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Table 1 Parameters used for the random FEM model simulation

From: A novel random finite element model for holistically modeling of the frost effects on soils and cold region pavements

Constant

Value

Units

Description

W

10

m

Horizontal distance of the study region

Dasphalt

0.2032

m

Thickness of the asphalt layer

Db

0.1524

m

Thickness of the base layer

Ds

1

m

Thickness of the silt layer

w

0.15

1

Initial water content

ρ

1708

kg/m3

Dry density of silt specimen

d

50

μm

Diameter of silt particle

Gs

2.65

1

Specific gravity of silt specimen

Es

12.7

GPa

Young’s modulus of silt particle

Ei

9

GPa

Young’s modulus of ice

Ew

3.9 × 10−5

Pa

Young’s modulus of water

Ea

0

Pa

Young’s modulus of air

Easphalt

9

GPa

Young’s modulus of the asphalt layer

Eb

0.3

GPa

Young’s modulus of the base layer

Eps

3

GPa

Young’s modulus of the polystyrene foam

Epu

0.1

GPa

Young’s modulus of the polyurethane foam

Egf

10

GPa

Young’s modulus of the glass fiber board

μs

0.3

1

Poisson’s ratio of silt particle

μi

0.3

1

Poisson’s ratio of ice

μw

0.5

1

Poisson’s ratio of water

μa

0

1

Poisson’s ratio of air

μasphalt

0.35

1

Poisson’s ratio of the asphalt layer

μb

0.3

1

Poisson’s ratio of the base layer

μps

0.4

1

Poisson’s ratio of the polystyrene foam

μpu

0.32

1

Poisson’s ratio of the polyurethane foam

μgf

0.25

1

Poisson’s ratio of the glass fiber board

ρs

2600

kg/m3

Density of silt particle

ρi

917

kg/m3

Density of ice

ρw

1000

kg/m3

Density of water

ρa

1.29

kg/m3

Density of air

ρasphalt

2243

kg/m3

Density of the asphalt layer

ρb

1680

kg/m3

Density of the base layer

ρps

46

kg/m3

Density of the polystyrene foam

ks

2

W/m·K

Thermal conductivity of silt particle

ki

2.2

W/m·K

Thermal conductivity of ice

kw

0.58

W/m·K

Thermal conductivity of water

ka

0.025

W/m·K

Thermal conductivity of air

kasphalt

0.75

W/m·K

Thermal conductivity of asphalt layer

kb

0.7

W/m·K

Thermal conductivity of base layer

kps

0.03

W/m·K

Thermal conductivity of the polystyrene foam

Cps

835

J/kg·K

Heat capacity of silt particle

Cpi

1960

J/kg·K

Heat capacity of ice

Cpw

4181.3

J/kg·K

Heat capacity of water

Cpa

1005

J/kg·K

Heat capacity of air

Cpasphalt

920

J/kg·K

Heat capacity of the asphalt layer

Cpb

840

J/kg·K

Heat capacity of the base layer

Cpps

1500

J/kg·K

Heat capacity of the polystyrene foam

Cppu

1450

J/kg·K

Heat capacity of the polyurethane foam

Lf

334

kJ/kg

Latent heat fusion of water

αs

9 × 10−6

1/K

Volumetric coefficient of thermal expansion of silt particle

αi

1.9 × 10−4

1/K

Volumetric coefficient of thermal expansion of ice

αw

2.07 × 10−4

1/K

Volumetric coefficient of thermal expansion of water

αa

3.43 × 10−3

1/K

Volumetric coefficient of thermal expansion of air

αasphalt

4 × 10−5

1/K

Volumetric coefficient of thermal expansion of the asphalt

αb

4 × 10− 5

1/K

Volumetric coefficient of thermal expansion of the base layer

αps

7 × 10−5

1/K

Volumetric coefficient of thermal expansion of the foam

αpu

6.5 × 10−5

1/K

Volumetric coefficient of thermal expansion of the polyurethane foam

αgf

3 × 10−5

1/K

Volumetric coefficient of thermal expansion of the glass fiber board