Page 212 - Soil and water contamination, 2nd edition

Substance transport 199

Box 11.III Physics of groundwater and soil water flow

The governing equations that describe ground and soil water movement are based on the
conservation laws of mass (continuity) and momentum (Newton’s second law of motion).
Water in the soil occupies the pore space between the soil particles. The porosity n is
defined as:
volume of pores
n (11.IIIa)
total volume
and the volumetric soil moisture content θ is defined as:
volume of water
(11.IIIb)
total volume
Note that both n and θ are dimensionless and θ equals n if the pores are completely
saturated with water. The total energy of water is described by the hydraulic head that
consists of three components, namely the elevation head, pressure head, and velocity
head. Because the flow velocity of ground and soil water is slow, the velocity head can be
neglected and the hydraulic head can be expressed as:
P
h z z (11.IIIc)
w g
where h = the hydraulic head [L], ψ = the pressure head [L], z = the elevation [L],
-3
-3
-1
-2
P = the pressure [M L T ], ρ = the density of water (= 1000 kg m ) [M L ], and g =
w
-2
-2
the gravitational acceleration constant (= 9.8 m s ) [L T ]. In the case of groundwater,
the hydraulic head at a particular location below the water table can be determined by
measuring the water level in a tube (piezometer) with the bottom opening at the location
where the hydraulic head is being determined and the top opening in contact with
the atmosphere. If the soil or rock matrix is not fully saturated, the pores are partially
occupied by air. This is responsible for the most important difference compared with
saturated conditions, namely that the pressure head ψ is negative because of capillary
suction by the soil matrix. The relation between pressure head (or suction head) ψ and
the soil moisture content θ is usually depicted in a water retention curve or pF curve
(pF = log(-ψ)).
The three-dimensional continuity equation for subsurface water is:
q q q 1 n
x y z w (11.IIId)
x y z w t

-1
where q = the volumetric flow rate per unit area of soil (= Q/A) [L T ]. Note that q is not
equal to the actual flow velocity of the water between the pores. To derive the actual flow
velocity, q must be divided by the effective porosity n , i.e. the porosity available for flow:
eff
q
u (11.IIIe)
n eff
-1
where u = the actual flow velocity of groundwater or soil water [L T ]. Because
groundwater flow is slow, it is laminar and free from turbulence.

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