WELCOMENAMITHA M R

ID. No: 2015664502M.Tech.

Land and Water Management Engineering

TNAU

LAND DRAINAGE- CLASSIFICATIONS ,

STEADY AND UNSTEADY STATE EQUATIONS

CLASSIFICATION OF DRAINSDRAINS

ACCORDING TO CONSTRUCTION

NATURAL ARTIFICIAL

ACCORDING TO FUNCTION

OPENSURFACE

SEEPAGE

SURFACE-CUM-SEEPAGE

CLOSED/

SUB-SURFACE

TILE DRAINS

MOLE DRAINS

VERTICAL

A. ACCORDING TO CONSTRUCTION

a) Natural drains: Lowest valley line between 2

ridges Naturally occurring Eg: Drainage lines, Nallahs etc.

b) Artificial drains: Man made structures Constructed along drainage line

NATURAL DRAINARTIFICIAL DRAIN

B. ACCORDING TO FUNCTION

a) Open drains

b) Closed/ Sub-surface drains

c) Vertical drains

a) Open drains

1-1.5m deep Caters the storm water Lowers water table Reduces sloughing of sides Removes large quantities of

surface as well as sub-surface water

OPEN DRAIN

Open drains are of three types:

Surface drains Seepage drainsSurface-cum-seepage drains

Surface drains:

Storm water drains Dispose off surplus

rain water and

irrigation water

Seepage drains:

Drain out the seepage

water from the

subsurface layer Depth upto

groundwater level

Surface-cum-seepage drains:

Serves dual purpose

of seepage and

storm water drain

b) Subsurface drains/ Closed drains

Drains laid deep in the ground and then covered

Used to lower the capillary surface and water table below ground

Provides aeration in the root zone Two types: Tile drains and Mole

drains

Tile drains:

Most efficient and permanent drains

Short length pipes called tiles are

laid with a grade 1-1.5m below ground surface Tiles:- Concrete or Burnt clay Pipes are held end to end without

joining

Mole drains:

Cylindrical channels

below ground surfaceFormed at desired depth

with a gradeNo lining materialClay soils are suitableConstructed using mole ploughs

Depth: 45-120 cm below ground

Diameter: 7.5-15 cm

Life span-10-15 yrs

c) Vertical Drains

Water table is controlled by pumping from a network of wells

Number of pumping points over a small area provides lasting effect of pumping in ground water decline

d) Bio drainage

Drainage effect produced by certain plants

Eg: Eucalyptus Caused by

withdrawal of high rate of water

STEADY STATE DRAINAGE EQUATIONS

a) Hooghout’s equation Assumptions:-

1. Soil profile is homogeneous

2. dy/dx=i

3.Darcy’s law is valid

Dupuit-Forchcheime

r assumptions

4. Drains are spaced evenly

5. An impermeable layer underlain the drain

6. Origin of co-ordinates is on the

impermeable layer below the

centre of one drain

7. Rate of replenishment of water table by irrigation rainfall is ‘R’

Hooghout’s equation for drain spacing:-

S2 = 4K/R [H2-2hd+2Hd-h2]where,

d- Depth to the impermeable layer from the

drain bottom

h- Height of water in the drain

H-Height of water in midway between 2 drains

S- Drain spacing

D-Distance from the impermeable layer to the maximum height of water between the drains

K- Hydraulic conductivity

R- Replenishment rate

When drain is considered as empty:-

S2 = 4KH/R [H+2d] {h= 0}

This equation is similar to ellipse equation – Luthin(1973)

Luthin has transformed the origin of coordinate system to the midpoint between the drains

Ellipse equation:-

y2/ (RS2/ 4K) + x2/ (S2/4) = 1

where,

S/2 is the semi-major axis and

S/2 √(R/K) is the semi-minor axis

Hooghout’s equivalent depth:-

Hooghout’s equation considers totally horizontal movement of water towards the drains

But, when ‘d’ increases beyond a certain level, horizontal flow transforms into vertical flow

This limits the application of Hooghout’s equation

Equivalent depth: Depth below the drain level which can transform the radial flow component into an equivalent horizontal flow component

Equivalent depth, d’ = S/8F

where,

S- Spacing between drains

F-Equivalence factor In original Hooghout’s equation,

d is replaced by d’

b) Earnst equation

Applicable to 2-layered soil Advantage over Hooghout’s

equation:The interspace between 2 drains can be either above or below the drain

Earnst equation:-

Total available head, h = hv + hh + hr

where, hv = Head due to

vertical flow hh = Head due to

vertical flow hr = Head due to radial

flow

Vertical head,

hv = qDv / Kv where,

q - Discharge per unit area

Dv -Thickness of the layer through which vertical flow is considered

Kv - Vertical Hydraulic Conductivity

Horizontal head,

hh = L2q / 8KhDh

where,

Kh – Horizontal Hydraulic Conductivity

Dh - Thickness of layer through

which horizontal flow is considered

L - Spacing

Radial Head:-

hr = (qL / πKr) ln(Dr /u)

where, Kr – Radial Hydraulic

Conductivity a - Geometric Factoru- Wetted Perimeter of

the drainDr – Thickness of the layer

in which radial flow is considered

i.e, Total Head,

h = [qDv / Kv]+[L2q / 8KhDh]+[(qL / πKr) ln(aDr /u)]

This is the Earnst equation in complete form

UNSTEADY STATE DRAINAGE EQUATIONSa) Glover Dumn equation

Assumptions: Flow pattern is unsteady Darcy’s law is applicable All velocity vectors are horizontal , v = -K

dy/dx The vertical column of water bounded

above by the phreatic surface and below by an impermeable layer

Glover-Dumn equation is used to describe a falling water table after its sudden rise due to an instantaneous recharge

Drain spacing = π (Kdt /µ)½ (ln 1.16(h0 / ht))-½

where,

d-Equivalent depth of soil layer below the drain levelK- Hydraulic ConductivityL- Drain spacingt- Time after instantaneous rise of water table µ- Drainage porosityh0 - Initial height of water table ht – Height of water table at t=t

THANK YOU !!!