12 burlingame
TRANSCRIPT
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Determination of Aquifer and Aquitard
Parameters from Inverse Modeling
Michael Burlingame, PEBureau of Design and Construction
New J ersey Department ofEnvironmental Protection
First International
FLAC/DEM Symposium
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Public
Supply
Well
Observation
Wells
Landfill with Supply and Observation Wells
Landfill
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Supply and Observation Wells
Supply
Well
Observation
Wells
Landfill
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OW-1
OW-2
OW-3
D
epth(m)
113
Observation Wells0
17
29
78
Public Supply Well
Mount Laurel Aquifer
Manasquan Aquitard
Kirkwood Aquitard
Cohansey Aquifer
114 m
Conceptual Site Model
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66.867.2
67.6
68.068.4
P
orePres
sure(kPa)
67.6
68.068.4
68.8
PorePressure
(cm
ofwater)
pump offpump on
Well OW-1
Well OW-2
Well OW-3
Elapsed Time (hours)0 5 10 15 20 25
420
440
460480
500
68.6
69.0
69.4
69.469.8
70.2
428.4
448.8
469.2489.6
Groundwater Monitoring Data
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Shallow aquifer exhibits increasing water level as a loweraquifer is pumped.
First documented by A. Verruijt, Delft University, who termed it
the NoordbergumEffect after a town in the Netherlands whereit was observed.
Reverse Water Level Fluctuations - Noordbergum Effect
aquifer
aquitard
pumped
aquifer
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Aquitard exhibits decreasing water level as a lower aquiferrecovers from pumping.
First documented by Langguth & Treskatis, who termed it the
Rhade Effect after a town in Germany where it was first observed.
aquitard
aquifer after pumping
aquifer
Reverse Water Level Fluctuations - Rhade Effect
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FLAC Axisymmetric Grid and Boundary Conditions
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Modeling Assumptions
Soil strata are horizontal, isotropic, and saturated.
Groundwater viscosity is constant and soil grains are incompressible.
Soil porosity and hydraulic conductivity is constant.
Hydraulic inefficiencies from well screen and sand pack are negligible.
Impermeable, incompressible layer forms the base of the model.
Effects of pumping on pore pressures and lateral strains are negligibleat the models limits.
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Governing Equation - Hydromechanical Formulation
In Biots Theory of 3-D consolidation, pore pressure (P) andvolumetric soil strain ( ) are coupled or covariant. For a FLACelement:
2w kk
w
P K k Pt n t
=
1 1
2 1 3
ii ii kk P
G K
= +
+
kk rr zz = + +
k is hydraulic conductivity, K is drained bulk modulus, is the drainedPoisson Ratio, G is the shear modulus, Kw is the bulk modulus of
water, n is porosity, w is the unit weight of water, is the meannormal stress.
where:
kk
kk
, ,i r z=
2 21 122 2 2
P P PP r
r r r r z
= + +
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Basic Modeling Strategy
Run sequence:
1) Run in hydraulic mode to establish pore pressure distribution.
2) Run in mechanical mode to develop body forces, then set
displacements to zero.
3) Run in coupled, hydromechanical mode until volumetric strains < 10-7.
4) Apply well discharge.
5) Run with Fast-Flow scheme for aquifer and in standard mode for
aquitards.6) Work from most highly stressed to least stressed layer.
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Inverse Modeling Strategy
Sensitivity Analysis:
Examine effects of soil parameters on pore pressure developmentto narrow down the number of unknowns.
Examine effects of modeling schemes (equilibration time, fast-flow,explicit/implicit, MC/elastic) on pore pressure development.
Model Calibration (trial and error assisted by contouring):
Use literature values to bound the variables.
Match modeled pore pressure histories to field data.
Calibrate each layer then make global runs to adjust for interactionbetween layers.
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42
43
44
45
46
47
48
49
50
51
0 2 4 6 8 10 12 14 16 18 20 22 24 26
Pore
Pressure
(mo
fH2
O)
Elapsed Time (hours)
Well OW-3 - Mount Laurel AquiferCurve Matching of Pore Pressure Histories
field data
sensitive to varying K and k
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Well OW-2 Manasquan AquitardCurve Matching of Pore Pressure Histories
6.85
6.90
6.95
7.00
7.05
7.10
7.15
0 2 4 6 8 10 12 14 16
Elapsed Time (hrs)
Po
rePressure(mo
fH2O)
field data
sensitive to varying K, G, and k
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6.84
6.86
6.88
6.90
6.92
6.94
6.96
6.98
7.00
0 2 4 6 8 10 12 14
Elapsed Time (hrs)
Por
ePressure
(mo
fH2O
)
Well OW-1 Kirkwood AquitardCurve Matching of Pore Pressure Histories
decreasing k*
decreasing K* and
* generally true but not always
field data
Manasquan Aquitard
M A it d
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Manasquan Aquitard
Pmodeled
- Pactual
x10-2
(Pa)
Flow Time = 3000 secs
20
10
1010
2020
30
40
-10
-10
0
0
0
0
0
0
0
Hydraulic Conductivity (cm/sec)
1e-8 1e-7 1e-6
D
rainedBulkM
odulus(MPa)
1e+2
1e+3
1e+4
Manasquan Aquitard
Contours of Pmodeled - Pactual x10-2 (Pa)
Flow Time = 3000 secs
DrainedBulkM
odulus,
K(MPa)
Hydraulic Conductivity, k (cm/sec)
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0
0
0
0
0
0
0
0
0
0
1e-8 1e-7
0
0
0
0
0
0
0
1e-8 1e-7
0
0
00
0
0
0
Hydraulic Conductivity (cm/sec)
1e-8 1e-7
D
rainedBulkM
odulus(MPa
)
2e+3
3e+3
4e+3
5e+3
6e+3
7e+3
8e+3
Manasquan AquitardZero Difference Pore Pressure Contours at Various Times
Manasquan AquitardZero Difference P Contours at Various Times
Dra
inedBulkM
odulus,
K(M
Pa)
Hydraulic Conductivity, k (cm/sec)
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Mount Laurel AquiferPore Pressure and Volumetric Strain Histories
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Simplified Diffusion Equation for Pumping Test Analysis
Commonly, for pumping test analysis, the change in pore pressure isuncoupled from mechanical strain:
2 1ww
P K k PKn
Ptt
=
k kP
so that:
rather than Biots more correct formulation:
2w
w
k kP K kP
tt n
=
k kP K or in terms of strainassume.
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Hydraulic Conductivity of Aquifer by Various Methods
Conclusion for aquifer:
k (hydromechanical) 2 x k (uncoupled)
The difference is due in large part to how volumetric soil strain is handled.
k
Formation Test Method Solution Method (cm/sec)
Mt. Laurel Pump Test* Hantush & Jacob, 1955 (confined) 2.1x 10-3
Pump Test* Hantush, 1961 (semi-confined) 2.3 x 10-3
Pump Test** Hantush & Jacob, 1955 (confined) 2.1 x 10-3
Pump Test* FLAC 2D, Ver. 5.1 (fast-flow) 5.0 x 10-3
* Kimball, 2006 ** Sammon, 1993
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Empirical Determination of Aquifers Shear Modulus
Use Richarts (1977) empirical equation for the small strainshear modulus, Gmax, for clean, round-grained sands as:
where:
is void ratio, for < 0.80 or n < 0.44, and for soil shear strains < 10-4
Get from the FLAC model and from laboratory tests.
0 522 17
1 3700
.( . ) kk
maxe
Ge
=
+
kk e
e e
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Density K G (FLAC) Gmax
Formation n (kN/m3
) (MPa) (MPa) (MPa)Mt. Laurel 0.2000 0.40 17.28 335.2 251.4 207.0
Aquifer Shear Modulus: Model and Empirical Equation
Conclusion for aquifer:
G (FLAC Model) is 21% ofGmax (Richart Equation).
Very good agreement even though the aquifer response is not very
sensitive to and G !
Manasquan Aquitard
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Manasquan AquitardPore Pressure and Volumetric Strain Histories
Sh ll Ki k dA it d
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Shallow Kirkwood AquitardPore Pressure and Volumetric Strain Histories
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Hydraulic Conductivity of Aquitards by Various Methods
Conclusion for aquitards:
k (hydromechanical)
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Denison Sampler for Aquitard (Stiff Silt & Clay)
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Denison Sample in 0.6 m Long Plastic Tube
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Resonant Column Testing - Testing Chamber
Resonant Column Testing
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Resonant Column TestingElectromagnetic Drive Causes Torsion
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0
20
40
60
80
100
120
140
160
1.E-06 1.E-05 1.E-04 1.E-03
Shear Strain
ShearModulus,
G(M
Pa)
Resonant Column Testing Results - Manasquan Aquitard
47.9 kPa
95.8 kPa
143.6 kPa
Gmax
Gmax
Gmax
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Aquitards Shear Moduli: Model and Resonant Column Tests
Conclusion:
G (FLAC Model) is between an order of magnitude and 35% ofGmax(Resonant Column).
Density K G (FLAC) Gmax
Aquitard n (kN/m3) (MPa) (MPa) (MPa)Manasquan 0.4945 0.55 11.62 4788.0 52.7 28.3 and 400.0
Kirkwood 0.4800 0.57 16.34 1197.0 48.4 74.9
* Resonant Column Testing by URS, 2008
*
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IN-SITU AQUITARD PROPERTIES: Modeling of reverse water
level fluctuations allows estimation of aquitard properties from apumping test.
TIME CONSUMING AND DIFFICULT: More than 200 runs, each
taking more than 8 hours (need faster processors and software). STRAINS: Fully-coupled modeling is more important as soil
modulus and permeability decrease. FLAC is able to account forboth solid-fluid stresses and strains.
APPROXIMATION: Order of magnitude precision is consideredpossible without perfectly matching the field data.
AUTOMATION: Use of calibration codes, such as UCODE, in a
FISH subroutine may be practical for aquifers but very difficult foraquitards due to the ill-poised, non-linear response.
FLAC TRICK (fully-coupled modeling): Use of FLACs implicit
scheme, with a time step as per the FLAC Manual, was up to 4Xfaster than the explicit scheme without much loss of accuracy.
Conclusions
Xi i G i
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Acknowledgements:
9 Mr. J uan Salguero, L. Robert Kimball & Associates, designed andconducted the pumping test.
9 Dr. Herb Wang, University of Wisconsin-Madison, provided anindependent interpretation of the data.
9 Mr. Greg Thomas, URS, conducted resonant column testing.
9 Dr. Christine Detournay, Itasca Consulting Group, gave helpfulguidance on modeling and some words of encouragement.
9 The Symposiums peer review committee made valuable comments.
ThankYou
Dziekuje
Merci Jag tackar
Gracias
ArigatoDanke schn
Efcharisto M goi
BanihaXie xie
Spasibo
GrazieToda
Hvala vam
Nandri