friction factor;

however, in lieu of this information, a value reported in the literature (see Newgard and Hay, 2007) of

about 0.01, was used in these this study.

http://woodshole.er.usgs.gov/staffpages/csherwood/sedx_equations/sedxinfo.html



Using the above equations, parameter values and estimated wind-wave conditions, the spatially variable

wind-wave induced bed sheer stress was estimated for both high and low tide conditions. These results

are presented in Figures 6 and 7. In the modeled area, the wind-wave bottom shear stress is estimated to

be less than 0.2 Pa for the conditions investigated (average winds). These calculations were limited to

areas where the wave depth exceeded 1 meter because the approach is not suited to areas where wave

energy is dissipated due to wave breaking, which occurs at shallower wave depths.

Conclusions and Recommendations

A numerical model was configured using Delft3d-FLOW. The model was used to estimate currents and

associated circulation-induced bed shear in the project area using tidal harmonics, chart bathymetry, and

maximum observed winds speed, and typical freshwater inputs from Sao Francisco Channel. These

bottom shear stresses were estimated to be as high as 0.5 Pa in the project area. Standard calculations

were used to estimate wind-generated wave conditions, near-bottom orbital velocities and associated

wind-wave induced bed shear stress. These were found to be less than 0.2 Pa in the project area. A

conservative approach to estimate the total bottom shear stress is to add the circulation and wind-wave

induced bed shear stresses. Doing so yielded an estimate of 0.7 Pa for the scenario described in this letter.

The analysis reported here does involve the use of higher wind-driven circulation combined with wind-

wave assessments using average winds. As larger winds are used for wind-wave estimates, the relative

roles of circulation and wind-wave induced bed shear stress will likely change where the wind wave will

become more dominant on storm-event time scales.

Further work is needed to complete the analysis. This includes:

Perform review and quality assurance of digital bathymetry survey data recently received from Haztec that covers the entirety of the bay

Evaluate the large wind-wave cases (16 m/s and 26.1 m/s wind waves),

Evaluate the sensitivity of the results to uncertain parameters,

Compare results to observational data that may be provided by Usiminas,

Report more detailed model results for specific areas of the bay at which the sediment will be disposed

If you have any questions, please feel free to contact me at (614) 424-7289.

Sincerely,



Stephen Rosansky, P.E.

Senior Engineer

Environmental Technology

cc: Ana Elisa Fonseca Silveira



REFERENCES

Barcellos, C. , L.D. de Lacerda, and S. Ceradini. 1996. “Sediment origin and budget in Sepetiba Bay

(Brazil) – an approach based on multielemental analysis,” Environmental Geology,

32(3):203-209.

Brand, A, J.R. Lacy, K. Hsu, D. Hoover, S. Gladding and M.T. Stacey. 2010. “Wind-enhanced

resuspension in the shallow waters of South San Francisco Bay: Mechanisms and potential

implications for cohesive sediment transport,” Journal of Geophysical Research, Volume

115, Paper C11024.

Coastal Engineering Research Center. 1984. Shore Protection Manual. U.S. Army Corps of Engineers,

Waterways Experiment Station. Vicksburg, Mississippi.

Cunha, C.L.N., P.C.C. Rosman, A.P. Ferreira, T.C.N. Monteiro. 2006. “Hydrodynamics and water quality

models applied to Sepetiba Bay,” Continental Shelf Research, 26:1940-1953.

Deltares. 2009. Delft3d-FLOW: Simulation of Multi-Dimensional Hydrodynamic Flows and Transport

Phenomena, Including Sediments Users Manual, Version 3.14, Revision 7864. Delft, The

Netherlands.

Molisani, M.M., R.V. Marins, W. Machado, H.H.M. Paraquetti, E.D. Bidone, and L.D. Lacerda. 2003.

“Environmental Changes in Sepetiba Bay, SE Brazil,” Reg. Environmental Change 4:17-27.

Newgard, J.P. and A.E. Hay. 2007. “Turbulence intensity in the wave boundary Layer and Bottom

Friction Under (Mainly) Flat Bed Conditions,” Journal of Geophysical Research, Volume

112. Paper C09024.

Quadros, J.P., E., Camillo, F. Pinheiro and M.A.S. Fernandez. 2009. “Imposex as an indicator of

organotin polluition at Rio de Janeiro South Coast: Sepetiba and Ilha Grande Bays,”

Thalassas. 25(1):19-30.

Nunes da Rosa, A. 2009. Estaleiro e Base Naval para a Construcao de Submarinos Convencionais e de

Propulsao Nuclear Estudo de Impacto Ambiental-Volume 2.

Wiberg, P.L. and C.R. Sherwood. 2008. “Calculating wave-generated bottom Orbital Velocities from

Surface-Wave Parameters,” Computers & Geosciences, 34. Pages 1243-1262. Elsevier.



FIGURES

Figure 1. Sepetiba Bay Circulation Model Mesh; Inset Box Shows Focus Area in Subsequent

Figures



Figure 2. Sepetiba Bay Bathymetry (m Below Mean Lower Low Water); Inset Box Shows

Focus Area in Subsequent Figures

Figure 3. Simulated Bottom Layer Currents on Flood Tide



Figure 4. Simulated Bottom Layer Currents on Slack Tide

Figure 5. Maximum Estimated Circulation-Induced Bottom Shear Stress in Pa (N/m2)

Figure 1. Wind-Wave Induced Bed Shear Stress during Low Tide Conditions



Figure 2. Wind-Wave Induced Bed Shear Stress during High Tide Conditions

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