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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
[email protected]
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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
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ODOT SHRP Test RoadODOT SHRP Test Road
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Test SectionsTest Sections
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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
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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
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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
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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
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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
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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)
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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)
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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
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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
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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
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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
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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
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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