Some Field methods to Measured Saturated Hydraulic Conductivity (Ksat), a review.

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Some Field methods to Measured Saturated
Hydraulic Conductivity (Ksat), a review.

• Cristian Kremer F.
• Bae 558 UI

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1) Introduction

• Hydraulic conductivity can be defined as a
  measured of the ability of a soil to transmit
  water. Under saturated conditions this parameter
  is usually denoted as Ksat or (Ks) and is
  assumed to be constant for a given space and
  time within a soil (Amoozegar and Wilson, 1999).
• The knowledge of Ksat for a specific soil is too
  important for instance in drainage design, the
  saturated hydraulic conductivity is used to
  compute the velocity in which water can move
  toward and into the drainlines below the water
  table (Amoozegar and Wilson, 1999).
• Laboratory determined values rarely agree with
  field measurements, the differences often being
  on the order of 100 fold or more. Field methods
  generally are more reliable than laboratory
  methods due to the closer approximation to
  natural conditions (Scott, 2000).

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2) It is possible to divide this review in two
kind of methods

• a) Measurement Below a Water Table.
• a.1) Single auger hole method.
• a.1.1) Hoodghoudts method, homogenous
  soil.
• a.1.2) Ernsts formula, homogenous
  soil.
• a.1.3) Ernsts method , layered soil.
• a.2) Piezometer method, Kirkhams method.
• a.3) Other methods.
• a.3.1) Two wells method.
• a.3.2) Four wells method.
• b) Measurement Above a Water Table.
• a) Tension Infiltrometer method.
• b) Ring infiltrometers.
• c) Constant head well permeameter method.

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• a) Measurement Below a
• Water Table.

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a.1) Single auger hole method.

• This method to consist, to dig a auger hole into
  the soil below the water table. After first
  determining the elevation of the water table by
  allowing the water surface to reach an
  equilibrium with the soil water, the hole is
  pumped out a new water level elevation, and the
  rate of rise water in the hole is measured. From
  these measurements Ksat is calculated.
• Advantages
• - Use the soil water for the measurement.
• - The sample used for the measurement is
  large.
• - The measurement is not greatly affected by
  the presence of rocks
• or root holes adjacent to the hole.
• - The measurement reflects the horizontal
  component of Ksat.

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a.1.1) Hoodghoudt's method

• This case consider a homogeneous soil having no
  stratification and uniform Ksat the auger hole
  may or may not reach the impervious layer.
• Assumptions
• - Water Table is not lowered around the
  auger hole when water is pumped out of it. This
  condition is satisfied for a short time after the
  auger hole has been pumped. (This condition is
  always difficult to reach).
• - Water flows horizontally into the sides of
  the auger hole and vertically up through the
  bottom of the hole. (Actually the paths of flows
  must be curvilinear (Luthin, 1957)).

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Figure 1.
Soil Surface
Water Table
2a
y2
y1
?y in ?t
d
h
S
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The formula to use in the case where the auger
hole does not terminate on a impermeable layer is
(see fig 10)
When the auger hole terminates on a impermeable
layer
In both equations, S is given by the relation S
0.19 ad Hoodghoudt determined that the constant
S is dependent of a, d and s expressed with the
above equation.
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a.1.2) Ernsts formula, homogenous soil

• Ernst developed some empirical equation to solve
  the auger hole problem aid by numerical analysis.
  The following formulas was obtained by Ernst in
  the case of homogenous soil with a impermeable
  layer at great depth below the bottom of the
  auger hole (Luthin, 1957)
• - Where C is a shape factor related to a, y, d
  and s, and C/864 is dimensionless Bouwer and
  Jackson (1974) and van Beers (1970) presented
  four nomographs for obtaining the shape factor
  for above equation.

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• The nomographs are for
• s gt 0.5 d and
• s 0
• For two different hole sizes (a4 and 5 cm).
• They also presented approximate equations for
  calculating the C factor
• based on a and y (average value of two
  consecutive measurements y1
• and y2), d and s (Amoozegar and Wilson, 1999).
  These equations are
• For s gt 0.5 d
• For s 0
• When 0ltslt0.5 d the Ksat value can be obtained
  with the arithmetic mean of the results obtained
  from above equations (Salgado, 2000).

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a.1.3) Ernsts method layered soil (Luthin, 1957)
Original Depth of Hole
Deepened Hole
Soil Surface
2a
2a
Water Table
y
K1
d1
y
h
d2
K2

• Assumptions
• K2 gt K1, if it is not this equation gives
  negative values.
• If there is a third layer, the bottom of the
  second hole should be stay
• above that layer.
• - (d- h) gt 15 cm

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a.2) Piezometer method

• Kirkham (1946) proposed a method which a tube is
  inserted into the auger hole below a water table
  with or without a cavity at the end of the tube.

Piezometer
Soil Removed
Soil Surface
2R
Water Table
y2
z
y1
?y in ?t
d
2a
L
Cavity
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• The piezometer method gives the Hz Ksat if the
  length of the cavity is
• larger than its radius (i.e., Lgta).
• As the length cavity decreases, the measured Ksat
  approaches to the
• vertical Ksat of the materials at the bottom of
  the piezometer tube.
• When the length of the cavity is zero, the
  measure of Ksat is vertical.
• This method is well suited for determination of
  Ksat of various layers of
• stratified soils (Amoozegar and Wilson, 1999).

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a.3) Other methods

• a.3.1) Childs (1952) proposed the two wells
  technique for determining Ksat.
  

• Two auger hole of equals diameter
• A distance d (recommend 1m) are dug to the
  desired depth below the water table (H) (fig 4).
• Water is taken from one well and deposited in the
  other well a constant rate.
• When the steady state is achieved, Ksat is
  calculated by
• Lf is an end correction factor related to both
  the thickness of the capillary fringe and the
  distance between the bottom of the holes and
  impermeable layer below the holes

pump
meter
flow direction
Soil Surface
Water Table
?H
H
2r
d
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a.3.2) Four wells method

• - To overcome the problem of clogging of he pores
  of the well receiving water in the two well
  method, two additional wells are bored
  symmetrically between the discharge and receiving
  wells.

• - The radius of the two inner wells may be less
  than the radius of the outer wells.
• Water is pumped a constant rate from one of the
  outer well to the other outer well.
• After equilibrium is achieved, the difference
  between the water levels in the two inner wells
  is measured (?H).
• For equals spacing between the wells (d D/3) and
  when D/rlt12
• (Snell and Schilfgaarde, 1964)

pump
meter
flow direction
?H
H
d
s
D
Impermeable Layer
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• b) Measurement Above a
• Water Table.

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• In general, the available procedures for
  measuring Ksat above the water table require
  special equipment. Some of the techniques are
  difficult to perform, time consuming and may
  required a large quantity of water to fill the
  device or/and saturate the soil. Yet, these
  techniques offer an opportunity to determine the
  Ksat of a volume of soil that may never become
  saturated in natural conditions or may be
  saturated for only a short a period of time
  (Amoozegar and Wilson, 1999)

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a) Tension Infiltrometer method.

• This figure is a representation of the
  tension infiltrometer.

• A number of procedures have recently been
  developed for estimating soil hydraulic
  conductivity from tension infiltrometer data.
  These includes methods by
• White and Perroux(1989)
• Ankeny et al (1991)
• Smettem and Clothier (1989)
• Elrick et al. (1987)
• These methods vary in their capabilities,
  complexities, advantages and limitations.
• The present method is an alternative one
  described by (Reynolds and Elrick, 1991).

air inlet
flow measuring reservoir
constant-head tube
air exit
base
membrane retaining band
z1
Soil Surface
z2
supply membrane
metal ring
layer of sand
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Theory Steady tension infiltration from a
surface disk.
Woodings solution for infiltration from a
shallow pond has been used to describe steady
tension infiltration from a surface disk source.
Where Qs steady state flux rate (L3/T) a
soil/texture parameter (L/T) a disk or ring
radius (L) Gd dimensionless shape factor for
tension Infiltration from a surface disk (Gd
0.25) ?o matrix flux potential (L2/T)
(1)
The a parameter is defined by Gardner (1958)
(2)
The ?o is defined by Gardner (1958)
?i background pore-water pressure head in the
soil (assumed constant). ?o pressure head at the
infiltration Surface.
(3)
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If equation 1 is substituted into equation 3,
then When K(?i)ltltltK(?o), equation 4 can
be approximated by Substituting equation 5
in equation 1 and using equation 2
produces Which readily logarithmically
transformed to
(4)
(5)
(6)
(7)
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Equation 7 describe a straight line
relationship between ln Qs and ?o where a can be
determined from the slope
?2
Ln Q2
(8)
a
Ln Q1
?1
Finally Ksat can be determined Ln Qs intercept
(?o)
(negative potential ?)
Where P ?1/ (?1-?2), (Reynolds and Elrick,1991)
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• Limitations of the proposed method
• -The above development is based on the assumption
  that equation 2 can provide an accurate
  description of the soils K(?) relationship,
  with the consequence that
• ln Qs vs. ?o is linear. This is not often the
  case (aa(?)).
• A reasonable compromise is to considered is
  therefore to assume that ln Qs vs. ?o is piece
  wise linear, which implies, that eq 2 can be
  accurately fitted in a piecewise fashion to K(?)
  data (a is considered constant over small range
  of ?
• ( see more Reynolds and Elrick, 1991).
• -The main theoretical limitation of the proposed
  is the requirement that
• K(?i)ltlt K(?o). This limit the analysis to low
  tension (large ?o) applied to relatively dry
  soils (small ?i). However this theoretical
  problem should be not a problem in practice since
  most application of interest are for K(?o) at ?o
  gt or equal -0.15 m in soils a field capacity (?i
  near -1m) or drier ( White and Perroux, 1989).

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b) Ring Infiltrometers.
Double ring infiltrometer The most common
hydraulic test carried out to estimate soil
hydraulic properties is the double ring
infiltrometer. The rings are inserted deep enough
to preclude the leakage from the outer ring and
to have the tops of the ring level with each
other. A constant water level is quickly
established in both rings to the same level, and
the infiltration water can be measured by
watching the drop of water level using a floating
ruler by using a Marriot bottle constant head
source (Selker and Keller, 1999). The data can
be analyzed using any of several infiltration
models. One of this was proposed by Brutsaert
(1977). Fitting this equation to
infiltration data allows ready determination of
both Ksat and S. (1/3 lt ß lt 1, soil parameter
related to the distribution of pores sizes)
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c) Constant head well permeameter.

• The constant head well permeameter is
  perhaps the most versatile procedure for
  measuring Ksat. In this technique, the steady
  state flow rate (Q) of water under a constant
  pressure (H) at the bottom of a cylindrical auger
  hole of radius (r) is measure, and Ksat is
  calculated by and appropriate equation using Q, H
  and r. Because the flow is three dimensional, the
  Ksat depends of both horizontal and vertically
  flow.
• To measure Ksat, a hole radius r is dug to the
  desired depth using a hand auger. For most
  practical applications, 4 to 10 cm diam. hole is
  suitable for this purpose. After cleaning the
  bottom of the hole and measuring the depth, a
  constant depth of water H is at the bottom of the
  hole (see fig). To maintain a constant depth of
  water at the bottom a marriotte siphon system or
  a float system can be used.
• The rate of flow of water into the soil is
  determined by measuring the change in the height
  of water in the reservoir (h2) with time
  (Ammozegar and Wilson, 1999).

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adjustable air tube
flow measuring reservoir
After establishing a constant head of water,
water is allowed to infiltrate the soil until
steady state is achieved. For practical
applications, it can be assumed that the steady
state is achieved when three consecutively
measured Qs are equal. The Glover solution
which ignores the unsaturated flow in its
analysis, has been recommended for calculating
Ksat when the distance between the bottom of the
hole and any impermeable layer below the hole (s)
is gt 2H. The Glover solution is Where
h1
h2
constant-head tube
reference level
Soil surface
d
constant water level
D
H
s
2r
Impermeable Layer
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Conclusions

• Like we saw during the presentation, there are
  too many models and system to describe saturated
  Hydraulic Conductivity, but the reliability of
  these depend in how accurate we can achieve the
  different assumptions which they were created.
• The interpretation of our finals results always
  must consider the models assumptions.
• The spatial variability of Ksat in a soil is too
  high, so some times when we want to represent a
  soil with a unique value is useful to do a
  statistical analysis in order to find to the most
  representative value of Ksat.
• The representative Ksat value is defined for the
  specific purpose, which will be used.