LAND DRAINAGE- CLASSIFICATIONS, STEADY AND UNSTEADY STATE EQUATIONS

WELCOME
NAMITHA M R
ID. No: 2015664502
M.Tech.
Land and Water
Management Engineering
TNAU

LAND DRAINAGE-
CLASSIFICATIONS , STEADY AND
UNSTEADY STATE EQUATIONS

CLASSIFICATION OF DRAINS
DRAINS
ACCORDING TO
CONSTRUCTION
NATURAL ARTIFICIAL
ACCORDING
TO FUNCTION
OPEN
SURFACE 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 DRAIN ARTIFICIAL 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 drains are of three types:
Surface drains
Seepage drains
Surface-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 surface
 Formed at desired depth
with a grade
 No lining material
 Clay soils are suitable
 Constructed 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-
Forchcheimer
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 Factor
u- Wetted Perimeter of the drain
Dr – 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 EQUATIONS
a) 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 level
K- Hydraulic Conductivity
L- Drain spacing
t- Time after instantaneous rise of water table
µ- Drainage porosity
h0 - Initial height of water table
ht – Height of water table at t=t

LAND DRAINAGE- CLASSIFICATIONS, STEADY AND UNSTEADY STATE EQUATIONS

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