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7/30/2019 12 Burlingame

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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

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