The recommended BDCCs consider human exposure from direct contact with contaminated dust and air and external exposure to contaminated building materials. The equations and technical discussion are aimed at developing concentration levels for risk-based cleanup. Calculation of the recommended BDCCs are based on the BDCC Calculator. The following text presents the recommended land use equations and their exposure routes. Table 1 presents the recommended definitions of the variables and their default values. Any alternative values or assumptions used in remedy evaluation or selection on a CERCLA site should be presented with supporting rationale in the Administrative Record.

4.1 Resident

The recommended BDCC equations for the residential exposure scenario, presented here, contain the following exposure pathways and exposure routes.

4.1.1 Exposure to Settled Dust on Surfaces

The resident is exposed to radioactive contaminants in dust that settles in a building. Exposure is via two exposure routes: external and ingestion. Ingestion of dust occurs when hands contact dust-laden surfaces and then come in contact with the mouth. Variation is allowed for contact with hard and soft surfaces, as the transfer to skin varies on surface type.

Graphical Representation

BDCC Equations

Ingestion:

External:

Total:

The resulting units for this recommended BDCC are in pCi/cm². The units are based on area, because external exposure SF uses ground plane and ingestion route is based on the hand surface area that contacts surface dust and subsequently transfers it from hand to mouth. 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.

CDI Equations

Ingestion:

External:

The resulting units for this recommended CDI are in pCi/cm². The units are based on area, because the SF used is the ground plane for external exposure, and the ingestion route is based on hand surface area contacting dust on surfaces and subsequent hand to mouth transfer events. 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.

Definitions of the input variables are in Table 1.

4.1.2 Exposure to Ambient Air With and Without Half-Life Decay

Ambient air exposure equations are presented below. These equations do not include a half-life decay function. In situations where the contaminant in the air has a continual source (e.g., indoor radon from radium in the soil), these equations should be used.

In situations where the contaminant in the air is not being replenished (e.g., contaminated settled dust from a previous release that is being resuspended), a half-life decay function should be used. These half-life functions are provided is section 4.3.

Residents are exposed to air in the building via two exposure routes. The first exposure route is inhalation of air. Inhalation is assumed to occur for the entire twenty-four hour day. The second exposure route is submersion. Submersion is external exposure from the contaminated air.

Graphical Representation

BDCC Equations

Inhalation:

Submersion:

Total:

CDI Equations

Inhalation:

Submersion:

Definitions of the input variables are in Table 1.

4.1.3 3-D Direct External Exposure

The resident is exposed to the radioactive contaminants in the building materials of the walls, floor, and ceiling.

Graphical Representation

BDCC Equations

Contaminated building materials in walls, floor, and ceiling using soil volume toxicity values

Contaminated building materials in walls, floor, and ceiling using 1cm soil volume toxicity values

Contaminated building materials in walls, floor, and ceiling using 5cm soil volume toxicity values

Contaminated building materials in walls, floor, and ceiling using 15cm soil volume toxicity values

Contaminated dust on walls, floor, and ceiling using ground plane toxicity values

The resulting units for this recommended BDCC are in pCi/cm². The units are based on area, because external exposure SF uses ground plane and ingestion route is based on the hand surface area that contacts surface dust and subsequently transfers it from hand to mouth.

CDI Equations

Contaminated building materials in walls, floor and ceiling using soil volume toxicity values

Contaminated building materials in walls, floor and ceiling using 1cm soil volume toxicity values

Contaminated building materials in walls, floor and ceiling using 5cm soil volume toxicity values

Contaminated building materials in walls, floor and ceiling using 15cm soil volume toxicity values

Contaminated dust on walls, floor and ceiling using ground plane toxicity values

The resulting units for this recommended CDI are in pCi/cm². The units are based on area, because the SF used is the ground plane for external exposure, and the ingestion route is based on hand surface area contacting dust on surfaces and subsequent hand to mouth transfer events.

Definitions of the input variables are in Table 1.

4.2 Indoor Worker

The recommended BDCC equations for the indoor worker exposure scenario, presented here, contain the following exposure pathways and exposure routes:

4.2.1 Exposure to Settled Dust on Surfaces

This worker is exposed to the radioactive contaminants in dust that settles in a building. Exposure is via two exposure routes: external and ingestion. Ingestion of dust occurs when hands contact dust-laden surface and then come in contact with the mouth. Variation is allowed for contact with hard and soft surfaces as the transfer to skin varies on surface type.

Graphical Representation

BDCC Equations

Ingestion:

External:

Total:

The resulting units for this recommended BDCC are in pCi/cm². The units are based on area, because external exposure SF uses ground plane and ingestion route is based on the hand surface area that contacts surface dust and subsequently transfers it from hand to mouth. 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.

CDI Equations

Ingestion:

External:

The resulting units for this recommended CDI are in pCi/cm². The units are based on area, because the SF used is the ground plane for external exposure, and the ingestion route is based on hand surface area contacting dust on surfaces and subsequent hand to mouth transfer events. 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.

Definitions of the input variables are in Table 1.

4.2.2 Exposure to Ambient Air With and Without Half-Life Decay

Ambient air exposure equations are presented below. These equations do not include a half-life decay function. In situations where the contaminant in the air has a continual source (e.g., indoor radon from radium in the soil), these equations should be used.

In situations where the contaminant in the air is not being replenished (e.g., contaminated settled dust from a previous release that is being resuspended), a half-life decay function should be used. These half-life functions are provided is section 4.3.

Workers are exposed to air in the building via two exposure routes. The first exposure route is inhalation of air. Inhalation is assumed to occur for the entire eight hour work day. The second exposure route is submersion. Submersion is external exposure from the contaminated air.

Graphical Representation

BDCC Equations

Inhalation:

Submersion:

Total:

CDI Equations

Inhalation:

Submersion:

Definitions of the input variables are in Table 1.

4.2.3 3-D Direct External Exposure

This worker is exposed to the radioactive contaminants in the building materials of the walls, floor, and ceiling.

Graphical Representation

BDCC Equations

Contaminated building materials in walls, floor, and ceiling using soil volume toxicity values

Contaminated building materials in walls, floor, and ceiling using 1cm soil volume toxicity values

Contaminated building materials in walls, floor, and ceiling using 5cm soil volume toxicity values

Contaminated building materials in walls, floor, and ceiling using 15cm soil volume toxicity values

Contaminated dust on walls, floor, and ceiling using ground plane toxicity values

The resulting units for this recommended BDCC are in pCi/cm². The units are based on area, because external exposure SF uses ground plane and ingestion route is based on the hand surface area that contacts surface dust and subsequently transfers it from hand to mouth.

CDI Equations

Contaminated building materials in walls, floor and ceiling using soil volume toxicity values

Contaminated building materials in walls, floor and ceiling using 1cm soil volume toxicity values

Contaminated building materials in walls, floor and ceiling using 5cm soil volume toxicity values

Contaminated building materials in walls, floor and ceiling using 15cm soil volume toxicity values

Contaminated dust on walls, floor and ceiling using ground plane toxicity values

The resulting units for this recommended CDI are in pCi/cm². The units are based on area, because the SF used is the ground plane for external exposure, and the ingestion route is based on hand surface area contacting dust on surfaces and subsequent hand to mouth transfer events.

Definitions of the input variables are in Table 1.

4.3 Exposure Parameter Justification

The following sections describe the exposure parameters and their default values, which are listed in Table 1.

4.3.1 Exposure Time (ET)

The exposure time represents the hours per day that a receptor spends exposed to a source. Exposure times vary by exposure scenario, age of the receptor, and whether the source is located on a hard or soft surface. The EPA Office of Pesticide Programs (OPP) recommended defaults for a child resident are 8 hr/d for carpets and 4 hr/d for hard surfaces. Hard surface time is based on the estimated time spent in the kitchen and bathroom. Carpet time is based on remaining indoor time not including sleeping. This recommendation was judged to be representative of many children under age 6, who spend most of their time at home. After 18, many individuals will spend more time in school or at work. Others, however, may not work or attend school and spend more time at home. To be protective, it was decided to recommend this second scenario and assume that adult residents would spend 8 hr/d on soft surfaces (carpet, sofa, etc.) and 4 hr/d on hard surfaces. This totals 12 hr/d. Assuming that an individual sleeps 8 hr/d, the total time in a residence is 20 hr/d. For this calculator, the remaining 4 hr/d were equally divided between exposure to hard and soft surfaces. This results in recommended default values of 10 hr/d on carpets and 6 hr/d on hard surfaces for adult and child residents. Ingestion of settled dust while sleeping is considered negligible, because dust doesn't collect between sheets. Note that inhalation and subsequent ingestion of dust particles trapped in mucous is not quantified in the recommended BDCC equations due to lack of exposure information; however, exposure to ambient air and direct external exposure continues during sleep. Additional dust ingestion may occur during food preparation or storage on hard surfaces but is not quantified in the recommended BDCC equations due to lack of exposure information.

For the indoor worker, exposure time for the dust ingestion exposure route is also divided between exposure to hard and soft surfaces. For this calculator, the recommended defaults were set at 4 hr/d for hard and soft surfaces. The recommended exposure time for exposure to ambient air and direct external exposure is the entire work day, or 8 hr/d.

4.3.2 Fraction Transferred from Surface to Skin (FTSS)

In general, this is the fraction of residue on a surface that can be transferred to skin. US EPA 2003 (pg D-5) states that hand press experiments were conducted on dry skin. Transfers of 10% were observed for carpets and 50% were observed for hard surfaces. These recommendations are considered representative of the WTC situation and were adopted for this calculator.

4.3.3 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 (EPA 2003). The exposure factors handbook (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 factors handbook (EPA 2011 Table 7.2). The exposure factor handbook presents hand surface areas for adult males and females of 1070 and 890 cm², respectively. These numbers were averaged to 980 cm², and the 5% assumption was applied to derive the adult hand surface area of 49 cm².

4.3.4 Frequency of Hand to Mouth (FQ)

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

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

4.3.5 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 recommended 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 purposes of this assessment, the OPP recommended default of 50% was selected for all ages.

4.3.6 Age-Adjusted Dust Ingestion Rate (IF)

To account for the variability in exposure activities between children and adults, a recommended age-adjusted dust ingestion rate equation was developed. This equation is designed to take into account the differences in hand to mouth behavior, hand surface area, and exposure to hard and soft surfaces for adults and children.

4.3.7 Dust Ingestion Rate (IR_d)

To account for the variability in exposure to hard and soft surfaces, a recommended dust ingestion rate equation was developed. This equation averages the differences in exposure to hard and soft surfaces by the exposure times.

4.3.8 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 cleaning and transfer to skin and clothing. Different surfaces may be cleaned at different rates, and 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. In fact, indoor concentrations of contaminants may be enhanced above their original outdoor source levels after repeated transfer inside (Paustenbach, Long, et al). The recommended 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 building materials or on material surfaces in the 3-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 recommended BDCC calculator, however. If a dissipation rate constant is used, it is generally 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 recommended BDCC is calculated into the future. The discussion below provides a review of the literature related to this issue and provides an alternative dissipation rate constant value. Site specific 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 studies presented in EPA 2003 (pg. D-5), there is strong support for considering dissipation in setting criteria for building clean-ups. A study of the Binghamton State Office Building found that dioxin dissipated over time according to first order kinetics with a 20 to 22 month half-life. 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 yr ^-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:

The above equation steps are shown for completeness. This recommended BDCC 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 recommended BDCC 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 BDCC resident and worker ingestion of dust equations, a higher recommended BDCC concentration would be calculated.

In the simplified BDCC equation: BDCC=DL/IFD*DCF*(1-e^(-kt))/(kt), where BDCC is building dose compliance concentration, DL is dose limit, IFD is ingestion fraction of dust, DCF is the radionuclide-specific dose conversion factor, and (1-e^(-kt))/(kt) is the dissipation term. The following exhibit displays the results obtained by changing the value k; t is equal to ED in all equations.

Exhibit 1. Results Obtained By Changing The Value k.

t (yr)	k (yr-1)	DCF (mrem/pCi)	IFD (cm2)	DL (mrem/yr)	(1-e(-kt))/(kt) (unitless)	BDCC (pCi/cm2)
1	0.01	1.00E-05	400	1.00E-06	9.95E-01	2.51E+02
1	0.05	1.00E-05	400	1.00E-06	9.77E-01	2.56E+02
1	0.08	1.00E-05	400	1.00E-06	9.59E-01	2.61E+02
1	0.12	1.00E-05	400	1.00E-06	9.42E-01	2.65E+02
1	0.16	1.00E-05	400	1.00E-06	9.25E-01	2.70E+02
1	0.2	1.00E-05	400	1.00E-06	9.08E-01	2.75E+02
1	0.23	1.00E-05	400	1.00E-06	8.92E-01	2.80E+02
1	0.27	1.00E-05	400	1.00E-06	8.77E-01	2.85E+02
1	0.31	1.00E-05	400	1.00E-06	8.61E-01	2.90E+02
1	0.34	1.00E-05	400	1.00E-06	8.46E-01	2.95E+02
1	0.38	1.00E-05	400	1.00E-06	8.32E-01	3.01E+02
1	0.42	1.00E-05	400	1.00E-06	8.18E-01	3.06E+02
1	0.45	1.00E-05	400	1.00E-06	8.04E-01	3.11E+02
1	0.49	1.00E-05	400	1.00E-06	7.90E-01	3.16E+02
1	0.53	1.00E-05	400	1.00E-06	7.77E-01	3.22E+02
1	0.57	1.00E-05	400	1.00E-06	7.64E-01	3.27E+02
1	0.6	1.00E-05	400	1.00E-06	7.51E-01	3.33E+02
1	0.64	1.00E-05	400	1.00E-06	7.39E-01	3.38E+02
1	0.68	1.00E-05	400	1.00E-06	7.27E-01	3.44E+02
1	0.71	1.00E-05	400	1.00E-06	7.15E-01	3.50E+02
1	0.75	1.00E-05	400	1.00E-06	7.03E-01	3.55E+02
1	0.79	1.00E-05	400	1.00E-06	6.92E-01	3.61E+02
1	0.82	1.00E-05	400	1.00E-06	6.81E-01	3.67+02
1	0.86	1.00E-05	400	1.00E-06	6.70E-01	3.73E+02
1	0.9	1.00E-05	400	1.00E-06	6.60E-01	3.79E+02
1	1.0	1.00E-05	400	1.00E-06	6.32E-01	3.95E+02

4.3.9 Dermal Exposure

Other possible exposure pathways that may be considered in a radiological analysis of a contaminated building 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 are likely to 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), however. Therefore, dermal pathways are not included in the current version of this BDCC 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 may 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 would be used to determine the significance of the sweat layer. If this value approaches zero, then contaminated soil particulates may 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 is expected to become 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 likely warranted. The dry deposition scenario 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.

4.3.10 Room Surfaces Factor (F_r-surf)

The 3-D direct external exposure equations (building materials and dust) without F_r-surf are single surface equations. The surfaces factor, in the recommended default and site-specific equations, is based on exposure to 4 walls, the floor, and the ceiling in a room. This calculator uses the relationship between the dose rate coefficients for exposures in a contaminated room and dose rate coefficients for an infinite source to calculate a surfaces factor (F_r-surf). The dose quantity evaluated is the air kerma rate one meter above the floor. The floor, walls, and ceiling of the rooms are assumed to be contaminated to the same level. In Finklea 2015, 5 room sizes, ranging from 10 by 10 by 10 to 400 by 400 by 40 feet, were modeled to account for the dose contribution from multiple surfaces. Several individual materials, including wood, glass, concrete, drywall, and adobe mud brick, were analyzed as well as 2 composite scenarios where multiple building materials are present in different ratios. Composite 1 is a drywall room with a glass window, wooden doors, and drywall walls. The floors for composite 1 are concrete, and the ceiling is drywall. Composite 2 is a concrete room with wooden doors, a drywall ceiling, and a concrete floor. Both composite cases used a homogeneous mix of material for the walls to represent the window and door mixed in with the wall. Four receptor positions were included for each material: average, center of room, corner of room and along the center of a wall. Contamination depths were considered to be surface, 1cm, 5cm, 15cm, and 100cm (infinite). The F_r-surf for the default option is set to the most protective value across the 5 room sizes and 4 receptor positions. In the site-specific option, the user can select from the 5 room sizes, 4 receptor positions, and the building material. Finklea 2015 presents the air kerma values, and additional appendices were developed for this BDCC Calculator to give the ratios compared to infinite dose coefficients. The F_r-surf values for nuclides for adobe and concrete are given in Appendix A and B. The F_r-surf values for nuclides for drywall, glass, and wood are given in Appendices C, D, and E. The F_r-surf values for nuclides for room composite 1 are given in Appendix F. The F_r-surf values for nuclides for room composite 2 are given in Appendix G. The F_r-surf values for the "+D" nuclides are given in Appendix H. The F_r-surf values for the "+E" nuclides are given in Appendix I

4.3.11 Radionuclide Decay Constant (λ) & Half-Life Decay Function

This section presents the decay calculation variable derivations and their application in the BDCC equations.

4.3.11.1 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 BDCC 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. However, in the absence of empirical data, the secular equilibrium BDCCs will provide a protective screening value. Definitions of the input variables are in Table 1.

4.3.11.2 Half-Life Decay Function

In situations where the contaminant in the dust or air is not being replenished, decay should be used. An air situation that would require decay includes an accidental one-time air release from a factory. A dust situation that would require decay is a a one-time settling of dust from a soil disturbance. In situations where the contaminant in the dust or air has a continual source (e.g., indoor radon from radium in the dust, an operating factory or landfill cap, or uranium mining), the equations without decay should be used.

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

The following decay functions should be multiplied by their respective BDCC Equations when applicable:

4.3.12 Gamma Shielding Factors (GSF_a and GSF_b)

A shielding factor GSF_a was added to the air submersion equations with a default of 1 (no shielding). If the user has a site-specific shielding factor, it can be applied in the calculator.

A shielding factor GSF_b was added to the 3-D building equations with a default of 1 (no shielding). If the user has a site-specific shielding factor, it can be applied in the calculator.

4.4 Equation Sources and Parameters

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

4.4.1 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 EPA 2003 (pg. D-4).

The external exposure from deposited materials equation was modeled after the equation found in ANL 2001 (Fig 8.7).

4.4.2 Ambient Air Exposure

The inhalation equation was modeled after the equation found in EPA 2003 (pg. D-1).

The submersion equation was modeled after the equation found in ANL 2001 (Fig 8.1).

4.4.2.1 Submersion Pathway Equation Derivation

The air submersion external dose from exposure to indoor contaminated air was calculated by using the following equation:

where:

F_in = fraction of time spent indoors

F_i = fraction of time spent in compartment i

= total annual air submersion effective dose equivalent from radionuclide n at time t in compartment i (mrem/yr)

= average concentration of radionuclide n at time t in the indoor air of compartment i (pCi/m³)

= air submersion DCF for radionuclide n (mrem/yr per pCi/m³)

4.4.3 External Exposure

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).

4.4.3.1 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

= 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.

4.4.3.1.1 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)

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.

4.4.3.1.2 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.

4.4.3.1.3 Off-set Factor ( F_OFF-SET)

The off-set factor, F_OFF-SET, is the ratio of the dose estimates from a non-circular 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 , summing the products, and dividing by the area factor of a circular contaminated material that is equivalent in area: