2.1. Physical Parameters
19
tion convention, Darey's Law, Eq. (2.1.36), can be written in a eompaet form:
oh
qi = -Kij-o
(i = 1,2,3)
(2.1.38)
x j
whieh will be used repeatedly. For an isotropie medium, the hydraulic eonduetivity reduees to a sealar, and the relevant Darey's Law beeomes
oh
q.=-K,
oX i
(i = 1,2,3).
(2.1.39)
Hydraulic eonduetivity K is a maeroseopie parameter whieh depends on
properties of both the porous matrix and the liquid, and may be expressed as
K = kpg
J1 '
(2.1.40)
where p and J1 are the maeroseopie averages of density and viseosity of the
fluid, i.e., p and Ji, g is the gravitational acceleration, and k is ealled the
permeability whieh is independent of the properties of the fluid and has the
dimensions of [L 2 ]. For an anisotropie porous medium, k is a seeond rank
symmetrie tensor.
With Eqs. (2.1.26), (2.1.35), and (2.1.40), Darey's Law, Eq. (2.1.36), ean be
rewritten as
V; =----"' - - + pgk..(op oz)
nJ1 oXj
oXj
(2.1.41)
(i = 1,2,3).
Storage Coeffieients
Specific storativity, Ss, is defined as the volume fraetion ofwater released from
a REV when the water head declines by one unit, i.e.,
AU w
Ss = Uo.Ah'
(2.1.42)
where AU w denotes the volume of water released from [U o ] as a result of
solid matrix deformation or water expansion, and Ah is the decline of water
head. The dimension of Ss is [ljL] and we have the following relationship
(Bear, 1972)
Ss = pg[oe(1 - n) + nß],
(2.1.43)
where oe and ß are the eompressibilities of the solid matrix and water,
respeetively.
Specific yield Sy is a property deseribing the water release ability of an
aquifer. It is defined as the volume of water released from a unit area of
aquifer per unit decline of water table, i.e.,
(2.1.44)