The Modified J&E Model

TACO uses risk-based indoor inhalation remediation objectives (ROs) derived from equations in a modified Johnson and Ettinger (J&E) model.

These ROs are calculated based on a 10-6 individual excess cancer risk and a hazard quotient of one for noncarcinogens. Exposure factors are consistent with the values used by the other TACO pathways; toxicity factors were obtained using U.S. EPA’s hierarchy and are chemical-specific.

The modified J&E model in TACO simulates the migration of contaminants from a subsurface source to the air inside a building. Like the SSL and RBCA models used for other exposure routes, modified J&E model parameters have conservative default values under Tier 1 that may be substituted for site-specific conditions under Tier 2. However, the indoor inhalation exposure route is unique in that Tiers 1 and 2 provide calculated remediation objectives for soil gas and groundwater, not soil.

Illinois EPA considers its use of the J&E model as “modified” because certain default parameters (e.g., system temperature for Dimensionless Henry’s Law Constant) have been adjusted to be state-specific as compared to values applied elsewhere by environmental regulatory agencies.

TACO provides 18 J&E equations and 54 default parameter values in Section 742.Appendix C, Tables L and M, respectively.

Assumptions used in the modified J&E model

The modified J&E model is based on an assumption that existing or potential buildings within the horizontal extent of contamination have full concrete floors. The modified J&E model may not be used where existing or potential buildings within the horizontal extent of contamination have earthen crawl spaces or earthen or partial concrete floors. In such cases, site evaluators have the option of excluding the indoor inhalation exposure route under Section 742.312, meeting the building control technology requirements under Subpart L, or proposing an alternative approach under Tier 3.

The modified J&E model assumes that man-made pathways into existing or potential buildings are controlled so that preferential pathways do not exist. The TACO definition of “man-made pathways” now includes elevator vaults and sumps. Site evaluators must account for these potential pathways just as they are required to address man-made pathways for the other exposure routes under their respective remediation program regulations. Note: For full concrete floors with sumps, site evaluators may not use the J&E model under Tier 1 and Tier 2 and must either exclude the pathway, show that the soil gas concentrations meet the remediation objectives developed from J&E1 and J&E2, meet building control technology requirements, or proceed to Tier 3.

The modified J&E model as well as the existing RBCA and SSL models operate on similar assumptions regarding saturation and solubility. These risk-based models assume steady state conditions with equilibrium between contaminant concentrations that exist as vapors in soil pores, contaminants that adhere to soil particles and contaminants that dissolve into water within soil pores. For the indoor inhalation exposure route, soil gas ROs cannot exceed the soil vapor saturation limit; groundwater ROs cannot exceed the solubility limit.

Three basic steps to develop soil gas and groundwater ROs

  1. Calculate a concentration of the contaminant of concern in indoor air that adequately protects humans who inhale this air (i.e., meets the above mentioned risk criteria).

  2. Calculate an acceptable concentration of the contaminant of concern in the soil gas at the source of contamination. This concentration will not cause the contaminant in indoor air to exceed the concentration calculated in Step 1. This calculation was made using an attenuation factor derived from the modified J&E model.

  3. Calculate acceptable groundwater remediation objectives using the soil gas remediation objective calculated in Step 2, with the assumption that this contaminant is in three- phase equilibrium.

    The ratio of the concentration in the indoor air from Step 1 to the soil gas concentration in Step 2 is called the attenuation factor. The primary use of model is to calculate the attenuation factor.

The attenuation factor accounts for the following processes

  1. Migration of contaminants from the source upwards through the vadose zone. The source of contaminant concentrations in the subsurface may be either soil or groundwater. If the source is groundwater, the attenuation factor considers the initial migration of contaminants through the capillary fringe.

  2. Migration of contaminants through the cracks in the full concrete slab-on-grade or basement floor.

  3. Mixing of the contaminants with air inside the building.

How the modified J&E model calculates ROs

The diagram below shows the relationship between parameter inputs, the modified J&E equations, and the calculated results.

The modified J&E model calculates indoor air ROs for purposes of deriving soil gas and groundwater ROs but TACO does not provide a table of indoor air ROs. This is because use of indoor air data to demonstrate compliance with remediation objectives under Tier 1 or 2 is not allowed. Indoor air samples are highly susceptible to bias from occupant sources (smoking, dry cleaning, household chemical use and storage, etc.). They are also invasive, requiring site evaluators to obtain access to indoor space. TACO does not prohibit the use of indoor air data; however, any such request would be a Tier 3 evaluation.

The modified J&E model also calculates an attenuation factor, but TACO does not provide a table of attenuation factors. This is because attenuation factors are chemical, building and soil specific. Soil specific means geotechnical parameter inputs such as water-filled soil porosity and dry soil bulk density.


Equations J&E1 through J&E3 are used to calculate the acceptable concentration of the contaminant in indoor air. Equation J&E1 applies only to chemicals that cause carcinogenic health effects, J&E2 applies only to chemicals that cause noncarcinogenic health effects, and J&E3 is used by both types of contaminants to convert from parts per million volume to milligrams per cubic meter.

Equation J&E4 calculates soil gas ROs using the appropriate indoor air remediation objective (from either J&E1 or J&E2) and an attenuation factor developed from Equations J&E7 through J&E18.

Soil gas ROs must be compared to the saturated vapor concentration (Cvsat). Section 742.222 presents the methods by which the Cvsat concentration is obtained; for example, site evaluators may use the list of Cvsat values in Section 742.Appendix A, Table K or calculate a site-specific Cvsat using equation J&E5.

Groundwater ROs are calculated using equation J&E6 instead of equation J&E4, and when determining the attenuation factor, the capillary fringe must be considered one of the layers in equation J&E9a.

Equation J&E7 or 8 may be used to calculate the attenuation factor. This is the heart of the predictive model, measuring how much contamination from the subsurface is expected to reach the indoor air. The source of the contaminant concentrations in the subsurface may be either soil, groundwater or soil gas. J&E8 assumes that there is no significant pressure difference between the subsurface soil and the building. This means that contaminants emanating from the source do not migrate into the building by advection. Migration by advection is represented by the parameter Qsoil, also known as the volumetric flow rate of soil gas into the enclosed space. When Qsoil is assumed to equal zero – as is the case with Appendix B, Table I – diffusion is the only contaminant transport mechanism. If advection and diffusion are the modes of contaminant transport, site evaluators would use equation J&E7 to calculate the attenuation factor.

The remaining equations, J&E9a through J&E18, are used to establish the input parameters for application in J&E7 and 8. Equation J&E9a calculates the total overall chemical-specific effective diffusion coefficient. For this equation, each layer of soil (sand, loamy sand, loam etc.) through which contaminant vapors migrate from source to building must be accounted for. The total thickness of the soil layers must equal the distance from the bottom of the slab to the top of the contamination; this relationship is presented in equation J&E9b. The distance, called the source to building separation distance, is calculated by equation J&E10.

Equation J&E11 calculates the chemical-specific effective diffusion coefficient for each soil layer and is used in equation J&E9a. Equations J&E12a and 12b are used to calculate the surface area of the enclosed space at or below grade through which vapors enter into the building. For slab-on-grade buildings, site evaluators must use J&E12a. For buildings with basements, site evaluators must use J&E12b. Equation J&E13 calculates the building ventilation rate using the air exchange rate and the size of the building. For equations J&E12a, J&E12b and J&E13, site evaluators must use the same default values as in Tier 1.

Equation J&E14 calculates the area of total cracks assumed to exist in the portion of the structure below grade through which contaminants migrate into the building; default values from Tier 1 must be used here as well. Contaminants intrude into the building only through cracks that completely penetrate the slab; these cracks are assumed to be filled with a loam soil which is consistent with the default soil type used to develop the Tier 1 remediation objectives for the other exposure routes. The thickness of these cracks is represented by the slab thickness, which is set at 10 cm for both Tier 1 and Tier 2. Equation J&E15 calculates the effective diffusion coefficient through the cracks using soil parameters representative of the soil within the cracks; as these parameters cannot be measured directly, the default values in Tier 1 apply.

Equations J&E16 through J&E18 calculate site-specific geotechnical parameters. J&E16 gives the total porosity, which is the ratio of the volume of voids to the volume of soil sample. J&E17 gives the water-filled soil porosity, which is the ratio of the volume of water to the volume of soil. J&E18 gives the air-filled soil porosity, which is a measure of the total porosity minus the water-filled porosity. Porosity values representative of the soil layer at the source of contamination as well as each soil layer through which contaminants migrate are needed to calculate the effective diffusion coefficient (J&E11). Additional methods for determining the physical soil parameters are presented in Section 742.Appendix C, Table F.

This fact sheet is for general information only and is not intended to replace, interpret, or modify laws, rules, or regulations.

June 2013