QD and ERI calculation in EQRS: method and acceptability thresholds

Written by Eric Azulay — SSP Engineer (contaminated land), Managing Director of SARL G.M.E.P · Published on July 3, 2026

What is the Hazard Quotient (QD)?

The Hazard Quotient (QD), sometimes called the hazard index, is the indicator used in EQRS to assess the risk associated with threshold substances, i.e. substances for which a toxic effect only appears above a certain exposure dose (non-carcinogenic effects: hepatotoxicity, neurotoxicity, renal effects, etc.). The QD compares the exposure dose actually received by an individual to a toxicological reference dose, below which no adverse effect is expected.

QD calculation formula

The general formula is:

QD = Exposure dose (DJE) / Threshold VTR (DJR or DJT)

where the DJE (Daily Exposure Dose) is the amount of substance received via the oral, dermal or inhalation route, expressed relative to body weight and exposure duration, and the threshold VTR — Acceptable Daily Intake (DJA), Tolerable Daily Intake (DJT) or Reference Dose (RfD) depending on the organization — is the dose below which exposure is considered to carry no appreciable risk to human health.

When several substances affect the same target organ, the individual QDs are summed (target-organ summation rule, US EPA RAGS Part A §8.2), to obtain a cumulative QD representative of the overall risk to that organ.

What is the Individual Excess Risk (ERI)?

The Individual Excess Risk (ERI) assesses the risk associated with non-threshold substances, mainly genotoxic carcinogens, for which it is assumed that there is no dose below which the risk is zero. The ERI expresses the additional lifetime probability of developing cancer as a result of exposure to the substance in question, relative to a non-exposed population.

ERI calculation formula

ERI = Exposure dose (DJE) × ERU (Unit Excess Risk)

The ERU (Unit Excess Risk), also known as the Cancer Slope Factor (CSF) for the oral route or Unit Risk for the inhalation route, quantifies the substance's carcinogenic dose-response relationship. As with the QD, individual ERIs are summed by type of carcinogenic effect (summation by tumor target) to obtain a cumulative ERI.

Toxicological reference values (VTR)

VTRs are threshold values or slope factors established by recognized scientific bodies (ANSES, US EPA IRIS, ATSDR, WHO) based on toxicological and epidemiological studies. The choice of VTR directly determines the QD or ERI result: the INERIS ERS 2021 methodology requires a hierarchy of VTR sources and their full traceability in the assessment report.

The ADAF factor and children's sensitivity

For carcinogenic substances with a mutagenic mode of action, exposure during childhood carries a higher toxicological weight than the same dose received in adulthood, due to the increased sensitivity of developing tissues and the longer remaining life expectancy during which the mutation can progress. This phenomenon is accounted for by the ADAF factor (Age-Dependent Adjustment Factor):

• ADAF = 3 for the 0-2 age group (early childhood)
• ADAF = 3 also applied in France for the "child" age group under ANSES 2018 doctrine, depending on the scenario
• ADAF = 1 for adults (no increase)

The ADAF factor directly multiplies the ERU for the fraction of exposure corresponding to this age group, which mechanically increases the calculated ERI for a child compared to an adult exposed to the same concentration.

Risk acceptability thresholds

The thresholds below are those commonly adopted by French doctrine and the INERIS/ANSES methodological guides to assess the acceptability of a health risk as part of an IEM or a management plan.

These thresholds are indicative and must be assessed case by case by the engineering firm and the relevant authority (DDT, DREAL, ARS) based on the local context, the number of people exposed and the site's use.

EQRS target populations

EQRS distinguishes several populations whose exposure parameters (duration, frequency, body weight, quantity of air inhaled, quantity of soil ingested) differ significantly:

• Resident adult — long-term chronic exposure at the residential site
• Child (0-6 years) — increased exposure parameters, application of the ADAF factor for non-threshold effects
• Employee — occupational exposure, comparison with Occupational Exposure Limit Values (VLEP) in addition to the QD

Compliance with INERIS ERS 2021 and ANSES 2018

The human health risk assessment methodology promoted by INERIS (ERS 2021) governs the entire process: substance selection, choice and hierarchy of VTRs, QD and ERI summation rules, and presentation of results in the report. The VTRs themselves, along with the ADAF factor applicable to children, are updated by ANSES, whose 2018 doctrine is the reference for French practitioners.

Practical calculation approach in EQRS

In the practice of an SSP engineering firm, the calculation of the QD and ERI is part of a structured methodological sequence, which flows directly from the conceptual site model (identification of sources, transfer pathways and receptors):

1. Selection of substances of interest

The list of substances to include in the calculation results from field investigations (soil, groundwater, soil gas, indoor air) and the site's activity history. Each substance is then classified according to its toxicological mode of action: threshold (QD) or non-threshold (ERI), with some substances showing both types of effects and requiring a parallel calculation of both indicators.

2. Building the exposure scenario

For each target population (adult, child, employee), the exposure scenario defines the relevant transfer pathways (soil ingestion, dermal contact, inhalation of outdoor air or indoor air via the Johnson & Ettinger model, water ingestion), the exposure frequency and duration, as well as the physiological parameters (body weight, inhaled air volume, quantity of soil ingested) taken from reference guides.

3. Calculating the Daily Exposure Dose (DJE)

The DJE aggregates, for each transfer pathway, the substance concentration at the point of exposure, the contact rate, the exposure frequency and duration, expressed relative to body weight and the calculation period (entire lifetime for the ERI, exposure duration for the QD).

4. Applying the VTRs and summation

The DJE is then compared to the threshold VTR (QD calculation) or multiplied by the ERU (ERI calculation), for each transfer pathway and substance. The results are finally summed by target organ for the QD, and by carcinogenic effect for the ERI, to obtain the cumulative indicators compared against the acceptability thresholds.

5. Interpretation and prioritization

When thresholds are exceeded, the assessor identifies the substances, transfer pathways and target organs that contribute most, which helps direct the management plan (remediation work, use restrictions, easements) toward the most effective levers for bringing the risk below the acceptability thresholds.

Limitations and methodological precautions

The calculation of the QD and ERI relies on conservative assumptions (representative maximum concentration, upper-bound exposure scenarios) intended to protect the most sensitive populations. These assumptions can lead to an overestimate of the actual risk, which in some cases justifies the use of a sensitivity analysis (for example by Monte-Carlo simulation) to assess the variability of the results and avoid disproportionate management measures. The quality of the calculation also depends heavily on the representativeness of the field data (number of measurement points, sampling period) and the traceability of the VTRs used, which must always be cited with their source and update date in the EQRS report.

FAQ — QD and ERI calculation in EQRS

Methodological references

• INERIS — ERS 2021 methodology
• ANSES — Toxicological reference values (VTR)
• US EPA — RAGS Part A (Risk Assessment Guidance)
• US EPA — Child-Specific Exposure Factors (ADAF)

Written by Eric Azulay — SSP Engineer (contaminated land), Managing Director of SARL G.M.E.P