Some Field methods to Measured Saturated

Hydraulic Conductivity (Ksat), a review.

Cristian Kremer F.Bae 558 UI

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).

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) Hoodghoudt’s method, homogenous soil. a.1.2) Ernst’s formula, homogenous soil. a.1.3) Ernst’s method , layered soil.

a.2) Piezometer method, Kirkham’s 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.

a) Measurement Below a

Water Table.

- 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.

a.1) Single auger hole method.

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)).

Figure 1.

S

dy1

y2

h

2a

∆y in ∆t

Soil Surface

Water Table

The formula to use in the case where the auger hole does not terminate on a impermeable layer is (see fig 10):

2

110log

2

3.2

y

y

tad

aSK

2

110log

2

3.2

y

y

dt

aSK

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.

When the auger hole terminates on a impermeable layer:

a.1.2) Ernst’s 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.

t

yCKsat *

864

-The nomographs are for:

s > 0.5 d and s = 0 For two different hole sizes (a=4 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 > 0.5 d

For s= 0

When 0<s<0.5 d the Ksat value can be obtained with the arithmetic mean of the results obtained from above equations (Salgado, 2000).

dyadyaC /2**20*/*000,4 2

dyadyaC /2**10*/*600,3 2

a.1.3) Ernst’s method layered soil (Luthin, 1957)

dkddkdk *1*21*1

Assumptions:- K2 > 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) > 15 cm

Original Depth of Hole

Deepened HoleSoil Surface

Water Table

K1

K2

y

y

hd1

d2

2a2a

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.

)12(*

)21ln(** 2

ttS

yya

K

Soil Removed Soil Surface

Water Table

∆y in ∆t

2aL

y2

y1

d

Cavity

Piezometer

z

2R

-The piezometer method gives the Hz Ksat if the length of the cavity is larger than its radius (i.e., L>a).

-As the length cavity decreases, the measured Ksat approaches to thevertical 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 ofstratified soils (Amoozegar and Wilson, 1999).

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

fLHHrdQKsat **/*2*cosh* 1

2r

H

∆H

Soil Surface

Water Table

flow directionpump meter

d

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 (ΔH).

- For equals spacing between the wells (d= D/3) and when D/r<12

(Snell and Schilfgaarde, 1964):

HHQGKsat */**221.0

flow directionpump

meter

Impermeable Layer

d

∆H

H

sD

b) Measurement Above a

Water Table.

- 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)

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).

Soil Surface

supply membrane layer of sand metal ring

membraneretaining band

air exit

base

flow measuring reservoir

air inlet

constant-headtube

z1

z2

a) Tension Infiltrometer method.

Theory: Steady tension infiltration from a surface disk.

Wooding’s solution for infiltration from a shallow pond has been usedto describe steady tension infiltration from a surface disk source.

oaGd

aQs

2

The α parameter is defined by Gardner (1958):

0a

Where:Qs: steady state flux rate (L3/T)α : soil/texture parameter (L/T)a : disk or ring radius (L)Gd: dimensionless shape factor for tensionInfiltration from a surface disk (Gd = 0.25)Фo: matrix flux potential (L2/T)

0; oidKoo

i

0;0;exp satKK

The Фo is defined by Gardner (1958):

Ψi= background pore-water pressurehead in the soil (assumed constant).Ψo= pressure head at the infiltrationSurface.

(1)

(2)

(3)

If equation 1 is substituted into equation 3, then:

When K(ψi)<<<K(ψo), equation 4 can be approximated by:

Substituting equation 5 in equation 1 and using equation 2 produces:

Which readily logarithmically transformed to:

ioK

o sat

expexp

iKoK

1

(4)

oKo (5)

oKaGd

aQs sat

exp2

(6)

satKaGd

aoQs 2lnln

(7)

ψ1 Ln Q1

ψ2Ln Q2

(negative potential ψ)

satKaGd

a 2ln

α

(ψo)

Equation 7 describe a straight line relationship between ln Qs and ψowhere α can be determined from the slope:

21

21ln

QQ(8)

Finally Ksat can be determined Ln Qs intercept:

psatQQaGda

QGdK

211

1

Where P= ψ1/ (ψ1-ψ2), (Reynolds and Elrick,1991)

Limitations of the proposed method:

-The above development is based on the assumption that equation 2 can provide an accurate description of the soil’s K(ψ) relationship, with the consequence that ln Qs vs. ψo is linear. This is not often the case (α=α(ψ)).

-A reasonable compromise is to considered is therefore to assume that ln Qs vs. ψo is piece wise linear, which implies, that eq 2 can be accurately fitted in a piecewise fashion to K(ψ) data (α is considered constant over small range of Ψ( see more Reynolds and Elrick, 1991).

-The main theoretical limitation of the proposed is the requirement that K(ψi)<< K(ψo). This limit the analysis to low tension (large ψo) applied to relatively dry soils (small ψi). However this theoretical problem should be not a problem in practice since most application of interest are for K(ψo) at ψo > or equal -0.15 m in soils a field capacity (ψi near -1m) or drier ( White and Perroux, 1989).

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 < β <= 1, soil parameter related to the distribution of pores sizes)

1

21

2

11S

tK

K

StKI sat

satsat

b) Ring Infiltrometers.

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).

c) Constant head well permeameter.

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 Q’s 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 >= 2H. The Glover solution is:

Where:

22 H

CQK sat

Hr

Hr

rHC

2

12

1 1sinhImpermeable Layer

constant water level

2r s

H

d

D

reference level

h2

h1

constant-headtube

adjustable airtube

flow measuringreservoir

Soil surface

•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 model’s 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.

Conclusions