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EVALUATION OF MOBILE SOIL PERMEAMETER TO PREDICT SATURATED

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    EVALUATION OF MOBILE SOIL PERMEAMETER TO PREDICT
           SATURATED HYDRAULIC CONDUCTIVITY

                                  E. Theron1 & P.A.L. le Roux2
1
    School of Civil Engineering and Built Environment, Central University of Technology, Free
                             State, South Africa, etheron@cut.ac.za
         2
           Department of Soil, Crop and Climate Science, University of the Free State


Abstract
Saturated hydraulic conductivity (Ksat) of soil controls subsurface water movement and
therefore serves as a key parameter for analysing water flow and chemical transport in the
landscape. This is important in irrigation agriculture and environmental pollution. Several
methods were used over the last thirty years to measure Ksat of soils. Most methods make
use of devices to measure the infiltration rate into the soil and in combination with
numerical models predict the Ksat parameter. Commonly used devices for infiltration
capacity measurements are infiltrometers, disc permeameters, sprinkler infiltrometers and
different types of constant head permeameters. This paper evaluates the theory and
practical application of the Mobile Soil Permeameter (MSP) in combination with the Glover
equation for field measurement of Ksat of a red apedal B horizon of a Hutton soil above the
water table. The Glover equation has been criticized during the eighties because only the
saturated flow around the hole was considered in its development. The measured Ksat
values, varying between 84 and 149 mm h-1, were in the same range as values measured
using the double ring infiltrometer. Several papers published since 2002, demonstrated
that the Glover equation results are relatively close to the results obtained by other models
for most practical applications and therefore the use of the Glover equation with a constant
head permeameter is justified.


1 INTRODUCTION

Hydraulic conductivity (K) is one of the more often used properties for evaluating soil
suitability for different uses and for predicting the fate of anthropogenic materials applied
on or in soil. It is therefore a key parameter for analysing or modelling water flow and
chemical transport in subsurface soil (1). This parameter varies both spatially and
temporally and is easily altered by management activities. Under saturated conditions the
parameter is noted as Ksat and is assumed to be a constant for a given time and space
within the soil (2). Under both saturated and unsaturated conditions, the measure of the
ability of soil to transmit water is described by Darcy’s Law (3).

A vast number of field methods have been developed over the past thirty years to measure
the saturated hydraulic conductivity of soils above the water table. These methods, which
include the constant head permeameter, air-entry permeameter, intake rate infiltrometer,
double ring infiltrometer, velocity permeameter or falling head permeameter as well as
several others, have been used with varying degrees of success. The most significant
practical limitations of all these methods usually include an installation time of up to
several hours, a measurement period of up to several days and water requirements of up
to a 1000 L or more per measurement. In addition, considerable equipment and usually
more than one operator are required.
The constant head permeameter method is the most versatile procedure for measuring
Ksat of the unsaturated sone from near the surface to a few meters deep (2). This
technique is based on the direct application of Darcy’s Law and the steady-state flow rate
of water (Q) under constant head (H) at the bottom of a cylindrical hole of radius (r) is
measured. In the original procedure this method took a few days and required a
considerable amount of equipment and large quantities of water. However, due to
development of equipment (e.g. mobile soil permeameter), development in the theoretical
evaluation of subsurface flow of water and modifications of the field procedure in the last
twenty years, steady-state flow rate from a small diameter cylindrical hole under a constant
depth of water can now be reached with a few liters of water within two to three hours (4).
Using a device such as the mobile soil permeameter (MSP) the equation to calculate Ksat
can be written in the form:

           Ksat = CQ                                                                      [1]

The constant (C) must be calculated using a model. Amoozegar (4) proved that the Glover
equation, as developed by R.E. Glover, is an appropriate model for determining Ksat. The
Glover equation is used frequently to determine the Ksat of the unsaturated sone in
combination with the constant head permeameter technique. The reason being, it only
uses field measured data, is relatively simple and does not require estimation of any soil
parameter. Provided that the values for Q, H and r are measured accurately, the ratio of
H/r ≥ 5 and the distance between the bottom of the hole and any impermeable layer below
the hole (s) is ≥ 2H, the Glover equation can be used to accurately calculate the Ksat value
of subsurface soil (4). The constant (C) as given by the Glover equation is:

           C = [sinh-1(H/r) – (1+ r2/H2 )1/2+(r/H)]/(2πH2)                                 [2]

The objective of this paper is to demonstrate that justifiable saturated hydraulic
conductivity (Ksat) values for subsurface soil horizons can be predicted by using the MSP
in combination with the Glover equation.

2 FIELD DATA COLLECTION

The study site is within 2 000 ha of land near Luckhoff in the southern Free State, South
Africa surveyed for delineation of land suitable for irrigation. The more conventional double
ring infiltrometer and the MSP were used to determine Ksat of the subsoil of soil of the
Hutton form at 800 mm depth. The results were compared. The Hutton soil form has a
diagnostic orthic A horizon and red apedal B horizon overlying a hardpan carbonate
horizon at 2.2 m depth. The red apedal B horizon is structureless with a deep red colour
implying that it is well drained.

The rate of the water movement into the subsoil horizon was measured in holes of radius
(r) 35 mm augered to a depth of 800 mm using a bucket type hand auger. After cleaning
the bottom of the hole carefully, the MSP was installed and a constant rate of water flow
into the soil under a constant head of water was established. The constant head of water
in the hole is set by hanging the tube (see figure 1) on a cord. To ensure that H/r is ≥ 5 for
an auger radius of 35 mm, the distance needed between the bottom of the tube and the
bottom of the hole (h2) was determined in the laboratory as a minimum of 175 mm to meet
the above-mentioned requirement. To be save it was decided to use a free height of
120 mm (h2) to ensure a corresponding value of 250 mm for H. The water level in the hole
was measured twice during measurements to assure that a constant head is maintained
throughout. A steady-state flow rate of water was reached within one to three hours using
20 l to 40 l. The flow of water into the soil was determined by a pressure meter water
gauge (probe) which recorded the height difference (h 1) of the water in the reservoir every
minute. The conversion factor of height to volume of water (l) was determined in the
laboratory as 0.013. The flow rate was calculated by dividing the volume by one minute
and then converts it to a flow rate of mm3 h-1 (Table 1).

The measurements were done in quadruplicate (P1 to P4) to accommodate spatial
variation, which was expected to be low in the subsoil of a sandy apedal soil. The MSP
site was 3 m from the pit where the double ring infiltrometer measurements were taken
(Figure 2). To minimise/prevent any effect of soil water around the auger holes on each
other after steady state of water flow was reached the auger holes were positioned more
than 1.5 m apart.




                                                                                          Rods
                                                                         Cord


                                            h1

                                             Water
                                            level in
                                           reservoir
                                                            Valve




                                                                         Depth of
                                                                         auger hole




                    Constant water level                                                  Tube
                            (H)
                                                       h2




                                                                                      s
                                                                    2r




              Figure 1: Schematic diagram of the Mobile Soil Permeameter.
                                       3 m to double ring infiltrometer site




                                         P2                         P3




                                                                               1m
                         North




                                                                               1m
                                         P1                         P4




                                              1m               1m
                     P = position

                                 Figure 2: Position of auger holes.


3 RESULTS AND DISCUSSION

The dataset of auger hole one (P1) for the first 26 minutes is given in Table 1. The graph
(Figure 3) indicates flow rate and an approximation of when steady-state of water flow rate
is reached. For P2 – P4 only the graphs are illustrated in respectively Figure 4, 5 and 6. In
order to calculate Ksat by using equation (1), it is necessary to first calculate C as given by
the Glover equation and then determine Q. The values necessary to calculate C are the
constant head and the radius. As discussed in the section on field data collection the
values are 250 mm and 35 mm respectively. The calculation of C by equation (2) is:

                      C = [sinh-1(250/35) – (1+ 352/2502 )1/2 + (35/250)]/(2π2502)

                         = 0.046 mm -2
                                                       Table 1: Dataset (26 min).



Time (h)                       Vol (l) Q (mm3 h-1)                           Time (h)                    Vol (l) Q (mm3 h-1)
                                       CF = 0.013                                                                CF = 0.013
             0.02               0.92 5538461.538                                  0.25                    0.69 4153846.154
             0.03               0.85 5076923.077                                  0.27                    0.62 3692307.692
             0.05               0.77 4615384.615                                  0.28                    0.69 4153846.154
             0.07               0.77 4615384.615                                  0.30                    0.62 3692307.692
             0.08               0.85 5076923.077                                  0.32                    0.69 4153846.154
             0.10               0.69 4153846.154                                  0.33                    0.62 3692307.692
             0.12               0.69 4153846.154                                  0.35                    0.54 3230769.231
             0.13               0.69 4153846.154                                  0.37                    0.69 4153846.154
             0.15               0.77 4615384.615                                  0.38                    0.62 3692307.692
             0.17               0.69 4153846.154                                  0.40                    0.54 3230769.231
             0.18               0.69 4153846.154                                  0.42                    0.62 3692307.692
             0.20               0.62 3692307.692                                  0.43                    0.62 3692307.692
             0.22               0.69 4153846.154                                  0.45                    0.54 3230769.231
             0.23               0.69 4153846.154                                  0.25                    0.69 4153846.154




                                                                  Site 3: P4; 800mm
              60000.00

              55000.00
                                                                                                               y = -7355.8Ln(x) + 27328
              50000.00                                                                                                   2
                                                                                                                     R = 0.8649
              45000.00
 Q (cm3/h)




              40000.00

              35000.00

              30000.00

              25000.00

              20000.00

              15000.00
                     0 .0 00




                                   0 .1 00




                                             0 .2 00




                                                        0 .3 00



                                                                   0 .4 00




                                                                                0 .5 00




                                                                                           0 .6 00



                                                                                                     0 .7 00




                                                                                                                    0 .8 00



                                                                                                                               0 .9 00




                                                                                                                                          1 .0 00




                                                                                Time (h)



                                  Figure 3: Flow rate measurements at auger hole 1.
                                                                        Site 3: P2; 800mm
                  50000.00

                                                                                                                     y = -4357.4Ln(x) + 30185
                  45000.00                                                                                                              2
                                                                                                                                     R = 0.5577

                  40000.00
Q (cm3/h)




                  35000.00


                  30000.00


                  25000.00


                  20000.00
                         0 .000



                                     0 .050



                                                      0 .100



                                                               0 .150



                                                                         0 .200



                                                                                           0 .250



                                                                                                     0 .300



                                                                                                                0 .350



                                                                                                                                     0 .400



                                                                                                                                                 0 .450



                                                                                                                                                          0 .500
                                                                                    Time (h)



                                     Figure 4: Flow rate measurements at auger hole 2.


                                                                        Site 3: P3; 800mm
                   60000.00


                   50000.00

                                                                                                              y = -7489.5Ln(x) + 14091
                                                                                                                                 2
                   40000.00                                                                                                R = 0.7186
      Q (cm3/h)




                   30000.00


                   20000.00



                   10000.00



                        0.00
                             0.000




                                              0.100




                                                                0.200




                                                                                   0.300




                                                                                                    0.400




                                                                                                                         0.500




                                                                                                                                              0.600




                                                                                                                                                             0.700




                                                                                  Time (h)


                                     Figure 5: Flow rate measurements at auger hole 3.
                                                                  Site 3: P4; 800mm
                6000 0.00

                5500 0.00
                                                                                                                    y = -7355.8Ln(x) + 27328
                5000 0.00                                                                                                     2
                                                                                                                          R = 0.8649
                4500 0.00
    Q (cm3/h)




                4000 0.00

                3500 0.00

                3000 0.00

                2500 0.00

                2000 0.00

                1500 0.00
                        0 .0 00



                                   0 .1 00



                                             0 .2 00



                                                        0 .3 00



                                                                   0 .4 00



                                                                                 0 .5 00



                                                                                             0 .6 00



                                                                                                          0 .7 00



                                                                                                                         0 .8 00



                                                                                                                                    0 .9 00



                                                                                                                                               1 .0 00
                                                                                  Time (h)



                                  Figure 6: Flow rate measurements at auger hole 4.

Logarithmic trend lines were added to the graphs to determine the reliability of the data
which was used to determine Q. The type of data determines the type of trend line which
should be use. A logarithmic trend line is a best-fit curve line when the rate of change in
the data increases or decreases quickly and then levels out. A trend line is most reliable
when its R2 value is at or near 1. This value shows how closely the estimated values for
the trend line correspond to the actual data. The R2 value is displayed on the graphs. The
values of Q for P1 – P4 as determined from the graphs (“constant” trend line value) are
given in Table 2. Ksat can now be calculated for each of the four auger holes with equation
(1). These values are also indicated in Table 2.

                    Table 2: Steady-state flow rate and saturated hydraulic conductivity.

                                  Auger
                                                 Q (mm3 h-1)                 Ksat (mm3 /h)             Ksat (mm/day)
                                  holes
                                    P1                 300 000                             137                        3288
                                    P2                 325 000                             149                        3576
                                    P3                 184 600                              84                        2016
                                    P4                 284 000                             130                        3120


The objective of this paper was to demonstrate that justifiable (Ksat) values for subsurface
soil horizons can be predicted by using the MSP in combination with the Glover equation.
The field measurements as done at a depth of 800 mm can now be compared with values
obtained by the double ring infiltrometer at the same depth, for this specific site (Table 3).
      Table 3: Ksat values obtained with the double ring infiltrometer in replicate1 & 2

                Rep 1   ΔH         Infiltration rate
                  Time
                  (min) mm        mm h-1 mm d-1          cf            mm d-1
                   0.96 10        6250.0 15000.0 0.0006667             14287
                   1.01 10        5940.6 14257.4 0.0007014             13580
                   1.11 10        5405.4 12973.0 0.0007708             12356
                   1.73 10        3468.2 8323.7 0.0012014               7928
                   1.92 10        3125.0 7500.0 0.0013333               7143
                   2.19 10        2739.7 6575.3 0.0015208               6263
                   1.97 10        3045.7 7309.6 0.0013681               6962
                   2.03 10        2955.7 7093.6 0.0014097               6756
                   2.22 10        2702.7 6486.5 0.0015417               6178


                  Rep 2    ΔH  Infiltration rate
                      min mm mm h-1 mm d-1                cf           mm d-1
                     0.35 10 17142.9 41142.9 0.0002431                 39187
                       0.9 10 6666.7 16000.0 0.0006250                 15239
                     0.95 10  6315.8 15157.9 0.0006597                 14437
                     1.34 10  4477.6 10746.3 0.0009306                 10235
                     2.61 10  2298.9       5517.2 0.0018125             5255
                     2.15 10  2790.7       6697.7 0.0014931             6379
                     2.71 10  2214.0       5313.7 0.0018819             5061
                     2.16 10  2777.8       6666.7 0.0015000             6350
                     2.96 10  2027.0       4864.9 0.0020556             4634
                     3.15 10  1904.8       4571.4 0.0021875             4354
                     2.73 10  2197.8       5274.7 0.0018958             5024


The average Ksat value was 4671 mm d-1.



4 CONCLUSION

The MSP has relieved most of the limitations in field measurements of saturated hydraulic
conductivity. The apparatus is lightweight and simple to install, it is inexpensive to
construct and can be operated by one person. All the necessary field data can be collected
within 1 to 2 hours per measurement and relative small quantities of water are required.
The resulting outcome of the Ksat values as determined by the MSP is fairly close to the
Ksat values as calculated by the more conventional double ring infiltrometer (3560 mm d -1
compared to 4670 mm d-1). The MSP may underestimate the Ksat values relative to the
double ring infiltrometer or the spatial variability of the red apedal B horizon of the sandy
Hutton may be higher than expected, however, it may be concluded that due to all the
practical advantages and closely correlated values the MSP is a reliable device to be used
in field measurements to determine saturated hydraulic conductivity.
5 REFERENCES

 [1] Mohanty, B.P., Shaggs, T.H. & Van Genuchten, M.Th. Impact of saturated hydraulic
     conductivity on the prediction of tile flow. Soil Sci Soc. Am, J. 62, pp1522-1529, 1998.
 [2] Amoozegar, A. & Wilson, G.V. Methods for measuring hydraulic conductivity and
     drainage porosity. Soil Sci Soc. Am, pp1149-1205, 1999.
 [3] Whitlow, R. Basic soil mechanics, Henry Ling Education Limited, Great Britian, 2001.
 [4] Amoozegar, A.Soil Science Society of North Carolina proceedings, Vol XLV, 2002.

				
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