Evaluation Of Seasonal Evaluation Of Seasonal Effects On Subgrade SoilsEffects On Subgrade Soils

 TRB PAPER 03-03801

 Andrew G. HeydingerMail Stop 307

Department of Civil EngineeringUniversity of Toledo

Toledo, OH 43606-3390(419) 530-8133 Voice(419) 530-8116 Fax

aheyding@eng.utoledo.edu

Purpose of PresentationPurpose of Presentation Present general expressions for the seasonal

variations of air temperature and subgrade soil temperature and moisture

Discuss effects of precipitation and depth to ground water table on the subgrade soil

Use seasonal variations of subgrade soil moisture to determine the mean monthly variations of resilient modulus and weighting factors

ODOT SHRP Test RoadODOT SHRP Test Road

Test SectionsTest Sections

General Expression General Expression Based on Fourier transform of the time series:

F(t) = A0 + B1 sin[(t-)]  t = time expressed as the day of the year 

A0 = mean value 

B1 = the amplitude  the normalized frequency

(=2π/365.25)  

= time shift in days

Measured and Computed Mean Measured and Computed Mean Daily Air Temperatures Daily Air Temperatures

T(t) = 10.70 + 12.39 sin[2π/365.25 (t - )]

-20

-10

0

10

20

30

40

1/1/96 12/31/96 12/31/97 12/31/98 1/1/00 12/31/00 12/31/01

Date

Dai

ly A

vera

ge

Air

Tem

per

atu

re (

oC

)

Measured Computed

Mean Daily Temperatures Mean Daily Temperatures (PCC Section(PCC Section))

-20

-10

0

10

20

30

40

1/1/96 12/31/96 12/31/97 12/31/98 1/1/00 12/31/00 12/31/01

Date

Me

an

Da

ily

Te

mp

era

ture

(oC

)

Measured (Air) Computed (Air) Sensor 4 Sensor 5

Sensor 6 Sensor 7 Sensor 12 Sensor 18

Mean Daily Temperatures Mean Daily Temperatures (AC Section(AC Section))

-20

-10

0

10

20

30

40

1/1/96 12/31/96 12/31/97 12/31/98 1/1/00 12/31/00 12/31/01

Date

Me

an

Da

ily

Te

mp

era

ture

(oC

)

Measured (Air) Computed (Air) Sensor 4 Sensor 5

Sensor 6 Sensor 7 Sensor 12 Sensor 18

Volumetric Water Content and Volumetric Water Content and Precipitation (AC Section)Precipitation (AC Section)

0

5

10

15

20

25

30

35

40

45

50

07/01/96 07/01/97 07/01/98 07/01/99 07/01/00 07/01/01

Date

Vo

lum

etri

c W

ater

Co

nte

nt

0

10

20

30

40

50

60

70

80

90

100

Pre

cip

itat

ion

(m

m)

1 2 3 4 10 Precipitation

Volumetric Water ContentVolumetric Water ContentAnd Depth to Water Table And Depth to Water Table (PCC Section)(PCC Section)

34.0

35.0

36.0

37.0

38.0

39.0

40.0

41.0

42.0

10/2/96 10/3/97 10/4/98 10/5/99 10/5/00 10/6/01Date

TD

R V

olu

me

tric

Wa

ter

Co

nte

nt

6.0

7.0

8.0

9.0

10.0

11.0

12.0

De

pth

to

Wa

ter

Ta

ble

(ft

)

Average TDR VMC (%) (TDR 2,3,4) Depth to Water Table (ft)

Volumetric Water ContentVolumetric Water ContentAnd Depth to Water Table And Depth to Water Table (AC Section)(AC Section)

34.0

35.0

36.0

37.0

38.0

39.0

40.0

41.0

42.0

6/24/96 6/25/97 6/26/98 6/27/99 6/27/00 6/28/01

Date

TD

R V

olu

me

tric

Wa

ter

Co

nte

nt

(%)

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

De

pt

to W

ate

r T

ab

le (

ft)

Average TDR VMC (%) (TDR 1,2,3) Depth to Water Table (ft)

Volumetric Water Content and Volumetric Water Content and Average Soil TemperatureAverage Soil Temperature (PCC Section)(PCC Section)

28

32

36

40

44

7/1/96 7/1/97 7/1/98 7/1/99 7/1/00 7/1/01 7/1/02

Date

Vo

lum

etr

ic M

ois

ture

Co

nte

nt

-20

0

20

40

60

80

100

So

il T

em

pe

ratu

re o

C

Average TDR 2,3,4 Average Soil Temperature

Volumetric Water Content and Volumetric Water Content and Average Soil TemperatureAverage Soil Temperature(AC Section)(AC Section)

VMC(t) = 37.1 + 1.66 sin[2π/365.25 (t - )]

32

36

40

44

7/1/96 7/1/97 7/1/98 7/1/99 7/1/00 7/1/01 7/1/02

Date

Vo

lum

etr

ic M

ois

ture

Co

nte

nt

-10

10

30

50

70

90

110

130

150

Av

era

ge

So

il T

em

pe

ratu

re oC

Average TDR 1, 2, 3 Computed Moisture Content

Average Soil Temperature

Calculation of Seasonal Calculation of Seasonal Variation Of Subgrade Soil Variation Of Subgrade Soil Resilient ModulusResilient Modulus

Equation for Mr from lab tests on subgrade soil

Mr(psi) = 77235.54 - 639.121S(%) - 5418.33d

Used mean values of VMC for each month and n = 40% to compute mean monthly S(%)

Used mean monthly S(%) and d = 1.2 psi to compute mean monthly Mr

Calculation of Weight Factors Calculation of Weight Factors for Resilient Modulusfor Resilient Modulus

Equation for weighting factors

Weighting factors are computed using the mean resilient modulus

Example Calculation for Example Calculation for Resilient Modulus Weighting Resilient Modulus Weighting Factors (AC Section)Factors (AC Section)

Mean Mean MeanVMC S Mri Mri Mri-2.32 Mri-2.32

Month (%) (%) (psi) (MPa) (psi) (MPa) WfiJan 35.61 89.0 13834 95.4 2.47E-10 2.56E-05 0.577Feb 35.50 88.7 14019 96.7 2.40E-10 2.48E-05 0.560Mar 35.80 89.5 13536 93.3 2.60E-10 2.69E-05 0.607Apr 36.46 91.1 12481 86.1 3.14E-10 3.25E-05 0.733May 37.30 93.2 11137 76.8 4.09E-10 4.23E-05 0.955Jun 38.10 95.2 9865 68.0 5.42E-10 5.6E-05 1.265Jul 38.63 96.6 9009 62.1 6.69E-10 6.91E-05 1.561

Aug 38.76 96.9 8800 60.7 7.06E-10 7.3E-05 1.648Sep 38.45 96.1 9300 64.1 6.21E-10 6.42E-05 1.450Oct 37.78 94.4 10369 71.5 4.83E-10 4.99E-05 1.127Nov 36.94 92.3 11716 80.8 3.63E-10 3.76E-05 0.849Dec 36.15 90.4 12979 89.5 2.87E-10 2.96E-05 0.669

Sum = 5.14E-09 5.31E-04 12.000

ConclusionsConclusionsData from Ohio SHRP Test Pavement was

analyzed for seasonal variationsSubgrade soil VMC was not correlated to

precipitation or depth to the GWTFourier transform analyses were used to

express seasonal variations using mean daily values

Subgrade soil VMC was used to predict mean monthly variations of resilient modulus and weighting factors