Environmental Engineering Reference
In-Depth Information
m
water
m
w
=
[9.2]
dry
It is easy to show that these two water contents per unit volume θ [m
3
.m
-3
] and
per unit mass
w
[kg.kg
-1
] are related by:
θ
w
.
d
[9.3]
where
d
is the stone
dry
or
bulk
density
, which ranges between 1.5 and 2.5 for most
stones [SCH 96]. Nevertheless, taking [9.1] or [9.2] to define the water content is
not equivalent from a practical point of view because:
- Most water content measuring techniques naturally give access to
“volumetric” values θ, although only
gravimetry
directly yields “gravimetric” water
content
w
(see next section). Transforming
w
into θ using [9.3] - or on the contrary
using its inverse form - can be fairly inaccurate if the density
d
is not precisely
known, as is often the case.
- Depending on the chosen variable, θ
or
w
, transfer laws described further on in
this chapter are slightly modified and transfer property units are modified.
For the sake of generality, the water
saturation rate
,
S
, can be defined by:
θ
S
=
[9.4]
N
t
where
N
t
is the stone
total
porosity
: the fraction of its volume
V
that is not occupied
by minerals.
N
t
is equal to the saturated water content θ
sat
when the stone is totally
saturated by water (i.e. no more air is trapped). For intermediate saturation rates we
can thus write:
θ
θ
w
S
=
=
=
;
0
≤
S
≤
1
[9.5]
N
θ
w
t
sat
sat
A particular
S
value of interest - called
S
48
because it is determined after a
48-hour soaking test on a stone sample without preliminary air purge [JEA 97, MER
91, RIL 80] - measures the capability of a stone to naturally absorb liquid water.
Normally,
S
48
< 1, because under these experimental conditions some air trapped in
the stone's porous structure always remains.
The concept of
residual saturation
S
r
can be also defined: water content
remaining inside the stone after a complete drainage or drying event.
Critical
saturation
S
c
(see section 8.2.2.2) gives one more “
S
point”: water content under
