1 soil bulk density & compaction - university of idaho assignments/soil... · soil bulk density...

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Copyright© Markus Tuller 2002-2006

Hydrologic Measurement Techniques• These are slides provided by Markus Tuller for students in Hydrologic

Measurement Techniques at the University of Idaho.

• Do not distribute these notes.

Soil Bulk Density & Compaction1

Copyright © Markus Tuller 2002-2006

2


Dry Bulk Density

Ratio of the mass of oven-dry soil and total sample volume

The dry bulk density is primarily affected by soil texture and structure, including aggregation and particle size distribution.

If the pore space is half of the bulk volume the dry bulk density ρb is about half of the particle density ρs (1300 to 1350 kg/m3)

Fine textured soils commonly have lower bulk densities than coarse textured soils.

tsb VM=ρ


Determination of Bulk DensityTo determine bulk density we need to measure the dry mass and the total volume occupied by the soil sample.

CORE METHOD:

A cylindrical metal sampler is driven into the soil to remove a known volume (core).

The core (soil + brass cylinder) is oven-dried at 105 oC to remove non-structural soil water until the mass remains constant (usually after 24–48 hrs).

3


Core Method

Brass InnerCylinder

SoilSurface

CuttingCylinder

“Undisturbed”Soil Sample

hrVV 2tc ⋅⋅== π

Volume Cylinder

Dry Mass Sample

Oven105oC


Core Method - Example

322t cm3391214.33hrV =⋅⋅=⋅⋅= π

r = 3 cm h = 12 cmMs = 480 g (oven-dry mass)

r

h

33t

sb cm/g42.1

cm339g480

VM ===ρ

4


Excavation Methods – Sand FunnelA quantity of soil is excavated in the field, dried at 105 oC and weighed.

The volume is determined by filling the excavated hole with a well defined standard sand of which the volume per unit mass is known. (SAND-FUNNEL Method)

Valve

StandardSand

Base Plate


Excavation Methods – Rubber BalloonIn the RUBBER BALLOON Method the volume is determined by inserting a balloon into the excavation and filling it with water or an other fluid with known density.

RubberMembrane

Valve

Water Towerwith Scale

5


Bulk Density – Clod MethodCLOD METHOD:


Bulk Density – Gamma Rays

GAMMA RAY TECHNIQUES:

Gamma ray techniques are based on attenuation and diffraction of gamma rays emitted from a 137Caesium or 241Americium source due to collision with other atoms of the soil phases.Attenuation and diffraction are dependent on bulk density and other soil properties (e.g., water content)

6


Gamma Rays

TRANSMISSION TECHNIQUE:Two probes at a fixed spacing are lowered into previously prepared openings in the soil. One probe contains a Geiger tube, which detects the attenuated radiation transmitted through the soil from the gamma source located in the second probe.


Gamma RaysSCATTERING TECHNIQUE:A single probe contains both, detector and source separated by shielding. Can be used on the surface or placed in a hole dependent on design of the equipment.

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Gamma Rays


• In agriculture and forestry soil compaction is undesirable.

•For many engineering applications a well compacted soil is crucial for safe foundations (the Leaning Tower of Pisa is an example of building on soft soil).

Soil Compaction – Desired or Not?

Image: Opera Primaziale Pisana

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Soil CompactionLow porosity (n) or high bulk density (ρb) are indicators for soil compaction.

Soil compaction results in mechanical impedance to plant root growth, poor aeration, and restrictions to water infiltration.

Forest ecosystems are extremely sensitive to soil compaction!

Compaction associated with timber harvest could disturb ecosystems for many years.


• Operation of heavy vehicles (e.g. harvesters, construction machines) on agricultural land can cause soil compaction.

Agricultural Soil Compaction – Causes

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• Compaction alters soil hydraulic and gaseous exchange properties and increases mechanical impedance to plant roots.

Soil Compaction – Indicators


• Compaction hampers plant growth and decreases crop yield.

• The extent of soil degradation due to compaction exceeds an area of 6.8x104 km2

worldwide (Oldeman1991).

Soil Compaction – Effects

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Soil Compaction - AgriculturePotato yield on a clay loam in Minnesota


Soil Compaction – Effects on Pore Spaces

uncompacted compacted

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Soil Compaction - Agriculture

Subsoiler



The tillage pan has been mechanically broken by a subsoiler. The vertical slot allows roots to penetrate into the subsoil to access water and nutrients.

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Loose zoneSubsoiling Chisel

Plowpan

Root distribution of a cotton plant


Soil Compaction - AgricultureSoil compaction can be reduced by spreading the applied weight.

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Soil CompactionSurface compaction can be partially reduced with an aerator

Characterization of the Liquid Phase

2


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Characterization of the Liquid PhaseThe two most important characteristics of the liquid phase are:• The amount of water in the soil (soil water content)• The forces by which water is held in the soil matrix (matric potential)These two soil attributes are related through a function known as the SOIL WATER CHARACTERISTIC (SWC).

Changes in soil water content and matric potential affect many soil transport and mechanical properties, such as (1) ability to transfer liquid and gases; (2) mechanical properties such as soil strength, compactibility, penetrability, and bulk density in swelling soils.

SOIL WATER CHARACTERISTIC

0.01

0.1

1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5

Volumetric Water Content [m3/m3]

Mat

ric P

oten

tial [

-m]


Soil Water Content – Measurement Methods

soildryovenmass)soildryovenmass()soilwetmass(

soildryofmasswaterofmass

m−

==θ

volumesamplewaterofdensity

waterofmass

soilofvolumebulkwaterofvolume

v

⎟⎟⎠

⎞⎜⎜⎝

⎛

==θ

GRAVIMETRIC WATER CONTENT:Samples obtained by digging, augering, or coring are weighed (moist sample), and weighed again after oven drying (105 oC).

VOLUMETRIC WATER CONTENT:Samples with known volume (core samples) may be processed the same way as in the gravimetric water content method.

The conversion between gravimetric and volumetric water content requires knowing the dry bulk density.

w

bmv ρ

ρθθ =

15


Soil Water Content – Gravimetric Determination


Soil Water Content – Volumetric Determination

16


Nondestructive Methods - Neutron Scattering

rrww

rrDDDryDry

WetWet

NeutronNeutronProbeProbe

AccessAccessTubeTube

Sphere ofSphere ofInfluenceInfluence

ProbeProbe(Source and(Source and

Detector)Detector)

● Neutron Scattering (or Neutron probe) is a widely used field method for repetitive measurement of volumetric soil water content.

● It is based on the propensity of water molecules to slow down (thermalize) high energy fast neutrons emitted from a radio active source (Americium-241 –Beryllium).

● Thermalized neutrons are counted by a detector present in the access tube (along with the source).


Nondestructive Methods - Neutron Scattering

DryDry

WetWet

● Fast neutrons are emitted radially into the soil and collide with various atomic nuclei. Collisions with most nuclei are virtually elastic with only minor loss of kinetic energy.

● Collisions with hydrogen nuclei causes significant loss of kinetic energy and slow down of the fast neutrons (thermalization).

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Neutron Scattering Method● Calibration of the Neutron Probe is necessary to account for

background hydrogen sources and other local effects like bulk density.

● Calibration is achieved by simultaneously measuring soil water content and count ratio CR - ratio of slow neutrons to standard count obtained with the radiation source in the shield.

)CR(bav +=θ


Limitations of Neutron Scattering Method

●Radiation hazards●Requires site specific calibration●Variable volume of measurement●Not suitable for near-surface measurements●Provides “snap shots”, difficult to automate● Installation and measurements are labor intensive●Limited accuracy

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SOIL 415 SOIL 415 –– Soil and Environmental PhysicsSoil and Environmental PhysicsCopyright Copyright ©© Markus Tuller 2002Markus Tuller 2002--20062006

Time Domain Reflectometry (TDR)



Time Domain Reflectometry (TDR) is a relatively new technique for measurement of volumetric soil water content using electromagnetic waves propagating along embedded waveguides.

TDR Cable Tester(Tektronix 1502B)

3-RodProbe

BNCConnector

Waveform

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Advantages:• Superior accuracy to within 1-2% of volumetric water content• Minimal calibration requirements (usually no soil specific

calibration necessary)• No radiation hazard such as associated with neutron probe or

gamma ray attenuation techniques• Excellent spatial and temporal resolution• Continuous measurements through automation and

multiplexing

Limitations:• Expensive – typical system costs ~ $4000• Limited performance in saline soils• Specialized – no “off the self” systems; requires training


Time Domain Reflectometry TDRThe propagation velocity v of an electromagnetic field along a transmission line (waveguide) of length L embedded in the soil is determined from the time response of the system to a pulse generated by the TDR cable tester.

The propagation velocity (v=2L/t) is a function of the soil bulkdielectric constant:

Coaxial Cable

Epoxy Stainless Steel Rods

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b L2tc

vc

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠⎞

⎜⎝⎛=ε

C….velocity of the electromagnetic wavein vacuum (3x108 m/s)

t…. travel time of the wave along the guideand back (2L)

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Time Domain Reflectometry TDRThe dielectric constant ε is the property of a material that determines the relative speed that an electrical signal will travel in that material.Low ε � high signal propagation speed (fastest ε=1)High ε � slow signal propagation

The bulk soil dielectric constant εb is governed by the dielectric of liquid water εw

Water εw ∼ 81Soil Minerals εs = 3 to 5Soil Air εa = 1

The large disparity between dielectric constant of water and other soil constituents results in dominance of soil bulk dielectric constant eb by the volume fraction of liquid water ew hence dielectric measurements are ideal for soil water content determination.

2

⎟⎠⎞

⎜⎝⎛=ε

vc

b


Time Domain Reflectometry TDR

Table 1-4: Tabulated values of the dielectric constant for fluids and solids

Material (Fluid)

Dielectric Constant(20-25oC)

Material (Solids)

Dielectric Constant (20-25oC)

Water 80.4-78.5 Ice (-12oC) 4.1-3.7

Ethanol 24.3 Fused Quartz (SiO2) 3.78

Ammonia 16.9 Sandy Soil (dry) 2.55

Benzene 2.29 Loamy Soil (dry) 2.51

Acetone 20.7 PVC 2.89

Air 1.0 Polyethylene 2.25

CO2 (liquid) 1.6 Teflon 2.1

CO2 (gas) 1.001 Wood (Douglas Fir) 1.90-1.95

Sources: CRC Handbook of Chemistry and Physics (1993), von-Hippel (1955).

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Distance [cm]

0 100 200 300 400 500

Ref

lect

ion

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6 ξ2ξ1

TDR – Basic PrinciplesThe travel time of the electromagnetic wave to traverse the length of the embedded waveguide (down and back 2L) is evaluated based on the “apparent” or electromagnetic length of the probe, which is characterized on the TDR output screen by diagnostic changes in the waveform:

The relationship between the locations of the two reflection points and bulk dielectric constant is:

Vp is the relative propagation velocity, often set at 0.99

2

p

12b LV

xx⎟⎟⎠

⎞⎜⎜⎝

⎛ −=ε


Coaxial Cable

EpoxyStainless Steel Rods

� �

�

Distance [cm]

0 100 200 300 400 500

Ref

lect

ion

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

�

�

�

TDR – Basic Principles

1: Reflection Coaxial Cable – Epoxy handle2: Transition Rods (Epoxy) – Rods in Soil3: Reflection end of rods

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TDR – Basic Principles

1: Reflection Coaxial Cable – Epoxy handleAs TDR signal leaves the shielded coaxial cable and enters the handle section, the impedance mismatch causes part of the electric energy to be reflected back (formation of a “blip”).

2: Transition Rods (Epoxy) – Rods in Soil As the signal leaves the handle the typically more “efficient” or lower impedance in the soil section causes the waveform to dive this marks the so-called 1st reflection (in salty soils the signal base shows a clear downward slope).

3: Reflection end of rodsThe end of the rods is marked by a strong reflection (the so-called 2nd reflection) as the electric field cannot propagate in the soil mass without a waveguide (rods)

Distance [cm]

0 100 200 300 400 500

Ref

lect

ion

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

�

�

�


TDR – Basic PrinciplesDifferent waveguide designs and associated electromagnetic fields

• TDR sensor designs seek fewer conductors to reduce disturbance to the porous medium.

• Measurement volume and sensitivity vary with design.

• Concentration of field lines near conductors emphasize permittivity of soil conditions in this region.

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TDR – Of the Shelf Systems


Soil Bulk Dielectric Constant to Water Content

Two basic approaches are used to relate Soil bulk dielectric constant εb to volumetric water content θv:

Empirical or calibation relationships: such as the 3rd order polynomial proposed by Topp et al. [1980] that seems to fit data for many mineral soils.

362422 10341055109221035 bbbv εεεθ −−−− ×+×−×+×−= ....

Topp’s Equation

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Physically Based Dielectric Mixing ModelsMaxwell was among the first to employ a physically based dielectric mixing model that incorporates volume fractions and geometrical arrangement of soil constituents to predict bulk dielectric constant of the mixture [Roth et al. 1990] :

n is soil porosity, and -1<β<1 summarizes applied EM field direction relative to medium (axial direction of waveguide).

β= 1 for an EM field parallel to soil layeringβ= -1 for EM field perpendicular to layeringβ= 0.5 for an isotropic two phase mixed medium

[ ]ββββ εθεεθε1

avswvb )n()n1( −+−+=


Dielectric Mixing ModelThe mixing model can be simplified using β=0.5 and the dielectric constants of the constituents: εw=81; εs=4; and εa=1



ββ

βββ

εε

εεεθ

aw

asbv

n)n1(

−

−−−=

8)n2(b

v−−

=ε

θ

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Mixing Model: Example

[ ] 61.91)2.05.0(4)5.01(812.0 5.01

5.05.05.0b =⋅−+⋅−+⋅=ε

5.0265013251n =−=

What is εb of a soil having θv = 0.2 and bulk density of 1325 kg/m3? What if the soil contained the same volume fraction of ethanol rather than water?First we estimate the porosity for this soil as:



Then we use β = 0.5 and the dielectric constants of the constituents εw = 81; εs = 4; and εa = 1 to solve the mixing model for the bulk dielectric constant εb:


Mixing Model: Example

[ ] 225.51)2.05.0(4)5.01(3.242.0 5.01

5.05.05.0b =⋅−+⋅−+⋅=ε

For ethanol and assuming 25oC we substitute the appropriate dielectric of 24.3 into the mixing model and receive:

Note that because ethanol undergoes relaxation (a change in dielectric constant) within the TDR frequency bandwidth, the apparent dielectric εethanol as measured using TDR is closer to 16. This means that some caution is required in attempting to model the apparent bulk dielectric of soils or other complex mixtures based on tabular values of the component dielectric constants.

26


Limitations of Empirical Relationships

Topp’s model works well for the water content range < 0.5 m3/m3 which covers the entire range of interest in most mineral soils.However it fails for water contents higher 0.5 m3/m3,and for organic soils or mineral soils with high organic matter content.The physically based models work well for the entire range of water content.

Note that the soil’s porosity needs to be known!

0

20

40

60

80

Bul

k D

iele

ctric

Con

stan

t

0 0.2 0.4 0.6 0.8 1 Volumetric Water Content (m^3/m^3)

Mixing Model

Practical Range ofWater ContentMeasurement

Topp


Time Domain Reflectometry TDR

DISADVANTAGES OF TDR:

● Relatively expensive equipment

● Limited applicability under highly saline conditions, due to signal attenuation.

● Soil specific calibration may be required for soils having largeamount of bound water or high organic matter content (large surface area).

● Requires training and experience.

● No “off the self” systems (yet)

27


Other Methods For Volumetric Water ContentCapacitance SensorsCapacitance sensors use an oscillator to generate an AC field which is applied to the soil in order to detect changes in soil dielectric properties linked to variations in soil water content.The sensors essentially consist of a pair of electrodes (either an array of parallel spikes or circular metal rings) which form a capacitor with the soil acting as the dielectric in between. This capacitor works with the oscillator to form a tuned circuit, andchanges in soil water content are detected by changes in the operating frequency.


Kidman and Taylors Flats SoilsHydrosense Calibration

y = 0.4481x + 0.0153R2 = 0.9917

0.0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6Hydrosense

Mea

sure

d

Kidman

Taylors

1 to 1

LinearTaylors Regression

Other Methods For Volumetric Water ContentHydroSense – Transmission Line Oscillator (TLO)The HydroSense probe has electronic components that generate high frequency electromagnetic energy along the length of the probe rods.

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Other Methods For Volumetric Water ContentECHO PROBES:The Echo probe measures the dielectric constant of a medium by finding the rate of change of voltage applied to the sensor once it is buried in the soil. (TDR measures the dielectric constant by finding the travel time of an electromagnetic wave that traverses a waveguide).


Other Methods For Volumetric Water ContentAdvantages of the ECHO probe are the insensitivity for saline conditions, and low expenses. Only a Datalogger or Hand Read Outis required to send excitation voltage and record the rate of voltage change.

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Other Methods For Volumetric Water Content

RESISTANCE BLOCKS (Gypsum or Fiberglass)

A pair of electrodes is embedded in a porous matrix (gypsum or fiberglass) that is brought in contact (buried) with soil.The porous material equilibrates with the surrounding soil, so that the matric potential (forces that hold the water) is the same. The resistance between the electrodes is measured and related to water content (high water content-low resistance; low water content – high resistance).

Two calibration functions are required:

• Matric potential versus resistance (for the block)

• Volumetric water content versus matric potential SOIL WATER CHARACTERISTIC (for the soil)




0.01

0.1

1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5


Mat

ric P

oten

tial [

-m]

RESISTANCE BLOCKS – Calibration Functions

Volumetric Water Content - Matric Potential

10 100 1000 10000 100000100

1000

10000

100000

1000000

W [ WS]

[]

Matric Potential - Resistance

Matric Potential [-cm]

Res

ista

nce

[Ohm

]

30


Other Methods For Volumetric Water ContentOTHER METHODS- X-Ray Computed Tomography (CT)- Nuclear Magnetic Resonance NMR- Ground Penetrating Radar GPR

New CT-Facility at WSU


Other Methods For Volumetric Water ContentGround Penetrating Radar (GPR)

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Ground Penetrating Radar GPR – suspended horn antenna

Millville silt loam, Θv(t), T(t)

Θv (

m3 /m

3 )

0.0

0.1

0.2

0.3

0.4

0.5

0.6GPR-SR Θg 0-1 cmΘg 1-5 cmTDR 2 cm

Elapsed time (days)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Tem

p. (o

C)

01020304050

Pond drained

Rainfall event

Soil temp. at 2 cm


Other Methods For Volumetric Water ContentGround Penetrating Radar GPR – measurements over wheat canopy

illuminatedregion

GPR

anten

na

SR

PT

TDRprobe

Reflecting canopy layers

Scale (cm)

Al termination

32

Measurement of Soil Water Potential Components

3



Measurement of Matric Potential – TensiometerA tensiometer consists of a porous cup, usually made of ceramic having very fine pores, that is connected to a vacuum gauge (or other measuring device) through a water filled tube.After installing the tensiometer in the field the tube is filled with de-aired water and sealed airtight. In this initial stage water inside the tube is under atmospheric pressure.

If the potential in the surrounding soil is lower than atmospheric pressure water will flow from the tensiometer through the porous cup into the soil until equilibrium is reached.

VacuumGauge

PressureTransducer

DigitalReadout

Needle Inserted into Septum

Stopper

Water-FilledTube

Water(inside)

SaturatedPorousCeramic

Soil Water(outside)

PorousCeramic

Cups

This flow will lower the potential energy inside the tensiometer and thereby create a suction that is sensed by the gauge or transducer.

When the soil is wetted flow can also occur in the reverse direction until a new equilibrium has been reached

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TensiometerThe gauge or transducer reading has to be corrected to account for the positive head that is exerted by the water column inside the tensiometer at the point of interest in depth of the ceramic cup

ψgauge � ��

��

��

ψm � ψgauge + (zgauge – zcup)

Tensiometer Equation

0 to – 100 kPa (-1bar; -10 m head)

Measurement Range

ψm � ψgauge + (zgauge – zcup)

Tensiometer Equation

ψm = -1.2 + (0.2 – (-0.5))ψm = -0.5 m


TensiometerSketch showing tensiometers with vacuum gauges and electronic pressure transducers.

34


Tensiometer & Potential Diagrams - Example The cups of tensiometers 1 and 2 are at a depth of 0.6 and 0.8 m below the soil surface. The gauges are 0.2 m above the soil surface. The gauge in tensiometer 1 indicates ψgauge = -0.9 m.

• Draw a potential diagram with the soil surface as reference level. Assume static equilibrium conditions.

• Estimate the gage reading in tensiometer 2.

First we set our reference level at the soil surface and calculate the matric potential in 0.6 m depth using the tensiometer equation:

]m[1.0))6.0(2.0(9.0m −=−−+−=ψ

)zz( cupgaugegaugem −+=ψψ


Tensiometer & Potential Diagrams - Example With known matric potential and assuming zero solute potential we now can calculate the hydraulic potential at 0.6 m depth. Note that under equilibrium conditions the hydraulic potential is uniform throughout the soil profile.

With known hydraulic potential we now can calculate the matric potential throughout the profile (tabulated values are in m head)

pzmh ψψψψ ++=

]m[7.0)6.0(1.0h −=−+−=ψ

Depth ψh ψz ψm ψp

0.0 -0.7 0.0 -0.7 0.0 -0.1 -0.7 -0.1 -0.6 0.0 -0.2 -0.7 -0.2 -0.5 0.0 -0.3 -0.7 -0.3 -0.4 0.0 -0.4 -0.7 -0.4 -0.3 0.0 -0.5 -0.7 -0.5 -0.2 0.0 -0.6 -0.7 -0.6 -0.1 0.0 -0.7 -0.7 -0.7 0.0 0.0 -0.8 -0.7 -0.8 0.0 0.1 -0.9 -0.7 -0.9 0.0 0.2 -1.0 -0.7 -1.0 0.0 0.3

The reading in tensiometer 2 is calculated as:

]m[9.00.11.0zpgauge −=−=−= Δψψ

35


Tensiometer & Potential Diagrams - Example As the final step we can draw the potential diagram for equilibrium conditions:

- 7 0 0- 1 0- 2 0- 3 0- 4 0- 5 0- 6 0- 8 0

Rh

Rm

Rp

Rz

W a t e r T a b l e

- 9 00 1 0 2 0

- 1 0

- 2 0

- 3 0

- 4 0

- 5 0

- 6 0

- 7 0

- 8 0

- 9 0

20 cm 1 2


Measurement of Matric Potential – Heat DissipationThe rate of heat dissipation in a porous medium is dependent on the medium‘s specific heat capacity, the thermal conductivity, and the density.The thermal conductivity and heat capacity of a porous matrix isaffected by its water content (matric potential).The measurement is based on application of a heat pulse through a heating element and analysis of the temperature response measured with a thermocouple. The measured magnitude of temperature change during a given heating period is linearly related to the natural logarithm of the matric potential.

The linearity coefficient a has to be determined through calibration of the heat dissipation sensor.

⎟⎠⎞

⎜⎝⎛ Δ

=⇒=ΔaTaT mm exp)ln( ψψ

measured

from calibration

36


Heat DissipationA typical line source heat dissipation sensor consists of a fine wire heating element that is axially centered in a cylindrical ceramic matrix having a diameter of about 1.5 cm and a length of 3.2 cm. The thermocouple is located adjacent to the heating element at mid-length. Both the thermocouple and the heating element are placed in the shaft portion of a hypodermic needle.

Line-Source Heat Dissipation Sensor

PorousMatrix

HeatingElement

Thermocouple

-10 to – 1000 kPa(-0.1 to -10 bar; -1 to – 100 m head)

Measurement Range


Measurement of Matric Potential- PsychrometerIn cases where the solute potential is considered to be negligible, matric potential can be inferred from psychrometer measurements.The potential energy of soil water is in thermodynamic equilibrium with the potential energy of water vapor in the ambient air.A psychrometer measures the relative humidity in the ambient air(vapor pressure in the soil air relative to the saturation vaporpressure of air at the same temperature) that is related to potential energy ψv of water vapor:

Mw Molecular weight of water (0.018 kg/mol)R Ideal gas constant (8.31 J K-1 mol-1)T Absolute temperature (K)ρw Density of water (1000 kg/m3 at 20°C)

⎟⎟⎠

⎞⎜⎜⎝

⎛==

TRM

eeRH

w

vw

ρψexp

0

37


Psychrometer

This equation can be further simplified for RH close to 1, a value often encountered in agricultural soils (entire range of plant available water is between RH = 0.98 and RH = 1.0).

⎟⎟⎠

⎞⎜⎜⎝

⎛=

0

lnee

MTR

w

wv

ρψ

ψv = ψm (no salts) Matric Potentialψv = ψw = ψm + ψs (salts present) Water Potential

⎟⎟⎠

⎞⎜⎜⎝

⎛−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−=⇒≈ 1

eeT4621

ee

MTR1

eeFor

00w

wv

0

ρψ

1ee

eeln1

eeIf

000−=⎟⎟

⎠

⎞⎜⎜⎝

⎛⇒≈Note:

Rearranging and log-transformation yields:


PsychrometerMeasurement Principle:A psychrometer infers relative humidity from the difference in temperature between a dry non evaporating surface (called dry bulb temperature), and the temperature of an evaporating surface (called wet bulb temperature)The wet bulb temperature is usually below the dry bulb temperature because of the latent heat loss that is associated with the evaporation process.The rate of evaporation from a wet surface depends on the relative humidity or vapor pressure of the ambient air.

Low humidity = high evaporation rateHigh humidity = lower evaporation rate

The higher the evaporation rate the larger is the temperature depression of the wet bulb below the dry bulb temperature.

38


PsychrometerA thermocouple psychrometer consists of a fine wire chromel constantan or other standard bimetallic thermocouple. A thermocouple is a double junction of two dissimilar metals. When the two junctions are subjected to different temperatures they generate a voltage difference explained as the SEEBECK effect.

Conversely when an electric current is applied through the junctions it creates a temperature difference between the junctions by heating one and cooling the other dependent on the current’s direction.

For typical soil use one junction of the thermocouple is suspended in a thin wall ceramic or stainless steel cup that is buried in the soil while the other one is embedded in an insulated plug to measure the ambient temperature at the same location.

Field Psychrometer


PsychrometerIn psychrometric mode the suspended thermocouple is cooled belowthe dew point so that a droplet of water forms on the junction. (this is called Peltier cooling). Then the cooling stops and water evaporates from the junction drawing heat and depressing the temperature below that of the ambient air. The difference in temperature between the wet bulb (suspended junction) and the dry bulb (insulated junction) is measured and used to infer the relative vapor pressure using the psychrometer equation.

Te

yseeRH Δ⎥

⎦

⎤⎢⎣

⎡ +−==

00

1measured

S....Slope of the saturation water vapor curvey....Psychrometer constant (about 0.067 kPa K-1 at 20°C)

39


Psychrometer

( )4R

3R

2RR t1299.0t6445.0t9760.1t3185.13

0 exp325.101e −−−=

The saturation vapor pressure e0 is also temperature dependent and can be approximated by integrating the previous equation:

The relation between water vapor pressure e, relative humidity RH, and temperature T is uniquely defined. That means knowledge of any two of them leads automatically to the third one:

The slope of the water vapor curve is temperature dependent and can be approximated according to Brutsaert [1982]:

Where tR=1-373.15/T

( )3R

2RR2

00 t5196.0t9335.1t952.33185.13T

e15.373Tdeds −−−==


A good Psychrometer can measure temperature depressions on the order of 0.000085 oC per kPa.Any error in measuring wet bulb depression introduces large errors into psychrometric determinations of water potential.THERMODYNAMIC EQUILIBRIUM BETWEEN SAMPLE AND AMBIENT AIR IS REQUIRED TO ACHIEVE ACCURATE MEASUREMENTS!

Psychrometer

40


Laboratory Psychrometer

-800 to – 10000 kPa(-80 to – 1000 m head)

Measurement Range

Psychrometer


Laboratory Psychrometer

Psychrometer

41


WP4 Potentiameter

A second procedure inferring water potential using thermocouple psychrometers is called the DEWPOINT METHODIn this method one surface is brought to dew point temperature and kept at exactly this temperature using a monitoring system and electronic circuitry.State of the art equipment (e.g., WP4 Potentiameter) uses a chilled mirror dewpoint technique combined with a photoelectric detection system to keep the surface of a mirror at dewpoint temperature. Ambient temperature at the sample surface is measured with an infrared thermometer.

Psychrometer

The Soil Water Characteristic -Introduction and Measurement

4


42


The Soil Water Characteristic Curve• The Soil Water Characteristic (SWC) curve describes the functional

relationship between soil water content (θv or θm) and matric potential under equilibrium conditions.

• The SWC is an important soil property related to pore space distribution (sizes, interconnectedness), which is strongly affected by texture and structure and related factors including organic matter.

• The SWC is a primary hydraulic property required for modeling water flow in porous materials.

• The SWC function is highly nonlinear and relatively difficult to obtain accurately.


The Soil Water Characteristic CurveTypical soil water characteristic curves for soils of different texture

43


The Soil Water Characteristic Curve• Early conceptual models for the SWC curve

and liquid distribution in partially saturated porous media are based on the "bundle of cylindrical capillaries" (BCC) representation of pore space geometry (Millington and Quirk, 1961; Mualem, 1976).

• The BCC representation postulates that at a given matric potential a portion of interconnected cylindrical pores is completely liquid filled, whereas larger pores are completely empty.

Soil Sample

ActualPore

EquivalentCapillary


The Soil Water Characteristic Curve

iwi rg

hρ

γσ=

cos2

ii nrA π= 2

• This convenient idealization of soil pore space enables a linkage between the soil pore size distribution and the SWC based on capillary rise equation

44


BCC Model - ExampleA bundle of cylindrical capillaries having the following diameters and numbers was vertically dipped into a water reservoir.# of capillaries 300 400 325 250 150 90 50 10 5 2 Diameter [mm] 0.001 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1 2

Compute and plot the relative saturation of the capillaries at different elevations above the free water surface :The first step is to calculate the capillary rise for various capillary diameters:

rgcos2hwρ

γσ=

For each elevation we then calculate the cross-sectional area of all filled capillaries:

We start with the highest elevation where only capillaries with the smallest diameter are likely to be filled. Then we gradually move down to the lowest elevation where all capillaries are expected to be filled. At each elevation increment we add the water filled cross-sectional areas of capillaries with smaller diameters.

n4

dA2π

=


BCC Model - ExampleFinally we calculate the relative saturation at each elevation as the ratio of water-filled cross-sectional area at a certain elevation and the total cross-sectional area.

# Diameter[m]

h [m]

A [m2] θvrel

300 1E-06 29.74 2.36E-10 0.000016

400 5E-06 5.95 8.09E-09 0.000544

325 1E-05 2.97 3.36E-08 0.002262

250 2E-05 1.49 1.12E-07 0.007548

150 5E-05 0.59 4.07E-07 0.027371

90 1E-04 0.30 1.11E-06 0.074945

50 2E-04 0.15 2.68E-06 0.180666

10 5E-04 0.06 4.65E-06 0.312817

5 1E-03 0.03 8.58E-06 0.577118

2 2E-03 0.01 1.49E-05 1.000000

45


BCC Model - Example

Characteristic Curve of a Bundle of Cylindrical Capillaries

0

10

20

30

Relative saturation of the capillaries

Elev

atio

n ab

ove

free

wat

er [m

]

0.000 0.001 0.002 0.008 0.027 0.075 0.181 0.313 0.577 1.000


Using SWC to Determine Pore Size Distribution

1)1) The total saturation water The total saturation water contentcontent θθss is divided into is divided into a certain numbera certain number M M of of equal incrementsequal increments ΔθΔθvvwhere the matric where the matric potentialpotential hhjj corresponds corresponds to a water content ofto a water content ofθθss-- jxjxΔθΔθvv

2)2) We assume that all tubes We assume that all tubes with radii greater thanwith radii greater than RRjjhave drained at matric have drained at matric potentialpotential hhjj

jwj hg

2Rrρ

σ−=>

46


3)3) The number of capillaries The number of capillaries having a radiushaving a radius RRjj per unit per unit area in each water content area in each water content interval is:interval is: nnjj==ΔθΔθvv//ππRRjj

22

(where(where ΔθΔθvv is interpreted as is interpreted as the fraction of the waterthe fraction of the water--filled cross sectional area filled cross sectional area that is reduced when all that is reduced when all capillaries having a radius capillaries having a radius ofof RRjj drain).drain).

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

1.E-11 1.E-09 1.E-07 1.E-05 1.E-03 1.E-01

Equivalent Pore Radius [m]

Freq

uenc

y [%

/m]

Using SWC to Determine Pore Size Distribution


•• The concept of Field Capacity and Wilting Point discussed in theThe concept of Field Capacity and Wilting Point discussed in theprevious section on water content have a more quantitative definprevious section on water content have a more quantitative definition ition in terms of potentials and SWC. in terms of potentials and SWC.

•• Field Capacity Field Capacity -- water content at water content at -- 1/3 bar (for sandy soils 1/3 bar (for sandy soils --0.1 bar)0.1 bar)

•• Wilting Point Wilting Point –– water content at water content at --15 bars15 bars

SWC and Plant Available Soil Revisited

47


Measurement Methods to Determine the SWC

Experimental Problems:

• The limited functional range (-10 m) of tensiometers used for in-situ measurements.

• Difficulty to obtain undisturbed samples for laboratory determination.

• Very long equilibration times for low matric potential values associated with dry soils

The basic requirement is to find pairs of water content θ and matric potential ψm over the wetness range of interest.


Measurement Methods to determine the SWCIN-SITU MEASUREMENTS ARE CONSIDERED MOST REPRESENTATIVE.

TDR Probes installed in close proximity to transducer tensiometers are commonly used for automated recording of changes in water content and matric potential with time.

Large changes in θ and ψm can be induced under highly evaporative conditions (e.g., fan), or active plant roots.

48


Tempe CellThe pressure flow cell (Tempe cell) is usually applied for the pressure (matric potential) range from 0 to -10 m.

Close to saturation soil water retention is strongly influenced by soil structure and the natural pore size distribution. Thereforeundisturbed core samples are preferred over repacked samples.


Tempe Cells

49


Bubbling Pressure

• The largest pore in the pore size distribution is an important characteristic of a porous material, because it drains first.

• The pressure required to drain the largest pore in the system iscalled BUBBLING PRESSURE or AIR ENTRY VALUE and determines the onset of air entering the saturated medium (Minimum pressure required to start desaturation).

• Given that the equivalent pore is cylindrical and liquid filled according to the capillary rise equation the Bubbling pressure would be the pressure on the atmospheric side necessary to offset the negative pressure on the liquid side of the meniscus formed in the largest pore (see equation next slide).

• The concept of Bubbling Pressure is also important for the design of porous materials that are required to remain saturated to a specific pressure (e.g., porous plates in Tempe cells and Pressure Plate devices, porous cups in tensiometers).


hgr

wργσ

=cos2


0.01

0.1

1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5


Mat

ric P

oten

tial [

-m]

��

Bubbling Pressure

50


Pressure Plate ApparatusThe pressure plate apparatus is applied for the pressure (matricpotential) range from -10 to -50 m.


Pressure Plate Apparatus

51


Hanging Water Column and Suction Table • Measurements at very low pressure ranges of 0 to 2 m.• Useful for coarse soils due to precise pressure application.• Wetting and drying cycles of the SWC (reversible flow into the sample).


Psychrometric MethodsA procedure inferring water potential using thermocouple psychrometers that is commonly used in newer instruments is called the DEWPOINT METHOD

In this method one surface is brought to dew point temperature and kept at exactly this temperature using a monitoring system and electronic circuitry.

State of the art equipment (e.g., WP4 Potentiameter) uses chilled mirror dewpoint technique combined with a photoelectric detection system to keep the surface of a mirror at dewpoint temperature. Ambient temperature at the sample surface is measured with an infrared thermometer.

WP4 Potentiameter

52


In-situ Measurement Methods – Sensor Pairing

Example - TDR Probes installed in close proximity to transducer-equipped tensiometers are commonly used for automated recording of changes of water content and matric potential with time.

SENSOR PAIRING: (TDR, Neutron Probe, Tensiometer, Heat Dissipation, etc)

IN-SITU MEASUREMENTS ARE CONSIDERED MOST REPRESENTATIVE.


Sensor PairingLimitations:

• Differences in the soil volumes sampled by each sensor, e.g. large volume averaging by a neutron probe vs. a small volume sensed by heat dissipation sensor or psychrometer

• In-situ water content measurement methods are instantaneous, matric potential sensors require time for equilibrium; hence thetwo measurements may not be indicative of the same wetness level

• Limited ranges and deteriorating accuracy of different sensor pairs; this often results in limited overlap in retention information and problems with measurement errors within the range of overlap.

53


Field Measurement Methods - Sensor Pairing

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