New Jersey Administrative Code
Title 7 - ENVIRONMENTAL PROTECTION
Chapter 26D - REMEDIATION STANDARDS
Appendix 12
DERIVATION OF EQUATION EQUIVALENCY USED FOR THE DEVELOPMENT OF SOIL AND INDOOR AIR REMEDIATION STANDARDS
This appendix demonstrates the equivalency between the equations used by the Department in the development of the soil and indoor air remediation standards, and the equations used by the USEPA in the development of soil and indoor air risk-based screening levels. This appendix demonstrates the equivalency for the following Department soil and indoor air remediation standard equations:
* N.J.A.C. 7:26D Appendix 2, Equation 1, Residential Carcinogenic Ingestion-Dermal Human Healthbased Criterion Equation;
* N.J.A.C. 7:26D Appendix 2, Equation 2, Residential Noncarcinogenic Ingestion-Dermal Human Healthbased Criterion Equation;
* N.J.A.C. 7:26D Appendix 2, Equation 3, Nonresidential Carcinogenic Ingestion-Dermal Human Healthbased Criterion Equation;
* N.J.A.C. 7:26D Appendix 2, Equation 4, Nonresidential Noncarcinogenic Ingestion-Dermal Human Health-based Criterion Equation;
* N.J.A.C. 7:26D Appendix 3, Equation 1, Carcinogenic Inhalation Human Health-based Criterion Equation;
* N.J.A.C. 7:26D Appendix 3, Equation 2, Noncarcinogenic Inhalation Human Health-based Criterion Equation;
* N.J.A.C. 7:26D Appendix 5, Equation 1, Carcinogenic Indoor Air Human Health-based Criterion Equation; and
* N.J.A.C. 7:26D Appendix 5, Equation 2, Noncarcinogenic Indoor Air Human Health-based Criterion Equation.
* N.J.A.C. 7:26D Appendix 2, Equation 1-Residential Carcinogenic Ingestion-Dermal Human Health-Based Criterion Equation
The origin of the Department residential soil remediation standard for the ingestion-dermal exposure pathway for a carcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):
This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by deleting the inhalation related screening level term:
The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the ingestion and dermal aspects, which is designated:
The RSLE states that:
and
The above two equations include the units for the listed input parameters. Deleting the units simplify the two equations to:
And
Because
the second equation further simplifies to:
Starting with the Department-modified base USEPA equation, as described above:
1. Insert the simplified equations for SLres-soil-ca-ing and SLres-soil-ca-der described above into the denominator of the SLres-soil-ca-ing-derm equation, which then becomes:
2. Simplify the reciprocal (in the denominator of the equation immediately above) containing the equivalent expression of SLres-soil-ca-ing by multiplying it by the term:
This is the same as multiplying the reciprocal of the expression by 1.
3. Similarly, simplify the reciprocal containing the equivalent expression of SLres-soil-ca-der by multiplying it by the term:
Again, this is effectively multiplying by 1.
4. This results in the expression:
5. After separating the common term Click here to view image
from both expressions in the denominator, multiply both the numerator and the denominator of the entire equation by the expression:
Performing steps 1 through 5 above results in the following expression:
This USEPA terminology (immediately above), which is for a residential land use scenario involving a carcinogenic contaminant, converts to the Department terminology as follows:
| USEPA Term | Department Term | USEPA Definition |
| TR | TR | Target cancer risk |
| ATres | AT | Averaging time |
| LT | LT | Lifetime |
| CSFo | CSFo | Oral cancer slope factor |
| RBA | None | Relative Bio-availability |
| IFSres-adj | IFSadj | Age-adjusted soil ingestion rate |
| CSFd | CSFD | Dermal cancer slope factor |
| DFSres-adj | DFSadj | Age-adjusted soil dermal contact factor |
| ABSd | ABSd | Dermal absorption fraction |
| 10-6kg | 10-6kg | Unit conversion factor |
| mg | mg | |
| GIABS | GIABS | Gastro-intestinal absorption fraction |
Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:
Note that the USEPA term SLres-soil-ca-ing-derm is the equivalent of the Department term IDc. In addition, there is no Department RBA parameter because the value is usually 1. Consequently, an RBA parameter does not appear in the translated equation. The equation presented immediately above is equivalent to the Department equation presented at N.J.A.C. 7:26D Appendix 2 as Equation 1 and verifies its equivalence with equations used by the USEPA.
N.J.A.C. 7:26D Appendix 2, Equation 1 is:
N.J.A.C. 7:26D Appendix 2, Equation 2-Residential Noncarcinogenic Ingestion-Dermal Human Health-Based Criteria Equation
The origin of the Department residential soil remediation standard for the ingestion-dermal exposure pathway for a noncarcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):
This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by deleting the inhalation related screening level term:
The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the ingestion and dermal aspects, which is designated:
The Department calculation of the residential noncarcinogenic ingestion-dermal criterion is based on a child exposure scenario. As such, the RSLE states that:
and
The above two equations include the units for the listed input parameters. Deleting the units simplify the two equations to:
and
Because
the second equation further simplifies to:
Starting with the Department-modified base USEPA equation, as described above:
1. Insert the simplified equations for SLres-soil-nc-ing-c and SLres-soil-nc-der-c described above into the denominator of the SLres-soil-nc-ing-der-c equation, which then becomes:
2. Simplify the reciprocals in the denominator of the equation immediately above (similar to what was done in the derivation of N.J.A.C. 7:26D Appendix 2, Equation 1 above) using the respective terms:
and
Again, this is the same as multiplying each of the reciprocals in the equation denominator by 1.
3. This results in the following:
4. After separating out the common terms
and
from both expressions in the denominator, multiply both the numerator and the denominator of the entire equation by the expression:
Performing steps 1 through 4 above results in the following expression:
This USEPA terminology (immediately above), which is for a residential land use scenario involving a noncarcinogenic contaminant, converts to the Department terminology as follows:
| USEPA Term | Department Term | USEPA Definition |
| THQ | THQ | Target hazard quotient |
| ATres-c | AT | Averaging time |
| EFres-c | EF | Exposure frequency-child |
| BWres-c | BW | Body weight - child |
| EDres-c | ED | Exposure duration - child |
| RBA | None | Relative Bio-availability |
| RfDo | RfDo | Oral reference dose |
| IRS | IR | Soil ingestion rate - child |
| RfDD | RfDD | Dermal reference dose |
| SAres-c | SA | Skin surface area - child |
| AFres-c | AF | Soil adherence factor - child |
| ABSd | ABSd | Dermal absorption fraction |
| 10-6kg mg | 10-6kg mg | Unit conversion factor |
| GIABS | GIABS | Gastro-intestinal absorption fraction |
Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:
Note that the USEPA term SLres-soil-nc-ing-der-c is the equivalent of the Department term IDnc. In addition, there is no Department RBA parameter because the value is usually 1. Consequently, an RBA parameter does not appear in the translated equation. The equation presented immediately above is equivalent to the Department equation presented in N.J.A.C. 7:26D Appendix 2 as Equation 2 and verifies its equivalence with equations used by the USEPA.
N.J.A.C. 7:26D Appendix 2, Equation 2 is:
N.J.A.C. 7:26D Appendix 2, Equation 3-Nonresidential Carcinogenic Ingestion-Dermal Human Health-Based Criteria
The origin of the Department nonresidential soil remediation standard for the ingestion-dermal exposure pathway for a carcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):
This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by deleting the inhalation related screening level term:
The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the ingestion and dermal aspects, which is designated:
The Department calculation of the nonresidential carcinogenic ingestion-dermal criterion is based on an adult outdoor worker exposure scenario.
As such, the RSLE states:
and
The above two equations include the units for the listed input parameters. Deleting the units simplify the two equations to:
And
Because
the second equation further simplifies to:
Starting with the Department-modified base USEPA equation, as described above:
1. Insert the simplified equations for SLow-soil-ca-ing and SLow-soil-ca-der described above into the denominator of the SLow-soil-ca-ing-der equation, which then becomes:
2. Simplify the reciprocals in the equation denominator immediately above (similar to what was done in the derivation of N.J.A.C. 7:26D Appendix 2, Equation 1 above) using the respective terms:
and
Again, this is the same as multiplying the reciprocals in the equation denominator by 1.
3. This results in the following:
4. After separating out the common terms (EFOW x EDOW) and
from both expressions in the denominator, multiply both the numerator and the denominator of the entire equation by the expression:
Performing steps 1 through 4 above results in the following expression:
This USEPA terminology (immediately above), which is for a nonresidential land use scenario involving a carcinogenic contaminant, converts to the Department terminology as follows:
| USEPA Term | Department Term | USEPA Definition |
| TR | TR | Target cancer risk |
| ATow | AT | Averaging time - outdoor worker |
| LT | LT | Lifetime |
| CSFo | CSFo | Oral cancer slope factor |
| RBA | None | Relative Bio-availability |
| IRow | IR | Soil ingestion rate-outdoor worker |
| CSFd | CSFD | Dermal cancer slope factor |
| AFow | AF | Soil adherence factor-outdoor worker |
| ABSd | ABSd | Dermal absorption fraction |
| 10-6kg mg | 10-6kg mg | Unit conversion factor |
| GIABS | GIABS | Gastro-intestinal absorption fraction |
Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:
Note that the USEPA term SLow-soil-ca-ing-der is the equivalent of the Department term IDc. In addition, there is no Department RBA parameter because the value is usually 1. Consequently, an RBA parameter does not appear in the translated equation. The equation presented immediately above is equivalent to the Department equation presented in N.J.A.C. 7:26D Appendix 2 as Equation 3 and verifies its equivalence with equations used by the USEPA.
N.J.A.C. 7:26D Appendix 2, Equation 3 is:
N.J.A.C. 7:26D Appendix 2, Equation 4--Nonresidential Noncarcinogenic Ingestion-Dermal Human HealthBased Criteria
The origin of the Department nonresidential soil remediation standard for the ingestion-dermal exposure pathway for a noncarcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):
This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by deleting the inhalation related screening level term:
The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the ingestion and dermal aspects, which is designated:
The Department calculation of the nonresidential noncarcinogenic ingestion-dermal criterion is based on an adult outdoor worker exposure scenario. As such, the RSLE states:
and
The above two equations include the units for the listed input parameters. Deleting the units simplify the two equations to:
and
Because
the second equation further simplifies to:
Starting with the Department-modified base USEPA equation, as described above:
1. Insert the simplified equations for SLow-soil-nc-ing and SLow-soil-nc-der described above into the denominator of the SLow-soil-nc-ing-der equation which then becomes:
2. Simplify the reciprocals in the equation denominator immediately above (similar to what was done in the derivation of N.J.A.C. 7:26D Appendix 2, Equation 1 above) using the respective terms:
and
Again, this is the same as multiplying each of the reciprocals in the equation denominator by 1.
3. This results in the following:
4. After separating out the common terms
from both expressions in the denominator, multiply both the numerator and the denominator of the entire equation by the term:
Performing steps 1 through 4 above results in the following expression:
This USEPA terminology (immediately above), which is for a nonresidential land use scenario involving a noncarcinogenic contaminant, converts to the Department terminology as follows:
| USEPA Term | Department Term | USEPA Definition |
| THQ | THQ | Target hazard quotient |
| ATow | T | Averaging time-outdoor worker |
| EFow | EF | Exposure frequency-outdoor worker |
| BWow | BW | Body weight-outdoor worker |
| EDow | ED | Exposure duration-outdoor worker |
| RBA | None | Relative Bio-availability |
| RfDo | RfDo | Oral reference dose |
| IRow | IR | Soil ingestion rate-outdoor worker |
| RfDD | RfDD | Dermal reference dose |
| SAow | SA | Skin surface area-outdoor worker |
| AFow | AF | Soil adherence factor-outdoor worker |
| ABSd | ABSd | Dermal absorption fraction |
| 10-6kg mg | 10-6kg mg | Unit conversion factor |
| GIABS | GIABS | Gastro-intestinal absorption fraction |
Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:
Note that the USEPA term SLow-soil-nc-ing-der is the equivalent if the Department term IDnc. In addition, there is no Department RBA parameter because the value is usually 1. Consequently, an RBA parameter does not appear in the translated equation. The equation presented immediately above is equivalent to the Department equation presented at N.J.A.C. 7:26D Appendix 2 as Equation 4 and verifies its equivalence with equations used by the USEPA.
N.J.A.C. 7:26D Appendix 2, Equation 4 is:
N.J.A.C. 7:26D Appendix 3, Equation 1--Carcinogenic Inhalation Human Health-Based Criteria
The Department addresses both residential and nonresidential land uses in calculating the carcinogenicbased inhalation exposure pathway soil criteria by applying the appropriate exposure assumptions. The equivalency demonstration made here uses the residential land use scenario equation and terminology as the specific example. The same equivalency logic also applies to the nonresidential land use scenario.
The origin of the Department residential soil remediation standard for the inhalation exposure pathway for a carcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):
This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by isolating the inhalation related screening level term:
The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the inhalation aspect, which is designated:
The RSLE states that:
The above equation includes the units for the listed input parameters. Deleting the units simplifies the equation to:
This USEPA terminology, which is for a residential land use scenario involving a carcinogenic contaminant, converts to the Department terminology as follows:
| USEPA Term | Department Term | USEPA Definition |
| TR | TR | Target cancer risk |
| ATres | AT | Averaging time - residential |
| LT | LT | Lifetime |
| IUR | IUR | Inhalation unit risk factor |
| EFres | EF | Exposure frequency - residential |
| VFulim | VF | Soil-to-air volatilization factor |
| PEF | PEF | Particulate emission factor |
| EDres | ED | Exposure duration - residential |
| ETres | ET | Exposure time - residential |
| 1000 ug /mg | 1000 ug/ mg | Unit conversion factor |
| 1 day/24 hours | 1 day/24 hours | Unit conversion factor |
Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:
As the USEPA term SL res-soil-ca-inh is the equivalent of the Department term Inhc, the equation presented above is equivalent to the Department equation presented at N.J.A.C. 7:26D Appendix 3 as Equation 1 and verifies its equivalence with equations used by the USEPA.
N.J.A.C. 7:26D Appendix 3, Equation 1 is:
N.J.A.C. 7:26D Appendix 3, Equation 2--Noncarcinogenic Inhalation Human Health-Based Criteria
The Department addresses both residential and nonresidential land uses in calculating the noncarcinogenicbased inhalation exposure pathway soil criteria by applying the appropriate exposure assumptions. The equivalency demonstration made here uses the residential land use scenario equation and terminology as the specific example. The same equivalency logic also applies to the nonresidential land use scenario.
The origin of the Department residential soil remediation standard for the inhalation exposure pathway for a noncarcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):
This is the equation used by the USEPA to develop soil contaminant screening levels where the human health risks from the ingestion exposure pathway, the dermal exposure pathway, and the inhalation exposure pathway are combined. However, the soil remediation standards the Department developed only combine the ingestion and dermal exposure pathways and address the inhalation exposure pathway separately. Consequently, the Department modified the USEPA equation listed above by isolating the inhalation related screening level term:
The resulting modified equation represents not the total of the ingestion, dermal, and inhalation exposure components, but just the inhalation aspect, which is designated:
The RSLE states that:
The above equation includes the units for the listed input parameters. Deleting the units simplifies the equation to:
This USEPA terminology, which is for a residential land use scenario involving a noncarcinogenic contaminant, converts to the Department terminology as follows:
| USEPA Term | Department Term | USEPA Definition |
| THQ | THQ | Target hazard quotient |
| ATres-a | AT | Averaging time-residential adult |
| EFres-a | EF | Exposure frequency-residential adult |
| EDres-a | ED | Exposure duration-residential adult |
| ETres-a | ET | Exposure time - residential adult |
| RfC | RfC | Reference concentration |
| VFulim | VF | Soil-to-air volatilization factor |
| PEF | PEF | Particulate emission factor |
| 1 day/24 hours | 1 day/24 hours | Unit conversion factor |
Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:
As the USEPA term SL res-soil-nc-inh is the equivalent of the Department term Inhnc, the equation presented above is equivalent to the Department equation presented at N.J.A.C. 7:26D Appendix 3 as Equation 2 and verifies its equivalence with equations used by the USEPA.
N.J.A.C. 7:26D Appendix 3, Equation 2 is:
N.J.A.C. 7:26D Appendix 5, Equation 1--Carcinogenic Indoor Air Human Health-Based Criteria
The Department addresses both residential and nonresidential land uses in calculating the carcinogenic indoor air human health-based criteria by applying the appropriate exposure assumptions. The equivalency demonstration made here uses the residential land use scenario equation and terminology as the specific example. The same equivalency logic also applies to the nonresidential land use scenario.
The origin of the Department residential indoor air remediation standard for the vapor intrusion exposure pathway for a carcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):
The above equation includes the units for the listed input parameters. Deleting the units simplifies the equation to:
This USEPA terminology, which is for a residential land use scenario involving a carcinogenic contaminant, converts to the Department terminology as follows:
| USEPA Term | Department Term | USEPA Definition |
| TR | TR | Target cancer risk |
| ATres | AT | Averaging time - residential |
| LT | LT | Lifetime |
| IUR | IUR | Inhalation unit risk factor |
| EFres | EF | Exposure frequency - residential |
| EDres | ED | Exposure duration - residential |
| ETres | ET | Exposure time - residential |
| 1 day/24 hours | 1 day/24 hours | Unit conversion factor |
Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:
As the USEPA term SLres-air-ca is the equivalent of the Department term IAc, the equation presented above is equivalent to the Department equation presented at N.J.A.C. 7:26D Appendix 5 as Equation 1 and verifies its equivalence with equations used by the USEPA.
N.J.A.C. 7:26D Appendix 5, Equation 1 is:
N.J.A.C. 7:26D Appendix 5, Equation 2--Noncarcinogenic Indoor Air Human Health-Based Criteria
The Department addresses both residential and nonresidential land uses in calculating the noncarcinogenic indoor air human health-based criteria by applying the appropriate exposure assumptions. The equivalency demonstration made here uses the residential land use scenario equation and terminology as the specific example. The same equivalency logic also applies to the nonresidential land use scenario.
The origin of the Department residential indoor air remediation standard for the vapor intrusion exposure pathway for a noncarcinogen is based upon the USEPA, Regional Screening Levels, Equations (November 2018) (RSLE):
The above equation includes the units for the listed input parameters. Deleting these units simplifies the equation to:
This USEPA terminology, which is for a residential land use scenario involving a noncarcinogenic contaminant, converts to the Department terminology as follows:
| USEPA Term | Department Term | USEPA Definition |
| THQ | THQ | Target hazard quotient |
| ATres-a | AT | Averaging time-residential adult |
| EFres | EF | Exposure frequency-residential adult |
| EDres | ED | Exposure duration-residential adult |
| ETres | ET | Exposure time - residential adult |
| RfC | RfC | Reference concentration |
| 1000 ug/ mg | 1000 ug/ mg | Unit conversion factor |
| 1 day/24 hours | 1 day/24 hours | Unit conversion factor |
Using the above terminology to translate this equation into Departmental nomenclature, the equation becomes:
As the USEPA term SLres-air-nc is the equivalent of the Department term IAnc, the equation presented above
is equivalent to the equation presented at N.J.A.C. 7:26D Appendix 5 as Equation 2 and verifies its equivalence with equations used by the USEPA.
N.J.A.C. 7:26D Appendix 5, Equation 2 is:
References
USEPA (2018) Regional Screening Levels (RSLs)--Equations (November 2018)
http://www.epa.gov/risk/regional-screening-levels-rsls-equations
TECHNICAL REQUIREMENTS FOR SITE REMEDIATION
