asce cold region conference-july 2015 (1)

÷

Frost Heave - A Semi-Empirical Model Based on Field Data

Pegah RajaeiGilbert Baladi

ASCE Cold Region Conference, Salt Lake City, July 2015

Department of Civil and Environmental Engineering

Background - Frost Heave Frost Heave Theories

Models - Gilpin Model

Revised Model - Statistical Frost Depth Model Revised Frost Heave Model Discussion; and Evaluation

Summary and Conclusion

Outline


Frost Heave (ΔH)

Bedrock

▼ GWT

GS

GS

Ice lenses

• Water and below freezing temperatures = ice lenses

• The growth of ice lenses causes ground heave causing damage to pavements, shoulders, utility lines, and unprotected foundations (Liu et al. 2012).

.

Frost Heave

Frost Heave

Frost Susceptible Materials

Below Freezing Temperatures and freezing rate

Water Availability

Frost Heave TheoriesTaber (Taber, 1930) was the first to address frost heave.

During the freezing process, water migrates toward the frozen front causing ice lenses to grow.Frost heave is a function of soil type, grain size, freezing rate, availability of water and the overburden pressure.

Capillary theory (primary frost heave)Theories

Frozen Fringe (secondary frost heave)

Capillary Theory

The Capillary theory is based on the Clapeyron equation

Where = ice pressure ; = water pressure; = density of water; = the latent heat of fusion at the bulk freezing temperature ;T= the thermodynamic equilibrium temperature of the system; and= bulk freezing temperature; (Peppin and Style, 2012b).

Frozen region

Unfrozen region (water moves upward toward the frozen front)

Problems

• It works well for uniform soil size.• It over predicts frost depth (Peppin and Style, 2012a). • Itdoes not explain the mechanism of ice lens formation.

Frozen Fringe Theory

Frost heave can continue to occur below freezing temperature.

Frozen region, which is controversial (may be in some systems) Frozen fringe region (temperature below freezing) Unfrozen region (Dash et al. 2006).





Outline

The first coupled heat and mass flow model in the soil was proposed by Harlan (Harlan, 1973) .

Later Giplin (Giplin,1980) Konrad and Morgenstern (Konrad and Morgenstern ,1980) Nixon (Nixon, 1991) Fowler and Krantz (Fowler and Krantz ,1994)

Models

Water flow

VH

POB X

TTBOT

Tff

Tl

H

a

Z

GWT

TTOP

x

Frozen Zone

Unfrozen Zone

Frozen Fringe

Bottom of ‘Active’ Ice Lens

The Gilpin Frost Heave Model

In this study, the Gilpin model was modified

Simplification of the required input data. Inclusion of a statistical frost depth model (MDOT) and (MnDOT). The modified model was evaluated using field data

The Gilpin Frost Heave Model Heat Balance Equations

Mass Balance Equations

Ice Lenses FormationNew ice lenses are initiated where the ice pressure in the frozen fringe exceeds a critical value of the separation pressure.





Outline

• Developed using MDOT temperature data collected at 18 Road Weather Information System (RWIS)

Revised ModelStatistical Frost Depth Model

Revised Model Statistical Frost Depth Model

• Verified using 9 years of soil temperature data collected by MNDOT at 8 stations.

The statistical model uses the thermal conductivity and heat capacity of six disturbed and saturated soil types measured in the lab using a KD2 pro thermal properties analyzer (ASTM D5334-08).


Station Name Material AASHTO Classification

Thermal Conductivity

(W/m.K)

Heat Capacity

(MJ/m3.K)

Houghton LakeSilty fine sand with

trace of gravel A-2 2.57 2.67

Fine sand A-3 2.55 2.84

Wolverine

Fine sand with trace of gravel A-2 2.49 2.69

Fine sand A-3 2.42 2.69Soft clayey sandy , some silt & some

gravelA-2 1.74 2.98

Williamsburg Silty clay - 1.51 3.1Rudyard Silty clay - 1.12 3.2


0 10 20 30 40 50 60 70 80 90 1000

102030405060708090

100

Line of equality between the measured and calculated dataClayey soil-MinnesotaSandy soil-Minnesota

Measured frost depth (in)

Cal

cula

ted

fros

t dep

th (i

n)

0 10 20 30 40 50 60 70 800

10

20

30

40

50

60

70

Line of equality between the measured and calculated dataClayey soil-MichiganSandy soil-Michigan

Measured frost depth (in)

Cal

cula

ted

frost

dep

th (i

n)

Revised Frost Heave Model

• Gilpin assumed that the initiation of new ice lenses starts where the ice pressure (Pi) in the frozen fringe exceeds the separation pressure (PSEP).

• The Gilpin model was calibrated using laboratory data.• The model was not correlated to the field data because the

required input parameters were not available. • The Gilpin model was revised to simplify the required inputs.

The revision of the Gilpin model was accomplished using:• The measured values of the unfrozen thermal conductivity (kuf).• The assumed thermal conductivity of the frozen fringe (kp) of 1.5

kuf (Farouki 1981). • The assumed temperature at the bottom of the unfrozen zone (TBOT)• The Gilpin equation to calculate the temperature at the base of the

frozen fringe (Tff).

• The developed statistical frost depth model.


𝑇 𝑓𝑓= 𝑓𝑟𝑜𝑠𝑡 h𝑑𝑒𝑝𝑡 −8𝜎 𝑖𝑤𝜈𝑤𝑇 𝑎

𝐷10∗𝐿;𝜎 𝑖𝑤=0.4 N / m

The total frost heave was estimated using the following equation:

Where = total frost heave;∆hu = frost heave due to water uptake;∆hi = heave due to freezing of in-situ pore water;VH = heave velocity (m/s);∆t = time interval;n = soil porosity, and the constant 0.09 is the ratio of volumetric expansion of water in phase change (Nixon 1982); and H= thickness of frozen zone, (m).


Discussion

Ground water table depth = 10m, TTOP = -3 oC, freezing duration 100 days, POB = 150 KPa .

10 30 50 70 900

5

10

15

20

25

30

35 Clayey siltSandy clayey siltFine sand

Time (Day)

Tota

l fro

st h

eave

(mm

)

10 30 50 70 900

2

4

6

8

10

12 Clayey siltSandy clayey siltFine sand

Time (Day)

Froz

en fr

inge

(mm

)

Discussion

ground water table depth = 10m, TTOP = -3 oC, freezing duration 100 days, and POB = 150 KPa .

Discussion

TTOP= -3 oC, freezing duration 100 days.

0 100 200 300 4000

10

20

30

40

50

60

70

z=2 mz=6 mz=10 m

Overburden pressure (KPa)

Tota

l fro

st h

eave

(mm

) Depth of GWT

Discussion

ground water table at 10 m, POB = 150 KPa

-11-10-9-8-7-6-5-4-3-2-105

101520253035404550

30 Days 60 Days 90 Days

TTOP (Surface temperature) (oC)

Tota

l fro

st h

eave

(mm

)Freezing period

EvaluationThe revised frost heave model was evaluated using measured frost heave data provided by MDOT under the shoulders and pavements of five sites located in Oakland County, Michigan.

Evaluation

Station Soil Type AASHTO Class.

Frost Depth (cm)

Max Heave in Shoulder

(cm)

Max Heave in

Pavement (cm)

Freezing Period (days)

Ttop (oC)

Hydraulic Conductivity

(cm/s)

GWT (m)

D10

(mm)

Sta/652+00

clayey, silty,

gravely, sand

A-2 86.4 2.3 2.2 60 -4 10-4 9 0.02

Sta/724+00 Fine sand and silt A-3 61.0 2.5 1.9 65 -2 5(10-5) 9 0.01

Sta/719+00 Fine sand with silt A-3 71.0 2.2 1.9 40 -3 5(10-5) 9 0.01

Sta/528+88 Sandy clayey silt - 76.0 1.9 1 70 -2 10-5 9 0.002

Sta/474+00 clayey silt - 63.5 2.5 2.3 55 -2 5(10-6) 9 0.001

Evaluation

0.600000000000001

1

1.4

1.8

2.2

2.6

3

3.4Line of equality between calculated and measured dataFrost heave under shoulderFrost heave under pavement

Measured heave (cm)

Cal

cula

ted

heav

e (c

m)





Outline


The Gilpin model was revised and simplified to decrease the number of required inputs that are not easily available or expensive to obtain or measure. The revision consisted of:• Replacing the heat balance equation for calculating the frost

depth by an empirical frost depth model. • The unfrozen hydraulic conductivity was used to estimate the

overall hydraulic conductivity of the frozen fringe.• The upper pavement layers were replaced by an equivalent

overburden pressure based on their thicknesses and density. • A single layer model was used to represent the roadbed soils.• The revised model was verified using measured frost heave

data at five sites in Michigan. Based on the results, it was concluded that the revised and simplified frost heave model yielded relatively accurate frost heave compared to the measured data.

÷

Frost Heave - A Semi-Empirical Model Based on Field Data

Pegah RajaeiGibert Baladi

ASCE Cold Region Conference, Salt Lake City, July 2015

Department of Civil and Environmental Engineering

asce cold region conference-july 2015 (1)

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