1. UNSATURATED FLOW OF
WATER IN PAVEMENTS
Prof. Björn Birgisson
The Royal Institute of Technology (KTH)
Transportforum 2009

2. Problem Statement
• Water in pavement systems can lead to detrimental
effects
• Complete prevention is not possible. Quick removal
of the water should be enhanced before any damage
can be initiated
• There is a need to develop an improved understanding
of the mechanics of water flow through pavement
systems
• Current drainage criteria is based on saturated flow
theory

3. Objectives
• How water moves through pavements
• How long the water stays in a pavement structure.
• What material properties control how long water
stays in a given structure
• What boundary and structure conditions (water
table, shoulder construction, edge drains, layering,
etc.) most affect the moisture conditions in the
pavement

4. Saturated Vs. Unsaturated
• Below water table • Above water table
• Volumetric water • Volumetric water
content (θ) = porosity content (θ) < porosity,
and f(ψ)
• No suction (negative • Suction (ψ < 0)
pressure, ψ > 0)
• Hydraulic • Hydraulic
conductivity is conductivity is a
constant (k = ksat) function of ψ.
• Faster Drainage • Slower Drainage

5. s
Volumetric Water Content (%)
20.0
Air entry = 10 kPa
15.0
Soil Water 10.0
Saturated condition
Unsaturated condition
Characteristic Curve 5.0
0.0
0.01 0.10 1.00 10.00 100.00 1000.00
Suction (kPa)
1.0E-04
Air entry = 10 kPa
Unsaturated condition
1.0E-06
Hydraulic Saturated condition
k (m/s)
Conductivity Curve 1.0E-08
1.0E-10
0.01 0.10 1.00 10.00 100.00 1000.00
Suction (kPa)

6. Calibration of cells 33, 34, 35
In order to understand the behavior of water
flow through flexible pavements under
unsaturated conditions, actual Mn/ROAD
pavement geometries and material
characteristics were used along with results
from automated time domain reflectometry
(TDR) probes placed in the base layers of the
sections studied

7. Cells 33, 34, 35
4.04’’ 3.92’’ 3.96’’
12’’ 12’’ 12’’
Cell 33 Cell 34 Cell 35
HMA
Class 6 Special

8. Cells geometry
3.05 m 4.27 m 4.27 m 1.83 m
CL
4:1 4:1
0.1 m Hot Mix Asphalt 0.3 m Class 6 Special
4.0 m
R-70 silty clay
16.5 m

9. Finite Element Model
Extended Subgrade Extended Subgrade
H=0m H=0m
Material characterization: Mn/DOT data
Impervious HMA
Same model for all cells
Infiltration (q [m/s]) on shoulders and subgrade
Initial water table
Total Head = 0 m at bottom to induce drainage

10. TDR Locations
Offset Centerline
(-1.83 m)
0.25m 0.13 m 0.10 m
0.38m 101
102 0.30 m
103
HMA
3.6 m
Class 6 Special
R-70 silty clay
subgrade
Automated
*TDR

11. TDR in FEM
CL
Hot Mix Asphalt
Base
Subgrade

12. Initial Results
(Cell 33-Location 101)
36.0
s
Volumetric Water Content (%)
32.0
28.0
24.0
20.0
16.0
12.0
8.0
Measured
4.0
Predicted
0.0
210 220 230 240 250 260 270
Time (Julian day)

13. Precipitation Adjustment
12.0
f
Volumetric Water Content (%)
11.0
10.0
9.0
8.0
7.0 Measured
Predicted
6.0
210 220 230 240 250 260 270
Time (Julian day)

14. Location 102
20.0
Volumetric Water Content (%) f
18.0
16.0
14.0
12.0
10.0
Measured
8.0
Predicted
6.0
210 220 230 240 250 260 270
Time (Julian day)
Location 103
Volumetric Water Content (%)
28.0
24.0
20.0
f
16.0
12.0 Measured
Predicted
8.0
210 220 230 240 250 260 270
Time (Julian day)

15. Density Adjustments
24.0
f
Volumetric Water Content (%)
22.0
20.0
18.0
16.0
14.0
12.0
10.0
Measured
8.0
Predicted
6.0
210 220 230 240 250 260 270
Time (Julian day)
24.0
f
Volumetric Water Content (%) 22.0
20.0
18.0
16.0
14.0
12.0
Measured
10.0
Predicted
8.0
210 220 230 240 250 260 270
Time (Julian day)

16. Parametric Study
• Purpose: Identify the effects of certain
material properties and boundary conditions
(Ground Water Table) on the water flow
through typical flexible pavement
configurations.
• Original conditions: Cell 33 was selected as
a representative pavement configuration,
with TDR location 101.

17. Parametric Study (cont…)
• Air entry potential Base Material
Volumetric Water Content (%)f
22.0
18.0
14.0
10.0
Predicted - 3 kPa
6.0
Predicted - 4kPa
Predicted - 5 kPa
2.0
210 220 230 240 250 260 270
Time (Julian day)

18. Parametric Study (cont…)
• Ksat Base Material
9.90
9.85
Volumetric Water Content (%)f
9.80
9.75
9.70
9.65
9.60
9.55
9.50
9.45
9.40
9.35 Predicted - 1.55E-06 m/s
9.30 Predicted - 1.55E-05 m/s
9.25 Predicted - 1.55E-04 m/s
9.20
210 220 230 240 250 260 270
Time (Julian day)

19. Parametric Study (cont…)
• Air entry potential Subgrade
9.8
Volumetric Water Content (%)f
9.7
9.6
9.5
9.4
9.3
9.2
Predicted - 0 kPa
9.1 Predicted - 5 k Pa
Predicted - 10 kPa
9.0
210 220 230 240 250 260 270
Time (days)

20. Parametric Study (cont…)
• Ksat Subgrade
Volumetric Water Content (%)f
12.0
11.5
11.0
10.5
10.0
9.5
9.0
8.5
8.0
7.5 Predicted -2.75E-8 m/s
7.0 Predicted - 2.75E-7 m/s
6.5 Predicted - 2.75E-6 m/s
6.0
210 220 230 240 250 260 270
Time ( Julian day)

21. Parametric Study (cont…)
• Infiltration event
12.5
Volumetric Water Content (%)f
12.0
11.5
11.0
10.5
10.0
9.5
9.0 Predicted -100%
Predicted - 70%
8.5
Predicted -70% and 30%
8.0
210 220 230 240 250 260 270
Time (Julian day)

22. Parametric Study (cont…)
• Water table position
10.0
Volumetric Water Content (%)f
9.5
9.0
8.5
8.0
7.5
7.0
6.5
6.0
5.5 Predicted -3.20 m
5.0 Predicted - 3.00 m
4.5 Predicted - 2.85 m
4.0
210 220 230 240 250 260 270
Time (Julian day)

23. Drainage Systems Comparison
• Edge Drain
Hot Mix Asphalt
Base
Subgrade
Edgedrain
Pressure head = 0 m

24. Drainage Systems Comparison
(cont…)
• Under Drain
Hot Mix Asphalt
Base
Under Drain
Subgrade
Pressure head = 0 m

25. Drainage Systems Comparison
(cont…)
24.0
Volumetric Water Content (%)s
20.0
16.0
12.0
8.0
Original case
4.0 Case 1:Under Drain
Case 2: Edgedrain
0.0
210 220 230 240 250 260 270
Time (Julian day)

26. Conclusions and Recommendations
• Saturated flow assumptions may not adequately
represent the physics of flow through pavement
systems
• Unsaturated material properties are needed to
simulate the drainage performance of a pavement
system. SWCC and hydraulic conductivity curves
allow us to evaluate when and how fast pavement
layers can drain

27. Conclusions and Recommendations
(cont…)
• Due to the installation procedures for the TDRs,
the density around the TDR probes in the field is
likely different from that in the laboratory.
• The SWCC tend to be sensitive to density and
gradation. These differences can result in a
variation in both the air entry value and the slope
of the soil water characteristic curve in the
unsaturated region.

28. Conclusions and Recommendations
(cont…)
• The air entry potential determines the transition of
a material from saturated to unsaturated conditions
- the higher the air entry potential the longer the
material will retain water.
• The higher the hydraulic conductivity, the faster
the material will drain.
• If the water table is set at different elevations, the
system will be under different initial suction and
volumetric moisture conditions.

29. Conclusions and Recommendations
(cont…)
• Under Drain systems provide a faster drainage
than Edge Drains. However, both systems keep
the water table really close to the base layer.
– Material with high air entry potential may not drain
well in the presence of “positive” drainage systems
• An improvement in the use of TDRs is suggested.
It would be more helpful having more
measurement points.

30. QUESTIONS ?