Evaluation Of Seasonal
Effects On Subgrade Soils
TRB PAPER 03-03801
Andrew G. Heydinger
Mail Stop 307
Department of Civil Engineering
University of Toledo
Toledo, OH 43606-3390
(419) 530-8133 Voice
(419) 530-8116 Fax
aheyding@eng.utoledo.edu
Purpose 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 Road
Test Sections
General Expression

Based on Fourier transform of the time series:
F(t) = A0 + B1 sin[(t-f)]
t = time expressed as the day of the year
A0 = mean value
B1 = the amplitude
 = the normalized frequency (=2π/365.25)
f = time shift in days
Measured and Computed Mean
Daily Air Temperatures
40
Computed
Daily Average Air Temperature (
o
C)
Measured
30
20
10
0
-10
-20
1/1/96
12/31/96
12/31/97
12/31/98
1/1/00
12/31/00
12/31/01
Date
T(t) = 10.70 + 12.39 sin[2π/365.25 (t - 109)]
Mean Daily Temperatures (PCC
Section)
Measured (Air)
Computed (Air)
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 12
Sensor 18
Mean Daily Temperature ( o C)
40
30
20
10
0
-10
-20
1/1/96
12/31/96
12/31/97
12/31/98
Date
1/1/00
12/31/00
12/31/01
Mean Daily Temperatures
(AC Section)
Measured (Air)
Computed (Air)
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Sensor 12
Sensor 18
Mean Daily Temperature ( o C)
40
30
20
10
0
-10
-20
1/1/96
12/31/96
12/31/97
12/31/98
Date
1/1/00
12/31/00
12/31/01
Volumetric Water Content and
Precipitation (AC Section)
2
3
4
10
Precipitation
50
100
45
90
40
80
35
70
30
60
25
50
20
40
15
30
10
20
5
10
0
07/01/96
0
07/01/97
07/01/98
07/01/99
Date
07/01/00
07/01/01
Precipitation (mm)
Volumetric Water Content
1
Volumetric Water Content
And Depth to Water Table
(PCC Section)
Average TDR VMC (% ) (TDR 2,3,4)
Depth to Water Table (ft)
12.0
41.0
11.0
40.0
10.0
39.0
38.0
9.0
37.0
8.0
36.0
7.0
35.0
34.0
10/2/96
6.0
10/3/97
10/4/98
10/5/99
Date
10/5/00
10/6/01
Depth to Water Table (ft)
TDR Volumetric Water Content
42.0
Volumetric Water Content
And Depth to Water Table
(AC Section)
Depth to Water Table (ft)
42.0
8.0
41.0
7.0
40.0
6.0
39.0
5.0
38.0
4.0
37.0
3.0
36.0
2.0
35.0
1.0
34.0
6/24/96
6/25/97
6/26/98
6/27/99
Date
6/27/00
6/28/01
Dept to Water Table (ft)
TDR Volumetric Water Content (%)
Average TDR VMC (% ) (TDR 1,2,3)
Volumetric Water Content and
Average Soil Temperature
(PCC Section)
Average TDR 2,3,4
Average Soil Temperature
100
80
40
60
36
40
20
32
0
28
7/1/96
-20
7/1/97
7/1/98
7/1/99
7/1/00
Date
7/1/01
7/1/02
Soil Temperature oC
Volumetric Moisture Content
44
Volumetric Water Content and
Average Soil Temperature
(AC Section)
Average TDR 1, 2, 3
Computed Moisture Content
Average Soil Temperature
150
130
110
40
90
70
50
36
30
10
32
7/1/96
Average Soil Temperature oC
Volumetric Moisture Content
44
-10
7/1/97
7/1/98
7/1/99
7/1/00
7/1/01
7/1/02
Date
VMC(t) = 37.1 + 1.66 sin[2π/365.25 (t - 130)]
Calculation of Seasonal
Variation Of Subgrade Soil
Resilient Modulus

Equation for Mr from lab tests on subgrade soil
Mr(psi) = 77235.54 - 639.121S(%) - 5418.33sd
Used mean values of VMC for each month
and n = 40% to compute mean monthly S(%)
 Used mean monthly S(%) and sd = 1.2 psi to
compute mean monthly Mr

Calculation of Weight Factors
for Resilient Modulus

Equation for weighting factors
WF
i
=
12 M
12

i =1

M
 2 . 32
Ri
 2 . 32
Ri
Weighting factors are computed using the
mean resilient modulus
Example Calculation for
Resilient Modulus Weighting
Factors (AC Section)
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Mean
VMC
(%)
35.61
35.50
35.80
36.46
37.30
38.10
38.63
38.76
38.45
37.78
36.94
36.15
S
(%)
89.0
88.7
89.5
91.1
93.2
95.2
96.6
96.9
96.1
94.4
92.3
90.4
Mean
Mri
(psi)
13834
14019
13536
12481
11137
9865
9009
8800
9300
10369
11716
12979
Mean
Mri
(MPa)
95.4
96.7
93.3
86.1
76.8
68.0
62.1
60.7
64.1
71.5
80.8
89.5
Sum =
Mri-2.32
(psi)
2.47E-10
2.40E-10
2.60E-10
3.14E-10
4.09E-10
5.42E-10
6.69E-10
7.06E-10
6.21E-10
4.83E-10
3.63E-10
2.87E-10
5.14E-09
Mri-2.32
(MPa)
2.56E-05
2.48E-05
2.69E-05
3.25E-05
4.23E-05
5.6E-05
6.91E-05
7.3E-05
6.42E-05
4.99E-05
3.76E-05
2.96E-05
5.31E-04
Wfi
0.577
0.560
0.607
0.733
0.955
1.265
1.561
1.648
1.450
1.127
0.849
0.669
12.000
Conclusions
Data from Ohio SHRP Test Pavement was
analyzed for seasonal variations
 Subgrade soil VMC was not correlated to
precipitation or depth to the GWT
 Fourier 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
