Yhd-12.3105 Subsurface Hydrology Unsaturated Flow Teemu KokkonenEmail: [email protected] Tel. 09-470 23838 Room:272 (Tietotie 1 E) Water Engineering

Yhd-12.3105 Subsurface Hydrology

Unsaturated Flow

Teemu Kokkonen Email: [email protected]. 09-470 23838Room: 272 (Tietotie 1 E)

Water EngineeringDepartment of Civil and Environmental EngineeringAalto University School of Engineering


Transient flow

Soil Moisture Profile – From Groundwater level to soil surface

• Recall some definitions– Groundwater level is defined to be that level

where soil water pressure is atmospheric– Below the groundwater level the soil is

saturated with water and above the groundwater level the soil is unsaturated

– Immediately above the groundwater level there is a capillary fringe that is (amost) fully saturated


Transient flow

Unsaturated Zone

• Water originating from precipitation or irrigation infiltrates through the soil surface and percolates through the unsaturated zone

– This forms recharge to an aquifer– Harmful substances move with water

• In unsaturated zone the water pressure is negative

– Water is retained in soil by capillary forces, which are a combination of cohesive and adhesive forces

Does the percolating water in the figure above enter the subsurface drain? Why / why not?


Transient flow

Tensiometer

Soil sample

hc

Porous plate

Water

1. How can you read the pressure head in the soil sample using the tensiometer shown in the figure?

2. The porous plate needs to be airtight. Why?

3. Why does the water entering the soil sample does not significantly affect the measurement?

• Negative water pressure in soil is measured using a tensiometer


Transient flow

Water Retention Curve

• A graph that shows the relationship between soil water pressure head and moisture content of soil is called the water retention curve

• In the water retention curve the soil water pressure head is typically expressed as a pF value

– pF value is the 10-based logarithm of the absolute value of the pressure head expressed in centimeters of water column height

Pressure head is – 100 cm. What is the corresponding pF value?

Pressure head is – 100 cm => pF value is 2

− As pressure head values range across a large scale taking a logarithm lead s to a garph that is easier to interpret


Transient flow


II

III

I

I: Porosity

II: Air-entry pressure head ha

ha

III: Residual moisture content qres

qres


Transient flow


• It will not be a great surprise that different soils have water retention curves of different shape

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 10.0 20.0 30.0 40.0 50.0 60.0

Volumetric soil water content [%]

pF

Clay

Sand

ClaySand

Which one of the shown water retention curves is for a clay soil and which one for a sand soil? Why?


Transient flow

Water Flow in Unsaturated Zone

• What are the differences to saturated (groundwater) flow?– Hydraulic conductivity is a function of the moisture content of soil

• When moisture content decreases large soil pores are emptied first, which leads both in reduced cross-sectional area of flow and increased tortuosity of the flow paths => hydraulic conductivity drops

– The air-filled pore space is a function of the moisture content of soil• Recall the large difference (several orders of magnitude) in the storativity of confined and

unconfined aquifers

• Recall that moisture content and pressure head are related via the water retention curve

– Hydraulic conductivity and the air-filled pore space can also be expressed as a function of pressure head


Transient flow

Darcy’s Law in Unsaturated Zone

• As presented earlier the hydraulic head H is the sum of pressure head h and gravity head z

• In the unsaturated flow the interest often is to study percolation to groundwater, so let us first write Darcy’s law in one dimension and in vertical direction

1)()()(dz

dhhKhz

dz

dhK

dz

dHhKq zzzz

Here the direction of the z-axis is points downward – hence the negative sign.


Transient flow

Darcy’s Law in Unsaturated Zone: 3D

1)()(

)()(

)()(

z

hhK

z

HhKq

y

hhK

y

HhKq

x

hhK

x

HhKq

zzz

yyy

xxx

Why is the -1 present in the equation of qz missing from the equations for qx and qy?


Transient flow

Unsaturated Hydraulic Conductivity

Pressure head

Hyd

rau

lic c

on

du

ctiv

ity

Coarse gravel

Fine sand

Clay

PeatRelationship between the pressure head and the hydraulic conductivity for different soil types


Transient flow

Unsaturated Hydraulic Conductivity

• The water retention curve (pF curve) and the unsaturated hydraulic conductivity can be described with the following equations originally proposed by M.Th. van Genuchten and Y. Mualem

aS

aaRSR

hh

hhhh

;

;1)(

a

aa

RS

R

hh

hhhhS;1

;1

2/1½ 11SSKR

RSKKK

Where is the soil moisture (cm3/cm3), R is the residual water content of soil (cm3/cm3), S is the saturated water content of soil (cm3/cm3), S is the saturation of soil (cm3/cm3), h is the pressure head (cm), and ha is the air entry pressure head. Symbols , , and refer to the parameters of the van Genuchten model, and = 1 – 1/. K is the unsaturated hydraulic conductivity, KS is the saturated hydraulic conductivity (cm/h), and KR is the relative conductivity of unsaturated soil (KR = K / KS).


Transient flow

Reminder: Transient Groundwater Flow in 3D

t

HS

zzH

K

y

yH

K

xxH

K

t

HS

zzH

K

y

yH

K

xxH

K zyxzyx

00

Hzyx

VS w

0

Specific storativity S0

volume of water added to storage, per unit volume and per unit rise in hydraulic head

t

HS

z

q

y

q

x

q zyx

0


Transient flow

Flow in Unsaturated Zone: Richards’ Equation

t

hhChK

z

hhK

zy

hhK

yx

hhK

xz

q

y

q

x

qzzyx

zyx

)()()()()(

Specific moisture capacity:

Differential water capacity:

Volume of water released from (or added to) storage per unit decrease (or increase) of pressure head

C [1/m]

t

hhChK

z

hhK

zy

hhK

yx

hhK

x zzyx

)()()()()(


Transient flow

Differential Water Capacity

The definition was:

Differential water capacity: C [1/m]Volume of water released from (or added to) storage per unit decrease (or increase) of pressure head

From the definition above it follows:

dh

dC

,where q is the volumetric moisture content

dt

d

t

h

dh

d

t

hC

So:


Transient flow

Differential Water Capacity

Moisture content q

Pre

ssur

e he

ad

h

dh

dC

Dq

Dh


Transient flow

Numerical Solution – Richards Equation

• Let us discretize the Richards equation in 2D for a longitudial section:

RKz

hK

zx

hK

x

Rz

hK

zx

hK

xt

hC

zzx

zx

1

z (j)

x (i)

Sink / source


Transient flow


tjih 1,

tjih ,1

tjih ,1

tjih 1,

tjih ,

z (j)

x (i)

11,

tjih

1,1

t

jih1,1

t

jih

11,

tjih

1,tjih

Dx

Dz

RKz

hK

zx

hK

xR

z

hK

zx

hK

xt

hC zzxzx

1


Transient flow


jitji

tji

t

ji

t

ji

t

ji

t

ji

tji

tji

ji

RKzKzz

hKz

z

hKz

zx

hK

x

hKx

x

t

hhC

,½,½,½,½,½,½,

,1

,,

11

jitji

tji

tji

tjit

ji

tji

tjit

ji

tji

tjin

ji

tji

tjit

ji

tji

tji

ji

RKzKzz

hhKz

z

hhKz

zx

hhKx

x

hhKx

x

t

hhC

,½,½,1,,

½,,1,

½,,1,

½,,,1

½,

,1

,,

11

RKz

hK

zx

hK

x

Rz

hK

zx

hK

xt

hC

zzx

zx

1


Transient flow


• Approximating the differential water capacity C1. Estimate using the Van Genuchten equation the moisture content that corresponds to

the pressure head at the desired time and location

2. Perturbate the pressure head with a small displacement of Dh

3. Compute the moisture content at h + Dh

Recall that .

How would you approximate C?

dh

dC

4. Now you can estimate C using the difference method as

h

hhhhC

)()(

)(

Documents

Yhd-12.3105 Subsurface Hydrology Unsaturated Flow Teemu KokkonenEmail: [email protected] Tel. 09-470 23838 Room:272 (Tietotie 1 E) Water Engineering