Soil physics

Magnus Persson

Surface tension

2·R·cos R

2·r

P1

P2

z

Due to surface tension water can be held at negative pressure in capillary tubes. (P1<P2 = Patm)

The smaller the diameter of the tube, the higher capillary rise.

An useful analogy is that the soil can be considered to act like a bundle of cappilary tubes with different diameters (representing the range of pore sizes)

pF curveThe soil moisture potential, or soil water suction, is sometimes given in pF = log(-pressure in cm H2O).

The water retention curve, soil moisture characteristic, or pF curve, is the relationship between the water content, θ, and the soil water potential, ψ. This curve is characteristic for different types of soil

(1 bar = 100 kPa = 1000 cm H2O)

Soil water potential

The total potential consists of the moisture potential (synonyms; pore water tension, soil water suction) and the elevation potential, z.

Normally the groundwater surface is used as a reference level (z = 0)

Water movement

Water movement is driven by total potential gradients

Theory of one-dimensional unsaturated water flow

z

q

dz

dz

dqq

Using continuity (inflow – outflow = change in storage over time) we get

dz

dq

dt

d

dt

d

dz

dqqq

where is the volumetric water content and t is time.

(1)

Theory of one-dimensional unsaturated water flow

dz

dHKq

1

)(

dz

dK

dz

zdKq

1

dz

dK

dz

d

dt

d

The Darcy law gives us that

where H is the total potential. The total potential consists of the moisture potential (synonyms; pore water tension, soil water suction) and the elevation potential, z. Thus

Combining (1) and (3) we get

This is called the Richard equation. Remember that and K both are functions of .

(2)

(4)

(3)

Theory of one-dimensional unsaturated water flow

There is a soil specific relationship between soil water content and moisture potential and hydraulic conductivity.

The soil moisture potential, or soil water suction, is sometimes given in pF = log(-pressure in cm H2O)

Theory of one-dimensional unsaturated water flow

Several models exists for these relationships, today, the most commonly used were presented by van Genuchten (1980).

mnrs

r ))(1()(

(5)

2/

21

))(1(

)))(1()(1()(

mn

mnn

sKK

where n, m, and are soil specific parameters, r and s are residual and saturated water content, respectively. The term Ks is the saturated hydraulic conductivity. The parameter r is usually assumed to be equal to the water content at a suitable low pressure head, e.g., -150 m H2O, i.e., the wilting point (pF 4.2).

(6)

Infiltration

A special case of one-dimensional unsaturated water flow is infiltration

Infiltration is of interest in hydrology (rainfall-runoff relationship) and Agriculture (irrigation).

Infiltration parameters for different soil types are determined in infiltration experiments

InfiltrationTwo cases of wetting fronts, in the first, the infiltration rate i is lower than the saturated hydraulic conductivity Ks

Infiltration models

Green-Ampt

where I is the cumulative infiltration, Lf is the wetting front depth, ΔΨ is the change in potential between the soil surface and the wetting front (tabled values exists, see next slide)

It can be assumed that I = Lf (θt - θi)

f

fs L

LK

dt

dIi

Infiltration modelsSoil parameters (Green-Ampt)

Infiltration models

Hortonkt

coc effftf )()(

where fo = infiltration capacity in dry soil (mm/h)fc = = infiltration capacity in wet soil (mm/h)k = time factor (h-1)

Solute transport

Solute transport processes in unsaturated soil

advection

Solute transport

The dispersion coefficient includes effect of both molecular diffusion and mechanical dispersion.

Dispersivity = Dispersion coefficient/velocity

Solute transport

The solute transport in the saturated and unsaturated zones can be modeled using the advection-dispersion equation (ADE)

z

Cv

z

CD

t

CR z

2

2

where D is the dispersion coefficient, R is the retardation coefficient (sorption), and vz is the (vertical) water velocity. In the groundwater, the water velocity is calculated by the Darcy law, in the unsaturated zone the water velocity is calculated using Richards’s equation. Can also include source/sink terms, (chemical reactions, biodegredation)

Solute transport

tD

tvz

tDA

MtxC

L

z

L 4

)(exp

2),(

2

Analythical solution of the CDE for a pulse input and constant v and D

where M is the applied mass and A is the cross sectional area.

Different conceptsIn the ADE concept described above, transport is governed by advection and dispersion. A different approach is the stochastic-advective concept. In this concept, solutes are transported in isolated stream tubes by advection only. The velocity distribution of the stream tubes can be described by a stochastic probability density function (pdf).

Different concepts

Convective-dispersive Stochastic-convective

Solute transport concepts

Stochastic convective approach

2

2

2

*rt

2

ln

exp2

1),(

l

ll

l

z

tl

ttzC

where l is the mean of the lognormal pdf and l2 is the corresponding variance for the reference depth l.

Assuming that the solute is spread instantaneously at z=0 and that the average solute transport velocity is constant, the Crt*(z,t) can be described by

Stochastic convective approach

The l parameter of the CLT model is related to the variability of the velocity

distribution. This can be considered to be a soil specific parameter, however, it will also be slightly dependent on the magnitude of the soil water flux. The where l can

be used to calculate the average pore water velocity v using

2exp

2l

l

lv

ALT vs. ADEALT-model vs. measured data

0

0.05

0.1

0.15

0.2

0.25

0 5 10 15 20 25 30 35 40

Days

Crt

0

0.05

0.1

0.15

0.2

0.25Measured

ALT

ADE

Both models calibrated to measurements at 0.235 m depth.

ALT vs. ADEALT-model vs. measured data

0

0.05

0.1

0.15

0.2

0.25

0 5 10 15 20 25 30 35 40

Days

Crt

0

0.05

0.1

0.15

0.2

0.25Measured

ALT

ADE

Predicted BTCs at 0.6 m depth

QuestionsDiscuss one of these questions in small groups and present the answer to the others

Spatial variability

Soil properties may change dramatically over short distances. Water will not flow uniformly in the soil profile, but may flow in so called macropores, i.e., along roots, desiccation cracks or worm holes. This is called preferential flow.Macropore flow is often triggered at a specific water content and may lead to that large amounts of solutes are transported directly to the groundwater.

Macropores

Macropores (desiccation cracks) in a clay soil in Egypt

Dye infiltration patterns

Water drop penetration test

Water repellency can be determined with the water drop penetration test (WDPT)The procedure is as follows:

•5 – 30 g sample of dry soil is put on a horizontal surface.•The samples are leveled and a small 2-3 mm drop of water is added to the surface of the soil.•On non-wetting soils the water will form a ball and stay on the surface for a time.•Record the time for the drop to infiltrate.•The test should be repeated at least three times and the average time should be recorded.

Water drop penetration test

Time for water to infiltrate (s)

Description

0-5 Not water repellent

5-60 Slightly water repellent

60-600 Moderately water repellent

600-3600 Severely water repellent

>3600 Extremely water repellent

How to account for variability

Dual porosity models (e.g., MACRO)

Stream tube models Stochastic models Fractal models

Fractal models

One model capable of generating fractal clusters i the DLA model. Diffusion limited aggregation conceptually describes the growth of crystals.

This model has been successfully applied to solute transport

DLA models

DLA cluster

0.00 20.00 40.00 60.00 80.00 100.00

W idth [g rids]

50.00

25.00

0.00

De

pth

[gri

ds]

DLA modeling

0.00 50.00 100.00W idth [cm ]

0.00

25.00

50.00

De

pth

[cm

]

0.00 50.00 100.00W idth [grids]

0.00

25.00

50.00

De

pth

[g

rid

s]

0.00 0.50 1.00D ye coverage

0.00

25.00

50.00

De

pth

[cm

]

0.00 0.50 1.00Sim ulated dye coverage

0.00

25.00

50.00

0.00 50.00 100.00W idth [cm ]

0.00

25.00

50.00

D ye im age data D LA m odel M icroscale

D ata not availab le

M acroscale

H orizonta l average

Literature and links

http://www.ars.usda.gov/Services/docs.htm?docid=15992 (models for download)

http://wwwbrr.cr.usgs.gov/projects/GW_Unsat/Unsat_Zone_Book/index.html (online textbook)

Persson and Berndtsson, 1999. Water application frequency effects on steady-state solute transport parameters J. Hydrol. 225:140-154

http://www.pc-progress.cz/Default.htm (hydrus 1D code)

http://bgf.mv.slu.se/ShowPage.cfm?OrgenhetSida_ID=5658 (MACRO model)