# Simulating the effect of slab features on vapor intrusion of crack entry.

**ABSTRACT** In vapor intrusion screening models, a most widely employed assumption in simulating the entry of contaminant into a building is that of a crack in the building foundation slab. Some modelers employed a perimeter crack hypothesis while others chose not to identify the crack type. However, few studies have systematically investigated the influence on vapor intrusion predictions of slab crack features, such as the shape and distribution of slab cracks and related to this overall building foundation footprint size. In this paper, predictions from a three-dimensional model of vapor intrusion are used to compare the contaminant mass flow rates into buildings with different foundation slab crack features. The simulations show that the contaminant mass flow rate into the building does not change much for different assumed slab crack shapes and locations, and the foundation footprint size does not play a significant role in determining contaminant mass flow rate through a unit area of crack. Moreover, the simulation helped reveal the distribution of subslab contaminant soil vapor concentration beneath the foundation, and the results suggest that in most cases involving no biodegradation, the variation in subslab concentration should not exceed an order of magnitude, and is often significantly less than this.

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**ABSTRACT:**In this study, the development and partial validation are presented for an analytical approximation method for prediction of subslab contaminant concentrations in PVI. The method involves combining an analytic approximation to soil vapor transport with a piecewise first-order biodegradation model (together called the Analytic Approximation Method, including Biodegradation, AAMB), the result of which calculation provides an estimate of contaminant subslab concentrations, independent of building operation conditions. Comparisons with three-dimensional (3-D) simulations and another PVI screening tool, BioVapor, show that the AAMB is suitable for application in a scenario involving a building with an impermeable foundation surrounded by open ground surface, where the atmosphere is regarded as the primary oxygen source. Predictions from the AAMB can be used to determine the required vertical source-building separation, given a subslab screening concentration, allowing identification of buildings at risk for PVI. This equation shows that the "vertical screening distance" suggested by U.S. EPA is sufficient in most cases, as long as the total petroleum hydrocarbon (TPH) soil gas concentration at the vapor source does not exceed 50-100mg/L. When the TPH soil gas concentration of the vapor source approaches a typical limit, i.e. 400mg/L, the "vertical screening distance" required would be much greater.Journal of Hazardous Materials 05/2014; 279:336-347. · 4.33 Impact Factor - SourceAvailable from: Yijun Yao[Show abstract] [Hide abstract]

**ABSTRACT:**Most current vapor-intrusion screening models employ the assumption of a subsurface homogenous source distribution, and groundwater data obtained from nearby monitoring wells are usually taken to reflect the source concentration for several nearby buildings. This practice makes it necessary to consider the possible influence of lateral source-building separation. In this study, a new way to estimate subslab (nonbiodegradable) contaminant concentration is introduced that includes the influence of source offset with the help of a conformal transform technique. Results from this method are compared with those from a three-dimensional numerical model. Based on this newly developed method, a possible explanation is provided here for the great variation in the attenuation factors of the soil vapor concentrations of groundwater-to-subslab contaminants found in the EPA vapor-intrusion database.Vadose Zone Journal 08/2013; 12(3). · 2.20 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The transport of volatile organic vapors from subsurface to building involves complex processes. Since the release of the draft subsurface vapor intrusion guidance by the U.S. EPA in 2002, great progress has been made in understanding these processes in various field and modeling studies. In these studies, the importance of analyzing and predicting the subslab volatile organic vapor concentration was noted. To quantitatively predict subslab vapor concentration is, however, complicated, especially for sites located over non-uniform vapor sources. This manuscript provides a method to estimate the vapor concentration beneath the subslab using a closed-form analytical solution that can approximate full three-dimensional modeling results, but does not require the use of advanced numerical simulation. This method allows prediction of the subslab vapor concentration profile beneath the slab for various source configurations, given inputs of building slab dimension and source depth. The interaction of the influences of non-uniform source and the slab capping effect on the subslab vapor concentration is addressed.Environmental Modelling and Software 04/2014; 54:1-4. · 3.48 Impact Factor

Page 1

Simulating the effect of slab features on vapor intrusion of crack entry

Yijun Yao, Kelly G. Pennell1, Eric M. Suuberg*

School of Engineering, Brown University, 182 Hope St., Providence, RI 02912, USA

a r t i c l e i n f o

Article history:

Received 19 June 2012

Received in revised form

12 September 2012

Accepted 13 September 2012

Keywords:

Vapor intrusion

Crack

Three-dimensional simulation

Slab features

a b s t r a c t

In vapor intrusion screening models, a most widely employed assumption in simulating the entry of

contaminant into a building is that of a crack in the building foundation slab. Some modelers employed

a perimeter crack hypothesis while others chose not to identify the crack type. However, few studies have

systematically investigated the influence on vapor intrusion predictions of slab crack features, such as the

shape and distribution of slab cracks and related to this overall building foundation footprint size. In this

paper, predictions from a three-dimensional model of vapor intrusion are used to compare the

contaminant mass flow rates into buildings with different foundation slab crack features. The simulations

show that the contaminant mass flow rate into the building does not change much for different assumed

slab crack shapes and locations, and the foundation footprint size does not play a significant role in

determining contaminant mass flow rate through a unit area of crack. Moreover, the simulation helped

reveal the distribution of subslab contaminant soil vapor concentration beneath the foundation, and the

results suggest that in most cases involving no biodegradation, the variation in subslab concentration

should not exceed an order of magnitude, and is often significantly less than this.

? 2012 Elsevier Ltd. All rights reserved.

1. Introduction

In any vapor intrusion study, one of the most important issues is

how the contaminant soil vapor enters a building of interest. This

issue cannot be avoided for research no matter with focus on soil

vapor transport [1e7], indoorair concentration [8e11] or both [12e

18]. Two general hypotheses have been used in the analysis of the

process. One is to assume that contaminants enter through

a permeable concrete slab [8,9,18], and the other involves assuming

existence of a crack or cracks in the slab as the main entry pathway

for soil vapor [1e7,12e14,19e21]. The use of the former is limited,

largely due to the generally accepted low permeability of the

typical concrete slab, while the latter was developed for radon

intrusion studies, and later widely employed in chemical vapor

intrusion studies [22e24]. One example of its use involves the

application of Nazaroff’s equation [25], to calculate soil gas flow

rate into a perimeter crack of a building, e.g. in the Johnsone

Ettinger (JeE) model [12].

Though the crack concept has also been used in many more

detailed studies beyond the JeE model, e.g. Abreu and Johnson’s

three-dimension (3-D) CFD numerical model [1e3], the Brown 3-D

CFD model [4e7,14] and some case studies [26], most of these

studies in vapor intrusion focused on the influence of environ-

mental factors such as soil characteristics and contaminant source

separation and distribution, and only a few of them considered the

details of crack features on predictions. In Abreu’s thesis [2], the

“center crack” scenario was simulated in a study of biodegradation

effects, and it showed that the crack location can play a significant

role in cases involving high biodegradation rate constants. Another

important issue is the variation with position of subslab contami-

nant soil vapor concentration and how this might influence entry

rates into a building. The question that this poses is whether taking

monitoring data fromone or two subslab sample points is sufficient

to fully describe the necessary subslab near-crack concentration

used in predicting contaminant entry rates?

Equation (1) shows the relationship between contaminant mass

flow rate into a structure and indoor air concentration [12].

cinzJck

QbAe

(1)

Where cin. the indoor air contaminant concentration [M/L3], Jck. the

contaminant mass flow rate into the building [M/T], Qb. the volume

of the enclosed space [L3/T] and Ae. The air exchange rate [1/T].

In this study, contaminant mass flow rate, rather than indoor air

concentration, is used as the index of vapor intrusion risk, as sug-

gested elsewhere [6,14]. In equation (1), both Qb. and Aeare in

* Corresponding author. Tel.: þ1 401 863 1420.

E-mailaddresses:

kpennell@umassd.edu

Brown.EDU (E.M. Suuberg).

1Current address: Department of Civil & Environmental Engineering University

of Massachusetts-Dartmouth, Dartmouth, MA 02747, USA.

(K.G.Pennell),Eric_Suuberg@

Contents lists available at SciVerse ScienceDirect

Building and Environment

journal homepage: www.elsevier.com/locate/buildenv

0360-1323/$ e see front matter ? 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.buildenv.2012.09.007

Building and Environment 59 (2013) 417e425

Page 2

practice often difficult to identify or measure, and will cause

uncertainties inpredicted cin. As an alternative, Jck. the contaminant

mass entry rate, can be obtained directly from 3-D numerical

models. This merely postpones the problem of establishing Qb. and

Ae. another point in the visual risk assessment based on cin, but it

more explicitly highlights the problem, and also allows comparing

the potential for the vapor intrusion impacts in different structures

without getting tied up in issues of idiosyncratic building

operation.

2. The 3-D numerical model

The full 3-D model examined here is essentially that presented

earlier by this group [4e7,14], and partly validated by previous

study. The case of interest here is the steady-state “base case”

discussed in the earlier studies, i.e., a single structure built atop an

otherwise flat, open field, underlain by a homogeneous soil that

stretches from the ground surface to a water table which serves as

an infinite source of the contaminant vapor of interest.

Fig. 1 presents a diagram of the base case situation, while Fig. 2

shows different hypothetical crack shapes and distribution in the

foundation slab. Table 1 shows the various parameters assumed in

the modeling work. The model equations solved here are those

shown in previous publications by our group [4e7,14].

Effective soil diffusivity is in reality correlated with soil

permeability [27]. However, in this paper we chose to assume

a constant soil diffusivity to keep the comparison clearer as the

small possible variation in dry soil diffusivity does not make a large

difference in the results, as also noted in our previous research [4e

7,14]. Permeability can show significant variability with soil type

and moisture content, but this is not a focus of this paper, which is

concernedwiththeinfluence

characteristics.

Briefly, the 3-D modeling approach used here solves Darcy’s Law

to obtain soil gas advection profiles, and then solves the contami-

nant gas diffusion-advection equation subject to the soil gas

advection velocity profiles obtained from solving Darcy’s law.

Again, details of the modeling procedure have been presented

elsewhere [4e7,14].

of thefoundation crack

The governing equation of non-compressible soil gas flow in

steady state is [14]:

q ¼ ?k

mg

Vp

(2)

Where q is the Soil gas velocity (L/T), k is the soil permeability (L2),

mgis the viscosity of soil gas (M/L/T) and p the pressure of soil gas

(M/L/T2).

And the general governingequation forconvection and diffusion

of non-biodegradable contaminant in soil is [14]

JT¼ qc ? DeffVc

Where JT. Bulk mass flux of contaminant (M/L2/T), c the concen-

tration of contaminant chemical in soil gas (M/L3) and Deff the

effective soil diffusivity (L2/T).

The entry rate of contaminant into the house is given by [12]

(3)

Fig. 1. Cross sectional view and boundary conditions of the model domain and house

with a foundation crack.

Fig. 2. Plan view of the location of the crack in the foundation of slab: (a) perimeter

crack; (b) center crack; (c) center hole (The crack area in three cases is the same.).

Table 1

Input parameters used in the 3-D simulations (unless otherwise noted in the figures

and table).

Building/foundation parametersContaminant vapor source

properties

Contaminant: TCE

Diffusivity of TCE in crack

(Dck). 7.4 ? 10?6m2/s

Effective diffusivity of TCE in

soil (Deff). 1.04 ? 10?6m2/s

Domain cross section size: 24 m ? 24 m or

50 m ? 50 m (for the foundation footprint

size 20 m ? 20 m).

Foundation foot print: 5 m ? 5 m,

10 m ? 10 m, or 20 m ? 20 m.

Depth of foundation (df). : 0.1 m or 2 m.

Crack/foundation slab thickness(dck). : 152 m

Crack width(wck). : 005 m

Depth to groundwater/source (ds). 35, 8, 11,

14, or 18 m bgs

3-D finite element analysis parameters

Size of the grid elements: 0.001 me1m

Number of elements: 200 ke1,000 k

Soil gas flow properties

Viscosity of air/soil gas

(mg). 1.8648 ? 10?5kg/m/s

Density of air/soil gas

(rg). 1.1614 kg/m3

Soil permeability (k). 10?10,

10?11, 10?12, 10?13or 10?14m2

Total soil porosity (ft). 0.35

Soil porosity filled with gas

(fg). 0.296

Y. Yao et al. / Building and Environment 59 (2013) 417e425

418

Page 3

Jck¼

Qscck

Ack

exp

?Qsdck

?Qsdck

?

DckAck

?

exp

DckAck

? 1

(4)

Where cckis the subslab concentration (M/L3), Ackthe crack area

(L2) and Jck. the bulk mass flux of chemical throughout the crack

(M/L2/T).

3. Results and discussion

3.1. The influence of crack configurations

The indoor air contaminant concentration is a key indicator of

indoor air quality of enclosed space, and it is determined by

contaminantentryrateJck.andindoorairexchangerate.Thelatteris

only influenced by building operation conditions, while the first is

a result of both convection and diffusion. For scenarios with the

same crack configuration it is the soil gas flow rate into a building

thatmainlydeterminestheorderofmagnitudeofcontaminantmass

entry rate, as near-crack subslab contaminant concentration does

not typically vary much with location (and indoor air contaminant

concentration is negligible compared to subslab crack concentra-

tion). The latter is true for a wide range of scenarios, because diffu-

sion dominates the soil gas concentration profile, and convection is

always too weak to affect the profile far from the crack.

Fig. 3 shows typical steady state contaminant concentration

profile plots for a building with a basement and a building built

atop a slab-on-grade. The cases here involve the different

assumptions of crack type, discussed below. The contour lines are

for contaminant concentration normalized to vapor concentration

at the groundwater source. They show the well-established

upward-necking of high concentration zones beneath the founda-

tion. This is attributed to the foundation acting as a diffusion

barrier, and is a common feature of all such modeling results [1e7].

Note that the variation of concentration with position beneath the

building is relatively modest.

Results for the soil gas entry flow rate for three different crack

types and two foundation types are summarized in Fig. 4. It should

be emphasized that this is total soil gas entry rate and not

contaminant entry rate, which is considered below. Note that the

center hole and center crack curves for basement and slab cases fall

atop one another.

Fig. 3. The normalized contaminant soil vapor concentration profile of simulations with 10?11m2soil permeability, 10 m ? 10 m foundation footprint and 8 m source depth: (a)

basement with perimeter crack; (b) slab-on-grade with perimeter crack; (c) basement with center hole; (d) slab-on-grade with center hole; (e) basement with center crack; (f) slab-

on-grade with center crack.

Y. Yao et al. / Building and Environment 59 (2013) 417e425

419

Page 4

In Fig. 4, the soil gas flow rate is the highest for a building with

a “perimetercrack”, and smallest fora building with a “centerhole”.

This difference arises from the difference in the distance between

the crack and the atmosphere in these two cases. This distance

defines the pressure gradient that drives the gas flow. The differ-

ence in the soil gas flow rate Qs. about one order of magnitude

between these two cases. The building foundation type (slab-on-

grade or basement) has the largest influence on soil gas flow rate in

simulations involving a “perimeter crack”, while for the other two

types of cracks the effect of foundation type is not significant.

Generally, the choice of crack type can induce at most one order of

magnitude difference in predicted soil gas entry rate, and founda-

tion type (basement or slab-on-grade) does not matter much,

except as noted.

The simulation results in Figs. 5 and 6 show the contaminant

mass flow rate into the subject building for cases with different

crack types, foundation types and soil permeabilities for different

contaminant source depths. Equation (2) was used to calculate the

indicated values of Jck, sing the valves of Qs. illustrated in Fig. 4 and

the relevant subslab concentration at the crack (which is obtained

from results such as in Fig. 3). Figs. 5 and 6 are plotted to show the

influence of groundwater source depth, in addition to crack type

and soil permeability. This variable is seen to have modest effect on

the results. The contaminant mass flow rate into the house is

determined by both soil gas flow rate and contaminant subslab

crack concentration in these high permeability cases (shown as

10?10e10?12m2soil permeability) and mainly by contaminant

subslab crack concentrations for low permeability cases (not

shown, but 10?14m2permeability). This is because in this latter

case contaminant entry building can only occur via diffusion

through the crack.

For cases with high soil permeabilities, such as all those shown

in Figs. 5 and 6, the subslab crack concentration is relatively lowest

adjacent to perimeter cracks due to their edge location nearest the

atmospheric sink outside the building footprint. For “center hole”

cases, advection into the building is weak as noted above, and

diffusion plays a more significant role in contaminant entry. This

results in a “sink effect” at the crack, which means the subslab

concentration right at the “center hole” crack is lower than that of

the surrounding subslab area. Without such a hole, contaminant

concentration will always be highest under the center of the slab.

For cases involving a center crack, the soil gas entry rate decreases

along length of the crack from the edge to the center of the foun-

dation slab. This is again attributable to the increase in lateral

separation distance of the depressurized house interior from the

surrounding atmospherein going fromedge tocenter. The diffusion

“sink effect”is notas significant in this casewhich ismoresimilar to

the perimeter crack case, so the subslab contaminant concentration

profile is also similar to that in the case of a perimeter crack. The

product of local contaminant concentration and soil gas entry rate

for the center crack case results in an almost equivalent

Fig. 4. The influence of crack types on soil gas flow rate into a house for the cases with

2 m (basement) and 0.1 m (slab-on-grade) foundation depth and foundation footprint

size of 10 m ? 10 m (PC, CH and CC indicate cracks of “Perimeter Crack”, “Center Hole”

and “Center Crack” types; “base” refers basement and “slab” to slab-on-grade; k

indicates soil permeability).

Fig. 5. The influence of crack types and sol permeability on contaminant mass entry

rate for the cases with 2 m foundation depth and building footprint size of

10 m ? 10 m (PC, CH and CC indicate cracks of “Perimeter Crack”, “Center Hole” and

“Center Crack” types. ds. indicates the depth of a groundwater contaminant source,

below ground surface).

1E-7

1E-6

1E-5

1E-4

1E-3

1E-2

05101520

PC-10-10

PC-10-11

PC-10-12

CH-10-10

CH-10-11

CH-10-12

CC-10-10

CC-10-11

CC-10-12

Jck (mol/s)

ds (m)

Fig. 6. The influence of crack types and soil permeability on contaminant mass entry

rate for the cases with 0.1 m depth foundation, i.e. slab-on-grade with footprint size as

10 m ? 10 m (PC, CH and CC indicate cracks of “Perimeter Crack”, “Center Hole” and

“Center Crack” types. ds. indicates the depth of a groundwater contaminant source,

below ground surface).

Y. Yao et al. / Building and Environment 59 (2013) 417e425

420

Page 5

contaminant mass entry rate to that for the perimeter crack cases,

which again exceed those of “center hole” cases.

As the soil permeability decreases, diffusion becomes the

process limiting contaminant entry since soil gas flow rate becomes

unimportant in determining contaminant mass entry rate for all

cases. Contaminant mass flow rate into a perimeter crack is greatly

decreased in the absence of advection. The influence of low soil

permeability in the “center crack” cases is not as significant as in

the “perimeter crack” cases because soil gas entry rate does not

contribute as much as in the “perimeter crack” cases. The predicted

subslab concentration of the “center crack” cases decreases only

a little due to the diffusion “sink effect”. The contaminant mass

entry rate of the “center hole” cases is least affected by low

permeability since advection already does not play a big role in this

instance.

Generally, the contaminant mass entry rate decreases for all

three crack types as advection decreases with reduced soil

permeability, and in the “center crack” and “center hole” cases, the

subslab crack concentration also decreases due to a the diffusion

“sink effect”.

All the differences of contaminant mass entry rate found for

different crack types for the cases of Figs. 5 and 6 are within an

order of magnitude of one another. In other words, making the

assumption of a perimeter crack in describing the vapor intrusion

situation does not influence the results much, as compared with

assuming other cracks of similar area. Moreover, it can be seen that

assuming a perimeter crack is a relatively conservative assumption,

generally giving the highest mass entry rate due to strong

convection, except in the case of slab-on-grade construction and

relatively high soil permeability.

1E-6

1E-5

1E-4

1E-3

1E-2

05101520

10m-10-10 m2

10m-10-11 m2

10m-10-12 m2

5m-10-10 m2

5m-10-11 m2

5m-10-12 m2

20m-10-10 m2

20m-10-11 m2

20m-10-12 m2

Jck/Ack (mol/(m2*s))

dsource(m)

Fig. 7. The influence of foundation footprint size on contaminant mass entry rate

through unit perimeter crack area for the cases with 2 m depth foundation (basement)

(10 me10?10m2means the building footprint size is 10 m ? 10 m and soil permeability

is 10?10m2).

1E-6

1E-5

1E-4

1E-3

1E-2

0510 1520

10m-10-10 m2

10m-10-11 m2

10m-10-12 m2

5m-10-10 m2

5m-10-11 m2

5m-10-12 m2

20m-10-10 m2

20m-10-11 m2

20m-10-12 m2

Jck/Ack (mol/(m2*s))

dsource(m)

Fig. 8. The influence of foundation footprint size on contaminant mass entry rate

through unit perimeter crack area for the cases with 0.1 m depth foundation (slab-on-

grade) (10me10?10m2means the building footprint size is 10 m ? 10 m and soil

permeability is 10?10m2).

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

05101520

S-10-11

S-10-13

G-10-11

G-10-13

cck/cs

ds (m)

Fig. 9. The influence of crack diffusivity on contaminant subslab crack concentration

for different contaminant source depths, with 2 m depth foundation (basement) (S and

G indicates that the effective diffusivity in the crack is assumed to be the effective

diffusivity in soil (S) or air (G). 10?11refers to the soil permeability).

0

5E-6

1E-5

1.5E-5

2E-5

2.5E-5

3E-5

3.5E-5

051015 20

S-10-11

S-10-13

G-10-11

G-10-13

Jck (mol/s)

ds (m)

Fig.10. The influence of crack diffusivity on contaminant mass entry rate through unit

perimeter crack area for the cases with 2 m depth foundation (S and G indicates that

the effective diffusivity in the crack is assumed to be the effective diffusivity in soil (S)

or air (G). 10?11refers to the soil permeability).

Y. Yao et al. / Building and Environment 59 (2013) 417e425

421

Page 6

3.2. The influence of foundation footprint size

Figs. 7 and 8 show the influence on contaminant mass entry rate

through the unit area of a perimeter crack as a function of foun-

dation size for basement and slab-on-grade cases, respectively.

The soil gas flow rate through a unit area of perimeter crack for

a certain soil permeability is determined by the pressure difference

between that at the crack and atmosphere, and the separation

distance from the open atmospheric surface surrounding the

building and the crack. The crack pressure is only determined by

the situation inside the building, while atmospheric pressure is the

same for foundations of difference sizes. The flow at the crack also

depends on foundation depth from the open ground surface.

Since the soil gas entry rate per unit crack area does not depend

on foundation size for the “perimeter crack” cases, the similar

contaminant mass entry rate per unit crack area for three different

building foundation sizes indicates that the subslab crack

contaminant soil vapor concentration varies little with foundation

size. This is why there are clusters of curves for different soil

permeabilities (soil gas flow is proportional to permeability for

a given pressure difference), but in which the effect of foundation

size is seen to be small (see Figs. 7 and 8).

3.3. The influence of soil vapor diffusivity in the crack

Figs. 9 and 10 show the influence of in-crack contaminant

diffusivity on subslab contaminant concentration and mass entry

rate.Theeffectivediffusivities

(1.04 ? 10?6m2/s) and in air (7.4 ? 10?6m2/s) were used as

different limiting cases, since both assumptions have been used in

the literature.

For cases with high soil permeability, such as 10?10and

10?11m2, convection dominates the flux through the crack, and the

diffusivity in the crack is not important in determining the

contaminant flow rate through the crack. The contaminant

concentration boundary condition at the crack is independent of

the crack diffusivity, as is the contaminant concentration profile in

the soil.

For cases with low soil permeability, less than 10?12m2, diffu-

sion dominates the flux through the crack. As the crack size is small

compared to the overall domain of interest, the influence of the

crack is limited as far as determining the contaminant concentra-

tion profile anywhere but near the crack. Fig. 9 shows that the

difference in contaminant subslab concentration caused by

changing crack diffusivity is not significant. In other words, the

ofcontaminantinsoil

Fig. 11. The normalized contaminant soil vapor concentration profile of simulations with 10?13m2soil permeability, 10 m ? 10 m foundation footprint and 8 m source depth: (a)

basement with perimeter crack; (b) slab-on-grade with perimeter crack; (c) basement with center hole; (d) slab-on-grade with center hole; (e) basement with center crack; (f) slab-

on-grade with center crack.

Y. Yao et al. / Building and Environment 59 (2013) 417e425

422

Page 7

contaminant mass entry rate is only determined by the crack

diffusivity itself since all other conditions remain the same. Source

depth is seen to be a far more important factor in determining

subslabconcentrationthan is

permeability.

anyassumptionregarding

3.4. The variation of subslab concentration

For vapor intrusion site investigation, subslab sampling location

is always a concern. How much does the sample position influence

observed contaminant subslab soil vapor concentration? Some VI

models [12,13] employ the subslab perimeter crack contaminant

concentration to calculate contaminant mass entry rate, using

Nazaroff’s equation [25] to estimate soil gas entry rate. But in

practice, it is generally not possible to examine the subslab soil

vapor concentration at the entrance of any particular crack. Of

course the Johnson-Ettinger model does not allow for any subslab

variation in concentration because it is a one-dimensional model.

Figs. 3 and 11 show the cross-sectional soil gas contaminant

concentration profiles for both basement and slab-on-grade foun-

dations, for different crack types and an assumed soil permeability

of 10?11and 10?13m2, respectively. The first thing these figures

suggest is that the crack type does not have much influence on

subslab concentration distribution. Since, (indoor air is relatively

clean compared to the soil gas) the subslab crack contaminant

concentration is always a bit lower than that of its immediate

Fig. 12. The normalized contaminant soil vapor concentration profile of simulations with 10?11m2soil permeability, perimeter crack and 8 m source depth: (a) 5 m ? 5 m

basement; (b) 10 m ? 10 m basement; (c) 20 m ? 20 m basement; (d) 5 m ? 5 m slab-on-grade; (e) 10 m ? 10 m slab-on-grade; (f) 20 m ? 20 m slab-on-grade.

Y. Yao et al. / Building and Environment 59 (2013) 417e425

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Page 8

surroundings. The so called “sink effect” becomes more obvious for

cases with low permeabilityas noted above. But in general, because

this “sink effect” is limited by the crack size. What mainly deter-

mines the concentration profile under the slab is the blockingeffect

of the foundation slab on contaminant diffusion. Second, the sub-

slab concentration contour shapes for the two cases of slab-on-

grade and basement are quite similar, except that the normalized

subslab concentration for a basement is about 0.1e0.2 larger than

that of a slab-on grade for the same horizontal location. The reason

is quite obvious; the subslab locations in the slab-on-grade case are

closer to the atmospheric sink around the building. Figs. 3 and 11

also suggest that for buildings with a typical 10 m ? 10 m foot-

print size, the normalized contaminant subslab concentration

range is 0.3e0.7 for basement cases and 0.1e0.5 for slab-on-grade

cases. It should be noted that such limited ranges of variation will

lead to only comparable variations in indoor air contaminant

concentration (where only even correct order of magnitude esti-

mates are still typically sought).

Figs.12 and 13 present the influence on subslab concentration of

increasing foundation slab size for different soil permeabilities.

Both figures show that the peak subslab concentration at the

middle increases as the foundation size increases. For basement

cases, the subslab concentration can for large structures reach

values almost as high as the source soilvaporconcentration, since it

becomes progressively more difficult for the contaminant soil

vapor to diffuse from the middle as the foundation size increases.

Fig. 13. The normalized contaminant soil vapor concentration profile of simulations with 10?13m2soil permeability, perimeter crack and 8 m source depth: (a) 5 m ? 5 m

basement; (b) 10 m ? 10 m basement; (c) 20 m ? 20 m basement; (d) 5 m ? 5 m slab-on-grade; (e) 10 m ? 10 m slab-on-grade; (f) 20 m ? 20 m slab-on-grade.

Y. Yao et al. / Building and Environment 59 (2013) 417e425

424

Page 9

These two figures also suggest that soil permeabilities play an

insignificant role in determining subslab contaminant concentra-

tion profile.

Except for something like the sink effect of a large hole in the

slab, the subslab concentration increases as the sampling location

approaches the center of the foundation slab. On the other hand,

the limit of the subslab concentration at the edge of the foundation

slab is zero, since the foundation slab edge approaches the open

atmosphere. Overall, though, subslab concentrations typically are

predicted to fall in a range of 0.1e1 [28]. In other words, it is

possible to conclude that the difference in subslab concentrations

attributable to the location of subslab soil vapor sample points

should be within an order of magnitude, and often much closer.

Larger variations than this strongly suggest some other type of

inhomogenously in the subslab (e.g. ventilation).

4. Conclusions

This paper presents 3-D simulations of vapor intrusion scenarios

withdifferentbuildingfoundationslabfeatures.Threetypesofcrack,

e.g. perimetercrack, centercrackand centerhole, weresimulated to

examine the influence of vapor intrusion entry pathway. The simu-

lation results show that soil gas flow rate can be influenced by crack

configuration, but the contaminant mass entry rate, which deter-

mines the indoor air contaminant concentration, does not vary

much, no more than one order of magnitude. Leaving aside the

scenario of a center hole, the crack scenarios offer much closer than

orderofmagnitudeagreement.Thesimulationsinthisstudyprovide

support for the application of models that employ various crack

descriptions. The location and the shape of an actual crack in the

foundation slab (as opposed to a hole) is not important for deter-

miningcontaminantmassflowrateintothebuilding.Thismeansitis

safeto applyamodelemployingaperimetercrackassumptionsince

other assumptions do not change this very much and assumption of

a hole in the center leads to lower entry rate predictions. The foun-

dationsizeaffectsneitherthesubslabperimetercrackconcentration

nor the contaminant entry rates much, as long as the overall crack

area is constant. It is the overall area of cracks that is the key

parameter. For an infinite homogenously distributed groundwater

source, the subslab concentration (normalized to source vapor

concentration) is predicted to range from lowest at the foundation

edgetohighestinthemiddleoftheslab,andinmostcaseswouldfall

in the range 0.1e1 [1,14]. This means that the subslab sampling

position should not make more than a comparable difference in

observed contaminant concentrations. Again, for any particular

scenario (e.g. basements), the variation in subslab concentration is

much less than an order of magnitude. It is the large slab on grade

scenarios that offer the greatest variation in subslab concentrations.

All the above discussions are based on the assumption of homoge-

nous source distribution.

Acknowledgment

This project was supported by Grant P42ES013660 from the

National Institute of Environmental Health Sciences. The content is

solely the responsibility of the authors and does not necessarily

represent the official views of the National Institute of Environ-

mental Health Sciences or the National Institutes of Health.

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