1. Tracer vs. Pressure Wave Velocities Through Unsaturated Saprolite
Todd C. Rasmussen
Associate Professor of Hydrology
The University of Georgia, Athens

3. Configuration for Intact Saprolite Column
Depth (cm)
Saprolite surface 0
TDR probe 4
Tensiometer 7
TDR probe 10
Suction lysimeter 13
TDR probe 16
Tensiometer 19
TDR probe 22
Suction lysimeter 25
TDR probe 28
Tensiometer 31
TDR probe 34
Ceramic plate 38

4. Representative Saprolite Properties
Particle sizes sand = g/g
silt = g/g
clay = g/g
Bulk density g/cm3
Porosity cm3/cm3
Field saturated K 25.1 cm/day
Lab saturated K 27.3 cm/day

6. Chloride Tracer Responses - Columns 1 and 2 -
z  v ne
cm days cm/d %

7. Possible Explanations for Rapid Unsaturated Transport
Preferential flow
Bypass flow
Macropore flow
Fracture flow
Boundary layer flow
Mobile zone flow
Finger flow
Funnel flow
Media heterogeneities
Ion exclusion
Colloid transport

8. Experimental Findings
A large saprolite core was used for an unsaturated flow and Cl- tracer experiment
The tracer traveled four times more quickly than homogeneous flow predicts
Unsaturated conditions were maintained using short irrigation pulses, 0.6 cm3/s
The pressure pulses traveled 1000 times more rapidly than expected.

10. Irrigation Schedules ID Spray† Interval # Duration Flux
sec min hours cm/day
1 A B
2 A B
† Spray rate = 0.6 cm3/s

12. ID Duration Interval # Duration Flux
sec min hours cm/day
3 A A A A A B B B B B C C C C

13. Types of Velocities Darcian flux (velocity) Fluid (transport) velocity
q = - K h
Fluid (transport) velocity
v = q / 
Kinematic (pressure wave) velocity
c = dq / d

15. Unit Gradient Formulation h = [0, 0, -1]
Darcian flux: q = K
Fluid velocity: v = K / 
Kinematic velocity: c = dK / d
Kinematic ratio: k = c / v
= d (ln K) / d (ln )

17. Moisture Characteristic Curves
Brooks - Corey  =  6
van Genuchten  = [ 1 - (1 - 7)0.1430]2
Broadbridge-White
 = 52 { 1 - 1/ - ln [ ( ) /  ( ) ] / 10.3 }
where  = ( - r ) / (s - r ) is the relative saturation

20. Advection Dispersion Equation for Pressure Waves
 is the fluid pressure head
c = dK / d is the kinematic wave velocity
D = K / Cp is the hydraulic diffusivity
Cp = d/d is the specific water capacity

21. Pressure Response to Spike Input
Co is the magnitude of the input

22. Peak Wave Velocity w is the wave peak velocity
tp is the time of peak at depth z
 = c z / D is the hydraulic Peclet Number

23. Effect of Hydraulic Peclet Number
 << 1 is dominated by diffusion
 >> 1 is dominated by a kinematic wave

24. Fluid Pressure Responses - Column 3 -
z p tp w D Cp
cm cm min cm/d cm2/d cm-1
, , e-6
, , e-6
, , e-6
, , e-6

26. Conclusions
The effective transport porosity of saprolite is less than the total porosity
This leads to at least a four-fold increase in the solute velocity relative to that predicted by homogeneous flow
The pressure wave velocity is even faster, about 1000 times greater than the darcian flux
A hydraulic advection-diffusion equation closely predicts observed pressure responses
The best fit occurs with a small specific water capacity, Cp = d / d

27. Implications Solute Transport: Fluid Pressure:
Consistent with other studies, saprolite from the Georgia Piedmont shows preferential solute transport
Use of the total porosity to predict solute transport underestimates solute travel times
Fluid Pressure:
Rapid pressure waves are associated with surface perturbations
These have attributes of displacement (piston) flow
Use of pressure responses overestimates solute travel times

28. Unsaturated Fractured Rock Hydraulic Properties

31. Galileo Number
Dimensionless number, ratio of two forces:

32. Hydraulic Conductivity
The unsaturated hydraulic conductivity is:
and the saturated hydraulic conductivity is:
which is just the Kozeny-Carman Equation