COM
EQUATION WORKBOOK
SCIENTIFIC PROTOCOL FOR
OCEAN DISPOSAL SITE DESIGNATION
Camp Dresser & McKee
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U.S. Environmental Protection Agency
Criteria and Standards Division
Washington, D.C. 20460
EQUATION WORKBOOK
SCIENTIFIC PROTOCOL FOR
OCEAN DISPOSAL SITE DESIGNATION
Prepared by
T.S. George
R. Walton
Camp Dresser & McKee
7630 Little River Turnpike, Suite 500
Annandale, Virginia 22003
Telephone: (703) 642-5500
February 1984
Revised: September 1984
Contract No. 68-01-6403
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TABLE OF CONTENTS
List of Figures iii
List of Tables iv
INTRODUCTION 1
STAGE 1. PRELIMINARY SITE EVALUATION 1-1
1.1 Introduction 1-1
1.2 Forms 1-1
1.3 Basemaps 1-3
STAGE 2. WASTE PROFILE AND LOADING CHARACTERIZATION 2-1
2.1 Introduction 2-1
2.2 Forms 2-1
2.3 Calculations for Multiple Sources 2-6
STAGE 3. TRANSPORT MAPPING AND RESUSPENSION ESTIMATION 3-1
3.1 Introduction 3-1
3.2 Forms 3-4
3.3 Evaluate and Map Benthic Impacts Areas for Negatively
Buoyant Solid Wastes 3-4
3.4 Sediment Resuspension Potential for Typical Conditions ... 3-9
3.5 Resuspension Probability Under Episodic (Storm)
Conditions 3-16
3.6 Estimate Annual Sediment Transport Rate 3-25
3.7 Calculate and Map Typical Long-Term Transport Contours ... 3-30
STAGE 4. INITIAL MIXING AND SOURCE STRENGTH CALCULATIONS 4-1
4.1 Introduction 4-1
4.2 Forms 4-1
4.3 Initial Dilution of Liquid Phase 4-1
4.4 Source Strengths and Initial Conditions 4-6
4.5 Vertical Distribution of Constituent Concentrations 4-10
STAGE 5. WATZR QUALITY CRITERIA COMPARISONS 5-1
5.1 Introduction 5-1
5.2 Form 5-1
5.3 Near Field Acute Exposure Level 5-1
5.4 Far Field Chronic Exposure Level Using Discrete Cloud
Model A 5-15
5.5 Far Field Chronic Exposure Level Using Plume Model 5-19
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TABLE OF CONTENTS
(Continued)
STAGE 6. HYPOXIC EVENT POTENTIAL ASSESSMENT
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
Introduction
Forms
Ambient BOD Without Disposal
Local Water Column BOD With Disposal
Initial Dissolved Oxygen After Disposal
Oxygen Depletion Curve For Net Flow, Urn > 0.0
Oxygen Deficit Growth Rate For Net Flow Urn = 0.0
Oxygen Deficit Growth Rate Comprehensive Example for Net
Flow Urn = 0.0
Page
6-1
6-1
6-3
6-3
6-8
6-9
6-10
6-12
6-19
STAGE 7. SPECIES SPECIFIC ASSESSMENT 7-1
7.1 Introduction
7.2 Procedure ...
LIMITATIONS
REFERENCES
APPENDIX A.
APPENDIX B.
APPENDIX C.
APPENDIX D.
APPENDIX E.
CROSS-REFERENCE TABLE OF EQUATIONS IN PRELIMINARY
MANUAL AND EQUATION WORKBOOK
DSP FORMS
TABLES FROM SITE DESIGNATION MANUAL
FIGURES FROM SITE DESIGNATION MANUAL
SUGGESTED SOURCES FOR DATA AND INFORMATION
7-1
7-1
8-1
ii
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LIST OF FIGURES
Figure Page
1-1 Example of Small Scale Basemap with Landmarks 1-5
1-2 Example of Large Scale Basemap with Bathymetry 1-6
3-1 Stage 3, Transport Mapping and Resuspension Overview 3-2
3-2 Example of Pycnocline Formation 3-3
3-3 Definition of Current Variables 3-7
3-4 Example of Benthic Deposition Area 3-10
3-5 Flowchart for the Estimation of Resuspension Correction
in Section 3.5.6 for Each Material 3-23
3-6 Volumetric Sediment Transport Rate Versus Mean Flow for
Various Wave Induced Bottom Velocities 3-28
3-7 Concentration (g/m ) Contours for Unit Load at Point of
Disposal, Assuming Continuous Point Source 3-35
3-8 Concentration (g/m ) Contours for Unit Load at Point of
Disposal, Assuming Discrete Point Source 3-38
3-9 Concentration (g/m ) Contours of Unit Load at Point of
Disposal, Assuming Discrete Distributed Source 3-42
4-1 Stage 4, Initial Mixing and source Strength Overview 4-2
4-2 Relative Vertical Sediment Concentration Profiles 4-14
5-1 Stage 5, Criteria Comparison Overview 5-2
5-2 Quadrilateral of Horizontal Area Over Which Criterion is
Exceeded 5-12
5-3 Horizontal Area Over Which Criterion for Lead is Exceeded
in Example of Equation 5-6 5-16
6-1 Stage 6, Dissolved Oxygen Assessment Overview 6-2
8-1 Area of Impact and Depth of Coverage Using Two Different
Estimates 8-4
iii
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LIST OF TABLES
Table Page
1-1 Example of Form DSP1 Basic Site Characterization
Information 1-2
2-1 Example of Form DSP2 Waste Source and Loading
Characterization 2-3
2-2 Example for Single Source of Form DSP3 Representative
Waste Profi1e Descri pti on 2-4
2-3 Example for Multiple Sources of Form DSP3 Representa-
tive Waste Profile Description 2-5
2-4 Example of DSP4 Geochemical Site Characterization 2-7
3-1 Example of Form DSPS Physical Oceanographic
Characterization 3-5
3-2 Example Wave Frequency Table 3-17
3-3 Example Wave Frequency Table for Sand 3-19
3-4 Calculation Example of Resuspending Wave Orbital
Vel oci ty for Sand 3-24
4-1 Bioturbation Coefficients, D, for Various Locations 4-12
5-1 Example of Form DSP6 Water Quality Criteria Comparison
Summary 5-3
6-1 Oxygen Deficit Growth Rate Worksheet 6-21
6-2 Example Oxygen Deficit Growth Rate Worksheet 6-22
7-1 Organization of Species Specific Impact Assessment 7-2
7-2 Species and Constituent-Specific Summary Table 7-4
iv
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INTRODUCTION
PURPOSE
The purpose of this Equation Workbook is to provide detailed guidance in
the use of the equations that have been incorporated into the scientific
protocol for ocean disposal site designation under development by EPA.
This was done by providing concise descriptions of the use of each
equation, hypothetical examples of the use of each equation, and tables and
graphs of necessary coefficients and constants.
BACKGROUND
The development of a scientific protocol for ocean disposal site designa-
tion is a result of the joint interest of the U.S. Environmental Protection
Agency (EPA) Criteria and Standards Division, Office of Water Regulations
and Standards and the EPA Environmental Research Laboratory in Nar-
ragansett, Rhode Island.
The efforts of these two groups have resulted in the preparation of the
following two documents:
A Preliminary Ocean Waste Disposal Site Designation Manual (ASA,
1983)
Proceedings of a Workshop for the Development of a Scientific Pro-
tocol for Ocean Dump Site Designation (Reed and Bierman, 1983)
Preliminary Site Designation Manual
A Preliminary Ocean Waste Disposal Site Designation Manual was prepared by
Applied Science Associates, Inc. (ASA, 1983) for the EPA Criteria and
Standards Division (OWRS). This Preliminary Manual presents the disposal
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site evaluation protocol in seven major stages. As reflected in the
Equation Workbook, the methodologies presented by ASA in their Preliminary
Manual have not been changed or modified by EPA.
The goal of the Preliminary Manual was to systematize the scientific
protocol for pre-disposal marine dumpsite designation studies. This
involved the development of a methodology and a series of mathematical and
mapping exercises to evaluate the capability of a given site to receive a
particular type of waste. The basic strategy of the manual was to attempt
realistic assessments, within the limitations of a non-computerized
approach, using conservative assumptions.
The Preliminary Manual presents numerical calculations which can be carried
out with a hand-held scientific calculator. In some situations, such as a
highly sensitive biological area where complex hydrodynamics prevail, the
approach presented in the manual may not be sufficient. In such cases, the
manual recommends a hydrodynamic and biological computer modeling approach
with a coordinated field survey effort.
Proceedings of a Workshop
The Proceedings of a Workshop for the Development of a Scientific protocol
for Ocean Dump Site Designation (Reed and Bierman, 1983) was prepard by Dr.
Mark Reed of Applied Science Associates, Inc., Wakefield, Rhode Island, and
Dr. Victor J. Bierman, Jr., of the EPA Environmental Research Laboratory,
Narragansett, Rhode Island. The Workshop, which was attended by 30
scientific and technical experts in the fields of physical, chemical, and
biological oceanography, was convened to assist in the development of the
protocol. Task group reports are contained in the Proceedings of the
Workshop which offer comments and recommendations on the protocol stages
presented in the Preliminary Manual.
The proceedings contain recommendations for the development of an
operational technical guidance manual for ocean dump site designations,
with emphasis on dredged material disposal in shallow coastal environments.
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These recommendations have not been adopted as official EPA policy and no
official EPA endorsement should be inferred.
EQUATION WORKBOOK
The Equation Workbook was developed directly from the Preliminary Manual.
No changes were made in the underlying assumptions, procedures or equations
presented in the Manual. The Workbook was prepared for use as guidance in
the scientific methods recommended by the Preliminary Manual for use in
ocean disposal site designation studies with particular emphasis on the
numerical calculations.
There are many mathematical equations in the protocol which are used to
describe physical, chemical and biological processes in the marine environ-
ment. The Workbook is designed to aid in the understanding and application
of these equations by providing additional information and example
calculations for each equation in each of the seven protocol stages. The
Workbook is geared for a level of use by EPA Regional Office personnel and
the District Office U.S. Army Corps of Engineers (CE) personnel with
general engineering and scientific backgrounds, but who may not necessarily
be familiar with the specialized equations and principles of the protocol.
In the Equation Workbook, the equations are numbered for each of the proto-
col stages. These numbers do not necessarily coincide with the numbering
system presented in the Preliminary Manual. This is due to the fact that
the Workbook provides additional equations, changes the order of equations
or breaks down large equations into parts to aid in the calculation proce-
dure. A cross reference table of equations and equation numbers is given
in Appendix A to provide a correlation between the equations of these two
documents.
FORMAT OF WORKBOOK
The Workbook presents a section on each of the seven protocol stages,
Sections 1.0 through 7.0. The sections and subsections for each stage are
presented in decimal outline form for easy cross-referencing. For each
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protocol stage a general introduction is presented followed by a discussion
of the disposal site protocol (DSP) forms that must be filled out for that
stage before any analysis can be carried out using the equations. Major
calculation sequences are then grouped together with an explanation of each
formula or equation. Special attention is given to the proper definition
of each variable in the equation and the units involved.
For each equation described, an example calculation is provided. The
example calculations for each equation in each stage use numerical values
that are on the example DSP forms or values that have been previously
calculated. This provides for a consistently understandable example
throughout the entire Workbook. The values used in the examples provided
in the Workbook are not default values and are not recommended for use when
no other values are available. They are only used to provide an example of
the calculations performed for each equation.
Section 8.0, Limitations, is presented as part of the Workbook to bring
out, in addition to the discussion in each protocol stage, several general
and specific points that the user should keep in mind as he applies the
scientific protocol to particular sites and wastes being considered.
Five appendices are included in the Workbook. Appendix A is a cross-
reference table of equations in the Preliminary Manual and in the Equation
Workbook. Blank disposal site protocol (DSP) forms are provided for use in
Appendix B. Appendices C and D are tables and figures of information that
are used to carry out the protocol. Additional sources of information and
recommended reading are given in Appendix E.
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STAGE 1. PRELIMINARY SITE EVALUATION
1.1 INTRODUCTION
The purpose of this stage is to collect pertinent information in and around
the site or sites chosen in the preliminary efforts of the site designation
procedure. The information collected is used to determine, at the earliest
stage, if a site is unacceptable or if potential problems are indicated.
The presence of specific conditions within the site itself would make it
unacceptable for disposal; and if those conditions were present in the
general area of the site, then they would indicate potential problems.
Such conflicting conditions would include:
Marine or estuarine sanctuary,
Military exclusion area,
t Interference with navigation, and
Engineering use of seafloor such as seabed mining and undersea
cables.
Potential problems are then addressed in the other stages of the protocol
as the designation procedure continues.
1.2 FORMS
Only one disposal site protocol form is required as part of Stage 1. It is
the Basic Site Characterization Form, DSP1. (See Appendix B for blank
form.) The form is used to provide basic physical information about the
disposal site and potential conflicts in the disposal site area such as the
location of areas used for fisheries and sanctuaries.
Table 1-1 is an example of Form DSP1. Each variable name is accompanied by
a value and the appropriate units for this value. All distances are given
1-1
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TABLE 1-1. EXAMPLE OF
FORM DSP1 BASIC SITE CHARACTERIZATION INFORMATION
Variable
Name
Value
Units
Source/Comments
Site Center Latitude
Longitude
Width
Length
Orientation of Longest Dimension
Site Shape
Distance to Nearest*
(1) Coastline
(2) Fishery Area
(3) Recreational Area
(4) Shipping Lane
(5) Military Exclusion Zone
(6) Ocean Disposal Site
(7) Marine Sanctuary
(8) Engineering Uses of Seafloor
(Specify)
(9) Living Resources
XX°XX'
YY"YY'
5
10
h
N
W
km
km
Rectangular
15
100
15
10
N/a
75
N/A
15
N/A
km
km
km
km
km
km
km
km
Assigned
Assigned
Assigned
Assigned
Assigned
Assigned
State Shoreline
Sport Fishing
Swimming beach at
Beach Town
To Major River
-
Industrial disposal
site
-
Sand mining
-
*From closest site extremity, not from site center
1-2
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in kilometers. There is also a column on this form for comments which may
be used to further clarify the variable name in the first column. For
example, in the comment column across from the variable "coastline" in
Table 1-1 the coastline is identified as being the state shoreline.
1.3 BASEMAPS
The first protocol stage requires the development of at least two basemaps
at different scales showing the location of the proposed waste disposal
site or sites. Coastal charts of the National Ocean Survey can provide
good information for basemap development. A small scale map of the site
should show the coastline and recognizable landmarks (cities, rivers, etc).
This map would generally include an area within a 100 km radius of the site
center. A more detailed, larger scale map of the site should show the site
bathymetry. A 25 km radius around the site center will typically be
included. All maps should locate such areas as fisheries, shipping lanes,
recreational uses, etc., which are listed on Form DSP1.
Along most open coastal areas the bathymetry provided by the standard
navigational charts will not be sufficient for site designation purposes
(transport calculations, determination of areas of deposition, bottom
roughness scales and the like). The boat sheets developed during the
survey and used to prepare the charts may, depending on line spacing and
sounding frquency, be more nearly adequate. These can be obtained, often
now in digital format, from the NOS (National Ocean Survey, NOAA). In the
absence of such detailed data a suplementary initial bathymetric survey
covering the area within a three to five mile radius of the disposal site,
may be necessary.
Figure 1-1 is an example of a small scale basemap with landmarks. This map
also shows the location of potential conflicting uses such as the shipping
lane, industrial disposal site and sport fishing areas which are listed on
the example Form DSP1 given in Table 1-1.
Figure 1-2 is an example of a closer look at the disposal site area on a
larger scale map which shows the bathymetry of the area. This map also
1-3
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shows the potential problem areas such as the recreational beach, the sand
mining use and the shipping lane.
The maps developed for Stage 1 provide general locational information about
the site and its relationship to other activities in the area. The maps
are, however, developed as "basemaps" on which results are displayed in the
other protocol stages. Such uses include plotting mean flow direction,
mapping benthic impact areas, drawing concentration contours and mapping
the distribution of specific organisms.
It is highly recommended that comprehensive consultation with local experts
and interest groups be carried out at the earliest part of Stage 1. This
will serve to address all important considerations which will often
eliminate several problems later on.
1-4
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_STATE_LINE_
STATE LINE
SPORT
FISHING
r ZZZZSHIPPING LANE
INDUSTRIAL
DISPOSAL
4
0 25
I I I I I I
KILOMETERS
Figure 1-1. Example of Small Scale Basemap with Landmarks
1-5
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Figure 1-2. Example of Large Scale Basemap with Bathymetry
1-6
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STAGE 2. WASTE PROFILE AND LOADING CHARACTERIZATION
2.1 INTRODUCTION
The purpose of this stage is to define the representative physical and
chemical information of a typical waste expected to be released at the site
or sites selected in the preliminary site evaluation of Stage 1. The
general procedure is to collect existing data or perform waste analyses to
provide information to be used in subsequent stages. Data cm be provided
for:
1. Specific waste, single source,
2. Specific waste, multiple sources, or
3. Non-specific wastes and sources.
2.2 FORMS
Three forms must be completed as part of Stage 2 of the protocol (Blank
forms are provided in Appendix B).
2.2.1 Form DSP2
The Waste Source and Loading Characterization form provides many physical
variables which are used in calculations performed in subsequent stages.
For each of several variables on DSP2 which are given in the first column,
the value is placed in the second column. For each variable the units
required are provided in the third column, and the fourth column provides
special comments and gives the variable symbol used in the equations
discussed in the text. Default values for some of the variables are also
provided. For completion of DSP2, fine particles are considered those
which have a diameter of less than 0.1 mm.
Table 2-1 is an example of a completed Form DSP2. In this example, the
waste type is dredge material and the annual loading rate is 5.0 x 10
cubic meters per year. The variable symbol used in the equations for
2-1
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annual loading rate is "Qa." The example values in Table 2-1 are also those
used throughout the other stages in the example computations provided for
each equation discussed.
2.2.2 Form DSP3
The Representative Waste Profile Description form is used to describe the
waste by providing the mean concentrations of various constituents measured
in the source materials. This form can be used for a single or multiple
.source specific waste, or for a non-specific waste. For a single source,
only column A is completed; and for multiple sources of specific wastes a
"weighted sum" approach is used as described in Section 2.3. For a generic
waste, Form DSPS is used to best describe whatever is known about the pro-
bable waste source or sources. The constituents listed on this form are
those that are mandatory.
Table 2-2 is an example of a completed form for a single source waste.
Since there is only one source, only column A in Table 2-2 is filled in
with percent solids (42) and concentrations for the other constituents such
as a 32 mg/kg concentration for BOD, the biological oxygen demand of the
waste. Table 2-3 is an example of a completed form for a multiple source
waste. In the example of Table 2-3, there are three sources having
fractional contributions of the total material of 0.2, 0.3 and 0.5. The
mean concentrations of the constituents measured in the source material are
recorded under each of the source headings. For example, the BOD concen-
trations for sources A, B and C are 30, 20 and 40, respectively. The
weighted sum of the BOD is calculated to be 32 mg/kg. The weighted sum
calculation is shown in Section 2.3.
Because a site is designated only for a class of waste such as dredged
material or sewage sludge, separate forms for DSP2 and DSPS must be
prepared for each distinct class of waste. Separate site designation
analysis will also be required if the evaluation of different classes of
waste is to be undertaken.
2-2
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TABLE 2-1 EXAMPLE OF
FORM DSP2 WASTE SOURCE AND LOADING CHARACTERIZATION
Variable Name
Value
Units
Comments
(Text Symbol )
Waste Type
Annual Loading Rate
Typical Duration of Dredging
Operation
Typical Number of Disposals
per day
Bulk Specific Gravity
Liquid Phase Specific Gravity
Particle Specific Gravity
Clay-Si It/ Sand-Gravel {Fine/
Coarse) Fractions (Total
Solid Phase)
Volumetric Solid/Liquid
Fractions
Fraction of Fines in Suspended
Cloud (Single Disposal)
Disposal Vessel
Vol ume
Width
Length
Speed
Individual Disposal
Duration
Frequency
Dredge material
S.OxlO6
0.25
14
1.7
1.0
2.65
0.41/
0.59
0.42/
0.58
0.9
4000
20
50
1.0
200
2
nr/yr
fraction
of year
none
none
none
none
none
none
m3
m
m
m/sec
sec
per day
(Qa)
(Tdd)
(Dd)
(sg) bulk
default: 1.0 (sg)
particle
default: 2.65
(sg) particle
(Ff/Fc)
(Fs/Fl)
default: 0.9
(Ffs)
(Vb)
(w)
(1)
(v)
(t)
2-3
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TABLE 2-2. EXAMPLE, FOR SINGLE SOURCE, OF
FORM DSP3 REPRESENTATIVE WASTE PROFILE DESCRIPTION
(Mean Concentration of Constituents Measured in Source Materials,
all concentrations in mg/kg)
Source
A
Source
B
Source
C
Source
D
Source
E
Weighted
Sum
(Cws)
Fractional
Contribution
(Fi)
Constituent
Percent Solids
BOD (5- day)
DO
pH
Total Chlorinated HC
Total Volatile
Organics
Cadmium
Copper
Lead
Mercury
1.00
42
32
0
6.0
0.005
1
7
15
O.Z5
1.00
2-4
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TABLE 2-3. EXAMPLE, FOR MULTIPLE SOURCES, OF
FORM DSP3 REPRESENTATIVE WASTE PROFILE DESCRIPTION
(Mean Concentration of Constituents Measured in Source Materials,
all concentrations in mg/kg)
Source
A
Source
B
Source
C
Source
D
Source
E
Weighted
Sum
(Cws)
Fractional
Contribution
(Fi)
Constituent
Percent Solids
BOD (5-day)
DO
DH
Total Chlorinated HC
Total Volatile
Organics
Cadmium
Copper
Lead
Mercury
0.2
63
30
0
0.005
1
8
20
0.30
0.3
28
20
0
0.005
1
6
15
0.15
0.5
42
40
0
0.005
1
7
13
0.29
1.00
42
32
0
6.0
0.005
1
7
15
0.25
2-5
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2.2.3 Form DSP4
The Geochemlcal Site Characterization form is used to record the background
contaminant values in the water column and in the sediments. These values
are used for water quality analysis in subsequent stages. The table
provides for concentration values of the constituents and provides for
physical characterization of the sediment (percent gravel, sand, silt and
clay) for both summer and winter seasons. Any additional constituents
included in this form are those studied in the source material as given in
Form DSP3. Table 2-4 is an example of a completed DSP4 form. Marine
stations or oceanography schools of nearby universities as well as
Environmental Protection Agency and National Marine Fisheries Services
Laboratories are potential sources of existing data.
Table 2-4 shows that at the proposed site the copper concentration is
0.0006 mg/kg in the water column and 0.60 mg/kg in the sediment. Also, the
bottom of the form shows that the percent of sand in the site sediment
during the summer season (60 percent) is only slightly greater than the
percent sand (58 percent) during the winter season.
2.3 CALCULATIONS FOR MULTIPLE SOURCES
The contaminants of each individual waste source are not considered
separately in the analyses of subsequent stages. Instead, a weighted sum
is calculated and used to represent the concentration in the combined or
composite waste.
EQUATION: Cws =£Ci * Fi (2-1)
i=l, n
where Cws = concentration of constituent in composite waste,
Ci = concentration of constituent in source i,
Fi = fractional contribution of total materials represented by
source i, and
n = number of water sources
2-6
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TABLE 2-4. EXAMPLE OF
FORM DSP4 GEOCHEMICAL SITE CHARACTERIZATION
Constituent
or
Characteristic
Water Column | Site Sediments
(Parts per Minion or mg/kg, Except Solids)
Percent Sol ids
BOD (5-day)
Dissolved Oxygen (DO)
PH
Total Chlorinated HC
Total Volatile Organic s
Cadmium
Copper
Lead
Mercury
Others
as required
0.000015
3.0
6.0
8.0
0.0000005
0.0001
0.0006
0.0004
0.00002
-
20
2.0
6.0
0.005
0.02
0.60
0.04
0.02
SEDIMENTS ONLY:
Percent Gravel
Percent Sand
Percent Silt
Percent Clay
Summer
2
60
33
5
Winter
1
58
35
6
2-7
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This formula is used for each of the constituents listed on Form DSP3. The
equation is calculated based on the concentrations in each of the sources
and the fractional contribution of each source.
EXAMPLES:
A) Given Three sources A, B and C as shown in Table 2-3 and the frac-
tional contribution of 0.2 for Source A, 0.3 for Source B and
0.5 for Source C; and the percent solids of 0.63 for Source
A, 0.28 for Source B and 0.42 for Source C,
then the weighted percent solids is
Cws = (0.2 * 0.63) + (0.3 * 0.28) + (0.5 * 0.42) = 0.42
B) Given The same three sources and fractional contributions as pre-
sented in example A from Table 2-3, and the BOD concentra-
tions of 30 for Source A, 20 for Source B and 40 for Source
C,
then The weighted concentration of BOD is
Cws = (0.2 * 30) + (0.3 * 20) + (0.5 * 40) = 32 mg/kg or mg/1.
2-8
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STAGE 3. TRANSPORT MAPPING AND RESUSPENSION ESTIMATION
3.1 INTRODUCTION
The purpose of this stage (see flow chart in Figure 3-1) is to estimate
sediment deposition and resuspension rates under typical and episodic
(storm) conditions, and to construct characteristic transport contour maps.
The water column is divided into three parts:
the upper water column (above pycnocline),
t the lower water column (below pycnocline), and
the sediments.
These parts correspond to the pelagic, demersal, and benthic biological
categories of Stages 5, 6, and 7.
A pycnocline is a location in the vertical profile representing a region of
high density gradients (Figure 3-2). In the ideal sense it separates two
liquids of different densities. Under actual conditions of interface
diffusion, it represents a zone of transition from one liquid density to
the other. Examples of pycnocline formation can be found along a shelf
break in which a warm upper layer 20-40 meters deep forms during the
summer, and on the shelf where a fresher upper layer, 5-10 meters thick,
can form following spring runoff.
On the appropriate basemaps (see Stage 1), the benthic area of sediment
deposition, and characteristic concentration contours for given disposal
practices are drawn. The concentration contours are drawn for the upper
and lower water columns, unless there is no season of the year during which
a pycnocline is present, in which case only one set of contours need be
drawn. If the pycnocline varies throughout the year, additional sets of
contours will be needed to define concentration limits.
3-1
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3.3
3.4
3.5
3.6
3.7
Complete
Form DSPS
portion
NO
V.of waste reach thex*
Evaluate and map
Benthic Impact Areas
t
Calculate
Sediment
Resuspension Potential
for typical conditions
t
Calculate
Resuspension
Probability under
episodic (storm)
conditions
t
Estimate
Annual Sediment
Transport Rate
t
Calculate and map
Typical Long-Term
Transport Contours
Figure 3-1. Stage 3, Transport Mapping and Resuspension Overview
3-2
-------
DENSITY (SIGMA T UNITS)
24.0
25.0
26.0
27.0
I T VI
Q.
HI
Q
20
40
60
80
100
120
140
160
180
200
Pycnocline
Depth
I I I I I I I I I A I
Figure 3-2. Example of Pycnocline Formation
3-3
-------
3.2 FORMS
To' perform the analyses of Stage 3, information from Forms DSP2 and DSPS
are required. Form DSP2 was filled out in Stage 2, Form DSPS should be
completed before continuing.
3.2.1 Form DSPS
The Physical Oceanographic Characteristics form provides many physical
variables used in this and subsequent stages. The variable name is listed
in column 1, its value is entered in column 2, units are given in column 3,
and column 4 gives the text symbol. A completed Form DSPS, which is used
for the example calculations in the text, is shown in Table 3-1. Using the
mean net surface drift, Urn, from Form DSPS, the positie x-axis is parallel
to Urn, and the y-axis is perpendicular and to the left on the appropriate
basemaps of Stage 1. Suggested information sources are listed in
Appendix E.
3.3 EVALUATE AND MAP BENTHIC IMPACT AREAS FOR NEGATIVELY BUOYANT SOLID
WASTES
3.3.1 Purpose and Procedure
For negatively buoyant solid wastes (i.e. those wastes containing solid
particles whose specific gravities are greater than the ambient seawater),
calculate the bottom area upon which the particles may accumulate.
This is a three-step process for each group of particles considered (e.g.
medium sand, coarse sand, etc.). Firstly, the time for the particles to
reach the bottom is estimated. Secondly, the limits of spreading undergone
during settling is estimated from horizontal mean currents and tidal
variability. Finally, the area of impact is drawn.
3.3.2 Comments
For positively or neutrally buoyant wastes, go to Section 3.7.
3-4
-------
TABLE 3-1. EXAMPLE OF
FORM DSPS PHYSICAL OCEANOGRAPHIC CHARACTERIZATION
Variable Name
Value
Units
Source/Comments
(Text Symbol )
Maximum Depth
Minimum Depth
Mean Depth
Pycnocllne Depth
Tidal Period
Ellipse Orientation
Major Axis Velocity
Minor Axis Velocity
Mean Net Surface Drift
Magnitude
Direction
Mean Net Bottom Drift
Magnitude
Direction
Mean Wave
Amplitude
Period
Storm Induced Bottom Current
Water Temperature (Annual
Range)
pH (Annual Range)
35
25
30
20
12.42
SW
0.15
0.07
0.05
SW
0.02
SW
0.5
6.5
m
m
m
m
hr
--
m/sec
m/sec
m/sec
m/sec
m
sec
m/sec
degrees
Celsius
(h)
(hp)
(To)
(Utx)
(Uty)
(Urn)
(Ubm)
(H)
(T)
(Usw)
(T)
3-5
-------
For wastes containing negatively buoyant solid particles, perform the
calculations below.
During descent, the cloud falls at a rate determined primarily by its total
mass and size, and entrains water. The cloud would descend to a
"dissipation" depth at which the initial momentum jet is balanced by
entrainment, and the particles fall approximately with their full
velocities in the ambient water column. The complete problem is not
simple and remains to be adequately parameterized (ASA, 1983). Instead,
the conceptually simple approach, below, is used.
3.3.3 Calculate Time for Particles to Reach Bottom
The time for a particle (or group of particles), with known fall velocity,
to reach the bottom is given by:
EQUATION:
t' =
(3-1)
where t' = time for particles to reach bottom in sec,
h = mean depth in m (Form DSPS), and
wf = particle fall velocity in m/sec (use Figure D-15 or
typical value for 0.1 mm diameter sand of 0.005 m/sec)
EXAMPLE:
Gi ven
h = 30 m (Table 3-1), and
wf = 0.005 m/sec
then
30
sec
3-6
-------
3.3.4 Calculate Limits of Area of Impact
The area of impact is an ellipse whose longitudinal and lateral dimensions
can be estimated by considering the mean net surface drift and tidal
velocities. Definition of the mean net tidal drift and tidal velocities
are shown in Figure 3-3.
NONTIDAL
NET FLOW (Urn)
TIDAL FLOW (UT)
Figure 3-3. Definition of Current Variables
EQUATIONS: dx+ = (Um + Utx) * t'
dx- = (Um - Utx) * t'
dy = Uty * t1
(3-2a)
(3-2b)
(3-2c)
where dx+ = maximum distance travelled downstream parallel to mean
net tidal drift (longitudinal direction) in m,
dx- = maximum distance travelled upstream parallel to mean net
tidal drift in m,
dy = maximum distance travelled in lateral direction on each
side of axis of mean net tidal drift in m,
Um = mean net tidal drift in m/sec (Form DSPS),
3-7
-------
Utx = maximum tidal velocity parallel to mean net tidal drift
direction in m/sec (Form DSP5),
Uty = maximum tidal velocity perpendicular to mean net tidal
drift direction in m/sec (Form DSPS), and
t1 = time for particle to reach bottom in sec (Eq. 3-1).
EXAMPLE:
Given
Urn = 0.05 m/sec (Table 3-1),
Utx = 0.15 m/sec (Table 3-1),
Uty = 0.07 m/sec (Table 3-1), and
t1 = 6000 sec (Eq. 3-1 example),
then dx+ = (0.05 + 0.15) * 6,000 = 1,200 m
dx- = (0.05 - 0.15) * 6,000 = -600 m
dy = 0.07 * 6,000 = 420 m
3.3.5 Calculate Area of Impact
The area of impact is an ellipse, and equals n multiplied by the product of
the lengths of the major and minor axes. The estimate for the area will be
used to calculate the extent of deposition on the seafloor.
EQUATION:
A =
* Utx * Uty * t
,2
(3-3)
where A = area of impact in m ,
Utx = maximum tidal velocity parallel to mean net tidal drift
direction in m/sec (Form DSP5),
Uty = maximum tidal velocity perpendicular to mean net tidal
drift direction in m/sec (Form DSP5), and
t1 = time for particles to reach bottom in sec (Eq. 3-1).
3-8
-------
EXAMPLE:
Given Utx = 0.15 m/sec (Table 3-1),
Uty = 0.07 m/sec (Table 3-1), and
t' = 6000 sec (Eq. 3-1 example),
then A = n * 0.15 * 0.07 * 60002 = 1.19 x 106 m2
3.3.6 Draw Area of Impact
The area of impact on the bottom is an ellipse, with point of disposal at
(0,0), contained within the coordinates,
t
.. _. , . _. dx- + dx+ , . \ / dx- + dx+
(dx+,0); (dx-,0);
EXAMPLE:
Given dx+ = 1200 m,
dx- = -600 m, and
dy = 420 m,
then the area of impact is drawn as an elipse within the four points,
(1200,0), (-600,0), (300,420), and (300,-420), on the base map,
centered on the point of disposal as the origin (0,0), as shown
in Figure 3-4.
3.4 SEDIMENT RESUSPENSION POTENTIAL FOR TYPICAL CONDITIONS
3.4.1 Purpose and Procedure
If the waste contains negatively buoyant solid particles that could
accumulate on the bottom, calculate the potential for particle resuspension
under typical conditions.
3-9
-------
Point of Disposal (0,0)
(300,-4'20)
II
(1 200.
Figure 3-4. Example of Benthic Deposition Area
3-10
-------
The procedure involves estimating total bottom velocity, as the superposi-
tion of a wave induced velocity, a mean tidal velocity, and a maximum
tidal velocity, and comparing it to an estimated threshold velocity. The
wave induced velocity is a function of the wave length.
To illustrate the method, calculations will be performed for a sand
material with diameter 0.1 mm (150 microns) only. In practice, the
calculations should be performed for each material in the waste.
3.4.2 Comments
For positively or neutrally buoyant wastes, go to Section 3.5.
For wastes containing negatively buoyant solid particles, perform the
calculation below for each group of particles identified.
If sufficient historical information exists to determine resuspension
estimates, this section may be omitted.
3.4.3 Calculate Wave Length
If the wave length is known, go to Stage 3.4.4, otherwise the iterative
procedure described below can be used. A first estimate of the wave length
is given by,
EQUATION: L =
where L = estimate of wave length in m,
o
g = acceleration due to gravity = 9.81 tn/sec , and
T = wave period in sec (Form DSP5).
This initial value for the wave length, L, can then be substituted into the
right hand side of the complete equation describing the wave length.
3-11
-------
EQUATION: L'=
*
* tanh 2 x
*
(3-5)
where L' = wave length in m,
h = mean depth in m (Form DSP5), and
x _ -x
tanh = hyperbolic tangent, e.g. tanh (x) = -.
ex + e"x
An iterative procedure is used in which a new estimated wave length, L'new,
is calculated
EQUATION: L'new =
L1 + L
(3-6)
and is substituted into Eq. 3-5 for L. The cycle described by Eqs. 3-5 and
3-6 is repeated until the values of L1 and L'new are approximately equal.
EXAMPLE:
Given g = 9.81 m/sec2,
T = 6.5 sec (Table 3-1), and
h = 30 m (Table 3-1),
then
,
a)
.
L =
9.81 * 6.5
cl- Q,
= 65.97 m
(Eq. 3-4)
,
(Eq. 3-5)
= 65.53
c) L'new - 65.53 * 65.97 . 65-?5
(Eq. 3-6)
d) L' - 9.81*6.5^tanh(,,,JO
(Eq. 3-5)
= 65.54
3-12
-------
e)
65.54 + 65.75
2
(Eq. 3-6)
f)
, - 9.81 * 6.5^ *
L. " ' " "K ^_
tanh
(Eq. 3-5)
= 65.54
g, L'new= 65'64 t 65'54 = 65.59m
(Eq. 3-6)
At this point L1 = 65.54 m and L'new = 65.59 m are reasonably close, and
the value for the wave length, L = 65.6 m is selected.
3.4.4 Maximum Wave-Induced Bottom Velocity
The maximum wave-induced bottom velocity for a wave of height, H, and
period, T, can be estimated from linear wave theory. The calculation is
performed for a mean wave condition.
EQUATION: Uw =
sinh 2n*
(3-7)
where Uw = maximum wave-induced bottom velocity in m/sec,
H = wave height in m (Form DSP5),
T = wave period in sec (Form DSP5),
h = mean depth in m (Form DSP5),
L = wave length in m (Eqs. 3-4, 3-5, and 3-6), and
ex - e"x
sinh = hyperbolic sine, e.g. sinh(x) = « .
3-13
-------
EXAMPLE:
Given
then
H = 0.5 m (Table 3-1),
T = 6.5 sec (Table 3-1),
h = 30 m (Table 3-1), and
L = 65.6 m (Final value of Eqs. 3-4, 3-5, and 3-6 example),
0.5 *
Uw =
6.5
sinh Zx *
3CJ
=0.03 m/sec.
3.4.5 Total Maximum Bottom Velocity
The total maximum bottom velocity is estimated as the summation of the
magnitudes of the mean net bottom drift, the maximum tidal velocity, and
the maximum wave-induced bottom velocity.
EQUATION: Utot = Ubm + Ut + Uw
(3-8)
where Utot =
Ubm =
Ut =
Utx =
Uty =
Uw =
total maximum bottom velocity in m/sec,
magnitude of mean net bottom drift in m/sec (Form DSP5),
magnitude of maximum of Utx and Uty,
maximum tidal velocity parallel to mean net tidal drift
direction in m/sec (Form DSP5),
maximum tidal velocity perpendicular to mean net tidal
drift direction in m/sec (Form DSPS), and
magnitude of maximum wave-induced bottom velocity (Eq.
3-7).
EXAMPLE:
Given
Ubm = 0.02 m/sec (Table 3-1),
Utx = 0.15 m/sec (Table 3-1),
Uty = 0.07 m/sec (Table 3-1),
3-14
-------
Ut = max (0.15, 0.07) = 0.15 m/sec, and
Uw = 0.03 m/sec (Eq. 3-7 example)
then Utot = 0.02 + 0.15 + 0.03 = 0.20 m/sec.
3.4.6 Potential for Resuspension
Referring to Figure D-6, or knowing or assuming typical grain diameters, a
threshold velocity, Vt, can be found using Figure D-7, above which erosion
of the portion of the disposed waste that reaches the bottom can be
expected. The threshold velocity is compared to the estimated total
maximum bottom velocity to see if erosion is expected.
EQUATION: Utot > Vt, site will tend to be dispersive (3-9a)
or Utot < Vt, site will tend to retain waste (3-9b)
where Utot = total maximum bottom velocity in m/sec (Eq. 3-8), and
Vt = threshold velocity in m/sec (Figure D-7).
EXAMPLE:
Given Utot =0.20 m/sec (Eq. 3-8 example),
then a) from Figure D-7, using a typical sand diameter of 100 microns
(0.1 mm),
Vt ^ 22 cm/sec =0.22 m/sec
b) from Eq. 3-9,
Utot = 0.20 < Vt = 0.22
therefore site will tend to retain waste.
3-15
-------
3.5 RESUSPENSION PROBABILITY UNDER EPISODIC (STORM) CONDITIONS
3.5.1 Purpose and Procedure
If the waste contains negatively buoyant solid particles that could
accumulate on the bottom, calculate the potential for particle resuspension
under episodic (storm) conditions.
The procedure is a tabular one in which the wave frequencies near the
proposed site are analyzed, and the cumulative probability of storm
occurrences that will cause resuspension estimated.
To illustrate the method, calculations will be performed for a sand
material with diameter 0.1 mm (100 microns) only. In practice, the
calculations should be performed for each material in the waste.
3.5.2 Wave Frequency Tables
Obtain a wave frequency table, of percent occurrence of wave height versus
wave period, for the site area, or as close as possible. These are
available for most continental U.S. coastal areas from the U.S. Naval
Weather Service Command. Examples are included in Tables C-3. In the
following examples, frequency values denoted by "*" are < 0.05, and will be
ignored.
EXAMPLE:
For the purpose of calculations in this section, we have arbitrarily
selected an actual frequency table to use for our example (see Table 3-2).
3.5.3 Wave Induced Sediment Suspension Figure
Referring to Figure D-8 for sand, D-9 for silt, or D-10 for clay (developed
by ASA (1983) from the work of Madson and Grant (1976), the line
corresponding to minimum depth at the site (Form DSPS) can be identified.
The line for each material can be either drawn directly on the wave
3-16
-------
TABLE 3-2 EXAMPLE WAVE FREQUENCY TABLE
Period
(sec)
<6
6-7
8-9
10-11
12-13
>13
INDET
TOTAL
PCT
<1
5.3
.1
*
*
.0
.0
4.0
1923
9.5
1-2
23.4
1.4
.4
.1
*
.1
.7
5291
76.0
3-4
23.3
5.6
.9
.3
.1
.1
.5
6241
30.7
5-6
8.3
7.4
1.5
.3
.2
.1
.2
3636
17.9
7
2.0
3.9
1.7
.5
.1
.1
.1
1726
8.5
8-9
.6
1.6
1.3
.3
.1
.1
.1
813
4.0
10-11
.2
.5
.6
.3
.1
*
*
373
1.8
12
*
.2
.3
.2
.1
*
*
165
.8
13-16
*
.1
.2
.2
.1
.1
*
130
.6
17-19
*
*
*
*
*
*
.0
20
.1
20-22
.0
*
*
*
*
*
.0
17
.1
23-25
.0
*
*
.0
.0
.0
*
4
*
26-32
0
*
*
*
*
.0
.0
7
*
33-40
.0
.0
.0
*
.0
.0
.0
1
*
41-48
.0
.0
.0
.0
.0
.0
.0
0
.0
49-60
.0
.0
.0
.0
.0
.0
.0
0
.0
61-70
.0
.0
.0
.0
.0
.0
.0
0
.0
71-86
.0
.0
.0
.0
.0
.0
.0
0
.0
87+
.0
.0
.0
.0
.0
.0
.0
0
.0
Total
12873
4234
1391
473
149
103
1144
20347
100.0
Mean
Hgt
2
3
6
7
7
7
1
3
CO
I
NOTE: Wave heights are in feet.
-------
frequency table for the site (discussed in Section 3.5.2) or else can be
directly overlaid, if the scales are similar. The line drawn on the wave
frequency table represents wave height and period combinations which may
induce resuspension. All combinations below and to the right of the line
will result in bottom velocities exceeding the threshold velocity.
EXAMPLE:
Given that the minimum depth at the site = 25 m (Table 3-1), the wave
frequency table (Table 3-2), and Figure D-8 for sand, the line representing
25 m can be drawn on the wave frequency table as shown in Table 3-3.
3.5.4 Estimate Probability of Resuspension
For each material considered, a probability of resuspension can be
calculated by summing all the percentage occurrences below and to the right
of the resuspension line (discussed in Section 3.5.3, and Figures D-8, D-9,
and D-10) on the wave frequency table (discussed in Section 3.5.2, and
Table C-3).
It should be noted that values in the bottom three rows of Table C-3
(INDET, TOTAL, and PCT) should m>t be included in the summation.
EQUATION: S = lp(i) (3-10)
where S = probability of resuspension for material considered, and
p(i) = percentage occurrence of a particular wave height
combination below and to the right of the resuspension
line drawn on the wave frequency table (Table C-3).
3-18
-------
TABLE 3-3 EXAMPLE WAVE FREQUENCY TABLE
Period
(sec)
<6
6-7
8-9
10-11
12-13
>13
INDET
TOTAL
PCT
<1
5.3
.1
*
*
.0
.0
4.0
1923
9.5
1-2
23.4
1.4
.4
.1
*
.1
.7
5291
76.0
3-4
23.3
5.6
.9
.3
.1
.1
.5
6241
30.7
5-6
8.3
7.4
1.5
.3
.2
.1
.2
3636
17.9
7
2.0
3.9
1.7
.5
.1
.1
.1
1726
8.5
8-9
.6
1.6
1.3
.3
.1
.1
.1
813
4.0
10-11
.2
.5
.6
.3
.1
*
*
373
1.8
12
*
.2
.3
.2
.1
*
*
165
.8
13-16
*
.1
.2
.2
.1
.1
*
130
.6
17-19
*>
*
*
*
*
*
.0
20
.1
''jniiu
20-22
.0
*
*
*
*
*
.0
17
.1
23-25
.0
*
*
.0
.0
.0
*
4
*
26-32
.0
*
*
*
*
.0
.0
7
*
33-40
.0
.0
.0
*
.0
.0
.0
1
*
41-48
.0
.0
.0
.0
.0
.0
.0
0
.0
49-60
.0
.0
.0
.0
.0
.0
.0
0
.0
61-70
.0
.0
.0
.0
.0
.0
.0
0
.0
71-86
.0
.0
.0
.0
.0
.0
.0
0
.0
87+
.0
.0
.0
.0
.0
.0
.0
0
.0
Total
12873
4234
1391
473
149
103
1144
20347
100.0
Mean
Hgt
2
3
6
7
7
7
1
3
-------
EXAMPLE:
Given a wave frequency table (Table 3-2), the resuspension line for
sand (Figure D-8) and the overlay of the two (Table 3-3),
then S(sand) = 2p(i - sand line in Table 3-3) = 7.8 percent,
3.5.5 Threshold Velocity Correction
The above technique (Sections 3.5.2-3.5.4) does not account for the effects
of mean and tidal velocities in estimating resuspension possibilities. The
above estimate is improved by estimating a new threshold velocity.
EQUATION: Vtnew = Vt - Ubm - Ut
(3-11)
where Vtnew =
Vt =
Ubm =
Ut =
Utx =
Uty =
new threshold velocity in m/sec,
magnitude of old threshold velocity in m/sec (Section
3.4.6),
magnitude of mean net bottom drift in m/sec (Form DSP5),
magnitude of maximum of Utx and Uty,
maximum tidal velocity parallel to mean net surface
drift direction in m/sec (Form DSP5), and
maximum tidal velocity perpendicular to mean net surface
drift direction in m/sec (Form DSP5).
EXAMPLE:
Given
Vt = 0.22 m/sec (Section 3.4.6 example),
Ubm = 0.02 m/sec (Table 3-1),
Utx = 0.15 m/sec (Table 3-1),
Uty = 0.07 m/sec (Table 3-1), and
Ut = max (0.15, 0.07) = 0.15 m/sec,
then Vtnew = 0.22 - 0.02 - 0.15 = 0.05 m/sec.
3-20
-------
3.5.6 Probability of Resuspenslon Correction
Using the new estimate for the resuspension threshold velocity from Eq.
3-11, the probability of resuspension, estimated in Eq. 3-10, can be
corrected to account for other than wave-induced ocean currents alone.
This is done by calculating wave-induced bottom velocities for all wave
height and period combinations not considered in the calculation of Eq.
3-10 (i.e. those combinations above and to the left of the depth line
overlaying the wave frequency table), and comparing each value to the new
threshold velocity of Eq. 3-11. If the wave-induced bottom velocity
exceeds the new threshold velocity, its associated percent frequency of
occurrence, p(i), should be added to the probability of resuspension, S,
estimated in Eq. 3-10.
This is a three-step process (see Figure 3-5), with each step being
repeated for each wave height and period combination not previously
considered. This entire procedure is repeated for each material (e.g.
clay, sand, silt, etc.).
Step 1 - Select a wave height and period combination not previously used,
and calculate the wave-induced bottom current using the
calculations of Sections 3.4.3 and 3.4.4 (Note that these
calculations are performed in metric units and the values of Table
3-3 are in English units).
EXAMPLE:
Given that we are calculating the probability of resuspension for 0.1 mm
diameter sand, we must also consider those wave height (H) and period (T)
combinations which were not used for the example calculation of Eq. 3-10.
In Table 3-3, these values lie above and to the left of the depth line for
3-21
-------
sand, and are listed in the first two columns of Table 3-4, with these
tabulated values representing mid-values of the range of values in Table
3-3. Consider for example
H = 7 ft (2.1 m) and T = 6 to 7 sec, represented by 6.5 sec (underlined in
Table 3-4),
then performing the calculations of Section 3.4.3 (Column 3 of Table 3-4)
and 3.4.4, the wave-induced bottom velocity, or orbital velocity (Column 4
of Table 3-4), is
Uw = 0.11 m/sec.
Step 2 - Compare with new threshold velocity.
EXAMPLE:
Given Uw = 0.11 m/sec, and
Vtnew = 0.05 m/sec (Eq. 3-11 example),
then Uw > Vtnew
and the wave height and period combination (H = 7 ft, T = 6 to 7 sec)
should be included in the probability of resuspension. (Note: If Uw <
Vtnew, then step 3 is omitted and the procedure repeated for a new wave
height/period combination.
Step 3 - Compute new probability of suspension.
EXAMPLE:
Given that (1) the wave height and period combination (H = 7 ft, and
T = 6 to 7 sec, columns 1 and 2 in Table 3-4) should
be included in the probability of resuspension,
3-22
-------
STEP 1: Select wave
height/period combination
not used in Section 3.5.4
calculate wave-induced
bottom velocity, Uw
NO
STEP 3: Add associated
% frequency of
occurrence P(i) to the
previous total, S
S(material) = S(material)
NO
Have all
height/period
combinations
now been
sponsiderecL
Figure 3-5. Flowchart for the Estimation of Resuspension
Correction in Section 3.5.6. for each Material
3-23
-------
TABLE 3-4
CALCULATION EXAMPLE OF RESUSPENDING WAVE ORBITAL VELOCITY FOR SAND
1
Height
(ft)
0.5
0.5
0.5
0.5
0.5
0.5
1.5
1.5
1.5
1.5
1.5
1.5
3.5
3.5
3.5
3.5
3.5
3.5
5.5
5.5
5.5
+ 5.5
+ 5.5
+ 5.5
7.0
7.0
+ 7.0
+ 7.0
+ 7.0
+ 7.0
2
Period
(sec)
3.0
6.5
8.5
10.5
12.5
15.0
3.0
6.5
8.5
10.5
12.5
15.0
3.0
6.5
8.5
10.5
12.5
15.0
3.0
6.5
8.5
10.5
12.5
15.0
3.0
6.5
8.5
10.5
12.5
15.0
3
Length
(m)
14
65
106
106
187
234
14
66
106
147
187
234
14
66
106
147
187
234
14
66
106
147
187
234
14
66
106
147
187
234
4
Speed
(m/sec)
0.00
0.00
0.00
0.01
0.03
0.03
0.00
0.02
0.05
0.08
0.09
0.10
0.00
0.05
0.13
0.19
0.22
0.24
0.00
0.09
0.21
0.30
0.35
0.39
0.00
0.11
0.27
0.38
0.45
0.49
5
Percent
Occurence
5.3
0.1
*
*
0.0
0.0
23.4
1.4
0.4
0.1
*
0.1
23.3
5.6
0.9
0.3
0.1
0.1
8.3
7.4
1.5
0.3
0.2
0.1
2.0
3.9
1.7
0.5
0.1
0.1
1
Height
(ft)
8.5
8.5
+ 8.5
+ 8.5
+ 8.5
+ 8.5
10.5
+ 10.5
+ 10.5
+ 10.5
+ 10.5
+ 10.5
12.0
+ 12.0
+ 12.0
+ 12.0
+ 12.0
+ 12.0
14.5
+ 14.5
+ 14.5
+ 14.5
+ 14.5
+ 14.5
2
Period
(sec)
3.0
6.5
8.5
10.5
12.5
15.0
3.0
6.5
8.5
10.5
12.5
15.0
3.0
6.5
8.5
10.5
12.5
15.0
3.0
6.5
8.5
10.5
12.5
15.0
3
Length
(m)
14
66
106
147
187
234
14
66
106
147
187
234
14
66
106
147
187
234
14
66
106
147
187
234
4
Speed
(m/sec)
0.00
0.14
0.33
0.46
0.54
0.60
0.00
0.17
0.41
0.57
0.67
0.74
0.00
0.19
0.47
0.66
0.77
0.85
0.00
0.24
0.57
0.79
0.93
1.03
5
Percent
Occurrence
0.6
1.6
1.3
0.3
0.1
0.1
0.2
0.5
0.6
0.3
0.1
*
*
0.2
0.3
0.2
0.1
*
*
0.1
0.2
0.2
0.1
0.1
NOTE: 1 and 2 are wave height (H) and period (T) combinations (combinations used in the
calculation of Eq. 3-10 are denoted by "+" and are not used in Section 3.5.6).
3 is wave length of above wave height and period combination
4 is wave-induced bottom velocity or orbital velocity.
5 is percent occurrence for wave height (H) and period (T) combination (* denotes a
value < 0.05 and is ignored for calculation purposes).
3-24
-------
(2) the associated percentage frequency of occurrence p(i)
(column 5 of Table 3-4), is
p(H = 7 ft, T = 6 to 7 sec) = 3.9 percent (This
value is obtained from Table 3-3 by moving along
the row 6-7 sec until arriving at column 7 feet
and is shown in Table 3-4, column 5) and
(3) the previous probability of resuspension for sand
S(sand) = 7.8 percent
then S(sand) = 7.8 + 3.9 = 11.7 percent
NOTE: If this example is completed for all wave height and period
combinations not considered in Section 3.5.4, then,
S(sand) = 23.8 percent.
3.6 ESTIMATE ANNUAL SEDIMENT TRANSPORT RATE
3.6.1 Purpose and Procedure
The annual sediment transport rate for each material considered (e.g.
medium sand, coarse sand, etc.) is estimated to determine whether or not
the site will tend to accumulate material.
The procedure is to perform a mass balance with the annual loading rate and
the transport rate.
To illustrate the method, calculations will be performed for a sand
material with diameter 0.1 mm (100 microns) only. In practice, the
calculations should be performed for each material in the waste.
3-25
-------
3.6.2 Estimate Resuspending Wave Orbital Velocity
For each percent occurrence value, p(i), of a wave height and period
combination that will probably cause resuspension under episodic (storm)
events, a resuspending wave orbital velocity can be calculated by summing
all the percentage values multiplied by their respective wave-induced
bottom velocities (calculated using Section 3.4.3 and 3.4.4) and dividing
by the probability of occurrence, for each material considered.
EQUATION: Uw =
p(i) * Uw(i)
(3-12)
where Uw = resuspending wave orbital velocity in m/sec,
p(i) = percent occurrence of each wave height (H), and period
(T) combination that can cause resuspension,
Uw(i) = wave-induced bottom velocity for each wave height (H) and
period (T) combination that can cause resuspension (using
calculations of Sections 3.4.3 and 3.4.4), and
S = probability of occurrence (Section 3.5.6).
EXAMPLE:
Given (1) the wave height and period combinations that cause
resuspension under episodic (storm) conditions from Section
3.5,
(2) the corresponding percent occurrence values, p(i), from
Table 3-3 or column 5 of Table 3-4,
(3) the corresponding wave-induced bottom velocities, Uw(i)
calculated using Sections 3.4.3 and 3.4.4 (column 4 of
Table 3-4),
3-26
-------
(4) the sum of multiples of percent occurrence values, P(i),
and corresponding wave-induced bottom velocities, Uw(i)
(found by multiplying columns 4 and 5 in Table 3-4) for
those wave height/period combinations that cause
resuspension:
Lp(i) Uw(8) = 4.94
i
(5) S(sand) = 23.8 percent,
4 Q4
then Uw(sand) = - = 0.21 m/sec,
3.6.3 Annual Unit Sediment Transport Rate
Using prepared curves for clay (Figure D-ll), silt (Figure D-12), very fine
sand (Figure D-13), and fine sand (Figure D-14), the annual unit sediment
transport rate per meter of site width, Qs, for each material considered,
can be read from the appropriate graph.
EXAMPLE: (note: values from previous examples do not cover sediment
transport, thus for calculations in Sections 3.6.3 - 3.6.6, new
values that would cause sediment transport are used)
Given (1) Fine sand (Figure 3-6),
(2) Mean net bottom drift, Ubm = 0.3 m/sec = 30 cm/sec (a new
value for this example only), and
(3) Wave-induced bottom velocity (Eq. 3-12 example) Uw = 0.21
m/sec = 21.0 cm/sec,
then from Figure 3-6,
3
annual unit sediment transport rate, Qs = 4000 m /m/yr.
3-27
-------
10'
10C
10"
CO
10'
101
10'
1 Uw=20 cm/sec
FINE SAND (0=0.187 mm)
I _ I _ 1 _ I
1 1
20 30 40 50 60 70 80 90 100
Ubm(cm/sec)
Figure 3-6.
Volumetric Sediment Transport Rate Versus Mean Flow for
Various Wave Induced Bottom Velocities (Source: Applied
Science Assoc., Inc.)
3-28
-------
3.6.4 Annual Sediment Transport Rate
The annual sediment transport rate is the annual unit sediment transport
rate multiplied by the width of the benthic receiving area calculated in
Section 3.3.4,
EQUATION:
where
Qt = B * Qs
(3-13)
o
Qt = annual sediment transport rate in m/yr,
B = width of the benthic receiving area in m (= 2 * dy),
dy = maximum distance travelled, in m, in lateral direction on
each side of axis of mean net surface drift (Eq. 3-2c),
and
Qs '= annual unit sediment transport rate in m /m/yr (Section
3.6.3).
EXAMPLE:
Given dy = 420 m (Eq. 3-2c example)
B = 2 * dy = 840 m, and
Qs = 4000 m3/m/yr (Section 3.6.3 example),
then
Qt = 840 * 4000 = 3.4xl06 m3/yr.
3.6.5 Potential for Mounding
If the annual sediment transport rate exceeds the annual disposal rate, no
long-term mounding is expected. If the annual disposal rate exceeds the
annual sediment transport rate, long-term mounding can be expected, and the
calculation should proceed to Section 3.6.6.
EQUATION:
Qt > Qa
Qt < Qa
implies no mounding
implies mounding
(3-14a)
(3-14b)
where Qt = annual sediment transport rate (Eq. 3-13), and
Qa = annual disposal rate (Form DSP2).
3-29
-------
EXAMPLE:
Given Qt = 3.4xl06 m3/yr (Eq. 3-13 example), and
Qa = 5.0xl06 m3/yr (Table 2-1),
then Qt < Qa
and long-term mounding is expected.
3.6.6 Recalculation for Long-Term Mounding
If long-term mounding is anticipated, from Section 3.6.5, the site depth
will decrease with time, and the annual sediment transport rate will
increase, until an equilibrium condition is reached. The equilibrium site
depth can be estimated by selecting a shallower site mean depth, h, and
repeating all the calculations in Stage 3 until the annual sediment trans-
port rate (Eq. 3-13) equals the annual disposal rate (Form DSP2) in Section
3.6.5.
3.7 CALCULATE AND MAP TYPICAL LONG-TERM TRANSPORT CONTOURS
3.7.1 Purpose and Procedure
Long-term transport contours, for the positively or neutrally buoyant
portion of the waste, are calculated and mapped to illustrate the far field
dilution associated with unit concentration waste loadings under conditions
of ambient advection and dispersion.
The procedure is to use closed-form, two-dimensional, horizontal solutions
of the steady-state mass transport equation, for both point and distributed
sources. A complete discussion of these equations and background can be
found in Fischer et al. (1979).
3-30
-------
3.7.2 Select Appropriate Contour Mapping Methodology
If the mean net surface drift is less than the mean magnitude of the tidal
current parallel to it (x-direction) over 1/2 tidal cycle then overlapping
of various disposal plumes might be expected and a continuous release plume
model should be used. Otherwise a discrete point source or distributed
source model should be used.
EQUATION: If Um < Utx * */4 then follow Sections 3.7.3-3.7.5. (3-15a)
If Um > Utx * */4 then follow Sections 3.7.3, 3.7.4, 3.7.6,
and 3.7.7 (3-15b)
where Um = mean net surface drift (Form DSP5), and
Utx = maximum tidal velocity parallel to mean net surface drift
direction, in m/sec (Form DSPS).
EXAMPLE:
Given Um = 0.05 m/sec (Table 3-1), and
Utx = 0.15 m/sec (Table 3-1),
then 0.05 < 0.15 * */4 = 0.12
and Sections 3.7.3-3.7.5 should be followed.
3.7.3 Estimate Tidal Excursions
To estimate dispersion coefficients in the x- and y-directions, the tidal
excursion in these directions is needed.
EQUATION: Lx = Utx * I * - (3-16a)
Ly = Uty * *- (3-16b)
3-31
-------
where Lx = tidal excursion parallel to mean net surface drift
direction in m,
Ly = tidal excursion perpendicular to mean net surface drift
direction in m,
Utx = maximum tidal velocity, parallel to mean net surface
drift direction in m/sec (Form DSPS),
Uty = maximum tidal velocity perpendicular to mean net surface
drift direction in m/sec (Form DSPS), and
To = period in sec.
EXAMPLE:
Given Utx = 0.15 m/sec (Table 3-1),
Uty = 0.07 m/sec (Table 3-1), and
To = 12.42 hr = 44712 sec (Table 3-1),
tnen
i v - n
LX - U.
m
m
AA.TIO n
Ly = 0.07 * -^4^- * x = 1229 m
3.7.4 Estimate Dispersion Coefficient
Using the tidal excursion lengths from Section 3.7.3, dispersion coeffici-
ents can be estimated in the x- and y-directions using a conservative
simplification of the "four-thirds rule" (Okubo, 1971).
EQUATION:
Dx = 0.0018 * Lx
Dy = 0.0018 * Ly
(3-17a)
(3-17b)
where Dx,Dy = dispersion coefficients parallel and perpendicular to
o
the mean net surface drift direction in m/sec,
respectively, and
Lx,Ly = tidal excursions parallel and perpedicular to the mean
net surface drift direction in m, respectively (Eq.
3-16).
3-32
-------
EXAMPLE:
Given Lx = 2634 m (Eq. 3-16a example), and
Ly = 1229 m (Eq. 3-16b example),
then
Dx = 0.0018 * 2634 = 4.7
Dy = 0.0018 * 1229 = 2.2 m2/sec
3.7.5 Two-Dimensional Continuous Point Source Plume Model
If the mean net surface drift, Urn, is less than the mean tidal velocity,
Utx *Jt/4, the site is assumed to behave as a continuous point source under
successive disposals. In this case, use a two-dimensional continuous point
source plume model with unit loading (q = 1) to develop characteristic
concentration contours.
EQUATION: C(x,y) =
q
d *
exp
( 4 n * Dy *
[ & \
[\ )
Urn * x
Urn
4 * Dy
,1/2
* X
(3-18)
where
C(x,y) = concentration at coordinate x,y (with x=0, y=0
as point of disposal),
q = mass input rate/sec (=1 for unit contours),
d = calculation depth in m (d = hp if above the
pycnocline, d = h - hp if below the pycnocline,
or d = h if entire water column depending on
application),
hp = pycnocline depth (Form DSPS),
h = mean depth (Form DSP5),
Dy = dispersion coefficient perpendicular to mean net
surface drift direction in m2/sec (Eq. 3-17b),
and
Urn = mean net surface drift (Form DSPS).
3-33
-------
EXAMPLE:
Given calculation above pycnocline,
x = 2 km = 2000 m,
y = 1 km = 1000 m,
q = 1 g/sec (for unit contours),
d = hp = 20 m (Table 3-1),
2
Dy = 2.2 m /sec (Eq. 3-17b example), and
Urn = 0.05 m/sec (Table 3-1),
then C(2000, 1000) =
20 * (4** 2.2 * 0.05 * 2000)1/2
* exp
-1000
2U 0.05
4 * 2.2 * 2000
= 5.55xlO"5 g/m3 or ppm
The above example calculates the concentrations, for a unit loading, at
a single point (x = 2000 m, y = 1000 m). By applying Eq. 3-18 for
several x, y locations, concentration contours can be drawn from the
center of the site, which is the origin (x = 0, y = 0).
An example of concentration contours for a unit loading is given in
Figure 3-7. For this particular example, the contours were developed
by calculating and plotting the concentrations for several sets of x, y
coordinates on a rectangular grid. Then, the concentrations contours
were formed by interplotating between the calculated values and
sketching lines of equal concentration.
3.7.6 Two-Dimensional Discrete Point Source Model
If the mean net surface drift, Urn, is greater than the mean tidal velocity,
Utx * */4, the site is assumed to behave as a series of discrete loadings
which never merge. In this model, the source is also assumed to be small
3-34
-------
STATEJJNE
STATE LINE
SPORT
FISHING
NEW CITY
~ ~ -~ Z SHIPPING LANE ~ ~ ~
DISPOSAL
SITE
0.001
0.00025
INDUSTRIAL
DISPOSAL
0.00012
0.0001
0 25
I I I I I I
KILOMETERS
Figure 3-7. Concentration (g/m3) Contours for Unit Load at Point of
Disposal, Assuming Continuous Point Source
3-35
-------
enough to be considered a point source when viewed from the far field. The
following two-dimensional equation discribes the horizontal movement and
dispersion of the plume through time.
EQUATION: C(x,y,t) =
4* * d * (Dx * Dy)1/2 * t
exp
(x - Um*t)2 y2
4 * Dx * t " 4 * Dy * t
(3-19)
where C(x,y,t) = concentration at coordinates x,y at time t (with x=0,
y=0, t=0 as the point and time of disposal),
Q = mass unit (= 1 for unit contours),
d = calculation depth in m (d = hp if above pycnocline,
d = h - hp if below pycnocline, and d = h if entire
water column, depending on application),
hp = pycnocline depth (Form DSPS),
h = mean depth (Form DSP5),
Dx,Dy = dispersion coefficients parallel and perpendicular to
mean net surface drift direction, respectively, in
m2/sec (Eq. 3-17), and
Dm = mean net surface drift in m/sec (Form DSP5).
EXAMPLE:
Given
calculation above pycnocline,
x = 920 m,
y = 300 m,
t = 1 hr = 3600 sec,
Q = 1 g (for unit contours),
d = hp = 20 m (Table 3-1),
Dx = 4.7 m2/sec (Eq. 3-17a example),
3-36
-------
Dy = 2.2 m2/sec (Eq. 3-17b example), and
Urn = 0.2 m/sec (chosen here to imply discrete sources from
Eq. 3-15b),
then 0(920,300,3600) =
4* * 20 * (4.7 * 2.2) * 3600
* exp
-(920 - 0.2*3600)2 3002
4.7 * 3600 4 * 2.2 * 3600
-8 3
= 1.11x10" g/m or ppm
The above example calculates the concentrations for a unit load, at a
single point in space (x = 920 m, y = 300 m) and time (t = 3600 sec). By
applying Eq. 3-19 for several x, y locations at different t times,
concentration contours can be drawn from the point of disposal, which is
the origin (x = 0, y = 0).
An example of concentration contours for a unit load at times of 2, 10, and
20 hours is given in Figure 3-8 with the positive x - direction parallel to
the mean net surface drift, Urn, the y-direction perpendicular and the
origin at the point of disposal. For this particular example, the contours
were developed by calculating and plotting on a rectangular grid the
concentrations for several sets of x, y coordinates at the three different
times. Then, the concentration contours were formed by interpolating
between the calculated values and sketching lines of equal concentration.
For this example, the concentrations, the x, y coordinates, and the various
times were chosen to produce the three separate sets of contours as shown
in Figure 3-8.
3.7.7 Two-Dimensional Discrete Distributed Source Model
If the mean net surface drift, Urn, is greater than the mean tidal velocity,
Utx**/4, the site is assumed to behave as a series of discrete loadings
which never merge. In this model, the source is assumed to have finite
3-37
-------
Figure 3-8. Concentration (g/m ) Contours for Unit Load at Point
of Disposal Assuming Discrete Point Source
3-38
-------
dimensions (distributed) produced by a moving barge. The following two-
dimensional equation describes the horizontal movement and dispersion
through time of the liquid phase of the waste, and is best applied within a
short distance and time of the initial disposal.
EQUATION:
C(x,y,t) = *
4
erf
Tj- - x + Um*t
(4 * Dx * t)1/2.
erf
f + x - Um*t
(4 * Ox * t)1/2J
erf
(4 * Dy * t)1/2.
+ erf
!*
(4 * Dy * t)1/2
(3-20)
where C(x,y,t) = concentration at coordinates x,y at time t (with x=0,
y=0, t=0 as the point and time of disposal),
Co = initial contaminant concentration (=1 for unit con-
tours),
erf = error function (Table C-2),
b = v * t' initial plume dimension along the x-axis in m,
v = disposal vessel speed in m/sec (Form DSP2),
t'= individual disposal duration in sec (Form DSP2),
a = 2 * w initial plume dimension along the y-axis in m
w = disposal vessel width in m (Form DSP2),
Urn = mean net surface drift in m/sec (Form DSP5), and
Dx.Dy = dispersion coefficients parallel and perpendicular to
mean net surface drift direction, respectively, in
m2/sec (Eq. 3-17).
EXAMPLE:
Gi ven
x = 460 m,
y = 100 m,
t = 0.25 hr = 900 sec,
3-39
-------
then
Co = 1 g/nr* or ppm (for unit contours),
v = 1.0 m/sec (Table 2-1),
t'= 200 sec (Table 2-1),
w = 20 m (Table 2-1),
b = v * t = 1.0 * 200 = 200 m
a = 2w = 2 * 20 = 40 m
Urn = 0.2 m/sec (chosen here to imply discrete source from
Eq. 3-15b),
Dx = 4.7 nf^/sec (Eq. 3-17a example), and
Dy = 2.2 m2/sec (Eq. 3-17b example),
0(280,100,900) =[ - 1*
4
200
- 280 + 0.2*900
erf
(4 * 4.7 * 900)1/2
+ erf
1200
~r
+ 280 - 0.2*900
(4 * 4.7 * 900)1/2
erfl
40
T
- 100
1(4 * 2.2 * 900
1+ erfl
100
(4 * 2.2 * 900) 1/2
= 0.037 g/m3 or ppm
The above example calculates the concentration for an initial unit con-
taminant concentration at a single point in space (x = 280 m, y = 100 m)
and time (t = 900 sec). By applying Eq. 3-20 for several x, y locations,
at different t times, concentrations contours can be drawn from the point
of disposal, which is the origin (x = 0, y = 0).
An example of concentration contours, for a unit concentration, at times of
0.5 and 1.5 hours is given in Figure 3-9 with the positive x - direction
parallel to the mean net surface drift, Urn, the y - direction perpendicular
3-40
-------
and the origin at the point of disposal. For this particular example, the
contours were developed by calculating and plotting on a rectangular grid
the concentrations for several sets of x, y coordinates at the two
different times. Then, the concentration contours were formed by
interpolating between the calculated values and sketching lines of equal
concentration. For this example, the concentrations, the x, y coordinates,
and the various times were chosen to produce the two separate sets of
contours as shown in Figure 3-9.
3-41
-------
KILOMETERS
0 1
30M
DISPOSAL SITE
BOUNDARY
Point of Disposal
t = 0.5 hrs
t= 1.5 hrs
Figure 3-9. Concentration (g/m ) Contours for Unit Load
at Point of Disposal Assuming Discrete Point Source
3-42
-------
STAGE 4. INITIAL MIXING AND SOURCE STRENGTH CALCULATIONS
4.1 INTRODUCTION
The purpose of this stage (see flow chart in figure 4-1) is to estimate
initial dilutions of the liquid phase in the wake of the barge, fractions
of the waste throughout the water column, and waste concentrations in the
bottom sediments. The liquid phase of the waste is assumed to be well
mixed in the zone of initial mixing generated by barge-induced turbulence,
and subsequently throughout the water column under conditions of ambient
turbulence. In order to make these assumptions, it is assumed that the
disposal operations occur while the barge is moving. Further, the estimate
of constituent concentrations in this stage are independent of background
concentrations and can be superimposed (in Stage 5).
4.2 FORMS
To perform the analyses of Stage 4, information from Forms DSP2, DSPS, and
DSPS are used. Forms DSP2 and DSPS were filled out in Stage 2, and Form
DSPS was filled out in Stage 3.
4.3 INITIAL DILUTION OF LIQUID PHASE
4.3.1 Purpose and Procedure
The initial dilution of the liquid phase of the disposed waste is estimated
from barge-induced turbulent mixing. It represents an immediate dilution
rather than the 4-hour approximation used in U.S. EPA/COE (1977). The
4-hour dilution (CFR #40.22721) is calculated in Stage 5 for constituents
exceeding EPA Acute Water Quality Criteria.
The procedure is to use an empirical formula which describes the initial
mixing volume generated by a typical barge. The equivalent depth of this
mixing volume is estimated from site characteristics. The liquid and sus-
pended particulate phases are assumed to be completely mixed into the
mixing volume.
4-1
-------
SECTION
4.3
4.4
4.5
Initial dilution
of liquid phase
I
Source strengths
and initial conditions
I
Vertical distribution
of constituent
concentrations
Figure 4-1. Stage 4, Initial Mixing and Source Strength Overview
4-2
-------
4.3.2 Equivalent Depth
The equivalent depth, d, is the minimum of the mean depth, h (Form DSPS),
the pycnocline depth, hp (Form DSPS), or a default value of 20 m.
EXAMPLE:
Given h = 30 m (Table 3-1), and
hp = 20 m (Table 3-1),
then d = minimum (30, 20, 20) = 20 m
4.3.3 Initial Liquid Phase Mixing Zone Volume
The initial mixing zone volume produced by a moving barge is the affected
cross-sectional area (assumed to be twice the barge width multiplied by the
equivalent depth) multiplied by the length of the disposal track, and is
empirically defined by
EQUATION: Vm = d * (2w) * v * t
(4-1)
where Vm = initial mixing zone volume in m ,
d = equivalent depth in m (Section 4.3.2),
w = disposal vessel width in m (Form DSP2),
v = disposal vessel speed in m/sec (Form DSP2), and
t = individual disposal duration in sec (Form DSP2).
EXAMPLE:
Given
d = 20 m (Section 4.3.2 example),
w = 20 m (Table 2-1),
v = 1.0 m/sec (Table 2-1), and
t = 200 sec (Table 2-1),
then Vm = 20 * (2*20) * 1.0 * 200 = 160,000 m3,
4-3
-------
4.3.4 Calculate Liquid Fraction
If the liquid fraction of the waste is unknown (Form DSP2), but specific
gravities are known, then the liquid fraction of the total waste is calcu-
lated from a ratio of specific gravities.
EQUATION- Fl = S?jbu1k) " sg(particle)
tquAiiUN. M sg(liquid) - sg(particle)
(4-2)
where Fl = liquid fraction,
bulk specific gravity (Form DSP2)
particle phase specific gravity (Form DSP2),
and
sg(liquid) = liquid phase specific gravity (Form DSP2).
Fl
sg(bulk)
sg(particle)
EXAMPLE:
Given sg(bulk) = 1.7 (Table 2-1),
sg(particle) = 2.65 (Table 2-1),
sg(liquid) = 1.0 (Table 2-1),
then Fl = i'Z " HE = 0.58
l.U -
-------
EXAMPLE:
Given Fl =0.58 (Eq. 4-2 example),
then Fs = 1 - 0.58 = 0.42
4.3.6 Immediate Dilution of the Liquid Phase
The initial dilution of the liquid phase of the total waste is the
volumetric ratio of the volume of the liquid phase to the initial mixing
zone volume generated by the barge-induced turbulence.
EQUATION:
Dl =
Fl * Vb
Vm
(4-4)
where Dl = initial dilution of liquid phase,
Fl = liquid fraction of the waste (Form DSP2 or Eq. 4-2),
Vb = volume of barge in m3 (Form DSP2), and
o
Vm = initial mixing zone volume in m (Eq. 4-1).
EXAMPLE:
Given Fl = 0.58 (Table 2-1 or Eq. 4-2 example),
Vb = 4000 m3 (Table 2-1), and
Vm = 160,000 m3 (Eq. 4-1 example),
then
°-58 * 40°°
160,000
= 0 015
U-Ui;s
4.3.7 Immediate Dilution of the Suspended Particulate Phase
The initial dilution of the suspended particulate phase of the total waste
is the volumetric ratio of the suspended particulate phase to the initial
mixing zone volume generated by the barge induced turbulence. Ff * Ffs is
the product of the fraction of total solids which is composed of fine
particles of diameters less than 0.1 mm multiplied by the estimated
fraction of these fines which remain in the water column.
4-5
-------
EQUATION: Ds =
Fs * Vb * Ff * Ffs
Vm
(4-5)
where Ds = Initial dilution of the suspended particulate phase,
Fs = solid fraction of the waste (Form DSP2 or Eq. 4-3),
Vb = volume of the barge in m3 (Form DSP2),
Ff = fine fraction (Form DSP2),
Ffs = fraction of fines in suspended particulate phase (Form
DSP2), and
Vm = initial mixing zone volume (Eq. 4-1).
EXAMPLE:
Given Fs = 0.42 (Table 2-1 or Eq. 4-3 example),
Vb = 4,000 m3 (Table 2-1),
Ff = 0.41 (Table 2-1),
Ffs = 0.90 (Table 2-1), and
Vm = 160,000 m3 {Eq. 4-1 example)
then nc _ 0.42 * 4,000 * 0.41 * 0.90 n nn,Q
us 160,000:u.uujy
4.4 SOURCE STRENGTHS AND INITIAL CONDITIONS
4.4.1 Purpose and Procedure
The source strengths and initial conditions are estimated throughout the
water column and bottom, for further dilution and water quality criteria
comparisons.
The following procedure assumes that the waste plume is approximately
uniformly distributed through the entire water column, and that material
not suspended in the water column goes to the bottom. As a first step,
various solid fractions are calculated using the data of Form DSP2. Then
the fraction of the waste in the upper water column above the pycnocline
and the fraction of the waste in the lower water column below the
4-6
-------
pycnocline are calculated. The whole water column fraction Is also calcu-
lated followed by the calculation of the fraction of the waste added to the
sediment compartment.
If there is no pycnocline, or it is assumed that the non-settleable waste
is distributed only through the upper water column, perform only the calcu-
lations of Section 4.4.2 (with h = hp) and go to Section 4.4.4.
4.4.2 Fraction of Waste in Upper Water Column
Assuming an approximately uniform vertical distribution of the waste plume
throughout the entire water column, the fraction of waste in the upper
water column is proportional to the pycnocline depth divided by the site
depth. If there is no pycnocline or it is assumed that the non-settleable
waste is distributed through the upper water column, assume that hp = h,
evaluate this section, and go to Section 4.4.4.
EQUATION: Fwu = -^ * [Fl + (Fs * Ff * Ffs)]
(4-6)
where Fwu = fraction of waste in upper water column,
hp = pycnocline depth in m (Form DSP5),
h = mean depth in m (Form DSPS),
Fl = liquid fraction of total waste (Form DSP2 or Eq. 4-2),
Fs = solid fraction of total waste (Form DSP2 or Eq. 4-3),
Ff = fraction of fines in solid fraction (Form DSP2), and
Ffs = fraction of fines in suspended cloud (Form DSP2).
EXAMPLE:
Given hp = 20 m (Table 3-1),
h = 30 m (Table 3-1),
Fl = 0.58 (Table 2-1 or Eq. 4-2 example),
Fs = 0.42 (Table 2-1 or Eq. 4-3 example),
Ff = 0.41 (Table 2-1), and
Ffs = 0.90 (Table 2-1),
4-7
-------
then
Fwu = - * [0.58 + (0.42 * 0.41 * 0.90)] = 0.49
4.4.3 Fraction of Waste in Lower Water Column
Assuming an approximately uniform vertical distribution of the waste plume,
the fraction of waste in the lower water column is equal to the fraction of
non-settleable waste not retained in the upper water column. If there is
no pycnocline, omit this section.
EQUATION: Fwl = (1 -
* [Fl + (Fs * Ff * Ffs)]
(4-7)
where Fwl = fraction of waste in lower water column,
hp = pycnocline depth in m (Form DSP5),
h = mean depth in m (Form DSP5),
Fl = liquid fraction of total waste (Form DSP2 or Eq. 4-2),
Fs = solid fraction of total waste (Form DSP2 or Eq. 4-3),
Ff = fraction of fines in solids fraction (Form DSP2), and
Ffs = fraction of fines in suspended cloud (Form DSP2).
EXAMPLE:
Given hp = 20 m (Table 3-1),
h = 30 m (Table 3-1),
Fl = 0.58 (Table 2-1 or Eq. 4-2 example),
Fs = 0.42 (Table 2-1 or Eq. 4-3 example),
Ff = 0.41 (Table 2-1), and
Ffs = 0.90 (Table 2-1),
then Fwl =(!-§§)* C0.58 + (0.42 * 0.41 * 0.90)] = 0.24
4-8
-------
4.4.4 Fraction of Waste in Whole Water Column
The fraction of the waste in the whole water column is the summation of
the fractions in the upper and lower water columns. If there is no pycno-
cline, or it is assumed that the non-settleable waste is distributed
through the upper water column, set Fwl = 0 for the calculation of Eq. 4-8.
EQUATION: Fwt = Fwu + Fwl
(4-8)
where Fwt = fraction of waste in whole water column,
Fwu = fraction of waste in upper water column (Eq. 4-6), and
Fwl = fraction of waste in lower water column (Eq. 4-7).
EXAMPLE:
Given Fwu = 0.49 (Eq. 4-6 example), and
Fwl = 0.24 (Eq. 4-7 example),
then Fwt = 0.49 + 0.24 = 0.73
4.4.5 Fraction of Waste That Falls to Sediment
The fraction of the waste that falls to the sediment is the remaining por-
tion of the waste that does not remain in the water column.
EQUATION: Fws = 1 - Fwt
where Fws = fraction of waste that falls to sediment, and
Fwt = fraction of waste in whole water column (Eq. 4-8).
EXAMPLE:
Given Fwt = 0.73 (Eq. 4-8 example),
then Fws = 1 - 0.73 = 0.27
(4-9)
4-9
-------
4.5 VERTICAL DISTRIBUTION OF CONSTITUENT CONCENTRATIONS
4.5.1 Purpose and Procedure
That portion of the waste not in the water column is assumed to settle
directly to the sediments and be evenly distributed over the site area.
For each contaminant constituent in the waste, the vertical distribution in
the sediment layer is calculated using a one-dimensional equation which is
analogous to the heat flow equation (Carslaw and Jaeger, 1959). The
equation assumes diffusion only (through bioturbation) into the sediment
layer with no resuspension of fluxes from the sediment layer to the water
column.
4.5.2 Contaminant Depositional Rate
The deposition of constituent i is estimated assuming that all the solid
portion of the waste goes to the sea floor. It should be noted that this
calculation is identical to that of Eq. 5-12.
EQUATION: Q(i) s Qa * sg(partM Ci (4-10)
where Q(i) = deposit!onal rate for constituent i in kg/m2/yr,
Qa = annual loading rate in m3/yr (Form DSP2),
sg(part) = particle specific gravity (Form DSP2),
Ci = concentration of constituent i in the bulk waste in mg/kg
(Form DSP3), and
A = direct impact deposition area in m2 (Eq. 3-3).
4-10
-------
EXAMPLE:
Given Qa = S.OxlO6 m3/yr (Table 2-1),
sg(part) = 2.65 (Table 2-1),
Ci = 7 mg/kg for copper (Table 2-2), and
A = 4.52xl07 m2 (Eq. 3-3 example),
then (j) _ S.OxlO6 * 2.65 * 7
4.52xl07 * 1000
= 0.00205 kg/m2/yr.
4.5.3 Vertical Contaminant Concentration Profile
The vertical contaminant distribution is given by a one-dimensional equa-
tion that assumes only diffusion into the sediment layer. Effects of
suspension and bed transport are neglected. The resulting concentration
profile gives a relative measure based on a constituent concentration of
unity within the waste.
EQUATION: C(z,t) = Q(i) *
.(4 * D * t)172
v /
where C(z,t) = concentration of contaminent in sediment in kg/m ,
z = depth down into sediment in m,
t = time in yrs,
Q(i) = contamination deposition rate for constituent in
kg/n^/yr (Eq. 4-10), and
p
D = bioturbation mixing coefficient in m /yr (default
5 2
value in D = 10 m /yr or use Table 4-1 for typical
values).
erfc = 1-erf (erf is error function Table C-2)
4-11
-------
TABLE 4-1
BIOTURBATION COEFFICIENT, D, FOR VARIOUS
LOCATIONS (FROM MATISOFF, 1982)
Bioturbation Coefficient,
o
D, Range (cm /sec)
1 x 10'6
5.4 x 10'8
2.5 x 10'9
3.5-6.3 x 10"8
1.2-3.2 x 10"7
2.9 x 10"7
1.2 x 10'6
0.01-0.99 x 10"6
7.6 x 10'8
4.1 x 10"5
1.5 x 10'4
3 x 10'8
7 x 10"8
8.7-140 x 10'8
1-4.6 x 10'6
1.6-10 x 10"7
1.2-3.4 x 10"7
3.2-41 x 10"9
6.3-16 x 10"9
Depth (cm)
-
-
-
2
2
3
4
5
38
38
30
20
8
8
12-15
5-9
7.5
9
8-15
Location
Chesapeake Bay
San Diego Basin
San Clemente Basin
Buzzards Bay
Long Island Sound
Long Island Sound
Long Island Sound
Long Island Sound
Holy Island Sanch
Caves Haven
Intertidal Sand
Gulf of Mexico
North Atlantic
Laboratory
Central Pacific
Narragansett Bay
New York Bight
New York Bight
Western Atlantic
4-12
-------
EXAMPLE:
Given z = 0.01 m (down into bottom sediment),
t = 1 yr, .
Q(i) = 0.00205 kg/m3/yr (for copper, Eq. 4-10 example), and
D = 10'5 m2/yr (default value),
then C(0.01,l) = 0.00205 *
0.01
2*10
-5
** 10
* erfc
-5
'1/2 * exp/. -<°'0l2>
V
4 * 10"5 * 1
0.01
(4 * iQ-5 * I)1/2
= .00205 [178.41*exp(-2.50) - 500 * erfc (1.58)]
= .0036 kg/nf
where
erfc (1.58) = 1-.9743 = .0257
PROFILES: The resulting concentration profiles are drawn in Figure 4-2,
after 1, 10, 100 and 1,000 years for various depths into the sediment.
4-13
-------
0.0
1 yr 10 yr
100 yr
c
0)
'5
0)
CO
o
*-
a
0)
O
0.1
0.2
1000 yr
468
Concentration (kg/m3)
10
12
Figure 4-2. Relative Vertical Sediment Concentration Profiles
-------
STAGE 5. WATER QUALITY CRITERIA COMPARISONS
5.1 INTRODUCTION
The purpose of this stage is to estimate, for the various constituents of
concern, the concentrations in the water column at the disposal site and
compare those values to water quality criteria, such as the EPA Saltwater
Quality Criteria or a species-specific value derived from bioassay
experiments. Equations are provided to calculate the near field exposure
levels, and the far field exposure levels for the discrete cloud model and
plume model which are discussed in Stage 3. Figure 5-1 presents an
overview of the procedures to be carried out for Stage 5.
5.2 FORM
Only one form is required to be filled in for this stage. The Water Quality
Criteria Comparisons Summary Form DSP6, given in Appendix B, is used to
record the calculated concentration values and compare them to criteria
values. A summary of the EPA saltwater quality criteria is presented in
Table C-l of Appendix C. For each substance or constituent to be con-
sidered, a maximum allowable near field (acute) concentration, in ppb, is
placed in column three of Form DSPS and an average level far field (chron-
ic) concentration in ppb is placed in column five of Form DSPS. An example
of Form DSPS for two constituent is given in Table 5-1. This example is
discussed below as part of the procedure for Stage 5.
5.3 NEAR FIELD ACUTE EXPOSURE LEVEL
5.3.1 Purpose and Procedure
The maximum near field acute water column exposure level is calculated as a
function of the constituent concentrations after disposal and the back-
ground level concentration of the constituents. The estimated concentration
is compared to the acute or near field criterion for that constituent. If
5-1
-------
SECTION
5.2
5.3
5.4
5.5
Select constituents and
obtain Near Field Acute
and Far Field Chronic
Criteria for Form DSP6
1
Compute
Near Field Acute
Exposure Levels and
compare to Criteria
1
Compute
Far Field Chronic
Exposure Levels using
Discrete Clour! Model A
for Urn > Utx * */4
and compare to criteria
I
Compute
Far Field Chronic
Exposure Levels
using Plume Model
for Urn < Utx * "74
and compare to criteria
Figure 5-1. Stage 5, Criteria Comparison Overview
5-2
-------
TABLE 5-1. EXAMPLE OF
FORM DSPS WATER QUALITY CRITERIA COMPARISONS SUMMARY
Substance
Estimated
Concentration
ppb
Near Field
(Acute)
Criterion
ppb
Far Field
(Chronic)
Criterion
ppb
Copper
Tead
0.65
1000
25.0
67.0
4.0
50.0
WQAi
WQCi
5-3
-------
it exceeds the criterion, then the dilution time to reach the criterion
concentration is calculated and a map is constructed to show the area over
which the criterion is exceeded.
5.3.2 Concentration of Constituent After Disposal
Prior to the calculation of the near field level, the concentration after
disposal of each constituent being considered is calculated.
EQUATION: Mi =
Vb * Fs * Ci * 1000
Vm
(5-1)
where
Mi= concentration of constituent i in water column
after disposal in ug/kg or ppb,
Vb = volume of barge or disposal vessel in m (Form
DSP2),
Fs = volumetric solid fraction of waste (Form DSP2),
Ci = concentration of constituent i in the bulk waste
in mg/kg or ppm (Form DSPS, use column A for
single source or weighted sum (cws) for multiple
sources of waste), and
Vm = initial mixing volume in m (Eq. 4-1).
EXAMPLE:
Given constituent i
Vb
Fs
Ci
Vm = 160,000 m* (Eq. 4-1 example),
copper,
4000 m3 (Table 2-1),
0.42 (Table 2-1),
7 mg/kg for copper (Table 2-2), and
then
M. 4000 * 0.42 * 7 * 1000 ,. ,.
Mi = 160,000 = 74 ug/kg or ppb
5.3.3 Suspended Solids Dimension!ess Mass Ratio
This term is also calculated before using the near field exposure level
equation which is given in the next section, 5.3.4.
5-4
-------
EQUATION: Css = Ds * sg (part) + Cs (5-2)
where Css = suspended solids mass ratio subsequent to a disposal,
dimension! ess,
Ds = dilution of suspended particulate phase, dimension-
less (Eq. 4-5),
sg(part) = the particulate specific gravity (Form DSP2), and
Cs = background water column percent suspended solids,
dimensionless (Form DSP4).
EXAMPLE:
Given Ds = 0.0039 (Eq. 4-5 example)
sg(part) = 2.65 (Table 2-1), and
Cs = ISxlO'6 (Table 2-4),
then Css = 0.0039 * 2.65 + 15xlO"6 = 0.01035.
5.3.4 Maximum Near Field Exposure Level
The near field acute water column exposure level is calculated from the
background constituent concentration, and the concentration of the
constituent after disposal. A petition coefficient, f i , for the
constituent is incorporated into the equation to allow for the tendency of
many contaminants to ahere to fine suspended particles instead of
dissolving. Metals and some organic compounds are examples.
EQUATION: ELi = f. f + BLi (5"3)
where ELi = maximum near field water column exposure concen-
tration of constituent i in ppb,
Mi = concentration of constituent i in water column
after disposal in ppb (Eq. 5-1)
fi = adsorbed-dissolved partition coefficient for
constituent i, dimensionless (Table C-l),
5-5
-------
Css = suspended solids mass ratio subsequent to dis-
posal, dimensionsless (Eq. 5-2), and
BLi = background level of constituent i in water col-
umn at site in ppb (Form DSP4)
EXAMPLE:
Given constituent i = copper,
Mi = 74 ppb (Eq. 5-1 example),
fi = 130,000 for copper (Table C-l),
Css = 0.01035 (Eq. 5-2 example),
BLi = 0.6 ppb (Table 2-4, 0.0006 ppm in table
converted to ppb),
then ELi = 13o)0007* 0.01o35 + 0.6 = 0.65 ppb.
The maximum near field acute water column exposure level (ELi) of 0.65 ppb
copper is recorded on Form DSP6 as shown in the example given in Table 5-1.
The EPA maximum allowable (acute) concentration for copper of 25 ppb from
Table C-l is also recorded in the example table for comparison to the cal-
culated concentration. For this example, the estimated concentration of
0.65 ppb is just slightly higher than the 0.6 ppb background concentra-
tions.
The EPA saltwater criterion for copper is 25 ppb and therefore the
estimated concentration is orders of magnitude less than the criterion. If
the estimated acute concentration calculated from Eq. 5-3 for a given
constituent is greater than the acute criterion, then it is necessary to
calculate the time to reach the criterion level as described in Section
5.3.5 and the horizontal area over which the criterion is exceeded as
described in 5.3.6.
The average level chronic criteria for the constituents under consideration
should also be recorded on Form DSP6 in the last column. If the estimated
concentration of the maximum near field water column exposure level (from
5-6
-------
Eq. 5-3 and recorded in column 2) for any given constituent is less than
the chronic criteron recorded in column 5 then there is no need to
calculate far field chronic exposure levels for that constituent as pre-
sented in Sections 5.4 and 5.5.
In the example shown in Table 5-1, the estimated maximum concentration of
copper is less than the far field criterion and therefore the far field
exposure levels are not evaluated for the example presented for Eq. 5-3.
5.3.5 Time to Reach Acute Water Quality Criteria
If the estimated concentration of a constituent immediately after disposal,
ELi, is greater than the acute water quality criterion, WQAi, (i.e., column
2 is greater than column 3 of Form DSP6) then the time required for that
waste to be diluted in the near field until its concentration is equal to
the criterion is calculated. Times on the order of a few hours should be
sufficient to achieve acceptable dilution.
Eq. 3-20 is used for this near field dilution calculation. In Stage 3,
this equation is used to calculate the concentration of a constituent at a
given location and at a given time, based on the initial contaminant
concentration. For application in this section, let the estimated acute
exposure level (ELi) equal the initial contaminant concentration (Co) and
let the acute water quality criterion (WQAi) equal the concentration
C(x,y,t) of equation 3-20, and solve for time, t1. In order to solve for
the time at which ELi = WQAi, an initial assumption for t1 must be made and
inserted into the equation to solve for WQAi. An iterative method is used,
that is, several choices of t are made until the correct value of WQAi is
computed. Once two different values of time are found that closely predict
a value higher and another value lower than the WQAi, the final time
estimate can be made by interpolation.
Eq. 3-20 of Stage 3 is transformed into the following equation for use in
computing the time it takes ELi to reach WQAi.
5-7
-------
WQA1 =
«rt
(5-4)
where WQAi
ELI
erf
b
acute water quality criterion for constituent i in ppb
(Form DSP6),
maximum near field water column exposure concentra-
tion for constituent i in ppb (Eq. 5-3),
error function presented in Table C-2,
initial disposal cloud dimension along x axis in m
equal to V*t
a =
where v = velocity of disposal vessel in m/sec
(Form DSP2), and
t = duration of disposal in sec (Form DSP2)
initial disposal cloud dimension along y axis in m
equal to 2*w
where w = width of disposal vessel in m
Ex = (4*Dx*t')1/2
where Dx = dispersion coefficient in x direction
(Eq. 3-17a), and
t1 = time in sec for ELi to equal EQAi
Ey = (4*Dy*t')1/2
x =
y =
where Dy = dispersion coefficient in y direction
(Eq. 3-17b), and
t1 = time in sec for ELi to equal WQAi
0.0 for this application of calculating time, and
0.0 for this application of calculating time.
5-8
-------
In the example calculation of ELi for copper, ELi was less than the WQAi
for copper and the time calculation was not necessary. For this example,
however, assume that the ELi for lead is equal to 1000 ppb as shown in
Table 5-1.
EXAMPLE:
Given WQAi = 67 ppb for lead (Table 5-1),
ELi = 1000 ppb for lead (Table 5-1),
b = l.O m/sec * 200 sec = 200 m (Table 2-1),
b/2 = 200 m/2 = 100 m,
a=2*20m=40m (Table 2-1),
a/2 = 40 m/2 = 20 m,
Ox = 4.7 n^/sec (Eq. 3-17a example),
Dy = 2.2 m2/sec (Eq. 3-17b example),
x1 = 0.0, and
y = o.o,
then first assume t' = 1 hr = 3600 sec
Solve for:
Ex = (4*4.7*3600)1/2 = 260,
Ey = (4*2.2*3600)1/2 = 178
a) Calculate value for WQAi using Eq. 5-4:
WQAi =
1000
erf
erf
100+0
~2~6TT
<"(^)
using Table C-2 to determine the value for erf
WQAi = (1000/4) * [0.41 + 0.41] * [0.13 + 0.13] = 53.3 ppb
5-9
-------
b) Compare to given value for WQAi:
the calculated WQAi of 53.3 ppb is smaller than the 67 ppb
criterion therefore, try a smaller t', let t' = 45 min = 2700
sec.
c) Solve for Ex and Ey as defined in Eq. 5-4:
Ex = (4*4.7*2700)1/2 = 225, and
Ey = (4*2.2*2700)1/2 =154
d) Calculate value for WQAi:
WQAi
1000 .
~ ^^_^^^^_ «
erf
erf
using Table C-2 to determine the value for erf
WQAi =
* [0.94] * [0.29] = 68 ppb
Let time to reach acute water quality criterion equal 2700 sec or 45 min
since 68 ppb is approximately equal to 67 ppb.
5.3.6 Horizontal Area Over Which Criteria Are Exceeded
For each of the constituents whose acute water column exposure level, ELi,
is greater than the acute water quality criterion and for which a time to
reach the criterion is calculated in 5.3.5, the horizontal area over which
the criterion is exceeded can be calculated. The area is calculated using
the time to reach the criterion, t1, and by applying Eq. 3-20 of Stage 3.
Four sets of vertices are computed which approximate the area exceeding the
criterion as a quadrilateral:
5-10
-------
[0,0], Cx(t'/2), y(t'/2)], Cx(t'/2), -y(t'/2)], [z(t'), 0].
Figure 5-2 is a schematic showing the vertices of the quadrilateral.
5.3.6.1 Downstream Travel Distance
The value x(t') is the downstream travel distance required to reach the
acute criterion and is equal to
EQUATION: x1 = Um * t1 (5-5)
where Um = mean net surface drift in m/sec (Form DSPS), and
t1 = time to reach acute criteria in sec (Section 5.3.5).
EXAMPLE:
Given Um = 0.05 m/sec (Table 3-1), and
t' = 45 min = 2700 sec (Eq. 5-4 example)
then x(t') = x' = 0.05 * 2700 = 135 m.
The value of x(t'/2) is equal to half the x(t') distance and therefore in
the example the x(t'/2) distance is approximately 68 m.
5-11
-------
[X(t'/2).Y(t'/2)]
[o.o]
[x(f).o]
Figure 5-2,
Quadrilateral for Horizontal Area Over Which
Criterion is Exceeded
5-12
-------
5.3.6.2 Lateral Distance of Area
The value for y(t'/2) and therefore -y(t'/2) is calculated by applying
Eq. 3-20 of Stage 3 for a t = t'/2 with C{x,y,t) = WQAi and Co = ELi. This
is also an iterative procedure in which various values of y are selected
until the equation is satisfied, i.e., the equation equals the acute water
quality criterion for the particular constituents under consideration.
WQAi =
erf
(5-6)
where WQAi
ELi
erf
b
a =
Ex =
Ey =
acute water quality criterion for constituent i in ppb
(Form DSP6),
maximum near field water column exposure concentration of
constituent i in ppb (Eq. 5-3),
error function (Table C-2),
initial disposal cloud dimension along x axis in m
equal to v*t,
initial disposal cloud dimension along y axis in m
equal to 2*w,
(4*0x*t'/2)1/2,
where Dx = dispersion coefficient (Eq. 3-17a), and
t'/2 = half the time in sec for ELi to equal WQAi,
(4*Dy*t'/2)1/2
where Dy = dispersion coefficient (Eq. 3-17b)
t'/2 = half the time in sec for ELi to equal WQAi,
x' = x - Urn * t'/2 = 0.0
where x = Urn * t'/2, thus x' = 0.0, and
y = distance in m for t'/2 = y(t'/2)
5-13
-------
EXAMPLE:
Given from the example for Eq. 5-4
WQAi = 67 ppb,
ELi = 1000 ppb,
b = 200 m,
a = 40 m,
o
Dx = 4.7 m /sec, and
Dy = 2.2 m2/sec,
and for this example
x1 = 0.0, and
t'/2 = 2700/2 = 1350 sec,
then
a) Solve for Ex and Ey:
Ex = (4*4.7*1350)1/2 = 159,
Ey = (4*2.2*1350)1/2 = 109,
b) Next let y = 100 m as first assumption and apply to equation 5-6
solving for WQAi,
WQAi =
1000
ipp-oY . /ioo+o\
-- --
*rf (Z° IW°\ *rf (210910°\
5-14
-------
using Table C-2 to determine the value of erf, noting that for this case,
the error function of a negative number is equal to minus the error func-
tion of the number in Table C-2, i.e., erf(-x) = -erf(x):
WQAi = - * [0.625+0.625] * [-0.70+0.88] = 56 ppb
c) Compare to criterion:
The calculated value of 56 ppb is too small. Try y = 90 m and solve
for WQAi
WQAi = . * [1.25] * [0.21]
= 66 ppb =* 67 ppb criterion. Select 90 m as value for y.
From the example of equation 5-6, the four vertices of the quadrilateral
for the horizontal area over which the criterion for lead is exceeded are:
(0,0), (68,90), (68, -90), (135,0). The area exceeding the acute criterion
of 67 ppb for lead is shown in Figure 5-3.
5.4 FAR FIELD CHRONIC EXPOSURE LEVEL USING DISCRETE CLOUD MODEL A
5.4.1 Purpose and Procedure
The estimated maximum exposure levels for each of the constituents of con-
cern as recorded in column 2 of Form DSP6 are also compared to the chronic
level criteria listed in column 5. If the maximum level is greater than the
chronic level, then a time-dependent dilution calculation is made to deter-
mine the time required to reach the criterion. This section describes the
use of Eq. 3-19 of Stage 3 for the far field transport of a point source to
estimate the time for the condition where Urn > Utx * */4, as discussed in
Section 3.7.6.
5-15
-------
(68,90)
(0.0)
(135,0)
(68,-90)
Figure 5-3.
Horizontal Area Over Which Criterion
in Example of Equation 5-6.
(Coordinates in Meters)
for Lead is Exceeded
5-16
-------
5.4.2 Initial Time
The initial time (to) for the assumed point source to reach the actual
initial horizontal area affected by the disposal of the waste is calculated
using the barge width, length of disposal and dispersion coefficients. The
equation for the initial time is based on the convention that the cloud
width is given by 4 * sigma (Csanady, 1973) where sigma is the standard
deviation of a Gaussian cloud and therefore the perpendicular width is
twice the barge width (2*w) and the parallel width is the length of the
dump (v*t). Then for sigma2 = [2*(Dx*Dy)1//2 * to] the initial time is
given by:
EQUATION:
EXAMPLE:
Given
to =
w
16 * (Dx*Dy)1/2
(5-7)
where to = initial time in sec,
w = width of disposal vessel in m (Form DSP2),
v = speed of disposal vessel in m/sec (Form DSP2),
t = individual disposal duration in sec (Form DSP2),
2
Dx = dispersion coefficient in x direction in m/sec
(Eq. 3-17a), and
p
Dy = dispersion coefficient in y direction in m/sec
(Eq. 3-17b).
w = 20 m (Table 2-1),
v = 1.0 m/sec (Table 2-1),
t = 200 sec (Table 2-1),
P
Dx = 4.7 m/sec (Eq. 3-17a example), and
Dy = 2.2 m2/sec (Eq. 3-17b example),
then to = (20*1.0*200)/(16*(4.7*2.2)1/2) = 78 sec
5-17
-------
5.4.3 Total Time for Constituent to Reach Criterion
The disposal cloud Is now visualized as an Initial point source. The total
time required for the maximum concentration of constituent i in the cloud
to equal the chronic criterion level, WQCi, is based on the following
formula which is derived from Eq. 3-19 in Stage 3. This equation results
from setting x and y to zero in Eq. 3-19, and neglecting the transport
velocity Urn.
EQUATION:
t =
ELi * Ym
D
=4«*d*D* WQCi
(5-8)
where t = time to reach chronic level in sec,
Q = total mass of constituent in water column.
For this equation let
Q = ELi*Vm
where ELi = estimated maximum water column exposure
level in ppb (Eq. 5-3), and
Vm = mixing zone volume in nr* (Eq. 4-1),
d = calculated depth in m
D = (Dx*Dy)1/2 in m/sec
where Dx = dispersion coefficient in the x direction
(Eq. 3-17a), and
Dy = dispersion coefficient in the y direction
(Eq. 3-17b), and
C = concentration of constituent in ppb.
For this equation let
C = WQCi = chronic criteria level in ppb
(Form DSP6).
5-18
-------
EXAMPLE:
Given ELi = 1000 ppb for lead (Table 5-1),
Vm = 160,000 m3 (Eq. 4-1 example),
d = 20 m (Section 3.3.2),
Dx = 4.7 m2/sec (Eq. 3.17a example),
Dy = 2.2 m2/sec (Eq. 3.17b example),
D = (Dx+Dy)1/2 = (4.7*2.2)1/2 = 3.22 m2/sec, and
WQCi = 50 ppb (Table 5-1),
5.5 FAR FIELD CHRONIC EXPOSURE LEVEL USING PLUME MODEL
5.5.1 Purpose and Procedure
If the two dimensional point source plume model is being used for the
condition Urn < (Utx * */4) and unit contours have been constructed for a
mass loading rate of one as described in Section 3.7.5, then the loading
rate of Eq. 3-18 is calculated as described below.
5.5.2 Loading Rate from Disposal Operation
Before the loading rate is calculated, first calculate the mass of the
constituent i per unit volume of the waste.
EQUATION: MVi = C1 * f* (Part) (5'9)
2
where MVi = mass of constituent per unit volume in kg/m ,
Ci = concentration of constituent i in the bulk waste in
mg/kg (Form DSP3),
Fs = solid fraction of waste (Form DSP2), and
sg(part) = particle specific gravity (Form DSP2).
5-19
-------
EXAMPLE:
Given Ci = 7 mg/kg for copper (Table 2-2),
Fs = 0.42 (Table 2-1),
sg(part) = 2.65 (Table 2-1),
7 * n &."> * ? fiR -j
then MY1 = - - U' *' = 0.00779 kg/m
The source strength or loading rate in kg/sec for a constituent in the
water column for use in the application of the two dimensional plume model,
Eq. 3-18, is calculated from
q = ^^.*** (5'10)
q 3600*24*365 * Tdd * (fi*Cs + 1.0)
where q = loading rate in kg/sec,
MVi = mass of constituent i per unit volume of waste in
kg/m3 (Eq. 5-9),
Qa = annual loading rate in m3/year (Form DSP2),
3600*24*365 = seconds/year,
Tdd = typical duration of dredging operation (Form DSP2),
fi = partition coefficient, dimensionless (Table C-l),
and
Cs = background percent suspended solids, dimensionless
(Form DSP4)
EXAMPLE:
Given MVi = 0.00779 kg/m3 (Eq. 5-9),
Qa = 5.0xl06 m3/yr (Table 2-1),
Tdd = 0.25 (Table 2-1),
fi = 130,000 for copper (Table C-l), and
Cs = 15x10, -6 (Table 2-4),
5-20
-------
0.00779 * 5.0x10
then q
3600*24*365 * 0.25 * (130,000*15xlO~6 + 1)
= 0.00167 kg/sec or 1.67 g/sec
5.5.3 Loading Rate from Bottom Sediment
Eq. 5-10 above is used to calculate the loading rate of a constituent to
the water column from the disposal operation. Bottom sediment may also
become a source of loading to the water column and a loading rate from the
sediment should be calculated.
The sediment source strength (or loading rate) of a constituent, is com-
puted based on a given number of years of site usage. In order to calculate
the loading rate, the maximum concentration at the water-sediment inter-
face, Ci(o,t), is calculated first. The Ci(o,t) is a function of the con-
centration in the sediment before the disposal, Co(i), and the depositional
rate, Q(i), for the constituent.
5.5.3.1 Concentration in Sediment Before Disposal
The concentration in the sediment before the proposed disposal activity is
calculated as a function of the concentration in the bulk waste.
EQUATION: Cod) =
where Co(i) = concentration of constituent i in sediment before
disposal activity in kg/m ,
Ci = concentration of constituent i in the bulk waste in
mg/kg (Form DSP3), and
sg(part) = particle specific gravity (Form DSP2).
EXAMPLE:
Given Ci = 7 mg/kg for copper (Table 2-2), and
sg(part) = 2.65 (Table 2-1).
5-21
-------
Co(1) = 7 *65 = 0.0186 kg/m3
then
5.5.3.2 Deposition Rate
Next, the rate of deposition of the constituent Is estimated assuming that
all the mass goes to the sea floor. This might be seen 1n an extreme case.
cn.iftTTnu. nm - °-a * s9(Part) * C1 /c
EQUATION: Q(i) -- A * 1000 - (5
where Q(1) = deposition rate for constituent 1 In kg/m2/yr,
Qa = annual loading rate In nrVyr (Form DSP2),
sg(part) = particle specific gravity (Form DSP2),
C1 = concentration of constituent 1 In the bulk waste In
mg/kg (Form DSP3), and
A = direct Impact deposition area In nr (Eq. 3-3).
EXAMPLE:
Given Qa = S.OxlO6 m3/yr (Table 2-1)
sg(part) = 2.65 (Table 2-1)
C1 = 7 mg/kg for copper (Table 2-2)
A = 1.19xl06m2 (Eq. 3-3 example)
then Qd)-5-0xlfl6 V-65*7
1.19x10° * 1000
= 0.0779 kg/m2/yr.
5.5.3.3 Maximum Concentration at Interface
Once the Co(1) and the Q(1) are calculated, the maximum concentration at
the interface is calculated by
EQUATION: Ci(o,t) = Cod ) + Q(i) * ( sf-J (5-13)
5-22
-------
where Ci(o,t) = maximum concentration at interface for t years in
kg/m3,
Co(i) = concentration of constituent i in sediment before dis-
posal activity in kg/m3 (Eq. 5-11),
o
Q(i) = deposition rate for constituents in kg/m /yr (Eq.
5-12),
t = time in years, and
D = bioturbation mixing rate (default 10"5 m2/yr).
EXAMPLE:
Given Co(i) = 0.0186 kg/m3 (Eq. 5-11 example),
Q(i) = 0.0779 kg/m2/yr (Eq. 5-12 example),
t = 10 years (assumed value to be consistent with example
of Eq. 5-14), and
D = 10"5 m2/yr (default value),
then Ci(0,10) = 0.0186 + 0.0779 *
10
31 * 10
-5
1/2
= 44 kg/nf.
5.5.3.4 Sediment Source Strength (Loading Rate)
Once the maximum concentration at the interface has been calculated, the
source strength of the dissolved phase for a given constituent, q(i), is
calculated based on a given number of years of site use and a vertical
diffusion coefficient. The variables enclosed within the brackets of Eq.
5-14 are those which define the maximum concentrations Ci(o,t) as presented
in Eq. 5-13. They are repeated here, however, so that different years, n,
of site use can be used.
EQUATION: q(i) =
Co(i) + Q(i) *
n it
Dz
fi * Scs
(5-14)
where q(i) = source strength of dissolved phase in kg/sec,
Co(i) = concentration of constituent i in sediment before dispos-
al activity in kg/m3 (Eq. 5-11),
5-23
-------
EXAMPLE:
Q(i) = deposition rate for constituent i in kg/m2/yr (Eq. 5-12),
n = number of years of use (default is 10 years for little or
no resuspension, one year for a dispersive benthic
environment,
D = bioturbation mixing rate (default 10"5 m2/yr),
Dz = vertical diffusivity from sediment to water column (de-
fault 0.001 m2/sec),
A 1/2
b = , the typical horizontal site dimension in m,
JT
2
where A = direct impact deposition area in m
(Eq. 3-3),
fi = partition coefficient, dimensionles (Table C-l), and
Scs = percent solids concentration in sediment (default 50
percent for dredged material, 20 percent for sewage
sludge).
Given Co(i) = 0.0186 kg/m3 (Eq. 5-11 example),
Q(i) = 0.0779 kg/m2/yr (Eq. 5-12 example),
n = 10 years (default for little or no resuspension),
D = 10'5 m2/yr (default value),
Dz = 0.001 m2/sec (default value),
b = (1.19xl06m2)1/2/* = 347 m (Area A, from Eq. 3-3 example)
fi = 130,000 for copper (Table C-l), and
Scs = 0.50 (default value for dredged material),
then q(i) =
0.0186 + 0.0779 *
* 0.001 * 347
10 \l/2
x * 10'5
130,000 * 0.50
2.35 x 10"4 kg/sec or = 0.235 g/sec
5-24
-------
STAGE 6. HYPOXIC EVENT POTENTIAL ASSESSMENT
6.1 INTRODUCTION
The purpose of this stage is to evaluate the potential for a dissolved oxy-
gen depletion at the site due to the disposal operation of neutrally or
positively buoyant wastes. Historical dissolved oxygen information in the
region around the selected site should first be used to determine if
hypoxia could become a problem and whether to continue with the potential
assessment. The analysis is based on the biochemical oxygen demand (BOD).
The oxygen depletion curve (for net flow Urn >0.0) and the oxygen deficit
growth rate (for Urn = 0.0 as an extreme event) are computed based on the
ambient BOD and the water column BOD after disposal. Figure 6-1 presents
the dissolved oxygen assessment overview for stage 6.
The analysis is performed under assumed critical conditions of high
temperature, quiescent weather and strong pycnocline which usually occur in
the summer. The following conditions for use in the calculations are spec-
ified as being critical:
1. Use the maximum disposal rate average over a 30-day period if data
available. Otherwise, use Qa/Tdd from Form DSP2,
2. Use low diffusivities. Let Dx and Dy equal 0.1 m2/sec,
3. Use highest water temperature expected or observed below the pycno-
cline, and
4. Use the lowest net flow observed, or use 0.0 m/sec as a default
value.
6-1
-------
6.3
6.4
6.5
6.6
6.7
Specify
critical conditions
I
Compute
Ambient BOD
without disposal
I
Compute
Local Water
Column BOO
with disposal
I
Compute
Initial DO
after disposal
I
Compute
DO Depletion Curve
with Net Flow >0
I
Compute
DO Deficit Growth Rate
with Net Flow =0
Figure 6-1. Stage 6, Dissolved Oxygen Assessment Overview
6-2
-------
6.2 FORMS
All the DSP Forms have been completed up to this stage. Data from several
of the forms are required in the calculations of this stage.
6.3 AMBIENT BOD WITHOUT DISPOSAL
6.3.1 Purpose and Scope
The ambient biochemical oxygen demand, BODa, at the site is required as a
base condition before disposal calculations are performed. BODa is
estimated as the sum of the ambient off -site value, BODu, the demand from
the site sediments, BODis, which could include the demand from previous
disposal; and the demand from resuspended sediments, BODrs.
6.3.2 Benthic Oxygen Demand
If the benthic oxygen demand is not known and not recorded on Form DSP4,
it is estimated from the demand of the accumulated sediment, decay factors,
deposition rate and accumulation period. The decay factor and deposition
rate are calculated first, and then applied to the formula for the benthic
oxygen demand.
6.3.2.1 Decay Factor
The decay factor is a function of the decay rate and water temperature.
«>UAT10N: C° 1 I ££{:! * koi
where Co = decay factor,
exp = exponential function,
ko = decay rate at 20°C (default is 0.23/day), and
k = ko * (1 + 0.05 * (T-20))
where T = ambient water temperature, degrees C.
6-3
-------
EXAMPLE:
Given ko = 0.23 per day, and
t = 25° (Form DSPS),
then k = 0.23 (1 + 0.05 * (25 - 20)) = 0.29 per day,
rn 1 - exp(-5 * 0.29) _ . 17
Co " 1 - exp(-5 * 0.23) " 1>12
6.3.2.2 Daily Deposition Rate Factor
The deposition rate factor, W, is computed directly from the daily desposi-
tion rate of organic solids, dd. First, the daily deposition rate of
organic solids is approximated by
EQUATION: dd = dwd * fv * sg (part) * (1-Ffs) * -yi * 100° (6'2)
o
where dd = daily deposition rate of organic solids in kg/m ,
dwd = daily waste dumping rate (default = [Qa/Tdd)/365],
for Qa and Tdd on Form DSP2),
fv = organic fraction of waste,
sg(part) = particle specific gravity (Form DSP2),
Ffs = fraction of fines in suspended cloud, (Form DSP2),
d = equivalent depth in m (Section 4.3.2), and
Vm = initial mixing zone volume in m (Eq. 4-1),
EXAMPLE:
Given Qa = S.OxlO6 m3/yr (Form DSP2),
Tdd = 0.25 (Form DSP2),
dwd = (Qa/Tdd)/365 = (5.0 x 106/0.25)/365 = 5.48 x 104,
fv = 0.002,
sg(part) = 2.65 (Form DSP2),
Ffs = 0.9 (Form DSP2),
d = 20 m (Section 4.3.2 example), and
6-4
-------
Vm = 160,000 m3 in m3 (Eq. 4-1 example),
then dd = 5.48xl04 * 0.002 * 2.65 * (1-0.9) * (20/160,000) *
1000 =3.63 kg/m2
Once the daily deposition rate, dd, is calculated , the deposition rate
factor, W, is calculated by
EQUAT,ON: . ,5-3,
o
where W = daily deposition rate factor kg/m , and
2
dd = daily deposition rate of organic solids in kg/m
EXAMPLE:
Given dd = 3.63 kg/m2 (Eq. 6-3 example),
* "*
6.3.2.3 Daily Benthic Oxygen Demand
If an observed daily benthic oxygen demand is not available (from Form
DSP4), then the calculated decay factor and deposition rate factor can be
applied to a formula for estimating the benthic oxygen demand (Fair, et al,
1968). The benthic oxygen demand, BODis, is the oxygen demand of the
insitu sediments including those resulting from previous dumps.
EQUATION: BODis = 0.0314 * BODw * Co * W * (ta)1/2 (6-4)
?
where BODis = benthic oxygen demand in g/m /day,
BODw = biochemical oxygen demand of the accumulated sediment in
/
g/kg (the BOD value of the original waste can be usd for
default, Form DSP3, convert mg/kg on Form DSP3 to g/kg
for this equation),
Co = decay factor (Eq. 6-1),
6-5
-------
W = deposition rate factor (Eq. 6-3), and
ta = time in days, up to 365, during which accumulation takes
place, or the time between resuspension episodes, or the
annual duration of dredging operation.
EXAMPLE:
Given BODw = (32 mg/kg)/(1000 mg/g) = 0.032 g/kg (Table 2-2 and con-
version to g/kg),
Co = 1.12 (Eq. 6-1 example),
W = 3.66 kg/m2 (Eq. 6-3 example), and
ta = 91 days or 0.25 yr (Tdd in Table 2-1),
then BODis = 0.0314 * 0.032 * 1.12 * 3.66 * (91)1/2
= 0.0393 g/m2/day.
6.3.3 Resuspended Sediment Oxygen Demand
The oxygen demand of the organic resuspended load is calculated as a func-
tion of the BOD of the accumulated sediment.
EQUATION: BODrs = BODw * (1 - exp(-5 * k)) (6-5)
where BODrs = oxygen demand of resuspended load in mg/kg,
BODw = biochemical oxygen demand of accumulated sediment in
mg/kg (note in Eq. 6-4 units are g/kg),
exp = exponential function, and
k = ko * (1 + 0.05 * (T-20)), temperature corrected decay
rate
where ko = decay rate at 20°C, and
t = water temperature °C.
EXAMPLE:
Given BODw = 32 mg/kg (original waste value in Table 2-2), and
k = 0.29 (Eq. 6-1 example),
6-6
-------
then BODrs = 32 * (1 - exp(-5 * 0.29)) = 24.5 mg/kg.
6.3.4 Ambient BOD Without Disposal
The total ambient BOD at the site without present disposal occurring is the
sum of the off-site BOD, the resuspended BOD and the benthic oxygen demand
acting on the waters up to the pycnocline.
EQUATION: BODa = BODu + BODrs + pp (6-6)
where BODa = ambient on-site biochemical oxygen demand in mg/kg or
ppm,
BODu = ambient off-site BOD in mg/kg or ppm,
BODrs = oxygen demand of resuspended load in mg/kg or ppm
(Eq. 6-5),
p
BODis = benthic oxygen demand g/m (Eq. 6-4), and
di = height of pycnocline above bottom (if no pycnocline and
well -mixed, use average depth of site).
EXAMPLE:
Given BODu = 3 mg/kg (or mg/1 ) ,
BODrs = 24.5 mg/kg (Eq. 6-5 example),
BODis = 0.0393 g/m2 (Eq. 6-3 example), and
di = 10 m (Table 3-1, mean depth of 30 minus pycnocline depth
of 20),
then BODa = 3 + 24.5 + - = 27.5 mg/kg.
Note: = (g/m2)/(m) = g/m3 = mg/kg
6-7
-------
6.4 LOCAL WATER COLUMN BOD WITH DISPOSAL
6.4.1 Purpose and Procedure
The local water column BOD with disposal operations is a function of am-
bient BOD and the waste load BOD of the disposal material. This BOD, con-
verted to ultimate BOD, is used in the oxygen depletion curve, Eq. 6-11, in
Section 6.5.
6.4.2 Five-Day Biochemical Oxygen Demand
The 5-day BOD is computed first and then converted to the ultimate BOD.
EQUATION: BODd = BODa + (^ * BODw * ^lj (6-7)
where BODd = biochemical oxygen demand in local water column with dis-
posal in mg/kg,
BODa = ambient biochemical oxygen demand in mg/kg (Eq. 6-6),
o
Vb = volume of disposal vessel in m (Form DSP2),
Vm = initial mixing zone volume m (Eq. 4-1),
BODw = biochemical oxygen demand of waste in mg/kg (Form DSP2),
di = height of pycnocline above bottom, in m, and
d = equivalent depth.
EXAMPLE:
Given BODa =27.5 mg/kg (Eq. 6-6 example),
Vb = 4000 m3 (Table 2-1),
Vm = 160,000 m3 (Eq. 4-1 example),
BODw = 32 mg/kg (Table 2-2),
di = 10 m (Table 3-1, mean depth of 30 minus pycnocline depth
of 20), and
d = 20 m (Section 4.3.2 example),
then BODd = 27.5 ^5 * 32 * )= 27.9 mg/kg,
6-8
-------
6.4.3 Ultimate Biochemical Oxygen Demand
The computed local water column BOD with dumping calculated in Equation 6-7
is the 5-day BOD value. It is converted to ultimate BOD by a factor of
1.46 which is based on an assumed decay rate of 0.23 per day, base e.
EQUATION: BODult = 1.46 * BODd
(6-8)
where BODult = ultimate biochemical oxygen demand of local water col-
umn with disposal in mg/kg, and
BODd = biochemical oxygen demand of local water column with
disposal in mg/kg (Eq. 6-7).
EXAMPLE:
Given BODd = 27.9 mg/kg (Eq. 6-7 example),
then BODult = 1.46 * 27.9 = 40.7 mg/kg.
6.5 INITIAL DISSOLVED OXYGEN AFTER DISPOSAL
The initial dissolved oxygen in the water column is required so that sub-
sequent dissolved oxygen calculations can be made as a function of time.
The initial dissolved oxygen is calculated as a function of the ambient
dissolved oxygen and the dissolved oxygen of the waste.
EQUATION:
nn. _ (DOa * Vm) + (DOw * Vb)
U1 " Vm + Vb
(6-9)
where
DOi
DOa
Vm
DOw
initial dissolved oxygen after disposal in mg/1,
ambient dissolved oxygen in mg/1 (Form DSP4 or Table C-4
for default values based on temperature and salinity),
initial mixing zone volume in m (Eq. 4-1),
dissolved oxygen of waste in mg/1 (Form DSP3 or use 0.0
as default), and
6-9
-------
Vb = volume of disposal vessel in m (Form DSP2).
EXAMPLE:
Given DOa = 6.0 mg/1 (Table 2-4),
Vm = 160,000 m3 (Eq. 4-1 example),
DOw = 0.0 mg/1 (Table 2-2), and
Vb = 4,000 m3 (Table 2-1),
thon nfH - (6-0 * 160,000) + (0.0 * 4,000)
tnen UU1 160,000 + 4,000
= 5.85 mg/1
6.6 OXYGEN DEPLETION CURVE FOR NET FLOW, Urn, > 0.0
6.6.1 Purpose and Procedure
The dissolved oxygen (DO) concentration is calculated as a function of the
down-current travel time, and a DO versus distance graph can be plotted.
At a given time, the dissolved oxygen is computed based on the ambient DO,
the initial DO, the ultimate BOD and a dilution factor. The downstream
dilution factor is estimated first, then applied to the oxygen depletion
curve formula.
6.6.2 Downstream Dilution Factor
The downstream dilution factor is approximated using the error function and
the lateral diffusion coefficient (Brooks, 1960).
EQUATION: DS =
where
erf
16 * D * t
1/2
(6-10)
DS
erf
b
downstream dilution factor,
error function (Table C-2),
characteristic source length (distance traveled by vessel
during disposal process or default of 200 m),
6-10
-------
D = constant lateral diffusion coefficient,
o
= 0.0018 * b in m /sec, and
t = time in seconds.
EXAMPLE:
Given
erf = error function in Table C-2,
b = disposal vessel speed * disposal duration = 1.0 m/sec *
200 sec = 200 m (Table 2-1),
D = 0.0018 * b = 0.0018 * 200 = 0.36 m2/sec, and
t = 86,400 sec (1 day); 432,000 sec (5 days); and 864,000 sec
(10 days),
then for 1 day DS =
then for 5 days DS =
then for 10 days DS =
erf
erf
erf
200'
,16
8674(11)
200'
16 * LT.36 * 432,000;
200' }
16 * 0.36 * 864,000i
1/2 = 0.300,
1/2 = 0.127,
= 0.089,
6.6.3 Dissolved Oxygen Depletion Curve
The dissolved oxygen concentration in the water column at any given down-
stream travel time is expressed as a function of DO, BOD and downstream
dilution after the initial mixing of the waste.
EQUATION: D0(t) = DOa -[DOa - DOi + BODult * (1 - exp (-k * t))] * DS
(6-11)
where D0(t)
DOa
dissolved oxygen concentration at time t (days) in mg/1,
ambient dissolved oxygen in mg/1 (Form DSP4 or Table C-4
for default values),
DOi = initial dissolved oxygen after disposal in mg/1
(Eq. 6-9),
6-11
-------
BODult = ultimate biochemical oxygen demand of local water column
with disposal in mg/kg (Eq. 6-8),
exp = exponential function,
k = temperature adjusted BOD decay rate per day
= ko * (1 + 0.05 * (T-20))
where ko = BOD decay rate at 20°C per day
t = ambient water temperature °C,
t = time in days, (not seconds), and
DS = downstream dilution factor (Eq. 6-10).
EXAMPLE:
Given DOa = 6.0 mg/1 (Table 2-4),
DOi = 5.85 mg/1 (Eq. 6-9 example),
BODult = 40.7 mg/kg (Eq. 6-8 example),
exp = exponential function,
k = 0.29 per day (Eq. 6-1 example),
t = 1, 5, 10 days, and
DS = 0.300 for 1 day,
= 0.127 for 5 days, and
= 0.089 for 10 days,
(Eq. 6-10 example),
then D0(l day) = 6.0 -[6.0 - 5.85 + 40.7 * (1 - exp(-0.29 * 1))]
* 0.30 = 2.88 mg/1,
D0(5 day) = 6.0 -[6.0 - 5.85 + 40.7 * (1 - exp(-0.29 * 5))]
* 0.127 = 2.02 mg/1,
D0(10 day) = 6.0 -[6.0 - 5.85 + 40.7 (1 - exp(-0.29 * 10))]
* 0.089 = 2.56 mg/1
6.7 OXYGEN DEFICIT GROWTH RATE FOR NET FLOW, Um, = 0.0
6.7.1 Purpose and Procedure
A extreme case scenario is represented here by setting the net flow, Um
equal to zero. Under this condition each day's disposal of BOD is treated
6-12
-------
as an independent dispersing cloud. The following procedure estimates the
oxygen reduction with respect to time. It is calculated for the area below
the pycnocline at the center of the disposal site. The method is carried
out by superimposing on one another the effects of the BOD cloud for each
day.
A series of equations and a specific procedure is required to analyze the
effects of the BOD decay, the oxygen reduction for each day, and the total
oxygen deficit for a given period of time. Each equation, with a simple
example is discussed in this Section. An overall example procedure on the
application of these equations is also given in Section 6.8 to show how the
equations are used in combination.
6.7.2 BOD Mass Loading Rate
The mass loading rate in grams per day for the area below the pycnocline is
calculated for application to the equations for the water column BOD in
Sections 6.7.3 and 6.7.4.
EQUATION: Qb = (BODw * Vb * Dd * Ff * Ffs) + (BODis * A)
(6-12)
where Qb
BODw
Vb
Dd
Ff
Ffs
BODis
A
mass loading rate of BOD in g/day,
o
biochemical oxygen demand of waste in g/m (Form DSP3,
units same as mg/1 or mg/kg),
volume of disposal vessel in m (Form DSP2),
number of barge loads dumped per day (Form DSP2) or
Qa/(Vb * Tdd * 365)
where from Form DSP2
Qa = annual loading rate in m /yr,
Vb = volume of disposal vessel in m , and
Tdd = typical duration of dredging operation in
fraction of a year,
fraction of fine particles in waste (Form DSP2),
fraction of fines in suspended cloud of a single disposal
(Form DSP2),
2
benthic oxygen demand in g/m /day, and
2
disposal settling area in m (Eq. 3-3),
6-13
-------
EXAMPLE:
Given BODw = 32 g/m3 (Table 2-2),
Vb = 4000 m3 (Table 2-1),
Dd = 5.0xl06/(4000 * 0.25 * 365) = 13.7 or say 14 disposals
per day (Table 2-1),
Ff = 0.41 (Table 2-1),
Ffs = 0.9 (Table 2-1),
BODis = 0.0393 g/m2/day (Eq. 6-4 example), and
A = 1.19xl06 m2 (Eq. 3-3 example),
then Qb = (32 * 4000 * 14 * 0.41 * 0.9) + (0.0393 * 1.19xl06)
= 7.08 x 105 g/day.
6.7.3 Basic Equation for Each Day's BOD Cloud
The following equation demonstrates the calculation of each day's BOD con-
centration. However this equation is actually incorported into Equation
6-14 which should be used instead of Equation 6-13 for solving problems.
An example is given here to illustrate the equation variables.
EQUATION: X(t) = ~ (6-13)
where X(t) = BOD concentration after t days in mg/1 ,
Qb = BOD mass loading rate in g/day (Eq. 6-12),
k = BOD decay rate per day (in Eq. 6-1),
t = time in days,
di = distance from bottom to pycnocline in m, and
D = dispersion coefficient = 0.1 m2/sec = 8640 m2/day (for
j
this equation units must be m /day).
6-14
-------
EXAMPLE:
Given Qb = 7.08xl05 g/day (Eq. 6-12 example),
k = 0.29 per day (Eq. 6-1 example),
t = one day,
di = 10 m (Eq. 6-7 example), and
D = default 8640 m2/day,
thon YM HI - 7.08xl05 * exp(-0.29 * 1)
then X(l day) -- 4a * 10 * 8640 * 1 -
= 0.49 mg/1 BOD.
6.7.4 BOD Concentration Near the Center of the Site
The central BOD concentration is calculated based on the idea that the dis-
persion clouds are superimposed on one another as the BOD is loaded into
the site on successive days. The equation can also be considored to show a
BOD cloud as it is followed through time. The central BOD concentration is
a function of the number of days that have passed since the release of the
waste.
EQUATION- X(n) -. Q* * £ exp(-k * j * dt)
tgimiiuN. xinj U* * ^ * D j .=- j * dt
where X(n) = central BOD concentration in mg/1 after n days,
Qb = BOD mass loading rate in g/day (Eq. 6-12),
di = distance from bottom to pycnocline in m,
2
D = dispersion coefficient, default = 8640 m /day,
£ = sum all values of following expression
j=l,n for 1 to n number of days,
k = BOD decay rate per day (in Eq. 6-1),
j = number of days from 1 to n, and
dt = computational time step equal to 1 day.
6-15
-------
EXAMPLES:
The following examples demonstrate the specific use of the variables in
Equation 6-14 for a three-day period; however, an overall procedure for
analyzing the oxygen deficit growth rate is given in Section 6.8 which uses
Equations 6-14, 6-15, and 6-16.
A) Superposition of dispersion clouds using summation
Given Qb = 7.08x10 g/day (Eq. 6-12 example),
di = 10 m (Eq. 6-7 example),
D = 8640 m2/day (default),
k = 0.29 per day (Eq. 6-1 example),
j = 1, 2, and 3 days, and
dt = one day,
then BOD concentration at the center of the site after 3 days is:
exp(-0.29 * 1 * 1)
7.08xl05
4* * 10 * 8640
1*1
, exp(-0.29 * 2 * 1)
r~*~i
, exp(-0.29 * 3 * 1)
3*1
= (0.65) * (0.748 + 0.280 + 0.140) = 0.76 mg/1
This value represents the BOD concentrations after superimposing the
dispersion clouds released on three successive days.
B) Single cloud followed through time without summation.
Given all values as in example A above,
6-16
-------
then X(l) = 0.65 * 0.748 = 0.49 mg/1
X(2) = 0.65 * 0.280 = 0.18 mg/1
X(3) = 0.65 * 0.140 = 0.09 mg/1
These values represent the central BOD concentration of a single cloud at
1, 2 and 3 days.
6.7.5 Dissolved Oxygen Deficit for Each Day's Release
The DO deficit is equal to that portion of the BOD that has been reduced as
a function of decay. The deficit resulting from a single release is
calculated for a given period of time in days.
EQUATION: DODn =
[x(i) - x(i+l)]
1=1,n-1
exp(-k * t)
i + exp{-k * t)
(6-15)
where
1=1,n-1
x(i) and x(i+l)
k
t
DODn = dissolved oxygen deficit after n days,
V = sum of all values of following expression
for 1 to (n minus 1) days,
BOD concentration in mg/1 for the i day and
the (1th plus one) day (Eq. 6-14),
BOD decay rate per day (in Eq. 6-1), and
i*dt for each i day and dt is a one day time
step.
EXAMPLE:
This example uses a single day's release and the same three day period as
example B for Equation 6-14. However, a general procedure for calculating
the DO deficit is presented in Section 6.8 using Equations 6-14, 6-15 and
6-16.
Given X(l) = 0.49 mg/1,
X(2) = 0.18 mg/1,
6-17
-------
X(3) = 0.09 mg/1 (all from Eq. 6-14 example B),
k = 0.29 per day (Eq. 6-1 example),
n = 3 days,
i = 1 to n-1 = 1, 2
dt = one day, and
t = i*dt =1,2,
then DOD3 = [0.49 - 0.18] *
exp(-0.29 * 1)
f- + exp(-0.29 * 1)
[0.18 - 0.09} *
exp(-0.29 * 2)
exp(-0.29 * 2)
. = (0.31 * 0.428) + (0.09 * 0.528) = 0.18 mg/1
Therefore, the total DO deficit from a single release over two days is
0.18 mg/1.
6.7.6 Total Dissolved Oxygen Deficit for Successive Releases
The total oxygen deficit for a series of BOD releases on successive days is
computed by summing the deficit due to each of the daily BOD releases.
EQUATION: TOD =
DODj
(6-16)
where TOD = total dissolved oxygen deficit mg/1, and
DODj = dissolved oxygen deficit for each j day.
EXAMPLE:
Given for a single release,
DOD for day 1 = 0.31*0.428 = 0.13 mg/1,
DOD for day 2 = 0.09*0.528 = 0.05 mg/1, (Eq. 6-15 example)
6-18
-------
then for successive releases after 2 days
TOD = (0.13) + (0.13 + 0.05) = 0.31 mg/1,
where 0.13 represents the effect of the first day's release on the
first day; and for the second day, (0.13 + 0.05) represents the
effect of the second day's release on the second day (0.13) plus
the effect of the first day's release on the second day (0.05).
6.8 OXYGEN DEFICIT GROWTH RATE COMPREHENSIVE EXAMPLE FOR NET FLOW Um = 0.0
This example demonstrates a procedure which uses a table of variables to
calculate the oxygen deficit. This tabulation permits a record keeping of
important variables as calculations are carried out. Table 6-1 is an ex-
ample of a blank calculation sheet used in this example. For each time
step in days, values are calculated for columns A through E which represent
functions as defined in the table. Table 6-2 is filled-in for the
following example which is based on the same assumptions and variable
values presented in the individual examples for Section 6.7.4 through
6.7.6.
Column A
Calculate the value of exp("J*k) USing j = 1, 2, 3 and k =0.29 per day.
For example, on the first day exP (-0.29*1) = 0>748
Column B
Calculate the value of [x(i)-x(i+l)]/m by using the differences in Column
A
For example 0.748 - 0.280 = Column B for first day
and 0.280 - 0.140 = Column B for second day.
6-19
-------
Column C
Calculate ratio using j = 1, 2 and k = 0.29 per day
exp(-0.29 * 2)
For example, on the second day
0.528
+ exp (-0.29 * 2)
Column D
Calculate by multiplying columns B times C
Column E
Qb
M = -j^ .* ^ p from Equation 6-14. In this example,
M =
7
* 1 8640
= °'65 Wh1ch is mult1'P11ed t1mes Column D.
For example, on the first day M times column D = 0.65 * 0.2 = 0.13
Note: Adding Column E gives a DO reduction of 0.18 mg/1 for each day's
release which is the same as calculated in the example for Equa-
tion 6-15.
6-20
-------
TABLE 6-1
OXYGEN DEFICIT GROWTH RATE WORKSHEET
Time
Step
j
(days)
1
2
3
4
5
6
7
8
9
10
(A)
exp(-jk)
J
BOD
Reduction
Rate
(B)
x(i)-x(i+l)
m
Daily
Differential
(C)
exp(-jk)
l/j+exp(-jk)
Ratio of
Decay of
Dispersion
Plus Decay
(D)
(B)*(C)
Daily
Differential
Due to
Decay
(E)
M*(D)
Daily
Contribution
to Oxygen
Deficit
6-21
-------
TABLE 6-2
EXAMPLE OXYGEN DEFICIT GROWTH RATE WORKSHEET
Time
Step
j
(days)
1
2
3
4
5
6
7
8
9
10
(A)
exp(-jk)
J
0.748
0.280
0.140
BOD
Reduction
Rate
(B)
x(1)-x(i+l)
m
0.464
0.140
-
Dally
Differential
(C)
exp(-jk)
l/j+exp(-jk)
0.428
0.528
-
Ratio of
Decay of
Dispersion
Plus Decay
(D)
(B)*(C)
0.200
0.074
-
Daily
Differential
Due to
Decay
(E)
M*(D)
0.13
0.05
-
Daily
Contribution
to Oxygen
Deficit
6-22
-------
STAGE 7. SPECIES SPECIFIC ASSESSMENT
7.1 INTRODUCTION
There are no new equations to be solved or specific DSP forms to be filled
out for Stage 7. This stage is a more detailed assessment of the disposal
activities on specific species in relation to breeding, spawning, nursery,
feeding or passage areas of living resources in adult or juvenile phases.
In order to.carry out this phase, a knowledge of the biological species
present at the site and in the surrounding affected areas is required. One
must also be familiar with toxic affects and bioaccumulation which are two
major aspects to be considered.
Stages 1 through 6 will provide basic information at the site from which to
proceed with the species specific assessments. As part of Stage 1 a
preliminary evaluation of the biological community should be undertaken.
Stages 2 through 4 develop the waste profile and loading characteristics,
the transport mapping and resuspension estimates, and the initial mixing
and source strength calculations. Stage 5 presents a procedure for making
comparisons of the predicted water quality at a site with water quality
criteria, and Stage 6 demonstrates a methodology for determining the
hypoxic potential of the disposal site.
7.2 PROCEDURE
For a given site, species specific toxicity data could be used where
available. However, if specific biological and toxicological information
is not available, a more general approach could be undertaken. One
approach is to define functional groups or types of biota in terms of
toxicological and bioaccumulation responses. An example of this generic
representation of biological types is presented in Table 7-1. For each
major domain (pelagic, demersal, and infaunal) generic types are
recommended in the table. Table 7-1 also includes columns for the site
specific species which may be of major consideration, the pollutant to be
analyzed, the acute and chronic criterion for that pollutant, and the FDA
7-1
-------
TABLE 7-1
ORGANIZATION OF SPECIES SPECIFIC IMPACT ASSESSMENT
Domain
PELAGIC
DEMERSAL
INFAUNAL
Generic
Type
Phyto-
Plankton
Zoo-
Plankton
Finfish
(Herring)
Crustacean
or
Mollusk
Finfish
(e.g. Cod)
Mollusk
Poly-
chaete
Site
Specific
Species
Pollutant
Acute
Criterion
Chronic
Criterion
FDA
Ti ssue
Limit
7-2
-------
tissue limit (or action level) of that contaminant for the generic type or
the site specific species.
The selection of the pollutants or contaminants of importance for Stage 7
assessment will be identified in Stage 2 where the mean concentration of
constituents measured in the source materials are determined. The
selection procedure of generic or specific species to be analyzed at the
site should first consider harvestable living resources and
protected/endangered species. Individual documents on acute and chronic
values for a specific toxic pollutant on a variety of different species
have been published by EPA for 65 toxic pollutants. Most of these were
published in 1980, however there have been some recent updates. These
documents are entitled Ambient Water Quality Criteria for "name of toxic
pollutant". The Food and Drug Administration (FDA) has developed action
levels for poisonous or deleterious substances in human food and animal
feed (FDA, 1982). The action levels and tolerances represent limits at or
above which FDA will take legal action to remove the products from the
market. Action levels for several substances are given for a variety of
commodities. Fish, shellfish, crustaceans, and other aquatic animals are
listed as a commodity for some of the substances in the publication.
The general assessment procedure requires the use of the basemaps developed
in Stage 3 which show the waste load transport contours for various types
of loading conditions. On these same maps (or on overlay maps) range maps
should be developed for the selected species to show their distribution.
This should be done seasonally and for both juvenile and adult life cycle
stages. A species specific summary table can be constructed for each stage
of development to record the criterion for a specific constituent for
various indicators such as mortality, reproduction, growth rate, and
behavior. An example of such a table is given in Table 7-2.
The potential impacts to be assessed in the upper water column (pelagic
domain) include increased turbidity, nutrient enrichment, oxygen depletion,
toxicological and bioaccumulation effects. The plume model methods
described in Stage 3 and Stage 5 should be used to approximate the spatial
and temporal distribution of the contaminants being investigated. For the
7-3
-------
TABLE 7-2
SPECIES AND CONSTITUENT - SPECIFIC SUMMARY TABLE
SPECIES:
CONSTITUENT:
Indicator
Mortality
Reproduction
Growth Rate
Behavior
Criterion
References
7-4
-------
demersal organisms (those on or near the bottom) an assessment should be
made of the effect of hypoxia, turbidity, toxicity, and bioaccumulation.
For each of the species investigated in these two domains the procedures,
including computations and mapping, discussed in Stages 3 through 6 provide
the methods for estimating these impacts. For burrowing and filter-feeding
infauna the exposure assessment should include not only the dissolved
concentrations but also the sediment absorbed concentrations of the
contaminants. Equation 5-13 can be used to obtain an estimate of the
contaminant concentration in the sediment after a given number of years of
deposition.
7-5
-------
LIMITATIONS
GENERAL DISCUSSION
The Equation Workbook was designed to provide detailed guidance, with
examples, in the use of the equations incorporated into each of the seven
protocol stages for ocean disposal site designation. The procedures and
equations were developed within the limitations of a non-computerized
approach so that the numerical calculations could be carried out on a
hand-held scientific calculator. The overall strategy was to use
conservative assumptions, recognizing that in some instances the simplicity
of the proposed approach might not be adequate for the analysis of highly
complex hydrodynamic and biological situations.
The disposal site designation study is considered to be a general exercise,
requiring a relatively low level of effort, in which a specific site(s) has
been proposed for the disposal of a single class of waste, such as dredged
material, sewage sludge or industrial by-products. This process is
considered to be a first-level evaluation. If the site were found to be
acceptable at this level, a more detailed waste-specific study would follow
as part of the permit application process.
A major limitation inherent to the equations and methods presented in the
protocol is the simplification of complex processes. At times these
simplifications may exclude processes that, under certain situations, would
be very important. Furthermore, the assumptions may not be particularly
applicable to certain disposal operations and waste characteristics. Some
of these cases are discussed below. Simplified procedures may be
appropriate for general disposal site designation studies, disposal site
comparisons based on major physical processes, and estimation of the risk
to biological resources. These procedures, however, may omit some
considerations of the physical behavior of the disposed waste which could
be important in the estimation of areal distribution, settling and initial
mixing.
8-1
-------
The physical behavior of the disposal materials such as dredged material or
sewage sludge may be characterized generically. In addition, the general
behavior of the disposed waste will depend on whether it is neutrally,
negatively or positively buoyant. Although the site designation protocol
is applicable for generic types of waste, many of the procedures and
equations are best suited for dredged materials. The treatment of other
wastes such as acid waste, may necessitate modifications to the general
assumptions in the protocol.
The general limitations discussed above are a result of the use of
simplified and conservative assumptions. In the next section, these
limitations are discussed in more detail for several specific sections of
the protocol.
It is important to bring out the limitations of the protocol presented in
the Preliminary Ocean Waste Disposal Site Designation Manual and in the
Equation Workbook. However, it is not the intent of the Equation Workbook
to offer alternative procedures and numerical calculations for specific
cases which may require modifications to the original assumptions so that a
more detailed analysis can be undertaken. The Equation Workbook offers to
the Corps Districts and EPA Regions a detailed look at equations that are
available for their use in ocean waste disposal site designations.
SPECIFIC LIMITATIONS
Several specific limitations are presented in detail in this section. The
titles and numbers given below correspond to the titles and numbers for the
appropriate stages.
Evaluate and Map Benthic Impact Areas for Negatively Buoyant Solid
Wastes (3.T)
During descent, the disposal cloud falls at a rate determined primarily by
its total mass and size, and entrains water. The cloud would descend to a
"dissipation" depth at which its initial momentum is balanced by en-
trainment. After that, the particles descend approximately with their fall
8-2
-------
velocities 1n the ambient water column. The complete problem is not
simple, and remains to be adequately parameterized (ASA, 1983). Instead,
the conceptually simpler approach of Section 3.3 is used.
If the depth required for dissipation is greater than the total depth of
the site, the vertical momentum will be transferred horizontally and the
cloud will spread out on impact with the bed. Several "rule-of-thumb"
observations are proposed by ASA (1983): (a) one can assume a fall
velocity of 3 m/sec for the main body of the solid waste; (b) for sites as
deep as 100 m, the horizontal displacement from the release point can be
regulated; and (c) for sites of less than 50 m, all the waste will be
deposited within a 200 m radius. It should.be noted that these observa-
tions are for dredged material waste, and will not necessarily apply to
other waste types, such as municipal waste.
It should be further noted that simple disposal models, such as that of Koh
and Chang (1973) can be used to better describe the initial disposal
dynamics for a variety of waste types and ambient water conditions.
A second simplification in this section deals with the estimated area of
impact. Using the maximum tidal components, Utx and Uty, an area is cal-
culated within which all the material is deposited. However, it may give
an average depth of coverage which does not well represent the actual
(near-Gaussian) distribution (Figure 8-1). A better method may be to cal-
culate the area of impact using the average tidal components, 2*Utx/* and
2*Uty/Jt , which will give a greater mean depth, and a closer fit to the
actual distribution in terms of standard deviation (i.e., width, see
Figure 8-1).
Sediment Resuspension Potential for Typical Conditions (3.4)
The techniques used in this section are based on a mean wave condition
using Naval Weather Service Command frequency tables, and neglects the
direct effect of wind-induced currents (except through generation of
waves). In addition, the use of Figure D-7 does not consider cohesive
8-3
-------
Depth
Depth of Coverage Using
Mean Tidal Components
Actual (near-Gaussian)
Distribution
Depth of Coverage
Using Maximum
Tidal Components
Distance
Distance
Area of Impact Using
Mean Tidal Components
Area of Impact Using
Maximum Tidal Components
Figure 8-1. Area of Impact and Depth of Coverage Using Two Different Estimates.
8-4
-------
material which would require higher threshold velocities, Vt, to cause
resuspension, and thus will tend to overestimate the potential to resuspend
in some cases.
There are several alternative approaches one might consider. The U.S. Army
Corps of Engineers uses a significant wave (defined as the average of the
1/3 highest waves) which is tabulated in the Shore Protection Manual
(1977). For sites where little information is available, the Corps
recommends a simple wave generation model to provide estimates of wave
parameters. Further, if a site has known cohesive material, a figure
similar to Figure D-7 would have to be developed to estimate Vt, or else
calculated directly through a knowledge of critical shear stresses.
Resuspension Probability Under Episodic (Storm) Conditions (3.5)
The same comments as for Section 3.4 apply.
Calculate and Map Typical Long-Term Transport Contours (3.7)
The calculations in this section assume that the entire liquid and fine
fraction phases of the waste mix uniformly throughout the water column (as
do the calculations in Stage 4). This assumes no settling of the fine
fraction phase to the bed. Furthermore, it assumes no resuspension of the
settled solids, and no contaminant release, through desorption, to the
overlying water column from the sediment layer.
If these rates are known, from whatever source, they can be easily added to
the estimation of the actual water column loading rates Q or q, which are
used in the calculations of Stages 5 and 6. An alternative to the
assumption of vertical homogeneity, and to perhaps include these other
contaminant sources to the water column, is to use computer disposal
models, some of which have been developed at the U.S. Army COE Waterways
Experiment Station.
Another limitation of this section is the distinction between choosing
continuous and discrete source models. Although a continuous model may be
8-5
-------
suggested by the calculations in Section 3.7.2, it is possible that the
actual disposals may be so infrequent that the previous disposal cloud has
been transported beyond the region of interest before the next disposal
takes place. In that event, it may be advisable to use a discrete source
model.
Initial Dilution of Liquid Phase (4.3)
The mixing formula used in Equation (4-1) is a reasonable approximation for
barge-induced mixing. In this case, the barge is assumed to be moving with
velocity, V, and to dispose the waste in time, t. Alternative formulae
could be used such as those presented by Csanady (1981), IMCO (1975), and
the Corps of Engineers (1977). None of these formulae can be used for a
stationary barge, however, as the dilution will tend to 0, which will tend
to ignore initial disposal dynamics.
Source Strengths and Initial Conditions (4.4)
The assumption in this section is that the liquid and fine fractions of the
waste are uniformly mixed throughout the entire water column. This may not
be the case. For dredged wastes, the initial cloud dynamics may penetrate
a shallow pycnocline (<40 m, for example) and mix the waste only in the
lower water column. For municipal, chemical, and acid wastes, the waste is
much closer to the density of sea water and the seasonal, or shallow,
pycnocline will often impede or prevent the waste penetrating to the lower
water column.
As a first approximation, one could perhaps assume complete mixing in the
lower water column for dredged wastes, and in the upper water column above
the seasonal pycnocline for these other wastes. If more detailed knowledge
of the waste characteristics and dynamics is available, it should be used
to modify procedures in this Workbook.
8-6
-------
Vertical Distribution of Constituent Concentrations (4.5)
The techniques In this section consider mixing processes Into the sediment
layers underlying the deposited solid fraction of the waste. Sources to
the overlying water column, through resuspension, desorption, and
diffusion, are neglected.
Near Field Acute Exposure Level (5.3)
The concentration of a constituent in the water column after disposal
(Equation 5-1) is a function of the barge volume, volumetric solid fraction
of waste, the concentration of the constituent in the waste and the initial
mixing volumes. Equation 5-1 does not adequately consider the mixing
characteristics of the waste itself and this may not be applicable in all
cases. For example, viscous materials such as rum distillery or some
pharmaceutical wastes disperse slowly in water. Other types of waste, such
as iron acid waste, flocculate in seawater and do not settle or disperse
readily. A more reliable prediction of the concentration of a constituent
in the water column will be obtained by modifying Equation 5-1 to take this
type of situation into account.
8-7
-------
REFERENCES
ASA, 1983. A Preliminary Ocean Waste Disposal Site Designation Manual by
Applied Science Associates, Inc. for U.S. Environmental Protection Agency,
Criteria and Standards Division. Washington, D.C.
Brooks, N.H., 1960. Diffusion of Sewage Effluent in an Ocean Current.
Proc. First Int'l. Conf. Waste Disposal in the Marine Environment,
Berkeley, Calif. July 1959, pp. 246-267.
Carslaw, M.S. and J.C. Jaegar, 1959. Conduction of Heat in Solids, Second
Edition, Oxford University Press, London, U.K.
Csanady, G.T., 1973. Turbulent Diffusion in the Environment. D. Reidel
Publishing Company, Dordrecht, Holland.
Csanady, G.T., 1981. An Analysis of Dumpsite Diffusion Experiments. In:
Ocean Dumping of Industrial Wastes (Ketchum, Kester and Park, eds.), Marine
Science 12, Plenum Press, New York, N.Y., pp. 109-129.
Fair, et al., 1968. Water and Wastewater Engineering, Volume 2. John
Wiley 1 Sons, Inc., New York.
FDA, 1982. Action Levels for Poisonous or Deleterious Substances in Human
Food and Animal Feed. Food and Drug Administration, Bureau of Foods,
Washington, D.C.
Fischer, H.B., E.J. List, R.C.Y. Koh, J. Imberger, and N.H. Brooks, 1979.
Mixing in Inland and Coastal Waters, Academic Press, 483 pp.
IMCO, 1975. Procedures and Arrangements for the Discharge of Various
Liquid Substances; Method for Calculation of Dilution Capacity in the
Ship's Wake. International Maritime Consultative Organization document,
MEPC III/7.
Koh, C.Y. and Y.C. Chang, 1973. Mathematical Model for Barged Ocean
Disposal of Wastes. Prepared for U.S. EPA by Tetra Tech Inc., Pasadena,
Calif., 178 p.
Madson, O.S. and W.D. Grant, 1976. Sediment Transport in the Coastal
Environment. Ralph M. Parson Laboratory Report No. 209, M.I.T., Cambridge,
Mass., 105 p.
Malisoff, 1982. Mathematical Models of Bioturbation. Ch. 7 in Animal-
Sediment Relations, The Biogenic Alteration of Sediments (P.L. McCall and
M.J.S. Tevesz, eds.), Plenum Press, New York, N.Y.
Okubo, A., 1971. Oceanic Diffusion Diagram. Deep Sea Research, 18.
-------
Reed, M. and V.J. Blerman, 1983. Proceedings of a Workshop for the
Development of a Scientific Protocol for Ocean Dump Site Designation.
Edited by Mark Reed, Applied Science Associates, Inc. and Victor J.
Blerman, Jr., U.S. Environmental Protection Agency, for U.S. Environmental
Protection Agency, Criteria and Standards Division, Washington, D.C.
U.S. Army Corps of Engineers, 1977. Shore Protection Manual. Coastal
Engineering Research Center, 3rd edition, 3 volumes.
U.S. Environmental Protection Agency/U.S. Army Corps of Engineers, July
1977. Technical Committee on Criteria for Dredged and Fill Material.
Environmental Effects Laboratory, U.S. Army COE Waterways Experiment
Station, Vicksburg, Miss.
-------
APPENDIX A
CROSS-REFERENCE TABLE OF EQUATIONS
IN PRELIMINARY MANUAL AND EQUATION WORKBOOK
-------
CROSS-REFERENCE TABLE OF EQUATIONS
IN PRELIMINARY MANUAL AND EQUATION WORKBOOK1
Equation Number in Equation Number in
Preliminary Manual EQUATION Equation Workbook
(2-1) Cws = 2 Ci * Fi (2-1)
1=1, n
(3-1) Uw = (H /T)/sinh(2 h/L) (not included)
(3-2) L -541 (3-4)
(3-3) L1 =
(3-4) L'new = L< * L (3-6)
(3-5) Utot = Ubm + Ut + Uw (3-8)
(3-6) Vtnew = Vt - Ubm - Ut (3-11)
(3-7) Lx = Utx * ^4 *-jr (3-16a)
Ly = Uty * I * - (3-16b)
(3-8) Dx = 0.0018 * Lx (3-17a)
Dy = 0.0018 * Ly (3-17b)
This table only lists those equations that are numbered in the
Preliminary Manual. Some equation variables have been changed in the
Wookbook for clarification. Some equations are deleted from Workbook
because they were only references to theory which is applied by other
equations that are included.
A-l
-------
Equation Number in
Preliminary Manual
EQUATION
Equation Number in
Equation Workbook
(3-9)
(4-1)
(4-2)
(4-3)
C(x,y)
d * (4* * Dy * Urn * x)
172
(3-18)
exp
Urn
"* *
Dy * x
(3-10) C(x,y,t) »
41* d * (Dx * Dy)1/2 * t
(3-19)
exp
(3-11) C(x,y,t) =
-(x - Um*t)'
4 * Dy
2
Dy * t
- x + Um*t
erf
(4 * Dx * t)
T72,
(3-20)
erf/ 7
+ x - Um*t
* *
Dx
erf
f-y
erf
k(4 * Dy * t)1/2/ \(4 * Dy * t)
Vm = d * (2w) * v * t
Dl =
FT * Vb
7m
Ds =
* Vb * Ff * Ffs
Ym
172
(4-1)
(4-4)
(4-5)
A-2
-------
Equation Number in
Preliminary Manual
EQUATION
Equation Number in
Equation Workbook
(4-4)
(4-5)
(4-6)
(4-7)
* [FI + (Fs * Ff * Ffs)]
(4-6)
Fwl =(!-!!£)* [F1 + (Fs * Ff * Ffs)] (4-7)
Fwt = Fwu + Fwl
C(z,t) =
(;
(5-1)
(5-2)
(5-3)
(5-4)
(5-5)
(5-6)
(5-7) q(i)
ELi = f.
2*D
Mi
t Y" * cr/ \
* D / exp\4 * D * tl
X n
(4-8)
l(4-ll)
X V
* erfc ( - ?
\(4 * D *
fi * Css
BLi
to =
t =
w * v * t
16 * (Dx*Dy)1/2
(5-3)
(5-7)
ELi * Vm
^ * d * D * C = 4;r * d * D * WQCi
..(5-8)
MVi * Qa
q " 3600*24*365 * Tdd * (fi*Cs + 1.0)
ci(o,t) = cod) + Qd)
1/2
(5-10)
(5-13)
C1
A * 100
Co(i) + Qd) *
(5-12)
/2
fi * Scs
(5-14)
A-3
-------
Equation Number in
Prelimi nary Manual
EQUATION
Equation Number in
Equation Workbook
(6-1) BODis = 0.0314 * BODw * Co * W * (ta)1/2
(6-4)
(6-1) dd = dwd * fv * sg (part) * (1-Ffs) * ^ * 1000 (6-2)
(6-3) BODrs = BODw * (I - exp(-5 * k))
(6-5)
(6-4) BODa = BODu + BODrs
(6-6)
(6-6) BODd = BODa +
BODw
(6-7)
(6-7) BODult = 1.46 * BODd
(6-8)
,, ft\ nn< -
(6-8) DOi -
(6-10) OS =
* Vm) + (DOw * Vb)
Vm + Vb
erf
1/2
(6-9)
(6-10)
(6-9) D0(t) = DOa -[DOa - DOi + BODult * (1 - exp (-k * t))] * DS
* exp(-k * t)
* di * D * t
>n
(6-14) DODn = [x(i) - x(i-H)] *
1=1,n-1
exp(-k * t)
+ exp(-k * t)
(6-11)
(6-13)
expj1 dtj * dt)) <«-
14)
(6-15)
A-4
-------
Equation Number in Equation Number in
Preliminary Manual EQUATION Equation Workbook
(6-16) TOD = X DOOj (6-16)
A-5
-------
APPENDIX B
DSP FORMS
-------
FORM DSP1 BASIC SITE CHARACTERIZATION INFORMATION
. 1
Variable Name
Site Center Latitude
Longitude
Width
Length
Orientation of Longest Dimension
.Site Shape
Distance to Nearest*
(1) Coastline
(2) Fishery Area
(3) Recreational Area
(4) Shipping Lane
(5) Military Exclusion Zone
(6) Ocean Disposal Site
(7) Marine Sanctuary
(8) Engineering Uses of Seafloor
(Specify)
(9) Living Resources
Value
Units
N
W
km
km
km
km
km
km
km
km
km
km
Source/Comments
Assigned
Assigned
Assigned
Assigned
Assigned
Assigned
*From closest site extremity, not from site center
B-l
-------
FORM DSP2 WASTE SOURCE AND LOADING CHARACTERIZATION
1I| Comments
I Value | Units I (Text Symbol)
Variable Name
Waste Type
Annual Loading Rate
Typical Duration of Dredging
Operation
Typical Number of Disposals
per day
Bulk Specific Gravity
Liquid Phase Specific Gravity
Particle Specific Gravity
Clay-Silt/Sand-Gravel (Fine/
Coarse) Fractions (Total
Solid Phase)
Volumetric Solid/Liquid
Fractions
Fraction of Fines in Suspended
Cloud (Single Disposal)
Disposal Vessel
Vol ume
Width
Length
Speed
Individual Disposal
Duration
Frequency
Dredge r
later ial
m3/yr
fraction
of year
none
none
none
none
none
none
m3
m
m
m/sec
sec
per day
(Qa)
(Tdd)
(Dd)
(sg) bulk
default: 1.0 (sg)
particle
default: 2.65
( sg) particle
(Ff/Fc)
(Fs/Fl)
default: 0.9
(Ffs)
(Vb)
(w)
(1)
(V)
(t)
B-2
-------
FORM DSP3 REPRESENTATIVE WASTE PROFILE DESCRIPTION
(Mean Concentration of Constituents Measured in Source Materials,
all concentrations in mg/kg)
Fractional
Contribution
(Fi)
Constituent
Percent Sol ids
BOD
DO
pH
Total Chlorinated HC
Total Volatile
Orgam'cs
Cadmium
Copper
Lead
Mercury
Source
A
Source
B
Source
C
Source
D
Source
E 1
Weighted
Sum
(Cws)
1.00
B-3
-------
FORM DSP4 GEOCHEMICAL SITE CHARACTERIZATION
Constituent
or
Characteristic
Percent Sol ids
Biochemical Oxygen Demand (BOD)
Dissolved Oxygen (DO)
pH
Total Chlorinated HC
Total Volatile Organics
Cadmium
Copper
Lead
Mercury
.
SEDIMENTS ONLY:
Percent Gravel
Percent Sand
Percent Silt
Percent Clay
Water Column
(Parts per Mill ion or
Summer
Site Sediments
mg/kg, Except Solids)
Winter
B-4
-------
FORM DSPS PHYSICAL OCEANOGRAPHIC CHARACTERIZATION
Variable Name
Maximum Depth
Minimum Depth
Mean Depth
Pycnocl ine Depth
Tidal Period
Ellipse Orientation
Major Axis Velocity
Minor Axis Velocity
Mean Net Surface Drift
Magnitude
Direction
Mean Net Bottom Drift
Magnitude
Direction
Mean Wave
Amp! itude
Period
Storm Induced Bottom Current
Water Temperature (Annual
Range
pH (Annual Range)
Value
Units
m
m
m
m
hr
m/sec
m/sec
m/sec
m/sec
m
sec
m/sec
degrees
Celsius
Source/Comments 1
(Text Symbol) |
(h)
(hp)
(To)
(Utx)
(Uty)
(Urn)
(Ubm)
(H)
(T)
(Usw)
(T)
B-5
-------
FORM DSP6 WATER QUALITY CRITERIA COMPARISONS SUMMARY
Substance
Copper
Lead
Concentration
Estimated
ppb
Near Field
(Acute)
Criterion
ppb
WQAi
Far Field
(Chronic)
Criterion
ppb
.
WQCi
B-6
-------
APPENDIX C
TABLES
(From Reference ASA, 1983)
-------
ASA
1/12/93
TAaLE C-l
EPA SALTWATER QUALITY CRITERIA SUMMARY
(ppb or micrograms/Iiter)
SUBSTANCE
Arsenic ( ~3 )
Cadmium
C fi * c m i u m ( - 6 )
Coo 3 ?r
LeaS
.»* a r IJT \j
N i : < e i
Zinc
Arenas ntr.ene
A 1 -3 r i ri
Antimony*
C n lorinated
Benzenes
Ch 1 or- a form*
DDT
-DE
DDE
D e i 1 d r i n
Dithlorosrooane
Ere a s u 1 ran
Enc r i n
cl'joranthene
H»D tac h 1 o^
Heracn lorotiutad iene
°C3 (Auroclor)
Psnta Chlorcohenoi
Phtrtalats Es^ars
Tetrachloroethu Iene
To 1 uene
Toxeohene
V i n u i Chloride
24 HOUR
AVERAGE
LEVEL
(CHRONIC )
A. 5
IS
4. 0
50
0. 025
7. 1
5S
97
610
129
1240
0. 0010
0. 0019
790
0. OO87 .
0. OO23
16
0. 0036
0. 030
34
3. 4
45O
300O
0. 071
MAXIMUM
ALLOWABLE
(ACUTE)
08
59
1260
25
67
3. a
137
170
SCO
1. 3
9, OOO
160
2S, 900
0 13
3. 6
14
0. 71
10, 300
0 034
0 037
40
0 053
32
>10. 0
53
2944
12- 200
6300
KL'MAN
HEALTH »*
( INGE5TICN
OF
ORGANISMS
ONLY)
1. 75 no /I
10
50
25
146 .
100
5000
20
45. 000
20
1. 57
0. C024 nq/1
14, 100
15 =
1. 0
54
0 C29 -ia/1
5
30
1. S
o aa
424, 000
52. 5
ACSCRSED-
DISSOLVED
PARTITION
CCEFr.
220, 000
130, COO
420, OOO
350, COO
1 1-50, OOC
* fresnuat»r data only
<* These criteria aoply to water containing organisms
ic n may be
consumed by humans, and take into consideration
bioaccumulation potential of the substance.
the
-------
TABLE C-2
ERROR FUNCTION (erf) AND
COMPLEMENTARY ERROR FUNCTION (erfc)
3.0.)
-------
PUCENI FREQUENCY OF WAVE HEICMI cm vs WAVE PCRIUU (SECONDS)
(SEC)
6-7
1-9
10-11
12-1)
lOTil
<1 1-2 »-< 5-6 1 «-9 lO-»« I* 13-16 1
V.6 2>.S i».8 2-6 1.0 .» .1 1 1 !
.9 1J.6 I.B 1.9 ,« I ,6 J . ,*J
I '.i | rH !i rV.i !e .1 i .1
.0 I .T .1 ».l -2 1 .1
.0 .1 -0 .0 .1 .5 < <
9.0 .S .7 .1 .1 « -0 0 «
1*21 2079 1^66 906 >7i 2«9 ISJ 92 97
silt . 3 and
7-1., 1
.0
.1
.1
.0
.0
, 16
a-u 11-1
.0 .(
.1
.0
.0
.0 .(
7
.1
i
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> .0
.0
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A
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.0
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.0
.0
o
0
. 0
9- 60 1
.0
.0
.0
.0
.0
.0
.0
0
0
1-70 1
.0
.0
.0
.0
.0
.0
.0
0
0
1-66
.0
.0
.0
.0
.0
.0
.0
0
.0
67, TOUl
.0 110*
.0 160S
.0 76)
.0 )<*
.0 1)0
.0 U9
.0 616
0 7(,10
0 1OO-0
HO I
2
6
7
10
0
Table C~to. l-:.xani|>le U.S. Naval Wc:aLluM S<;rvict; SSMO UaLa Table
(lU)sLon a lea)
Lines lor ieiuis|)ens ion thresholds tor sand and sill are superimposed
for a site depth of 2^ melers, usiiuj Ficjures C-H and C-'J.
-------
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MIC!
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100.0
Tub It; C-'Jf. l'x le from I lie National 'rocliiilc.il
In formal ion Sri v Ire (NI'IS) in Washington D.C.
-------
Dissolved Oxygen Saturation, mq/1
Tenser jtur a
'° C'
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c. 7
'able C-4. Dissolved oxygen saturation values
in relation to salinity
(Source: Tetra Tech, Inc., 1982
and temperature
-------
corrt-
xptl laced
chemical !o« ^*B lo« K*
hepcachlor
<°:" -5:55
<°-3 = -0-3 =
Too -°'32
.3SB <0.32 -0.32
FWA-2-A <0.32 0.48
FV/A-3-A <0.32 0.16
FWA-4-A <0.32 -0.12
nitrobenzene 1.13 1.51
p-nttrophenoi 2.10 1.59
naphthalene 2.53 2.27
chiorobenzene 2.55 2.47
2.4.5-'.nchlorophenol 3. 23 2.40
endrin 3.17 3.24
1.1.2.2-tetrachloroethylen« 1.59 1.56
hexacnlorobenzene 3.39 3.91
p-diphenylyl phenyl ither 2.74 4.23
dipnenyl «ther 2.29 2.39
carbon :etrichlorsde 1.24 1.32 _ . , ,
2.33 2.2i zxperinental ar.d r.oce.-
2.64 lie correlated biocor.cer.t r a:
cnioropyrifo* 2.S7 3.50 c ,-..,.-- v r^^ , . . . . ^ ^ . .
2.5.5-'..-:chloropyndinol 0.49 0.03 ' "" ' " . ' 3 'I' ' 7 '--'-'
r.urene 3. 3.0 cr.emicals. ,he value -..:
3.ii 3.06
dibenzofuran 3.13 2.80 U5 e ~QT 0 i C magn i f i C at i O ;
2-chioropnen«nthrene 3.63 3.84 _,--,. -I..;,-,. ;- ....a«
pnen.nthrene 3.42 3.14 w d . - ai d >. * w ..a .3 s - - - . - -.
2-me'.ny iphenanthrene 3.48 3.54
heptacmor epoxide 4.15 4.08
?.? -DDE 4.71 4.37
pentachiorophenol 2.39 3.59 , ^ ^ , .
h«xaoromobiph«nyl 4.25 5.07 \frCi7l MaC.\ay, 1 r 3 . .1
mechoxychior 3.92 3.76
.T.irex 4.26 4.34
hexabromocycJododecane 4.2S 4.49
hexachiorocyc!open(adiene 1.47 4.19
hepcachloronorOornene 4.05 3.96
hexachioronorbornaaiene 3*. 31 3.96
A/ocior lOl^S 4.53 4.56
Aroclor 1243 4.35 . 4.79
Arocior 1254 5.00 5.15
Aroclor 1260 5.29 5.59
chlordane 4.53 4.58
octacnloro«tyr«nt 4.52 4.97
p,p -DDT 4.47 4.43
a.p'-DDT 4.57 4.43
1,2,4-triehlorobenzene 3.32 2.91
5-bromotndole 1.15 1.55
2.4.5-cribromoanisole 2.94 3.16
jV-phenyl-2-naphthylamine 2.17 3.06
tri*(2.3-dibromopropyi) 0.44 3.66
phosphate
:ricresyi phoiphatt 2.22 2.10
chlor-.nated ecoiane 1.53 5. 73
diphenylamine 1.43 2.10
toluenediamine 1.96 1.34
chloroform 0.78 0.63
aeenaphthene 2.59 2.60
benz(a)anthracene 4.00 4.29
1.2.3.5-trichlorobenzene 3.26 3.14
tnfluralin 3.76 4.02
pyrene 3.43 3.56
9-methy!inthracene 3. 66 3.75
benzene 1.10 0.79
anthracene 2.98 3.02
4 chlorodiphenyl oxide 2.37 2.75
4-chlorobiphenyl 2.77 2.94
pencachlorobenzene 3.70 3.37
dieldrin 4.11 4.16
-------
APPENDIX D
FIGURES
(From Reference ASA, 1983)
-------
Figure
0-1
o*t 10 it 12 is
12
10
«
4
4
2
0
z
ta
ii
1<
12
10
a
«
4
2
0
2
12
30
;s
is
a
22
20
i«
l«
14
12
10
8
t
4
I
0
2
\/
221: mil. N.
is i« 17 is 19 :o
1 T7
* FRANCISCO
I W . \/i V :
A' >l A A A
/ \J\J W V4
f .** V V v ,\
\/ \ /
! 1
SCATTUE
XETCHIKAN
WOT
ftfH
/ v\ 7
-V-
$m
fc
i
t '
I |
'
DUTCH HARBOR
A
i
»: Uil
234.
( from Notional Octon Sgr»rj, NOAA , Tidi
Typical Tide Curves Along Pacific Coasts of the
United States (Source: U.S. Army Coascai Engir.e
Research Cancer , 1973)
ering
-------
Figure D-2
OAT 10 II U
11
10
U 19 I* 17 II if 20
HAMPTON *OAO$
ni
A7\ A .l \ A /\-A~A A /\ /VA / \i/\ / \i A /' /\ I
v
ft
yry v: v v v ^ v v y \y y V \7 TV y
MC
SAVANNAH *IVC* tNTB
A
^^
:tS
-^
ptHSAcem !
gAtvcrroM
II 1 i 1
W^?
i
Ml. 1.
Z3i.
( from Notional Oeton S»r»t j, NOAA, Tiai TOOIII)
Typical Tide Curves Along Atlantic and
Gulf Coasts (Source: U.S. Arr.y Coasral
Research Cancer, 1973)
-------
Figure D-3
Oregon-Washington
Jen Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mean Monthly Nearshore Wave Periods (Including Calms) for Five
Coastal Segments (Source: 'J.5. ArT.y Coastal Engir.eerir.g
Ceacar, 1973)
-------
Figure D-4
Oregon-Washington
Atlantic (south)-*-
1 I
Atlantic (north)
Jan
Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mean Monthly Nearshore Wave Heights for rive Coastal Segnents
(Source: U.S. Arny Ccascal Engineering Research Cenzer, 1972)
-------
Figure D-5
Mem Wa«« Height it Co.cia
Location
Mean Anno.i
Vive Height (ft.)
Lortlilir* of Conierminoua United Suica
, . Mein Annual
Luutinn _, ,, , !
|Wtv« Hei^nt (ft.) !
Atlantic COMI
Mini*
MOOJC Peak
>tw Himpaiure
Hampton Bcadi
MaaMcJiuMlta
INjuart
Cipe Cod
Rhode laiand
Point judilh
MiM|u«mieut
New York
Southampton
*'c«tliam|iton
Jonet Beach
Sliort [Veaeli
New Jer»ey
Monmoutli
Deal
Tom« River
Brigantine
Atlantic City
1.3
1.4
1.3
2.5
1.3
1.4
1.9
2.6
2.6
1.7
i.r
2J
2.0
1 «»
2.8
TAllanlicCity (BEP1 1.3
tAllanlic City 'CO 1 1.9
>« Jency (com.)
l.ndlani Itland
Maryland
Ocean Cljr
Vlrpni*
AiMlcaijue
Virginia Ocich
Virfinia Beach
Nort]> Carolina)
Mag* Mead
Ntf* Head
WrigiidviHe
Oak laland
lloldrn Ueacii
Georgia
St. Simon laland
Florida
'Diytona Beach
Ponce deLeon
Lake Worlli
Pilm Be*cli
Ituca Raton
Hilltboro
1.9
1-3
2.6
1.3
2.0
3.0
3.9
2.3
1.2
1.7
0.4
1.9
* ^
2.3
2.3
1.9
1.3
CuJf Coajt
Florida
."
t CIRC &«*CA £»iiu«oo«
(fuwbrtiktt) obnrrttiooi.
(Source: U..S. Army Coascai Engineering Research Center, 1973)
-------
Figure D-6
Wenfworth Scale
(Size Description)
Boulder
Cobble
Pebble
Granule
Sand
Very Coarse
Coarse
Medium
Fine
Very Fine
Silt
Clay
Colloid
Grain
Diameter
d (mm)
256
76.2
64.0
19.0
4.76
4.0
2.0
1.0
0.5
0.42
0.25
0.125
0.074
0.0625
0.00391
0.00024
U-S. Standard
Sieve Size
3 in.
s/4 in.
No. 4
No. 10
No. 40
No. 200
Unified Soil
Classification
(USC)
1
Cobble
Coarse
Fine
. Coarse
Medium
Fine
Gravel
Sand
Silt or Clay
Grain Size Scales (Soil Classification)
(Source: U.S. Army Coascal Zr.gir.eerir.g
Research Center, 1973)
-------
Figure D-7
1000
10 I02
SIZE OUMETES IN MICRONS
10'
Current velocities required to transport particulates
(Source: Poscaa. 1967)
-------
Wave lit-ij;lit (ft)
-6
6-7
S 8-9
to
i) 10-11
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Fiy. D-8. W.ive Induced Sedimc'iit Suspension
sediment s i ze -O.'I^U mm (mini i inn saiul)
(Suture: A|i|)lii'tl Sc iuuro Assnf i
-------
Wave llei.jjlil (ft)
-6
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6-7
8-9
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2-1 J
1 3f
Fifj. D-10. W.ivo Induced Si,-d iiniMil SuspiMiiJ ion
sfdim.'nl size - 0.001 mm (clriy)
(Source: A|)|)lloil Sr icii« c- Assix i .il >; , I
-------
CLAY CD « 0.001 nun)
20 30
40
90
100
U (cm/sec)
m
Figure D-ll.
Volumetric sediment transport rate versus
mean flow for various wave - induced bcttcr.
velocities.
(Source: Applied Science Associacas, Ir.c.)
-------
in
10S
105
4,
10'
ic3
in2
r
C
c
L
r
F
f
u
to
C
r
L
L
k
F
C
1
r ,<:
r >"" :
J.= LOOcr./sec ,..^>
r " .^;^'
c /^y
L /. ' t{ y
i / ' ''''f
\ 'f/
-- r
SILT (D = 0.033 mm;
20 en/sec
lo1 t-
.. L
30
70
U (cm/sec)
m
Figure D-12. Volumetric sediment transport rate ve:
mean flow for various wave-induced bo1
velocities.
(Source: Applied 5cier.ce Associacas, lac.)
3 us
-------
VERY FINE SAND (D = 0.074.
.=.CCcn/sacX
2
:0cr./sec
20
50
50
60
70
30
U (c m / 5 e c)
.-igure D-13.
Volumetric sediment transport rate ve
mean flew for various wave - induced bo
velocities.
(Source: Applied Science Associates, Inc.)
-------
10
10'
s _
10
1 * w
FINE SAND (D = 0. Id7 mm)
:J -LCOcn/sec.'
10° Ir
10
10°
-'J
40
oO
/ 0
Figure D-14.
U (cm/s e c)
m
Volumetric sedimsr.t transport rate versus
mean flow for various wave-induced bottcm
velocities.
(Source: Applied Science Associates, Inc.)
-------
:crj io
O»meier cm
D-15. Settling velocities of discrete spherical
particles in cuiescent water at IOC. /Fro
Fain et al . , 1963) Settling velocitv -...-ill
" 1 ' ^ a -
'U. i. - y " - -1
temperature.
(Source: Fair, ec al, 1963)
increase about 1.> per degree ncrease
-------
APPENDIX E
SUGGESTED SOURCES FOR DATA AND INFORMATION
-------
The reports and publications denoted by "*" are recommended reading for all
designation efforts. Others are suggested as additional sources of data or
information. This section is Appendix D in ASA (1983).
Butson, K.D. and W.L. Hatch, 1979. Selective Guide to Climatic Data
Sources. U.S. Department of Commerce, National Oceanic and Atmospheric
Administration, 142 pp.
Center for Natural Areas, 1977. A Summary and Analysis of Environmental
Information on the Continental Shelf from the Bay of Fundy to Cape
Hatteras, 3 Volumes, U.S. Department of the Interior. Bureau of Land
Management.
Csanady, G.T., 1973. Turbulent Diffusion in the Environment. D. Reidel
Publishing Company, Dordrecht, Holland, 248 pp.
EPA/COE, 1977. Technical Committee on Criteria for Dredged and Fill
Material. Environmental Effects Laboratory, U.S. Army Engineer
Waterways Experiment Station, Vicksburg, Miss.
*GESAMP, 1982. Scientific Criteria for the Selection of Waste Disposal
Sites at Sea. IMCO/FAO/UNESCO/WMO/IAEA/UN/UNEP Joint Group of Experts
on the Scientific Aspects of Marine Pollution. Reports and Studies No.
18. Intergovernmental Maritime Consultative Organization.
*Goldberg, E.D. (ed.), 1980. Assimilative Capacity of U.S. Coastal Waters
for Pollutants. Crystal Mount, Washington, July 29-August 4, 1979. UTS'.
Dept. of commerce, National Oceanic and Atmospheric Administration,
Env'l. Res. Lab., Boulder, Colorado. Proceedings of Workshop, 284 pp.
Harris, D.L., 1981. Tides and Tidal Datums in the United States. U.S.
Army Corps of Engineers, Coastal Engineering Research Center, Fort
Belvoir, Va., 382 pp.
Komar, P.O., 1976. Beach Processes and Sedimentation. Prentice-Hall,
Inc., Englewood Cliffs, New Jersey, 429 pp.
*MTS (Marine Technology Society), 1982. Marine Pollution Papers.
Reprinted from the Marine Pollution Sessions of OCEANS '82 Conference
Proceedings by the NOAA Office of Marine Pollution Assessment,
Rockvllle, Md. 20852. (M.A. Champ or R.L. Swanson) pp. 995-1189.
*Pequegnat, W.E., D.D. Smith, R.M. Darnell, B.J. Presley, and R.O. Reid,
1978. Art Assessment of the Potential Impact of Dredged Matrlal Disposal
in the Open Ocean"U.S. Army Corps of Engineers, Vicksburg, Miss., 635
pp.
Stanley, D.J. and D.J.P. Swift, 1976. Marine Sediment Transport and
Environmental Management. John Wiley & Sons, N.Y., 602 pp.
E-l
-------
U.S. Army Coastal Engineering Research Center, 1973. Shore Protection
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E-2
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