Modeling reaction of non-sorted circles to changes in

Additional insulation layer

Effect of snow and temperature

The effect of snow is modeled by increasing the surface temperature in the inter boil area by

interboil frost boilT Tβ=

frost boil Frunkin bluffT Tα=

Location of the frost boil system on the Arctic gradient, can be modeledby specifying the surface temperature

The value of the maximal frost heave does not depend on the surface temperature explicitly, but rather on the difference between and .inter boilT frost boilT

0 0.2 0.4 0.6 0.8 1 1.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1.0β =0.5β =

Hea

ve,m

Distance from the center, m

0.6,0.8,...,1.6α =

Unfrozen water content

0 0.2 0.4 0.6 0.8 1 1.20

0.05

0.1

0.15

0.2

0.25

0.4B = −

0.5B = −

0.6B = −

0.8B = −


Hea

ve,m

-16 -14 -12 -10 -8 -6 -4 -2 00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Temperature, C

Sat

ura

tio

n

0.4 fine grained, i.e. siltB = − −0.8 coarse grained, i.e. sand, organic matter, mossB = − −

Higher values of B correspond to higher amount of liquid water in partially frozen pores, andlarger body forces caused by the “cryogenic suction”.

Hydraulic permeability is

Higher values of the hydraulic permeability implies higher liquid water fluxes in the unfrozen region and more available water to form ice in the partially frozen area.

Hydraulic properties

0 ,k k αχ=

0 unfrozen state

saturation

'rate'

k

χα

−−−

where

0 0.2 0.4 0.6 0.8 1 1.20

0.05

0.1

0.15

0.2

0.25

4α =

5α =

6α =

7α =


Hea

ve,m

10 810 , 10m

ks

− −⎡ ⎤∈ ⎣ ⎦

Radius stability

0 0.2 0.4 0.6 0.8 1 1.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Hea

ve,m


The value of maximal frost heave non-linearly depends on the radius of the frost boil.

The model

where the unfrozen water content is a function of temperature and porosity

( ) ( )ii i i

T UC L L k T

t t t

θρ ρ θ∂ ∂ ∂− − ∇⋅ = ∇⋅ ∇∂ ∂ ∂

* *

(1 ) ((1 ) 1) ,ii f w w w

w

U LT f LTk P f

t t T T

θδ δ θ ρ θ ρθ

⎛ ⎞⎡ ⎤⎛ ⎞∂ ∂ ∂⎛ ⎞− − −∇⋅ − − = ∇⋅ ∇ + + ∇⎜ ⎟⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟∂ ∂ ∂⎝ ⎠ ⎝ ⎠⎣ ⎦⎝ ⎠

(1 ) 0n U

nt t

∂ ∂⎛ ⎞−∇⋅ − =⎜ ⎟∂ ∂⎝ ⎠

( ) (( ) )U U Pμ λ μ∇⋅ ∇ + ∇ + ∇⋅ = ∇

0

00

0

min ,B

we

e

n T T

T Tn n T T

T T

θ −

≥⎧⎪⎪ ⎡ ⎤= ⎛ ⎞−⎨ <⎢ ⎥⎜ ⎟⎪ −⎢ ⎥⎝ ⎠⎪ ⎣ ⎦⎩

w i nθ θ+ =

i

w

ρδρ

=

Energy conservation principle for a multi-component system

wθ

Mass conservation law for the water and mineral skeleton components:

Linear elasticity model is adopted for the soil

Liquid moisture conservation principle, derived from the generalized Darcy’s law

, volumetric fraction of water and ice

porosityw i

n

θ θ −−

We examine sensitivity of a general model of the frost boil dynamics with respect to changes in thermal, rheological and hydraulic properties of the ground material and boundary conditions. We apply the model to non-sorted circles along the low Arctic Climate gradient and investigate the seasonal dynamics of them. This investigation allows evaluation/detemination of physical mechanisms and driving forces that play the most decisive role in creating the differential frost heave in the non-sorted circles. Using this model we explore interactions between vegetation cover and thermo-mechanical processes. As the conclusion, we investigate the reaction of the non-sorted circles at several sites along the Dalton highway in the Arctic tundra in Alaska to changes in climate, in the active layer depth and in vegetation cover.

Distance from the center,m0 0.4 0.8 1.2 1.6

2

1

0

-3-3 -3-2.5

-2.5 -2.5-2-2 -2

-1.5-1.5 -1.5

-1-1 -1

-0.5-0.5 -0.50 0

0 00.50.5 0.5

**

*

Fictitious domain

21

3

0U =r

( )0

0x

y

U

σ ν=⋅ =r

( )0

0x

y

U

σ ν=⋅ =r

0σ ν⋅ =r

Computational geometry,boundary and initial conditions

A fictitious domain is separated from a real one (soil) by a red line which plays a role of the ground surface.

are points at which temperature and moisture are compared with experimental data.The soil consists of three parts, namely, 1,2,3 which have common and distinctive properties.

*

1 1

2 2

3 3

0.8 0.4

1.45 1.1

1.45 1.1

f t

f t

f t

λ λλ λλ λ

= =

= =

= =

61

62

63

2 10

2 10

20 10

E

E

E

= ⋅

= ⋅

= ⋅

51

42

43

2 10

2 10

2 10

a

a

a

−

−

−

= ⋅

= ⋅

= ⋅

Heat conductioncoefficient

Young modulus “Cryogenic Suction”

300 350

-15

-10

-5

0

300 350

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Tem

per

atu

re, C

Date, calendar day

Measured Computed

Date, calendar day

Vo

lum

etric

Wat

er C

onte

nt

Inter boil, initial depth 15 cm Frost boil, initial depth 20 cm

300 350

-15

-10

-5

0

300 350-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Measured Computed

Tem

pera

ture

, C

Date, calendar day Date, calendar day

Vol

umet

ric W

ater

Con

tent

300 350-20

-15

-10

-5

0

Date, calendar day

Tem

pera

ture

,C

Measured at 17cm depth Measured at 24cm depth Calucaled at 20 cm depth

Frost boil, initial depth 35 cm

Modeling reaction of non-sorted circles to changes in climate and vegetation cover

D. J Nicolsky1, V. E. Romanovsky1, G. S. Tipenko1, D. A. Walker2, R. Daanen1, P.P. Overduin3

1. Permafrost Laboratory, Geophysical Institute, University of Alaska Fairbanks 2. Alaska Geobotany Center, Institute of Arctic Biology, University of Alaska Fairbanks, 3. Alfred Wegener Institute for Polar and Marine Research

Field measurements along Artic climate gradientAbstract

Frost boil: “a patterned ground form that is equidimensional in several directions with a dominantly circular outline which lacks a border of stones…” van Everdingen 1998

Soil horizons

Non-sorted circles are defined as circular patterned ground features without a border of stones, usually with barren or sparsely vegetated central area 0.5 to 3.0 m in diameter.

The non-sorter circles occur on Turbic Cryosols.

[h]-A horizon enriched with organic matter.[m]-A horizon slightly altered by hydrolysis, oxidation, or solution, or all three to give a change in color or structure, or both.[y]-A horizon affected by cryoturbation as manifested by disrupted and broken horizons, incorporation of materials from other horizons, and mechanical sorting in at least half of the cross section of the pedon.[z]-A frozen layer.

Measured and calculated temperature and water content at some points ( )*

A departure of the calculated temperature and moisture from the measured one is small and can be partially explained by uncertainties in boundary conditions and soil properties.

ACKNOWLEDGEMENTS: This research was funded by ARCSS Program and by the Polar Earth Science Program, Office of Polar Programs, National Science Foundation (OPP-0120736, OPP-9732126, OPP-9870635, IARC-NSF CA: Project 3.1 Permafrost Research), and by the State of Alaska.

R e la tiv e mo v e m e n t o f s e n so r s (Hap p y Valle y #1 , m e sic)

-1

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10S e nsor's nu m b e r

Ver

tica

l mo

vem

ent

of

the

stic

k, c

m

A ugust 2 001 A pri l 2002 June 2002 A pri l 20 03

1 2 3 54 76 8 9 10

Happy Valley

Relative movement of sensors across the frost boil (Franklin Bluffs #1)

-5

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10Sensor's number

Ver

tical

mo

vem

ent o

f th

e st

ick,

cm

August 2000 April 2001 June 2001 July 2001

April 2002 June 2002 April 2003 Septem 2003

Franklin Bluffs

-2.5

-2

-1.5

-1

-0.5

0 0.5 1

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Temperature

Distance from the center

Dep

th

-1

0

1

2

3

4

5

6

7

8

0 0.5 1

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Pressure


0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0 0.5 1

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Porosity


0T

ν∂ =∂ r 0

T

ν∂ =∂ r 0

P

ν∂ =∂ r 0P = 0

n

ν∂ =∂ r 0

n

ν∂ =∂ r

( )1T

oν

∂ =∂ r 0

P

ν∂ =∂ r 0

n

ν∂ =∂ r

0P = 0n

ν∂ =∂ r( )surfaceT T t=

• Phase change occurs around –0.05 C.• Pore pressure correlates with temperature, and shows sinks and sources of water. • If the system is open then water migrates from the outer boundary through an unfrozen region to the so-called “frozen fringe”, where the

cryogenic suction makes the majority of liquid water migrate upwards. If the system is closed then water merely redistributes.• Increase in porosity in a frozen region is associated with ice lens formation. Just the volumetric expansion of water due to the phase

change cannot explain an observed frost heave. Cryogenic suction plays an important role.

Temperature, pore pressure and porosity (from the left to the right) distribution at the same moment of time in the entire computational domain, the ground is below the white line.

0 0.2 0.4 0.6 0.8 1 1.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Hea

ve,m


Each blue line correspondsto the different depth of an additional insulation layer over frost and inter boil areas. The insulation simulates the effect of vegetation cover on frost heave.

No additional insulation

2cm

4cm

6cm10cm

Thicker vegetation layer causes better thermal insulation and lower values cryogenic suction, hence the smaller frost heave of the ground.

Area of study

Maximum frost heave, 2001-2005

0

5

10

15

20

25

Mou

ld Bay

, mes

ic

Mou

ld Bay

, dry

slop

e

Mou

ld Bay

, wet

slop

e

Mou

ld Bay

, sand

y

Mou

ld Bay

, wet

lowes

t

Green

Cab

in, d

ry

Green

Cab

in, m

esic

Green

Cab

in, w

etHowe

Islan

dW

est D

ock

Deadh

orse

Fran

klin

Bluffs

Sagwon

MNT

Sagwon

MAT

Sagwon

MAT

, veg

Happy V

alley

Happy V

alley

, veg

Fro

st h

eave

, cm

Inter Circles In Circles

-2.2

-2

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0 0.5 1

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Temperature


Dep

th

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

0 0.5 1

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Pressure


0.3485

0.349

0.3495

0.35

0.3505

0.351

0.3515

0.352

0.3525

0 0.5 1

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

Porosity


0T

ν∂ =∂ r 0

T

ν∂ =∂ r 0

P

ν∂ =∂ r 0P = 0

n

ν∂ =∂ r 0

n

ν∂ =∂ r

( )1T

oν

∂ =∂ r 0

P

ν∂ =∂ r 0

n

ν∂ =∂ r

0P = 0n

ν∂ =∂ r( )surfaceT T t=

Ideal fluid

Mold BayActive layer dynamics 2004

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.47/12/2004 7/22/2004 8/1/2004 8/11/2004 8/21/2004 8/31/2004 9/10/2004 9/20/2004

Time

Dep

th (

m)

Freezing inter circle

Freezing in circles

Poorly drained site

DenserVeg.

Slower freezing More ice

More ice lenses

Largerheave

Macrostructure of soil

KH, E

Greater contrastcircle/inter

Smaller contrastcircle/inter

Macrostructure of soil

Well drained site

LessVeg.

Fasterfreezing Less ice

Less ice lenses

Lessheave

KH, E

Water availabilty and its effect on non-sorted circle system

Non-linear heat conduction equation + Liquid water balance

Equation

Soil particles conservation equation

Thermo-Mechanical Model of Frost Heave

Active Layer(organic soil)

Active Layer(mineral soil)

Permafrost

Heat Flux

Ice LensesSoil movem

ent &

leaching

Permafrost change over time

Ice Lens Heave

Seasonal frost

Water Flux

Thermo-Mechanical Model of Non-sorted circles

Free energy of the pore with respect to the thickness d of the liquid water film

d

Solid

Liquid

Ice

ψ

d

10/1/2003 11/1/2003 12/1/20030.00

0.04

0.08

0.12

0.16

0.20

0.24

Fro

st h

eave

,m

Time, days

λ=0.9 λ=1.1 λ=1.3

Maximal frost heave

Distance from the center,m

Dis

pla

cem

ent,

m

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Water permeable boundary

Water impermeable boundary

R e la t iv e m o v e m e n t o f s e n s o r s a c ro s s fr o s t b o il (S a g w o n M N T # 2 , S o u th e r n )

0

5

1 0

1 5

2 0

1 2 3 4 5 6 7 8 9 1 0S e n s o r 's n u m b e r

Ver

tica

l mo

vem

ent

of

the

stic

k, c

m

A u g u s t 2 0 0 1 A p r il 2 0 0 2 J u n e 2 0 0 2 A p r il 2 0 0 3

Sagwan

0 0.2 0.4 0.6 0.8 1 1.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2Maximal frost heave

Distance for the center, m

Dis

pla

cem

ent,

m

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

Fro

st h

eave

,m

Distance from the center,m

Homogeneous Different E Different E, λ Different E, λ,θ

w

Modeling differential frost heave for water impermeable external boundary

without a suction potential

(1 )i

w

heave ndρρ

= −,

porosity

active layer depth

water and ice densityw i

n

d

ρ ρ

−−

−

0.35 0.55 0.09 0.017∗ ∗ ≈

Each curve represents the maximal displacement of the ground surface and is computed for different combinations of soil properties.

Results from numerical model

Modeled displacement of the soil surfacein the center of the frost boil

Measured active layer depth Simulated displacement of the soil surface for circles at typical sites along the climate gradient

Franklin Bluffs,poorly drained and non-vegetated

Happy Valley,moderately drained and well vegetated

Howe Island,well drained and non-vegetated

11 cm frost heave4 cm frost heave

Hydraulically permeable boundary with suction potential

Green Cabin, wetMould Bay, mesic

Documents

Modeling reaction of non-sorted circles to changes in