4.1 Resident

Exposure to Settled Dust on Outdoor Surfaces

The resident is exposed to contaminated dust settled on outdoor surfaces. The resident spends some time inside and some time outside. Three exposure routes are presented: (1) exposure to contamination deposited on surfaces via incidental ingestion, (2) inhalation of resuspended particulates, and (3) external exposure to ionizing radiation from dust settled on contaminated surfaces. For the portion of the time that the resident is indoors, this equation includes an indoor air dilution factor for inhalation and a gamma shielding factor for external exposure.

Graphical Representation

SPRG Equations

These scenarios evaluate age-adjusted incidental ingestion, age-adjusted inhalation of particulates, and external exposure to ionizing radiation from settled dust using ground plane toxicity values.

Ingestion

Inhalation with PEF _wind

Inhalation with PEF _mechanical

Inhalation with PEF _wind for State-Specific

Inhalation with PEF _mechanical for State-Specific

External

Total

Definitions of the input variables are in Table 1.

CDI Equations

These scenarios evaluate age-adjusted incidental ingestion, age-adjusted inhalation of particulates, and external exposure to ionizing radiation from settled dust using ground plane toxicity values.

Ingestion

Inhalation with PEF _wind

Inhalation with PEF _mechanical

Inhalation with PEF _wind for State-Specific

Inhalation with PEF _mechanical for State-Specific

External

Definitions of the input variables are in Table 1.

3-D External Exposure to Dust on Outdoor Surfaces

Graphical Representations

The resident is exposed to gamma radiation on outdoor surfaces. The only pathway considered is external exposure to ionizing radiation. It is assumed that the street (horizontal) and the building walls (vertical) on both sides of the street are radioactively contaminated.

SPRG Equations

This scenario evaluates fixed contaminated dust on surface of outside walls, streets, and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate fixed contaminated dust on building materials of outside walls, streets, and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

CDI Equations

This scenario evaluates fixed contaminated dust on surface of outside walls, streets, and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate fixed contaminated dust on building materials of outside walls, streets, and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

2-D External Exposure to Dust on Outdoor Surfaces

Graphical Representations

The resident is exposed to gamma radiation from settled dust on finite slabs. The only pathway considered is external exposure to ionizing radiation. It is assumed that the dust on the finite slab (horizontal) is radioactively contaminated. It is also assumed the resident lives in a structure built on top of the middle of the slab.

SPRG Equations

This scenario evaluates fixed contaminated dust on surfaces of outside streets and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane toxicity values

These scenarios evaluate contaminated building materials of streets and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

CDI Equations

This scenario evaluates fixed contaminated dust on surfaces of outside streets and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane toxicity values

These scenarios evaluate contaminated building materials of streets and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

4.2 Composite Worker

Exposure to Settled Dust on Outdoor Surfaces

The composite worker is comprised of the most protective exposure parameters from the indoor and outdoor worker land uses. Three exposure routes are presented: (1) exposure to contamination deposited on surfaces via incidental ingestion, (2) inhalation of particulates, and (3) external exposure to ionizing radiation from dust settled on contaminated surfaces.

Graphical Representation

SPRG Equations

These scenarios evaluate incidental ingestion, inhalation of particulates, and external exposure to ionizing radiation from settled dust using ground plane toxicity values.

Ingestion

Inhalation with PEF _wind

Inhalation with PEF _mechanical

Inhalation with PEF _wind for State-Specific

Inhalation with PEF _mechanical for State-Specific

External

Total

Definitions of the input variables are in Table 1.

CDI Equations

These scenarios evaluate incidental ingestion, inhalation of particulates, and external exposure to ionizing radiation from settled dust using ground plane toxicity values.

Ingestion

Inhalation with PEF _wind

Inhalation with PEF _mechanical

Inhalation with PEF _wind for State-Specific

Inhalation with PEF _mechanical for State-Specific

External

Definitions of the input variables are in Table 1.

3-D External Exposure to Dust on Outdoor Surfaces

Graphical Representations

The composite worker is exposed to settled dust on outdoor surfaces. The only pathway considered is external exposure to ionizing radiation. It is assumed that the street (horizontal) and the building walls (vertical) on both sides of the street are contaminated with settled dust.

SPRG Equations

This scenario evaluates fixed contaminated dust on surface of outside walls, streets, and sidewalks using ground plane toxicity values

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate fixed contaminated dust on building materials of outside walls, streets, and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

CDI Equations

This scenario evaluates fixed contaminated dust on surface of outside walls, streets, and sidewalks using ground plane toxicity values

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate fixed contaminated dust on building materials of outside walls, streets, and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

2-D External Exposure to Dust on Outdoor Surfaces

Graphical Representations

The composite worker is exposed to settled dust on finite slabs. The only pathway considered is external exposure to ionizing radiation. It is assumed that the dust on the finite slab (horizontal) is radioactively contaminated.

SPRG Equations

This scenario evaluates fixed contaminated dust on surfaces of outside streets and sidewalks using ground plane toxicity values.

These scenarios evaluate contaminated building materials of streets and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

CDI Equations

This scenario evaluates fixed contaminated dust on surfaces of outside streets and sidewalks using ground plane toxicity values.

These scenarios evaluate contaminated building materials of streets and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

4.3 Outdoor Worker

Exposure to Settled Dust on Outdoor Surfaces

The outdoor worker is exposed to contaminated dust settled on outdoor surfaces. The outdoor worker spends his entire shift outside. Three exposure routes are presented: (1) exposure to contamination deposited on surfaces via incidental ingestion, (2) inhalation of particulates, and (3) external exposure to ionizing radiation from dust settled on contaminated surfaces.

Graphical Representation

SPRG Equations

These scenarios evaluate incidental ingestion, inhalation of particulates, and external exposure to ionizing radiation from settled dust using ground plane toxicity values.

Ingestion

Inhalation with PEF _wind

Inhalation with PEF _mechanical

Inhalation with PEF _wind for State-Specific

Inhalation with PEF _mechanical for State-Specific

External

Total

Definitions of the input variables are in Table 1.

CDI Equations

These scenarios evaluate incidental ingestion, inhalation of particulates, and external exposure to ionizing radiation from settled dust using ground plane toxicity values.

Ingestion

Inhalation with PEF _wind

Inhalation with PEF _mechanical

Inhalation with PEF _wind for State-Specific

Inhalation with PEF _mechanical for State-Specific

External

Definitions of the input variables are in Table 1.

3-D External Exposure to Dust on Outdoor Surfaces

Graphical Representations

The outdoor worker is exposed to settled dust on outdoor surfaces. The only pathway considered is external exposure to ionizing radiation. It is assumed that the street (horizontal) and the building walls (vertical) on both sides of the street are contaminated with settled dust.

SPRG Equations

This scenario evaluates fixed contaminated dust on surface of outside walls, streets, and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate fixed contaminated dust on building materials of outside walls, streets, and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

CDI Equations

This scenario evaluates fixed contaminated dust on surface of outside walls, streets, and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate fixed contaminated dust on building materials of outside walls, streets, and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

2-D External Exposure to Dust on Outdoor Surface

Graphical Representations

The outdoor worker is exposed to settled dust on finite slabs. The only pathway considered is external exposure to ionizing radiation. It is assumed that the dust on the finite slab (horizontal) is radioactively contaminated.

SPRG Equations

This scenario evaluates fixed contaminated dust on surfaces of outside streets and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate contaminated building materials of streets and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

CDI Equations

This scenario evaluates fixed contaminated dust on surfaces of outside streets and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate contaminated building materials of streets and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

4.4 Indoor Worker

Exposure to Settled Dust on Outdoor Surfaces

Graphical Representation

SPRG Equations

These scenarios evaluate incidental ingestion, inhalation of particulates, and external exposure to ionizing radiation from settled dust using ground plane toxicity values.

Ingestion

Inhalation with PEF _wind

Inhalation with PEF _mechanical

Inhalation with PEF _wind for State-Specific

Inhalation with PEF _mechanical for State-Specific

External

Total

Definitions of the input variables are in Table 1.

CDI Equations

These scenarios evaluate incidental ingestion, inhalation of particulates, and external exposure to ionizing radiation from settled dust using ground plane toxicity values.

Ingestion

Inhalation with PEF _wind

Inhalation with PEF _mechanical

Inhalation with PEF _wind for State-Specific

Inhalation with PEF _mechanical for State-Specific

External

Definitions of the input variables are in Table 1.

3-D External Exposure to Dust on Outdoor Surfaces

Graphical Representations

The outdoor worker is exposed to settled dust on outdoor surfaces. The only pathway considered is external exposure to ionizing radiation. It is assumed that the street (horizontal) and the building walls (vertical) on both sides of the street are contaminated with settled dust.

SPRG Equations

This scenario evaluates fixed contaminated dust on surface of outside walls, streets, and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate contamination on building materials of outside walls, streets, and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

CDI Equations

This scenario evaluates fixed contaminated dust on surface of outside walls, streets, and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

These scenarios evaluate contamination on building materials of outside walls, streets, and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

2-D External Exposure to Dust on Outdoor Surfaces

Graphical Representations

The indoor worker is exposed to settled dust on finite slabs. The only pathway considered is external exposure to ionizing radiation. It is assumed that the dust on the finite slab (horizontal) is radioactively contaminated. It is also assumed the worker is employed in a structure built on top of the middle of the slab.

SPRG Equations

This scenario evaluates fixed contaminated dust on surfaces of outside streets and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

Definitions of the input variables are in Table 1.

These scenarios evaluate contaminated building materials of streets and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

CDI Equations

This scenario evaluates fixed contaminated dust on surfaces of outside streets and sidewalks using ground plane toxicity values.

Contaminated building materials using ground plane external exposure toxicity values

Definitions of the input variables are in Table 1.

These scenarios evaluate contaminated building materials of streets and sidewalks using various soil volume toxicity values.

Contaminated building materials using 1 cm soil volume toxicity values

Contaminated building materials using 5 cm soil volume toxicity values

Contaminated building materials using 15 cm soil volume toxicity values

Contaminated building materials using infinite soil volume toxicity values

Definitions of the input variables are in Table 1.

4.5 Exposure Parameter Justification

The following sections describe the exposure parameter default variables and the values selected.

4.5.1 Exposure Time (ET)

The exposure time represents the hours per day that a receptor spends exposed to a source. The exposure times vary by exposure scenario, age of the receptor, and whether the source is located on a hard or soft surface. This calculator only calculates exposure to hard surfaces. For the resident ingestion pathway, the hard surface exposure time of 4 hours per day is used for adult and child. This value is from the EPA Office of Pesticide Programs (OPP). For inhalation and external exposure, the exposure time indoors is set at 16.4 hours per day, and the exposure time outdoors is set at 1.752 hours per day. These values are from the 1997 Exposure Factors Handbook. Note that inhalation and subsequent ingestion of dust particles trapped in mucous is not quantified in the SPRG equations due to lack of exposure information.

For the outdoor and indoor worker, exposure time for the dust ingestion exposure route is based on exposure to hard surfaces. For this calculator, the defaults were set at 8 hour/day. The exposure time for direct external exposure is the entire work day or 8 hour/day.

4.5.2 Fraction Transferred from Surface to Skin (FTSS)

In general, this is the fraction of residue on a surface that can be transferred to skin. U.S. EPA 2003 (pg D-5) states that hand press experiments were conducted on dry skin. Transfers of 50% were observed for hard surfaces. These are considered representative of the WTC situation and were adopted for this calculator.

4.5.3 Surface Area (SA)

In general, this is the skin area contacted during the mouthing event. The OPP recommended default was based on the surface area of the 3 fingers that a child will most likely use for hand to mouth transfer. It was assumed that 3 fingers of one hand represents about 5% of the total area of both hands (U.S. EPA 2003). The exposure factor handbook (U.S. EPA 2011 Table 7.2) presents hand surface areas for adults and children. For children, the surface areas were time-weight averaged across all age groups from birth to 6 years (317 cm²,) and the 5% assumption was applied to derive the child hand surface area of 16 cm².

The hand surface area for the adult was also derived from data presented in the exposure factor handbook (U.S. EPA 2011 Table 7.2), which presents hand surface areas for adult males and females of 1070 and 890 cm², respectively. These numbers were averaged (980 cm², and the 5% assumption was applied to derive the adult hand surface area of 49 cm².

4.5.4 Frequency of Hand to Mouth (FQ)

The exposure factors handbook (U.S. EPA 2011 Table 4-1) and the world trade center report (U.S. EPA 2003) provide hand to mouth contact rates for many age groups. For the child FQ, all age groups for mean outdoor and indoor contact from birth to 6 years old were time-weight averaged from the exposure factor handbook. Missing data points were substituted with data from the nearest age group. The outdoor FQ for children was determined to be 10 times/hour, and indoor FQ was determined to be 17 times/hour.

For the adult FQ, all age groups for mean outdoor and indoor contact from 6 to 26 years old were time-weight averaged from the exposure factor handbook and world trade center report. The outdoor FQ for adults was determined to be 2 times/hour. The indoor FQ for adults was determined to be 3 times/hour. The composite worker uses the outdoor FQ.

4.5.5 Saliva Extraction Factor (SE)

In general, the fraction transferred from skin to mouth will depend on the contaminant, mouthing time, and other behavioral patterns. The OPP default is 50%, based on pesticide studies. Michaud et al (1994) assumed that all of the residues deposited on the fingertips would be transferred to the mouth twice per day. In the Binghamton re-entry guideline derivation, a range of factors were used (0.05, 0.1, and 0.25) representing the fraction of residue on hand that is transferred to the mouth (Kim and Hawley 1985). For the purposes of this assessment, the OPP default of 50% was selected for all ages.

4.5.6 Resident Age-Adjusted Dust Ingestion Rate (IFD_r)

To account for the variability in exposure activities between children and adults, the age-adjusted dust ingestion rate equation was developed. This equation takes into account the differences in hand to mouth behavior, hand surface area, and exposure to hard and soft surfaces over the exposure durations of an adult and child.

4.5.7 Worker Dust Ingestion Rate (IFD_w)

This dust ingestion equation calculates the intake for a worker based on exposure to hard surfaces.

4.5.8 Dissipation Rate Constant (k)

In some circumstances, the load of dust on a contaminated surface to which receptors are exposed may decline over time. Dissipation of dust may result from weather, cleaning, and transfer to skin and clothing. Different surfaces may be cleaned at different rates; any dissipation rate used should consider a representative cleaning frequency. To determine whether dissipation is a factor at a given site, the site manager should establish whether a significant reservoir of contaminated dust is present. Such reservoirs may function as sources of dust and negate the impacts of dissipation mechanisms. The first step in identifying the presence of a reservoir is to examine site history. If a waste site was created through disposal, deposition, or equipment leaks over an extended period of time, then the contaminant may have seeped deep into the surface. Porous surfaces such as cement or wood are also more likely to have subsurface contamination. When reservoirs are less likely to exist, such as at sites where contamination is the result of a single spill, dust cloud, or event, it may be more important to account for dissipation of surface loads. For fixed contamination in materials (outside walls, streets, and pavement) or on material surfaces in the 3-D and 2-D equations, the dissipation term is not included, as dissipation is not expected.

The recommended default value for the dissipation rate constant is 0.0. This assumes that a contaminant reservoir is present. The variable is adjustable in the SPRG calculator, however. If a dissipation rate constant is used, it is assumed that the dust was deposited as a one-time event (i.e., dust cloud). Also, if a dissipation rate is applied, it is assumed that it is applicable from the point in time the SPRG is calculated into the future. The discussion below provides a review of the indoor surfaces literature related to this issue and provides an alternative dissipation rate constant value. Site-specific outdoor dissipation rate constants can be used. This equation is for values of k that are greater than 0; when k=0, the dissipation term is not quantified to avoid division by zero. See the following text.

Based on many indoor studies presented in U.S. EPA 2003 (pg. D-5), there is strong support for considering dissipation in setting criteria for outdoor building clean-ups. A study of the Binghamton State office Building found that dioxin has dissipated over time according to first order kinetics with a 20-22 month half-life. Even though this was an indoor study, the same principles would apply for outdoor surfaces. This dissipation is thought to occur from a combination of cleaning, resuspension, and dilution with uncontaminated dust (and possibly some volatilization). These same physical dissipation processes would apply to other compounds addressed in this study as well. Therefore, the other compounds were assumed to dissipate at the same rate as dioxin. In summary, a 22 month half-life (dissipation rate constant of 0.38 year ^-1) was adopted. Exposures were calculated in a series of time steps where the residue level was assumed to dissipate according to first order kinetics:

CSL = CSL_initial e^-kt
CSL = Contaminant Surface Load (ug/cm²)
CSL_initial = Initial Contaminant Surface Load (ug/cm²)
k = Dissipation Rate Constant (year^-1)
t = Time (year)

This SPRG calculator computes a concentration of contaminants in dust that will not exceed a target risk. The equation above simply derives the amount of dust. For this SPRG calculator, the only parts of the above equation that are relevant are the dissipation rate constant and time. By putting these variables in the denominator of the recommended SPRG resident and worker ingestion of dust equations, a higher recommended SPRG concentration would be calculated.

Further evidence that care should be taken in selecting a dissipation rate comes from the classic example of leaded gasoline. According to "The Role of Resuspended Soil in Lead Flows in the California South Coast Air Basin", the soil lead concentration is still over 6 times the baseline lead level from 1919 to 1933 levels. Despite leaded gasoline being phased out from 1967 to 1970 (40 years ago), the lead dissipation rate in soil is not expected to reach a steady state for more than 100 years.

Users of this website should note that dissipation rates may vary for different types of hard surfaces due to traffic exposure, weather exposure, material, etc. Andersson (2002) provides details of dissipation on streets, walls, and roofs of outdoor hard surfaces.

Dissipation rates may differ greatly from pre-remediation to post-remediation, because readily remediated material may dissipate more quickly than residual materials.

WARNING: Using a dissipation rate constant or changing the value of t should only be done once a complete understanding of the mathematics involved in deriving the equation is gained and the site conditions have been fully investigated. Exhibit 1 displays the results obtained by changing the value t. t is equal to ED in all equations.

In the simplified SPRG equation: SPRG=TR/CDI*SF*(1-e^(-kt))/(kt), where SPRG is preliminary remediation goal, TR is target risk, CDI is chronic daily intake, SF is the radionuclide-specific slope factor, and (1-e^(-kt))/(kt) is the dissipation term, Exhibit 1 shows the results of changing t. Exhibit 2 shows the results of changing k.

Exhibit 1. Results Obtained By Changing The Value t.

t	k	SF	CDI	TR	(1-e(-kt))/(kt)	SPRG
year	year-1	risk/pCi	cm2	risk	unitless	pCi/cm2
0	0.38	1.00E-05	400	1.00E-06	1.00E+01	2.5E-04
1	0.38	1.00E-05	400	1.00E-06	8.32E-01	3.01E-04
2	0.38	1.00E-05	400	1.00E-06	7.00E-01	3.57E-04
3	0.38	1.00E-05	400	1.00E-06	5.97E-01	4.19E-04
4	0.38	1.00E-05	400	1.00E-06	5.14E-01	4.86E-04
5	0.38	1.00E-05	400	1.00E-06	4.48E-01	5.59E-04
6	0.38	1.00E-05	400	1.00E-06	3.94E-01	6.35E-04
7	0.38	1.00E-05	400	1.00E-06	3.50E-01	7.15E-04
8	0.38	1.00E-05	400	1.00E-06	3.13E-01	7.98E-04
9	0.38	1.00E-05	400	1.00E-06	2.83E-01	8.84E-04
10	0.38	1.00E-05	400	1.00E-06	2.57E-01	9.72E-04
11	0.38	1.00E-05	400	1.00E-06	2.36E-01	1.06E-03
12	0.38	1.00E-05	400	1.00E-06	2.17E-01	1.15E-03
13	0.38	1.00E-05	400	1.00E-06	2.01E-01	1.24E-03
14	0.38	1.00E-05	400	1.00E-06	1.87E-01	1.34E-03
15	0.38	1.00E-05	400	1.00E-06	1.75E-01	1.43E-03
16	0.38	1.00E-05	400	1.00E-06	1.64E-01	1.52E-03
17	0.38	1.00E-05	400	1.00E-06	1.55E-01	1.62E-03
18	0.38	1.00E-05	400	1.00E-06	1.46E-01	1.71E-03
19	0.38	1.00E-05	400	1.00E-06	1.38E-01	1.81E-03
20	0.38	1.00E-05	400	1.00E-06	1.32E-01	1.90E-03
21	0.38	1.00E-05	400	1.00E-06	1.25E-01	2.00E-03
22	0.38	1.00E-05	400	1.00E-06	1.20E-01	2.09E-03
23	0.38	1.00E-05	400	1.00E-06	1.14E-01	2.19E-03
24	0.38	1.00E-05	400	1.00E-06	1.10E-01	2.28E-03
25	0.38	1.00E-05	400	1.00E-06	1.05E-01	2.38E-03
26	0.38	1.00E-05	400	1.00E-06	1.01E-01	2.47E-03
27	0.38	1.00E-05	400	1.00E-06	9.75E-02	2.57E-03
28	0.38	1.00E-05	400	1.00E-06	9.40E-02	2.66E-03
29	0.38	1.00E-05	400	1.00E-06	9.07E-02	2.76E-03
30	0.38	1.00E-05	400	1.00E-06	8.77E-02	2.85E-03

Exhibit 2. Results Obtained By Changing The Value k.

t	k	SF	CDI	TR	(1-e(-kt))/(kt)	PRG
year	year-1	risk/pCi	cm2	risk	unitless	pCi/cm2
30	0.000001	1.00E-05	400	1.00E-06	1.00E+00	2.50E-04
30	0.033331	1.00E-05	400	1.00E-06	6.32E-01	3.95E-04
30	0.066661	1.00E-05	400	1.00E-06	4.32E-01	5.78E-04
30	0.099991	1.00E-05	400	1.00E-06	3.17E-01	7.89E-04
30	0.133321	1.00E-05	400	1.00E-06	2.45E-01	1.02E-03
30	0.166651	1.00E-05	400	1.00E-06	1.99E-01	1.26E-03
30	0.199981	1.00E-05	400	1.00E-06	1.66E-01	1.50E-03
30	0.233311	1.00E-05	400	1.00E-06	1.43E-01	1.75E-03
30	0.266641	1.00E-05	400	1.00E-06	1.25E-01	2.00E-03
30	0.299971	1.00E-05	400	1.00E-06	1.11E-01	2.25E-03
30	0.333301	1.00E-05	400	1.00E-06	1.00E-01	2.50E-03
30	0.366631	1.00E-05	400	1.00E-06	9.09E-02	2.75E-03
30	0.399961	1.00E-05	400	1.00E-06	8.33E-02	3.00E-03
30	0.433291	1.00E-05	400	1.00E-06	7.69E-02	3.25E-03
30	0.466621	1.00E-05	400	1.00E-06	7.14E-02	3.50E-03
30	0.499951	1.00E-05	400	1.00E-06	6.67E-02	3.75E-03
30	0.533281	1.00E-05	400	1.00E-06	6.25E-02	4.00E-03
30	0.566611	1.00E-05	400	1.00E-06	5.88E-02	4.25E-03
30	0.599941	1.00E-05	400	1.00E-06	5.56E-02	4.50E-03
30	0.633271	1.00E-05	400	1.00E-06	5.26E-02	4.75E-03
30	0.666601	1.00E-05	400	1.00E-06	5.00E-02	5.00E-03
30	0.699931	1.00E-05	400	1.00E-06	4.76E-02	5.25E-03
30	0.733261	1.00E-05	400	1.00E-06	4.55E-02	5.50E-03
30	0.766591	1.00E-05	400	1.00E-06	4.35E-02	5.75E-03
30	0.799921	1.00E-05	400	1.00E-06	4.17E-02	6.00E-03
30	0.833251	1.00E-05	400	1.00E-06	4.00E-02	6.25E-03
30	0.866581	1.00E-05	400	1.00E-06	3.85E-02	6.50E-03
30	0.899911	1.00E-05	400	1.00E-06	3.70E-02	6.75E-03
30	0.933241	1.00E-05	400	1.00E-06	3.57E-02	7.00E-03
30	0.966571	1.00E-05	400	1.00E-06	3.45E-02	7.25E-03
30	1	1.00E-05	400	1.00E-06	3.33E-02	7.50E-03

4.5.9 Dermal Exposure

Other possible exposure pathways to be considered in a radiological analysis of contaminated outside surfaces would include internal contamination due to puncture wounds and dermal absorption of radionuclides deposited on the skin. The radiation doses caused by these two pathways, however, would be de minimis and much smaller than the doses caused by the other potential pathways already considered for most radionuclides (Kennedy and Strenge 1992 in Section 3.1.2). Therefore, dermal pathways are not included in the current version of this SPRG calculator. If one desires to calculate dermal risk, one method would be to calculate the dose based on either adherence of dust/soil to dry or wet skin. The mobility of the radionuclide, the range of the emitted beta particles, and the assumed exposure parameters could be used to determine the percentage contribution of each component to the total calculated risk. The partitioning coefficient (Kd) of the beta-emitting radionuclide of concern could be used to determine the significance of the sweat layer. If this value approaches zero, then contaminated soil particulates are expected to dissolve, and diluted concentrations should be estimated from the original soil concentrations. If Kd is greater than zero, then the range of the emitted beta particles becomes the most important factor in determining if the radionuclide yields an unacceptable dose. If the range exceeds the average distribution of the sweat layer, then risk calculations are generally warranted. The dry deposition scenario typically dominates the whole exposure interval. Otherwise, the radionuclide is shielded by the sweat layer, and the corresponding indirect deposition contributions to the total risk are negligible.

4.5.10 Silt Loading Factor

It is assumed that dust is being resuspended from the road surface. The amount of dust on an area of road is called the silt loading factor (SLF). For this calculator, a default value of 0.015 g/m² was selected from 2011 National Emissions Inventory, version 1 Technical Support Document June 2014 - DRAFT , Table 63, Page 104, concerning paved roads. This value, combined with the California annual vehicle kilometers traveled by length of California interstates, resulted in the most protective PEF. Multiple SLFs were given for specific circumstances. The values range from 0.015 to 0.6 g/m². The Table is reproduced below. The SLFs for urban collector roadway class are used for both major and minor collector roadway classes found in annual vehicle kilometers traveled by the length of each roadway class. Also, rural interstate roadway class SLFs were used for the "other freeways and expressways" roadway class. The SLF used in the risk equations is the inverse of 0.015 g/m² converted to units of cm²/kg.

To obtain more accurate SPRG results, the SLF should be measured in the field. Table 13.2.1-3 from AP42 is reproduced below showing the high end typical industrial facility SLF ranges. The values range from 0.09 to 400 g/m². AP 42 suggests the following:

"Limited access roadways pose severe logistical difficulties in terms of surface sampling, and few silt loading data are available for such roads. Nevertheless, the available data do not suggest great variation in silt loading for limited access roadways from one part of the country to another. For annual conditions, a default value of 0.015 g/m² is recommended for limited access roadways. Even fewer of the available data correspond to worst-case situations, and elevated loadings are observed to be quickly depleted because of high traffic speeds and high ADT rates. A default value of 0.2 g/m² is recommended for short periods of time following application of snow/ice controls to limited access roads."

The default state road class and road type, the California urban interstate, yields a mechanical PEF of 1.86 × 10⁶ using a SLF of 0.015 g/m². This was chosen as the default for this calculator to produce more protective default SPRGs; however, selecting a site-specific state and roadway class will provide a more accurate SLF and VKT. The United States Department of Transportation's Federal Highway Administration maintains an interactive HEPGIS website that supplies a map of the 50 States and Puerto Rico depicting functional roadway classes. The user can use the zoom controls to reach the area of interest. This resource could be consulted to apply site-specific inputs for calculating VKT and SLF for a risk assessment. The color classification schemes are general indicators of functional classes. Roadways are presented for the National Highway system, Eisenhower System, and Federal Highway Administration. A brief description of the classifications are given in here and a detailed description is here. Further state-specific information can be found by consulting the representatives found on this contact list.

The image and table below depict the color schemes.

NHS Classification	Color (NHS)	Eisenhower Classification	Color (Eisenhower)	FHWA Functional Classification (Rural)	Color (FWHA Rural)	FHWA Functional Classification (Urban)	Color (FWHA Urban)
Interstate Highways	Blue	Interstate Highways	Red	Interstate	Blue	Interstate	Blue
MAP-21 Principal Arterials	Black	Principal Arterials	Dark Red	Other Principal Arterial	Red	Other PrincipalArterial	Red
Other NHS Route	Red
Non-Interstate STRAHNET	Brown
Major STRAHNET Connector	Green
NHS Intermodal Connector	Purple
Intermodal/STRAHNET Connectors	Orange
		Minor Arterials	Orange	Minor Arterial	Green	Minor Arterial	Green
		Major Collectors	Yellow	Major Collector	Purple	Major Collector	Purple
		Minor Collectors	Light Yellow	Minor Collector	Yellow or Orange	Minor Collector	Yellow or Orange
		Local Roads	White	Local	Gray	Local	Gray
		Freeways and Expressways	Blue	Other Freeways and Expressways	Brown	Other Freeways and Expressways	Brown

4.5.11 Area Correction Factor

The RAGS/HHEM Part B model assumes that an individual is exposed to a source geometry that is effectively an infinite slab. The concept of an infinite slab means that the thickness of the contaminated zone and its aerial extent are so large that it behaves as if it were infinite in its physical dimensions. In practice, soil contaminated to a depth greater than about 15 cm and with an aerial extent greater than about 1,000 m² will create a radiation field comparable to that of an infinite slab (U.S. EPA. 2000a).

Since the assumption of an infinite slab source will result in overly protective PRGs for most residential settings, an adjustment for source area is considered to be an important modification to the RAGS/HHEM Part B model. Thus, an area correction factor, ACF, has been added to the calculation of recommended PRGs. For the 2-D exposure models addressing finite areas, the ACF is made variable by isotope and area for site-specific analysis. In addition, ACFs are now available for all alternate soil analysis source depths (ground plane, 1 cm, 5 cm, 15 cm, and infinite source volume). This calculator allows the user to select from 19 different soil area sizes. If the default mode is selected, the ACF from the most protective area size is selected. If site-specific mode is selected, the user must select the source area. For further information on the derivation of the isotope-specific/area-specific ACF values for 2-D areas see the Center for Radiation Protection Knowledge ACF report and appendix containing +D and +E values. For the calculation of soil area correction factors, a standard soil density of 1.6 g/cm³ has been used. For a description of other EPA default ACF values that predate this guidance, follow the link here.

4.5.12 Street Surfaces Factor F_s-surf

The 3-D direct external exposure equations (building materials and dust) without F_s-surf are single surface equations. The surfaces factor, in the default and site-specific equations, are based on exposure to two vertical surfaces (outside building surfaces on either side of a street) and a horizontal surface (road and sidewalk). This calculator uses the relationship between the dose rate coefficients for exposures in a contaminated outdoor setting and dose rate coefficients for an infinite source to calculate a surfaces factor (F_s-surf). The dose quantity evaluated is the air kerma rate one meter above the sidewalk. The outdoor surfaces are assumed to be contaminated to the same level. Locations in the midpoint of the sidewalk, next to the buildings, and in the middle of the street for building heights of 12.5, 30, 59, 150, and 200 feet were modeled to account for the dose contribution from multiple surfaces. Further, photon energies of each radioisotope were incorporated into the modeling. Please see the attached PDF file for a detailed explanation of the process. Side Walk Dose Rate shows that building height doesn't effect the dose rate significantly after 150 feet. The above link shows a table of the F_s-surf values used in this calculator for each radioisotope. F_s-surf values were calculated for each position-specific and building-height specific combination.

4.5.13 Radionuclide Decay Constant (λ)

The decay constant term (λ), which is based on the half-life of the isotope, is used for some media in nearly all land uses. λ = 0.693/half-life in years (where 0.693=ln(2)). The term (1 - e^-λt) takes into account the number of half-lives that will occur within the exposure duration to calculate an appropriate value. For the secular equilibrium SPRG output option, decay is not used. In most cases, site-specific analytical data should be used to establish the actual degree of equilibrium between each parent radionuclide and its decay products in each media sampled. In the absence of empirical data, however, the secular equilibrium SPRGs will provide a protective screening value. Definitions of the input variables are in Table 1.

4.5.14 Gamma Shielding Factors (GSF)

A default gamma shielding factor for indoor exposure to ionizing radiation (GSF_i) is established at 0.4 (60% shielding).

A default gamma shielding factor for outdoor exposure to ionizing radiation on surfaces (GSF_s) is established at 1 (0% shielding).

4.6 Supporting Equations

The above land use equations require further explanation for particulate emission factors.

4.6.1 Particulate Emission Factors (PEFs)

Two types of particulate emission factors are presented in this calculator: mechanically driven and the traditional wind driven emission factor.

4.6.1.1 Mechanically Driven PEF for Paved Public Roads

These equations allow the user to change site dimensions, distance traveled, mean vehicle weight, road dimensions, particle size multiplier, time, and number of rain days. These equations can be used to simulate emission factors after an incident. The receptor is assumed to be exposed to contaminants in the form of particulate matter with an aerodynamic particle diameter of less than 10 microns (PM₁₀). Fugitive dust emissions are generated by vehicle traffic on paved roads.

The following fugitive dust emission equations represent approximations of actual emissions at a specific site. Sensitive emission model parameters include the soil silt content and mean vehicle weight. Silt is defined as soil particles smaller than 75 micrometers (Fm) in diameter and can be measured as that proportion of soil passing a 200-mesh screen, using the American Society for Testing and Materials (ASTM) Method C-136. Mean vehicle weight is presented in tons. The default value is 3.2 tons, but site-specific values can be used. In general, silt loading and mean vehicle weight are the most sensitive model parameters for which default values have been assigned; however, site-specific values will produce more accurate modeling results. Other emission model parameters have not been assigned default values and are typically defined on a site-specific basis. These parameters include the total distance traveled by vehicles, average vehicle speed, and the area of roadway.

Mean vehicle weight (W) in tons is calculated by determining vehicle weight classes and numbers in that class. An example is presented below for site-specific data. The default mean vehicle weight selected for this calculator is 3.2 tons, based on page 4-285 in Procedures Document for National Emission Inventory, Criteria Air Pollutants 1985-1999. EPA-454/R-01-006. There is wide variation in vehicle weights when considering industrial facilities. AP42 supporting documentation reveals in Table A1-6 that the mean vehicle weight can range up to 42 tons. Site-specific conditions should be considered or measured. The table is reproduced below.

W = [(20 cars × 2 tons/car) + (10 trucks × 20 tons/truck)]/30 vehicles = 8 tons mean vehicle weight.

Sum of vehicle kilometers traveled during the exposure duration, ∑VKT, is estimated based on the size of the area of the contamination, the configuration of the road, and amount of traffic. The default ∑VKT is based on California urban interstate statistics. The value of 2,683,117 kilometers was calculated by multiplying the length of contaminated surface(L_S) by the annual vehicle kilometers divided by the total number of kilometers of that road class. This number is then multiplied by the ED. These values resulted in the most protective PEF. The area of the site contamination is assumed to be a square. Therefore, the square root of the area gives the distance traveled in the contaminated area. A half-acre site is 0.002024 km². The square root is 0.045 km. For the site-specific option of the calculator, the ∑VKT is determined as presented below.

VKT = 30 vehicles × 0.045 km/trip × ps/day × 26 weeks/year × 5 days/week × 25 years (ED) d = 5265 km.

The table below is taken from AP42 for Paved Roads and gives values for k.

4.6.1.1.1 State-Specific Equation for Mechanically Driven PEF for Paved Public Roads

Below is the equation used to determine the state-specific and default mechanical PEF for public paved roads. In state-specific mode, the site dimensions, mean vehicle weight, road dimensions, particle size multiplier, time, and number of rain days can be changed. The state, geographic setting, and roadway class must be selected for the equation to operate. The default PEF is based on data for California.

4.6.1.1.2 Site-Specific Equation for Mechanically Driven PEF for Paved Public Roads

Below is the equation used to determine the site-specific mechanical PEF for public paved roads. The site dimensions, road dimensions, particle size multiplier, number of rain days, silt loading factor, mean vehicle weight inputs, time, and ∑VKT inputs can be changed.

4.6.1.2 Mechanically Driven PEF for Unpaved public Roads

This equation allows the user to change emission factor for fleet exhaust, brake and tire wear, silt percentage, silt moisture content, mean vehicle speed, site dimensions, distance traveled, mean vehicle weight, road dimensions, particle size multiplier, time, and number of rain days. The receptor is assumed to be exposed to contaminants in the form of particulate matter with an aerodynamic particle diameter of less than 10 microns (PM10). Fugitive dust emissions are generated by vehicle traffic on unpaved public roads.

The following fugitive dust emission equation represents approximations of actual emissions at a specific site. Sensitive emission model parameters include the soil silt percentage, silt moisture content, and mean vehicle speed. Silt is defined as soil particles smaller than 75 micrometers (µm) in diameter and can be measured as that proportion of soil passing a 200-mesh screen, using the American Society for Testing and Materials (ASTM) Method C-136. Soil moisture content is defined on a percent gravimetric basis [(g-water/g-soil) × 100] and should be approximated as the mean value for the duration of the construction project. In general, soil silt and moisture content are the most sensitive model parameters for which default values have been assigned;, however, site-specific values will produce more accurate modeling results. Other emission model parameters have not been assigned default values and are typically defined on a site-specific basis. These parameters include the site dimensions and average vehicle speed.

The silt moisture content default is 7.9%; however, moisture can range from 0.03 to 13%, according to AP42 section 13.2.2-3 on unpaved roads. There is wide variation in moisture content when considering industrial facilities. Table 13.2.2-3 is presented below.

Sum of vehicle kilometers traveled during the ED, ∑VKT, is estimated based on the size of the area of the contamination, the configuration of the road, and amount of traffic. There is not a default value for this equation. This equation is only accessible in the site-specific option. The VKT can be determined on a site-specific basis by following the example presented below.

VKT = 30 vehicles × 0.045 km/trip × 1 trips/day × 26 weeks/year × 5 days/week × 30 years (ED) d = 5265 km.

The table below is taken from AP42 for Unpaved Roads and gives values for k.

The table below is taken from AP42 for Unpaved Roads and gives values for C.

The table below is taken from AP42 for Unpaved Roads and gives values for S.

4.6.1.3 Mechanically Driven PEF for Unpaved Industrial Roads

This equation allows the user to change silt percentage, site dimensions, distance traveled, mean vehicle weight, road dimensions, particle size multiplier, time, and number of rain days. The receptor is assumed to be exposed to contaminants in the form of particulate matter with an aerodynamic particle diameter of less than 10 microns (PM10). Fugitive dust emissions are generated by vehicle traffic on unpaved industrial roads.

The following fugitive dust emission equation represents approximations of actual emissions at a specific site. Sensitive emission model parameters include the silt percentage and mean vehicle weight. Silt is defined as soil particles smaller than 75 micrometers (µm) in diameter and can be measured as that proportion of soil passing a 200-mesh screen, using the American Society for Testing and Materials (ASTM) Method C-136. Site-specific values for mean vehicle weight and silt percentage will produce more accurate modeling results. Other emission model parameters have not been assigned default values and are typically defined on a site-specific basis. These parameters include the total distance traveled by vehicles, mean vehicle weight, and the area of the site.

The silt percentage default is 8.5%; however, percentage can range from 1.8 to 25.2%, according to AP42 section on unpaved roads. There is wide variation in silt percentage content when considering industrial facilities. Table 13.2.2-3 is presented below.

W = [(20 cars × 2 tons/car) + (10 trucks × 20 tons/truck)]/30 vehicles = 8 tons mean vehicle weight.

Sum of vehicle kilometers traveled, (VKT), is estimated based on the size of the area of the contamination, the configuration of the road, and amount of traffic. There is not a default value for this equation. This equation is only accessible in the site-specific option. The VKT can be determined on a site-specific basis by following the example presented below.

VKT = 30 vehicles × 0.045 km/trip × 1 trips/day × 26 weeks/year × 5 days/week × 30 years (ED) d = 5265 km.

The table below is taken from AP42 for Unpaved Roads and gives values for k.

4.6.1.4 Wind Driven PEF

This equation allows the user to select geographical regions and input fraction of vegetative cover and wind speed. Inhalation of isotopes adsorbed to respirable particles (PM10) was assessed using default input parameters. This equation relates the contaminant concentration in soil with the concentration of respirable particles in the air due to fugitive dust emissions from contaminated soils. Regional-specific PEFs are derived using default values that correspond to a receptor point concentration of approximately 0.76 ug/m³. The relationship is derived by Cowherd (1985) for a rapid assessment procedure applicable to a typical hazardous waste site, where the surface contamination provides a relatively continuous and constant potential for emission over an extended period of time (e.g., years). This represents an annual average emission rate based on wind erosion that should be compared with chronic health criteria; it is not appropriate for evaluating the potential for more acute exposures. Definitions of the input variables are in Table 1.

The equation below forms the basis for deriving a generic PEF for the inhalation pathway. For more details regarding specific parameters used in the PEF model, refer to Soil Screening Guidance for Radionuclides: Technical Background Document. The use of alternate values on a specific site should be justified and presented in an Administrative Record if considered in CERCLA remedy selection.

Wind-driven

4.6.2 Decay Functions

The following decay functions should be multiplied by their respective CDI equations when applicable:

The following decay functions should be multiplied by their respective PRG equations when applicable:

4.7 Equation Sources and Parameters

This section presents details on some of the equation sources and parameters.

4.7.1 Exposure to Settled Dust on Surfaces Equations

The inadvertent ingestion from materials deposited on surfaces equation was modeled after the equation found in ANL 2001 (Fig 8.3). The ingestion rate term in this equation was modeled after U.S. EPA 2003 (pg. D-4). External exposure from deposited materials equation was modeled after the equation found in ANL 2001 (Fig 8.7).

4.7.2 Direct External Exposure Equations

The direct external exposure from a volume and surface of a large area equation was modeled after ANL 2001 (Fig 8.6). External exposure from deposited materials equation was modeled after the equation found in ANL 2001 (Fig 8.7).

4.7.2.1 External Exposure Equation Derivation

The external exposure pathway dose from exposure to an area or a volume source containing radionuclide n in compartment i,
, is expressed as:

where:

F_in = fraction of time spent indoors;

F_i = fraction of time spent in compartment i;

=average concentration of radionuclide n;

= FGR-12 dose conversion factor for infinite volume source; and

= geometrical factor for finite area, source thickness, shielding, source material, and position of receptor relative to the source for radionuclide n.

The geometrical factor is the ratio of the effective dose equivalent for the actual source to the effective dose equivalent for the standard source. The standard source is a contaminated soil of infinite depth and lateral extent with no cover. The geometrical factor is expressed as the product of the depth-and-cover factor, F_CD, an area and material factor, F_AM, and the off-set factor, F_OFF-SET.

So,
= effective dose from actual source/effective dose from standard source.

Then,
= F_CD x F_AM x F_OFF-SET.

4.7.2.1.1 Depth-And-Cover Factor (F_CD)

Note: The F_CD would traditionally be included in this type of analysis; however, it is not included in the equations for this calculator. This calculator includes depth-specific dose conversion factors for surface (ground plane) and uniformly distributed volume sources at four specific thicknesses (1, 5, and 15 cm and effectively infinite). Inclusion of these dose conversion factors eliminates the need for the F_CD.

Dose conversion factors in FGR-12 (Eckerman and Ryman 1993) are given for surface and uniformly distributed volume sources at four specific thicknesses (1, 5, and 15 cm and effectively infinite) with a soil density of 1.6 g/cm³. FGR-12 assumes that sources are infinite in lateral extent. In actual situations, sources can have any depth, shape, cover, and size. A depth and-cover factor function, F_CD, was developed with regression analysis to express the attenuation for radionuclides. Three independent radionuclide-specific parameters were determined by using the effective dose equivalent values of FGR-12 at different depths. Kamboj et al. (1998) describes how the depth-and-cover function was derived using the effective dose equivalent values of FGR-12 at different depths. A depth-and-cover factor function was derived from the depth factor function by considering both dose contribution and attenuation from different depths:

where:

A, B = fit parameters (dimensionless);

K_A, K_B = fit parameters (cm²/g);

t_c = shielding thickness (cm) (the sum of all shielding thicknesses between the source and the receptor), the shielding is placed immediately adjacent to the source;

ρ_c= shielding density (g/cm³)(the thickness-averaged density between the source and receptor);

t_s = source thickness (cm);

ρ_s = source density (g/cm³);

T_c = shielding parameter (m); and

T_s = source depth parameter (m).

The following constraints were put on the four fitting parameters:

1. All the parameters were forced to be positive;

2. A + B = 1; and

3. In the limit source depth, t_s → zero, the DCF should match the contaminated surface DCF.

All the four unknown parameters (A, B, K_A, and K_B) were found for 67 radionuclides available in the RESRAD-BUILD computer code. The fitted values of A, B, K_A, and K_B for radionuclides were used in the dose calculations.

4.7.2.1.2 Area-And-Material Factor (F_AM)

For actual geometries (finite area and different materials), the area and material factor, F_AM, was derived by using the point-kernel method. This factor depends not only on the lateral extent of the contamination but also on source thickness, shielding thickness, gamma energies, and source material through its attenuation and buildup factors. All energies from radionuclide decay were considered separately and weighted by its yield, y, energy, E, and an energy dependent coefficient, K, to convert from air-absorbed dose to effective dose equivalent:

where:

(x')² = r² + (t_a + t_c + t)²;

(x)² = r² + (1m + t)²;

B and µ are the buildup factor and the attenuation factor, respectively, for the appropriate material (a for air, c for shield material, and s for source material or soil reference). The integration volume V' is the desired geometry of specified material with radius R, shielding thickness t_c, and air thickness t_a; whereas V is the reference geometry of soil extending infinitely laterally with no shield and the receptor midpoint located 1 m from the surface.

4.7.2.1.3 Off-set Factor ( F_OFF-SET)

The off-set factor, F_OFF-SET, is the ratio of the dose estimates from a noncircular shaped contaminated material to a reference shape. The concept of the shape factor is used to calculate the off-set factor. The reference shape is a fully contaminated circular area encompassing the given shape, centered about the receptor. This factor is derived by considering the area, material factors of a series of concentric circles, and the corresponding contamination fraction of the annular regions. The off-set factor is obtained by enclosing the irregularly shaped contaminated area in a circle, multiplying the area factor of each annulus by the fraction of the contaminated annulus area, f_i, summing the products, and dividing by the area factor of a circular contaminated material that is equivalent in area: