34
Geotechnical News • June 2013
GROUNDWATER
In this paper, recent analytical solu-
tions for stratified aquifers have been
used. These solutions were verified
numerically using finite elements
(Chapuis 2015). The predictive eq. (1)
for
n
e HEHA
involves the mean and vari-
ance of the
ln
(
K
) distribution: here,
eq. (1) was verified experimentally.
For laboratory tests with homogenized
soils, the variability in
K
was shown
to be low. The theory predicts that the
large scale
n
e HEHA
is almost equal to
n
,
as usually observed in these laboratory
tests. For field tracer tests, the spatial
variation in
K
controls dispersion. The
most permeable layers have a strong
influence upon transport and disper-
sion and
n
e HEHA
may be much lower
than
n
. It is only for a low variance
(
σ
2
ln
K
≤1
) that normal and lognormal
K
distributions predict close break-
through curves. Using the data experi-
ments obtained by several authors, an
excellent agreement is found between
predicted and calculated (curve fitting)
n
e HEHA
values.
Field tracer tests depend upon aqui-
fer heterogeneity but also complex
geometric conditions, time-variable
boundary conditions, and processes
such as sorption. However, the new
findings here, for simplified cases,
help to understand early tracer arriv-
als, and they are supported by field
data.
Acknowledgments
The paper is the result of a research
program subsidized by the Natural
Sciences and Engineering Research
Council of Canada (NSERC) to
improve the quality of groundwater
parameters.
References
ASTM. Test methods for maximum
index density and unit weight
of soils using a vibratory table
(D4253). Annual CDs of Stan-
dards, vol. 04.08, ASTM Interna-
tional, West Conshohocken, PA.
ASTM. Test methods for minimum
index density of soils and calcula-
tion of relative density (D4254).
Annual CDs of Standards, vol.
04.08, ASTM International, West
Conshohocken, PA.
Bales, R.C, Li, S., Yeh, T.-C.J.,
Lenczewski, M.E., and Gerba,
C.P. 1997. Bacteriophage and
microsphere transport in saturated
porous media: Forced-gradient
experiment at Borden, Ontario.
Water Resources Research, 33(4):
639–648.
Bear, J. 1972. Dynamics of Fluids in
Porous Media. American Elsevier,
New York.
Bear, J., and Jacobs, M. 1965. On the
movement of water bodies injected
into aquifers. Journal of Hydrol-
ogy, 3: 37–57.
Bierschenk, W.H. 1959. Aquifer
characteristics and groundwater
movement at Hanford. Report
HW-60601, 83 pp., Hanford
Atomic Products Operation, Rich-
land, Washington.
Chapuis, R.P. 2016.
Extracting Infor-
mation from Grain Size Distribu-
tion Curves
. Geotics, Montreal.
Chapuis, R.P. 2015. Effective poros-
ity and dispersion in stratified
aquifers: Closed-form solutions,
Internal Research Report EPM-
RT-2015-01, 28 p, Polytechnique,
Montreal.
Chapuis, R.P. 2013. Permeability scale
effects in sandy aquifers: a few
case studies. In Proceedings of
18th Int. Conf. on Soil Mechan-
ics and Foundation Engineering,
Paris, France, pp. 505–510.
Chapuis, R.P. 2012a. Estimating the
in situ porosity of sandy soils
sampled in boreholes. Engineering
Geology, 141-142: 57–64.
Chapuis, R.P. 2012b. Predicting the
saturated hydraulic conductivity of
soils: a review. Bulletin of Engi-
neering Geology and the Environ-
ment, 71(3): 401–434.
Chapuis, R.P. 2011. Pumping a
recharged unconfined aquifer:
solutions for the hydraulic head
and the transfer time (in French).
Bulletin of Engineering Geol-
ogy and the Environment, 70(2):
309–316.
Chapuis, R.P. 2004. Predicting the
saturated hydraulic conductivity
of sand and gravel using effective
diameter and void ratio. Cana-
dian Geotechnical Journal, 41(5):
787–795.
Chapuis, R.P., and Aubertin, M. 2003.
On the use of the Kozeny–Carman
equation to predict the hydraulic
conductivity of a soil. Canadian
Geotechnical Journal, 40(3):
616–628.
Chapuis, R.P., and Chesnaux, R. 2006.
Travel time to a well pumping
an unconfined aquifer without
recharge. Ground Water, 44(4):
600–603.
Chapuis, R.P., Dallaire, V., Marcotte,
D., Chouteau, M., Acevedo, N.,
and Gagnon, F. 2005. Evaluat-
ing the hydraulic conductivity at
three different scales within an
unconfined aquifer at Lachenaie,
Quebec. Canadian Geotechnical
Journal, 42(4): 1212–1220.
Chin, D.A. 1986. Estimation of disper-
sion coefficients in porous media.
ASCE Journal of Hydraulic Engi-
neering, 112(7): 591–609.
Dentz, M., Le Borgne, T., Englert,
A., and Bileljic, B. 2011. Mixing,
spreading and reaction in hetero-
geneous media: A brief review.
Journal of Contaminant Hydrol-
ogy, 120–121(SI):1–17.
Fernandez-Garcia, D., Rajaram, H.,
and Illangasekare, T.H. 2005.
Assessment of the predictive
capabilities of stochastic theories
in a three-dimensional laboratory
test aquifer: Effective hydrau-
lic conductivity and temporal
moments of breakthrough curves.
Water Resources Research, 41(4):
W04002.
Freeze, R.A. 1975. A stochastic-
conceptual analysis of one-
dimensional groundwater flow in
nonuniform homogeneous media.
